diff options
| -rw-r--r-- | blueprint.tex | 10 | ||||
| -rw-r--r-- | essays/admissable_contraditions.tex | 246 | ||||
| -rw-r--r-- | essays/dissociation_physics.tex | 5029 | ||||
| -rw-r--r-- | essays/energy_cube1966.tex | 4 | ||||
| -rw-r--r-- | essays/flaws_underlying_beliefs.tex | 2 | ||||
| -rw-r--r-- | essays/perception_dissociator.tex | 2 | ||||
| -rw-r--r-- | essays/philosophical_reflections.tex | 4 | ||||
| -rw-r--r-- | essays/post_formalism_memories.tex | 55 | ||||
| -rw-r--r-- | essays/studies_in_constructed_memories.tex | 40 | ||||
| -rw-r--r-- | essays/walking_through_walls.tex | 2 | ||||
| -rw-r--r-- | img/illusions.png | bin | 18102 -> 8184 bytes | |||
| -rw-r--r-- | img/illusionstructure.png | bin | 14830 -> 22999 bytes | |||
| -rw-r--r-- | salitter.sty | 6 |
13 files changed, 386 insertions, 5014 deletions
diff --git a/blueprint.tex b/blueprint.tex index bf286d3..74c1b5f 100644 --- a/blueprint.tex +++ b/blueprint.tex @@ -1,4 +1,4 @@ -\documentclass[10pt,twoside,draft]{memoir} +\documentclass[10pt,twoside]{memoir} \usepackage{salitter} \usletterlayout @@ -10,6 +10,7 @@ \usepackage{stix} \usepackage{xfrac} \usepackage{ulem} +\usepackage{enumitem} % fonts \coelfont @@ -24,7 +25,7 @@ \speech{#1}} \newcommand{\essaytitle}[1]{ - \emph{#1}} + \textit{#1}} \newcommand{\gap}{\plainbreak{2}} @@ -74,6 +75,7 @@ \newcommand{\cubedown}{ \includegraphics[width=1em]{img/cubedown}} + \begin{document} \frontmatter \graphicspath{{img/}} @@ -81,6 +83,10 @@ \chapterstyle{tandh} \openany +\renewcommand*{\cftpartfont}{\bfseries\scshape} +\renewcommand*{\cftchapterfont}{\normalfont} +\renewcommand*{\cftsectionfont}{\itshape} + % Title \thispagestyle{empty} { diff --git a/essays/admissable_contraditions.tex b/essays/admissable_contraditions.tex deleted file mode 100644 index f66bb98..0000000 --- a/essays/admissable_contraditions.tex +++ /dev/null @@ -1,246 +0,0 @@ -\chapter{The Logic of Admissible Contradictions (Work in Progress)} - -\section{Chapter III. A Provisional Axiomatic Treatment} - - -In the first and second chapters, we developed our intuitions -concerning perceptions of the logically impossible in as much detail as we -could. We decided, on intuitive grounds, which contradictions were -admissible and which were not. As we proceeded, it began to appear that the -results suggested by intuition were cases of a few general principles. In this -chapter, we will adopt these principles as postulates. The restatement of our -theory does not render the preceding chapters unnecessary. Only by -beginning with an exhaustive, intuitive discussion of perceptual illusions -could we convey the substance underlying the notations which we call -admissble contradictions, and motivate the unusual collection of postulates -which we will adopt. - -All properties will be thought of as "parameters," such as time, -location, color, density, acidity, etc. Different parameters will be represented -by the letters x, y, z, .... Different values of one parameter, say x, will be -represented by $x_1$, $x_2$, .... Each parameter has a domain, the set of all values -it can assume. An ensembie ($x_0$, $y_0$, $z_0$, ...) will stand for the single possible -phenomenon which has x-value $x_0$, y-value $y_0$, etc. Several remarks are in -order. My ensembles are a highly refined version of Rudolph Carnap's -intensions or intension sets (sets of all possible entities having a given -property). The number of parameters, or properties, must be supposed to be -indefinitely large. By giving a possible phenomenon fixed values for every -parameter, I assure that there will be only one such possible phenomenon. In -other words, my intension sets are all singletons. Another point is that if we -specify some of the parameters and specify their ranges, we limit the -phenomena which can be represented by our "ensembles." If our first -parameter is time and its range is $R$, and our second parameter is spatial -location and its range is $R^2$, then we are limited to phenomena which are -point phenomena in space and time. If we have a parameter for speed of -motion, the motion will have to be infinitesimal. We cannot have a -parameter for weight at all; we can only have one for density. The physicist -encounters similar conceptual problems, and does noi find them -insurmountable. - -Let ($x_1$, $y$, $z$, ...), ($x_2$, $y$, $z$, ...), etc. stand for possible phenomena -which all differ from each other in respect to parameter x but are identical in -respect to every other parameter $y$, $z$, ... . (If the ensembles were intension -sets, they would be disjoint precisely because $x$ takes a different value in -each.) A "simple contradiction family" of ensembles is the family [($x_1$,$y$,$z$, -...), ($x_2$, $y$, $z$, ...), ...]. The family may have any number of ensembles. It -actually represents many families, because $y$, $z$, ... are allowed to vary; but -each of these parameters must assume the same value in all ensembles in any -one family. $x$, on the other hand, takes different values in each ensemble in -any one family, values which may be fixed. A parameter which has the same -value throughout any one family will be referred to as a consistency -parameter. A parameter which has a different value in each ensemble in a -given family will be referred to as a contradiction parameter. -"Contradiction" will be shortened to "con." A simple con family is then a -family with one con parameter. The consistency parameters may be dropped -from the notation, but the reader must remember that they are implicitly -present, and must remember how they function. - -A con parameter, instead of being fixed in every ensemble, may be -restricted to a different subset of its domain in every ensemble. The subsets -must be mutually disjoint for the con family to be well-defined. The con -family then represents many families in another dimension, because it -represents every family which can be formed by choosing a con parameter -value from the first subset, one from the second subset, etc. - -Con families can be defined which have more than one con parameter, -i.e. more than one parameter satisfying all the conditions we put on x. Such -con families are not "simple." Let the cardinality of a con family be -indicated by a number prefixed to "family," and let the number of con -parameters be indicated by a number prefixed to "con." Remembering that -consistency parameters are understood, a 2-con $\infty$-family would appear as -[($x_1$, $y_1$). ($x_2$, $y_2$), ...]. - -A "contradiction" or "$\varphi$-object" is not explicitly defined, but it is -notated by putting "$\varphi$" in front of a con family. The characteristics of $\varphi$-objects, -or cons, are established by introducing additional postulates in the -theory. - -In this theory, every con is either "admissible" or "not admissible." -"Admissible" will be shortened to "am." The initial amcons of the theory -are introduced by postulate. Essentially, what is postulated is that cons with -a certain con parameter are am. (The cons directly postulated to be am are -on 1-con families.) However, the postulate will specify other requirements for -admissibility besides having the given con parameter. The requisite -cardinality of the con family will be specified. Also, the subsets will be -specified to which the con parameter must be restricted in each ensemble in -the con. A con must satisfy all postulated requirements before it is admitted -by the postulate. - -The task of the theory is to determine whether the admissibility of the -cons postulated to be am implies the admissibility of any other cons. The -method we have developed for solving such problems will be expressed as a -collection of posiulates for our theory. - -\postulate{1} Given $\varphi[(x\in A),(x\in B),\ldots]$ am, where $x\in A$, $x\in B$, ... are the -restrictions on the con parameter, and given $A_1\subset A$, $B_1\subset B$, ..., where $A_1,B_1,...\neq\emptyset$, then -$\varphi[(x\in A_1),(x\in B_1),...]$ is am. This postulate is obviously -equivalent to the postulate that $\varphi[(x\in A\cap C),(x\in B\cap C),...]$ is am, where $C$ is -a subset of $x$'s domain end the intersections are non-empty. (Proof: Choose -$C=A_1\cup B_1\cup\ldots$ .) - -\postulate{2} If $x$ and $y$ are simple amcon parameters, then a con with con -parameters $x$ and $y$ is am if it satisfies the postulated requirements -concerning amcons on $x$ and the postulated requirements concerning amcons -on $y$. - -The effect of all our assumptions up to now is to make parameters -totally independent. They do not interact with each other at all. - -We will now introduce some specific amcons by postulate. If $s$ is speed, -consideration of the waterfall illusion suggests that we postulate -$\varphi[(s>O),(s=O)]$ to be am. (But with this postulate, we have come a long way from -the literary description of the waterfall illusion!) Note the implicit -requirements that the con family must be a 2-family, and that $s$ must be -selected from $[O]$ in one ensemble and from ${s:s>O}$ in the other ensemble. - -If $t$ is time, $t\in R$, consideration of the phrase "b years ago," which is an -amcon in the natural language, suggests that we postulate $\varphi[(t):a-b\leq t\leq v-b \&a\leq v]$ to be am, -where $a$ is a fixed time expressed in years A.D., $b$ is a fixed -number of years, and $v$ is a variable---the time of the present instant in years -A.D. The implicit requirements are that the con family must have the -cardinality of the continuum, and that every value of $t$ from $a-b$ to $v-b$ must -appear in an ensemble, where $v$ is a variable. Ensembles are thus continually -added to the con family. Note that there is the non-trivial possibility of using -this postulate more than once. We could admit a con for $a=1964$, $b=\sfrac{1}{2}$ -then admit another for $a=1963$, $b=2$, and admit still another for $a=1963$, -$b=1$; etc. - -Let $p$ be spatial location, $p\in R^2$. Let $P_i$ be a non-empty, bounded, -connected subset of $R^2$. Restriction subsets will be selected from the $P_i$. -Specifically, let $P_1\cap P_2=\emptyset$. Consideration of a certain dreamed illusion -suggests that we admit $\varphi[(p\in P_1),(p\in P_2)]$. The implicit requirements are -obvious. But in this case, there are more requirements in the postulate of -admissibility. May we apply the postulate twice? May we admit first -$\varphi[(p\in P_1),(p\in P_2)]$ and then $\varphi[(p\in P_3),(p\in P_4)]$, where $P_3$ and $P_4$ are arbitrary -$P_i$'s different from $P_1$ and $P_2$? The answer is no. We may admit -$\varphi[(p\in P_1),(p\in P_2)]$ for arbitrary $P_1$ and $P_2$, $P_1\cap P_2=\emptyset$, but having made this "initial -choice," the postulate cannot be reused for arbitrary $P_3$ and $P_4$. A second -con $\varphi[(p\in P_3),(p\in P_4)]$, $P_3\cap P_4=\emptyset$, may be postulated to be am only if -$P_1\cup P_3$,$P_2\cup P_3$,$P_1\cup P_4$, and $P_2\cup P_4$ are not connected. In other words, you -may postulate many cons of the form $\varphi[(p\in P_i),(p\in P_j)]$ to be am, but -your first choice strongly circumscribes your second choice, etc. - -We will now consider certain results in the logic of amcons which were -established by extensive elucidation of our intuitions. The issue is whether -our present axiomization produces the same results. We will express the -results in our latest notation as far as possible. Two more definitions are -necessary. The parameter $\theta$ is the angle of motion of an infinitesimally -moving phenomenon, measured in degrees with respect to some chosen axis. -Then, recalling the set $P_1$, choose $P_5$ and $P_6$ so that $P_1=P_5\cup P_6$ and -$P_5\cap P_6=\emptyset$. - -The results by which we will judge our axiomization are as follows. - -\begin{enumerate} % TODO with colons? - - \item $\varphi[S, C_1\cup C_2]$ can be inferred to be am. - -Our present notation cannot express this result, because it does not -distinguish between different types of uniform motion throughout a finite -region, \ie the types $M$, $C_1$, $C_2$, $D_1$, and $D_2$. Instead, we have infinitesimal -motion, which is involved in all the latter types of motion. Questions such as -"whether the admissibility of $\varphi[M,S]$ implies the admissibility of $\varphi[C_1,S]$" -drop out. The reason for the omission in the present theory is our choice of -parameters and domains, which we discussed earlier. Our present version is -thus not exhaustive. However, the deficiency is not intrinsic to our method; -and it does not represent any outright falsification of our intuitions. Thus, -we pass over the deficiency. - -\item $\varphi[(p\in P_1,s_0),(p\in P_2,S_0)]$ and other such cons can be inferred to be am. -With our new, powerful approach, this result is trivial. It is guaranteed by -what we said about consistency parameters. - -\item There is no way to infer that $\varphi[C_1,C_2]$ is am; and no way to infer that -$\varphi[(45^\circ,s_0\greater O),(60^\circ,s=s_0)]$ is am. - -The first part of the result drops out. The second part is trivial with our new -method as long as we do not postulate that cons on $\theta$ are am. - -\item $\varphi[(p\in P_2),(p\in P_5)]$ can be inferred to be am. - -Yes, by Postulate 1. - -\item $\varphi[(s>O, p\in P_1),(s=O, p\in P_2)]$ and $\varphi[(s>O, p\in P_2),(s=O, p\in P_1)]$ can -be inferred to be am. - -Yes, by Postulate 2. These two amcons are distinct. The question of whether -they should be considered equivalent is closely related to the degree to -which con parameters are independent of each other. - -\item There is no way to infer that $\varphi[(p\in P_5),(p\in P_6)]$ or $\varphi[(p\in P_1),(p\in P_3)]$ -is am. Our special requirement in the postulate of admissibility for -$\varphi[(p\in P_1),(p\in P_2)]$ guarantees this result. -\end{enumerate} - -The reason for desiring this last result requires some discussion. In -heuristic terms, we wish to avoid admitting both location in New York in -Greensboro and location in Manhattan and Brooklyn. We also wish to avoid -admitting location in New York in Greensboro and location in New York in -Boston. If we admitted either of these combinations, then the intuitive -rationale of the notions would indicate that we had admitted triple location. -While we have a dreamed illusion which justifies the concept of double -location, we have no intuitive justification whatever for the concept of triple -location. It must be clear that admission of either of the combinations -mentioned would not imply the admissibility of a con on a 3-family with -con parameter p by the postulates of our theory. Our theory is formally safe -from this implication. However, the intuitive meaning of either combination -would make them proxies for the con on the 3-family. - -A closely related consideration is that in the preceding chapter, it -appeared that the admission of $\varphi[(p\in P_1),(p\in P_2)]$ and $\varphi[(p\in P_5),(p\in P_6)]$ -would tend to require the admission of the object $\varphi[(p\in P_2),\varphi[(p\in P_5),(p\in P_6)]]$ -(a Type 1 chain). Further, it this implication held, then by the same -rationale the admission of $\varphi[(p\in P_1),(p\in P_2)]$ and $\varphi[(s>O,p_0\in P_1),(s=O,p=p_0)]$, - both of which are am, would require the admission of the object -$\varphi[(p\in P_2), \varphi[(s>O,p_0\in P_1),(s=O, p=p_0)]]$. -We may now say, however, -that the postulates of our theory emphatically do not require us to accept -these implications. If there is an intuitively valid notion underlying the chain -on s and p, it reduces to the amcons introduced in result 5. As for the chain -on p alone, we repeat that simultaneous admission of the two cons -mentioned would tend to justify some triple location concept. However, we -do not have to recognize that concept as being the chain. It seems that our -present approach allows us to forget about chains for now. - -Our conclusion is that the formal approach of this chapter is in good -agreement with our intuitively established results. - -\section*{Note on the overall significance of the logic of amcons:} - -When traditional logicians said that something was logically impossible, -they meant to imply that it was impossible to imagine or visualize. But this -implication was empirically false. The realm of the logically possible is not -the entire realm of connotative thought; it is just the realm of normal -perceptual routines. When the mind is temporarily freed from normal -perceptual routines---especially in perceptual illusions, but also in dreams and -even in the use of certain "illogical" natural language phrases---it can imagine -and visualize the "logically impossible." Every text on perceptual -psychology mentions this fact, but logicians have never noticed its immense -significance. The logically impossible is not a blank; it is a whole layer of -meaning and concepts which can be superimposed on conventional logic, but -not reduced or assimilated to it. The logician of the future may use a drug or -some other method to free himself from normal perceptual routines for a -sustained period of time, so he can freely think the logically impossible. He -will then perform rigorous deductions and computations in the logic of -amcons. - diff --git a/essays/dissociation_physics.tex b/essays/dissociation_physics.tex index e60d685..d78631a 100644 --- a/essays/dissociation_physics.tex +++ b/essays/dissociation_physics.tex @@ -1,4718 +1,329 @@ -\chapter{1966 Mathematical Studies} +\chapter{The Perception-Dissociation of Physics} + + +From the physicist's point of view, the human dichotomy of sight and +touch is a coincidence. It does not correspond to any dichotomy in the +objective physical world. Light exerts pressure, and substances hot to the +touch emit infrared light. It is just that the range of human receptors is too +limited for them to register the tactile effect of light or the visual effect of +moderate temperatures. + +Our problem is to determine what observations or experiences would +cause the physicist to say that the objective physical world had split along +the humen sight-touch boundary, to say that the human sight-touch +dichotomy was an unavoidable model of objective physical reality. Our +discussion is not about perfectly transparent matter, or light retlection and +emission in the absence of matter, or the dissociation of electromagnetic and +inertial phenomena, or the fact that human sight registers light, while touch +registers inertia, bulk modulus, thermal conduction, friction, adhesion, and +so on. (However, these concepts may have to be introduced to complete our +discussion.) Our discussion is about a change in the physicist's observations +or experiences, such that the anomalous state of affairs would be an +experimental analogue to the sight-touch dichotomy of philosophical +subjectivism. Of course, philosophical subjectivism itself will not enter the +discussion. + +Because of the topic, our discussion will often seem psychological and +even philosophical. However, the psychology involved always has to do with +experimentally demonstrable aspects of perception. The philosophy involved +is always scientific concept formation, the relating of concepts to +experiments. Sooner or later it will be clear that our only concern is with +experiences that would cause a physicist to modify physics. + +Throughout much of the discussion, we have to assume that the human +physicist exists before the sight-touch split occurs, that he continues to exist +after it occurs, and that he functions as a physicist after it occurs. Therefore, +we begin as follows. A healthy human has a realm of sights, and a realm of +touches: and there is a correlation between the two which receives its highest +expression in the concept of the object. (In psychological jargon, intermodal +organization contributes to the object Gestalt. Incidentally, for us "touch" +includes just about every sense except sight, hearing, smell.) Suppose there is +a change in which the tactile realm remains coherent, if not exactly the same +as before, and the visual realm also remains coherent; but the correlation +between the two becomes completely chaotic. A totally blind person does +not directly experience any incomprehensible dislocation, nor does a person +with psychogenic tactile anesthesia (actually observed in hysteria patients). +Let us define such a change. Consider the sight-touch correlation identified +with closing one's eyes. The point is that there is a whole realm of sights +which do not occur when one can feel that one's eyes are closed. + +Let $T$ indicate tactile and $V$ indicate visual. Let the tactile sensation of +open eyes be $T_1$, and of closed eyes be $T_2$. Now anything that can be seen +with closed eyes---from total blackness, to the multicolored patterns produced +by waving the spread fingers of both hands between closed eyes and direct +sunlight---can no doubt be duplicated for open eyes. Closed-eye sights are a +subset of open-eye sights. Thus, let sights seen only with open eyes be $V_1$, +and sights seen with either open or closed eyes be $V_2$: If there are sights seen +only with closed eyes, they will be $V_3$; we want disjoint classes. We are +interested in the temporal concurrence of sensations. Combining our +definitions with information about our present world, we find there are no +intrasensory concurrences (eyes open and closed at the same time). Further, +our change will not produce intrasensory concurrences, because each realm +will remain coherent. Thus, we will drop them from our discussion. There +remain the intersensory concurrences, and four can be imagined; let us +denote them by the ordered pairs $(T_1, V_1), (T_1, V_2), (T_2, V_1), (T_2, V_2)$. In +reality, some concurrences are permitted and others are forbidden, Let us +designate each ordered pair as permitted or forbidden, using the following +notation. Consider a rectangular array of "places" such that the place in the +ith row and jth column corresponds to $(T_i, V_j)$, and assign a $p$ or $f$ (as +appropriate) to each place. Then the following state array is a description of +regularities in our present world. + +$$\begin{pmatrix} + p & p\\ + f & p +\end{pmatrix}$$ + + +So far as temporal successions of concurrences (within the présent +world) are concerned, any permitted concurrence may succeed any other +permitted concurrence. The succession of a concurrence by itself is +excluded, meaning that at the moment, a $V_1$, is defined as lasting from the +time the eyes open until the time they next close. + +We have said that our topic is a certain change; we can now indicate +more precisely what this change is. As long as we have a 2x2 array, there are +16 ways it can be filled with p's and f's. That is, there are 16 imaginable +states. The changes we are interested in, then, are specific changes from the +present state +$\begin{pmatrix} + p & p \\ + f & p +\end{pmatrix}$ to another state such as +$\begin{pmatrix} + p & f \\ + p & p +\end{pmatrix}$. + +However, +we want to exclude some changes. The change that changes nothing is +excluded. We aren't interested in changing to a state having only f's, which +amounts to blindness. A change to a state with a row or column of f's leaves +one sight or touch completely forbidden (a person becomes blind to +open-eye sights); such an "impairment" is of little interest. Of the remaining +changes, one merely leaves a formerly permitted concurrence forbidden: +closed-eye sights can no longer be seen with open eyes. The rest of the +changes are the ones most relevant to perception-dissociation. They are +changes in the place of the one f; the change to the state having only p's; +and finally -% TODO start these section numbers at 0? (this should work) -\section*{0. Introduction} - -Pure mathematics is the one activity which is intrinsically formalistic. It -is the one activity which brings out the practical value of formal -manipulations. Abstract games fit in perfectly with the tradition and -rationale of pure mathematics; whereas they would not be appropriate in -any other discipline. Pure mathematics is the one activity which can -appropriately develop through innovations of a formalistic character. - -Precisely because pure mathematics does not have to be immediately -practical, there is no intrinsic reason why it should adhere to the normal -concept of logical truth. No harm is done if the mathematician chooses to -play a game which is indeterminate by normal logical standards. All that -matters is that the mathematician clearly specify the rules of his game, and -that he not make claims for his results which are inconsistent with his rules. - -Actually, my pure philosophical writings discredit the concept of -logical truth by showing that there are flaws inherent in all non-trivial -language. Thus, no mathematics has the logical validity which was once -claimed for mathematics. From the ultimate philosophical standpoint, all -mathematics is as "indeterminate" as the mathematics in this monograph. -All the more reason, then, not to limit mathematics to the normal concept -of logical truth. - -Once it is realized that mathematics is intrinsically formalistic, and need -not adhere to the normal concept of logical truth, why hold back from -exploring the possibilities which are available? There is every reason to -search out the possibilities and present them. Such is the purpose of this -monograph. - -The ultimate test of the non-triviality of pure mathematics is whether it -has practical applications. I believe that the approaches presented on a very -abstract level in this monograph will turn out to have such applications. In -order to be applied, the principles which are presented here have to be -developed intensively on a level which is compatible with applications. The -results will be found in my two subsequent essays, \essaytitle{Subjective Propositional -Vibration} and \essaytitle{The Logic of Admissible Contradictions}. - -\section{Post-Formalism in Constructed Memories} -\subsection{Post-Formalist Mathematics} - -Over the last hundred years, a philosophy of pure mathematics has -grown up which I prefer to call "formalism." As Willard Quine says in the -fourth section of his essay "Carnap and Logical Truth,' formalism was -inspired by a series of developments which began with non-Euclidian -geometry. Quine himself is opposed to formalism, but the formalists have -found encouragement in Quine's own book, \booktitle{Mathematical Logic}. The best -presentation of the formalist position can be found in Rudolph Carnap's -\booktitle{The Logical Syntax of Language}. As a motivation to the reader, and -as a heuristic aid, I will relate my study to these two standard books. (It will -heip if the reader is thoroughly familiar with them.) it is not important -whether Carnap, or Quine, or formalism---or my interpretation of them---is -"correct," for this essay is neither history nor philosophy. I am using history -as a bridge, to give the reader access to some extreme mathematical -innovations. - -The formalist position goes as follows. Pure mathematics is the -manipulation of the meaningless and arbitrary, but typographically -well-defined ink-shapes on paper 'w,' 'x,' 'y,' 'z,' '{}',' '(,' '),' '$\downarrow$,' and '$\in$.' -These shapes are manipulated according to arbitrary but well-detined -mechanical rules. Actually, the rules mimic the structure of primitive -systems such as Euclid's geometry. There are formation rules, mechanical -definitions of which concatenations of shapes are "sentences." One sentence -is '$((x) (x\in x) \downarrow (x) (x\in x))$.' There are transformation rules, rules for the -mechanical derivation of sentences from other sentences. The best known -trasformation rule is the rule that $\psi$ may be concluded from $\varphi$ and -$\ulcorner \varphi \supset \psi \urcorner$; -where '$\supset$' is the truth-functional conditional. For later convenience, I will -say that $\varphi$ and $\ulcorner \varphi \supset \psi \urcorner$ are "impliors," -and that $\psi$ is the "implicand." -Some sentences are designated as "axioms." A "proof" is a series of -sentences such that each is an axiom or an implicand of preceding sentences. -The last sentence in a proof is a "theorem." - -This account is ultrasimplified and non-rigorous, but it is adequate for -my purposes. (The reader may have noticed a terminological issue here. For -Quine, an implication is merely a logically true conditional. The rules which -are used to go from some statements to others, and to assemble proofs, are -rules of inference. The relevant rule of inference is the modus ponens; $\psi$ is -the ponential of $\varphi$ and $\ulcorner \varphi \supset \psi \urcorner$. What I -am doing is to use a terminology of -implication to talk about rules of inference and ponentials. The reason is -that the use of Quine's terminology would result in extremely awkward -formulations. What I will be doing is sufficiently transparent that it can be -translated into Quine's terminology if necessary. My results will be -unaffected.) The decisive feature of the arbitrary game called "mathematics" -is as follows. A sentence-series can be mechanically checked to determine -whether it is a proof. But there is no mechanical method for deciding -whether a sentence is a theorem. Theorems, or rather their proofs, have to be -puzzled out, to be discovered. in this feature lies the dynamism, the -excitement of traditional mathematics. Traditional mathematical ability is -the ability to make inferential discoveries. - - -A variety of branches of mathematics can be specialized out from the -basic system. Depending on the choices of axioms, systems can be -constructed which are internally consistent, but conflict with each other. A -system can be "interpreted," or given a meaning within the language of a -science such as physics. So interpreted, it may have scientific value, or it may -not. But as pure mathematics, all the systems have the same arbitrary status. - -By "formalist mathematics" I will mean the present mathematical -systems which are presented along the above lines. Actually, as many authors -have observed, the success of the non-Euclidian "imaginary" geometries -made recognition of the game-like character of mathematics inevitable. -Formalism is potentially the greatest break with tradition in the history of -mathematics. In the Foreward to \booktitle{The Logical Syntax of Language}, Carnap -brilliantly points out that mathematical innovation is still hindered by the -widespread opinion that deviations from mathematical tradition must be -justified---that is, proved to be "correct" and to be a faithful rendering of -"the true logic." According to Carnap, we are free to choose the rules of a -mathematical system arbitrarily. The striving after correctness must cease, so -that mathematics will no longer be hindered. \said{Before us lies the boundless -ocean of unlimited possibilities.} In other words, Carnap, the most reputable -of academicians, says you can do anything in mathematics. Do not worry -whether whether your arbitrary game corresponds to truth, tradition, or -reality: it is still legitimate mathematics. Despite this wonderful Principle of -Tolerance in mathematics, Carnap never ventured beyond the old -ink-on-paper, axiomatic-deductive structures. I, however, have taken Carnap -at his word. The result is my "post-formalist mathematics." I want to stress -that my innovations have been legitimized in advance by one of the most -reputable academic figures of the twentieth century. - -Early in 1961, I constructed some systems which went beyond -formalist mathematics in two respects. 1. My sentential elements are -physically different from the little ink-shapes on paper used in all formalist -systems. My sentences are physically different from concatenations of -ink-shapes. My transformation rules have nothing to do with operations on -ink-shapes. 2. My systems do not necessarily follow the axiomatic-deductive, -sentence-implication-axiom-proof-theorem structure. Both of these -possibilities, by the way, are mentioned by Carnap in \papertitle{Languages as -Calculi.} A "post-formalist system," then, is a formalist system which differs -physically from an ink-on-paper system, or which lacks the -axiomatic-deductive structure. - -As a basis for the analysis of post-formalist systems, a list of structural -properties of formalist systems is desirable. Here is such a list. By -"implication" I will mean simple, direct implication, unless I say otherwise. -\begin{enumerate} -\item A sentence can be repeated at will. - -\item The rule of implication refers to elements of sentences: sentences -are structurally composite. - -\item A sentence can imply itself. - -\item The repeat of an implior can imply the repeat of an implicand: an -implication can be repeated. - -\item Different impliors can imply different implicands. - -\item Given two or three sentences, it is possible to recognize -mechanically whether one or two directly imply the third. - -\item No axiom is implied by other, different axioms. - -\item The definition of "proof" is the standard definition, in terms of -implication, given early in this essay. - -\item Given the axioms and some other sentence, it is not possible to -recognize mechanically whether the sentence is a theorem. -Compound indirect implication is a puzzle. -\end{enumerate} - -Now for the first post-formalist system. - -{ \centering \large "\textsc{Illusions}" \par} - -\begin{sysrules} -A "sentence" is the following page (with the figure on it) so long as the -apparent, perceived ratio of the length of the vertical line to that -of the horizontal line (the statement's "associated ratio") does not -change. (Two sentences are the "same" if end only if their -associated ratios are the same.) - -A sentence Y is "implied by" a sentence X if and only if Y is the same as X, -or else Y is, of all the sentences one ever sees, the sentence having -the associated ratio next smaller than that of X. - -Take as the axiom the first sentence one sees. - -Explanation: The figure is an optical illusion such that the vertical line -normally appears longer than the horizontal line, even though their -lengths are equal. One can correct one's perception, come to see -the vertical line as shorter relative to the horizontal line, decrease -the associated ratio, by measuring the lines with a ruler to convince -oneself that the vertical line is not longer than the other, and then -trying to see the lines as equal in length; constructing similar -figures with a variety of real (measured) ratios and practicing -judging these ratios; and so forth. -\end{sysrules} - -\img{illusions} - -"IIlusions" has Properties 1, 3--5, and 7--8. Purely to clarify this fact, the -following sequence of integers is presented as a model of the order in which -associated ratios might appear in reality. (The sequence is otherwise totally -inadequate as a model of "Illusions.") 4 2 1; 4 2; 5 4 2 1; 4 3 1. The -implication structure would then be - -\img{illusionstructure} - -The axiom would be 4, and 5 could not appear in a proof. "IIlusions" has -Property 1 on the basis that one can control the associated ratio. Turning to -Property 4, it is normally the case that when an implication is repeated, a -given occurrence of one of the sentences involved is unique to a specific -occurrence of the implication. In "Illusions," however, if two equal -sentences are next smaller than X, the occurrence of X does not uniquely - belong to either of the two occurrences of the implication. Compare '\begin{tabular}{c c c} t & h & e \\ h & & \\ e & & \end{tabular}', -where the occurrence of 't' is not unique to either occurrence of 'the'. -Subject to this explanation, "Illusions" has Property 4. "Illusions" has -Property 8, but it goes without saying that the type of implication is not -modus ponens. Properties 3, 5, and 7 need no comment. As for Property 2, -the rule of implication refers to a property of sentences, rather than to -elements of sentences. The interesting feature of "IIlusions" is that it -reverses the situation defined by Properties 6 and 9. Compound indirect -implication is about the same as simple implication. The only difference is -the difference between being smaller and being next smaller. And there is -only one axiom (per person). - -Simple direct implication, however, is subjective and illusive. It -essentially involves changing one's perceptions of an illusion. The change of -associated ratios is subjective, elusive, and certainly not numerically -measurable. Then, the order in which one sees sentences won't always be -their order in the implications and proofs. And even though one is exposed -to all the sentences, one may have difficulty distinguishing and remembering -them in consciousness. If I see the normal illusion, then manage to get -myself to see the lines as being of equal length, I know I have seen a -theorem. What is difficult is grasping the steps in between, the simple direct -implications. If the brain contains a permanent impression of every sensation -it has received, then the implications objectively exist; but they may not be -thinkable without neurological techniques for getting at the impressions. In -any case, "proof" is well-defined in some sense---but proofs may not be -thinkable. "Illusions" is, after all, not so much shakier in this respect than -even simple arithmetic, which contains undecidable sentences and -indefinable terms. - -In \booktitle{The Logical Syntax of Language}, Carnap distinguishes pure syntax -and descriptive syntax; and says that pure syntax should be independent of -notation, and that every system should be isomorphic to some ink-on-paper -system. In so doing, Carnap violates his ov'n Principle of Tolerance. Consider -the following trivial formalist system. - -{ \centering \large "\textsc{Order}" \par} - -\begin{sysrules} -A "sentence" is a member of a finite set of integers. - -Sentence Y is "implied by" sentence X if and only if Y=X, or else of all the -sentences, Y is the one next smaller than X. - -Take as the axiom the largest sentence. -\end{sysrules} - - -Is the pure syntax of "\textsc{Illusions}" insomorphic to "\textsc{Order}"? The preceding -paragraph proved that it is not. The implication structure of "Order" is -mechanical to the point of idiocy, while the implication structure of -"Illusions" is, as I pointed out, elusive. The figure - - -\img{orderstructure} - - -where loops indicate multiple occurances of the same sentence, could -adequately represent a proof in "Order," but could not remotely represent -one in "Illusions." The essence of "Illusions" is that it is coupled to the -reader's subjectivity. For an ink-on-paper system even to be comparable to -"IIlusions," the subjectivity would have to be moved out of the reader and -onto the paper. This is utterly impossible. - -Here is the next system. - -{ \centering \large "\textsc{Innperseqs}" \par} - -\begin{sysrules} -Explanation: Consider the rainbow halo which appears to surround a small -bright light when one looks at it through fogged glass (such as -eyeglasses which have been breathed on). The halo consists of -concentric circular bands of color. As the fog evaporates, the halo -uniformly contracts toward the light. The halo has a vague outer -ring, which contracts as the halo does. Of concern here is what -happens on one contracting radius of the halo, and specifically -what happens on the segment of that radius lying in the vague -outer ring: the outer segment. - -A "sentence" (or halopoint) is the changing halo color at a fixed point, in -space, in the halo; until the halo contracts past the point. - -Several sentences "imply" another sentence if and only if, at some instant, -the several sentences are on an outer segment, and the other -sentence is the inner endpoint of that outer segment. - -An "axiom" is a sentence which is in the initial vague outer ring (before it -contracts), and which is not an inner endpoint. - -An "innperseq" is a sequence of sequences of sentences on one radius -satisfying the following conditions. 1. The members of the first -sequence are axioms, 2. For each of the other sequences, the first -member is implied by the non-first members of the preceding -sequence; and the remaining inembers (if any) are axioms or first -members of preceding sequences. 3. All first members, of -sequences other than the last two, appear as non-first members. 4. -No sentence appears as a non-first member more than once. 5. The -last sequence has one member. - -In the diagram on the following page, different positions of the vague outer -ring at different times are suggested by different shadings. The -outer segment moves "down the page." The figure is by no means -an innperseq, but is supposed to help explain the definition. -\end{sysrules} - -Successive bands represent the vague outer ring at successive times as it fades in -toward the small bright light. - -Innperseqs Diagram - -\img{innperseqs} - -"Sentences" at - - \begin{tabular}{ c r l } - \bimg{time1} & $time_1$: & $a_1 a_2 a_3 a_4 a_5 a_6 a_7 b$ \\ - & & $a_1,a_2 \rightarrow\ b$ \\ - \end{tabular} - - \begin{tabular}{c r l} - \bimg{time2} & $time_2$: & $a_2 a_3 a_4 a_5 a_6 a_7 b c$ \\ - & & $a_3 \rightarrow\ c$ \\ - \end{tabular} - - \begin{tabular}{c r l} - \bimg{time3} & $time_3$: & $a_4 a_5 a_6 a_7 b c d$ \\ - & & $a_4,a_5 \rightarrow\ d$ \\ - \end{tabular} - - \begin{tabular}{c r l} - \bimg{time4} & $time_4$: & $a_6 a_7 b c d e$ \\ - & & $a_6,b \rightarrow\ e$ \\ - \end{tabular} - - \begin{tabular}{c r l} - \bimg{time5} & $time_5$: & $a_7 b c d e f$ \\ - & & $a_7,c \rightarrow\ f$ \\ - \end{tabular} - - \begin{tabular}{c r l} - \bimg{time6} & $time_6$: & $c d e f g$ \\ - & & $d,e \rightarrow\ g$ \\ - \end{tabular} - -"Axioms" $a_1 a_2 a_3 a_4 a_5 a_6 a_7$ - - -Innperseq \\ -$(a_3,a_2,a_1)$ -$(b,a_3)$ -$(c,a_5,a_4)$ -$(d,b,a_6)$ -$(e,c,a_7)$ -$(f,e,d)$ -$(g)$ - - -In "Innperseqs," a conventional proof would be redundant unless all -the statements were on the same radius. And even if the weakest axiom were -chosen (the initial outer endpoint), this axiom would imply the initial inner -endpoint, and from there the theorem could be reached immediately. In -other words, to use the standard definition of "proof" in "Innperseqs" -would result in an uninteresting derivation structure. Thus, a more -interesting derivation structure is defined, the "innperseq." The interest of -an "innperseq" is to be as elaborate as the many restrictions in its definition -will allow. Proofs are either disregarded in "Innperseqs"; or else they are -identified with innpersegs, and lack Property 8. "Innperseqs" makes the -break with the proof-theorem structure of formalist mathematics. - -Turning to simple implication, an implicand can have many impliors; -and there is an infinity of axioms, specified by a general condition. The -system has Property 1 in the sense that a sentence can exist at different -times and be a member of different implications. It has Property 4 in the -sense that the sentences in a specific implication can exist at different times, -and the implication holds as long as the sentences exist. It has Property 3 in -that an inner endpoint implies itself. The system also has Properties 5 and 7; -and lacks Property 2. But, as before, Properties 6 and 9 are another matter. -Given several sentences, it is certainly possible to tell mechanically whether -one is implied by the others. But when are you given sentences? If one can -think the sentences, then relating them is easy---but it is difficult to think the -sentences in the first place, even though they objectively exist. The diagram -suggests what to look for, but the actual thinking, the actual sentences are -another matter. As for Property 9, when "theorems" are identified with last -members of innperseqs, I hesitate to say whether a derivation of a given -sentence can be constructed mechanically. If a sentence is nearer the center -than the axioms are, an innperseq can be constructed for it. Or can it? The -answer is contingent. "Innperseqs" is indeterminate because of the difficulty -of thinking the sentences, a difficulty which is defined into the system. It is -the mathematician's capabilities at a particular instant which delimit the -indeterminacies. Precisely because of the difficulty of thinking sentences, I -will give several subvariants of the system. - - -{ \centering \large \textsc{Indeterminacy} \par} -\begin{sysrules} -A "totally determinate innperseq" is an innperseq in which one thinks all the -sentences. - -An "implior-indeterminate innperseq" is an innperseq in which one thinks -only each implicand and the outer segment it terminates. - -A "sententially indeterminate innperseq" is an innperseq in which one thinks -only the outer segment, and its inner endpoint, as it progresses -inward. -\end{sysrules} - - -Let us return to the matter of pure and descriptive syntax. The interest -of "Illusions" and "Innperseqs" is precisely that their abstract structure -cannot be separated from their physical and psychological character, and -thus that they are not isomorphic to any conventional ink-on-paper system. I -am trying to break through to unheard of, and hopefully significant, modes -of implication; to define implication structures (and derivation structures) -beyond the reach of past mathematics. - -\subsection{Constructed Memory Systems} - -In order to understand this section, it is necessary to be thoroughly -familiar with \essaytitle{Studies in Constructed Memories,} the essay following this -one. (I have not combined the two essays because their approaches are too -different.) I will define post-formalist systems in constructed memories, -beginning with a system in an M*-Memory. - -{ \centering \large "\textsc{Dream Amalgams}" \par} - -\begin{sysrules} -A "sentence" is a possible method, an $A_{a_i}$. with respect to an M*-Memory. -The sentence $A_{a_p}$ "implies" the sentence $A_{a_q}$ if and only if the $a_q$th -M*-assertion is actually thought; and either $A_{a_q} = A_{a_p}$, or else there is -cross-method contact of a mental state in $A_{a_q}$ with a state in $A_{q_p}$\footnote{sic?} - -The axioms must be chosen from sentences which satisfy two conditions. -The mental states in the sentences must have cross-method contact -with mental states in other sentences. And the M*-assertions -corresponding to the sentences must not be thought. - -Explanation: As \essaytitle{Studies in Constructed Memories} says, there can be -cross-method contact of states, because a normal dream can -combine totally different episodes in the dreamer's life into an -amalgam. -\end{sysrules} - -"\textsc{Dream Amalgams}" has Properties 1-5. For the first time, sentences are -structurally composite, with mental states being the relevant sentential -elements. Implication has an unusual character. The traditional type of -implication, modus ponens, is "directed," because the conditional is -directed. Even if $\ulcorner\varphi\supset\phi\urcorner$ is true -$\ulcorner\varphi\supset\phi\urcorner$ may not be. Now implication is also -directed in "\textsc{Dream Amalgams,}" but for a very different reason. -Cross-method contact, unlike the conditional, has a symmetric character. -What prevents implication from being necessarily symmetrical is that the -implicand's M*-assertion actually has to be thought, while the implior's -M*-assertion does not. Thus, implication is both subjective and mechanical, -it is subjective, in that it is a matter of volition which method is remembered -to have actually: been used. It is mechanical, in that when one is -remembering, one is automatically aware of the cross-method contacts of -states in $A_{a_q}$. The conditions on the axioms ensure that they will have -implications without losing Property 7. - -As for compound implication in "\textsc{Dream Amalgams,}" the organism -with the M*-Memory can't be aware of it at all; because it can't be aware -that at different times it remembered different methods to be the one -actually used. (In fact, the organism cannot be aware that the system has -Property 5, for the same reason.) On the other hand, to an outside observer -of the M*-Memory, indirect implication is not only thinkable but -mechanical. It is not superfluous because cross-method contact of mental -states is not necessarily transitive. The outside observer can decide whether a -sentence is a theorem by the following mechanical procedure. Check -whether the sentence's M*-assertion has acually been thought; if so, check all -sentences which imply it to see if any are axioms; if not, check all the -sentences which imply the sentences which imply it to see if any are axioms; -etc. The number of possible methods is given as finite, so the procedure is -certain to terminate. Again, an unprecedented mode of implication has been -defined. - -When a post-formalist system is defined in a constructed memory, the -discussion and analysis of the system become a consequence of constructed -memory theory and an extension of it. Constructed memory theory, which -is quite unusual but still more or less employs deductive inference, is used to -study post-formalist modes of inference which are anything but deductive. - -To aid in understanding the next system, which involves infalls in a -D-Memory, here is an - -{ \centering \large \framebox[1.1\width]{"Exercise to be Read Aloud"} \par} - -(Read according to a timer, reading the first word at O' O", and prolonging -and spacing words so that each sentence ends at the time in parentheses after -it. Do not pause netween sentences.) - -\begin{tabular}{ r l } - ($event_1$) & All men are mortal. (17") \\ - - ($Sentence_1=event_2s$) & The first utterance lasted 17" and ended at 17"; and lasted 15" and ended 1" ago. (59") \\ - - ($S_2=event_3$) & The second utterance lasted 42" and ended at 59": and lasted 50" and ended 2" ago. (1' 31") \\ - - ($S_3=event_4$) & The third utterance lasted 32" and ended at 1' 31"; and lasted 40" and ended 1" ago. (2' 16") \\ -\end{tabular} - -Since '32' in $S_3$ is greater than '2' in $S_2$, $S_2$ must say that $S_1$ ($=event_2$) -ended 30" after $S_2$ began, or something equally unclear. The duration of $S_2$ -is greater than the distance into the past to which it refers. This situation is -not a real infall, but it should give the reader some intuitive notion of an -infall. - - -\newcommand{\midheading}[1]{ - { \centering \large \textsc{#1} \par}} - -\midheading{"Infalls"} - -\begin{sysrules} - A "sentence" is a D-sentence, in a D-Memory such that $event_{j+1}$ is the first -thinking of the jth D-sentence, for all j. - -Two sentences "imply" another if and only if all three are the same; or else -the three are adjacent (and can be written $S_{j+1},S_j,S_{j-1}$), and are such -that $\delta_j=x_{j+1}-x_j> z_j,$ $S^D_{j-1}$ is the implicand. (The function of $S_{j+1}$ is to -give the duration $\delta_j=x_{j+1}-x_j$ of $S_j$. $S_j$ states that $event_j$, the first -thinking of $S^{D}_{j-1}$, ended at a distance $z_j$ into the past, where $z_j$ is smaller -than $S^D_j$'s own duration. The diagram indicates the relations.) -\end{sysrules} - -\img{infallsdiag} - -In this variety of D-Memory, the organism continuously thinks successive -D-sentences, which are all different, just as the reader of the above exercise -continuously reads successive and different sentences. Thus, the possibility -of repeating a sentence depends on the possibility of thinking it while one is -thinking another sentence---a possibility which may be far-fetched, but which -is not explicitly excluded by the definition of a "D-Memory." If the -possibility is granted, then "\textsc{Infalls}" has Properties 1--5. Direct implication is -completely mechanical; it is subjective only in that the involuntary -determination of the $z_j$ and other aspects of the memory is a 'subjective' -process of the organism. Compound implication is also mechanical to an -outside observer of the memory, but if the organism itself is to be aware of -it, it has to perform fantastic feats of multiple thinking. - -"\textsc{Dream Amalgams}" and "\textsc{Infalls}" are systems constructed with -imaginary elements, systems whose "notation" is drawn from an imaginary -object or system. Such systems have no descriptive syntax. Imaginary objects -were introduced into mathematics, or at least into geometry, by Nicholas -Lobachevski, and now I am using them as a notation. For these systems to -be nonisomorphic to any ink-on-paper systems, the mathematician must be -the organism with the M*-Memory or the D*-Memory. But this means that -in this case, the mathematics which is nonisomorphic to any ink-on-paper -system can be performed only in an imaginary mind. - -Now for a different approach. Carnap said that we are free to choose -the rules of a system arbitrarily. Let us take Carnap literally. I want to -construct more systems in constructed memories---so why not construct the -system by a procedure which ensures that constructed memories are -involved, but which is otherwise arbitrary? Why not suspend the striving -after "interesting" systems, that last vestige of the striving after -"correctness," and see what happens? Why not construct the rules of a -system by a chance procedure? - -To construct a system, we have to fill in the blanks in the following rule -schema in such a way that grammatically correct sentences result. - -\newcommand{\blankspace}{\_\_\_\_\_\_\_\_\_\_} - -\midheading{Rule Schema} - -\begin{sysrules} -A "sentence" is a(n) \blankspace. - -Two sentences "imply" a third if and only if the two sentences \blankspace\ the third. - -An "axiom" is a sentence that \blankspace. -\end{sysrules} - - -I now spread the pages of \essaytitle{Studies in Constructed Memories} on the floor. -With eyes closed, I hold a penny over them and drop it. I open my eyes and -copy down the expressions the penny covers. By repeating this routine, I -obtain a haphazard series of expressions concerning constructed memories. It -is with this series that I will fill in the blanks in the rule schema. In the next -stage, I fill the first (second, third) blank with the ceries of expressions -preceding the-first (second, third) period in the entire series. - -\midheading{"Haphazard System"} - -\begin{sysrules} -A "sentence" is a the duration D-sentences $\triangle\ (\mathparagraph^m)$ conclude these -"$\Phi*$-Reflection," or the future Assumption voluntarily force of -conviction for conclusion the Situation or by ongoing that this -system? be given telling between the Situation 1. - -Two sentences "imply" a third if and only if the two sentences is\slash was -contained not have to the acceptance that a certain and malleable -study what an event involves material specifically mathematics: -construct accompanies the rest, extra-linguistically image organism -can fantasy not remembering $\Phi*$-Memory, the future interval defined -in dream the third. - -An "axiom" is a sentence that internally D-sentences, just as the -"$\Phi*$-Memory" sentences $A_{a_1}$ is $A_{a_2}$. - -In the final stage, I cancel the smallest number of words I have to in -order to make the rules grammatical. -\end{sysrules} - -\midheading{"Fantasied Amnesia"} - -\begin{sysrules} -A "sentence" is a duration or the future force of conviction for the Situation -or this system given Situation 1. - -Two sentences "imply" a third if and only if the two sentences have the -acceptance that a certain and malleable study extra-linguistically can -fantasy not remembering the future interval defined in the third. - -An "axiom" is a sentence that internally just sentences $A_{a_2}$. -\end{sysrules} - -It becomes clear in thinking about "Fantasied Amnesia" that its -metametamathematics is dual. Describing the construction of the rules, the -metamathematics, by a systematic performance, is one thing. Taking the -finished metamathematics at face value, independently of its origin, and -studying it in the usual manner, is another. Let us take "Fantasied Amnesia" -at face value. As one becomes used to its rules, they become somewhat more -meaningful. I will say that an "interpretation" of a haphazard system is an -explanation of its rules that makes some sense out of what may seem -senseless. "Interpreting" is somewhat like finding the conditions for the -existence of a constructed memory which seemingly cannot exist. The first -rule of "Fantasied Amnesia" is a disjunction of three substantives. The -"Situation" referred to in the second substantive expression is either -Situation 1 or else an unspecified situation. The third substantive expression -apparently means "this system, assuming Situation 1," and refers to -"Fantasied Amnesia" itself. The definition of "sentence" is thus meaningful, -but very bizarre. The second rule speaks of "the acceptance" as if it were a -written assent. The rule then speaks of a "malleable study" as "fantasying" -something. This construction is quite weird, but let us try to accept it. The -third rule speaks of a sentence that "sentences" (in the legal sense) a possible -method. So much for the meaning of the rules. - -Turning to the nine properties of formalist systems, the reference to -"the future interval" in the implication rule of "Fantasied Amnesia" -indicates that the system has Property 2; and the system can perfectly well -have Property 8. It does not have Property 6 in any known sense. Certainly -it does have Property 9. it just might have Property. 1. But as for the other -four properties, it seems out of the question to decide whether "Fantasied -Amnesia" has them. For whatever it is worth, "Fantasied Amnesia" is on -balance incomparable to formalist systems. - -My transformation rule schema has the form of a biconditional, in -which the right clause is the operative one. If a transformation rule were to -vary, in such a way that it could be replaced by a constant rule whose right -clause was the disjunction of the various right clauses for the variable rule, -then the latter would vary "trivially." 1 will say that a system whose -transformation rule can vary non-trivially is a "heterodeterminate" system. -Since 1 have constructed a haphazard metamathematics, why not a -heterodeterminate metamathematics? Consider a mathematician with an -M-Memory, such that each $A_{a_i}$. is the consistent use of a different -transformation rule, a different definition of "imply," for the mathematics -in which the mathematician is discovering theorems. The consistent use of a -transformation rule is after all a method---a method for finding the -commitments premisses make, and for basing conclusions in premisses. When -the mathematician goes to remember which rule of inference he has actually -been using, he "chooses" which of the possible methods is remembered to -have actually been used. This situation amounts to a heterodeterminate -system. tn fact, the metamathematics cannot even be written out this time; I -can only describe it metametamathematically in terms of an imaginary -memory. - -We are now in the realm of mathematical systems which cannot be -written out, but can only be described metametamathematically. I will -present a final system of this sort. It is entitled \textsc{"System Such That No One -Knows What's Going On."} One just has to guess whether this system exists, -and if it does what it is like. The preceding remark is the -metametamathematical description, or definition, of the system. - -\subsection{Epilogue} - -Ever since Carnap's Principle of Tolerance opened the floodgates to -arbitrariness in mathematics, we have been faced with the prospect of a -mathematics which is indistinguishable from art-for-art's-sake, or -amusement-for-amusement's-sake. But there is one characteristic which saves -mathematics from this fate. Mathematics originated by abstraction from -primitive technology, and is indispensable to science and technology---in -short, mathematics has scientific applications. The experience of group -theory has proved, I hope once and for all, the bankruptcy of that narrow -practicality which would limit mathematics to what can currently be applied -in science. But now that mathematics is wide open, and anything goes, we -should be aware more than ever that scientific applicability is the only -objective value that mathematics has. I would not have set down constructed -memory theory and the post-formalist systems if I did not believe that they -could be applied. When and how they will be is another matter. - -And what about the "validity" of formalism? The rise of the formalist -position is certainly understandable. The formalists had a commendable, -rationalistic desire to eliminate the metaphysical problems associated with -mathematics. Moreover, formalism helped stimulate the development of the -logic needed in computer technology (and also to stimulate this paper). In -spite of the productiveness of the formalist position, however, it now seems -beyond dispute that formalism has failed to achieve its original goals. (My -pure philosophical writings are the last word on this issue.) Perhaps the main -lesson to be learned from the history of formalism is that an idea does not -have to be "true" to be productive. - - -\section{Note} -Early versions of \textsc{"Illusions"} and \textsc{"Innperseqs"} appeared in my essay -"Concept Art," published in An Anthology, ed. La Monte Young, New -York, 1963. An early, July 1961 version of \textsc{"System Such That No One -Knows What's Going On"} appeared in dimension 14, Ann Arbor, 1963, -published by the University of Michigan College of Architecture and Design. - -\section{Studies in Constructed Memories} - -\subsection{Introduction} - -The memory of a conscious organism is a phenomenon in which -interrelations of mind, language, and the rest of reality are especially evident. -In these studies, I will define some conscious memory-systems, and -investigate them. The investigation will be mathematical. In fact, the nearest -precedent for it is perhaps the geometry of Nicholas Lobachevski. -Non-Euclidian geometry had many founders, but Lobachevski in particular -spoke of his system as an "imaginary geometry." Lobachevski's system was, -so to speak, the physical geometry of an "imaginary," or constructed, space. -By analogy, my investigation could be called a psychological algebra of -constructed minds. It is too early to characterize the investigation more -exactly. Let us just remember Rudoiph Carnap's Principle of Tolerance in -mathematics: the mathematician is free to construct his system in any way -he chooses. - -I will begin by introducing a repertory of concepts informally, -becoming more formal as I go along. Consider ongoing actions, which by -definition extend through past, present, and future. For example, "I am -making the trip from New York to Chicago." Consider also past actions -which have probable consequences in the present. "I have been heating this -water" (entailing that it isn't frozen now). I will be concerned with such -actions as these. - -Our language provides for the following assertion: "I am off to the -country today; I could have been off to the beach; I could not possibly have -been going to the center of the sun". We distinguish an actual action from a -possible action; and distinguish both from an action which is materially -impossible. People insist that there are things they could do, even though -they don't choose to do them (as opposed to things they couldn't do). What -distinguishes these possible actions from impossible ones? Rather than -trying to analyze such everyday notions in terms of the logic of -counterfactual conditionals, or of modalities, or of probability, I choose to -take the notions at their face value. My concern is not to philosophize, but -to assemble concepts with which to define an interesting memory system. - -What is the introspective psychological difference between a thought -that has the force of a memory, and a thought that has the force of a -fantasied past, a merely possible past? I am not asking how I know that a -verbalized memory is true; I am asking what quality a naive thought has that -marks it as a memory. Let Alternative E be that I went to an East Side -restaurant yesterday, and Alternative W be that I went to a West Side one. -By the "thought of E" I mean mainly the visualization of going into the East -Side restaurant. My thought of E has the force of memory. It actually -happened. W is something I could have done. I can imagine I did do W. There -is nothing present which indicates whether I did E or W. Yet W merely has -the force of possibility, of fantasy. How do the two thoughts differ? Is the -thought of E involuntarily more vivid? Is there perhaps an "attitude of -assertion" involuntarily present in the thought of E? - -Consider the memory that I was almost run down by a truck yesterday: -I could have been run down, but wasn't. In such a case, the possibility that I -could have been run down would be more vivid than the actuality that I -wasn't. (Is it not insanity, when a person is overwhelmed by the fear of a -merely possible past event? ) My hold on sanity here would be the awareness -that I am alive and well today. - -In dreams, do we not wholeheartedly "remember" that a misfortune -has befallen us, and begin to adjust emotionally to it? Then we awake, and -wholeheartedly remember that the misfortune has not befallen us. The -thought that had the force of memory in the dream ceases to have that force -as we awake. We remember the dream, and conclude that it was a fantasy. -Even more characteristic of dreams, do I not to all intents and purposes go -to far places and carry out all sorts of actions in a dream, only to awaken in -bed? We say that the dream falsifies my present environment, my -sensations, my actions, memories, the past, my whole world, in a totally -convincing way. Can a hypnotist produce artificial dreams, that is, can he -control their content? Can the hypnotist give his subject one false memory -one moment, and replace it with a contradictory memory the next -moment? - -I will now specify a situation involving possible actions and -remembering. - -Situation 1. "I could have been accomplishing G by doing $A_{a_1}$, or by -doing $A_{a_2}$, \ldots, or by doing $A_{a_n}$; but I have actually been accomplishing G by -doing $A_{a_1}$." Here the ongoing actions $A_{a_i}$, $i=1,...,n$,$a_i\neq a_h if i\neq h$, are -the possible methods of accomplishing G. (The subscripts are supposed to -indicate that the methods are distinct and countable, but not ordered.) The -possible methods cannot be combined, let us assume. - -In such a situation, perhaps the thought that I have been doing $A_{a_1}$ -would be distinguished from similar thoughts about $A_{a_2}, ..., A_{a_n}$ by the -presence of the "attitude of assertion". Since the possible methods are -ongoing actions, the thought that I have been doing $A_{a_i}$ has logical or -probabie consequences I can check against the present. - -Now $A_{a_1}$, is actual and $A_{a_2}$ is not, so that $A_{a_1}$, simply cannot have -possible jar in $A_{a_3}$ to contain it. The only "connection" $A_{a_1}$ could have -material contact with $A_{a_2}$. An actual liquid in $A_{a_1}$ could not require a -with $A_{a_2}$, would be verbal and gratuitous. Therefore, in order to be possible -methods, $A_{a_2}$, ..., $A_{a_n}$ must be materially separable. A liquid in $A_{a_2}$ must -not require a jar in $A_{a_3}$ to contain it. If it did, $A_{a_2}$ couldn't be actualized -while $A_{a_3}$, remained only a possibility. - -Enough concepts are now at hand for the studies to begin in earnest. - -\subsection{M-Memories} - -\newcommand{\definition}{\textbf{Definition.}} -\newcommand{\assumption}[1]{\textit{Assumption #1.}} -\newcommand{\conclusion}[1]{\textbf{Conclusion #1.}} - -\definition Given the sentences "I have actually been doing $A_{a_i}$", where -the $A_{a_i}$ are non-combinable possible methods as in Situation 1, an -"M-Memory" is a memory of a conscious organism such that the organism -can think precisely one of the sentences at a time, and any of the sentences -has the force of memory. - -This definition refers to language, mind, and the rest of reality in their -interrelations, but the crucial reference is to a property of certain sentences. -I have chosen this formulation precisely because of what I want to -investigate. I want to find the minimal, elegant, extra-linguistic conditions, -whatever they may be, for the existence of an M-Memory (which is defined -by a linguistic property). I can say at once that the conditions must enable -the organism to think the sentences at will, and they must provide that the -memory is consistent with the organism's present awareness. - -\definition The "P-Memory" of a conscious organism is its conscious -memory of what it did and what happened to it, the past events of its life. I -want to distinguish here the "personal" memory from the preconscious. - -\definition An "L-Memory" is a linguistic P-Memory having no -extra-linguistic component. Of course, the linguistic component has -extra-linguistic mental associations which give it "meaning"--otherwise the -memory wouldn't be conscious. But these associations lack the force of a -mental reliving of the past independent of language. An L-Memory amounts -to extra-linguistic amnesia. - -\assumption{1.1} With respect to normal human memory, when I forget -whether I did x, I can't voluntarily give either the thought that I did x, or -the thought that I didn't do x, the force of memory. I know that I either did -or didn't do x, but I can create no conviction for either alternative. (An -introspective observation.) - -\conclusion{1.2} An L-Memory is not sufficient for an M-Memory, even -in the trivial case that the $A_{a_i}$ are beyond perception (as internal bodily -processes are). True, there would be no present perceptions to check the -sentences "I have actually been doing $A_{a_i}$" against. True, the L-Memory -precludes any extra-linguistic memory-"feelings" which would conflict with -the sentences. But the L-Memory is otherwise normal. And \textit{Assumption 1.1} -indicates that normally, either precisely one of a number of mutually -exclusive possibilities has the force of memory; or else the organism can give -none of them the force of memory. - -\assumption{1.3} I cannot, from within a natural dream, choose to swith -to another dream. (An introspective observation. A "natural" dream is a -dream involuntarily produced internally during sleep.) - -\conclusion{1.4} An M-Memory could not be produced by natural -dreaming. It is true that in one dream one sentence could have the force of -memory, and in another dream a different sentence could. But an M-Memory -is such that the organism can choose one sentence-memory one moment and -another the next. See Assumption 1.3. - -\assumption{1.5} Returning to the example of the restaurants, I find -that months after the event, my thought of E no longer has the force of -memory. All I remember now is that I used to remember that I did E. I -remember that I did E indirectly, by remembering that I remembered that I -did E. (My memory that I did E is becoming an L-Memory.) The assumption -is that a memory of one's remembering can indicate, if not imply, that the -event originally remembered occurred. - -\conclusion{1.6} The following are adequate conditions for the existence -of an M-Memory. -\begin{enumerate} -\item The sentences are the organism's only memory of which -method he has been using. - -\item When the organism thinks "I have actually been doing $A_{a_i}$". -then (he artificially dreams that) he has been doing $A_{a_i}$ --- and is -now doing it. - -\item When the dream ends, he does not remember that he -remembered that "he has been doing $A_{a_i}$," That is, he does not remember -the dream; and he does not remember that he thought the sentence. These -conditions would permit the existence of an M-Memory or else a memory -indistinguishable to all intents and purposes from an M-Memory. -\end{enumerate} - -What I have in mind in \conclusion{1.6} is dreams which are produced -artificially but otherwise have all the remarkable qualities of natural dreams. -There would have to be a state of affairs such that the sentence would -instantly start the dream going. - -So much for the conditions for the existence of an M-Memory. -Consider now what it is like as a mental experience to have an M-Memory. -What present or ongoing awareness accompanies an M-Memory? -\conclusion{1.6.2} already told what the remembering is like. For the rest, I will -informally sketch some conclusions. The organism can extra-linguistically -image the $A_{a_i}$. The organism can think "I could have been doing $A_{a_i}$." When -not remembering, the organism doesn't have to do any $A_{a_i}$, or he can do any -one of them. The organism must not do anything which would liquidate a -possble method, render the action no longer possible for him. - -\assumption{2.1} A normal dream can combine two totally different -past episodes in my life into a fused episode, or amalgam; so that I "relive" it -without doubts as.a single episode, and yet remain vaguely aware that -different episodes are present in it. Dreams have the capacity not only to -falsify my world, but to make the impossible believable. (An introspective -observation.) - -\conclusion{2.2} The conditions for the existence of an M-Memory -further permit material contact between the possible methods, the very -contact which is out of the question in a normal Situation 1. The dream is so -flexible that the organism can dream that an (actual) liquid is\slash was contained -by a jar in a possible method. See \assumption{2.1} Thus, the $A_{a_i}$ do not have -to be separable to be possible methods. - -I will now introduce further concepts pertaining to the mind. - -\definition\ A "mental state" is a mental "stage" or "space" or "mood" -in which visualizing, remembering, and all imaging can be carried on. - -Some human mental states are stupor, general anxiety, empathy with -another person, dizziness, general euphoria, clearheadedness (the normal -state in which work is performed), and dreaming. In all but the last state, -some simple visualization routine could be carried out voluntarily. Even ina -dream, I can have visualizations, although here I can't have them at will. The -states are not defined by the imaging or activities carried on while in them, -but are "spaces" in which such imaging or activities are carried on. - -By definition. - -\conclusion{3.2} An M-Memory has to occur within the time which the -possible methods require, the time required to accomplich G. By definition. - -\definition An "M*-Memory" is an M-Memory satisfying these -conditions. -\begin{enumerate} -\item $A_{a_i}$, for the entire time it requires, involves the voluntary -assuming of mental states. $i=1,...,n$. -\item The material contact between the -possible methods, the cross-method contact, is specifically some sort of -contact between states. -\end{enumerate} - -\conclusion{3.3} For an M*-Memory, to remember is to choose the -mental state in which the remembering is required to occur (by the -memory). After all, for any M-Memory, to remember is to choose all the -$A_{a_i}$-required things you are doing while you remember. - -By now, the character of this investigation should be clearer. I seek to -stretch our concepts, rather that to find the "true" ones. The investigation -may appear similar to the old discipline of philosophical psychology, but its -thrust is rather toward the modern axiomatic systems. The reasoning is -loose, but not arbitrary. And the investigation will become increasingly -mathematical. - - -\subsection{D-Memories} - -\definition\ A "D-Memory" is a memory such that measured past time -appears in it only in the following sentences: "$Event_j$ occurred in the interval -% TODO\<F11><F12> ? whats up with AF -of time which is $x_j-x_{j-1}$ long and ended at $x_j$ AF, and is Yj long and ended $z_j$ -\ ago," where $x_j$, $y_j$ and $z_j$ are positive numbers of time units (such as hours) -and '$AF$' means "after a fixed beginning time." $x_O=O;$ $x_j> x_{j-1}$; and at any -one fixed time, the intervals $|z_j, z_j+y_j|$ nowhere overlap. $y_j+z_j\leq x_j$ For an -integer $m$, the $m$th sentence acquires the force of memory, is added to the -memory, at the fixed time $x_m$. $j=1, ..., f(t)$, where the number of sentences -$f(t)$ is written as a function of time $AF$. Then $f(t)=m$ when $x_m \leq t \less x_{m+1}$. -The sentences have the force of memory involuntarily. The organism does -not make them up at will. - -Let me explain what the D-Memory involves. $Event_j$ is assigned to an -abnormal "interval," a dual interval defined in two unrelated ways. The -intervals defined by the $y_j$ and $z_j$ are tied to the present instant rather than to -a fixed time, and could be written $|N-z_j-y_j, N-z_j|$, where '$N$' means "the time -of the present instant relative to the fixed beginning time." - -\newcommand{\proof}{\textit{Proof}} - -\conclusion{4} The intervals $|N-z_j-y_j, N-z_j|$ nowhere overlap. - -\proof: By definition, the intervals $|z_j, z_j+y_j|$ nowhere overlap. If $j\neq k$, -$|z_j, z_j+y_j|\cap|z_k, z_k+y_k|=\emptyset$ -This fact implies that \eg $z_j\less z_j+y_j\less z_k\less z_k+y_k$. -Then $N-z_k-y_k\less N-z_k\less N-z_j-y_j\less N-z_j$. -Then $|N-z_k-y_k, N-z_k|\cap|N-z_j-y_j, N-z_j|=\emptyset$ -At any one time, the organism can think of all the sliding intervals, and they -partly cover the time up to now without overlapping. - -Suppose you find the deck of n cards - -{ \centering -\framebox[1.1\width]{ - \centering - $event_j$ \linebreak - $z_j$ ago}} - - -($j=1,...,n$ and $z_j$ is a positive number of days), and you have no -information to date them other than what they themselves say. If you -believe the cards, your mental experience will be a little like having a -D-Memory. Then, the definition does not require that $y_j=x_j-x_{j-1}$. Again, it is -not that two concepts of "length" are involved, but that the "interval" is -abnormal. Of course this is all inconsistent, but I want to study the -conditions under which a mind will accept inconsistency. - -\assumption{5.1} With respect to normal human memory, it is possible -to forget what day it is, even though one remembers a past date. (An -empirical observation.) - -\assumption{5.2} This assumption is based on the fact that the sign -'CLOSED FOR VACATION. BACK IN TWO WEEKS' was in the window of -a nearby store for at least a month this summer; and the fact that a -filmmaker wrote in a newspaper, "When an actor asks me when the film will -be finished, I say 'In two months," and two months later I give the same -answer, and I'm always right.' Even in normal circumstances, humans can -maintain a dual and outright inconsistent awareness of measured time. [n -general, inconsistency is a normal aspect of human thinking and even has -practical value. - -Imagine a child who has been told to date events by saying, for -example, x happened two days ago, and a day later saying again, x happened -two days ago---and who has not been told that this is inconsistent. What -conditions are required for the acceptance of this dating system? It is -precisely because of Assumptions 5.1 and 5.2 that a certain answer cannot -be given to this question. The human mind is so flexible and malleable that -there is no telling how much inconsistency it can absorb. I can only study -what flaws might lead the child to reject the system. The child might "feel" -that an event recedes into the past, something the memory doesn't express. -An event might be placed by the memory no later than another, and yet -"feel" more recent than the other. I speculate that if anything will discredit -the system, it will be its conflict with naive, "felt," extra-linguistic memory. - -\conclusion{5.3} The above dating system would be acceptable to an -organism with an L-Memory. - -\conclusion{5.4} The existence of an L-Memory is an adequate condition -for the existence of a D-Memory. With extra-linguistic amnesia, the -structure of the language would be the structure of the past in any case. The -past would have no form independent of language. Anyway, time is gone for -good, leaving nothing that can be checked directly. Without an -extra-linguistic memory to fall back on, and considering Assumptions 5.1 -and 5.2, the dual temporal memory shouldn't be too much to absorb. - -As I said, the real difficulty with this line of investigation is putting -limits on anything so flexible as the mind's capacity to absorb inconsistency. - -Now the thinking of a sentence in a D-Memory itself takes time. Let -$\delta(S^D_j)$ be the minimum number of time units it takes to think the jth -D-sentence. This function, abbreviated '$\delta_j$', is the duration function of the -D-sentences. - -\conclusion{6.1} If $\delta_j\greater z_j$, the memory of the interval defined by $y_j$ and -$z_j$ places the end of the interval after the beginning of the memory of it, or -does something else equally unclear. If $\delta_j\greater y_j+z_j$, the entire interval is placed -after the beginning of the memory of it. When $\delta_j\greater z_j$, let us say that the end -of the remembered interval falis within the interval for the memory of it, or -that the situation is an "\textsc{infall}." (Compare \said{The light went out a half-second -ago}.) - -\conclusion{6.2} If $\delta_j\greater x_{j+k}-x_j$, then $S^D_{j+k}$ is added to the preconscious -before $S^D_j$ can be thought once. The earliest interval during which the jth -sentence can be thought "passes over" the (j+k)th interval. Let us say that -the situation is a "\textsc{passover}." (Something of the sort is true of humans, -whose brains contain permanent impressions of far more sensations than can -be thought, remembered in consciousness.) - -\conclusion{6.3} If there are passovers in a D-Memory, the organism -cannot both think the sentences during the earliest intervals possible and be -aware of the passovers. - -\proof: The only way the organism can be aware of $\delta(S_j)$ -is for $event_{j+h}$ (h a positive integer) to be the thinking of $S_j$. -If the thinking of $S_j$ takes piace as the $(j+1)^{th}$ event, then the organism gets two -values for $\delta(S_j)$, namely $x_{j+1}-x_j$ and $y_{j+1}$. Assume that only $x_{j+1}-x_j$ -is allowed as a measure of $\delta(S_j)$. Since $\delta(S_j)=x_{j+1}-x_j$, there is no passover. If -the thinking of $S_j$ takes place as the $(j+2)^{th}$ event, then $x_{j+2}-x{j+1}=\delta(S_j)$ -could be greater than $x_{j+1}-x_j$. But since $S_j$ goes into the preconscious at $x_j$, -$S_j$ is not actually thought in the earliest interval during which it could be -thought. See the diagram. - -\img{dmemdiag} - -\conclusion{6.4} Let there be an \textsc{infall} in the case where $event_{j+1}$ is the -thinking of $S_j$. $\delta(S_j)=x_{j+1}-x_j$ and $\delta(S_j)\greater z_j$. $S_{j+1}$ gives $\delta(S_j)$, -so that the organism can be aware of it. -It is greater than $z_j$. Thus, the organism can be -aware of the \textsc{infall}. However, the \textsc{infall} will certainly be no more difficult to -accept than the other features of the D-Memory. And the thinking of $S_j$ has -to be one of the events for the organism to be aware of the infall. - -\subsection{$\Phi$-Memories} -I will conclude these studies with two complex constructions. - -\definition A "$\Phi$-Memory" is a memory which includes an M*-Memory -and a D-Memory, with the following conditions. -\begin{enumerate} -\item The goal G, for the M*-Memory, is to move from one point to another. - -\item For the D-Memory, "$event_j$" becomes a numerical term, the decrease in the organism's distance -from the destination point during the temporal interval. \said{A 3-inch move -toward the destination} is the sort of thing that "$event_j$' here refers to. - -\item The number of $A_{a_i}$ equals the number of D-sentences factorial. The number -of D-sentences, of course, increases. -\end{enumerate} - -Consider the consecutive thinking of each D-sentence precisely once, in -minimum time, while the number of sentences remains constant. Such a -"D-paragraph" is a permutation of the D-sentences. Let $\mathparagraph^m$ be a -D-paragraph when the number of sentences equals the integer m. There are -$m!$ $\mathparagraph^m$s. When $f(t)=m=3$, one of the six $\mathparagraph^3$s is $S^D_3 S^D_1 S^D_2$, -thought in -minimum time. Assume that the duration $\triangle$ of a D-paragraph depends only -on the number of D-sentences and the $\delta_j$. We can write - -$$ \triangle(\mathparagraph^m)=\sum_{j=1}^{m} \delta_j $$ - -The permutations of the D-sentences, as well as the D-paragraphs, can be -indexed with the $a_i$, just as the possible methods are. - -Definition. A "$\Phi*$-Memory" is a $\Phi$-Memory in which the order of the -sentences in the $a_i$th $\mathparagraph^m$ has the meaning of \said{I have actually been doing $A_{a_i}$} -assigned to it. The order is the indication that $A_{a_i}$ has actually been used; it -is the $a_j$th M*-assertion. \said{I have actually been doing $A_{a_i}$} is merely an English -translation, and does not appear in the $\Phi*$-Memory. - -\conclusion{7} Given a $\Phi*$-Memory, if one D-sentence is forgotten, not -only will there be a gap in the awareness of when what events occurred; it -will be forgotten which method has actually been used. - -This conclusion points toward a study in which deformations of the -memory language are related to deformations of general consciousness. - -\definition A "$\Phi*$-Reflection," or reflection in the present of a -$\Phi*$-Memory, is a collection of assertions about the future, derived from a -$\Phi*$-Memory, as follows. -\begin{enumerate} - \item There are the sentences "$Event_j$ will occur in the -interval of time which is $x_j-x_{j-1}$ long, and begins at twice the present time -$AF$, minus $x_j AF$; and which is $y_j$ long and begins $z_j$ from now." If $event_j$ was -a 3-inch move toward the destination in the "$\Phi*$-Memory, the sentence in the -$\Phi*$-Reflection says that a 3-inch move will be made in the future temporal -interval. - \item The $a_i$th permutation of the sentences defined in (1) is an -assertion which has the meaning of \said{I will do $A_{a_i}$}; and the organism can -think precisely one permutation at a time. The $A_{a_i}$, $x_j$, $y_j$, $z_j$, and the rest are -defined as before (so that in particular the permutations can be indexed with -the $a_i$). -\end{enumerate} - -\conclusion{8} Given that the $\Phi*$-Memory's temporal intervals $|x_{j-1}, x_j|$ -are reflected as $|2N-x_j, 2N-x_{j-1}|$, the reflection preserves the intervals' -absolute distances from the present. - -\proof: The least distance of $|x_{j-1}, x_j|$ -from $N$ is $N-x_j$; the greatest distance is $N-x_{j-1}$. Adding the least distance, and -then the greatest distance, to $N$, gives $|2N-x_j, 2N-x_{j-1}|$. - -I will end with two problems. If a $\Phi*$-Memory exists, under what -conditions will a $\Phi*$-Reflection be a precognition? Under what conditions -will every assertion be prescience or foreknowledge? By a "precognition" I -don't mean a prediction about the future implied by deterministic laws; I -mean a direct "memory" of the future unconnected with general principles. - -Finally, what would a precognitive $\Phi*$-Reflection be like as a mental -experience? What present or ongoing awareness would accompany a -precognitive $\Phi*$-Reflection? - -\part{The New Modality} - -\chapter{Representation of the Memory of an Energy Cube Organism (1966 VERSION)} - - -The energy cube organism is a conscious organism which is nothing but -energy confined to a cubical space. It rests on a rectangular energy slab, in a -stationary, colorless liquid, separated from the slab by a thin film of liquid. -It has been on the slab for an indefinitely long time. There are in fact two -infinite bodies of the liquid, alternating with two infinite empty spaces; the -four volumes are outlined by two intersecting planes which just miss being -perpendicular. The slab is poised, at a slant, on the faces of the upper body -of liquid, near where they meet. There are no other objects in the bodies of -liquid. The slab, liquid, and spaces are the energy cube organism's entire -cosmology. (See the illustration.) - -\img{energycube} - -The energy cube organism can continuously change position, -continuously and instantly moving the liquid from its path into its wake so -as to make no current in the liquid. For almost as long as it has been on the -slab, the organism has devoted itself to crossing the slab, from the slab's edge -on one face of the liquid to its edge on the other. - -The energy cube organism has a conscious memory (by which I mean -strictly a memory of what it did and what happened to it, the past events of -its existence). The memory consists of symbols which are given "meaning" -by their extra-linguistic mental associations---in human terms, it consists of -language. The complete memory contains tens of thousands of partial -memories, which the organism can only have one at a time. Going through -the partials---which it does as if they were the phonemes of one long -word---constitutes its one complete memory. Each partial is a memory of the -difference in the organism's minimum distances from the destination edge, at -the beginning, and at the end, of some interval of time. Call the difference its -"progress." The total of time intervals in all the partials completely covers -the interval from the earliest remembered event to the most recent -remembered event. As time passes, more partials are added to the complete -memory. The production of partial memories is an involuntary process of -the organism. - -The memory is temporally dual. The interval for each partial is an -interval of fixed time, defined by its duration, and the distance from the -fixed time when the energy cube organism appeared on the slab up to the -interval's end. But it is also a sliding interval, defined by its duration, and a -constant distance from the present instant back to the interval's end. When -partials are added to the memory, each of the former intervals exactly covers -the tire not already covered, up to the absolute time when the partial is -added. But the latter intervals, while they never overlap, can have gaps -between them. The intervals generally are of different durations. The energy -cube organism lacks any independent extra-linguistic memory, any mental -reliving of the past, which could conflict with the dual temporal memory. -There is no form to the past other than that of the memory's language. (See -the graph.) - -The order of the partials in the complete memory is a linguistic -phenomenon which indicates the method the organism has been using to -move itself--and thus the order (with its extra-linguistic associations) is the -memory of the method. A single method" is everything to be done by the -energy cube organism to move itself, throughout the entire time it takes to -reach the destination edge. There are different possible methods, and each -could get the organism across; but the methods cannot be combined in any -way. Every order of all partials signifies a different possible method. These -possible methods are in no special order. When a partial is added to the -memory, the number of possible methods is increased by a factor equal to -the new number of partials. - -\img{energycubegraph} - -{ - \centering - \textsc{Graph} showing a possible relationship in the dual temporal memory - \par -} - - -Now the complete memory is obtained by going through the partials---in -any order! Any order gives the memory. This feature, which can be -precisely characterized in terms of the memory language, is perhaps the most -remarkable feature of the whole cosmology. An approach to this feature in -human terms is to say that when the organism goes through the partials, (it -dreams that) it has been using the method indicated---and is presently using -it. It (does not remember the dream, and) does not remember going through -the partials. It has no other memory of which method it has been using. - -The organism moves itself by mental exertion, teleports itself. The -"possible methods" are mental routines. These routines draw on the -following standard mental resources. The organism can assume at will many -"mental states." By 'mental state' I refer to a mental "stage" or "space" or -"mood" in which visualizing, remembering, and all imaging can be carried -on. Some human mental states are general euphoria, stupor, general anxiety, -dreaming, dizziness, empathy with another person, and clearheadedness, the -normal state in which work is performed. These states are not defined by -specific imagings, but are "spaces" in which imaging is carried on. The -organism changes its state by changing from one form of energy to another, -gravity, magnetism, electric energy, radiated heat, or light. In these states, -the organism has an unlimited capacity to image; in human terms, to -visualize. There are visualized regions of colored liquids. Call them "fluid -colors." There are visualized glowing surfaces, and there are black regions or -"holes." There are visualized "covers," "lattices," and "shells," which are all -formed from transparent planes, spherical surfaces and the like. Call them -"orojected surfaces." The fluid colors can be stationary or flowing. There are -"channels," which are strung-out series of fluid colors. There are -"reservoirs," which are clusters of fluid colors. A channel can be closed or -open. Two channels can cross each other. There are pairs of channels such -that earlier members of each channel flow into later members of the -other---called "screw-connected" channels. Fluid colors often occur on or -within projected surfaces. Projected surfaces can be growing or held. A -visualization can be at the forefront of attention, or in the back of the mind. -That is, states have depth, and visualizations can be at different depths. The -state as a whole can be "frozen" or "melted." A human approach is to say -that a "frozen" state is set or fixed; while a "melted" state is fluid---the state -itself flows. A state can be projected into "superstate," gaining an abnormal -amount of mental energy and becoming superdizziness or superanxiety, for -instance. - -Most interesting, states in different possible methods can have contact -with each other. A human approach is to say that dreams are so flexible that -the organism can dream that an actual state is\slash was in contact with a state in -a possible method. One sort of cross-method contact is for states to be -"interfrozen"---more easily frozen because they are somehow mixed. They -can also be "intermelted." - -I will describe a method, as the organism would be conscious of it in -remembering. For concreteness, I will refer to the different states with the -names of human states rather than with letters. Channels are generated in a -frozen stupor, and become fixed at the forefront of attention of euphoria -intermelted with a possible state. The screw-crossed channels erode crevices -in a held lattice, which breaks into growing sheets (a variety of covers). The -sheets are stacked, and held in a frozen dream thawed at intervals for -reshuffling of the stack. The dream becomes melted, and proceeds in a -trajectory which shears, and closes, open channels. If no violation of the -channels cross-mars the melt, the stack meshes with the sharp-open channels. -The dream becomes interfrozen, and mixed clear-headed states compress the -closed channels which were not fixed at the dream's surface. A fused -exterior double-flash (a certain maximally "glowing surface") is -expand-enveloped by euphoria, which becomes dizziness; and oblique -lattices are projected from the paralinear deviation of guided open channels -in it. Growing shells are dreamed into violet sound-slices (certain synesthetic -"fluid colors") by the needed jumped drag (a generic state), a crossfrozen -dream. Channels in a growing anxiety enspiral concentric shells having -intermixed reservoirs between them, during cyclic intersection of the anxiety -in superstate. And on and on. Time is here the time it takes to carry out the -successive steps of the routine. - -The energy cube organism language, the symbols constituting the -partials, are themselves mental entities. A partial is a rectangular plane -glowing surface, which has two stationary plane reservoirs on it, and has a -triangular hole in it. As a mental entity, in other words, a partial is a -visualization like those which are part of the methods. The perimeter of the -triangular hole equals the organism's progress in the corresponding time -interval. Absence of the hole indicates zero progress. - -The fluid colors in each of the reservoirs on each partial memory are -primary colors, and are mixed together. Speaking as accurately as possible in -human terms, in each reservoir there is precisely one point of "maximum -mixture" of the primary colors. The primary colors are mentally mixed in -any way until the right amount of mixture is reached. There is a scale of -measurement for amounts of mixture of the colors. There is a scale for -vertical distances on the surface---for how far one point is below another. The -difference in amounts of mixture at the two points of maximum mixture -corresponds to the length of the first temporal interval; and the difference -between the maximum possible amount of mixture and the lesser of the two -amounts of maximum mixture on the surface corresponds to the distance -from the fixed beginning time to the interval's and. The vertical distance -between the two points of maximum mixture corresponds to the length of -the second temporal interval; and the vertical distance from the middle of -the surface to the point nearer it corresponds to the constant distance from -the present instant back to the interval's enc. The middle of the surface -represents the present, and the upper half represents the future; the -reservoirs are all in the lower half. For each partial it is necessary to -determine (1) the number of units of duration per unit difference in -amounts of mixture; and (2) the number of units of duration per unit -difference in vertical distances. The average glow per unit area of each -glowing surface (excepting the hole) is correlated with a pair of numbers -constituting this information. - -Finally, turning all the partial memories upside down--and reflecting the -first temporal memory in the present instant, so that the intervals' absolute -distances from the present are preserved--gives the precognition of the -organism's future course of action, tells what progress will be made when -and by which method. - - -\section*{The Representation} - -This essay accompanies a representation of the energy cube organism's -memory--hence its title. The way to picture the memory, naturally, is to -make something that looks like the partials. I have represented the partials -by rectangular sheets of paper of different translucencies with mixtures of -inks of primary colors on them and holes cut in them; together in an -envelope, which bears the injunction not to have more than one sheet out at -a time. Three of the tens of thousands of partials are represented. - - -\chapter{Representation of the Memory of an Energy Cube Organism (Original 1961 Version)} - -\section*{Foreward} - -I have refrained from editing the Original Version except where -absolutely necessary. It is full of inconsistencies and inadequate -explanations, but I have flagged only two major ones, by placing them -between the signs $\ltimes$ and $\rtimes$. Part of the fourth paragraph is flagged because a -sequence of units is not analogous to a sequence of inflected words; it is -rather more like permutations of letters which form words ('rat', 'tar', 'art'). -Most of the seventh paragraph is flagged because I promise to define intervals -by their lengths and ends, but instead give their beginnings and ends. - -In the fourth paragraph, there are two different versions of the -correspondence between possible methods and sequences of units, and of -why any sequence is acceptable. Passages belonging exclusively to the -"multiplex" version are set off by the sign \#. Passages which belong -exclusively to the "style" version and which should be deleted if the -"multiplex" version is used are placed between slashes (\slash). The "style" version is -the main version. In the fifth paragraph, a notion appears which is -interesting, but unconvincingly explained. It is not clear whether this notion -relates only to the "multiplex" version, or whether it would relate to the -"style" version if the word 'multiplex' were omitted. The passages suggesting -this notion are placed in brackets. - -\begin{enumerate} -\item Energy cube organisms are conscious organisms which are cubical -spaces containing only energy. The particular energy cube organism of -concern here has, for an indefinitely long time, been in a body of liquid, -"resting on' a rectangular energy slab also in the body of liquid; the -organism's "bottom" face is separated from the slab by only a very thin film -of the liquid. The "universe" the organism and slab are in is made up of four -infinite triangular right prisms, prismatic spaces, as defined geometrically by -two intersecting planes almost perpendicular to each other. The prismatic -spaces defined by the vertical obtuse dihedral angles are empty. The other -spaces, defined by the vertical acute dihedral angles, are infinite bodies of a -stationary, colorless liquid--the "upper" body of liquid being what the -organism and slab are in. The two opposite shorter edges of the slab are at -the faces of the body of liquid, the planes, near their intersection; the slab is -"slanted," so that the edges are at slightly different distances from the line -of intersection. The organism and slab are the only "objects" in the bodies -of liquid. (See the illustration.) The organism can move (the energy cube can -continuously change position) without creating currents in the liquid. For -almost as long as it has been in the liquid, the organism has devoted all its -"intelligence," all its "energies," to moving across the slab, from one of the -shorter edges to (any point on) the other. - -\item The organism's conscious, distinct memory is entirely concerned -with, is entirely of, its efforts to cross the slab. (I am using 'memory' -narrowly to refer to an organism's memory of its past. I am counting its -"general information," for example knowing a language, not as part of its -memory but as imagings not memories. Thinking the sequence 1, 2, 1, 2 is -not in itself remembering.) The total memory consists of a large number of -units (tens of thousands), of which the organism can be attentive to precisely -one at a time. "Total recall," the total memory, involves considering, having, -all units in any succession, which the organism can do very rapidly. Now -from one point of view, the memory consists of its content; from another, it -consists of symbols, just as human memories often consist of language. In -describing the memory, I will go from considering primarily the content, -what the memory is of; to considering the specific character of the units, -specific symbolism used in the memory, and specific content. Each unit is -first a memory of the amount of progress made toward the destination edge -in a particular interval of time. The amount of progress is the difference -between the minimum distance of the organism from the destination edge at -the beginning of the interval, and the minimum distance at the end of the -interval. The total of intervals, in the total of units, cover the "absolute" -interval of time from the earliest to the most recent remembered event; as -time passes, more units are added to the memory. - -\item Now the memory is temporally dual: the interval of time for each -unit is first, an interval of 'absolute' time; defined by its duration, and the -"absolute" time of its end (stated with respect to an "absolute event" such -as the appearance of the organism on the slab); and secondly, an interval -defined by its duration, and how far from the present instant its end is. It is -like remembering that so much progress was made during one year which -ended at January 1, 1000 A.D.; as well as remembering that it was made -during one year which ended 1,000 years ago. In the second temporal -memory, the absolute time of the end of the interval to which the progress is -assigned changes according as the absolute time of the present instant -changes. For example, it is like remembering \said{that so much progress was -made during one year ending 1,000 years ago,} and, 100 years later, -remembering---\said{that so much progress was made during one year ending -1,000 years ago}; and in general, always remembering \said{that so much -progress was made during one year ending 1,000 years ago.} Both temporal -memories are in their own ways "natural," the first being anchored at an -"absolute beginning," the second at the present instant. When a unit is added -to the memory, the interval of time of the first temporal memory is added at -the end, exactly covers the time not already covered, up to the absolute time -when the unit is added; so that the total of intervals of the first temporal -memory exactly cover, without overlap, the absolute total time. In contrast, -although the intervals of the second temporal memory do not overlap at any -time, there can be gaps between them; so that when a unit is added to the -memory, the interval for the second temporal memory may be placed -between existing intervals and not have to cover an absolute time which they -have left behind, that is, not have to be placed farther back than all of them. -Intervals of both temporal memories are of different sizes, a "natural -complexity." (See the graph.) Incidentally, the condition for coincidence of -the two temporal intervals of a unit is: if the two intervals are of the same -duration, they will coincide at the absolute time which is the sum of the -absolute time of the end of the first interval, and the distance from the -present instant of the end of the second interval. The two temporal -memories complement each other; aside from this comment I will not be -concerned to "explain" the duality with respect to when the amounts of -progress were made, whether when they were "really" made stayed the same -and changed, or whether the memory is inconsistent about it, or what. - -\item I will now turn to the aspect of the memory concerned with the -method the organism has used to move itself. \# Methodologically, the -memory is a multiplex symbol. \# A "single method" is everything to be done -by the organism, to move itself, throughout the total time it takes to reach -the destination edge; so that the organism could not use two different -"single methods," must, after it chooses its method, continue with it alone -throughout. The organism has available different (single) methods, has -different methods it could try. The different sequences, of all units, are -assigned to the different (single) methods available to the organism to signify -them; are symbols for them. (Thus, the number of available methods -increases as units are added to the memory.) \slash Now all this only approximates -what is the case, because contrary to what I may have implied, which -method is used is not a matter of "fact" as are the temporal intervals and -amounts of progress. As I have said, having all units in any succession -constitutes the total memory, total recall ("factually")--different sequences -of all units are each the total memory, total recall, $\ltimes$ but, as language, the -total memory in different styles (like words in different orders in a highly -inflected language); and the matter of method (which might better be said to -be "manner") corresponds to the matter of style, rather than factual -content, of language. Different styles exclude each other, but not what is -said in each other's being true.$\rtimes$ Thus it is that the number of available -methods can increase; and that any sequence of all units can constitute the -total memory, total recall ("factually"), although different sequences signify -different methods used. \slash \# As an indicator of the method used, the whole -memory is a multiplex symbol. Names for each of the methods are combined -in a single symbol, the totality of units. In remembering, the organism -separates any single name by going through all the units in succession, and -that name is the complete reading of the multiplex symbol, the complete -information about the method used. I will not be concerned to "explain" -the matter of the increasing number of available methods; or the matter of -any sequence of all units' constituting the complete reading, the total -memory, total recall, but different sequences' signifying different methods -used. \# - -\item I will give just an indication of what the available methods [and -their relations through the multiplex memory] are like. Throughout this -description, there has been the difficulty that English lacks a vocabulary -appropriate for describing the "universe" I am concerned with, but the -difficulty is particularly great here, in the case of the methods [and their -relations through the multiplex memory]; so that I will just have to -approximate a vocabulary with present English as best as I can. The -methods, instruments of autokinesis, are all mental, teleportation, result in -teleportation. The "consciousnesses" available to the organism to be -combined into methods are infinitely many. It has available many states of -mind (as humans have non-consciousness, autohypnotic trance, dizziness, -dreaming, clear-headed calculation, and so forth), corresponding to different -forms its energy can assume. To give this description more content I will -differentiate its states of mind by referring to them with the names of the -human states of mind (rather than just with letters). It has available an -indefinite variety of contents, as humans have particular imagings, in its -conscious states of mind. I will outline the principal contents. There are -"visualized" fluid regions of color (like colored liquids), first-order contents. -There are 'visualized' radient surfaces, and non-radient surfaces or regions -("holes"), the intermediate contents. The second-order contents are -"projective" constructs of imaged geometric surfaces, "covers," "lattices," -and "shells." Fluid colors can be stationary or flowing. They can occur in -certain series, "channels"; and in certain arrays, "reservoirs." A channel can -be "closed" or "open"; two channels can be "crossed," or -"screw-connected" (earlier members of each channel flowing into later -members of the other). First-order contents (fluid colors) often occur on or -within second-order ones (projective surfaces). Second-order contents can be -"held" or "growing." States of mind have depth, 'deeper' being 'farther from -the forefront of attention'; and contents can be at different depths. A state -of mind as a unity can be "frozen," which is more than just unchanging (in -particular having its contents stationary or held). It can be projected into -"superstate," remaining a state of mind but being superenergized. [Most -interesting, states of mind, in different methods signified by different -symbols combined in the multiplex methodological memory, can have -contact with each other, for example be "interfrozen."] A partial description -of a method will give an idea of the complexity of the methods. Channels are -generated by a frozen non-conscious state, and become fixed in the surface -layer of an [inter] melted trance. The screw-crossed channels erode crevices -in a held shell, which breaks into growing sheets (certain covers). The sheets -are stacked, and held in a frozen dream thawed at intervals for reshuffling. -The dream becomes melted, and proceeds in a trajectory which shears, and -closes, open channels. If no violation of the channels cross-mars the melt, the -stack meshes with the sharp-open channels. The dream becomes [inter] -frozen, and mixed calculation states compress the closed channels which -were not surface-fixed in it. A fused exterior double-flash (a certain -maximally radient surface) is expand-enveloped by a trance, which becomes -dizziness; and oblique lattices are projected from the paralinear deviation of -guided open channels in it. Growing shells are dreamed into violet -sound-slices (certain fluid colors) by the needed jumped drag (a certain -consciousness), a [cross] frozen dream. Channels in a growing trance enspiral -concentric shells having intermixed reservoirs between them, during cyclic -intersection of the trance in superstate. I will not say more about the -available methods, because in a sense the memory does not: a sequence of -units is a marker arbitrarily assigned to a method to signify it, like an -arbitrary letter, say 'q', assigned to a certain table to signify it; it no more -gives characteristics of the method than 'q' does of the table. In fact, the -available methods and sequences do not have any particular order; one -cannot speak of the "first" method, the "second," or the like. - -\item I will now concentrate on the character of the memory as a mental -entity, and the rest of the symbolism used in it and specific content. A unit -is a rectangular plane ("visualized") radient surface (! ---the terminology is -that introduced in the last paragraph), which has two stationary plane -reservoirs (!) on it, and has a triangular hole (!) in it. The triangular hole is -a simple symboi not yet explained: its perimeter equals the amount of the -organism's progress, the difference in its minimum distances from the -destination edge, in the interval the unit is concerned with. Absence of the -hole indicates zero perimeter and no progress. - -\item As for the symbols for the temporal interval. The colors in each of -the two reservoirs on each unit are primary, and are mixed together. -Speaking as accurately as possible in English, in each reservoir there is -precisely one point of "maximum mixture' of the primary colors. (The rest -of the reservoirs are not significant: the primary colors are mentally mixed in -any way to get the right amount of mixture, as pigments are mixed on a -palette.) $\ltimes$ For the first temporal memory, these points are two points on a -scale of amounts of color mixture. For the second memory, the points are -two points on a scale of vertical distances from the imaginary horizontal line -which bisects the rectangular surface, divides it into lower and upper halves. -The units are marked in their lower halves only; because for the second -memory the imaginary dividing line represents the present instant, distances -below it represent distances into the past, and distances above it distances -into the future (lower and upper edges representing equal distances from the -present). Now a scale is required so that it can be told what temporal -intervals the interval on the amount of mixture scale and the interval on the -distance scale represent. The parts of the scale which may vary from unit to -unit and have to be specified in each unit are the "absolute" time -corresponding to the maximum possible color mixture, the number of units -of absolute duration per unit difference in amounts of mixture, and the -number of units of absolute duration per unit difference in distances from -the imaginary dividing line. The markers arbitrarily assigned to the triples of -information giving these parts of the scale are average radiences per unit -areas of the units (excepting the holes). $\rtimes$ - -\item A final aspect of interest. Not too surprisingly, the transformation -which is inverting all units gives, if one considers not the first temporal -memory but its reflection in the present instant, the organism's precognized -course of action in the future, specifically, what progress will be made when. -\end{enumerate} - - -\section*{The Representation} - -With this background, it is not surprising that the method of -representation I have chosen is visual representation of the units, the -"visualizations." Units are represented by rectangular sheets of paper of -different translucencies with mixtures of inks of primary colors on them and -holes cut in them, together in an envelope. Only one sheet should be out of -the envelope at a time. A sheet should be viewed while placed before a white -light in front of a black background, so that the light illuminates the whole -sheet as evenly as possible without being seen through the hole, only the -black being seen at the hole. The ultimate in fidelity would be to learn to -visualize these sheets as they look when viewed properly; then one could -have the memory as nearly as possible as the organism does. I have -represented eleven of the tens of thousands of units in the total memory. - - -\chapter{Concept Art} -{ \raggedleft (1961) \par } - - -Concept art is first of all an art of which the material is concepts, as the -material of e.g. music is sound. Since concepts are closely bound up with -language, concept art is a kind of art of which the material is language. That -is, unlike e.g. a work of music, in which the music proper (as opposed to -notation, analysis, etc.) is just sound, concept art proper will involve -language. From the philosophy of language, we learn that a concept may as -well be thought of as the intension of a name; this is the relation between -concepts and language.\footnote{The extension of the word 'table' is all -existing tables; the intension of 'table' is all possible instances of a table.} -The notion of a concept is a vestige of the notion of -a platonic form (the thing which e.g. all tables have in common: tableness), -which notion is replaced by the notion of a name objectively, metaphysically -related to its intension (so that all tables now have in common their -objective relation to table). Now the claim that there can be an objective -relation between a name and its intension is wrong, and (the word) concept, -as commonly used now, can be discredited (see my book, Philosophy -Proper). If, however, it is enough for one that there be a subjective relation -between a name and its intension, namely the unhesitant decision as to the -way one wants to use the name, the unhesitant decisions to affirm the names -of some things but not others, then concept is valid language, and concept -art has a philosophically valid basis. - -Now what is artistic, aesthetic, about a work which is a body of -concepts? This question can best be answered by telling where concept art -came from; I developed it in an attempt to straighten out certain traditional -activities generally regarded as aesthetic. The first of these is structure art, -music, visual art, etc., in which the important thing is "structure." My -definitive discussion of structure art is in my unpublished essay \essaytitle{Structure -Art and Pure Mathematics}; here I will just summarize that discussion. Much -structure art is a vestige of the time when \eg music was believed to be -knowledge, a science, which had important things to say in astronomy \etc -Contemporary structure artists, on the other hand, tend to claim the kind of -cognitive value for their art that conventional contemporary mathematicians -claim for mathematics. Modern examples of structure art are the fugue and -total serial music. These examples illustrate the important division of -structure art into two kinds according to how the structure is appreciated. In -the case of a fugue, one is aware of its structure in listening to it; one -imposes relationships, a categorization (hopefully that intended by the -composer) on the sounds while listening to them, that is, has an (associated) -artistic structure experience. In the case of total serial music, the structure is -such that this cannot be done; one just has to read an analysis of the -music, definition of the relationships. Now there are two things wrong with -structure art. First, its cognitive pretensions are utterly wrong. Secondly, by -trying to be music or whatever (which has nothing to do with knowledge), -and knowledge represented by structure, structure art both fails, is -completely boring, as music, and doesn't begin to explore the aesthetic -possibilities structure can have when freed from trying to be music or -whatever.The first step in straightening out e.g. structure music is to stop -calling it music, and start saying that the sound is used only to carry the -structure and that the real point is the structure--and then you will see how -limited, impoverished, the structure is. Incidentally, anyone who says that -works of structure music do occasionally have musical value just doesn't -know how good real music (the Goli Dance of the Baoule; Cans on Windows -by La Monte Young; the contemporary American hit song Sweets for My -Sweets, by the Drifters) can get. When you make the change, then since -structures are concepts, you have concept art. Incidentally, there is another, -less important kind of art which when straightened out becomes concept art: -art involving play with the concepts of the art such as, in music, the score, -performer vs. listener, playing a work. The second criticism of structure art -applies, with the necessary changes, to this art. - -The second main antecedent of structure art is mathematics. This is the -result of my revolution in mathematics, presented in my 1966 \essaytitle{Mathematical -Studies}; here I will only summarize. The revolution occured first because for -reasons of taste I wanted to deemphasize discovery in mathematics, -mathematics as discovering theorems and proofs. I wasn't good at such -discovery, and it bored me. The first way I thought of to de-emphasize -discovery came not later than Summer, 1960; it was that since the value of -pure mathematics is now regarded as aesthetic rather than cognitive, why not -try to make up aesthetic theorems, without considering whether they are -true. The second way, which came at about the same time, was to find, as a -philosopher, that the conventional claim that theorems and proofs are -discovered is wrong, for the same reason I have already given that 'concept' -can be discredited. The third way, which came in the fall-winter of 1960, -was to work in unexplored regions of formalist mathematics. The resulting -mathematics still had statements, theorems, proofs, but the latter weren't -discovered in the way they traditionally were. Now exploration of the wider -possibilities of mathematics as revolutionized by me tends to lead beyond -what it makes sense to call mathematics; the category of mathematics, a -vestige of Platonism, is an unnatural, bad one. My work in mathematics leads -to the new category of concept art, of which straightened out traditional -mathematics (mathematics as discovery) is an untypical, small but -intensively developed part. - -I can now return to the question of why concept art is art. Why isn't it an -absolutely new, or at least a non-artistic, non-aesthetic activity? The answer -is that the antecedents of concept art are commonly regarded as artistic, -aesthetic activities; on a deeper level, interesting concepts, concepts -enjoyable in themselves, especially as they occur in mathematics, are -commonly said to have beauty. By calling my activity art, therefore, I am -simply recognizing this common usage, and the origin of the activity in -structure art and mathematics. However: it is confusing to call things as -irrelevant as the emotional enjoyment of (real) music, and the intellectual -enjoyment of concepts, the same kind of enjoyment. Since concept art -includes almost everything ever said to be music, at least, which is not music -for the emotions, perhaps it would be better to restrict art to apply to art for -the emotions, and recognize my activity as an independent, new activity, -irrelevant to art (and knowledge). - -\section*{Concept Art Version of Mathematics System 3/26/61 (6/19/61)} - -An element is the adjacent area (with the figure in it) so long as the -apparent, perceived, ratio of the length of the vertical line to that of the -horizontal line (the element's associated ratio) does not change. - -A selection sequence is a sequence of elements of which the first is the one -having the greatest associated ratio, and each of the others has the associated -ratio next smaller than that of the preceding one. (To decrease the ratio, -come to see the vertical line as shorter, relative to the horizontal line, one -might try measuring the lines with a ruler to convince oneself that the -vertical one is not longer than the other, and then trying to see the lines as -equal in length; constructing similar figures with a variety of real (measured) -ratios and practicing judging these ratios; and so forth.) - -[Observe that the order of elements in a selection sequence may not be the -order in which one sees them.] - - -\img{implications} - -\section*{Implications---Concept Art Version of Colored Sheet Music No. 1 3/14/61 (10/11/61)} - -[This is a mathematical system without general concepts of statement, -implication, axiom, and proof. Instead, you make the object, and stipulate -by ostension that it is an axiom, theorem, or whatever. My thesis is that -since there is no objective relation between name and intension, all -mathematics is this arbitrary. Originally, the successive statements, or sheets, -were to be played on an optical audiorecorder.] - -\begin{sysrules} -The axiom: a sheet of cheap, thin white typewriter paper - -The axiom implies statement 2: soak the axiom in inflammable liquid which -does not leave solid residue when burned; then burn it on horizontal -rectangular white fireproof surface---statement 2 is ashes (on surface) - -Statement 2 implies s.3: make black and white photograph of s.2 in white -light (image of ashes' rectangle with respect to white surface (that is, of the -region (of surface, with the ashes on it) with bounding edges parallel to the -edges of the surface and intersecting the four points in the ashes nearest the -four edges of the surface) must exactly cover the film); develop film---s.3 is -the negative. - -s.2 and s.3 imply s.4: melt s.3 and cool in mold to form plastic doubly -convex lens with small curvature; take color photograph of ashes' rectangle -in yellow light using this lens; develop film---s.4 is color negative. - -s.2 and s.4 imply s.5: repeat last step with s.4 (instead of 3), using red -light---s.5 is second color negative - -s.2 and s.5 imply s.6: repeat last step with s.5, using blue light---s.6 is third -color negative - -s.2 and s.6 imply s.7: make lens from s.6 mixed with the ashes which have -been being photographed; make black and white photograph, in white fight, -of that part of the white surface where the ashes' rectangle was; develop film ---- s.7 is second black and white negative - -s.2, s.6, and s.7 imply the theorem: melt, mold, and cool lens used in last -step to form negative, and make lens from s.7; using negative and lens in an -enlarger, make two prints, an enlargement and a reduction--enlargement and -reduction together constitute the theorem. -\end{sysrules} - -\section*{Concept Art: Innpersegs (May--July 1961)} - -\begin{sysrules} -A "halpoint" iff whatever is at any point in space, in the fading rainbow halo -which appears to surround a small bright light when one looks at it through -glasses fogged by having been breathed on, for as long as the point is in the -halo. - -An "init`point" iff a halpoint in the initial vague outer ring of its halo. - - -An "inn`perseq" iff a sequence of sequences of halpoints such that all the -halpoints are on one (initial) radius of a halo; the members of the first -sequence are initpoints; for each of the other sequences, the first member (a -consequent) is got from the non-first members of the preceding sequence -(the antecedents) by being the inner endpoint of the radial segment in the -vague outer ring when they are on the segment, and the other members (if -any) are initpoints or first members of preceding sequences; all first members -of sequences other than the last [two] appear as non-first members, and -halpoints appear only once as non-first members; and the last sequence has -one member. -\end{sysrules} - -\section*{Indeterminacy} - -\begin{sysrules} -A $\ulcorner$totally determinate innperseq' iff an innperseq$\urcorner$ in which one is aware of -(specifies) all halpoints. - -An $\ulcorner$antecedentally indeterminate innperseq' iff an innperseq$\urcorner$ in which one is -aware of (specifies) only each consequent and the radial seqment beyond it. - -A $\ulcorner$halpointally indeterminate innperseq' iff an innperseq$\urcorner$ in which one is -aware of (specifies) only the radial segment in the vague outer ring, and its -inner endpoint, as it progresses inward. -\end{sysrules} - -\subsection*{Innperseqs Diagram} - -In the diagram, different positions of the vague outer ring at different times -are suggested by different shadings. The radial segment in the vague outer -ring moves down the page. The figure is by no means an innperseq, but is -supposed to help explain the definition. - -\img{innperseqsdiagram} - -\chapter{Exhibit of a Working Model of a Perception-Dissociator} - -\section{\textsc{Statement of Objectives}} - -To construct a model of a machine a thousand years before the machine -itself is technologically feasible---to model a technological breakthrough a -thousand years before it occurs - -\begin{sysrules} -(Analogies: constructing a model of an atomic power plant in ancient -Rome; chess-playing-machine hoaxes of 19th-century Europe as -models of computers; Soviet Cosmos Hall at Expo 67 as model -of anti-gravity machine) - -To construct the model almost entirely from the visitors coming to see it, so -that each visitor regards the others as the model! - -What the hypothetical perception-dissociator will do that is not -possible now: -\end{sysrules} - -\begin{itemize} -\item Physically alter the world (relative to you): sound disappears; sights and -touches are dissociated; other people unconsciously signal you. - -\item Physically, "psychoelectronically" induce conditioned reflexes in your -nervous system. Physically break ddwn your sense of time. -\end{itemize} - -{ \centering - \large - [\textsc{Invitation}] \par} - -{ \centering -Because of your interest in technology and science, you are invited to visit \\ - \textsc{Exhibit of a Working Model of a} \\ - \textsc{Perception-Dissociator} \\ -Sponsored by (legitimate sponsor) Open continuously from (date) \\ -to (date) At (lunar colony or space station) \par - } - -"The perception-dissociator is a machine which is the product of a -technology far superior to that of humans. With it, a conscious organism can -drastically transform its psychophysical relation to objects and to other -conscious organisms\ldots The exhibit spotlights the technical interest of the -perception-dissociator, giving the visitor a working model of the machine -which he can use to 'transform' himself." ---from the Guidebook - -It isn't possible for this exhibit to be open or public, because of the nature of -the model. You have been invited in the belief that you will be a cooperative -visitor. Come alone. Don't discuss the exhibit at all before you see it; and -don't discuss it afterwards except with other ex-visitors. Come prepared to -spend several hours without a break. There will be absolutely no risk or -danger to you if you follow instructions. - -\section*{\textsc{To the Director}} - -Exhibit requires two adjacent rooms, on moon or other low-gravity -location, so that humans can easily jump over each other and fall without -being hurt. First room, the anteroom, has "normal" entrance door leading in -from "normal" human world. Is filled with chairs or school desks. At far -corner from normal door is two-step lock, built in anteroom, connecting -rooms. Normai door on hinges leads from anteroom into first step of lock. -Sliding panel door leads into second step; and smooth curtain with slit in -middle leads into the exhibit hali. Another sliding door leads from lock's -first step directly back out to normal human world, bypassing anteroom. -Shelf required in first lock to check watches and shoes. - -Exhibit hall large and empty with very high ceiling (Fuller dome?). I -Room must be strongly lighted, so that objects in front of closed eyes will -cast highly visible shadows on eyelids. Room's inner surfaces must be -sound-absorbing, and moderate noise must be played into room to mask -accidental sounds; thus humans will cease to notice sound. Floor must be of -hard rubber or other material that will not splinter, and will not be too hard -to fall and crawl on. - -Exhibit open continuously for days. Invite people who will seriously -try to play along---preferably engineers; and invite many of them, because -is better to have many in exhibit. Sample invitation enclosed. Attendants -working in shifts must be at two posts throughout. Try to keep surprising -features of exhibit secret from those who have not been through it. - -Procedure. Visitor arrives and enters anteroom. Entrance attendant -gives him a Guidebook and sends him to sit down and start reading. Then -visitor goes to lock. Lock attendant must try hard to see that no more than -one visitor is in lock at a time. If lock is empty of visitors, attendant lets -entering visitor into first step, checks his watch and shoes, and sends him -alone into second step and on to exhibit room. When visitor comes out of -exhibit hall for any reason, he must be gotten into first step, and then -attendant sends him out the exit. When a visitor comes out, he just goes out -and doesn't go back in. - -\img{dissociatordiag} - - -\clearpage - -\textsc{Exhibit of a working model of a perception-dissociator (conceived by Henry Flynt)} - - -\img{guidebook} - - -\textsc{Read this guidebook as directed---straight through or as otherwise directed. Don't leaf around.} - - -\textsc{Read pages 2--3 before you go in to see the exhibit.} - -\clearpage - -Introduction. The perception-dissociator is a machine which is the -product of a technology far superior to that of humans. With it, a conscious -organism can drastically transform its psychophysical relation to objects and -to other conscious organisms. When the organism has transformed itself, -sound disappears, time is immeasurable; and the relation between seeing and -touching becomes a random one. That is, the organism never knows whether -it will be able to touch or feel what it sees, and never knows whether it will -be able to see what it touches or what touches it. The world ceases to be a -collection of objects (relative to the physically altered organism). Further, -the machine induces a pattern of communication in the organism's nervous -system, an involuntary pattern of responses to certain events, to help the -organism cope with the invisible tactile phenomena. A dimension is added of -involuntarily relating to other organisms as unconscious signalling devices. -The transformation induced by the machine is permanent unless the -organism subsequently uses the machine to undo it. - - -The perception-dissociator is not conscious or alive in any human sense. -The components of the machine that the user is aware of are: -\begin{enumerate} - \item Optical phenomena that are seen---"sights." - \item Solid or massive phenomena that are felt cutaneously---"touches." -\end{enumerate} -If the user tries to touch a sight, he may not be -able to feel anything there. If he looks for a component that touches him, he -may not be able to see it. - - -(Keep reading) - -\clearpage - -In other words, from the beginning the machine has properties that the -entire world comes to have to the transformed organism. - -The exhibit spotlights the technical interest of the -perception-dissociator, giving the visitor a working model of the machine -which he can use to "transform" himself. Nothing is said about the purpose -of the perception-dissociator in the society that can make one. The model is -sophisticated enough that it can run independently of the visitor's will, and -can affect him. In fact, the visitor may be hurt if he doesn't follow the -instructions for using the machine. - - -When you have absorbed the above, go to the entrance and be admitted -to the exhibit. You must check your shoes, and your watch (if you have -one), with the attendant. As you enter, turn this page and begin reading Page -4. - -\clearpage - -\textsc{Do not talk or make any other uncalled-for noise.} - - -Be prepared for the touch of pulling your feet out from under you -from behind. Don't resist; just fall forward, break your fali with your arms -(and retrieve this Guidebook). The floor is not hard and the gravity is weak, -so the fall should leave you absolutely unhurt. - -\plainbreak{2} - -\textsc{Avoid all touches (except floor and yourself) unless directed otherwise.} -(You have been directed not to resist having your -feet pulled out from under you.) -\textsc{In effect, if you bump into a solid object or step on one, draw back. Remember -that you avoid touches by your tactile senses alone.} -Whether your eyes are open or closed makes no difference. It is not necessary to avoid -sights unless you touch something. - -\plainbreak{2} - -There may be the touch of being pushed forward at your shoulder -blades. Don't resist; just move forward. - -\plainbreak{2} - -As for the sights in this model, it happens that they will be humanoid. -All the human appearances other than you in the exhibit hall are sights from -the machine. This is just the way the model is; don't give it a thought. Sights -may appear or disappear (for example, at the curtain) while you are looking. - -\plainbreak{2} - -I am referring to the components of the model with the names of the -components of the perception-dissociator. - -\plainbreak{2} - -As soon as you understand the above and are prepared to remember -and follow the instructions, go immediately to Page 6. - -\clearpage - -\img{dissoceqns} - -\clearpage - -You will now begin the first phase of perception-dissociation by the -machine. Throughout this phase, you walk erect. - -Instructions for operating the machine and for protecting yourself from -it will be given both in English and in an abbreviated symbolism. It is -important to master the symbolism, because later instructions can't be -expressed without it. - -\begin{itemize} -\item u means you - -\item $s$, $s_1$, $s_2$, $s_3$ mean different sights from the machine - -\item $t$, $t_1$, $t_2$, $t_3$ mean different touches from the machine - -\item $a\wedge$ means a's eyes are open or a opens its eyes - -\item $a\vee$ means a's eyes are shut or a shuts its eyes - -\item $a\equiv b$ means a blows on b's hand - -\item $a\sqsupset b$ means a pushes b, typically from behind -(a holds Guidebook under arm or elsewhere) - -\item $a\overbracket{b}$ means a jumps over b, crossing completely above b (weak gravity -should make this easy) - -\item $a^\infty b$ means a rapidly waves both hands in front of and near b's eyes so that -moving shadows are cast on b's eyes (a "shadows" b) - -\item $a\overbrace{b}$ means a pulls b's ankles back and up and immediately lets them go, so -that b falls forward (a "tackles" b) - -\item $a\longdivision{b}$ means a jumps and falls on b, or a steps on b - -\item $a\lrcorner$ means a rapidly moves aside - -\item $()$ parentheses around the symbol for an action mean the action will -probably happen - -\item A line of action symbols constitutes an instruction. The order of symbols -indicates the order of events. If one symbol is right above another, the -actions are simultaneous. -\end{itemize} - -\textsc{You may always turn back to these explanations if you forget them.} - -(Keep reading) - -\clearpage - -Instructions 1--3 apply \textsc{when your eyes are open.} - -\begin{enumerate} -\item If you see a sight close its eyes, a heavy touch from the machine -may be falling toward you. You must instantly jump aside. - -\begin{tabular}{ c c } - \begin{tabular}{ c c } - $s_1\wedge$ & $s_1\vee$ \\ - $u\wedge$ & $(t\longdivision{u})$ \\ - \end{tabular} & - $u\lrcorner$ \\ -\end{tabular} - -\textsc{You must follow this and succeeding instructions as long as you stay in the exhibit. Stay with each instruction until you have it thoroughly in memory; and check out the symbolic version so you learn to read the symbols.} - -\item If a sight in front of you jumps over you, a touch may be about to -tackle you. You must instantly jump to one side. - -\begin{tabular}{ r c l } - $u\wedge$ & \begin{tabular}{ c } - $s\overbracket{u}$ \\ - $(t\overbrace{u})$ \\ - \end{tabular} & $u\lrcorner$ \\ -\end{tabular} - -\item If a sight waves its hands in front of your open eyes, a touch may -be about to shove from behind. Jump to one side. - -\begin{tabular}{ r c l } - $u\wedge$ & \begin{tabular}{ c } - $s^\infty u$\\ - $(t\sqsupset u)$ \\ - \end{tabular} & $u\lrcorner$ \\ -\end{tabular} - -\textsc{If there are any sights, try standing around and following these instructions for a short while.} - -\item If you close your eyes, you must keep them closed until a touch -tackles you, a touch shoves you, or you can't keep your mind on the exhibit -(which you should also consider to be an effect of the machine). Then you -immediately open your eyes. - -\begin{tabular}{ r c l } - $u\vee$ & \begin{tabular}{ c } - $t\overbrace{u}$ \\ \midrule - $t\sqsupset u$ \\ \midrule - $u$ inattentive \\ - \end{tabular} & $u\wedge$ \\ -\end{tabular} - -\emph{(A horizontal line between action symbols means \emph{or.} With it, instructions can be combined)} - -\textsc{The next three instructions tell you what to do when your eyes are closed. Learn them well.} - -\item If you feel a breath blowing on one of your hands, a touch may be -falling on you. You must instantly jump to the side away from the breath. - -\begin{tabular}{ r c l } - $u\vee$ & \begin{tabular}{ c } - $t_1\equiv u$ \\ - $t_2\longdivision{u}$ \\ - \end{tabular} & $u\lrcorner$ \\ -\end{tabular} - -(Turn page and continue) - -\clearpage - -\item If your closed eyes are shadowed, a touch may be about to tackle -you. You must instantly jump aside. - -\begin{tabular}{ r c l } - $u\vee$ & \begin{tabular}{ c } - $s^\infty u$ \\ - ($t\overbrace{u}$) \\ - \end{tabular} & $u\lrcorner$ \\ -\end{tabular} - -\item If you sense a massive touch going above your head, another touch -may be about to shove you from behind. Jump aside. - -\begin{tabular}{ r c l } - $u\vee$ & \begin{tabular}{ c } - $t_1\overbracket{u}$ \\ - ($t_2\sqsupset u$) \\ - \end{tabular} & $u\lrcorner$ \\ -\end{tabular} - -\item If you have any time left over from following other instructions, -close your eyes and go around with your hands in front of you, shoving -touches whenever you feel them. - -\begin{tabular}{ c c } - $u\vee$ & $u\sqsupset t$ \\ -\end{tabular} - -\textsc{Now try instr. 8, remembering and following the other instructions about closed eyes (instr. 4--7). -When you have to open your eyes again, as per instr. 4, check anything you forgot: and then go to the -succeeding instructions. Now---close your eyes.} - -\textsc{The next three instructions apply when your eyes are open.} - -\item If you see a sight falling toward or about to step on another sight -whose eyes are open, run until you face the sight on the ground and close -your eyes. - -\textsc{Before you follow this instruction you must have mastered the preceeding instructions about closed eyes.} - -$$ -u\wedge\ s_2\wedge(s_1\longdivision{s_2}) u\vee -$$ - -(Keep going) - -\clearpage - -\item If you see a sight about to tackle another whose eyes are open, run -until you face the sight about to be tackled and jump over both sights. If the -sight about to be tackled has closed eyes, you must immediately shadow -them. - -\begin{tabular}{ r c } - $u\wedge$ & \begin{tabular}{ c c c } - $s_2\wedge$ & $s_1\overbrace{s_2}$ & $u\overbracket{s_1s_2}$ \\ \midrule - $s_2\vee$ & $(s_1\overbrace{s_2})$ & $u^\infty s_2$ - \end{tabular} \\ -\end{tabular} - -\item If you see a sight about to push another with open eyes from -behind, you must shadow the sight about to be pushed. But if the sight -about to be pushed has closed eyes, you must immediately jump over both -sights. - -\begin{tabular}{ r c } - $u\wedge$ & \begin{tabular}{ c c c } - $s_2\wedge$ & $(s_1\sqsupset s_2)$ & $u^\infty s_2$ \\ \midrule - $s_2\vee$ & $(s_1\sqsupset s_2)$ & $u\overbracket{s_1s_2}$ \\ - \end{tabular} \\ -\end{tabular} -\end{enumerate} - -You must now put all the instructions into practice until you have -learned them thoroughly by doing as they say. In other words, carry out -Instr. 8, and the other instructions as they apply. - -If you can't practice the instructions because you still have not seen a -sight or felt a touch, skip directly to Page 18. - -Learning the instructions in practice should take a good while. When -you have mastered them, the first phase is over. Turn to Page 10 and begin -the second phase. - -\clearpage - -{\centering \textit{Page 10} \par} - -\subsection*{Second Phase} - -You are now in the second phase of transforming yourself with the -perception-dissociator. Throughout this phase, you must stoop or crouch -somewhat. That is, you must keep yourself below the height of your neck -when you stand straight---except when you jump over a sight. The symbol is -$u\sfrac{3}{4}$. $u\sfrac{3}{4}\wedge$ means that you crouch and close your eyes. Now crouch. - -The numbered instructions for this phase are so similar to those in the -preceeding phase that they will be given in symbols only. Changes are noted -parenthetically. You may turn back if you forget symbols. - -\begin{enumerate} -\item \begin{tabular}{ c l } - \begin{tabular}{ c c } - $s_1\wedge$ & $s_1\vee$ \\ - $u\sfrac{3}{4}\wedge$ & $(t\longdivision{u})$ \\ - \end{tabular} & $u\lrcorner$ \\ -\end{tabular} - -\item \begin{tabular}{ c c c } - $u\sfrac{3}{4}\wedge$ & \begin{tabular}{ c } - $s\overbracket{u}$ \\ - $t\overbrace{u}$ \\ - \end{tabular} & $u\lrcorner$ \\ -\end{tabular} - -\item \begin{tabular}{ c c c } - $u\sfrac{3}{4}\wedge$ & \begin{tabular}{ c } - $t\equiv u$ \\ - $t_2\sqsupset u$ \\ - \end{tabular} & $u\lrcorner$ \\ -\end{tabular} - -\emph{(change component blows on you instead of shadowing you)} - -\item \begin{tabular}{ c c c } - $u\sfrac{3}{4}\vee$ & \begin{tabular}{ c } - $t\overbrace{u}$ \\ \midrule - $t\sqsupset u$ \\ \midrule - $u$ inattentive \\ - \end{tabular} & $u\wedge$ \\ -\end{tabular} - -\item \begin{tabular}{ c c c } - $u\sfrac{3}{4}\vee$ & \begin{tabular}{ c } - $t_1\equiv u$ \\ - $(t_2\longdivision{u})$ \\ - \end{tabular} & $u\lrcorner$ \\ -\end{tabular} - -\item \begin{tabular}{ c c c } - $u\sfrac{3}{4}\vee$ & \begin{tabular}{ c } - $s^\infty u$ \\ - $(t\overbrace{u})$ \\ - \end{tabular} & $u\lrcorner$ \\ -\end{tabular} - -\item \begin{tabular}{ c c c } - $u\sfrac{3}{4}v$ & \begin{tabular}{ c } - $t_1\overbracket{u}$ \\ - $(t_2\sqsupset u)$ \\ - \end{tabular} & $u\lrcorner$ \\ -\end{tabular} - -\item \begin{tabular}{ c c } - $u\sfrac{3}{4}\vee$ & $u\sqsupset t$ \\ -\end{tabular} - -The big change comes next. - -\emph{(Keep going)} - -\clearpage - -\item \begin{tabular}{ c c } - $u\sfrac{3}{4}\wedge s_2\wedge (s_1\longdivision{s_2}) u\vee$ & and also \\ - $u\sfrac{3}{4}\wedge s_2\vee (s_1\longdivision{s_2})$ & $u\equiv s_2$ \\ -\end{tabular} - -That is, if you see a sight falling or stepping on another sight with closed -eyes, you must immediately blow on the sight on the ground. This is an -addition. - -\item \begin{tabular}{ r c } - $u\sfrac{3}{4}\wedge$ & \begin{tabular}{ c } - $s_2\wedge (s_1\overbrace{s_2}) u\overbracket{s_1s_2}$ \\ \midrule - $s_2\vee (s_1\overbrace{s_2}) u^\infty s_2$ \\ - \end{tabular} -\end{tabular} - -\item \begin{tabular}{ c c } - $u\sfrac{3}{4}\wedge$ & \begin{tabular}{ c } - $s_2\wedge (s_1\sqsupset s_2) u\equiv s_2$ \\ \midrule - $s_2\vee (s_1\sqsupset s_2) u\overbracket{s_1s_2}$ \\ - \end{tabular} -\end{tabular} -\emph{(change: you blow on $s_2$)} - -So far there have been only three changes in the instructions. Memorize -them. Then go on to Instr. 12, which is new, and carry it out along with the -other eleven instructions. - -\textsc{As soon as you have put any changed instruction (3, 9, or 11) into practice, -the second phase is over. Turn to page 12 and the third phase.} - -If you can't practice the instructions because all the components have -vanished, skip to Page 18. - -\item Adding to Instruction 8, if you have time left over from following -other instructions, you may also keep your eyes open and jump over, blow -on, or shadow sights. - -\begin{tabular}{ r c } - $u\sfrac{3}{4}\wedge$ & \begin{tabular}{ c } - $u\overbracket{s}$ \\ \midrule - $u^\infty s$ \\ \midrule - $u\equiv s$ \\ - \end{tabular} \\ -\end{tabular} -\end{enumerate} - -\clearpage - -\emph{(page 12)} - -\subsection*{Third Phase} - -Throughout the third phase, you must squat or move on your hands -and knees. That is, you must always keep yourself below the height of your -waist when you stand straight---unless you are able to jump over a sight from -your low position. The symbol is $u\sfrac{1}{2}$. Now get down. - -Instr. 1--7 from the last phase apply here without change. They are thus -stated in the most abbreviated form. - -1--3. -(i will put these in when im confident in my interpretation of the syntax) - -4--7. -(i will put these in when im confident in my interpretation of the syntax) - -The biggest change comes next. - -8. If you have any time left over, close your eyes and go around with -your hands in front of you. If you encounter touches standing higher than -you, tackle them. If you encounter touches as near the ground as you, shove -them. You must be sensitive and judge heights with eyes closed. - -\begin{tabular}{ r c } - $u\sfrac{1}{2}\vee$ & \begin{tabular}{ c } - $t_\greater u\overbrace{t}$ \\ \midrule - $t_\less u\sqsupset t$ \\ - \end{tabular} \\ -\end{tabular} - -\emph{($t\greater$ means "if t stands high relative to you" \\ -$t\less$ means "if t is near ground relative to you")} - -9. No change. - -\begin{tabular}{ r c } - $u\sfrac{1}{2}$ & \begin{tabular}{ c } - $s_2\wedge (s_1\longdivision{s_2}) u\vee$ \\ \midrule - $s_2\vee (s_1\longdivision{s_2}) u\equiv s_2$ \\ - \end{tabular} -\end{tabular} - -10. The previous Instr. 10 applies if $s_2$ is near the ground, that is, it -applies unless $s_2$ is too high for you to jump or shadow it. - -\begin{tabular}{ r c } - $u\sfrac{1}{2}$ & \begin{tabular}{ c } - $s_2\wedge\less\ (s_1\overbrace{s_2}) u\overbracket{s_1 s_2}$ \\ \midrule - $s_2\vee\less\ (s_1\overbrace{s_2}) u^\infty s_2$ \\ - \end{tabular} -\end{tabular} - -(Keep going) - -\clearpage - -11. $u\sfrac{1}{2}\wedge\ s_2\wedge\ (s_1\sqsupset s_2)\ u\equiv s_2$ - -The second half of the previous Instr. 11 is dropped. - -Except for the instruction to tackle touches, the changes are simply -limitations to make the instructions feasible for $u\sfrac{1}{2}$. They should be easy -to remember. - -You will next go on to Instr. 12, and carry it out along with the other -instructions. As soon as you encounter an actual situation where you cannot -act because $u\sfrac{1}{2}$, the third phase will be over. -\textsc{At that point you must turn to page 14 and the fourth phase.} - -If you can't carry out the instructions because all the components have -vanished, the third phase is over. Turn to Page 14 and the fourth phase. - -12. Adding to Instr. 8, if you have time left over, you may also keep -your eyes open and blow on sights. You may also shadow or jump over -sights unless they are too high. - -\begin{tabular}{ r c } - $u\sfrac{1}{2}\wedge$ & \begin{tabular}{ c } - $u\equiv s$ \\ \midrule - \begin{tabular}{ r c } - $s\less$ & \begin{tabular}{ c } - $u^\infty s$ \\ \midrule - $u\overbracket{s}$ \\ - \end{tabular}\\ - \end{tabular} \\ - \end{tabular} \\ -\end{tabular} - -\subsection*{Fourth phase} - -You are in the fourth phase of perception-dissociation. Throughout this -phase, you must crawl on your stomach (keep below knee height). The -symbol is $u\sfrac{1}{4}$. Now get on the floor. - -You can no longer be tackled, nor can you jump. Thus, the numbered -instructions are greatly limited, and they will be restated fully. - -\textsc{The first two instructions apply when your eyes are open.} - -\begin{enumerate} -\item If you see a sight close its eyes, a touch may be falling or stepping -on you, and you must immediately scramble aside. - -\begin{tabular}{ c l } - \begin{tabular}{ c c } - $s_1\wedge$ & $s_1\vee$ \\ - $u\sfrac{1}{4}\wedge$ & $(t\longdivision{u})$ \\ - \end{tabular} & $u\lrcorner$ \\ -\end{tabular} - -\item \begin{tabular}{ r c l } - $u\sfrac{1}{4}\wedge$ & \begin{tabular}{ c } - $t_1\equiv u$ \\ - $(t_2\sqsupset u)$ \\ - \end{tabular} & $u\lrcorner$ \\ -\end{tabular} - -\textsc{The next three instructions tell you what to do when your eyes are closed.} - -\item When to reopen your eyes. \begin{tabular}{ r c l } - $u\sfrac{1}{4}\vee$ & \begin{tabular}{ c } - $t\sqsupset u$ \\ \midrule - $u$ inattentive \\ - \end{tabular} & $u\wedge$ -\end{tabular} - -\item If your closed eyes are shadowed, a touch may be falling or -stepping on you. Scramble aside. - -\begin{tabular}{ r c l } - $u\frac{1}{4}\vee$ & \begin{tabular}{ c } - $s^\infty u$ \\ - $(t\longdivision{u}$ - \end{tabular} & $u\lrcorner$ -\end{tabular} - -\item \begin{tabular}{ c c c } - $u\frac{1}{4}\vee$ & \begin{tabular}{ c } - $t_1\overbracket{u}$ \\ - $(t_2\sqsupset u)$ \\ - \end{tabular} & $u\lrcorner$ \\ -\end{tabular} - -\item \begin{tabular}{ r c } - $u\sfrac{1}{4}\vee$ \begin{tabular}{ c c } - $t\greater$ & $u\overbrace{t}$ \\ \midrule - $t\sfrac{1}{4}$ & $u\sqsupset t$ \\ - \end{tabular} -\end{tabular} - -\textsc{Try instr. 6, remembering and following instr. 3--5.} \\ -\textsc{When you have to reopen your eyes as per instr. 3, check on anything you forgot. - Then go to page 15. Now---close your eyes.} - - -The rest of the instructions apply when your eyes are open. - -\item \begin{tabular}{ r c } - $u\sfrac{1}{4}\wedge$ & \begin{tabular}{ c c c } - $s_2\wedge$ & $(s_1\longdivision{s_2})$ & $u\vee$ \\ \midrule - $s_2\vee\less$ & $(s_1\longdivision{s_2})$ & $u^\infty s_2$ \\ - \end{tabular} \\ -\end{tabular} - -If $s_2$'s eyes are closed, you must shadow them unless they are too high. - -\item $$u\sfrac{1}{4}\wedge\ s\wedge\less\ (s_1\sqsupset s_2)\ u\equiv s_2$$ - -You blow on $s_2$'s hand unless it is too high. - -\item Adding to Instr. 6, if you have time left over from following -instructions, you may also shadow or blow on sights if they aren't too high. - -\begin{tabular}{ c c c } - $u\sfrac{1}{4}\wedge$ & $s\less$ & \begin{tabular}{ c } - $u^\infty s$ \\ \midrule - $u\equiv s$ \\ - \end{tabular} \\ -\end{tabular} -\end{enumerate} - -You must now put these nine instructions into practice until you have -learned them thoroughly in practice; and even continue after that until you -have difficulty keeping your mind on the exhibit. - -\textsc{If you can't practice the instructions because all the components have vanished, skip to page 18.} - -Otherwise, stay with this phase until you have difficulty keeping your -mind on it. Then turn to Page 16 and the final phase of -perception-dissociation. - -\clearpage - -\subsection*{Final Phase} -\emph{(Page Sixteen)} - -You are now in the final phase of transforming yourself with the -perception-dissociator. When you finish transforming yourself, you will have -lost track of time, and will have ceased to notice sound. You will be dealing -with sights and touches as unrelated phenomena; and you will be responding -by reflex action to unconscious signals from "other people." - -For this last phase, you will turn to Page 5. You will go through the -symbols there in any order you like as if they were one long instruction, -carrying out that instruction. You are to "use" each symbol once. There -have been enough precedents in the interpretation of the symbols that you -should now be able to interpret any combination of them. Continue to -follow the previous numbered instructions as they apply, depending on -whether you are 1, \sfrac{3}{4}, \sfrac{1}{2}, or \sfrac{1}{4}. -(But forget the instructions for time left -over; you won't have any extra time.) -\textsc{Remember the instructions about when to reopen your eyes if you close them.} - -When you are through, you will be transformed. -\textsc{Now turn to page 5 and begin.} - -\clearpage - -If you have found these words and are reading them in desperation -because you are completely confused; or because you have lost interest in -the exhibit; or because you have finished; then you are transformed. - - -If you want to use the model to simulate the reversal of your -transformation before you leave the exhibit, do the following. Spend 50 -seconds erect, with open eyes, walking up to sights and pushing -them---assuming that you will find touches where you see sights. Count the -seconds "one-thousand-and-one," "one-thousand-and-two," etc. - - -Then you will close your eyes. If you are blown on or pushed before -250 seconds have passed, you will open your eyes and--assuming that you -will find a sight where you were touched--you will shadow it. Otherwise you -will open your eyes when the 250 seconds have passed. Now close your eyes -and do as instructed. - - -It is now suggested that you leave the exhibit. Go out through the -curtain. - -\clearpage - -Stay in the exhibit and follow every instruction that is relevant, until -you become thirsty. - - -If you begin to encounter components, return to the page you were on -before you turned to this one. - - -lf you still don't encounter components, the model must be broken. -Leave the exhibit by the same passage through which you entered. - -\clearpage - - -2/22/1963 - - -Henry Flynt and Tony Conrad demonstrate against the Metropolitan Museum of Art, -February 22, 1963 - - -(foto by Jack Smith) - -\chapter{Mock Risk Games} - - -Suppose you stand in front of a swinging door with a nail sticking out of it -pointing at your face; and suppose you are prepared to jump back if the -door suddenly opens in your face. You are deliberately taking a risk on the -assumption that you can protect yourself. Let us call such a situation a "risk -game." Then a mock risk game is a risk game such that the misfortune which -you risk is contrary to the course of nature, a freak misfortune; and thus -your preparation to evade it is correspondingly superficial. - -If the direction of gravity reverses and you fall on the ceiling, that is a -freak misfortune. If you don't want to risk this misfortune, then you will -anchor yourself to the floor in some way. But if you stand free so that you -can fall, and yet try to prepare so that if you do fall, you will fall in such a -way that you won't be hurt, then that is a mock risk game. if technicians -could actually effect or simulate gravity reversal in the room, then the risk -game would be a real one. But I am not concerned with real risk games. I am -interested in dealing with gravity reversal in an everyday environment, where -everything tells you it can't possibly happen. Your 'preparation' for the fall -is thus superficial, because you still have the involuntary conviction that it -can't possibly happen. - -Mock risk games constitute a new area of human behavior, because they -aren't something people have done before, you don't know what they will be -like until you try them, and it took a very special effort to devise them. -They have a tremendous advantage over other activities of comparable -significance, because they can be produced in the privacy of your own room -without special equipment. Let us explore this new psychological effect; and -let us not ask what use it has until we are more familiar with it. - -Instructions for a variety of mock risk games follow. (I have played -each game many times in developing it, to ensure that the experience of -playing it will be compelling.) For each game, there is a physical action to be -performed in a physical setting. Then there is a list of freak misfortunes -which you risk by performing the action, and which you must be prepared -to evade. The point is not to hallucinate the misfortunes, or even to fear -them, but rather to be prepared to evade them. First you work with each -misfortune separately. For example, you walk across a room, prepared to -react self-protectingly if you are suddenly upside down, resting on the top of -your head on the floor. In preparing for this risk, you should clear the path -of objects that might hurt you if you fell on them; you should wear clothes -suitable for falling; and you should try standing on your head, taking your -hands off the floor and falling, to get a feeling for how to fail without -getting hurt. After you have mastered the preparation for each misfortune -separately, you perform the action prepared to evade the first misfortune -and the second (but not both at once). You must prepare to determine -instantly which of the two misfortunes befalls you, and to react -appropriately. After you have mastered pairs of misfortunes, you go on to -triples of misfortunes, and so forth. - -The principal games are for a large room with no animals or distracting -sounds present. - -\textbf{A.}Walk across the lighted room from one corner to the diagonally -opposite one, breathing normally, with your eyes open. -\begin{enumerate} -\item You are suddenly upside down, resting on the top of your head on the -floor. You must get down without breaking your neck. - -\item Although the floor looks unbroken and solid, beyond a certain point -nothing is there. If you step onto that area, you will take a fatal fall. Thus, as -you walk, you must not shift your weight to your forward foot until you are -sure it will hold. Put the ball of the forward foot down before the heel. - -\item Something happens to the cohesive forces in your neck so that if your -head tips in any direction, it will come right off your body, killing you -immediately. Otherwise everything remains normal. Thus, as you walk, you -must "balance" your head on your neck. When you reach the other side of -the room, your neck will be restored to normal. (Prepare beforehand by -walking with a book balanced on your head.) - -\item Invisible conical weights fall around you with their points down, each -whistling as it falls. You must evade them by ear in order not to be stabbed. -Walk softly and fast. - -\item The room is suddenly filled with water. You have to control your lungs -and swim to the top. Wear clothes suitable for swimming. -\end{enumerate} - -\textbf{A'.} Play game A while on a long walk on an uncrowded street. The floor -is replaced by the sidewalk. The fifth misfortune becomes for space suddenly -to be filled with water to a height of fifteen feet above the street. - -\textbf{B.} Lie on your back on a pallet in the dimly lit room, hands at your -sides, with a pillow on your face so that it is slightly difficult to breathe, for -thirty seconds at a time. -\begin{enumerate} -\item The pillow suddenly hardens and becomes hundreds of pounds heavier. It -remains suspended on your face for a split second and then "falls," bears -down with full weight. You must jerk your head out from under it in that -split second. - -\item The pillow adheres to your skin with a force greater than your skin's -cohesion, and begins to rise. You must rise with it in such a way that your -skin is not torn. -\end{enumerate} - -\textbf{C.} Lie on your back on the pallet in the dimly lit room. - -\begin{enumerate} -\item Gravity suddenly disappears completely, so that nothing is held down by -it; and the ceiling becomes red-hot. You must avoid drifting up against the -ceiling. - -\item The surface you are lying on becomes a vast lighted open plane. From the -distance, giant steel spheres come rolling in your direction. You must evade -them. - -\item Your body is split in half just above the waist by an indefinitely long, -rather high, foot-thick wall. Your legs and lower torso are on one side, and -your upper torso, arms, and head are on the other side. Matter normally -exchanged between the two halves of your body continues to be exchanged -through the. wall by telekinesis. It is as if you are a foot longer above the -waist. In order to reunite your body, you must first roll over and get up, -bent way forward. There are depressions in the wall on the same side as your -feet. You have to climb the wall, putting your feet in the depressions and -balancing yourself. You will be reunited when you reach the top and your -waist passes above the wall. -\end{enumerate} - -\textbf{D.} Sit in a plain, small, straight chair, on the edge of the seat, hands -hanging at the sides of the seat, feet together in front of the chair, in the -lighted room, for about thirty seconds at a time. - -\begin{enumerate} -\item The chair is suddenly out from under you and sitting on you with Its legs -straddling your lap and legs. You have to get your weight over your feet so -you won't take a hard fall. - -\item The direction of gravity reverses and the chair remains anchored to the -floor. You have to grab the seat and hold on in order not to fall on the -ceiling. - -\item You are suddenly in a contra-terrene universe, in which the atmosphere is -unbreathable and prolonged contact with either the atmosphere or the -ground will disintegrate you. The seat and back of the chair become a -penetrable hyperspatial sheet between the alien universe and your own. As -soon as you feel the alien atmosphere, you must jerk your feet off the -ground and deliberately sink or plunge through the seat and back of the chair -in the best way that you can. You will end up on the floor under the chair in -your universe. - -\item You are suddenly in dark empty space in a three-dimensional lattice of -gleaming wires. Segments of the lattice alternately burst into flame and cool -off. You adhere to the chair as if it were part of you. With your hands -holding onto the seat, you can move yourself and the chair forward by - -\end{enumerate} - -\plainbreak{2} - -\textbf{[NOTE: TWO PAGES MISSING HERE IN SCAN]} - -\plainbreak{2} - -from blundering into a radiation beam, you have to communicate -pre-verbally to the other mind by every means from vocal cries to -pantomine, and get your-body/his-mind out of range of the radiation. When -the body is out, you will both be restored to normal. (The first thing to -anticipate is the basic shift in viewpoint by which you will be looking at -your own body from the other's position. There is no point in tensing your -muscles in preparatiton for the misfortune, because if it occurs, you will be -working with a strange set of muscles anyway. The next thing to prepare to -do is to spot the radiation beams; and then to yell, gesture, or -whatever--anything to get the "other" to avoid the radiation. Note finally -that neither player prepares for the possibility that he will be surrounded by -radiation. Each player prepares for the same role in an asymmetrical pas de -deux.) - -\emph{Asymmetry:} The two of you play a given duo game, but each prepares -to evade a different misfortune. - -\textbf{AB.} Stay awake with eyes closed for an agreed upon time between one -and fifteen minutes. Use a timer with an alarm. - -\begin{enumerate} -\item Each suddenly has the other's entire present consciousness in addition to -his own, from perceptions to memories, ideologies, ambitions, and -everything else---threatening both with psychological shock. - -The couple must take up positions such that their sensory perceptions -are as nearly identical as possible. Beforehand, each must discuss with the -other the aspects of the other's attitude to the world which each must fears -having impused on his consciousness. During the game, each must think -about these aspects and try to prepare for them. - -\item Each suddenly relives the other's most intense past feelings of depression -and suicidal impulses. In other words, if five years ago the other attempted -suicide because he failed out of college, you suddenly have the consciousness -that "you" have just failed out of college, are totally worthless, and should -destroy yourself. Presumably the other has since learned to live with his past -disasters, but you do not have the defenses he has built up. You are -overwhelmed with a despair which the other felt in the past, and which is -incongruous with the rest of your consciousness. In summary, both of you -risk shock and suicidal impulses. Beforehand, of course, each must tell the -other of his worst past suicidal or depressed episode; and discuss anything -else that may minimize the risk of shock. -\end{enumerate} - -\section*{Intrusions in Duo Games} - -As before, distractions and modulations can be openly studied by -consent of the players. As for bogies, it is possible in duo games for one -player to create a bogy without warning, in effect acting as a saboteur. As -soon as a game is sabotaged, though, confidence is lost, and each player just -watches out for the other's bogies. Here are some sample intrusions. - -\begin{tabular}{ r c c c } - \textsc{Game} & \textsc{Distraction} & \textsc{Bogy} & \textsc{Modulation} \\ - AA 1. & cough & shout in other's face & each take a different drug \\ - 2. & talk and laugh \linebreak get out of step & $\rightarrow$ \linebreak (stomp hard) & \\ - 3. & spin around & $\rightarrow$ & \\ - AB 1. & cough \linebreak talk and laugh & gasp \linebreak silently pass palm back \& forth in front of other's face & \\ - 2. & & & \\ -\end{tabular} - - -\chapter{The Dream Reality} - - -\section{Memo on the Dream Project} - - -Original aim: To recreate the effect of e.g. Pran Nath's singing---transcendent -inner escape---in direct life rather than art. I needed material which could -function as an alien civilization (since the source of Pran Nath's expression is -an alien civilization relative to me); yet which was encultured in me and not -an affectation or pretense. I decided to use dreams as the material, assuming -that my dreams would take me to alien worlds. But mostly they did not. -Mostly my dreams consist of long periods of tawdry, familiar life interrupted -occasionally by senseless, unmotivated anomalies. In contrast, my original -aim required alluring, psychically gratifying material. - -The emphasis shifted to redefining reality so that dreams were on the same -level as waking life; so that they were apprehended as what they seem to be: -literal reality (and not memory, precognition, or symbolism). The project -was still arcane, but in a drastically different way. I was getting into an -alternate reality which was extremely bizarre but not psychically gratifying. -It was boringly frightful and sometimes obscene. I became concerned with -analytical study of the natural order of the dream world, a para-scientific -investigation. As I grappled with the rational arguments against treating -dreams as literal reality, the project became a difficult analytical exercise in -the philosophy of science. The original sensuous-esthetic purpose was lost. - -Now I would like to return to the original aim, but how to do it? Obtain -other people's dreams---see if they are more suitable? Work only with my -very rare dreams which do take me to alien worlds? Try to alter the content -of my raw dreams? Attempt to affect content of dreams by experiment in -which many people sleep in same room and try to communicate in their -sleep? The most uncertain approach to a solution: set up a transformation -on my banal dreams, so that to the first-order activity of raw dreaming is -added a second-order activity. The transformation procedure to somehow -combine conscious ideational direction---coding of the banal dreams---with -alteration of my experience, my esthesia, my lived experience. - - -\section{Dreams and Reality---An Experimental Essay} - -Excerpts from my dream diary which are referred-to in the essay that -follows. - -\dreamdate{12/11/1973} - -I notice a state between waking and dreaming: a waking dream. I have -been asleep; I wake up; I close my eyes to sleep again. While not yet asleep, I -experience isolated objects before me as in a dream, but with no -background, only a dark void. In this case, there are two pocket combs, both -with teeth broken. In the waking world, I threw away one of my two pocket -combs because I broke it; the other comb is still in good condition. - -\dreamdate{12/30/1973} - -I am chased by the police for one block west on West Market Street in -Greensboro. I reach the intersection with Eugene Street, and in the north -direction there is a steep hill rather than the street. The surface of the hill is -bare ground and grass. I run up the hill, sensing that if I can get over the hill -I will find Friendly Road and the general neighborhood of my mother's -houses on the other side. The police start shooting. If I can get a few yards -farther on the top of the hill I will be past the line of fire. I take a headlong -dive and awaken in the middle of the dive to find myself diving forward on -my mattress in the front room of my apartment. The action is carried on -continuously through waking up and through the associated change of -setting. - - -\dreamdate{1/12/1974} - -Just before I go to sleep for the night, I am lying in bed drowsy. I think -of being, and suddenly am, at the south edge of the Courant Institute plaza, -which is several feet above the sidewalk. The edge of the plaza and the drop -are all I see. It is night; and there is only a void where the peripheral -environment should be. (Comment: It is of great theoretical importance that -while most of the internal reality cues were present in this experience, some, -like the peripheral environment, were not. In my dream experiences, all -reality cues are present.) The drop expands to twenty or thirty feet, and I -start to fall off. Fright jolts me completely awake. I have had something like -a waking nightmare and have awakened from being awake. I thought of the -scene, was suddenly in it (except for peripheral reality cues), lost control and -became endangered by it, and then snapped back to my bedroom. - -\dreamdate{1/1-/1974} - -One or two nights after 1/12/74 I was lying in bed just before going to -sleep. I could see women standing on a sidewalk. The scene was real, but I -was not in it; I was a disembodied spectator. Also, the peripheral -environment was absent. The reality was between that of a waking -visualization and that of the Courant Institute incident of 1/12/74. -Comment: The differences between this experience and a waking -visualization are that the latter is less vivid than seeing and is accompanied -by waking reality cues such as cues of bodily location. - - -\dreamdate{1/16/1974} - -\begin{enumerate} -\item I am in an apartment vaguely like the first place in which I lived, at -1025 Madison Avenue in Greensboro. I am a spy. I am teen-aged and short; -and I am in the apartment with several enemy men, who are middle-aged and -adult-sized. My code sheets look like the sheets of Yiddish I have been -copying out in waking life. Eventually the men discover me in the front -room with the code sheets on a fold-up desk. They chase me out the front -door and onto the west side of the lawn, and shoot me with a needle gun. At -that moment my consciousness jumps from my body and becomes that of a -disembodied spectator watching from an eastward location, as if I were -watching a film. - -\item I am living in a dormitory in a rural setting with other males. At one -point I walking barefoot in weeds outside the dormitory, and Supt. Toro -tells me I am walking in poison ivy. My feet begin to show the rash, but I -recognize that I am in a dream and think that the rash will not carry over to -the waking state. I then begin to will away the rash in the dream, and I -succeed, -\end{enumerate} - - -\dreamdate{1/20/1974} - -For some reason the dream associates Simone Forti with flute-like -music. It is shortly before midnight. In the dream I believe that Simone lives -in a loft on the east side of Wooster Street. The blocks in SOHO are very -small. If I walk through the streets and whistle, she will hear me. I start to -whistle but can only whistle a single high note. I half awaken but continue -whistling, or trying to; the dream action continues into waking. But I cannot -change pitch or whistle clearly because my mouth is taped. As I realize this, I -awaken fully. - -Comments: I tape my mouth at night so I will sleep with my mouth closed. I -experimented at trying to whistle with the tape on while fully awake. The -breath just hisses against the tape. The pitch of the hiss can be varied. - - -\dreamdate{2/1/1974} + $\begin{pmatrix} + p & p \\ + f & p + \end{pmatrix}$ & + -> + & + $\begin{pmatrix} + f & p \\ + p & f + \end{pmatrix}$ \\ +\end{tabular} + +In general, we speak of a partition of a sensory realm into disjoint +classes of perceptions, so that the two partitions are $[T_j]$ and $[V_j]$. The +number of classes in a partition, m for touch and n for sight, is its +detailedness. The detailedness of the product partition $[T_j]\times [V_j]$ is written +$m\times n$. This detailedness virtually determines the $(mn)^2$ imaginable states, +although it doesn't determine their qualitative content. Now suppose one +change is followed by another, so that we can speak of a change series. It is +important to realize that by our definitions so far, a change series is not a +conposition of functions; it is a temporal phenomenon in which each state +lasts for a finite time. (A function would be a genera! rule for rewriting +states. A 2X2 rule might say, rotate the state clockwise one place, from +$\begin{pmatrix}a & b \\ c & d\end{pmatrix}$ to +$\begin{pmatrix}c & a \\ d & b\end{pmatrix}$. + +But a composition of rules would not be a temporal series; it would be a new +rule.) Returning to the sorting of changes, we always exclude the no-change +changes, and states having only f's. We are unenthusiastic about "impairing" +changes, changes to states with rows or columns of f's. Of the remaining +changes, some merely forbid, repiacing p's with f's. The rest of the changes +are the most perception-dissociating ones. + +As for changes in the succession state in the eye case, either they leave +the forbidden concurrence permitted; or else they merely leave permitted +successions forbidden---for example, in order to open your eyes in the dark +you might have to open them in the light and then turn the light off. These +secondary changes are of secondary interest. + +If we simply continue with the material we already have, two lines of +investigation are possible. The first investigation is mathematical, and +apparently amounts to combinatorial algebra. The second investigation +concerns the relation between concurrences and commands of the will +(observable as electrochemica! impulses along efferent neurons). If a change +occurs, and the perceptual feedback from a willed command consists of a +formerly forbidden concurrence, is it T or V that conflicts with the +command? Is it that you tried to close your eyes but couldn't get the sight +to go away, or that you were trying to look at something but felt your eyes +close anyway? + +Before we carry out these investigations, however, we must return to +our qualitative theory. If one of our eye changes happens to a physicist, he +may immediately conclude that the cause of the anomaly is in himself, that +the anomaly is psychological. But suppose that starting with a state for an +extremely detailed product partition describing the present world, a whole +change series occurs. Let p's be black dots and f's be white dots, and imagine +a continuously shaded gray rectangle whose shading suddenly changes from +time to time. We evoke this image to impress on the reader the +extraordinary qualities of our concept, which can't be conveyed in ordinary +English. Suppose also that to the extent that communication between +scientists is still possible, perhaps in Braille, everybody is subjected to the +same changes. !f the physicist turns to his instruments, he finds that the +anomalies have spread to his attempts to use them. The changes affect +everything-- everything, that is, except the intrasensory coherence of each +sensory realm. Intrasensory coherence becomes the only stable reference +point in the "world." The question of "whether the anomaties are really +outside or only in the mind" comes to have less and less scientific meaning. +If physics survived, it would have to recognize the touch-sight dichotomy as +a physical one! This scenario helps answer a question the reader may have +had: what is the methodological status of our states? They don't seem to be +either physics or psychology, yet it is quite clear how we would know if the +asserted regularities had changed; in fact, that is the whole point of the +states. The answer is that the states are perfectly good assertions (of +observed regularities) which would acquire primary importance if the +changes actually occurred. In fact, the changes would among other things +shift the boundaries of physics and psychology; but we insist that our +interest is in the physicist's side of the boundary. To complete the +investigation we have outlined, the relation between what the states say and +what existing physics says should be established, so that we will know what +has to be done to the photons and electrons to produce the changes. It is the +same as with time travel: the hard part is deciding what it is and the even +harder part is making it happen. + +\visbreak + +However, the foundations of our qualitative theory are not yet +satisfactory, We have assumed that the physicist will be able to identify the +subjective concurrences of perceptions, and will be able to identify his +perceptions themselves, even if sense correlation becomes completely +chaotic. We have assumed that the physicist will be able to say "I see a book +in my hand but I concurrently feel a pencil." These assumptions may not be +justified at all. It is quite likely that the physicist will say, "I don't even +know whether the sight and the touch seem concurrent; I don't even know +whether I think I see a book; I don't even know whether this sensation is +visual." In fact, the anomalies may cause the physicist to decide that books +never looked like books in the first place. In this case, the occurrence of the +changes would render meaningless the terms in which the changes are +defined. Alternately, if the changes produce a localized chaos, so that +everything fits together except the book seen in the hand, the physicist may +literally force himself to re-see that-book as a pencil, and in time this +compensation may become habitual and "pre-conscious." In this case, if the +physicist remembers the changes, he will be convinced that they were a +temporary psychological malfunction. + +These criticisms are based on the fact that our simple perceptions are +actually learned, "unconscious" interpretations of raw data which by +themselves don't look like anything. This fact is demonstrated by a vast +number of standard experiments in which the raw data are distorted, the +subject perceptually adapts to the distorted data, and then the subject is +confronted with normal sensations again. The subject finds that the old +familiar sensation of a table looks quite wrong, and that he has to make an +effort to see the table which he knows is there. + +Consider a modification of the clock-bell simultaneity experiment. The +subject sits facing a large clock with a second-hand. His hearing is blocked in +some way. Behind him, completely unseen, is a device which can give hima +quick tap, a tactile sensation. There is also an unseen movie camera which +photographs both the tactile contact and the clock face. The subject is +tapped, and must call out the second-hand reading at the time of the tap. We +expect a discrepancy between what the subject says and what the film says; +but even if there is none, the experiment can proceed. Teli the subject that +he always placed the tap earlier than it actually occurred, and that he will be +given a reward if he learns to perceive more accurately. The purpose of the +experiment is to demonstrate to the subject that even his perception of +subjective simultaneity can be consciously modified. In the course of +modification, he may not even know whether two perceptions seem +simultaneous. + +This criticism of the changes defined earlier is important, but it may +not be insurmountable. Although Stratton became used to his trick +eyeglasses, the image continued to seem distorted. There is some stability to +our identification of our perceptions. Also, the physicist in our earlier +scenario might ultimately adapt to the changes. He might realize that it is +possible separately to identify sights and touches. Only the sight-touch +correlation is unidentifiable; and the concept of such a correlation might +become an abstract concept of physics just as the concept of particle +resonance is today. + +Time is inescapably involved in our discussion; so we must decide what +happens to time as a distinct physical category, and as a sense, in +perception-dissociation. Here, we will simply distinguish three sorts of time. +First, there is subjective concurrence, which we have already begun to +discuss. Secondly, there is the physicist's operational definition of time. +There must be two repeating processes, which to the best of our knowledge +are causally independent, so that irregularities in one process aren't +automatically introduced in the other. !f the ratio of the repetitions of the +two processes is constant, we assume that the repetitions divide time into +equal intervals. Eventually the physicist arrives at a concept of time as a real +line along which movement can be both forward and backward (Feynman). +One effect of perception-dissociation relating to this sort of time would be +to disrupt the ratios of visual clocks (such as electric wall clocks) to tactile +clocks (such as the pulse). The third idea of time comes from an unpublished +manuscript by John Alten, a Harvard classmate of mine. According to Alten, +our most intimate sensation of futurity is associated with our acts of will. +"The future" is simply the time of willing. In comparison with volitional +futurity, the physicist's linear, reversible time is a mere spatial concept. The +empirical importance of Alten's idea is thet it raises the question of what the +perceptual frustration of the will (as we defined it) would do to the sense of +futurity. + +\visbreak + +We now come to some considerations which will help us develop the +state descriptions, and which also show that from one point of view, the +states are actually necessary for the operational definition of physical +language. Let parallel but separated sheets of clear plastic and colored plastic +be mounted in lighting conditions so that the subject can't see the clear +plastic. He touches the clear plastic, but from what he sees, he believes he is +touching the colored plastic. The lighting is then changed and his error is +exposed. In some sense, the sight-touch concurrence identifying an object +was a mere coincidence. Next, we produce another colored sheet for the +subject to touch, and we are able to convince him that this time the +object-identifying concurrence is more than a coincidence. + +The physicist interprets this latter case by saying that the matter which +resists the pressure of the subject's finger also reflects the light into his eyes. +To the extent that the physicist's interpretation is causal, it employs the +concept of "matter," a concept which is not really either visual or tactile. +The physicist explains a sight and a touch with a reference beyond both sight +and touch. It is important, then, to know the operational definition of the +physicist's statement, the testing procedures which give the statement its +immediate meaning. What is significant is that the testing procedures cannot +be reduced to purely visual procedures or purely tactile procedures. +Affecting the world requires tactile operations; and the visual "reading" of +the world is so woven into physics that it can't be given up. Yet our +experiment showed that the subject can be fooled by object-identifying +concurrences, and the physicist is supposed to te!l us how to avoid being +fooled. + +We find, then, that there is nothing the physicist can appeal to, in +testing object-identifying concurrences, that doesn't immediately rely on +other object-identifying concurrences, the very concurrences which are +suspect. It is as if the physicist proposed to prove that clicks come from a +certain metronome by manipulating a detecting device that outputs its data +as sounds. But suppose the physicist proves that the clicks come from the +metronome by showing (1) that the metronome has to be stopped or +removed to stop the clicks, and (2) that the clicks stop if the metronome is +stopped or removed. The physicist proves that the object-identifying +concurrence is not a coincidence by demonstrating that certain related +concurrences are forbidden. We suggest that the physicist ultimately handles +touch-sight concurrences in just this way. The operational basis of the +physicist's activity comes down to our states. (But note that the physicist +has tests, which do not rely directly on his hearing, to determine whether the +clicks come from the metronome!) One way to develop our states, then, +may be to develop substates which express the differences between those +object-identifying concurrences that are coincidental and those that +aren't---the differences illustrated by the plastic sheet experiment. -1. I try to assist a man in counterfeiting ten dollar bills by taking half -of a ten, scotch taping it to half of a one, and then coloring over the one -until it looks like the other half of the ten. The method fails because I bring -old crumpled tens rather than new tens, and the one doilar bills are new. - -Comments: There are no natural anomalies in this dream at all. What is -anomalous is that this counterfeiting method seems perfectly sensible, and I -only begin to question it when we try to fit the crumpled half-bill to the -crisp half-bill. Why am I so foolish in this dream? I retain my identity as -Henry Flynt, and yet my outlook, my sense of what is rational, is so -different that it is that of a different person. More generally, the person I am -in my dreams is much more limited in certain ways that I am in waking life. -My waking preoccupations are totally absent from my dreams. Instead there -is bland material about my early life which could apply to any child or -teen-ager. Thus, I must warn readers who know me only from this diary not -to try to make the image of me here fit my waking life. - - -\dreamdate{2/3/1974} - -3. I have had several dreams that I am taking the last courses of my -student career. (In waking life I have completed all course work.) I am -usually failing them. Tonight I dream that I have gone all semester without -studying (in a course in English?). Now I am in the final exam and sinking. I -will have to repeat these courses. Subsequently, I am sitting in a school -office (of a professor or psychologist?), giving him a long list (of words, a -foreign vocabulary?). (I mention this episode because I remember that while -I retained my nominal identity as Henry Flynt, I had the mind of a different -person. I experienced another person's existence instead of mine. Professor -Nell also appeared somewhere in this dream; as he has in several school -dreams I have had recently. - - -\dreamdatecomment{2/3/1974}{This is the date I recorded, but it seems that it would have to be later.} - -I get up in the morning and decide to have a self-indulgent breakfast -because of the unpleasantness of working on my income tax the day before. -So I put two slices of pizza in the oven, and also eat two bakery sweets, -possibly \'{e}clairs. Then I think that a Mexican TV dinner would have been -better all around, but it is too late; I have to eat what I am already preparing. -Subsequently, I go with John Alten to a Shoreham Cafeteria at Houston and -Mercer Streets. The cafeteria chain is a good one, but this cafeteria is dark -and extremely dingy upstairs where the serving line is. John complains that -there is no ventilation and that he is suffocating, and he stalks out. - -Comment: When I awoke, my first thought was that the pizza in the oven -would be burning. (I assumed that I had arisen, put the pizza in the oven, -and gone back to sleep.) But then I realized that the breakfast was a dream. I -got up and prepared the Mexican dinner which I had decided was best in the -dream, but I also ate one \'{e}clair. - -\dreamdate{7/8/1974} - -I am caught out in a theft of money, and I feel that the rest of my life -will be ruined. - -Comment: The quality of the episode depended on my -strong belief in the reality of the social future and in my ability to form -accurate expectations about it. When I awakened, the whole misadventure -vanished. - - -End of excerpts from my dream diary. - -\begin{quotation} -"... It is correct to say that the objective world is a synthesis of private views -or perceptions... But ... inasmuch as it is the common objective world that -renders ... general knowledge possible, it will be this world that the scientist -will identify with the world of reality. Henceforth the private views, though -just as real, will be treated as its perspectives. ... the common objective -world, whether such a thing exists or is a mere convenient fiction, is -indispensable to science ... -."\footnote{A. d'Abro, The Evolution of Scientific Thought (New York, Dover, 1950), pp. 176--7} -\end{quotation} - - -\textbf{A.} We wish to postulate that dreams are exactly what they seem to be -while we are dreaming, namely, literal reality. Naively, we want to get closer -to literal empiricism than natural science is. But science has worked out a -very comfortable world-view on the assumption that both dreams and -semi-conscious quasi-dreams are mere subjective phenomena of individual -consciousness. If we wish to carry through the postulate that dreams are -literal reality, then we will have to adopt a cognitive model quite different -from that of natural science. It is of crucial importance that we are not -interested in superstition. We do not wish to adopt a cognitive model which -would simply be defeated in competition with science. We wish to be at least -as rational, as empirical, and as cognitively parsimonious as science is. We -want our cognitive model to be compelling, and not to be a plaything which -is easily taken up and easily discarded. - -The question is whether there can be a rational empiricism which -differs from science in placing dreamed episodes on the same level as waking -episodes, but which stops short of the "nihilistic empiricism" of my -philosophical essay entitled \essaytitle{The Flaws Underlying Beliefs}. (In effect, the -latter essay rejects other minds, causality, persistent objective entities, past -time, the possibility of objective categories and significant language, and so -forth, ending up with ungraded immediate experience.) - -As an example of our problem, the waking scientific outlook assumes -that a typewriter continues to exist even when we turn our backs on it -(persistence of objective entities). In many of our dreams we make the same -sort of assumption. In other words, in some of our dreams the natural order -is not noticeably different from that of the waking world; and in many -dreams our conscious world-view has much in common with waking -common sense or scientific pragmatism. On 2/3/1974 I had a dream in which -a typewriter was featured. I certainly assumed that the typewriter continued -to exist when my back was turned to it. On 7/8/1974 I dreamed that I was -caught out in a theft of money, and I felt my life would be ruined because of -it. I certainly assumed the reality of the social future, and my ability to form -accurate expectations about it. These examples illustrate that we are not -nihilistic empiricists in our dreams. The question is whether acceptance of -the pragmatic outlook which we have in dreams is consistent with not -regarding the dream-world as a subjective phenomenon of individual -consciousness. Can we accept dreams as "literal reality"; or must we reject -the very concept of "reality" on order to defend the placing of the dream -world on the same level as the waking world? - -In summary, the question is whether we can place dreams on the same -fevel as the waking world while stopping short of nihilistic empiricism. A -further difficulty in accomplishing this aim is that neurological science might -succeed in gaining complete experimental control of dreams. Scientists might -become able to produce dreams at will and to monitor them. The whole -phenomenon of dreaming would then tend to be totally assimilated to the -outlook of scientists. Their decision to treat dreams as subjective phenomena -of individual consciousness would be greatly supported by these -developments. Would we have to go all the way to nihilistic empiricism in -order to have a basis for rejecting the neurologists' accomplishments? - -Still another difficulty is presented for us by semi-conscious -quasi-dreams such as the ones described in my diary. Semi-conscious -quasi-dreams exhibit some reality cues, but lack other important internal -reality cues. Science handles these experiences easily, by dismissing them -along with dreams as subjective phenomena of individual consciousness. -Suppose we accept that the semi-conscious quasi-dreams are illusory reality. -But if they can be illusory reality, how can we exclude the possibility that -dreams might be also? If, on the other hand, we accept the quasi-dreams as -literal reality, what about the missing reality cues? Can we justify different -treatment for dreams and quasi-dreams by saying that all reality cues have to -be present before an experience is accepted as non-illusory? If we propose -to do so, the question then becomes whether we should accept the weight -which common sense places on reality cues. - -Why do we wish to stop short of nihilistic empiricism? Because we do -wish to assert that dreams can be remembered; that they can be described in -permanent records; that they can be compared and studied rationally. We do -want to cite the past as evidence; we do want to distinguish between actual -dream experience and waking fabrications, waking lies about what we have -dreamed; and we do want to describe what we experience in intersubjective -language. - -As easy way out which would offend nobody would be to treat dreams -as simulations of alternate universes. But this approach is a cowardly evasion -for several reasons. It excludes the phenomenon of the semi-conscious -quasi-dream, which poses the problem of internal reality cues in the sharpest -way. Further, we cannot give up the notion that our project is nearer to -literal empiricism than natural science is. We cannot accept the notion that -we must dismiss some of our experiences as mere illusions, but not all of -them. We do not see dreams as simulations of anything. Some of the most -interesting observations I have made about connections between adjacent -dreamed and waking episodes in my own experience are noticeable only -because I take both dreamed and waking experience literally. - -\gap - - -\textbf{B.} Before we continue our attempt to resolve our methodological -problem, we will provide more detail on topics which we have mentioned in -passing. We begin with the purported empiricism of natural science. The -philosopher Hume postulated that experience was the only raw material of -reality or cognition. However, he did not content himself with ungraded -experience. He insisted on draping the experiential raw material on an -intellectual framework in such a way that experience was used to simulate -the inherited conception of. reality, a conception which we will call -Aristotelian realism. Similarly for the purported empiricism of natural -science. In fact, the working scientist learns to think of the framework or -model as primary, and of experiences and verification procedures as ancillary -to it. The quotation by d'Abro which heads this essay concedes as much. - -What we are investigating is whether experiences can be draped on a -different intellectual framework in which dreamed and waking life come out -as equally real. Some examples of alternate verification conventions follow. - -\begin{enumerate} -\item Accept intersubjective confirmation of my experience of the dream world -which occurs within the dream as confirmation of the reality of the dream -world. - -\item Accept intersubjective confirmation of the past of the dream world which -occurs in the dream itself as confirmation of the reality of the dreamed past. - -\item Recognize that there is no infallible way to tell whether other people are -lying about their dreamed experience or their waking experience. - -\item Develop sophisticated interrogation techniques as a limited test of -whether people are telling the truth about their dreams. - -\item Accept that a certain category of anomalies occurs in dreams only when -several people have reported experiences in that category. -\end{enumerate} - -The principal characteristic of the approach which these conventions -represent is that each dream is treated as a separate world. There is no -attempt to arrive at an account, for a given "objective" time period, which is -consistent with more than one dream or with both dreamed and waking -periods. Thus, many parallel worlds could be confirmed as real. As our -discussion proceeds, we will move away from this approach, probably out of -a sense that it is pointless to maintain a strong notion of reality and yet to -forego the notion of the consistency of all portions of reality. - -\textbf{C.} Something that I have learned from a study of my dream records is -that while dreams are not chaotic, while they can be compared and -classified, it is not possibie to apply the method of natural science to them in -the sense of discerning a consistent, impersonal natural order in the dream -world. It is not that the natural order is different in dreams from what it is in -the waking world; it is that the dream worlds are incommensurate with the -discernment of a natural order in the scientific sense. Here are some specific -observations which relate to this whole question. - -\begin{enumerate} - \item Some dreams are not noticeably anomalous. The laws of science are not -violated in them. This observation is important in giving us a normal base for -our investigation. Dreams are not all crazy and chaotic. - -\item In some dreams, it is impossible to abstract an impersonal natural order -from personal experiences and anecdotes. There are no impersonal events. -There is no nature whose order can be defined impersonally. The dreams are -full of personal magic which cannot be generalized to a characteristic of an -impersonal natural order. - -\item As a special case of (2), in some dreams, we jump back in time and move -discontinuously in time and space. Chronological personal magic. - -\item In dreams, the distinction between myself and other people is blurred in -many different ways. Also, I sometimes become a disembodied -consciousness. - -\item As a generalization of (4), sometimes it becomes impossible to distinguish -objects from our sensing and perceiving function. The mediating sensory -function becomes obtrusively anomalous. Stable object gestalts cannot be -identified. - -\item Sometimes we experience the logically impossible in dreams. My father -was both dead and buried, and alive and walking around, in one dream. - -\item The possibility of identifying causal relationships is sometimes lacking in -dreams. It is not just that actions have unexpected effects. It is that events -are strung together like beads on a string. There is no sense of willful acting -on the world or manipulation of the world which can be objectified as a -causal relation between impersonal events. -\end{enumerate} - -The possibility arises of using dreams as philosophical experiments in -worlds in which one or more of the preconditions for application of the -scientific method is absent. (But in the one case in which Alten and I tried -this, we reached opposite conclusions. Alten said that dreams in which one -can jump around in time proved that the irreversibility of time is the basis -for distinguishing between time and space; I said that the dreams proved that -time and space can be distinguished even when the irreversibility of time is -lacking.) - -Observation (2) above can lead us to an insight about the waking world. -Perhaps science insists on the elimination of personal anecdotes from the -natural order which it recognizes because the scientist wants results which -can be transferred from one life to another and which will give one person -power over another. At any rate, science excludes anecdotal anomalies which -cannot be made somehow into "objective" events. As an example, I may be -walking down the street and suddenly find myself on the other side of the -street with no awareness of any act of crossing the street. - -What dreams provide us with is worlds in which anecdotal anomalies -cannot be relegated to limbo as they are in waking science. They are so -prominent in dreams that we can become accustomed to identifying them -there. We may then learn to recognize analogous anomalies in the waking -world, where we had overlooked them before because of our scientific -indoctrination. - -Of course, we run the risk that superstitious people will misuse our -theory to justify their folly. But the difference between our theory and -superstition is clear. When the superstitious person says that he -communicates with spirits, he either lies outright; or alse he misinterprets his -experiences---embedding them in an extraneous pre-scientific belief system, -or treating them as controversions of scientific propositions. We, on the -other hand, maintain more literally than science does that the only raw -material of cognition is experience. We differ from science in draping -experiences on a different organizational framework. The "reality" we arrive -at is incommensurate with science; it does not falsify any scientific -proposition. As for science and superstition, we headed this essay with the -quotation by d'Abro to emphasize that the scientist himself is superstitious: -he is determined to believe in the common objective world, even though it is -a fiction, because it is necessary to science. The superstitious person wants -you to believe that his communication with spirits is intersubjectively -consequential. Thus our theory, which tends toward the attitude that -nothing is intersubjectively consequential, offers him even less comfort than -science does. - -\textbf{D.} We next turn to semi-conscious quasi-dreams. Referring to my -experience on the morning of 1/12/1974, I describe the experience by saying -that I was on the Courant Institute plaza. But I cannot conclude that I was -on the Courant Institute plaza. The reason is that important internal reality -cues are missing in the experience. For one thing, the peripheral environment -is missing; in its place is a void. Referring to my experience on 1/1-/1974, -still other cues are missing. I am awake, and the scene is unstable and -momentary. The slightest attention shift will cause the scene to vanish. - -When we recognize that we have disallowed falling asleep, awaking, and -anomalous phenomena in dreams as evidence of unreality, a careful analysis -yields only two types of reality cues. - -\begin{enumerate} -\item Presence of the peripheral environment. - -\item "Single consciousness." This cue is missing when we see a -three-dimensional scene and move about in it, and yet have a background -awareness that we are awake in bed; and lose the scene through a mere shift -of attention. Its absence is even more marked if the scene is a momentary -one between two waking periods. -\end{enumerate} - -Let us recall our earlier discussion of the empiricism of science. Science -does not content itself with ungraded experience. it drapes experience on an -intellectual framework in such a way as to simulate Aristotelian realism. It -feeds experience into a maze of verification procedures in order to confirm a -model which is not explicit in ungraded experience. It short, science grades -experience as to its reality on the basis of standards which are -"intellectually" supplied. Internal reality cues are thus characteristics of -experience which are given special weight by the grading procedure. The -immediate problem for us is that ordinary descriptive language implicitly -recognizes these reality cues; one would never say without qualification that -one was on the Courant Institute plaza if the peripheral environment was -missing and if one was also aware of being awake in bed at the time. (In -contrast, it is fair to use ordinary descriptive language with respect to -dreamed episodes when our consciousness is singulary, that is, when -everything seems real and unqualified.) - -For purposes of further comparison I may mention an experience I -have had on rare occasions while lying on my back in bed fully awake. It is -as if colored spheres whose centers are located a few feet or yards in front of -my chest expand until they press against me, one after the other. I use the -phrase "as if" because reality cues are missing in this experience, and thus I -cannot use the language of stable object gestalts without qualification in -describing it. The colors are not vivid as real colors are. They are like -visualized colors. The spheres pass through each other, and through me---with -only a moderate sensation of pressure. I can turn the experience off by -getting out of bed. The point, again, is that it is inherent in ordinary -language not to use unqualified object descriptions in these circumstances. -Yet the only language I have for such sensory configurations is the language -of stable object gestalts-this is particularly obvious in the example of the -Courant Institute plaza. (Is "ringing in the ears' in the same class of -phenomena?) - -An insight that is crucial in elucidating this problem is that when I -describe episodes, the descriptions implicitly convey not only sensations but -beliefs, as when I speak of a typewriter in a dream on the assumption that it -persisted while I was not looking at it. The peculiar quality of a quasi-dream -comes about not only because it is an anomaly in my sensations but because -it is an anomaly in the scientific-pragmatic cognitive model which underlies -ordinary language. If I discard this cognitive model and then report the -event, it will not be the same event: the beliefs implicit in ordinary language -helped give the event its quality. As a further example, now that I have -recognized experiences such as that of 1/12/1974, I am willing to entertain -the possibility that they are the basis for claims by superstitious persons to -have projected astrally. But to use the phrase "astral projection" is to embed -the experiences in a pre-scientific belief system extraneous to the -experiences themselves. If we learn to report such experiences by using -idioms like "ringing in the ears" and blocking any comparison with notions -of objective reality or intersubjective import, we will have flattened out -experience and will have moved in the direction of ungraded experience and -nihilistic empiricism. - -\textbf{E.} We next take up connections between adjacent dreamed and waking -periods. As a preliminary, we reject conventional notions that dreams are -fabricated from memories of waking reality; or that dreams are precognitions -of waking reality; or that dreams are mental phenomena which symbolize -waking reality. We reject these notions because they conflict with the placing -of the dream world on the same level as the waking world. - -Connections between dream and waking periods are important in this -study because we may wish to create such connections deliberately, and even -to attribute causal significance to them. Initially, we define the concept of -dream control: it is to conduct one's waking life so that it is supportive of -one's dreamed life in some sense. We also define controlled dreaming: it is to -manipulate a person "from outside" before sleep (or during sleep) so as to -influence the content of that person's dreams. (An example would be to give -somebody a psychoactive sleeping pill.) - -A careful analysis of connections between dream and waking periods -yields the following classification of such connections. - -\begin{enumerate} - \item I walk around the kitchen in a dream, then awaken and walk around the -kitchen. Voluntary continued action. - -\item Given a project with causally separate components, voluntarily -assembled, I can carry out the project entirely while awake, entirely in -dreams, or partly while awake and partly in dreams. - -\item I walk around the kitchen while awake, then sleep. I may then walk -around the kitchen in a dream. Also, I draw a glass of water while awake. I -may have the glass of water to use in the dream. We could postulate that -such connections are not mere coincidences, if they occur. However, we -certainly cannot produce such connections at will. We call these connections -echoes of waking actions in dreams. Note the case in which I taped my -mouth shut before sleeping, and could not whistle in the subsequent dream. - -\item We next have connections from dreamed to waking periods which can be -postulated to have causal significance. First, misfortune or danger in dreams -is regularly followed by immediate awaking. Secondly, I have had -experiences in which a headlong dive or an attempt to whistle continued -from dream to waking, right through waking up. These experiences are -causally continuous actions. However, I cannot bring them about at will. - -\item We can manipulate a person "from outside" before sleep (or during sleep) -so as to influence the content of that person's dreams. The dream is not an -echo of the waking action; the causal relationship is manipulative. Examples -are to give someone a psychoactive sleeping drug or to create a special -environment for sleep. The case in which I taped my mouth shut before -sleeping was a remarkable borderline case between an echo and a -manipulation. -\end{enumerate} - -in conclusion, dream control is any of the connections described in -(1)--(4). Controlled dreaming is (5). We have analyzed these concepts -meticulously because we want to exclude all attempts at magic, all -superstition from the project of placing dreamed and waking life on the same -level. There must be no rain dancing, no false causality, in this project. - -\textbf{F.} Until now, we have analyzed our experience episode by episode. We -could make this approach into a principle by assuming that each episode is a -separate and complete world, which has its reality confirmed internally. In -particular, the notion of objective location in space and time would be -maintained if it appeared in a dream and was intersubjectively confirmed in -the dream, but the notion would be purely internal to each episode. The -objection to these assumptions, as we mentioned at the end of (B), is that -they propose to maintain the notion of objective location, and yet they -forego the notion of the consistency of all portions of reality. if we adopt -these assumptions and then compare all the reports of our dreamed and -waking periods, we may find that we have experienced different events -attributed to the same location---and indeed, that is exactly what we do -experience. - -One of the main discoveries of this essay has been that dreamed and -waking periods are more symmetrical than our scientific-pragmatic -indoctrination would have us suppose. The reality of the dream world is -intersubjectively confirmed---within the dream. Anecdotal anomalies can be -found in waking periods as well as in dreams. Entities which resemble -common object gestalts but which lack some of the reality cues of object -gestalts can be encountered whicle we are fully awake. Now we can -recognize a further symmetry between dreamed and waking life. A dreamed -misfortune is usually "lost" when we awaken, and its disappearance is taken -as evidence of the unreality of the dream (the nightmare). But we can also -"lose" a waking misfortune by going to sleep and dreaming. Further, just as -a waking misfortune can persist from one waking period to another, a -dreamed misfortune can persist from one dream to another (recurrent -nightmares). Thus, we conclude that in regard to the consistency of episodes -with each other, there is no basis for preferring any one episode, dreamed or -waking, as the standard by which the reality of other episodes will be judged. -Of course, rather than maintaining the reality of each episode as a separate -world, we can block all attributions of events to objective locations. This -approach would alter the quality of the events and bring us closer to -nihilistic empiricism. - -A further problem arises if we take the dream reports of other people as -reports of reality. Suppose I am awake in my apartment at 3 AM on -2/6/1974, but that someone dreams at that time that I am out of my -apartment. Multiple existences which I do not even experience are now being -attributed to me. (My own episodes also pose a problem of whether -"multiple existences" are being attributed to me, but that problem concerns -events I experience myself.) What we should recognize is that the problem of -"multiple existences" is not as unique to our investigation as may at first -appear. Natural science has an analogous problem in disposing of the notion -of other minds. The notion of the existence of many minds, none of which -can experience any other, is difficult to assimilate to the cognitive model of -science. On the other hand, to deny the existence of any mind, as -behaviorists do, is to repudiate the scientist's observations of his own mental -life. And if the scientist's observations of his own mental life are repudiated, -then there is no good reason not to repudiate the scientist's observations of -his budily sensations and of external phenomena also; that is, to repudiate -the very possibility of scientific observation. Further, when behaviorists try -to convince people that they have no awareness, whom (or what) are they -trying to convince? And what is the behaviorist explanation of the origin of -the fiction of consciousness? Who benefits from perpetuating this fiction, -and how does he benefit? - -We must emphasize that the above critique is not applicable to every -philosophical outlook. It applies specifically to science---because the scientist -wants to have the benefits of two incompatible conceptual frameworks. -Some of the common sense about other minds is necessary in the operational -preliminaries to formal science; and the scientist's role as observer is -indispensable to formal science. Yet the conceptual framework of science is -essentially physicalistic, and can allow only for external objects. What this -difficulty reveals is that the cognitive model of science has stabilized and -prevailed even though it has blatent discrepancies in its foundations. The -foremost discrepancy, of course, is that the scientist is willing to have his -enterprise rest on a fiction, that of the common objective world. Thus, the -example of science suggests an additional way of dealing with the problems -which arise for our theory: we can allow discrepancies to persist unresolved. - -There is an interesting observation to be made about one's own dreams -in connection with multiple existences. I have found that the person I am in -my dreams is significantly different from the waking identity I take for -granted, as in my dream of 2/1/1974. As for the problem of other people's -dreams, one way of handling them would be simply to reject the existence of -other people's dream worlds and of their consciousnesses, and to limit one's -consideration to one's own dreams. But perhaps the most productive way to -handle the problem would be to construe it as one involving language in the -way that the problems concerning quasi-dreams did. Our descriptive language -is a language of stable object gestalts, of scientific-pragmatic reality. If we -accept reports of other people's dreams in language which blocks any -implications concerning objective reality, then our perceptual interpretations -will be different and the quality of the events will be fundamentally -different. The experience-world will be flatter. But maybe this is a -revolutionary advance. Maybe reports of our appearances in other people's -dreams, in language which blocks any implications about reality, are what we -should strive for. And if ve cease to be stable object gestalts for others, -maybe our stable object gestalts will not even appear in their dreams. - - -\section*{Note on how to remember dreams} - -The trick in remembering a dream is to fix in your mind one incident or -theme in the dream immediately upon awaking from it. You will then be -able to remember the whole dream well enough to write a description of it -the next day, and you will probably find that for weeks afterwards you can -add to the description and correct it. - - -\part{Social Philosophy} - -\chapter{On Social Recognition} - -The most important tasks which the individual can undertake arise not -from personal considerations but from the general conditions of society. The -standards of accomplishment for these tasks are implicit in the tasks, and are -objective in the sense that they can be applied without reference to public -opinion. For example, given that humans express themselves in statements -which are supposedly true or false, there arises a fundamental philosophical -"problem of knowledge." Then, the fact that societies are organized in -different ways at different times and places poses fundamental problems of -"political" thought and action. Sometimes the most important task posed by -the conditions of society is to invent a whole new activity. The origination -of experimental science in Europe in the seventeenth century is an example. -For lack of a better term, these tasks will be referred to as "fundamental -tasks." - -The fact that a fundamental task is posed by the general conditions of -society does not mean that public opinion will be aware of the task, or that -the ruling class will commission someone to undertake it. It may well be that -the first person to perceive the problem is the person who solves it; and -public opinion may not catch up with him for decades or centuries. - -The person who devotes himself to a fundamental task is, more often -than not, persecuted or ignored by society. Society puts up an immense -resistance to solutions of fundamental problems, even when, as in the cases -of Galois and Mendel, those solutions are politically innocuous. There is no -evidence that this state of affairs is limited to some particular organization of -society. Further, there are cases in which an objectively valid result is -known, and yet apparently society can never adopt the result institutionally. -Art is objectively inferior to brend, as I have shown, and yet all indications -are that art will always be a major institution. The persecution of individuals -who undertake fundamental tasks is an instance of a general human social -irrationality which runs throughout history, from human sacrifice in ancient -times to present-day war between communist countries. The conclusion is -that for an individual to commit himself to a fundamental task tends to -preclude social approval for his activities. - -Quite apart from the fundamental tasks which are posed by general -social conditions, the ruling class needs a continual supply of new talent at -all levels of society. At the lower levels, this supply is assured by the -necessity of selling one's labor power in order to eat. At the higher levels of -accomplishment, the ruling class assures itself of a continual supply of new -talent by offering publicity or fame---social recognition---as a reward for -accomplishing the tasks specified by the ruling class. Famous men such as -Einstein are held up to children as examples of the proper relationship -between the talented individual and society; and an international institution, -the Nobel Prize, exists to implement this system of supplying talent. -According to the doctrine, the individual has a duty to benefit society, to -choose a task posed by the ruling class as his occupation. (His publicly -known occupation is supposed to correspond to his real goals.) If he -performs successfully, he will receive publicity as an indication that he is -indeed benefiting society. - -Our analysis of fame is the opposite of that of Ben Vautier. Vautier -asserts that the desire for personal publicity is an instinctive drive of human -beings, and that the accumulation of publicity is a genuinely selfish act like -the accumulation of food. In fact, Vautier goes so far as to make no -distinction between what Gypsy Rose Lee and Lenin, for example, did to -gain fame; and he assumes that a pacifist, for example, would welcome -military honors equally as much as he would a peace award. We assert, on -the contrary, that the desire for publicity is not instinctive; it is inculcated in -the young so that the ruling class may have a continual supply of new talent -to serve its purposes. The desire for publicity, far more than the desire for -money, is establishment-serving more than self-serving. (We suggest that the -principal reason why Vautier seeks publicity is not instinct, but economics. -Vautier has no inherited source of income, and has never been trained for a -profession. For him, the alternative to the art\slash publicity racket would be -common labor. If he had the opportunity for a life of leisure, he might feel -differently about publicity.) - -The issues which are raised here are extremely important for the person -who perceives a fundamental task, because his sanity may depend on -whether he understands the rationality of his motives for undertaking the -task. He will already have been inculcated with the establishment's concepts -of service and recognition, concepts which are epitomized in the image of -Einstein's career. What we suggest is that it is vital to disabuse oneself of -these concepts. To repeat, fundamental tasks are posed by the general -conditions of society. Yet the individual who undertakes such a task will -probably be persecuted or ignored. Given these circumstances, the doctrine -that the individual has a duty to benefit society is a hypocritical fraud, an -obscenity. For the individual to commit himself to a fundamental task tends -to preclude social recognition for his activities; or, to reverse the remark, -social recognition is not a reward to accomplishment of a fundamental task -(just as military honors are not a reward to pacifism). Thus, it is not rational -for the individual to undertake a fundamental task in order to gain fame. - -The motive for undertaking a fundamental task should be genuine -selfishness. (We will continue our argument that the striving for fame is not -genuinely selfish below.) The individual who perceives a fundamental task -should undertake it for his private gratification. The task is of primary -importance to society. By accomplishing it, the individual gains the privilege -of knowing something which is socially important, but which society cannot -deal with honestly. The individual should undertake the task in order to -utilize his real abilities, to develop his potentiality for its own sake. The -undertaking of a significant task which utilizes one's real abilities is the true -source of happiness. To perceive a fundamental task and not to undertake it -is to be stunted: one loses one's self-respect and becomes progressively -demoralized. (Another rational motive for undertaking a fundamental task is -to transform the social environment by methods which do not depend on -society's approval or comprehension.) - -We do not mean to suggest that the individual who undertakes a -fundamental task should conceal his results. Even though such tasks may -seem individualistic, they require cooperative, social activity for their -accomplishment. A proposed solution to a fundamental problem can hardly -develop without being scrutinized from a variety of perspectives. It is -essential to have qualified critics, and it is unfortunate that they are so rare. -Solutions to fundamental problems are social consumption goods (their -consumption is not exclusionary), so that critics or collaborators have as -much opportunity to benefit from them as their originators do. As an -example, most of my writings are really collaborations with Tony Conrad. I -often find that I do not understand my own position until I know how it -appears to him. When communication of results is essentially a form of -collaboration, it is very different from the attempt to gain publicity or fame. - -It is precisely in the context of the generalized social irrationality which -runs throughout history that the attempt to gain fame must be seen as -foolishly un-selfish. What difference can it possibly make whether the masses -venerate one's name a hundred years after one's death? The adulation of the -masses after one is dead is of no conceivable value to oneself. It is society -which indoctrinates one to worry about one's reputation after one is dead, in -order to condition one to serve the interests of the ruling class. - -Then, what does it mean to the individual who solves a fundamental -problem to have his name publicized in the mass media, to be a celebrity -among people who cannot possibly understand what he has done? Even -more important, we must recognize that publicity carries a definte risk for -the individual committed to a fundamental task. The solution of such a -problem must usually be expressed in categories which are incommensurate -and incompatible with the categories of thought which are common coin at -the time. In order for the solution of a fundamental problem to be exposed -in the mass media, it has to be translated into media categories and this -usually results in irreparable distortion. In fact, the solution is distorted in -precisely such a manner that it begins to serve the interests of the ruling -class. One encounters an immense pressure which tends to harness one to -goals which have nothing to do with objective value. More precisely, when an -individual who has solved a fundamental problem is publicized in the mass -media, a process of mutual subversion takes place as between the -establishment\slash media and the individual. In the process, the establishment is -likely to come out far ahead. - -There are two other reasons why it is actually advantageous to the -individual who undertakes a fundamental task to avoid publicity. Since one's -activity is likely to be treated as a threat by society, one can minimize the -energy required to defend it, and can carry the activity further, if one -receives no publicity. Then, there will unavoidably be false starts made in -developing the solution to a fundamental problem. If one is not operating in -the glare of publicity, it is far easier to abandon these false starts. - -It used to be that when I saw publicity being given to an inferior way of -doing a thing, and I knew a better way, then I reacted with a sense of duty. I -had to appoint myself as a missionary, to enter the public arena and start a -campaign to replace the inferior approach with the better approach. But this -sense of duty must now be called into question. Is it really in my interest to. -thrust myself on the media as a missionary? The truth is that in the context -of generalized social irrationality, it is un-selfish and self-sacrificing to believe -that I must either agree with current fads or else contest them publicly. The -genuinely selfish attitude is *hat it is sufficient for me to know what the -superior approach is. I can ignore the false issues which fill the mass media; I -do not have to participate in public opinion at all. The genuinely selfish -attitude is that "it does not concern me." Genuine selfishness is living one's -life on a level which does not communicate with the level of the mass media -and public opinion. - -If we recognize that it is irrational to undertake a fundamental task in -order to benefit society and gain social approval, then our very choice of -fundamental tasks shouid be affected. The most visible fundamental tasks -are those which the establishment is to some extent aware of, and which if -accomplished would immediately be rewarded with social approval. (In the -natural sciences, there literally may be a race to solve a well-known problem). -But if our motives are genuinely self-serving, and have to do with the -development of our potentiality for its own sake, then there is no reason to -limit ourselves to widely understood problems. We can undertake to discover -timeless results---permanent answers to questions which will be important -indefinitely---without concerning ourselves with whether society can adopt -the results institutionally. We can pose problems of which neither the -establishment, the media, nor public opinion are aware. We can undertake -tasks which draw on our unique abilities, so that our personal contribution is -indispensable. - -There is a difficulty which we have postponed mentioning. The -individual is always compelled to engage in some socially approved activity -in order to obtain the means of subsistence. We cannot assume that the -individual will have an inherited source of income. In order to pursue a -fundamental task, he will have to pursue a legitimate occupation at the same -time. It may be extremely difficult to lead such a double life, because to do -so requires precisely the self-assurance. that comes from accomplishing the -fundamental task. Leading a double life is not a game for the person who is -unsure about his real abilities or his vocation. If the individual is capable of -leading a double life, our suggestion is to obtain the means of subsistence by -the most efficient swindle available. Do not hesitate to practice outward -conformity in order to exploit the establishment for your own purposes. - -There remains the case of the individual who, like Galois, is not -prepared to lead a double life. His problem is one of destitution. However, -he is different from an ordinary pauper. By assumption, he is more talented -than the members of the establishment; he does not belong to the -establishment because he is overqualified for it. Given that he is more -talented than members of the establishment, and that his survival is -threatened, a collateral fundamental task emerges, the task of immediately -transmuting his talent into power to handle the establishment on his own -terms. To perceive this task is a major resuit of this essay. The task cannot be -defined accurately without a perfect understanding of the difference -between fundamental tasks and the serve-society-and-get-famous fraud. We -contend that Galois should have regarded the task of immediately -transmuting his talent into power over the establishment as an inseparable -collateral problem to his mathematical researches. From a common sense -point of view, this collateral task will seem utterly impossible. However, we -are talking about individuals whose vocation is to do the seemingly -impossible. Thus, we conclude by leaving this unsolved fundamental problem -for the reader to ponder. - -\chapter{Creep} - - -When Helen Lefkowitz said I was "such a creep" at Interlochen in -1956, her remark epitomized the feeling that females have always had about -me. My attempts to understand why females rejected me and to decide what -to do about it resulted in years of confusion. In 1961-1962, I tried to -develop a theory of the creep problem. This theory took involuntary -celibacy as the defining characteristic of the creep. Every society has its -image of the ideal young adult, even though the symbols of growing up -change from generation to generation. The creep is an involuntary celibate -because he fails to develop the surface traits of adulthood--poise and -sophistication; and because he is shy, unassertive, and lacks self-confidence -in the presence of others. The creep is awkward and has an unstylish -appearance. He seems sexless and childish. He is regarded by the ideal adults -with condescending scorn, amusement, or pity. - -Because he seems weak and inferior in the company of others, and -cannot maintain his self-respect, the creep is pressed into isolation. There, -the creep doesn't have the pressure of other people's presence to make him -feel inferior, to make him feel that he must be like them in order not te be -inferior. The creep can develop the morale required to differ. The creep also -tends to expand his fantasy life, so that it takes the place of the -interpersonal life from which he has been excluded. The important -consequence is that the creep is led to discover a number of positive -personality values which cannot be achieved by the mature, married adult. -During the period when I developed the creep theory, I was spending almost -all of my time alone in my room, thinking and writing. This fact should -make the positive creep values more understandable. - -\begin{enumerate} -\item Because of his isolation, the creep has a qualitatively higher sense of -identity. He has a sense of the boundaries of his personality, and a control of -what goes on within those boundaries. In contrast, the mature adult, who -spends all his time with his marriage partner or in groups of people, is a mere -channel into which thoughts flow from outside; he lives in a state of -conformist anonymity. - -\item The creep is emotionally autonomous, independent, or -self-contained. He develops an elaborate world of feelings which remain -within himself, or which are directed toward inanimate objects. The creep -may cooperate with other people in work situations, but he does not develop -emotional attachments to other people. - -\item Although the creep's intellectual abilities develop with education, -the creep lives in a sexually neutral world and a child's world throughout his -life. He is thus able to play like a child. He retains the child's capacity for -make-believe. He retains the child's lyrical creativity in regard to -self-originated, self-justifying activities. - -\item There is enormous room in the creep's life for the development of -every aspect of the inner world or the inner life. The creep can devote -himself to thought, fantasy, imagination, imaging, variegated mental states, -dreams, internal emotions and feelings towards inanimate objects. The creep -develops his inner world on his own power. His inner life originates with -himself, and is controlled and intellectually consequential. The creep has no -use for meditations whose content is supplied by religious traditions. Nor has -he any use for those drug experiences which adolescents undertake to prove -how grown-up they are, and whose content is supplied by fashion. The -creep's development of his inner life is the summation of all the positive -creep values. -\end{enumerate} - -After describing these values, the creep theory returned to the problem -of the creep's involuntary celibacy. For physical reasons, the creep remains a -captive audience for the opposite sex, but his attempts to gain acceptance by -the opposite sex always end in failure. On the other hand, the creep may -well find the positive creep values so desirable that he will want to intensify -them. The solution is for the creep to seek a medical procedure which will -sexually neutralize him. He can then attain the full creep values, without the -disability of an unresolved physical desire. - -Actually, the existence of the positive creep values proves that the -creep is an authentic non-human who happens to be trapped in human social -biology. The positive creep values imply a specification of a whole -non-human: social biology which would be appropriate to those values. -Finally, the creep theory mentioned that creeps often make good grades in -school, and can thus do clerical work or other work useful to humans. This -fact would be the basis for human acceptance of the creep. - -In the years after I presented the creep theory, a number of -inadequacies became apparent in it. The principal one was that I managed to -cast off the surface traits of the creep, but that when I did my problem -became even more intractable. An entirely different analysis of the problem -was required. - -My problem actually has to do with the enormous discrepancy between -the ways I can relate to males and the ways I can relate to females. The -essence of the problem has to do with the social values of females, which are -completely different from my own. The principal occupation of my life has -been certain self-originated activities which are embodied in "writings." Now -most males have the same social values that I find in all females. But there -have always been a few males with exceptional values; and my activities have -developed through exchanges of ideas with these males. These exchanges -have come about spontaneously and naturally. In contrast, I have never had -such an exchange of ideas with females, for the following reasons. Females -have nothing to say that applies to my activities. They cannot understand -that such activities are possible. Or they are a part of the "masses" who -oppose and have tried to discourage my activities. - -The great divergence between myself and females comes in the area -where each individual is responsible for what he or she is; the area in which -one must choose oneself and the principles with which one will be identified. -This area is certainly not a matter of intelligence or academic degrees. -Further, the fact that society has denied many opportunities to females at -one time or another is not involved here. (My occupation has no formal -prerequisites, no institutional barriers to entry. One enters it by defining -oneself as being in it. Yet no female has chosen to enter it. Or consider such -figures as Galileo and Galois. By the standards of their contemporaries, these -individuals were engaged in utterly ridiculous, antisocial pursuits. Society -does not give anybody the "opportunity" to engage in such pursuits. Society -tries to prevent everybody from being a Galileo or Galois. To be a Galileo is -really a matter of choosing sides, of choosing to take a certain stand.) - -Let me be specific about my own experiences. When I distributed the -prospectus for \journaltitle{The Journal of Indeterminate Mathematical Investigations} to -graduate students at the Courant Institute in the fall of 1967, the most -negative reactions came from the females. The mere fact that I wanted to -invent a mathematics outside of academic mathematics was in and of itself -offensive and revolting to them. Since the academic status of these females -was considerably higher than my own, the disagreement could only be -considered one of values. - -The field of art provides an even better example, because there are -many females in this field. In the summer of 1969 I attended a meeting of -the women's group of the Art Workers Coalition in New York. Many of the -women there had seen my Down With Art pamphlet. Ail the females who -have seen this pamphlet have reacted negatively, and it is quite clear what -their attitude is. They believe that they are courageously defending modern -art against a philistine. They consider me to be a crank who needs a "modern -museum art appreciation course." The more they are pressed, the more -proudiy do they defend "Great Art." Now the objective validity of my -opposition to art is absolutely beyond question. To defend modern art is -precisely what a hopeless mediocrity would consider courageous. Again, it is -clear that the opposition between myself and females is in the area where -one must choose one's values. - -I have found that what I really have to do to make a favorable -impression on females is to conceal or suspend my activities----the most -important part of my life; and to adopt a facade of conformity. Thus, I -perceive females as persons who cannot function in my occupation. I -perceive them as being like an employment agency, like an institution to -which you have to present a conformist facade. Females can he counted on to -represent the most "social, human" point of view, a point of view which, as I -have explained, is distant from my own. (In March 1970, at the Institute for -Advanced Study, the mathematician Dennis Johnson said to me that he -would murder his own mother, and murder all his friends, if by doing so he -could get the aliens to take him to another star and show him a higher -civilization. My own position is the same as Johnson's.) - -It follows that my perception of sex is totally different from that of -others. The depictions of sex in the mass media are completely at variance -with my own experience. I object to pornography in particular because it is -like deceptive advertising for sex; it creates the impression that the physical -aspect of sex can be separated from human personalities and social -interaction. Actually, if most people can separate sex from personality, it is -because they are so average that their values are the same as everybody else's. -In my case, although I am a captive audience for females for physical -reasons, the disparity between my values and theirs overrides the physical -attraction I feel for them. It is hard enough to present a facade of -conformity in order to deal with an employment agency, but the thought of -having to maintain such a facade in a more intimate relationship is -completely demoralizing. - -What conclusions can be drawn by comparing the creep theory with my -later experience? First, some individuals who are unquestionably creeps as -far as the surface traits are concerned simply may not be led to the deeper -values I described. They may not have the talent to get anything positive out -of their involuntary situation; or their aspirations may be so conformist that -they do not see their involuntary situation as a positive opportunity. Many -creeps are female, but all the evidence indicates that they have the same -values I have attributed to other females---values which are hard to reconcile -with the deeper creep values. - -As for the positive creep values, I may have had them even before I -began to care about whether females accepted me. For me, these values may -have been the cause, not the effect, of surface creepiness. They are closely -related to the values that underlie my activities. It is not necessary to appear -strangely dressed, childish, unassertive, awkward, and lacking in confidence -in order to achieve the positive creep values. (I probably emphasized surface -creep traits during my youth in order to dissociate myself from conformist -opinion at a time when I hadn't yet had the chance to make a full -substantive critique of it.) Even sex, in and of itself, might not be -incompatible with the creep inner life; what makes it incompatible is the -female personality and female social values, which in real life cannot be -separated from sex and are the predominant aspect of it. - -Having cast off the surface traits of the creep, I can now see that -whether I make a favorable impression on females really depends on whether -I conceal my occupation. Celibacy is an effect of my occupation; it does not -have the role of a primary cause that the creep theory attributed to it. -However, it does have consequences of its own. In the context of the entire -situation I have described, it constitutes an absolute dividing line between -myself and humanity. It does seem to be closely related to the deeper creep -values, especially the one of living in a child's world. - -As for the sexual neutralization advocated in the creep theory, to find a -procedure which actually achieves the stated objective without having all -sorts of unacceptable side effects would be an enormous undertaking. It is -not feasible as a minor operation developed for a single person. Further, as -the human species comes to have vast technological capabilities, many -special interest groups will want to tinker with human social biology, each in -a different way, for political reasons. I am no longer interested in petty -tinkering with human biology. As I make it clear in other writings, I am in -favor of building entities which are actially superior to humans, and which -avoid the whole fabric of human biosocial defects, not just one or two of -them. - -\clearpage -{ - - -2/22/1963 -Henry Flynt and Jack Smith demonstrate against Lincoln Center, February 22, 1963 -(photo by Tony Conrad) -} \clearpage +{ 2/22/1963 -\chapter{The Three Levels of Politics} - - -Political activity and its results can occur on three levels. The first level -is the personal one. An individual may vote to re-elect a local politician -because of patronage he has received, for example. On this level the -individual's motivation is narrow, immediate self-interest. Often the action -has a defensive character; the individual is trying to hold on to something he -already possesses. - -The second level may be called the historical level. It is exemplified by -the Civil War in the United States. Certain political movements result in -largescale, irreversible social change. The Civil War set in motion the -industrialization of the United States, as well as abolishing slavery. In 1860, -slavery was viewed by large numbers of Americans as a legitimate institution. -One hundred years later, even American conservatives did not often defend -it. To re-establish a plantation economy in the South today would be out of -the question. These observations prove that on the second level, society -really does change. On this level, political action does make a difference. - -However, there is a further aspect to the Civil War which indicates that -politics does not make the difference people think it makes. According to -the ideology of the abolitionists, the accomplishment of the Civil War would -be to raise the slaves to a position of equality with whites. In fact, nothing of -the sort happened. The real accomplishment of the Civil War was to -transform the United States into an industrial capitalist society (and to -abolish an institution which was incompatible with the capitalists' need for a -free labor market). By the time the Northern businessmen brought -Reconstruction to an end, it was clear that the position of blacks in -American society was where it had always been: at the bottom. The Civil -War changed American society, but is did not make the society any more -utopian. On the contrary, it brought into prominence still another violent -social conflict---the conflict between labor and capital. - -The third level of politics has to do with the utopian aspect of modern -political ideologies, the aspect which calls not only for society to change, but -to change for the better. Typical third-level political goals are the abolition -of war, the abolition of the oligarchic structure of society, and the abolition -of economic institutions which value human lives in terms of money. in all -of human history, society has never changed on this third level. - -The successful Communist revolutionists of the twentieth century (in -the underdeveloped countries) have repeatedly claimed to have accomplished -third-level change in their societies. However, these claims of third-level -change have always turned out to be illusions which cover a recapitulation of -capitalist development. Communist revolutions are typical examples of real -second-level change which is accomplished under the cover of claims of -third-level change, claims which are pure and simple frauds. - -By introducing the concept of levels of politics, we can resolve the -apparent paradox that society certainly changes, but that it really does not -change. It is important to understand that empirical evidence on the -question of the levels of politics can only be drawn from the past, the -present, and the immediate future (five to ten years). Recent technological -developments have brought into question the very existence of the human -species. In addition, technology is developing much faster than society is. It -is meaningless to discuss the issue of second versus third-level social change -with reference to the more distant future, because there may not be any -human society in the more distant future. - -This essay is concerned with the politics of the third level. The first and -second levels are certainly real enough, but we are not the least interested in -them. As we have just said, we make the restriction that any empirical -analysis of the third level must refer to the past, the present, or the -immediate future. Our purpose is to present a substitute for the politics of -the third level. - -There are a number of present-day political tendencies which hold out -the promise of third-level social change. These tendencies are all descended -from the leftist working-class movements of nineteenth century Europe, -most of them by way of the early Soviet regime. The promises of third-level -change held out by these tendencies are nothing but cheap illusions. What is -more, a careful examination of leftist ideologies in relation to the historical -record will show that the promises of third-level change are extremely vague -and without substance. Beneath the surface of vague promises, leftist -ideologies do not even favor third-level change; they are opposed to it. - -One example will serve to demonstrate this contention. In my capacity -as a professional economist, I have become familiar with the official -economic policies---the doctrines of the professional economists---of the -various socialist governments and leftist movements throughout the world. It -should be mentioned that most of the followers of leftism are not familiar -with these technical economic policies; they are aware only of vague, -meaningless promises of future bliss coming from leftist political -speechmakers. When we turn to technical economic realities, we find that -virtually every leftist tendency in the world today accepts economic -principles which in the parlance of the layman are referred to as -"capitalism." The most important principle is stated by Ernest Mandel: "the -economy continues to be fundamentally a money economy, with the -satisfaction of the bulk of people's needs depending on the number of -currency tokens a person possesses." When it comes to the realities of -technical economics, virtually every leftist in the world accepts this -principle. So far as the third level is concerned, there is no such thing as a -non-capitalist polical tendency, and there is no point in hoping for one. A -similar conclusion holds for virtually every aspect of third-level politics. -Leftists claim that Communism eliminates the causes of war; while at the -same time war breaks out beween China and the Soviet Union. - -We propose to draw a far-reaching conclusion from these -considerations. Returning to the example of first-level politics, it is rational -for the patronage-seeker to be in favor of the election of one focal politican -and against the election of his opponent. This is a matter which is within the -scope of human responsibility, and with respect to which individual action -can make a difference. But it is not rational to be either for against -"capitalism," to be either for or against war. As we have seen, "capitalism" -and war are permanent aspects of human society, and no political tendency -genuinely opposes them. It is meaningless to treat them as if they were -within the scope of human responsibility in the sense that the election of a -local politician is. in other words, the third-level aspects of society are not -partial, limited aspects which can be eliminated by conscious human action -while the bulk of human life is retained. The only way you can meaningfully -be against the third-level aspects of human society is by adopting a different -attitude to the human species as such. - -This attitude is the one you would adopt if you were suddenly thrown -into a society of apes---apes which perpetually preyed within their own -ecological niche. It is clear that if you proposed to be "against" such a -situation, and to do something about it, then politics as it is normally -conceived would be out of the question. To anticipate our later discussion, -the first thing you must do is to protect yourself against society. The way to -do this is to create an invisible enclave for yourself within the Establishment. -Having such an enclave certainly does not imply loyalty to the -Establishment. On the contrary, there is no reason why you should be toyal -to any faction among the apes. You only pretend to be loyal to one faction -or another when it is necessary for self-defense. If there is a change of regime -in the country where you are living, you either leave or join the winning side. -Transfer your invisible enclave to whatever Establishment is available. But all -this is an external, defensive tactic which has nothing to do with the primary -goals of our strategy. - -We will finish our critique of third-level politics, and then continue the -description of the substitute which we propose. In addition to making vague -promises of third-level change, leftism encourages indignation at social -conditions which are beyond anyone's power to affect. Leftism attributes -great ethical merit to such indignation and morally condemns anyone who -does not share it. But this attitude is totally irrational and dishonest. In -philosophy and mathematics, it is possible for a proposition to be valid even -though it has no chance of institutional acceptance. But in social, economic, -and political matters, attitudes which have policy implications are nonsense -unless the policies are actually implemented. Institutional acceptance is the -only arena of validation of a social doctrine. It is absurd to attribute ethical -merit to a longing for the impossible. Indignation at a social condition which -is beyond anyone's power to affect is meaningless. (Indeed, to the extent -that such indignation diverts social energy into a dead end, it is -"counter-revolutionary.") To be more radical in social matters than society -can possibly be is not virtuous; it is idiotic. - -Although third-level politics is a fraud, it is the contention of this essay -that there exists a rational substitute for it. Once you perceive that you exist -in a society of apes who attack their own ecological niche, there are rational -goals which you can adopt for your life that correspond to third-level change -even though they have nothing to do with leftism. The preliminary step, as -we have said, is to create an invisible enclave for yourself within. the -Establishment. The remainder of the strategy is in two parts which are in -fact closely related. - -The first part is based on a consideration of the effects which such -figures as Galileo, Galois, Abel, Lobachevski, and Mendel have had on -society. These men devoted themselves to researches which seemed to be -purely abstract, without any relevance to the practical world. Yet, through -long, tortuous chains of events, their researches have had disruptive effects -on society which go far beyond the effects of most political movements. The -reason has to do with the peculiar role which technology has in human -society. Society's attitude in relation to technology is like that of a child -who cannot refrain from playing with matches. We find that -the abstract researches of the men being considered accomplished a dual -result. On the one hand, they represented inner escape, the achievement of a -private utopia now. Of course, the general public will not understand this; -only the few who are capable of participating in such activities will -appreciate the extent to which they can constitute inner escape. On the -other hand, they have had profoundly disruptive effects on society, effects -which still have not run their course. - -Thus, the first part of our strategy is to follow the example of these -individuals. Of course, we do not stay within the bounds of present-day -academic research, any more than Galileo or Mendel did in their time. What -we have in mind is activities in the intellectual modality represented by the -rest of this book. - -It should be clear that such activities do represent a private utopia, and are at -the same time the seeds of disruptive future technologies which lead directly -to the second part of our strategy. - -It is important to realize that by speaking of inner escape we do not -mean fashionable drug use, or Eastern religions, or occultism. These -threadbare superstitions are embraced by the cosmopolitan middle -classes---intellectually spineless fools who are always grasping for spiritual -comfort. Superstitious fads are escapism in the worst sense, as they only -serve to further muddle the heads of the fools who embrace them. In -contrast, the inner escape which we propose is original and consequential, -leading to an increase in man's manipulative power over the world. It has -nothing to do with irrationality or superstition. - -The second part of our strategy is predicated on the following states of -affairs. First, it is the human species as such which is the obstacle to -third-level political change. Secondly, technology is developing far more -rapidly than society is, and no feature of the natural world need any longer -be taken for granted. Society cannot help but foster technology in the -pursuit of military and economic supremacy, and this includes technology -which can contribute to the making of artificial superhuman beings. Every -fundamental advance in logic, physics, neurophysiology, and -neurocybernetics obviously leads in this direction. Thus, the second part of -the strategy is to participate in the making of artificial superhumans, -possibly by infiltrating the military-scientific establishment and diverting -research in the appropriate direction. - -{ \itshape -Note: This essay provides a specific, practical strategy for the present -environment. It also shows that certain types of opposition to the status quo -are meaningless. Subversion Theory, on the other hand, was a general theory -which was not limited to any one environment, but also which failed to -provide a specific strategy for the present environment. \par } - - -\part{Science (Logic)} - -\chapter{The Logic of Admissible Contradictions (Work in Progress)} - -\section{Chapter III. A Provisional Axiomatic Treatment} - - -In the first and second chapters, we developed our intuitions -concerning perceptions of the logically impossible in as much detail as we -could. We decided, on intuitive grounds, which contradictions were -admissible and which were not. As we proceeded, it began to appear that the -results suggested by intuition were cases of a few general principles. In this -chapter, we will adopt these principles as postulates. The restatement of our -theory does not render the preceding chapters unnecessary. Only by -beginning with an exhaustive, intuitive discussion of perceptual illusions -could we convey the substance underlying the notations which we call -admissble contradictions, and motivate the unusual collection of postulates -which we will adopt. - -All properties will be thought of as "parameters," such as time, -location, color, density, acidity, etc. Different parameters will be represented -by the letters x, y, z, .... Different values of one parameter, say x, will be -represented by $x_1$, $x_2$, .... Each parameter has a domain, the set of all values -it can assume. An ensembie ($x_0$, $y_0$, $z_0$, ...) will stand for the single possible -phenomenon which has x-value $x_0$, y-value $y_0$, etc. Several remarks are in -order. My ensembles are a highly refined version of Rudolph Carnap's -intensions or intension sets (sets of all possible entities having a given -property). The number of parameters, or properties, must be supposed to be -indefinitely large. By giving a possible phenomenon fixed values for every -parameter, I assure that there will be only one such possible phenomenon. In -other words, my intension sets are all singletons. Another point is that if we -specify some of the parameters and specify their ranges, we limit the -phenomena which can be represented by our "ensembles." If our first -parameter is time and its range is $R$, and our second parameter is spatial -location and its range is $R^2$, then we are limited to phenomena which are -point phenomena in space and time. If we have a parameter for speed of -motion, the motion will have to be infinitesimal. We cannot have a -parameter for weight at all; we can only have one for density. The physicist -encounters similar conceptual problems, and does noi find them -insurmountable. - -Let ($x_1$, $y$, $z$, ...), ($x_2$, $y$, $z$, ...), etc. stand for possible phenomena -which all differ from each other in respect to parameter x but are identical in -respect to every other parameter $y$, $z$, ... . (If the ensembles were intension -sets, they would be disjoint precisely because $x$ takes a different value in -each.) A "simple contradiction family" of ensembles is the family [($x_1$,$y$,$z$, -...), ($x_2$, $y$, $z$, ...), ...]. The family may have any number of ensembles. It -actually represents many families, because $y$, $z$, ... are allowed to vary; but -each of these parameters must assume the same value in all ensembles in any -one family. $x$, on the other hand, takes different values in each ensemble in -any one family, values which may be fixed. A parameter which has the same -value throughout any one family will be referred to as a consistency -parameter. A parameter which has a different value in each ensemble in a -given family will be referred to as a contradiction parameter. -"Contradiction" will be shortened to "con." A simple con family is then a -family with one con parameter. The consistency parameters may be dropped -from the notation, but the reader must remember that they are implicitly -present, and must remember how they function. - -A con parameter, instead of being fixed in every ensemble, may be -restricted to a different subset of its domain in every ensemble. The subsets -must be mutually disjoint for the con family to be well-defined. The con -family then represents many families in another dimension, because it -represents every family which can be formed by choosing a con parameter -value from the first subset, one from the second subset, etc. - -Con families can be defined which have more than one con parameter, -i.e. more than one parameter satisfying all the conditions we put on x. Such -con families are not "simple." Let the cardinality of a con family be -indicated by a number prefixed to "family," and let the number of con -parameters be indicated by a number prefixed to "con." Remembering that -consistency parameters are understood, a 2-con $\infty$-family would appear as -[($x_1$, $y_1$). ($x_2$, $y_2$), ...]. - -A "contradiction" or "$\varphi$-object" is not explicitly defined, but it is -notated by putting "$\varphi$" in front of a con family. The characteristics of $\varphi$-objects, -or cons, are established by introducing additional postulates in the -theory. - -In this theory, every con is either "admissible" or "not admissible." -"Admissible" will be shortened to "am." The initial amcons of the theory -are introduced by postulate. Essentially, what is postulated is that cons with -a certain con parameter are am. (The cons directly postulated to be am are -on 1-con families.) However, the postulate will specify other requirements for -admissibility besides having the given con parameter. The requisite -cardinality of the con family will be specified. Also, the subsets will be -specified to which the con parameter must be restricted in each ensemble in -the con. A con must satisfy all postulated requirements before it is admitted -by the postulate. - -The task of the theory is to determine whether the admissibility of the -cons postulated to be am implies the admissibility of any other cons. The -method we have developed for solving such problems will be expressed as a -collection of posiulates for our theory. - -\postulate{1} Given $\varphi[(x\in A),(x\in B),\ldots]$ am, where $x\in A$, $x\in B$, ... are the -restrictions on the con parameter, and given $A_1\subset A$, $B_1\subset B$, ..., where $A_1,B_1,...\neq\emptyset$, then -$\varphi[(x\in A_1),(x\in B_1),...]$ is am. This postulate is obviously -equivalent to the postulate that $\varphi[(x\in A\cap C),(x\in B\cap C),...]$ is am, where $C$ is -a subset of $x$'s domain end the intersections are non-empty. (Proof: Choose -$C=A_1\cup B_1\cup\ldots$ .) - -\postulate{2} If $x$ and $y$ are simple amcon parameters, then a con with con -parameters $x$ and $y$ is am if it satisfies the postulated requirements -concerning amcons on $x$ and the postulated requirements concerning amcons -on $y$. - -The effect of all our assumptions up to now is to make parameters -totally independent. They do not interact with each other at all. - -We will now introduce some specific amcons by postulate. If $s$ is speed, -consideration of the waterfall illusion suggests that we postulate -$\varphi[(s>O),(s=O)]$ to be am. (But with this postulate, we have come a long way from -the literary description of the waterfall illusion!) Note the implicit -requirements that the con family must be a 2-family, and that $s$ must be -selected from $[O]$ in one ensemble and from ${s:s>O}$ in the other ensemble. - -If $t$ is time, $t\in R$, consideration of the phrase "b years ago," which is an -amcon in the natural language, suggests that we postulate $\varphi[(t):a-b\leq t\leq v-b \&a\leq v]$ to be am, -where $a$ is a fixed time expressed in years A.D., $b$ is a fixed -number of years, and $v$ is a variable---the time of the present instant in years -A.D. The implicit requirements are that the con family must have the -cardinality of the continuum, and that every value of $t$ from $a-b$ to $v-b$ must -appear in an ensemble, where $v$ is a variable. Ensembles are thus continually -added to the con family. Note that there is the non-trivial possibility of using -this postulate more than once. We could admit a con for $a=1964$, $b=\sfrac{1}{2}$ -then admit another for $a=1963$, $b=2$, and admit still another for $a=1963$, -$b=1$; etc. - -Let $p$ be spatial location, $p\in R^2$. Let $P_i$ be a non-empty, bounded, -connected subset of $R^2$. Restriction subsets will be selected from the $P_i$. -Specifically, let $P_1\cap P_2=\emptyset$. Consideration of a certain dreamed illusion -suggests that we admit $\varphi[(p\in P_1),(p\in P_2)]$. The implicit requirements are -obvious. But in this case, there are more requirements in the postulate of -admissibility. May we apply the postulate twice? May we admit first -$\varphi[(p\in P_1),(p\in P_2)]$ and then $\varphi[(p\in P_3),(p\in P_4)]$, where $P_3$ and $P_4$ are arbitrary -$P_i$'s different from $P_1$ and $P_2$? The answer is no. We may admit -$\varphi[(p\in P_1),(p\in P_2)]$ for arbitrary $P_1$ and $P_2$, $P_1\cap P_2=\emptyset$, but having made this "initial -choice," the postulate cannot be reused for arbitrary $P_3$ and $P_4$. A second -con $\varphi[(p\in P_3),(p\in P_4)]$, $P_3\cap P_4=\emptyset$, may be postulated to be am only if -$P_1\cup P_3$,$P_2\cup P_3$,$P_1\cup P_4$, and $P_2\cup P_4$ are not connected. In other words, you -may postulate many cons of the form $\varphi[(p\in P_i),(p\in P_j)]$ to be am, but -your first choice strongly circumscribes your second choice, etc. - -We will now consider certain results in the logic of amcons which were -established by extensive elucidation of our intuitions. The issue is whether -our present axiomization produces the same results. We will express the -results in our latest notation as far as possible. Two more definitions are -necessary. The parameter $\theta$ is the angle of motion of an infinitesimally -moving phenomenon, measured in degrees with respect to some chosen axis. -Then, recalling the set $P_1$, choose $P_5$ and $P_6$ so that $P_1=P_5\cup P_6$ and -$P_5\cap P_6=\emptyset$. - -The results by which we will judge our axiomization are as follows. - -\begin{enumerate} % TODO with colons? - - \item $\varphi[S, C_1\cup C_2]$ can be inferred to be am. - -Our present notation cannot express this result, because it does not -distinguish between different types of uniform motion throughout a finite -region, \ie the types $M$, $C_1$, $C_2$, $D_1$, and $D_2$. Instead, we have infinitesimal -motion, which is involved in all the latter types of motion. Questions such as -"whether the admissibility of $\varphi[M,S]$ implies the admissibility of $\varphi[C_1,S]$" -drop out. The reason for the omission in the present theory is our choice of -parameters and domains, which we discussed earlier. Our present version is -thus not exhaustive. However, the deficiency is not intrinsic to our method; -and it does not represent any outright falsification of our intuitions. Thus, -we pass over the deficiency. - -\item $\varphi[(p\in P_1,s_0),(p\in P_2,S_0)]$ and other such cons can be inferred to be am. -With our new, powerful approach, this result is trivial. It is guaranteed by -what we said about consistency parameters. - -\item There is no way to infer that $\varphi[C_1,C_2]$ is am; and no way to infer that -$\varphi[(45^\circ,s_0\greater O),(60^\circ,s=s_0)]$ is am. - -The first part of the result drops out. The second part is trivial with our new -method as long as we do not postulate that cons on $\theta$ are am. - -\item $\varphi[(p\in P_2),(p\in P_5)]$ can be inferred to be am. - -Yes, by Postulate 1. - -\item $\varphi[(s>O, p\in P_1),(s=O, p\in P_2)]$ and $\varphi[(s>O, p\in P_2),(s=O, p\in P_1)]$ can -be inferred to be am. - -Yes, by Postulate 2. These two amcons are distinct. The question of whether -they should be considered equivalent is closely related to the degree to -which con parameters are independent of each other. - -\item There is no way to infer that $\varphi[(p\in P_5),(p\in P_6)]$ or $\varphi[(p\in P_1),(p\in P_3)]$ -is am. Our special requirement in the postulate of admissibility for -$\varphi[(p\in P_1),(p\in P_2)]$ guarantees this result. -\end{enumerate} - -The reason for desiring this last result requires some discussion. In -heuristic terms, we wish to avoid admitting both location in New York in -Greensboro and location in Manhattan and Brooklyn. We also wish to avoid -admitting location in New York in Greensboro and location in New York in -Boston. If we admitted either of these combinations, then the intuitive -rationale of the notions would indicate that we had admitted triple location. -While we have a dreamed illusion which justifies the concept of double -location, we have no intuitive justification whatever for the concept of triple -location. It must be clear that admission of either of the combinations -mentioned would not imply the admissibility of a con on a 3-family with -con parameter p by the postulates of our theory. Our theory is formally safe -from this implication. However, the intuitive meaning of either combination -would make them proxies for the con on the 3-family. - -A closely related consideration is that in the preceding chapter, it -appeared that the admission of $\varphi[(p\in P_1),(p\in P_2)]$ and $\varphi[(p\in P_5),(p\in P_6)]$ -would tend to require the admission of the object $\varphi[(p\in P_2),\varphi[(p\in P_5),(p\in P_6)]]$ -(a Type 1 chain). Further, it this implication held, then by the same -rationale the admission of $\varphi[(p\in P_1),(p\in P_2)]$ and $\varphi[(s>O,p_0\in P_1),(s=O,p=p_0)]$, - both of which are am, would require the admission of the object -$\varphi[(p\in P_2), \varphi[(s>O,p_0\in P_1),(s=O, p=p_0)]]$. -We may now say, however, -that the postulates of our theory emphatically do not require us to accept -these implications. If there is an intuitively valid notion underlying the chain -on s and p, it reduces to the amcons introduced in result 5. As for the chain -on p alone, we repeat that simultaneous admission of the two cons -mentioned would tend to justify some triple location concept. However, we -do not have to recognize that concept as being the chain. It seems that our -present approach allows us to forget about chains for now. - -Our conclusion is that the formal approach of this chapter is in good -agreement with our intuitively established results. - -\section*{Note on the overall significance of the logic of amcons:} - -When traditional logicians said that something was logically impossible, -they meant to imply that it was impossible to imagine or visualize. But this -implication was empirically false. The realm of the logically possible is not -the entire realm of connotative thought; it is just the realm of normal -perceptual routines. When the mind is temporarily freed from normal -perceptual routines---especially in perceptual illusions, but also in dreams and -even in the use of certain "illogical" natural language phrases---it can imagine -and visualize the "logically impossible." Every text on perceptual -psychology mentions this fact, but logicians have never noticed its immense -significance. The logically impossible is not a blank; it is a whole layer of -meaning and concepts which can be superimposed on conventional logic, but -not reduced or assimilated to it. The logician of the future may use a drug or -some other method to free himself from normal perceptual routines for a -sustained period of time, so he can freely think the logically impossible. He -will then perform rigorous deductions and computations in the logic of -amcons. - -\chapter{Subjective Propositional Vibration (Work in Progress)} - -Up until the present, the scientific study of language has treated -language as if it were reducible to the mechanical manipulation of counters -on a board. Scientists have avoided recognizing that language has a mental -aspect, especially an aspect such as the 'understood meaning" of a linguistic -expression. This paper, on the other hand, will present linguistic constructs -which inescapably involve a mental aspect that is objectifiable and can be -subjected to precise analysis in terms of perceptual psychology. These -constructs are not derivable from the models of the existing linguistic -sciences. In fact, the existing linguistic sciences overlook the possibility of -such constructs. - -Consider the ambiguous schema '$A\supset B\&C$', expressed in words as '$C$ and -$B$ if $A$'. An example is - -\begin{equation} - \label{firstvib} - \parbox{4in}{Jack will soon leave and Bill will laugh if Don speaks.} -\end{equation} - -In order to get sense out of this utterance, the reader has to supply it with a -comma. That is, in the jargon of logic, he has to supply it with grouping. Let -us make the convention that in order to read the utterance, you must -mentally supply grouping to it, or "bracket" it. If you construe the schema -as '$A\supset (B\&C)$', you will be said to bracket the conjunction. If you construe -the schema as '$(A\supset B)\&C$', you will be said to bracket the conditional. There -is an immediate syntactical issue. If you are asked to copy \ref{firstvib}, do you write -"Jack will soon leave and Bill will laugh if Don speaks"; or do you write -"Jack will soon leave, and Bill will laugh if Don speaks" if that is the way -you are reading \ref{firstvib} at the moment? A distinction has to be made between -reading the proposition, which involves bracketing; and viewing the -proposition, which involves reacting to the ink-marks solely as a pattern. -Thus, any statement about an ambiguous grouping proposition must specify -whether the reference is to the proposition as read or as viewed. - -Some additional conventions are necessary. With respect to \ref{firstvib}, we -distinguish two possibilities: you are reading it, or you are not looking at it -(or are only viewing it). Thus, a "single reading" of \ref{firstvib} refers to an event -which separates two consecutive periods of not looking at \ref{firstvib} (or only -viewing it). During a single reading, you may switch between bracketing the -conjunction and bracketing the conditional. These switches demarcate a -series of "states" of the reading, which alternately correspond to "Jack will -soon leave, and Bill will laugh if Don speaks" or "Jack will soon leave and Bill -will laugh, if Don speaks". Note that a state is like a complete proposition. -We stipulate that inasmuch as \ref{firstvib} is read at all, it is the present meaning or -state that counts---if you are asked what the proposition says, whether it is -true, \etc - -Another convention is that the logical status of -\begin{quotation} -(Jack will soon leave and Bill will laugh if Don speaks) if and only if (Jack -will soon leave and Bill will laugh if Don speaks) -\end{quotation} -is not that of a normal tautology, even though the biconditional when -viewed has the form '$A\equiv A$'. The two ambiguous components will not -necessarily be bracketed the same way in a state. - -We now turn to an example which is more substantial than \ref{firstvib}. - -Consider - -\begin{quotation} -Your mother is a whore and you are now bracketing the conditional in (2) if -you are now bracketing the conjunction in (2). (2) -\end{quotation} - -If you read this proposition, then depending on how you bracket it, the -reading will either be internally false or else will call your mother a whore. In -general, ambiguous grouping propositions are constructs in which the mental -aspect plays a fairly explicit role in the language. We have included (2) to -show that the contents of these propositions can provide more complications -than would be suggested by \ref{firstvib}. - -There is another way of bringing out the mental aspect of language, -however, which is incomparably more powerful than ambiguous grouping. -We will turn to this approach immediately, and will devote the rest of the -paper to it. The cubical frame \cubeframe\ is a simple reversible perspective figure -which can either be seen oriented upward like \cubeup\ or oriented downward -like \cubedown. Both positions are implicit in the same ink-on-paper image; it is -the subjective psychological response of the perceiver which differentiates -the positions. The perceiver can deliberately cause the perspective to reverse, -or he can allow the perspective to reverse without resisting. The perspective -can also reverse against his will. Thus, there are three possibilities: deliberate, -indifferent, and involuntary reversal. - -Suppose that each of the positions is assigned a different meaning, and -the figure is used as a notation. We will adopt the following definitions -because they are convenient for our purposes at the moment. - -$$ \cubeframe \left\{\parbox{4in}{for '3' if it appears to be oriented like \cubeup \linebreak -for '0' if it appears to be oriented like \cubedown}\right\} $$ - -We may now write - -\begin{equation} - \label{cubefour} -1+\cubeframe = 4 -\end{equation} - -We must further agree that \ref{cubefour}, or any proposition containing such -notation, is to be read to mean just what it seems to mean at any given -instant. If, at the moment you read the proposition, the cube seems to be -up, then the proposition means $1+3=4$; but if the cube seems to be down, -the proposition means $1+O=4$. The proposition has an unambiguous -meaning for the reader at any given instant, but the meaning may change in -the next instant due to a subjective psychological change in the reader. The -reader is to accept the proposition for what it is at any instant. The result is -subjectively triggered propositional vibration, or SPV for short. The -distinction between reading and viewing a proposition, which we already -made in the case of ambiguous grouping, is even more important in the case -of SPV. Reading now occurs only when perspective is imputed. In reading -\ref{cubefour} you don't think about the ink graph any more than you think about the -type face. - -in a definition such as that of '\cubeframe', '3' and 'O' will be called the -assignments. A single reading is defined as before. During a single reading, \ref{cubefour} -will vibrate some number of times. The series of states of the reading, which -alternately correspond to '$1+3=4$' or '$1+O=4$', are demarcated by -these vibrations. The portion of a state which can change when vibration -occurs will be called a partial. It is the partials in a reading that correspond -directly to the assignments in the definition. - -Additional conventions are necessary. Most of the cases we are -concerned with can be covered by two extremely important rules. First, the -ordinary theory of properties which have to do with the form of expressions -as viewed is not applicable when SPV notation is present. Not only is a -biconditional not a tautology just because its components are the same when -viewed; it cannot be considered an ordinary tautology even if the one -component's states have the same truth value, as in the case of '$1+\cubeframe\neq2$'. -Secondly, and even more important, SPV notation has to be present -explicitly or it is not present at all. SPV is not the idea of an expression with -two meanings, which is commonplace in English; SPV is a double meaning -which comes about by a perceptual experience and thus has very special -properties. Thus, if a quantifier should be used in a proposition containing -SPV notation, the "range" of the "variable" will be that of conventional -logic. You cannot write '\cubeframe' for '$x$' in the statement matrix -'$x=\cubeframe$'. - -We must now elucidate at considerable length the uniqué properties of -SPV. When the reader sees an SPV figure, past perceptual training will cause -him to impute one or the other orientation to it. This phenomenon is not a -mere convention in the sense in which new terminology is a convention. -There are already two clear-cut possibilities. Their reality is entirely mental; -the external, ink-on-paper aspect does not change in any manner whatever. -The change that can occur is completely and inherently subjective and -mental. By mental effort, the reader can consciously control the orientation. -If he does, involuntary vibrations will occur because of neural noise or -attention lapses. The reader can also refrain from control and accept -whatever appears. In this case, when the figure is used as a notation, -vibrations may occur because of a preference for one meaning over the -other. Thus, a deliberate vibration, an involuntary vibration, and an -indifferent vibration are three distinct possibilities. - -What we have done is to give meanings to the two pre-existing -perceptual possibilities. In order to read a proposition containing an SPV -notation at all, one has to see the ink-on-paper figure, impute perspective to -it, and recall the meaning of that perspective; rather than just seeing the -figure and recalling its meaning. The imputation of perspective, which will -happen anyway because of pre-existing perceptual training, has a function in -the language we are developing analogous to the function of a letter of the -alphabet in ordinary language. The imputation of perspective is an aspect of -the notation, but it is entirely mental. Our language uses not only -graphemes, but "psychemes" or "mentemes". One consequence is that the -time structure of the vibration series has a distinct character; different in -principle from external, mechanical randomization, or even changes which -the reader would produce by pressing a button. Another consequence is that -ambiguous notation in general is not equivalent to SPV. There can be mental -changes of meaning with respect to any ambiguous notation, but in general -there is no psycheme, no mental change of notation. It is the clear-cut, -mental, involuntary change of notation which is the essence of SPV. Without -psychemes, there can be no truly involuntary mental changes of meaning. - -In order to illustrate the preceding remarks, we will use an SPV -notation defined as follows. - -\begin{equation*} - \cubeframe \left\{\parbox{4in}{is an affirmative, read "definitely," if it appears to be oriented - like \cubeup\linebreak - is a negative, read "not," if it appears to be oriented like \cubedown}\right\} -\end{equation*} - -The proposition which follows refers to the immediate past, not to all past -time; that is, it refers to the preceding vibration. - -\begin{quotation} -You have \cubeframe deliberately vibrated (4). (4) -\end{quotation} - - -This proposition refers to itself, and its truth depends on an aspect of the -reader's subjectivity which accompanies the act of reading. However, the -same can be said for the next proposition. - -\begin{quotation} -The bat is made of wood, and you have just decided that the second -word in (5) refers to a flying mammal. (5) -\end{quotation} - - -Further, the same can be said for (2). We must compare (5), (2), and (4) in -order to establish that (4) represents an order of language entirely different -from that represented by (5) and (2). (5) is a grammatical English sentence -as it stands, although an abnormal one. The invariable, all-ink notation 'bat' -has an equivocal referental structure: it may have either of two mutually -exclusive denotations. In reading, the native speaker of English has to choose -one denotation or the other; contexts in which the choice is difficult rarely -occur. (2) is not automatically grammatical, because it lacks a comma. We -have agreed on a conventional process by which the reader mentally supplies -the comma. Thus, the proposition lacks an element and the reader must -supply it by a deliberate act of thought. The comma is not, strictly speaking, -a notation, because it is entirely voluntary. The reader might as well be -supplying a denotation io an equivocal expression: (5) and (2) can be -reduced to the same principle. As for (4), it cannot be mistaken for ordinary -English. It has an equivocal "proto-notation," '\cubeframe'. You automatically -impute perspective to the proto-notation before you react to it as language. -Thus, a notation with a mental component comes into being involuntarily. -This notation has an unequivocal denotation. However, deliberate, -inditferent, and most important of all, involuntary mental changes in -notation can occur. - -We now suggest that the reader actually read (5), (2), and (4), in that -order. We expect that (5) can be read without noticeable effort, and that a -fixed result will be arrived at (unless the reader switches in an attempt to -find a true state). The reading of (2) involves mentally supplying the comma, -which is easy, and comprehending the logical compound which . results, -which is not as easy. Again, we expect that a fixed result will be arrived at -(unless the reader vacillates between the insult and the internally false state). -In order to read (4), center your sight on the SPV notation, with your -peripheral vision taking in the rest of the sentence. A single reading should -last at least half a minute. If the reader will seriously read (4), we expect that -he will find the reading to be an experience of a totally different order from -the reading of (5) and (2). It is like looking at certain confusing visual -patterns, but with an entire dimension added by the incorporation of the -pattern into language. The essence of the experience, as we have indicated, is -that the original imputation of perspective is involuntary, and that the reader -has to contend with involuntary changes in notation for which his own mind -is responsible. We are relying on this experience to convince the reader -empirically that (4) represents a new order of language to an extent to which -(5) and (2) do not. - -To make our point even clearer, let us introduce an operation, called -"collapsing," which may be applied to propositions containing SPV -proto-notation. The operation consists in redefining the SPV figure in a given -proposition so that its assignments are the states of the original proposition. -Let us collapse (4). We redefine - -\begin{equation*} - \cubeframe \left\{\parbox{4in}{for 'You have deliberately vibrated (4)' if it appears to be oriented - like \cubeup\linebreak - for 'You have not deliberately vibrated (4)' if it appears to be oriented - like \cubedown}\right\} -\end{equation*} - -(4) now becomes - -\begin{quotation} -\cubeframe (4) -\end{quotation} - - -We emphasize that the reader must actually read (4), for the effect is -indescribable. The reader should learn the assignments with flash cards if -necessary. - -The claim we want to make for (4) is probably that it is the most -clear-cut case yet constructed in which thought becomes an object for itself. -Just looking at a reversible perspective figure which is not a linguistic -utterance---an approach which perceptual psychologists have already -tried---does not yield results which are significant with respect to "thought." -In order to obtain a significant case, the apparent orientation or imputed -perspective must be a proposition; it must be true or false. Then, (5) and (2) -are not highly significant, because the mental act of supplying the missing -element of the proposition is all a matter of your volition; and because the -element supplied is essentially an "understood meaning." We already have an -abundance of understood meanings, but scientists have been able to ignore -them because they are not "objectifiable." In short, reversible perspective by -itself is not "thought"; equivocation by itself has no mental aspect which is -objectifiable. Only in reading (4) do we experience an "objectifiable aspect -of thought." We have invented an instance of thought (as opposed to -perception) which can be accomodated in the ontology of the perceptual -psychologist. +Henry Flynt and Jack Smith demonstrate against the Metropolitan Museum of Art, +February 22, 1963 \\ +(foto\footnote{sic} by Tony Conrad) +} \clearpage -\end{document} diff --git a/essays/energy_cube1966.tex b/essays/energy_cube1966.tex index d925445..227738d 100644 --- a/essays/energy_cube1966.tex +++ b/essays/energy_cube1966.tex @@ -11,7 +11,7 @@ of liquid, near where they meet. There are no other objects in the bodies of liquid. The slab, liquid, and spaces are the energy cube organism's entire cosmology. (See the illustration.) -\img{energycube} +\imgw{3.75in}{img/energycube} The energy cube organism can continuously change position, continuously and instantly moving the liquid from its path into its wake so @@ -61,7 +61,7 @@ possible methods are in no special order. When a partial is added to the memory, the number of possible methods is increased by a factor equal to the new number of partials. -\img{energycubegraph} +\imgw{4in}{img/energycubegraph} { \centering diff --git a/essays/flaws_underlying_beliefs.tex b/essays/flaws_underlying_beliefs.tex index 0eda09e..31fe124 100644 --- a/essays/flaws_underlying_beliefs.tex +++ b/essays/flaws_underlying_beliefs.tex @@ -117,7 +117,7 @@ is no way to "go back before the natural language." As we mentioned before, the aphorism that "saying a thing is so doesn't make it so" is an example of the natural language's semantics in the natural language. -in summary, the crucial assertion is the assertion that there is language, +In summary, the crucial assertion is the assertion that there is language, made in the natural language. This assertion is true if it is meaningful. It is too true; it must be a definitional trick. Beliefs stand or fall on the question of whether there is language. There is no way to get outside the definitional diff --git a/essays/perception_dissociator.tex b/essays/perception_dissociator.tex index 69e1b59..e907883 100644 --- a/essays/perception_dissociator.tex +++ b/essays/perception_dissociator.tex @@ -98,7 +98,7 @@ and doesn't go back in. \textsc{Exhibit of a working model of a perception-dissociator (conceived by Henry Flynt)} -\img{guidebook} +\imgw{3.5in}{guidebook} \textsc{Read this guidebook as directed---straight through or as otherwise directed. Don't leaf around.} diff --git a/essays/philosophical_reflections.tex b/essays/philosophical_reflections.tex index 7abca34..41bf1ce 100644 --- a/essays/philosophical_reflections.tex +++ b/essays/philosophical_reflections.tex @@ -1,6 +1,6 @@ \chapter{Philosophical Reflections I} -\begin{enumerate} % TODO letters, sub numbers +\begin{enumerate}[label=\textbf{\Alph*.}, wide] \item If language is nonsense, why do we seem to have it? How do these intricate pseudo-significant structures arise? If beliefs are self-deceiving, why are they there? Why are we so skilled in the self-deceptive reflex that I find @@ -98,7 +98,7 @@ evidence. Our "immediate experience" is mediated; it is a derived phenomenon which only subsists in an objective reality that is outside our subjective standpoint. -\begin{enumerate} +\begin{enumerate}[label=\textbf{\arabic*.}, leftmargin=2em] \item But Alten does not seriously defend the claim that he does not distinguish between immediate and non-immediate. The claim that there is diff --git a/essays/post_formalism_memories.tex b/essays/post_formalism_memories.tex index bf7decc..9b77855 100644 --- a/essays/post_formalism_memories.tex +++ b/essays/post_formalism_memories.tex @@ -1,3 +1,6 @@ +\newcommand{\midheading}[1]{ + { \vskip 1em \centering \large \textsc{#1} \par \vskip 1em }} + \chapter{Post-Formalism in Constructed Memories} \section{Post-Formalist Mathematics} @@ -125,7 +128,7 @@ Compound indirect implication is a puzzle. Now for the first post-formalist system. -{ \centering \large "\textsc{Illusions}" \par} +\midheading{"Illusions"} \begin{sysrules} A "sentence" is the following page (with the figure on it) so long as the @@ -151,7 +154,7 @@ figures with a variety of real (measured) ratios and practicing judging these ratios; and so forth. \end{sysrules} -\img{illusions} +\imgw{2in}{img/illusions} "IIlusions" has Properties 1, 3--5, and 7--8. Purely to clarify this fact, the following sequence of integers is presented as a model of the order in which @@ -159,7 +162,7 @@ associated ratios might appear in reality. (The sequence is otherwise totally inadequate as a model of "Illusions.") 4 2 1; 4 2; 5 4 2 1; 4 3 1. The implication structure would then be -\img{illusionstructure} +\imgw{4in}{img/illusionstructure} The axiom would be 4, and 5 could not appear in a proof. "IIlusions" has Property 1 on the basis that one can control the associated ratio. Turning to @@ -202,7 +205,7 @@ notation, and that every system should be isomorphic to some ink-on-paper system. In so doing, Carnap violates his ov'n Principle of Tolerance. Consider the following trivial formalist system. -{ \centering \large "\textsc{Order}" \par} +\midheading{"Order"} \begin{sysrules} A "sentence" is a member of a finite set of integers. @@ -218,7 +221,7 @@ paragraph proved that it is not. The implication structure of "Order" is mechanical to the point of idiocy, while the implication structure of "Illusions" is, as I pointed out, elusive. The figure -\img{orderstructure} +\imgw{4in}{img/orderstructure} where loops indicate multiple occurances of the same sentence, could adequately represent a proof in "Order," but could not remotely represent @@ -229,7 +232,7 @@ onto the paper. This is utterly impossible. Here is the next system. -{ \centering \large "\textsc{Innperseqs}" \par} +\midheading{"Innperseqs"} \begin{sysrules} Explanation: Consider the rainbow halo which appears to surround a small @@ -261,20 +264,12 @@ members of preceding sequences. 3. All first members, of sequences other than the last two, appear as non-first members. 4. No sentence appears as a non-first member more than once. 5. The last sequence has one member. - -In the diagram on the following page, different positions of the vague outer -ring at different times are suggested by different shadings. The -outer segment moves "down the page." The figure is by no means -an innperseq, but is supposed to help explain the definition. \end{sysrules} -Successive bands represent the vague outer ring at successive times as it fades in -toward the small bright light. - -Innperseqs Diagram - -\img{innperseqs} +{\centering +\begin{minipage}{1.6in}\imgw{1.3in}{img/innperseqs}\end{minipage} + \begin{minipage}{2.25in} "Sentences" at \begin{tabular}{ c r l } @@ -318,7 +313,12 @@ $(d,b,a_6)$ $(e,c,a_7)$ $(f,e,d)$ $(g)$ + \end{minipage}\par} +In the diagram, different positions of the vague outer +ring at different times are suggested by different shadings. The +outer segment moves "down the page." The figure is by no means +an innperseq, but is supposed to help explain the definition. In "Innperseqs," a conventional proof would be redundant unless all the statements were on the same radius. And even if the weakest axiom were chosen (the initial outer endpoint), this axiom would imply the initial inner @@ -354,7 +354,8 @@ the mathematician's capabilities at a particular instant which delimit the indeterminacies. Precisely because of the difficulty of thinking sentences, I will give several subvariants of the system. -{ \centering \large \textsc{Indeterminacy} \par} +\midheading{Indeterminacy} + \begin{sysrules} A "totally determinate innperseq" is an innperseq in which one thinks all the sentences. @@ -384,7 +385,7 @@ one. (I have not combined the two essays because their approaches are too different.) I will define post-formalist systems in constructed memories, beginning with a system in an M*-Memory. -{ \centering \large "\textsc{Dream Amalgams}" \par} +\midheading{"Dream Amalgams"} \begin{sysrules} A "sentence" is a possible method, an $A_{a_i}$. with respect to an M*-Memory. @@ -445,13 +446,13 @@ study post-formalist modes of inference which are anything but deductive. To aid in understanding the next system, which involves infalls in a D-Memory, here is an -{ \centering \large \framebox[1.1\width]{"Exercise to be Read Aloud"} \par} +{ \vskip 1.5em \centering \large \framebox[1.1\width]{"Exercise to be Read Aloud"} \par\vskip 1.5em} (Read according to a timer, reading the first word at O' O", and prolonging and spacing words so that each sentence ends at the time in parentheses after it. Do not pause netween sentences.) -\begin{tabular}{ r l } +\begin{tabular}{ r p{2.5in} } ($event_1$) & All men are mortal. (17") \\ ($Sentence_1=event_2s$) & The first utterance lasted 17" and ended at 17"; and lasted 15" and ended 1" ago. (59") \\ @@ -467,10 +468,6 @@ is greater than the distance into the past to which it refers. This situation is not a real infall, but it should give the reader some intuitive notion of an infall. - -\newcommand{\midheading}[1]{ - { \centering \large \textsc{#1} \par}} - \midheading{"Infalls"} \begin{sysrules} @@ -485,7 +482,7 @@ thinking of $S^{D}_{j-1}$, ended at a distance $z_j$ into the past, where $z_j$ than $S^D_j$'s own duration. The diagram indicates the relations.) \end{sysrules} -\img{infallsdiag} +\imgw{4in}{img/infallsdiag} In this variety of D-Memory, the organism continuously thinks successive D-sentences, which are all different, just as the reader of the above exercise @@ -547,7 +544,7 @@ preceding the-first (second, third) period in the entire series. \begin{sysrules} A "sentence" is a the duration D-sentences $\triangle\ (\mathparagraph^m)$ conclude these -"$\Phi*$-Reflection," or the future Assumption voluntarily force of +"$\Phi^*$-Reflec\-tion," or the future Assumption voluntarily force of conviction for conclusion the Situation or by ongoing that this system? be given telling between the Situation 1. @@ -555,11 +552,11 @@ Two sentences "imply" a third if and only if the two sentences is\slash was contained not have to the acceptance that a certain and malleable study what an event involves material specifically mathematics: construct accompanies the rest, extra-linguistically image organism -can fantasy not remembering $\Phi*$-Memory, the future interval defined +can fantasy not remembering $\Phi^*$-Memory, the future interval defined in dream the third. An "axiom" is a sentence that internally D-sentences, just as the -"$\Phi*$-Memory" sentences $A_{a_1}$ is $A_{a_2}$. +"$\Phi^*$-Memory" sentences $A_{a_1}$ is $A_{a_2}$. In the final stage, I cancel the smallest number of words I have to in order to make the rules grammatical. diff --git a/essays/studies_in_constructed_memories.tex b/essays/studies_in_constructed_memories.tex index 80303cd..2612ead 100644 --- a/essays/studies_in_constructed_memories.tex +++ b/essays/studies_in_constructed_memories.tex @@ -54,7 +54,7 @@ Consider the memory that I was almost run down by a truck yesterday: I could have been run down, but wasn't. In such a case, the possibility that I could have been run down would be more vivid than the actuality that I wasn't. (Is it not insanity, when a person is overwhelmed by the fear of a -merely possible past event? ) My hold on sanity here would be the awareness +merely possible past event?) My hold on sanity here would be the awareness that I am alive and well today. In dreams, do we not wholeheartedly "remember" that a misfortune @@ -227,7 +227,7 @@ By definition. \conclusion{3.2} An M-Memory has to occur within the time which the possible methods require, the time required to accomplich G. By definition. -\definition An "M*-Memory" is an M-Memory satisfying these +\definition An "$M^*$-Memory" is an M-Memory satisfying these conditions. \begin{enumerate} \item $A_{a_i}$, for the entire time it requires, involves the voluntary @@ -237,7 +237,7 @@ possible methods, the cross-method contact, is specifically some sort of contact between states. \end{enumerate} -\conclusion{3.3} For an M*-Memory, to remember is to choose the +\conclusion{3.3} For an $M^*$-Memory, to remember is to choose the mental state in which the remembering is required to occur (by the memory). After all, for any M-Memory, to remember is to choose all the $A_{a_i}$-required things you are doing while you remember. @@ -375,7 +375,7 @@ could be greater than $x_{j+1}-x_j$. But since $S_j$ goes into the preconscious $S_j$ is not actually thought in the earliest interval during which it could be thought. See the diagram. -\img{dmemdiag} +\imgw{4in}{img/dmemdiag} \conclusion{6.4} Let there be an \textsc{infall} in the case where $event_{j+1}$ is the thinking of $S_j$. $\delta(S_j)=x_{j+1}-x_j$ and $\delta(S_j)\greater z_j$. $S_{j+1}$ gives $\delta(S_j)$, @@ -388,10 +388,10 @@ to be one of the events for the organism to be aware of the infall. \section{$\Phi$-Memories} I will conclude these studies with two complex constructions. -\definition A "$\Phi$-Memory" is a memory which includes an M*-Memory +\definition A "$\Phi$-Memory" is a memory which includes an $M^*$-Memory and a D-Memory, with the following conditions. \begin{enumerate} -\item The goal G, for the M*-Memory, is to move from one point to another. +\item The goal G, for the $M^*$-Memory, is to move from one point to another. \item For the D-Memory, "$event_j$" becomes a numerical term, the decrease in the organism's distance from the destination point during the temporal interval. \said{A 3-inch move @@ -415,28 +415,28 @@ $$ \triangle(\mathparagraph^m)=\sum_{j=1}^{m} \delta_j $$ The permutations of the D-sentences, as well as the D-paragraphs, can be indexed with the $a_i$, just as the possible methods are. -Definition. A "$\Phi*$-Memory" is a $\Phi$-Memory in which the order of the +Definition. A "$\Phi^*$-Memory" is a $\Phi$-Memory in which the order of the sentences in the $a_i$th $\mathparagraph^m$ has the meaning of \said{I have actually been doing $A_{a_i}$} assigned to it. The order is the indication that $A_{a_i}$ has actually been used; it -is the $a_j$th M*-assertion. \said{I have actually been doing $A_{a_i}$} is merely an English -translation, and does not appear in the $\Phi*$-Memory. +is the $a_j$th $M^*$-assertion. \said{I have actually been doing $A_{a_i}$} is merely an English +translation, and does not appear in the $\Phi^*$-Memory. -\conclusion{7} Given a $\Phi*$-Memory, if one D-sentence is forgotten, not +\conclusion{7} Given a $\Phi^*$-Memory, if one D-sentence is forgotten, not only will there be a gap in the awareness of when what events occurred; it will be forgotten which method has actually been used. This conclusion points toward a study in which deformations of the memory language are related to deformations of general consciousness. -\definition A "$\Phi*$-Reflection," or reflection in the present of a -$\Phi*$-Memory, is a collection of assertions about the future, derived from a -$\Phi*$-Memory, as follows. +\definition A "$\Phi^*$-Reflection," or reflection in the present of a +$\Phi^*$-Memory, is a collection of assertions about the future, derived from a +$\Phi^*$-Memory, as follows. \begin{enumerate} \item There are the sentences "$Event_j$ will occur in the interval of time which is $x_j-x_{j-1}$ long, and begins at twice the present time $AF$, minus $x_j AF$; and which is $y_j$ long and begins $z_j$ from now." If $event_j$ was -a 3-inch move toward the destination in the "$\Phi*$-Memory, the sentence in the -$\Phi*$-Reflection says that a 3-inch move will be made in the future temporal +a 3-inch move toward the destination in the "$\Phi^*$-Memory, the sentence in the +$\Phi^*$-Reflection says that a 3-inch move will be made in the future temporal interval. \item The $a_i$th permutation of the sentences defined in (1) is an assertion which has the meaning of \said{I will do $A_{a_i}$}; and the organism can @@ -445,7 +445,7 @@ defined as before (so that in particular the permutations can be indexed with the $a_i$). \end{enumerate} -\conclusion{8} Given that the $\Phi*$-Memory's temporal intervals $|x_{j-1}, x_j|$ +\conclusion{8} Given that the $\Phi^*$-Memory's temporal intervals $|x_{j-1}, x_j|$ are reflected as $|2N-x_j, 2N-x_{j-1}|$, the reflection preserves the intervals' absolute distances from the present. @@ -453,13 +453,13 @@ absolute distances from the present. from $N$ is $N-x_j$; the greatest distance is $N-x_{j-1}$. Adding the least distance, and then the greatest distance, to $N$, gives $|2N-x_j, 2N-x_{j-1}|$. -I will end with two problems. If a $\Phi*$-Memory exists, under what -conditions will a $\Phi*$-Reflection be a precognition? Under what conditions +I will end with two problems. If a $\Phi^*$-Memory exists, under what +conditions will a $\Phi^*$-Reflection be a precognition? Under what conditions will every assertion be prescience or foreknowledge? By a "precognition" I don't mean a prediction about the future implied by deterministic laws; I mean a direct "memory" of the future unconnected with general principles. -Finally, what would a precognitive $\Phi*$-Reflection be like as a mental +Finally, what would a precognitive $\Phi^*$-Reflection be like as a mental experience? What present or ongoing awareness would accompany a -precognitive $\Phi*$-Reflection? +precognitive $\Phi^*$-Reflection? diff --git a/essays/walking_through_walls.tex b/essays/walking_through_walls.tex index b45f201..04ec9d2 100644 --- a/essays/walking_through_walls.tex +++ b/essays/walking_through_walls.tex @@ -135,7 +135,7 @@ object Gestalt."} From a different traditon, the critique of scientific fact and of measurable time which is suggested in Luk\'{a}cs' \booktitle{Reification and the -Consciousness of the Proletariat} might be of value if it were developed.\footnote{Lulkacs also implied that scientific truth would disappear in a communist +Consciousness of the Proletariat} might be of value if it were developed.\footnote{Luk\'{a}cs also implied that scientific truth would disappear in a communist society---that is, a society without necessary labor, in which the right to subsistence was unconditional. He implied that scientific quantification and facticity are closely connected with the work discipline required by the diff --git a/img/illusions.png b/img/illusions.png Binary files differindex 28eb282..e6dca1c 100644 --- a/img/illusions.png +++ b/img/illusions.png diff --git a/img/illusionstructure.png b/img/illusionstructure.png Binary files differindex 9720f16..29d435f 100644 --- a/img/illusionstructure.png +++ b/img/illusionstructure.png diff --git a/salitter.sty b/salitter.sty index 0aeae06..0c64324 100644 --- a/salitter.sty +++ b/salitter.sty @@ -38,6 +38,10 @@ \includegraphics[scale=1]{#1} \end{center}} +\newcommand{\imgw}[2]{ + {\centering\vskip 1em\includegraphics[width=#1]{#2} + \vskip 1em\par}} + % ---- font (antiqua) \newcommand{\antiquafont}[0]{ @@ -66,7 +70,7 @@ % ---- metadata for a title page \newcommand{\visbreak}{ - \fancybreak{{*}\\{* * *}\\{*}}} + \fancybreak{\vskip 1em {$\diamond$ \hskip 0.5in $\star$ \hskip 0.5in $\star$ \hskip 0.5in $\diamond$}\vskip 1em}} % ---- semantic punctuation, etc % quoting a word when speaking of a word itself |
