diff options
Diffstat (limited to 'essays/dissociation_physics.tex')
| -rw-r--r-- | essays/dissociation_physics.tex | 5029 |
1 files changed, 320 insertions, 4709 deletions
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} |