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diff --git a/essays/dissociation_physics.tex b/essays/dissociation_physics.tex new file mode 100644 index 0000000..e60d685 --- /dev/null +++ b/essays/dissociation_physics.tex @@ -0,0 +1,4718 @@ +\chapter{1966 Mathematical Studies} + +% 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} + +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 + + +\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. + +\end{document} |