From 8548929f5fcdc5dde833337247b223ce614a8199 Mon Sep 17 00:00:00 2001
From: grr <grr@lo2.org>
Date: Thu, 2 May 2024 20:51:35 -0400
Subject: para-science breakout

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+\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}
-- 
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