\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}
