From 8548929f5fcdc5dde833337247b223ce614a8199 Mon Sep 17 00:00:00 2001 From: grr Date: Thu, 2 May 2024 20:51:35 -0400 Subject: para-science breakout --- essays/studies_in_constructed_memories.tex | 465 +++++++++++++++++++++++++++++ 1 file changed, 465 insertions(+) create mode 100644 essays/studies_in_constructed_memories.tex (limited to 'essays/studies_in_constructed_memories.tex') diff --git a/essays/studies_in_constructed_memories.tex b/essays/studies_in_constructed_memories.tex new file mode 100644 index 0000000..80303cd --- /dev/null +++ b/essays/studies_in_constructed_memories.tex @@ -0,0 +1,465 @@ +\chapter{Studies in Constructed Memories} + +\section{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. + +\section{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. + + +\section{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\ ? 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. + +\section{$\Phi$-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? + -- cgit v1.2.3