On engrams

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The following note on engrams was inserted Jan. 27, 2023.

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Assuming the existence of one or more types of engram, or fundamental memory unit, it is to be expected that the process of association implies some form of energy value attached to engram links. A --> B says that basic memory A instigates basic memory B, not not necessarily the converse. A <--> B means A instigates B and B instigates A, whichever is triggered first.

But, under what conditions does A --> B? The link value must exceed that of competing possibilities, such as R --> S. In most situations, this means that A and B are sets, indeed subsets of engrams. So A --> B requires that A ⊆ X and B ⊆ Y, so that X ∩ Y = AB. The strength of the association between X and Y is determined by the subset of common links.

I suppose a way to represent engram associations and sets of associations would be with a weighted graph.

(A --> B) <--> C is a possible way to write of simple associations. Obviously association sets become very complicated.

In any case, suppose we have A --> B and A --> C, but the AB link is far stronger than the AC link. So we have AB >> AC, whereas if the link magnitudes are roughly equal, we have AB ~ AC.

Freud on telepathy

First published Oct. 10, 2013.
An amended copy published on Substack Jan. 18, 2023.
The version below has been further amended, tho not extensively.

Following Kant, I have taken lately to using the terms "noumena" and "noumenal world" to describe the reality behind the phenomenal world of appearances.

If one concedes a noumenal world, does not that open a Pandora's box of delusional thinking from untutored enthusiasts? Unfortunately, that is the case. In fact this is why Ernest Jones, Freud's collaborator, reportedly urged Freud to tone down discussion of phenomena known under the heading of telepathy. Freud however revealed his thoughts in an article, Dreams and Telepathy, that appeared in Imago, a journal for Freudian ideas in society and culture, in 1922 and in New Introductory Lectures on Psycho-analysis (Chapter 2, Dreams and the Occult, Lecture XXX) that was published in 1933.

In the Introductory Lectures, Freud points out that if one were to say the earth's core contains carbonic acid, that idea would be viewed with suspicion, but as not altogether inconceivable. However, if one claimed the core is composed of jam, we have a right to dismiss the claim out of hand, jam coming from human actions on fruit. So, though one is entitled to reject some claims prior to examination, Freud is concerned that claims about occult phenomena may sometimes be rejected too quickly. He recalled the negative reaction that greeted his ideas about unconscious influences and sexual impulses.

In this light, Freud cites the scientific derision that greeted those who claimed that certain rocks found on the ground had fallen from the sky or that shells found on mountains implied that that terrain had once been seabed.

Using the term "occult" in the sense of unseen influences without suggesting a spirit domain, Freud sees much of occultist literature as representing a reflection of the anti-rationalism found among humans. Even scientists, after the conference is over, enjoy poking fun at their own activities; serious men enjoying a joke (and, as Freud observed, jokes reflect a need of the unconscious for irrationality, relief from "control"). So Freud is saying that occultist literature often expresses the strong anti-rationalist impulses common to all humans. We like to suspend the cold laws of nature, the machine-side of existence.

He grants that it may be "hard to avoid suspicion that the interest in occultism is a religious" ploy to overturn hard science, whereby the occultists are secretly trying to aid religion, but he argues, "at some point, we must overcome our disinclinations."

A problem is that "we are told that in fact our unbelieving -- that is to say, critical -- attitude may prevent the expected phenomena from happening." Freud is talking here about seances and mediums, most of whom he sees as charlatans. However, as pointed out in my paper, Toward a Signal Model of Perception, the reality construction process described there could very well be limited by negative belief.

Toward a signal model of perception
http://paulpages.blogspot.com/2013/03/toward-signal-model-of-perception.html

At any rate, Freud sees a "real core of yet unrecognized facts in occultism around which cheating and phantasies have spun a veil which is hard to pierce."

In the particular case of telepathy, most reported instances can be dismissed, he says. But a few remain that are hard to wave away. Freud insists he remains neutral on the subject, but it is clear that he is quite persuaded of something odd going on.

He asserts that in a telepathic dream the telepathic element plays the same role as any other residue (dream "trigger") of the day.

Freud gives an example of a man who dreamed his wife had twins; not long after, his daughter, who was some distance away, gave birth to twins (this was in the era before technology might have tipped him off). Freud weighs in with a psychoanalytic explanation, but nevertheless concedes what appears to be a telepathic element, which even so may have a natural explanation.

Freud's discussion of another situation -- his patient P's thought transference with respect to "Dr. Forsyth" -- would be dismissed by many probabilists on the random coincidence idea as discussed in Toward. However, it is often the case that those who have such experiences as described by Freud regard them as meaningful. There is a "shock of recognition" or a "strumming of an inner cord" that in my estimate may sometimes equate to a realization that we are seeing some effect of a noumenal world. Jung gave the name synchronicity to effects of the noumenal world; others describe such effects as the work of the realm of spirits. I could defend the idea of spirit as that part of the personality that inhabits the noumenal world, analogous to a software program inhabiting a mainframe computer. If the software program were conscious, it would not directly relate to the mainframe.

"One is led to the suspicion," maintains Freud, that telepathy is "the original, archaic method of communication between individuals and in the course of phylogenetic evolution it has been replaced with the better method of giving information via signals which are picked up by the sense organs."

Freud relates a report of Dorothy Burlingham, a psychoanalyst and "trustworthy witness." (She and colleague Anna Freud did pioneering work in child psychology.)

A mother and child were in analysis together. One day she spoke during analysis of a gold coin that had played a particular part in one of her childhood experiences. On returning home, her boy, who was about 10, came to her room and gave her a gold coin which he asked her to keep for him. Astonished, she asked him where he had got it. It turned out that it had been given him as a birthday present a few months previously, but there was no obvious reason why he had chosen that time to bring her the coin.

Freud sees this report as potential evidence of telepathy. One might also suspect it as an instance of "synchronicity" or the reality construction process described in Toward.

At any rate, a few weeks later the woman, on her analyst's instructions, sat down to write an account of the gold coin incident. Just then her child approached her and asked for his coin back, as he wanted to show it during his analysis session.

Freud argues that there is no need for science to fear telepathy (though his collaborator, Ernest Jones, certainly seems to have feared the ridicule the subject might bring); he is even open-minded about other paranormal phenomena. His suspicion that such phenomena are occurring via some unknown pathway never convinced him to renounce his atheism.

At the end of his earlier paper, Dreams and Telepathy, Freud wrote, "Have I given you the impression that I am secretly inclined to support the reality of telepathy in the occult sense? If so. I should very much regret that it is so difficult to avoid giving such an impression. In reality, however, I was anxious to be strictly impartial. I have every reason to be so, for I have no opinion; I know nothing about it."

Clearly his opinion had evolved over the years. Yet when he denied "occult" phenomena, he meant to deny the spirit domain, the mystical. The trouble is that since he knew nothing about the physics of telepathy, he could not help but seem sympathetic to the mystics.

From our perspective, we argue that reports of "paranormal" communication and other such phenomena tip us off to an interaction with a noumenal world that is the reality behind appearances -- appearances being phenomena generally accepted as ordinary, whether or not unusual.

Freud, of course, was no mathematician and could only give what seemed to him a reasonable assessment of what was going on. J.M. Keynes's view was similar to Freud's. He was willing to accept the possibility of telepathy but rejected the "logical limbo" of explaining that and other "psychic phenomena" with other-worldly spirits.

Many scientists, of course, are implacably opposed to the possibility of telepathy in any form, and there has been considerable controversy over the validity of statistical studies for and against such an effect.

On the other hand, Nobelist Brian Josephson has taken on the "scientific system" and upheld the existence of telepathy, seeing it as a consequence of quantum effects.

Josephson's page of psychic phenomena links
http://www.tcm.phy.cam.ac.uk/~bdj10/psi.html

Footnote JH.36

Footnote JH.36: A useful discussion of this contentious issue is found in The Classical Mind by W.T. Jones (2d ed. of Vol. I of A History of Western Philosophy, Harcourt Brace Jovanovich 1970).

Toward footnote Xz.151

Added Jan. 19, 2023

Footnote Xz.151.

Freud in The Interpretation of Dreams (1914 translation by A.A. Brill) highlights the idea that the difference between waking reality and dream reality stems from "tests" applied by the awake-state's reality perceiver.

In fact, when such tests fail, the perceiver is deemed to be hallucinating and-or suffering from delusive notions. (Still, one must concede that it can occur that the "ailing" person perceives that our reality is faulty, being based on flawed tests -- as with the assumption that "our government officials would never collude to tell us a monstrous lie.")

It is a question now of attempting to explain the credulity of the mind in reference to the dream hallucinations, which can only appear after the suspension of a certain arbitrary activity. Strümpell asserts that the mind behaves in this respect correctly, and in conformity with its mechanism. The dream elements are by no means mere presentations, but true and real experiences of the mind, similar to those that appear in the waking state as a result of the senses (p. 34). Whereas in the waking state the mind represents and thinks in word pictures and language, in the dream it represents and thinks in real tangible pictures (p. 35). Besides, the dream manifests a consciousness of space by transferring the sensations and pictures, just as in the waking state, into an outer space (p. 36). It must therefore be admitted that the mind in the dream is in the same relation to its pictures and perceptions as in the waking state (p. 43). If, however, it is thereby led astray, this is due to the fact that it lacks in sleep the criticism which alone can distinguish between the sensory perceptions emanating from within or from without. It cannot subject its pictures to the tests which alone can prove their objective reality. It furthermore neglects to differentiate between pictures that are arbitrarily interchanged and others where there is no free choice. It errs because it cannot apply to its content the law of causality (p. 58). In brief, its alienation from the outer world contains also the reason for its belief in the subjective dream world.

But how important are such tests?

Delbœuf reaches the same conclusion through a somewhat different line of argument. We give to the dream pictures the credence of reality because in sleep we have no other impressions to compare them with, because we are cut off from the outer world. But it is not perhaps because we are unable to make tests in our sleep, that we believe in the truth of our hallucinations. The dream may delude us with 43all these tests, it may make us believe that we may touch the rose that we see in the dream, and still we only dream. According to Delbœuf there is no valid criterion to show whether something is a dream or a conscious reality, except—and that only in practical generality—the fact of awakening. “I declare delusional everything that is experienced between the period of falling asleep and awakening, if I notice on awakening that I lie in my bed undressed” (p. 84). “I have considered the dream pictures real during sleep in consequence of the mental habit, which cannot be put to sleep, of perceiving an outer world with which I can contrast my ego.”

The criterion for awake-state reality seems to be heightened alertness and cohesive sense of self. When self-cohesion is weak, the person is often perceived as "troubled" or perhaps "dreamy" and possibly in need of psychiatric attention.

What lies at the root of the awake sense of self? An old notion is that in a timeless noumenal realm a being exists, which is denominated as "the soul." Even if true, we would have here only a glimmering of the problems associated with reality construction.

Toward Footnote GA156

Footnote GA156 (added Jan. 18, 2023):

Consider this passage from The Interpretation of Dreams by Sigmund Freud (A.A. Brill's 1914 translation):

If we read, e.g., three of Hildebrandt’s “Alarm Clock Dreams,” we will then have to inquire why the same stimulus evoked so many different results, and why just these results and no others.

 “I am taking a walk on a beautiful spring morning. I saunter through the green fields to a neighbouring village, where I see the natives going to church in great numbers, wearing their holiday attire and carrying their hymn-books under their arms. I remember that it is Sunday, and that the morning service will soon begin. I decide to attend it, but as I am somewhat overheated I also decide to cool off in the cemetery surrounding the church. While reading the various epitaphs, I hear the sexton ascend the tower and see the small village bell in the cupola which is about to give signal for the beginning of the devotions. For another short while it hangs motionless, then it begins to swing, and suddenly its notes resound so clearly and penetratingly that my sleep comes to an end. But the sound of bells comes from the alarm clock.”

“A second combination. It is a clear day, the streets are covered with deep snow. I have promised to take part in a sleigh-ride, but have had to wait for some time before it was announced that the sleigh is in front of my house. The preparations for getting into the sleigh are now made. I put on my furs and adjust my muff, and at last I am in my place. But the departure is still delayed, until the reins give the impatient horses the perceptible sign. They start, and the sleigh bells, now forcibly shaken, begin their familiar janizary music with a force that instantly tears the gossamer of my dream. Again it is only the shrill sound of my alarm clock.”

Still a third example. “I see the kitchen-maid walk along the corridor to the dining-room with several dozen plates piled up. The porcelain column in her arms seems to me to be in danger of losing its equilibrium. ‘Take care,’ I exclaim, ‘you will drop the whole pile.’ The usual retort is naturally not wanting—that she is used to such things. Meanwhile I continue to follow her with my worried glance, and behold! at the door-step the fragile dishes fall, tumble, and roll across the floor in hundreds of pieces. But I soon notice that the noise continuing endlessly is not really a rattling but a true ringing, and with this ringing the dreamer now becomes aware that the alarm clock has done its duty.”

Here we note that the dream construction appears to extend time backward. That is, the stimulus of the external sound is seemingly "forgotten" long enough for the formation of a passage of dream time.

These dream reports demonstrate the principle of dream reality construction that includes a sense of presence and an "unfolding of history" or passage of time. That is, the dream self invents its own history and dwells within it as if it is within a flow of objective time. The "now" of the dream self is out of synchrony with the "now" of the waking self.

Of course, we must concede another possibility: that the dreamer's body is precisely clocking the passage of linear time (as with a computer clock) and is somehow anticipating the alarm and so signals the self to begin preparing to wake up. In that case, a part of the person's mind-body system is setting up a defense against too much of a wake-up shock. Further, that would appear to be a motive for the first case. By "forgetting" the noise and inventing a dream reality, the mind-body system avoids what it regards as too forceful a transition into the unforgiving world of "cold reality," where it is no longer free to easily express its impulse life.

In fact, there is reason to suspect that both forms of mentation occur, tho not usually simultaneously.

Freud goes on:

The following dream of Maury[48] has become celebrated. 21He was sick, and remained in bed; his mother sat beside him. He then dreamed of the reign of terror at the time of the Revolution. He took part in terrible scenes of murder, and finally he himself was summoned before the Tribunal. There he saw Robespierre, Marat, Fouquier-Tinville, and all the sorry heroes of that cruel epoch; he had to give an account of himself, and, after all sort of incidents which did not fix themselves in his memory, he was sentenced to death. Accompanied by an enormous crowd, he was led to the place of execution. He mounted the scaffold, the executioner tied him to the board, it tipped, and the knife of the guillotine fell. He felt his head severed from the trunk, and awakened in terrible anxiety, only to find that the top piece of the bed had fallen down, and had actually struck his cervical vertebra in the same manner as the knife of a guillotine.

This dream gave rise to an interesting discussion introduced by Le Lorrain and Egger in the Revue Philosophique. The question was whether, and how, it was possible for the dreamer to crowd together an amount of dream content apparently so large in the short space of time elapsing between the perception of the waking stimulus and the awakening.

From the perspective of the awake state, the "internal clock" explanation will not do. The "crowding" surely implies that the dreamer invented a reality that projected "back in time" from the rude interruption from the external world. The dream self proceeded down an invented time stream. The dream's self's "now" was encased in a flow of time that was invented by the organism's psyche. The Maury dream's "crowding" idea, Freud adds, has been countered by "many arguments." We may suspect that the objection refers to the back formation of a time flow.

Yet, we must concede the possibility of a false memory of a dream sequence that was concocted after the intrusion of the external stimulus. But such an explanation is incomplete without accounting for the purported experiencing of the subjective passage of time.

Are the reals actually well-ordered?

The well-ordering theorem, also known as Zermelo's theorem, says that every set can be well-ordered. A set X is well-ordered by a strict total order if every non-empty subset of X has a least element under the ordering.

A strict total order on a set X is a strict partial order on X in which any two elements are comparable. That is, a total order is a binary relation < on some set X, which satisfies the following for all a,b and c in X:

Not a < a (irreflexive).
If b < c and a < b, then a < c (transitive).
If a =/= b, then a < b or b < a (connected).

Zermelo's approach was to argue that each element of a set could be withdrawn from it sequentially and then, if necessary, put into correspondence with a set controlled by the < relation. That is, the members of X are ranked in accordance with Y, a set of numbers ordered by <.

In the point set (0,1] it is obvious that no smallest number can exist after 0.

That is, lim_n-->inf. rⁿ = 0. Otherwise, rⁿ --> rⁿ⁺¹. That is a "small number" always implies a yet smaller number. Or see the epsilon-delta proofs.

But then, the same applies to any real, not only 0, that appears in the point set [0,1].

This then means that if there is a smallest set after 0, that set must be empty -- which would violate the well ordering concept. Only if we permit well-ordering to mean that any two members of a set imply a strict ordering, are we out of the woods.

Consider:

x₁ < x₂ -->
x₂ < x₃ -->
.
.
.
x_n-1 < x_n

That is, redefining well-ordering and using ordinary mathematical induction should help.

Of course, it has been argued that the axiom of choice proves well-ordering (in first order logic). I suppose that would mean if we have a set of ever smaller elements, we should be able to pick out one by some metaphysical method and call that the smallest. Rather than go to that length, I prefer a modified definition of well-ordering. In fact, all we really need to say is that any two members of a set of numbers obey the relation <, as in a < b or b < a. That is, ALLx e R(x_a < x_b or the converse).

Where are the non-computablesin the binary tree picture of the reals?

 

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NOTE. Occasionally, over the years, I have published discussions of the binary tree picture of the reals. This post continues in that vein.

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We accept the idea that the set of decimal extensions is bijective with the reals. For convenience, we convert to the base-2 number system, such that the reals are comprhended by the set of binary extensions.

To help us in our intuition, we employ a binary tree with a denumerable infinity of stages/levels. That is, at each level is a set of 2ⁿ nodes, or branching points. At level 1, there are 2 nodes...at level 10, 1024 nodes... Every left branch is designated 1 and every right branch 0.

Example: At level 3, we have,

  
  L R L R L R L R
  
  which is equivalent to
  
  1 0 1 0 1 0 1 0
  
  

The complete set of stages corresponds to the set of natural numbers N. The number of nodes in the "final" stage is taken to be 2^ℵ_o.

Hence, we see that every path is well-ordered. (But AC is needed to tell us those distinct paths reach the "bottom" stage.) Now we know from the Goedel and Turing theorems that the cardinality of the computables is ℵ_o, which is that of N.

It is also evident that every rational is represented as a finite digit string that recurs infinitely often. That is a set of all 0's means 0; a set of all 1's means 1; a finite string of 0's and 1's that is either followed by all 0's or that recurs infinitely often means some rational.

In addition, we have the set of computable irrationals. This means there exists at least one procedure that converts a numerical input into some 1's and-or 0's without ever doing so periodically and that this procedure is infinitely (or indefinitely) recursive, as in f(x) = x_next.

Now each path, up to any finite level, we must construe as a proto-number. All one can prove about any such path one follows is that if we know the algorithm, we can say whether the number is rational or irrational. And, if one does not know the algorithm, all one can say is that -- thus far -- the number is computable, as it can be defined stage by stage. In fact, at any finite level, the path has thus far been computed. So there is really no way to discern a noncomputable from the ordinary perspective.

But if we accept that the power set of N exists, in that case it must be that the "bottom line" point set of 2^ℵ_o "originates" the non-computables.

That could only mean, I suggest, that there must be many digit strings (from the "top" or "our" perspective) followed by an infinity of 0's that are then followed by a "finite" (from "bottom" perspective) string of 0's and 1's.

Such numbers are said to be undefined because their paths vanish as they climb skyward. Their paths all converge to the number 2. But they have vanished "before" coming into our finite range.

I concede such talk is inexact. Our language is unsuited for such conceptualization. Yet, I suggest, that intuitively we can discern that the "bottom up" paths must contain the non-computables, but that we cannot, from "top down" obtain them.

This picture does not suggest much beyond what is already known: that the continuum hypothesis is independent of the axioms of standard set theory.

A way to think about that is to note that the set of the computables K and its complement K^c comprise the reals. And R\K is equinumerous to R.

But we must use AC to "pick out" an arbitrary x ∈ K^c because there is no method in our posession for specifying any x. That is, if we define K^c by its elements, we say K^c is defined such that x is not definable. This is almost an abuse of the usual set notation {x|x ... }, which means that "any element x is defined..." So for K^c we have {x|x is undefinable}. That expression, to me, makes clear why CH is such an elusive beast.