Making science relative to a cognitive subject by vincent douzal

Dear Michel,

Your comments are challenging, because the content of the article you refer to involves many technicalities that you connect in a broad way, and require much thinking. I shall need more time to ponder it carefully.

However it is striking that you mention many phenomena, like phase-locking (which bear many pertinent analogies in biology, like the capture effect in perception, e.g., by one of two possibilities in an ambiguous figure; the term is also used when two close sounds are heard blend in just one), or the definition of a perceptual continuum by Poincaré --which I wanted to mention in my essay, but eventually did not by lack of space, and because it was not absolutely necessary. As I understand it, Poincaré made the perceptual continuum the root of our concept of continuity, which we end up representing by the real numbers (after many centuries). Hence "is the world continuous or discrete" is not a question in the framework I adopt, but by all means, the world appears to us as a continuum, and that is what our representations must cope with.

It is interesting how you connect things from the `top'. My attempt is less specialised, more basic, more abstract and general, and from the bottom. The starting point is elementary: Mach for instance has clearly stated that "It is utterly beyond our power to measure the changes of things by time. Quite the contrary, time is an abstraction at which we arrive through the changes of things." There is no way to `have' any sort of time elapsed if no change is witnessed, and the primary change (even if nothing happens within the restricted frame of attention of an experiment), is that you remember, that is, to make it clear and observable, you had written something, and now you write down something else. That is time, in its most elementary form. It is quite general: a lake that is silting, a tree growing, a wrinkled face, words cumulating on a sheet of paper, all are occurrences of visible time, recorded time.

And just by the same token, any measurement implies a change, recording a change: the hand of the clock was there when the race started, and is now there when the race finishes. The first end of the measure tape is there at the end of the table, and now I see the mark at the other end of the table.

As for the groups you mention, I am again at the lowest possible level. I regard with much interest the sort of results you mention, but I am far from the involved topics of Bost, Connes and the monster group. However, to my knowledge (I have not made specific researches) at least since Tits, mathematicians have felts that the idea of being the same, similarity, classes, etc., which are of course at the core of perception and cognition, are strongly represented by the concept of group, or symmetry. For instance, Eleanor Rosch, or Lakoff have discussed `categories' in cognition; but earlier Uexküll has clearly shown how the world of each animal can be seen as made of different categories, or signs, and inspires very much semiotics and its roots in biosemiotics now (see Semiotica 134:1-4); and even much earlier, Aristotle has put in very clear words that the identity (sameness) of things, and the relativity to the cognitive subject. In the words of Ross' Aristotle book: (The first principles of demonstration): "If either the object or the percipient's body undergoes certain changes a different sensum is produced. [...] the fact that I now call sweet an object which before I called bitter only shows that either the object or something in my body has changed." And even before, The Fragments of Heraclites show that he had identified how much the notion of sameness, or symmetry (or group) is important to cognition, since "you cannot step twice into the same river" means simultaneously that it is the same, and not the same, depending on the point of view. So here again I stick at an elementary, but fundamental level.

So I look forward to hear some other news from "the other side of the spectrum".

Dear Luca,

Here are some answers before I read you prose.

1. Indeed, I did not mention quantum mechanics because this elaborated theory is `at the leaves of the tree', while I really start from the base of the trunk (and even try to show some roots).

However, with more room available, an interesting remark was possible. I noted that mathematically, any structure is characterised by its invariants. An accomplished theory is axiomatised; and the structure of the axioms carries its invariants in all the further developments. Gilles Cohen-Tannoudji gives an illuminating interpretation of universal constants of physics in terms of such invariants, for which he uses concept of horizon, inspired by Ferdinand Gonseth (see his contribution, alongside those of Bohr, Einstein, de Broglie, Heisenberg, Reichenbach notably, in Dialectica 2:3/4 (1948) pp. 305--424).

Now, the very first hypothesis of physics expels the subject (cognitive subject). That applies to all physics, with consequent limitations I have pointed at. It could only happen that in some cases, it would become absolutely necessary to reintegrate the observer. That has happened in quantum mechanics. The most spectacular illustration is the von Neummann-Wigner interpretation of quantum mechanics or any of its variants, whereby to make it short, consciousness causes the collapse. (This is not the place to discuss whether this interpretation is right or not. Suffices to say that many prominent actors of physics took it seriously, and that its core still holds.) My comment is that it is no surprise that when it becomes absolutely necessary to take the subject into account --and this is very closely connected to measurement-- he suddenly lands in the middle of the discourse. (The close connection to measurement is clearly seen in quantum mechanics, and this is why in the essay I have mentioned the relative nature of any measurement, and the formal closeness between measurement, modelling, perception, and formalisation, which is connected to the subject making categories --symmetries--, and going from what is given in the theory as a description at infinite resolution --in real numbers--, to a reduced, categorised view --the transition to macroscopic in a quantum mechanics measurement.)

So there could be a criticism addressed to `quantum mechanics' --say von Neumann: that he should have explicitly stated that a subject was to be added as an additional basic element, to his axioms of quantum mechanics, from the moment he was summoned to effectively make something happen, to collapse the wave function.

Adding the subject is basically what I do. But in the same movement, I find unnecessary to carry with me all the usual established axioms, I proceed straightforwardly by restarting from scratch.

2. With these topics of perception, measurement, I have a natural transition to time, your next question, with this quotation of Heisenberg, in an interview by Paul Buckley, in Glimpsing reality: ideas in physics and the link to biology:

PB--How does quantum mechanics deal with time flow or does it in fact say anything at all about it?

WH--I would have to repeat what C. von Weizsäcker said in his papers: that time is the precondition of quantum mechanics, because we want to go from one experiment to another, that is from one time to another. But this is too complicated to go into in detail. I would simply say that the concept of time is really a precondition of quantum theory.

It makes strikingly clear that Heisenberg would never have considered non-existence of time as a conceivable consequence of any theory of physics, for the very reasons I have raised in the essay, and that his position is just one step away from subjective relativity.

3. As to whether time is discrete or continuous (is perceived as, or represented as), I would refer to the definition of a perceptive continuum by Poincaré (he writes physical continuum), which is mentioned in a previous answer of mine:

It has, for instance, been observed that a weight A of 10 grammes and a weight B of 11 grammes produced identical sensations, that the weight B could no longer be distinguished from a weight C of 12 grammes, but that the weight A was readily distinguished from the weight C. Thus the rough results of the experiments may be expressed by the following relations: A = B, B = C, A < C, which may be regarded as the formula of the physical continuum.

The reported effect is quite common, and works as well for mere categories (not only something that purports to a scalar, as in the given example). It works, e.g., for our concept of species: a man is not a monkey, however, if men beget men, and monkeys beget monkeys, we admit since Darwin that man is without interrupt in the descent of monkeys. So monkey = monkey = [...] = man, man ≠ monkey. Of course that property conflicts with objects we can calculate with. (There is a contradiction.)

To sum up, the world is perceptively a continuum. (Perceived) space is continuous, (perceived) time is continuous. But as explained in the essay, a continuous, homogeneous space is only apprehended by its discontinuities: you could not measure a span of space without objects in it, breaking is homogeneity, breaking its invariance under displacement. This is completely consistent with the fact that you cannot see, or feel any sort of space, except by the object that are obstacles to your sight, or your movement, any sort of sensitivity. As for time, these singularities are called events. (Thom has made interesting discussions on saillances and prégnances, discrete objects out of a continuum, but not up to that stage.)

However, as soon as I want to speak about anything, time for instance, I have to pass through categorisation. If, to make it really clear, I put it in writing, I shall attach symbols to categories, and the discrete nature of my discourse will be clearly reflected in a succession of symbols on a paper.

Hence time is discrete as long as it is put in most elementary, formal representation: writing. But here is an example where you can see time, at once both continuous and discrete: when you see time [recorded] in a cliff of sedimentary rocks, you have a basic continuum, within which you can delimit discrete layers (that your geologic eye will interpret as sedimentary events).

Dear Joe,

I feel absolutely nothing disrespectful in your comment.

As must have understood, I chose to describe physics as a disciplined way for men to account for some aspects of their world, and abstract physics looks more and more like mathematics. In this sense, actually, physics cannot be said to rule the universe.

I do agree that (which means: in the framework I have outlined), every event, snowflake or other is primarily unique, and our activity as living beings, especially cognitive beings, compiles an organised view of all these events.

However, I have difficulties following the linking of your ensuing statements, probably because you packed too much in just a few lines. Feel free to elaborate.

Regards,

Dear Joe,

Apologies. As you can see from my answer, it is obviously a mistake if your comment has been reported as inappropriate.

I am going to write to forums@fqxi.org, to have that corrected.

Regards.

Michel,

Thank you for your warm comments (it seems that your rating is lost in a mass of low tendency, however...).

I have read early your essay, too, and have been looking at a few of your articles, and have jotted notes about it; I only have not secured time to write a proper comment yet.

If you really like the thread, you may take a look at Derek Wises's http://fqxi.org/community/forum/topic/2494, which touches similar topics. I have just posted a comment to it, where you should be in familiar terrain.

Dear Janko,

Thank you for your kind comment, and since you are pointing connections to your essay, iis a good reason to put it duly on my schedule.

I do not stress consciousness so much in the essay, rather cognition.

If I understand your particular strand of interest, and are yet unaware of the following article, you will probably find much interest in it:

John Conway, Simon Kochen The Free Will Theorem Foundations of Physics October 2006, Volume 36, Issue 10, pp 1441-1473

(That's the Conway which is such a productive mathematician.)

So about that section聽5. I have probably tried to pack too many things in too few lines. The general idea is in the title: because we completely elide the subject, it is impossible to talk properly about perception, because perception occurs when a subject meets the world.

The illustration is straightforward: open any book on the physiology of perception, nowhere you will see that meeting occur. Take a diagram about vision: you have a scene, and it is shown projected (reverted) on the retina. Fine. Then the information is said to proceed along the optical nerve, and is projected on cortical areas that happen to be at the back of the brain. (I stop here but the process can go on.)

So initially the subject was watching the scene, seeing something. Now, the visual cortical area does not see. Who sees? A small subject must be added, hidden somewhere in the brain, watching the visual cortical areas.

If we where supposed to learn something about seeing, the experience of vision, we have not advanced at all. We have implied a full-fledged little man, inside the brain, doing exactly what the initial, complete subject was doing. This has come to be called the homunculus fallacy.

You will find a short, clear description of the argument in The Oxford companion to the mind. (Or even, I check it now: http://en.wikipedia.org/wiki/Homunculus_argument.)

Thus what I say, again, is: If you take the usual, unexplicited hypothesis that comes from physics and pervades all science and all Occidental thought, there is no way to build a theory of perception proper, because you need both the world and the subject to be actually describing perception.

It is a matter of elementary logic.

Regards,

Dear `En',

So you are curious about my name. The origin is quite obscure, I never found any etymological clue, but the unique source seems to be a small village in Tarn, France. There is a variant with an ending `s'. That's in the vicinity of Albi, and during the cruzade against the Albigeois in the early 13th century, many families moved to the area of Strasbourg for instance, and into the territory of (now) Germany, and perhaps further, areas which were more welcoming for protestants. This seems to be the reason why the name is found also there.

I am learning from you that the name is also found up further in Eastern Europe and up to Turkey.

`En passant', I would not dare asking you the origin neither of your first name, nor your surname...

Regards.