Sunday, February 5, 2012

The Māya Theory of (Visual) Perception

A visit recently to the Center for Brain and Cognition at UCSD by an Indian medical student has prompted me to advance a rather skeptical theory at which I have only hinted previously. It is surprising how sometimes in the course of informal conversation even a profound idea can take shape, and that was the case the other evening when Rama and some of us in the lab were actually joking about the absurd predicament that I described below under my posting "Summation," viz. that the causal theory of perception leads to empirical evidence that does not support it, but actually contradicts it.

As I have intimated previously it is not necessarily the case that classical "action-by-contact" ("billiard ball") causality is wrong, but that the causal theory of perception is wrong by invoking it, the locus classicus being The Analysis of Matter by Lord Russell. This state of affairs may/may not be related to putative non-local causality ("non-locality") in Quantum Mechanics, which it has been claimed by theoretical physics implies "action at a distance" at the quantum level, and though a number of theorists have speculated that consciousness may have a quantum mechanical basis. I say "may/may not" because the rejection of the causal theory of perception is not because it is contradicted by anything stemming from Q.M., but by the disparity between brain structure/events and the structure of visual objects, a topic of much previous discussion here already, but something that was noted by John Smythies already over half a century ago in his Analysis of Perception.

Just as Fred Hoyle thought the universe was a "put up job," much the same might be said for the (visual) world--and perhaps for a similar reason: Highly unlikely relationships between physical constants in the case of the universe, and so-called perceptual constancies in the case of the visual world. The geometrical structure of objects in visual space is usually explained in terms of a perspective projection resulting from the geometrical optics of the eyes. It is often depicted as being something like an artist using perspective to simulate depth and distance on a flat surface. But whereas the artist can compare what he sees of the world with his perspective drawing or painting, we as perceivers cannot do that with the whole of our visual world with the physical world, so the analogy does not really hold.

Perhaps it is the case that as much as departing from "veridical" perception, visual illusions and the study of them may may actually lead to understanding perception and the visual world as māya, a Sanscrit word usually translated as "illusion" but also as "projection." How apt in the case of visual perception! Could it be that it is the nature of perception to foster a belief in an objective external world, but that such a world always remains for each of us only a belief? When one doubts the existence of an external world beyond the senses, one is a skeptic or phenomenalist, but when one doubts the existence of God, one is only an atheist. Yet both involve belief or disbelief in something beyond the senses. On the one hand, "seeing is believing," yet on the other, one "doubts their senses."

The "put up job" in the case of perception may just be predictability and repeatability in the perceptual world--as it happens, the hallmarks of scientific empiricism. But how can one know a priori that this guarantees knowledge of reality, if reality is only a belief? The argument is circular. This may be the "naive faith" which Whitehead wrote science never questions.

24 comments:

  1. Thanks for keeping the conversation going here Bill, although I am afraid that I am not convinced by what you have to say. I am not sure anyone ever convinces anyone of much of anything in this business, but it is still useful to make a few points and counterpoints and try to be reasonably friendly in doing it.
    Regarding action at a distance in quantum mechanics I have been doing some work in explaing it in terms of global effects of the electromagnetic field together with multi-photon absorption, even among spatially disparate absorbers. I hope to get an experiment going on this this summer at UMBC in Baltimore.
    Secondly, I don't think that it is consciouness that reduces wave packets but rather the physical absorption process per se, as for example occurs in the rods and cones of the retina.
    Regarding any tension between projective geometry and the psychological constancies I think that in fact the two are compatible. As Robert Thouless points out in his papers on the phenomenal regress to the real object, the "constancy" in size and shape constancy at least is not complete but instead a compromise between what comes out under projective geometry and complete constancy. A key point here is that the nature of the projection depends on the nature of the surface being projected onto, for example whether it is a plane or a sphere (peripheral marginal distortions being present for the planar projection but not the spherical). In my paper on the geometry of visual space in NOUS, I try to explicate the experimental results on size and shape constancy in terms of a projection onto a two-dimensional surface of variable curvature, where a depth function acting on a sphere makes the resulting projection have a tendency towards both size and shape constancy.

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  2. Thanks for sharing these thoughts, Bob, though they do not directly bear on the points I raised, as the idea I was advancing is not contingent upon quantum nonlocality nor action-at-a-distance (at least in any obvious way).

    Nor was I talking about the relationship between perceptual constancies and projective geometry, but about “object constancy,” and perhaps I should have been more explicit. Presumably you were assuming the definition “The tendency for objects to be perceived as unchanging despite variations in the positions in and conditions under which the objects are observed; e.g., a book's shape is always perceived as a rectangle regardless of the visual angle from which it is viewed.”

    What I really had in mind was the most fundamental object constancy, that which is also called “object permanence” by developmental psychology, as it is something only experienced after a certain stage of development in childhood. Very young children seeing a ball roll behind a chair are often surprised when it reappears, as if the ball by ceasing to be visible had ceased to be altogether, and then upon reappearing came back into existence.

    This is something that we now know is deficient in persons with Borderline Personality Disorder, for one, and in patients with brain injuries or pathology as well, as a form of agnosia, in which individuals may no longer be able to recognize shapes under various transformations (so-called "apperceptive agnosia").

    What I am arguing is that structures in visual space are in some sense recursive, they refer to each other in such a way as to form a closed system of internal relations which indeed promote object permanence, and thus the belief in there being a world independent of our senses in which there are such objects. Of that, I have become increasingly skeptical, because I believe that the study of visual illusions points the way to another realization, that described in Hindu philosophy, that maintains that the shapes and forms we perceive are an illusory projection of something without objecthood in any sense that we can experience in the perceptual world.

    I called into question the identification of visual shapes with any known structures in the brain because, as John Smythies pointed out over 50 years ago, they are not congruence. This refutes the psychoneural identity theory on the face of it, and it is not clear how the structural of cortical events could even in principle give rise to the shapes we experience in visual space, as Hubel and Wiesel realized in the course of their pioneering work exploring the visual cortex already 30 years ago.

    Something is therefore wrong with the causal theory of perception, whose logic dictates that percepts are in the brain, or are somehow generated by the structural organization of the cortex.

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    1. This helps some Bill, although it isn't clear to me why what you call "object permanence" cannot be accounted for under a causal theory of perception if that is used in a broad sense. As I use the term I certainly don't for example want to preclude the possibility that the brain, in effect, makes any number of presumptions when it reconstructs a conscious visual image in depth. In fact I think that this is necessary since many of the details for such a reconstruction are underdetermined by the retinal images, and certainly this is consistent with getting things wrong as with optical illusions. It might help if you said something about what you take the "causal theory of perception" to be, and then we could at least see whether we are using the term the same way or not. Also, as far as I can see Smythies holds a version of the causal theory of perception.

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  3. It is just because the logic of the causal theory of perception is so compelling that its failure at the brain level is baffling. And yet if we look at the details of the causal process, the compelling logic soon becomes insufficient to maintain the theory, given the neurophysiology of the visual system (and other sensory systems) alone.

    Mainly, though, we have no explanation even in principle for how the brain creates or mediates so-called "qualia" (aka sensations), for one, so I think we must reject the theory as untenable because it ultimately fails to explain that which it seeks to to explain: perception--ergo, no cigar! A visual space without qualia is not even a void, as we have discussed here previously in the context of cortical blindness, so a theory of perception that cannot explain qualia is therefore unsustainable.

    To echo Wittgenstein and Ray Tallis, it is not the brain that makes assumptions, but people; to assert that the brain is doing these things is to personify or "homunculize" the brain. I don't think the brain is "reconstructing" anything, including a visual image (in depth or not), and it is not clear to me why we should believe that it is (there is that word "believe" again).

    The chief conceptual defect of the causal theory is that it employs a notion of representation that fails to meet the criteria of a representation, a point that I have argued here before, because a representation is something that in principle can be compared to that which it is a representation of, but that is something we cannot do in the case of our perceptions (you may recall William Gooddy's paper from the 1950s in which he refutes the validity of the notion).

    If the so-called "sensory" systems of the brain are not making representations, and not making qualia, what are they doing? It seems to me that we have over intepreted the brain and read far too much into its workings when, for all intents and purposes, its main function seems to be to control or regulate other bodily functions.

    Science only commits itself to theories that "work." The causal theory of perception doesn't "work."

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    1. Rather than the relatively specialized formalistic focus of geometry and topology, it occurs to me that it might have been more apt for John Smythies and I to have called this blog "The Structure of Appearance" after Nelson Goodman's 1951 monograph, in which he developed a logical calculus of sense qualities (qualia). Culbertson independently developed a similar analysis of "quality orders" starting in the 1940s. Of course, as I noted previously, what are being bandied about as "qualia" today in the context of neuroscience are closer to the "complex qualities" or "Ganzheit qualities" defined by Felix Krueger in the 1920s as the Second Leipzig School of Psychology (Krueger being Wilhelm Wundt's successor there).

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  4. I think that we covered some of this material before Bill, so I may end up repeating myself a bit. I want to reply to two of your points. Regarding the danger of something like anthropormorphizing the brain, this only occurs if in stating things like that "the brain is making assumptions" these statements cannot be cashed out in non-intentional language. Dennett gives a good discussion of this in his book "The Intentional Stance" (I don't know if you have seen it, but I think that it is a much better book than his books on consciousness). An example (and again I don't know if you have seen this) is Shimon Ullman's work on visual cues for motion, such as rotating objects. He assumes with his mathematical algorithms that there is assumption by the brain that objects seen retain rigid shapes over time, but the algorithm per se doesn't state this; it is just the case that otherwise the resulting visual experience of a rotating object is underdetermined by the retinal images.
    Regarding what you say that we need to have knowledge of both sides of the perceptual representation, I know that we got into this in detail before. I certainly concede that the epistemology is quite different on the two sides; it is immediate access for the percept, but only indirect, through the methods of science, for knowledge of the object as being comprised of atoms, reflecting and absorbing different wavelengths of light etc. We don't gain certainty for the latter sort of knowledge (if you want to call it knowledge) but unless you want to discredit this type of science in general I don't see why you have a problem with it.

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  5. Thanks for staying with me here, Bob, and for reprising some points. Pace Dennett, but I think Ray Tallis in his "Why the Brain is Not a Computer: A Pocket Lexicon of Neuromythology" as well as his posting here on this blog "The Disappearance of Appearance" already disposed of intentionality in general being attributable to the brain or any other part of the body (e.g., a pianist's hands) rather than the whole person. In many different ways Wittgenstein did the same et passim.

    We just have no empirical evidence in the brain of there being anything like assumptions there, so it remains a philosopher's fantasy to believe otherwise (again, note the word "believe"). Yes, one can certainly devise mathematical fiction based upon neuromythology that is internally consistent, but if the axioms have no empirical basis (Reichenbach's "co-ordinative definitions"), then it remains just that: fiction. As Crick would say we want to know how Nature does it, not how it might be modeled mathematically.

    Ullman sounds like he is lapsing into direct realism because by "cues" he is obviously referring to something within visual space, not objects in physical space. From time to time here I have mentioned how such accounts of perception seem to be talking about events within perceptual space as if they are talking about relationships between perceptual and physical space instead.

    Like most people, most scientists in the physical sciences are naive realists and never stop to realize that in making an observation (or prediction) even in particle physics still requires perception. The 'indirectness' of all scientific observation then is thus something within perception, not outside it.

    Schroedinger used this example in his "Mystery of the Sensual Qualities":

    "Many helpful devices can facilitate this work [experimental physics], for instance photometric recording across a plate of its transparency, which yields a magnified diagram on which the positions of the lines can be easily read. But they must be read! The observer's senses have to step in eventually. The most careful record, when not inspected, tells us nothing."

    Do you have a different understanding of this situation, Bob?

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  6. Just a couple of points in reply to what you have to say here Bill. Regarding Dennett, he is just referring to what he calls "as if" intentionality where he is referring to ascribing purposes for what can be cashed out in detail in mechanistic terms. For example I may treat a chess-playing computer as if it is trying to win the game even though I also realize that what it does can be completely explained in terms of electronic circuitry. Dennett is very leary of other senses of that notoriously ambiguous word and has had a long debate with Searle on the topic.
    Regarding quantum mechanics, certainly the Copenhagen interprertation emphasized bringing in such concepts as measurements and possibly consciousness, but as I have mentioned before, as far as I can tell it is absorption that does the collapsing of a wave packet, and this gets amplified with measurement processes. Still the collapse would occur in the microcosm, although you are right that to learn about this we would have to look at a measuring device in some sense.

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  7. Dennett is just equivocating. The notion of translating (as it were) any intentional state into brain "wetware" even "as if" leads to the same difficulty of attributing something said of a whole person to a part of their body. Instantiation of any mental state in wetware in general involves a huge conceptual leap, and Ray Tallis has to my satisfaction defined the pitfalls of that quite lucidly in a talk he gave on neuromythology: http://www.youtube.com/watch?v=ku-GmndXDXo
    Automation in the case of chest playing computers is only possible because people have created such computer programs. Neither the computers nor the programs create themselves--but then, neither to we.

    Schroedinger's point was that there is no scientific knowledge without conscious human observers. He wasn't talking specifically about the "observer problem" in the interpretation of Q.M., and it is not just "in some sense" that we must look at a measuring device. We use our eyes to look at it, therefore our senses. There simply is no other way, is there?

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  8. Perhaps I should also mention Thomas Kuhn's point in his "Structure of Scientific Revolutions" that even our scientific instruments that make the measurements embody theoretical paradigms.

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    1. Regarding Dennett, he is rather notorious for equivocations in some of his works, such as on the word "seemings" in Consciousness Explained, but it is not readily apparent to me that he does something similar on "intentionality," which he at least claims to be a complete instrumentalist about. Maybe you could point out exactly where you think that the equivocation occurs.
      We already had some pretty lengthy discussions about measurements, as with examples from carpentry, but there is probably something more to say. Even a carpenter observes his/her measuring devices, but does this preclude that they also give us accurate information about the physical world?
      Regarding Tom Kuhn, I partially agree with him about scientific revolutions (I think that a few may be occurring in physics right now), but I also think that he tends to overstate his case. For example I think that there can be intelligent conversations between people holding incommensurable paradigms. Also, I at least read him as not holding an objective theory of scientific truth. I was wondering whether you also interpret him this way, and, if so, whether you agree with him.

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  9. I don't really think that statements about intentionality can be translated into instrumentalist ones (or vice versa) without loss of sense. Reasoning by analogy, though useful, easily leads to equivocation (conflation of word senses and/or meanings). The "as if" situation Dennett offers suggests a relationship by analogy rather than by any rigorous equivalence, let alone identity.

    Again we are back to the identity of indiscernibles: By what means can an intentionalist's account of perception be equated with an instrumentalist's? The former favors the subjective, whereas the latter, the objective. In other words, there's a problem.

    As for the carpenter using his senses for the purposes of carpentry, the results speak for themselves: They work, but don't necessarily tell us anything about the "physical world" as defined by the physical sciences. For the carpenter or lay person "physical world" is just the perceptual world (or "world of the senses").

    Knowing Popper's critique of Kuhn (at least superficially) I tend to side with his view that Kuhn overstated his case, and that incommensurability of paradigms cannot be asserted a priori, but only as a result of analysis and comparison of axioms and primitives that are not convertible into one another with auxiliary linking concepts.

    What I am arguing is that scientific truth may only exist in the perceptual world, supported by the reality it contains. But physics, for one, fails to see that, because it is dominated by a form of naive realism. You can see that naivete in the futile debates that have taken place between skeptical scientists and Deepak Chopra. The skeptical science types, adherents to "scientism" as has been said, never once question their "naive faith," that is, their tacit commitment to scientific (monistic) materialism (that and antheism), apparently not realizing that they are committed to a metaphysical position, one that they believe is rooted in pure logic (something like Sherlock Holmes), when most of their skepticism really derives from the limitations of empiricism rather than rationalism (this is the problem Wittgenstein struggled with at the end in his deliberations published as "On Certainty"). They fall into the trap of thinking that scientific theories are something empirical, rather than being empirically confirmable/testable. But then, few scientists are trained in philosophy, and therefore are not aware of conceptual pitfalls and the role conceptual analysis plays in sorting them out.

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  10. I agree with you Bill that the typical carpenter, and probably also the typical scientist, is probably a naive realist, or at least has probably not thought that much about these issues. Nevertheless, just because their methods work in most circumstances, apart from optical illusions for example, quite well, I think that this is evidence that they are working with a reasonably accurate model of at least macroscopic properties of the physical world. Certainty is not gained here, but I think that it is a mistake to look for certainty in science, and probably also in philosophy.

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  11. The implications from both the naive carpenter's and scientist's views is that they regard what they are working with as (physical) reality, not a representation of it made by the brain. Both Gooddy and Culbertson were of the opinion that the so-called "maps" of the visual world were nothing of the sort, and that the spatial order of the retinas is preserved fortuitously because of proximal contiguity of the sensitive tissues which just reflects embryogenesis: both ontogenically and phylogenically the organs of sight grow/grew out of the skin (the ectoderm), therefore the sense of touch.

    If I draw a square on my hand with a pen which I both see and feel, and compare it with one I see on a wall, I could say the one is a map of the other--but that is a relation within the perceptual world, not between that and the physical world. That is not the same relationship between events in the physical world and so-called visual "maps" in the brain.

    What I am calling into question is the ontological status of a physical world existing beyond the senses, just as Hindu philosophy does. If the The Māya theory is correct (a theory that has existed for millennia now), then reality as we think of it only exists in the perceptual world, though Hindu philosophers might not put it that way. I have voiced much the same view here independently already. Both reality and illusion are found in the perceptual world.

    Once stripped of all qualities that can be sensed, there is not much left of a "physical world" beyond the senses, for the reasons I have recently given, that even the instruments of physics must be read to provide information, and that is something going on in the perceptual world. As I have also noted, the arguments in favor of a physical world existing beyond our senses often resemble those of theology, the articles of faith being the laws of physics (which are proving to be less immutable than once thought).

    As for certainty, in his last writings Wittgenstein gives a number of concrete examples that illustrate instances where one can be certain about things for all intents and purposes in everyday life (thus the existence of the word "certainty" in our language). Again it is the stochastic nature of the putative physical world that does not lead to equal certainty.

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  12. I just discovered this blog and I look forward to read it in detail.

    Re: "What I am calling into question is the ontological status of a physical world existing beyond the senses."

    Also in relation to the mind-body dualism, I think there is a logical contradiction in the "Cartesian Theater" argument by Dennett, due to the fact that the fact that Dennett's theater is a theater in a box, already designed for a dualist homunculus-stage space perception (in contradistinction with the older, original Greek Theater).

    http://chorasimilarity.wordpress.com/2011/06/06/the-cartesian-theater-philosophy-of-mind-versus-aerography/

    http://chorasimilarity.wordpress.com/2012/01/07/theatron-as-an-eye/

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  13. Thank you for your posting, Marius Buliga, and welcome! It is great to have a mathematician join us, for obvious reasons, especially since you are interested in problems in geometry.

    Your idea of the eye as a "theatron" is interesting, though I do not believe that the brain is computing anything, for the simple reason that it is not a computer, and doesn't behave like one, as some neuroscientists are now publicly saying. It is people who perform computations, not brains.

    Raymond Tallis, who posted "The Disappearance of Appearance" here two years ago, went to some pains to articulate the fallacious reasoning behind the computational metaphor of mind and brain in his marvelous little book WHY THE MIND IS NOT A COMPUTER.

    It has long been a truism in cognitive psychology that we do not see our retinal images, and the "function" or process of vision is probably very different from the creation of images, because there is no image in the brain, nor anything like one. If anything, the pattern of stimulation on the retinae is "digested" by the visual system, broken down rather like food is into nutrients (as an alternative, think of chemical communication among insects).

    To my knowledge, Descartes did not invoke the analogy of a theater for vision (or perception in general), so for Dennett to construe his ideas on such an analogy is dubious at the outset and, in this instance, just seems to make for a straw man. For that matter, Dennett does not seem to understand the reasons for dualism very fully, and as nearly as I can determine, never bothered to acquaint himself with the excellent volume edited by John Smythies and John Beloff, THE CASE FOR DUALISM (1989). His ill-informed refutations just strike me as facile and unconvincing (and his computational theory of mind has been roundly rejected by Ray Tallis as being fallacious).

    My own invoking of theater here as an analogy is to reality itself, not just perception, and is therefore quite different from the view Dennett imputes to Cartesian dualism, though. I propose that physics studies the stagecraft of a reality that only (fully) exists when perceived--which is closer to Berkeley than Descartes, and is a view consistent with John Wheeler's "observer-participant" model of the universe.

    Theoretical physicist Saul-Paul Sirag advanced a "many realities" alternative to the Everett-Wheeler "many worlds" hypothesis, arguing that other realities are mathematically possible. That is why I have tendered the provocative notion that the reality we know is a sort of construction, one that is maintained by the physical constants--or so it seems. Sirag argued that it is not the only possible reality for that reason, and that the constants are comparable to the "chains" that hold the cave dwellers captive to the shadow play on the wall.

    I propose instead that the senses are part of the reality-making "mechanism," and that vision has more the character of a resolving mechanism than a picture-making one (not quite like the Bohm-Pribram holographic reality/brain analogy, though). That gets rid of the homunculus problem, because it turns the perception process inside out: The person and homunculus are one and the same, and visual space is just where it appears to be, viz. in front of us, not a picture made by the visual system in the brain. The forerunner of this view was James Culbertson. The flaw is that it requires a rejection or modification of the causal theory of perception, as we have discussed here. But causality is a metaphysical principle, not a physical one, and perhaps in this context at least requires some close scrutiny, just as Culbertson gave it.

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    1. "...for Dennett to construe his ideas on such an analogy is dubious at the outset and, in this instance, just seems to make for a straw man." This is my impression also, but what can we learn from this about vision?

      As a mathematician, maybe, I am quite comfortable with vagueness. What I get from the greek theater/theater in a box argument is that the homunculus is as artificial as the scenic space, or the outer, physical space. These two notions come in pairs: either one has both, or none. The positive conclusion of the argument is that we have to go higher: there is a relation, akin to a map-territory relation, which has on one side the homunculus and on the other side the space.

      Let me elaborate a bit on the map-territory relation. What is a map of a territory? It is the outcome of a collection of procedures agreed by the cartographer and the map reader. The cartographer wanders through the territory and constructs a map by some procedure, say by measuring angles and distances using some apparatus. The cartographer follows a convention of representation of the results of his experiments on a piece of paper, let us call this convention "euclidean geometry" (but it might be "quantum mechanics" as well, or "relativity theory"...). The map reader knows that such convention exists and moreover, at least concerning basic facts, he knows how to read the map by applying the convention (for example, the reader of the map of a city, say, knows that straight lines are shortest on the maps as well as across the city). We may say that the map-territory relation (correspondence between points from the territory - pixels from the map) IS the collection of agreed procedures of representation of experiments of the cartographer on the map. The relation between the particular map and the particular territory is just an outcome of this map-territory relation.

      Looking at this level, instead of speaking about the perception of the exterior by the homunculus, it is maybe more reasonable to speak, like in "The structure of visual spaces" by J.J. Koenderink, A.J. van Doorn, Journal of mathematical imaging and vision, Volume: 31, Issue: 2-3 (2008), pp. 171-187, about the structure of the visual space as being the result of a controlled hallucination, based on prior experiences which led to coherent results.

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    2. Thank you, Marius! What can we learn from Dennett's faulty analysis of vision, you ask? The "moral of the story" IMO is that any model based on computation presupposes that we know how people perform computations--or how the human minds does--which is something we presently unknown, because we don't really know what the "mind" really is--it's just a name. All a computer does is automate a procedure we humans perform. To assume that Nature makes computers strikes me as a classic example of anthropormorphism, and Ray Tallis would agree. How then to get beyond that fallacy? Or, in the case of vision, to echo John Wheeler's style of formulating foundational problems in physics, "How do you get vision without vision?"--that is, how to understand vision without presupposing it? That's quite a feat!

      A few months ago when Bob French and I were last debating some of these points I suggested that we turn to the evolution of the eye and see what that tells us. Conveniently the evolution of the eyes has been one of Richard Dawkins' favorite examples to refute the idea of "intelligent design":
      http://www.youtube.com/watch?v=lEKyqIJkuDQ

      In light of all the questions the account Dawkins raises but leaves unanswered, intelligent design seems to make more sense (I offer no opinion on that myself). So it is a question of what the simplist eyes do and how the organisms possessing them use them. There is a nice little video on YouTube that highlights all that Dawkins does not explain in his simplist account of the evolution of the eye:
      http://www.youtube.com/watch?v=rRDAY39Zd9M&feature=related

      As for the map-territory analogy you suggest, it is comparable to the idea of "cortical maps" but shares the same conceptual pitfall as that of the perspective projection analogy I gave above, because as I noted, unlike being able to compare the flat perspective projection (map) with the 3-D *visual space* of which it is (supposedly) a projection, we cannot do that with visual space in relation to putative physical space, which lies beyond our senses. It seems to me that we are to some extent each trapped solipsistically within our own perceptual world.

      Koenderink's idea just seems like nonsense to me, because we don't even really know what hallucinations are any more than how a hallucinatory space is created relative to our "normal" waking visual space (BTW we invited Koenderink to join the blog a few years ago, but he never replied). The *concept* of a hallucination is only useful when one has some non-hallucinatory experience to which to compare it--thus the same problem as the projection analogy above.

      Trouble is we seem to be *inside* the system we are trying to understand, and therefore cannot assume an Archimedean point outside it from which to better grasp it (one of the fundamental realizations Einstein had in developing the theory of relativity, i.e., relativity is all *within* the system = universe).

      As for visual space being non-Euclidean or not, I called into question many years ago the interpretation of the data upon which all theories of the geometry of visual space are based, because the "alley experiments" never took into account changes of projection on the retinae as a function of eye movement, i.e., the angles of objects projected on the retina are constantly changing as the eyes move. This has never been modeled mathematically, but it should be. Just look at the point where a wall meets the ceiling an run your eyes along its length, back and forth. You will notice that the angle of the line changes as you move your eyes along it.

      Yes, the space and homunculus are an inseparable pair IMO--just look at Wheeler's symbolic representation of the observer-participant universe (the eye looking at the U).

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    3. I should hasten to emend my remarks above by stating that when we speak of "eyes" and "brains" such objects are only known to us by perception. So like any physical object, we cannot presuppose their existence as such separate from our perception of them--except by an act of a kind of faith (belief), much as we believe that the sun will rise every morning. Therefore talking about their "function" etc. is still all resting upon perceptions, without which we would have no knowledge of anything, ergo, something like Aristotle's dictum "There is nothing in the mind that was not first in the senses." Are there eyes and brains that exist independently of perceptions of them?

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    4. Dear Bill, thank you for the interesting comments! I have several of my own (please feel free to edit the post if it is too long, boring or otherwise repellent for the readers of this blog):

      1. It looks to me we agree more than my faulty style of exposition shows: one cannot base an explanation of how the space is "re-constructed" in the brain on the structure of the physical space, point. It may be that what we call structure of physical space is formed by features selected as significant by our brain, in the same way as a wind pipe extracts a fundamental note from random noise (thank you Neal Stephenson).

      2. We both agree (as well as Koenderink, see his "Brain a geometry engine") that, as you write, "the senses are part of the reality-making "mechanism," and that vision has more the character of a resolving mechanism than a picture-making one".

      3. Concerning "computing", is just a word. In the sense that "computing" is defined as something which could be done by Turing machines, or expressed in lambda calculus, etc, I believe too that the brain is not computing in this sense. With efforts and a lot of dissipation, it seems that the brain is able to compute in this sense, but naturally it does not. (It would be an interesting project to experimentally "measure" this dissipation, starting for example from a paper by Mark Changizi “Harnessing vision for computation”, here is the link to a pdf:

      http://www.changizi.com/viscomp.pdf

      )

      4. But if we enlarge the meaning of the word "computing" then it may as well turn out that the brain does compute. The interesting question for a mathematician is: find a definition of "computation in enlarged sense" which fits with what the brain does in relation to vision. This is a project dear to me, I don't want to bother you with this (unless you are interested), which might have eventual real world applications. I started it with the paper "Computing with space, a tangle formalism for chora and difference"

      http://arxiv.org/abs/1103.6007

      and I reached the goal of connecting this (as a matter of proof of principle, not because I believe that the brain really computes in the classical sense of the word) with lambda calculus in the paper "Local and global moves on locally planar trivalent graphs, lambda calculus and lambda-Scale",

      http://arxiv.org/abs/1207.0332

      (By the way, I cannot solve the problem of where to submit a paper like "Computing with space...")

      5. Concerning "hallucination", as previously, is just a word. What I think is likely to be true is that, even if the brain does not have direct access to the physical space, it may learn a language of primitives of this space, by some bayesian or other, unknown, procedure, which is akin to say that we may explain why we see (suppose, for the sake of the discussion) an euclidean 3d space not by using as hypothesis the fact that the physical space has this structure, but because our brains learn a family of primitives of such a structure and then lay in front of our eyes a "hallucination" which is constructed by the consistent use of those primitives.

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  14. Thanks for these stimulating thoughts and ideas, Marius. Not to worry about the length of your blog postings. Mine are often (too) long, too. My remarks will be in two parts. This is part I.

    When John Smythies and I started this blog (which was really intended to be a "think tank" rather than a blog), we agreed that, following the lead of Einstein, it may be necessary to re-examine fundamental concepts of space and geometry (not to mention time), thus John's very first posting about Jean Nicod's work in this regard, and a number of mine which followed.

    One of these fundamental concepts that calls for closer scrutiny is space itself, or, to be more precise, the nature of *spatial extension,* both of which are abstractions, especially in mathematics (in this regard see Graham Nerlich's excellent monograph, "The Shape of Space").

    We need to better understand the basis of those two abstractions--space and extension--IMO if we are to make progress on the nature of visual space, or the other sensory modalities that occupy perceptual space as a whole (auditory, tactile, olfactory, gustatory). Abstractions reflect both what they omit and what they assume, and it is the assumptions that we especially need to examine here. While clearly visual space is extended, what about smell? Are smells extended in space?

    What we find is that there is a *hierarchy* in perceptual space, one that in man is dominated by visual sensation--what has been called the "dominant visual matrix" by psychologists studying perception. Even sounds are referred to visual loci ("localized"), and I think that can be said of smells, too. But in of themselves it is not clear that even auditory sensations are extended in the same way that visual sensations are, because it is as if when a sound is gone, that part of the "soundscape" is also gone, but that which remains is visual space. In visual space an object may disappear, but the locus it occupied does not also disappear. For example, though we can point to the *visual* source of a sound we hear, we do not point to a sound--even the phrase sounds strange, and ordinary language reveals much about the nature of the perceptual world--or what the man of the street calls the "physical world."

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  15. Part II.

    If that is so, why should we assume that physical space has all the properties of visual space and is perhaps not more like smell? Physics is making one big assumption!

    I will always remember what Caltech mathematician Richard M. Wilson told me when I consulted him many years ago on ideas I had about how the geometry of visual space reflects changing perspective projections on the retinas. He said, "Keep it simple!" By that he meant being parsimonious and not jumping into fancy mathematical formulations without necessity. I am suggesting that we need to keep the mathematical apparatus here to a minimum, lest its elegance obscure the deeper truth we are seeking--just as Einstein cautioned.

    So when we talk about the brain, I think we need to be mindful of what Ray Tallis says about it in his posting "The Disappearance of Appearance," and just *how* we know about the brain, because we cannot talk about the extended world of physical space and exclude the brain itself from that as a (presumably) physically extended biophysical object. It is not that there is the physical world and there is the brain apart from it.

    This ultimately becomes question-begging, because in talking about the brain, we are presupposing physical space, rather than explaining how we have arrived at the notion of physical space and extension. Certainly physical science would deny that physical space is created by the brain. Yet David Bohm would say that physics is largely based on an optical lens-like conception of the physical world, but that physical reality may be more like a hologram (now once again a popular analogy in cosmology because of Leonard Susskind's theory).

    Of course when Karl Pribram then talks about the brain being a mechanism that resolves the holonomic reality ("implicate order") into a hologram or holographic image ("explicate order"), he forgets that the brain itself would presumably be part of the same holonomic implicate order, and would therefore be resolving itself. By what special power can it perform that trick?

    So the very "picture" we have of the brain itself is no different from any other physical entity, as Ray Tallis has been at pains to show.

    For now, I'm going to rest with just these rejoinders, and return to your other points later.

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  16. Dear Bill, I took our exchange of comments and put it at my blog, here:

    http://chorasimilarity.wordpress.com/2012/10/02/a-discussion-about-the-structure-of-visual-space/

    because I think it was an interesting interaction.

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  17. It seems a pity that this interesting line of discussion trailed off early this year, because the one thing that few of us seem willing to confront and question is how immutable are the fundamental metaphysical assumptions taken for granted in all of science, first and foremost causality, ergo, cause and effect, which underlies the so-called causal theory of perception which, there is reason to believe, doesn't quite work as it has been formulated.

    Philosophers such as Whitehead have challenged causality, but even he does not give any a priori grounds other than empirical generalization to accept causality as a given, as physics does (perhaps what he means by the "naive faith of science" as I quoted in a previous posting here).

    There was a good reason why the ancients distinguished metaphysics from physics, viz. because from the beginning physics has presupposed metaphysics, but never talks about it. Instead theoretical physics bends over backwards to salvage causality with the dubious notion of non-local causality, whereas Newton was loathe to grant the existence of "action at a distance."

    Science has exorcised the supernatural, or tried to, apparently never questioning the remaining metaphysical precepts it presupposes, and certainly not providing any physical means for proving that they are inviolate. No one has ever questioned, for example, whether repeatability is the sine qua non of physical existence (the JOURNAL OF IRREPRODUCIBLE RESULTS being a symptom of that presumption), so we are left with a universe, whose "creation" has no creator, nor any knowable physical cause!

    Only one stalwart theoretician had the courage to predict certain conditions in which the laws of physics themselves might come to an end--and that was John Archibald Wheeler, who thought they might not be operative once gravitational collapse of a star is complete resulting in a black hole. But now, rather mysteriously, cosmologists are claiming that the "information" of a star is not lost after all. "Information"? Sounds like fancy metaphysics to me, and for a time, Stephen Hawking didn't buy it. Now he does.

    The universe just gets stranger and stranger, but spokesmen for scientism like Dawkins just naively continue to talk like 19th century naturalists, as if the perceptual world were the natural/physical world.

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