Sunday, September 30, 2007

The dimensionality of the CBS

As I had already discussed, the common binding space (CBS), the substrate of qualia, is three-dimensional. It is for this reason that all living beings, I suspect, are aware of belonging to a three-dimensional space. It seems like this is not a mere coincidence, but has to do with the three dimensional nature of our universe itself.

This begs the question that, if there were a hypothetical universe that has a higher-dimensional space, can there be conscious entities in it with a correspondingly higher dimensional CBS?

If you feel I am jumping the gun here, you are right. We aren't anywhere close to solving the hard problem for our present 3-D universe, so the last thing we need to think of at this point is fictitious universes of higher space dimensionality.

But, it could be quite plausible that there is some kind of logical reasoning (the same kind of logical reasoning that might be used to solve the hard problem in the first place) which rules out CBS's of higher dimensions.

I am less interested in species-specific qualia spaces. For example, we don't know what it is to be a bat. For this reason, I had discussed the concept of platonic qualia spaces, which encompasses every possible qualia space possible by any physical process in our universe according to its known laws. It is possible that, if there are living beings on neutron stars as postulated by Frank Drake, they have access to entirely different subspaces of the platonic qualia space as compared with carbon-based life forms. But the platonic qualia space is a superset of all possible qualia spaces that can occur in a 3-D physical setting.

But I had also postulated that, whatever be the physical process, the CBS itself is 3-dimensional.

But, if we assume the hard problem does eventually get solved, can we come up with a hypothetical universe with physical laws of higher dimensionality which lead to CBS's of higher dimensionality? This would be an "extra-hard problem", so to speak.

Mathematicians would love to be able to visualize four dimensions. They can actually then "see" the beautiful relationship between pi and e given by e^(i. pi) = -1. If only there existed a 4-D CBS!

Note- the dimensionality of the CBS should not be confused with the dimensionality of the platonic qualia space. The latter can be thought of the dimensionality of a vector that gives all the possible combination of orthogonal sensations at any point in the CBS perceived by a conscious entity. It can approach infinity, as in the case of sound. At any rate, the platonic qualia space has a dimensionality much greater than three.

Wednesday, September 19, 2007

On dreams

Imagine there being no such thing as dreams. Everything that we experience would then be intimately tied to the real universe that we seem to be part of, and matters would have been a lot less complicated for the philosophy of consciousness. In fact, the argument for solipsism which relies heavily on the analogy of dreams would have been considerably weaker.

In the waking state, our sensory qualia seem to be virtually memoryless, providing an instantaneous representation of our own physical selves and the world around us. All qualia states which have memory like feelings, thoughts, etc. can be lumped together as emotional qualia, for lack of a better term. In digital electronics parlance, sensory qualia can be termed as "combinatorial".

Given the current world population of 6 billion or so, it is safe to assume that there are hundreds of millions of people, right now as you read this, who believe they are standing on solid grounds which we know don't even exist.

There obviously is no correspondence between the spatial coordinates in dreams and those of the waking state. However, it seems fairly certain to me that there is a close correlation between the flow of time in dreams and the waking state. Even if the scaling factor may not be exactly unity, I am pretty certain that a second of my dream time corresponds to some positive time of my bedroom clock. Certainly I don't believe anyone dreams in reverse play mode, nor in some other time dimension (which would correspond to a fixed time of my clock). This is because, our brains, which we assume to be the source of our dreams, still belong to the "real" world.

So it seems that my CBS can decouple itself from reality and stage a different set of consistent sensory qualia, and I wouldn't even know the fact during that time. (If I know it's being staged, it's called lucid dreaming.) Since our own consciousness is more faithful to our CBS (we always live in our CBS), we can make our CBS the reference universe. And why not? For a good portion of our time, our CBS locks onto the physical universe that we all seem to agree to as being the source of our consciousness in the first place, and we are led to believe that our experiences during these times have direct relevance to happenings in this universe. The concept of spacetime itself is tied to our CBS. It is possible that the "real" universe is nothing but a bunch of computer bits arranged in a one-dimensional array in some dusty basement of the Creator's abode. This is not too far-fetched from reality anyway, since when we see perfect circles or straight lines, in dreams or the waking state, the brain maps corresponding to such experiences are anything but these. Certainly even if there were a final physical theory, it wouldn't be able to explain the magic of why we are aware of our 3-D universe as such, let alone the qualia that we experience in it.

I had already discussed backward binding in dreams in this post. In the waking state, where the sensory qualia are more or less combinatorial outcomes of the sensory inputs from the various sense organs, we can think of the brain as a giant neural network that extracts patterns and features. Thus it is common to talk of a "grandmother cell" that fires when one sees one's grandmother. Of course, the "grandmother cell" theory is now discredited, since it is overly simplistic. But if we assume that information flows one way from the sense organs to the portions of the brain that extracts higher and more abstract features (like one's grandmother), then if one sees one's grandmother in a dream, is it enough if the last stage (corresponding to grandma) alone fires? Or does the entire chain have to fire just like how it would in the presence of the real-life grandma, to maintain consistency? If the latter is true, at least in principle, we should be able to tell what someone is seeing in his dreams by scanning his retinal cells (assuming back-propagation goes all the way).

As a chip designer, I know that combinatorial circuits are a lot more easier than recursive networks. If dreams occur because earlier stages take part, how do those stages "know" the main theme behind the dream in order to fire consistently? For example, when I am hearing someone talk in my dream, the audio has to get synchronized to the visual lip movements and has to emanate from the same direction as the speaker. Given that the lower level stages of the visual and auditory cortices don't seem to have any kind of link between them, how can participation of these lower level stages (if it's the case) be synchronized? I think that it is probably only the mid and high level stages that participate in dreams. The lower level stages are still coupled to the sense organs, but are shut out from the rest of the brain during dreams. Only when there is some abnormal external stimulus (such as the alarm going off), do the lower level areas interrupt the dream and force the consciousness back to the waking state. Sometimes, the output from the lower level areas gets incorporated into the dream, and the whole theme of the dream might change direction to accommodate this new intruding stimulus, in a consistent manner. This is quite astonishing, since how does the part of the brain that orchestrates the entire dream immediately come up with a sequence that would fit the external stimulus, all in real-time? For example, if you hear a baby cry, the dream would immediately summon a baby and fit it in with the rest of the characters and events.

A related question is, what is the evolutionary purpose of dreams anyway? Most of the answers given by psychologists have to do more with the emotional aspects than the sensory ones. I feel the latter are probably as important, if not more.

Also, it seems like dreams are capable of reproducing all kinds of physical and mental states that a person can possibly experience in his waking state. These are not just limited to sight and sound, but also smell, vestibular, etc. Strangely enough, I cannot recall any dream where I have experienced significant physical pain of any sort. I am not sure if others have either.

Also, in this post, I had referred to being drunk in a dream. But, after posting it, I realized that I didn't recall any dream where I'd been drunk either. I assumed that, unlike other senses, the state of being drunk is not derived from any sensory organ(s), but the large scale compromising of the function of the brain itself. So I assumed that it may be theoretically impossible for us to dream being drunk, because it is an unnatural state of the brain.

But less than a month ago, that is exactly what happened. I had a dream where I was quite drunk (even though I went to sleep sober). I am now wondering if the reverse can be true - can someone with a blood alcohol level that corresponds to being drunk, have dreams where he is completely sober? It should be possible to do a controlled experiment where alcohol is administered through IV through the entire period of the subject's sleep to keep it at some level, and ask him to recall his dreams. If in his dreams, he is completely sober and drives vehicles normally, then there is something quite mysterious. This would imply that a blunt-force compromising effect of alcohol can be completely negated in the CBS, if the brain decides to.

This, and the overall meta nature of dreams leads me to believe that there is more to it than meets the eye, when it comes to the brain. Even if we leave the hard problem aside, and assume that other beings are zombies, we can still assume they dream. (Since when asked what dream he had, a zombie would answer no differently from a conscious human.) And the fact that the brain seems to have seemingly infinite power when it comes to staging the entire set in real time, as well as negating the effect of blunt acting drugs, I am wondering whether there is an infinite-complexity engine powering the brain. With such an engine, a small part of it still equals the whole. Maybe that's the secret behind consciousness too. In terms of information theory, the entropy of the brain can be infinite. The entropy of purely random phenomena is also infinite. Quantum mechanics, which reconciles to the randomness of nature, and which led Einstein to proclaim "God doesn't play dice with the universe", may quite well be the key to the hard problem as well as the seemingly infinite capacity of the brain, even a zombie one.

Saturday, August 18, 2007

The binding problem (part 2)

I wish to give my own thoughts on the binding problem. It refers to how all our sensory qualia seem to be tied to each other in a consistent way. We all can ascribe spatial attributes to all sensory qualia. In the case of sight, this is pretty obvious. Same is true of sound also (although it is not as localized). Same goes for the somatosensory qualia (touch, pain, etc).

In case of smell, it still resides in the same 3-D space (which I call the CBS), but is spot bound. In other words, the sense is not distributed among a finite region of the CBS, but still belongs to this space (somewhere in the head region).

The brain being an amazingly plastic network, I am not sure how the binding occurs. Is it through a purported higher level association between different types of qualia emanating from the same source (or direction) that the brain figures out automatically over a period of time?

As an experiment, if you wear active goggles that makes you see what you would if you stood facing backwards, and if someone were to clap his hands behind you (so you would now get to see it), you would be confused because the sound comes from the back while your vision is to your front (because your eyes point to the front). But if this experiment were to be performed on a baby monkey, with permanent goggles, it is quite plausible that the senses would recalibrate and "rebind" after a period of time, so that the grown-up monkey would now actually see and hear in the same direction of the CBS. The brain seems to like consistency and keep working at it. I think that even in humans there is a continuous rebinding taking place, since as a person grows up the shape, size and separation of the pinnae (external ears) keep changing, but doesn't really throw off the binding between sight and sound. But I also wonder if a person who is blind from birth can ever afford this kind of recalibration since there is nothing to calibrate against. Another related condition occurs in the case of squint eyed children. When the brain determines that the eyes can never get to focus together, it simply starts discarding the information from one eye, and a condition called amblyopia in which that eye loses its vision results.

But this whole thing seems a bit spooky to me. It seems like there is a hidden observer within our brains that seems to be tweaking our senses without our conscious perception. And this observer needs to be fairly intelligent too to associate sight with the corresponding sound, and may require higher level processing. For example, how does binding take place in a kitten's brain? Let's say, we have a newborn kitten in a cage, and there is a circular arrangement of lights and loudspeakers on the floor a distance of a few feet from the cage, with the cage at the center. Further, let us assume that the sounds of the speakers is all the kitten can hear. Now, if one light is turned on, but at the same time, the speaker on the opposite side is sounded, and this pattern is repeated randomly for all the lights, over some time it is possible that the kitten's hearing binds inverted in its CBS. So the kitten might actually start hearing the sound from the same direction as the bulb. What drives the recalibration in the poor kitty's brain is the fact that its higher cognitive areas somehow associate the light with the sound, detect an inconsistency, and requests the lower areas responsible for the binding to reorient. But what if, instead of a simple association as above, we had a more complex one like as follows- initially the kitten is taught to associate a low-pitched sound to a circular figure and a high-pitched sound to a star figure. Then we show the circular and star figures on opposite sides of the cages, but sound the speakers in the reversed sense (so that the low-pitched sound comes from the star figure side and the high-pitched sound comes from the circular figure side), and keep repeating this for different directions. Now the question is, will the higher-level association of the shape to the pitch compel a rebinding to take place? If the answer is yes, it would seem absolutely creepy! Had the kitten not been taught to associate the shape with pitch, no such rebinding would have taken place. Actually, this is just a hypothesis, and I am not sure if this will happen, even assuming the experiment is practical. Plus it would be difficult to know if the rebinding actually took place, or the cat now consciously associates sound with the opposite direction (the end effect would be the same in both cases).

I call the above examples forward binding. For, the binding takes place from the various sensory inputs in the waking state. But in dreams, there are no external sensory inputs. The different groups of neurons that are responsible for different senses (in dreams) still have to make sure the combined experience is bound properly in the CBS. Therefore, it seems like in dreams, the different sets of neurons don't work independently, but rather get instructions from the binding center to create a consistent sensory experience. I call this backward binding. I think backward binding is more difficult to accomplish than the forward case. In the forward case, once the sensory parameters have been tuned, any external stimuli will automatically lead to binding (assuming the external stimuli are themselves consistent). Exceptions occur with inconsistent stimuli like in the case of motion sickness. In backward binding, all sensory qualia (sight, hearing, smell, somatosense, vestibular sense, etc.) have to kind of mesh with each other, with another portion of the brain orchestrating the whole scene at the higher level (including the theme). And all in real time! That's truly amazing, if you think about it.

Also I wish to bring up the concept of access once again. As I had already discussed in previous posts, we have access limitations with respect to the nature of the hues (eigenhues), as well as intensities. But there is also a spatial variation of intensities (or access), determined by the location in the CBS. For example, it is easy to perceive a sound coming from the back of your head (try snapping your fingers at the back of your head). For the same reason, we can imagine or dream the same. But it is impossible to even imagine or dream seeing anything at the back of your head. This is because of access limitation of sight. The access intensity limit falls off to zero outside of the normal field of vision.

The above observation leads me to believe that the intensity limit of a particular eigenhue as a function of the position in the CBS is decided by the number of corresponding "entities" that are mapped to the same position of the CBS that can be simultaneously excited to produce the corresponding quale. I have left out what the "entity" refers to. It could be the excited state of an "eigenhue molecule" or maybe some fundamental pattern of neuronal firing. For sight, the density of such entities corresponding to any part of the CBS to the back of one's head would be nil (although in the case of hearing, it's obviously not the case).

Also, I believe that this access gateway is common to the waking state, dream state, or the imagination state. It is possible that under the action of psychotropic drugs, the access gateway may get modified somewhat (and this might explain the "heightened experiences" reported by some). But it is very unlikely that drugs can actually cause a new eigenhue to be perceived (such as a fourth fundamental color). It seems like they can only modify the intensity maps.

But does it mean we cannot ever hope to perceive a fourth color? Or feel what it is like to be a bat? I refer to this as the "integration problem" as opposed to the "binding problem". It may well be possible. But that will be for a future post.

Tuesday, August 7, 2007

The Terra Firma assumption trap

Most religions posit one form of dualism or another. After all, they all have to do with the recognition of suffering (qualia, if you wish), and this leads to the classic mind-body problem.

In Abrahamic religions, the universe itself is a real entity whose existence is undisputed, and independent of the souls that use it as their turf. The souls reside in bodies (that are part of the universe), and interact with other bodies (and hence with other souls). Souls do not interact directly with one another, but have to do so through the medium of the physical universe. After the departure of the soul from the body, it goes to various places like paradise or hell depending on certain criteria. It is unclear whether these places are part of the same universe or are different. But souls get to interact with each other once again (through bodies) at these places!

In Vedanta hinduism, however, the universe itself is an illusion, and is a product of the brahman (the universal consciousness, see this post). While many call this monism (which I think is a mistake), I think the closest modern philosophical idea that mirrors this is solipsism. Actually, according to my idea, we can admit the existence of multiple souls, but have a single brahman behind all of them. The multiple souls may or may not inhabit the same universe as I think I inhabit. If I admit other conscious beings in my same universe, I wish to term it inclusive solipsism. But if I am just dreaming up the universe, even admitting that other conscious beings exist in it makes no sense (in the same way as admitting that other people in our dreams are conscious).

Therefore, whether or not one is an inclusive solipsist, admitting that other conscious beings can also cohabit the same universe automatically leads us to concede that the universe has some kind of an independent reality of its own (and not a product of our mind). I have called this assumption the terra firma assumption in one of the earliest posts.

Of course, solipsism doesn't imply that there cannot be other souls in parallel universes which do not interact in any way with this universe.

Scientists are now trying to figure out the hard problem. The very recognition of this problem assumes that the universe is real, and that consciousnesses are a product of physical processes in this universe. Solipsism assumes the reverse - that the universe is a creation of the individual's mind.

Perhaps the most persuasive evidence for solipsism comes from our my dreams - the world in my dream is as real as the world in the waking state. Searching for a solution of the hard problem in my dream seems silly upon waking up - definitely my subjective experiences during the dream had nothing to do with the physical processes that were part of the dream universe. I might imbibe alcohol in my dream and consequently feel drunk, but the cause and effect are just an illusion that becomes apparent on waking up. Substance dualism assumes the same, but at one level up in the heirarchy.

The reason so many scientists have tried to explain consciousness (and even God) is because they have all become victims of the terra firma assumption trap.

Experimental physics (including the WMAP satellite, or the LHC currently being built) gives us all goosebumps. We (solipsists included) are euphoric and get carried away closer and closer to this trap, in moments of weakness. Physicists like Weinberg, Capra, and even Penrose now seek to explain everything in terms of a few fundamental equations. Then there is the mystery of the anthropic principle which explains why fundamental constants are tuned in such a way as to support life.

But if we abandon the terra firma assumption, there is no need for any anthropic principle. In fact, the only thing that the WMAP satellite and the LHC will tell me is that the observations are consistent with the scientist's predicted theories. It does not tell me that the age of the universe that I feel around me is 13.7 billion years. The whole universe that I perceive (LHC, WMAP satellite et al included) is through my qualia. I have no way to vouch for the existence of this universe in a fashion that is independent of my qualia. Therefore, it is irrelevant to conjure as to how long the universe had been there before my existence. The notion that experimental evidence corresponds to reality itself comes under question, since "experimental evidence" in whatever form ultimately boils down to qualia states of my own mind.

Friday, July 27, 2007

The binding problem

I had in this post suggested a universal consciousness behind all conscious entities. The motivation for this had to do with ethics. I strongly feel that ethics and fairness are not just Darwinian concepts with survival value, but something more fundamental. In fact, I would say that the presence of pain qualia (both physical and emotional) implies ethics as a concept at the platonic level.

As a take on the famed Schrodinger's cat experiment, let us consider a cat in a sealed steel box that is slowly heated by a flame on the outside. Also consider a vial of a tranquilizer inside the box that may or may not get broken early on (if broken, it anesthesizes the cat). Now, at the end of the experiment, the temperature inside gets so high that everything gets charred (including the vial) and the chemical composition of the remains is the same whether or not the cat got anesthesized. However in one case, the cat suffers a great deal (getting roasted alive), and in the other case, the cat suffers a painless death.

Now, if a human being were given a choice to either break the vial (through some remote control mechanism) from the outside or not, is there a moral obligation for him to choose to break it? From an ethical standpoint, the answer is a resolute yes. I don't think that even those who strongly believe in functionalism would choose otherwise (especially if it is their pet cat).

But from a physical standpoint, since both the initial and final states are the same in both cases, and the intermediate states are bounded to within the dimensions of the box that is shielded to the outside , it should make no difference one way or the other. It is obvious that there is a glaring inconsistency in functionalism from an ethical standpoint.

Even if we leave aside compassion, the thought that some conscious entities enjoy a good life while others suffer irrevocably during their brief existence for no fault of theirs, is aesthetically repugnant, given that pain qualia exist. This is the primary motivation for most religions explaining that such injustices are either corrected in an afterlife, or are the corrections to some injustices in a past life.

However, if we assume that all conscious experiences are in the end perceived by the same entity, a lot of the moral and ethical conundrum dissappears.

So, if there is a "mother consciousness" behind all conscious beings, then how does it get compartmentalized into the varied experiences of multiple beings?

The answer may lie in the "binding problem". Recall that the binding problem refers to how the subjective experiences of different qualia (sight, hearing, touch, etc) all come together to form a consistent and unified experience for a single individual.

I speculate that at a higher level, the subjective experiences of this "mother consciousness" (which would be all the experiences of all conscious entities in any physical universe) gravitate towards multiple binding spaces, with each binding space associated with what we call a conscious entity (or a soul).

I postulate that these spaces are 3-dimensional, and I have already referred to these as the "common binding space" (CBS). When a conscious entity is created or destroyed (as in death), a new instance of the CBS associated with that particular entity is created/annihilated.

As I had already suggested in this post, emotional qualia are bound to (or dwell in) the CBS of a particular entity. So any CBS basically carries with it the entire works of the conscious experience of an individual entity, including physical and emotional qualia.

So, even if pain and emotional suffering may be associated with individual CBSes, the actual perceiver is the mother consciousness, although the neat packaging of the collective experience into individual CBSes gives the notion of identity and individual experience.

As alluded in the above referenced post, the CBS serves as the substrate for qualia. This I feel, is true of a worm as much as a human. And since the physical world we live in is 3-dimensional, the CBS in each case is also 3-dimensional.

Each instance of the CBS pops in and out of existence based on physical processes. A patient given an anesthesia loses his CBS. And with that goes not just his physical qualia, but also his emotional ones (in other words, he is now unconscious). Of course, he regains a CBS once he comes out of it (there is no point in talking about whether the new CBS is the same as before - it is immaterial, and all sense of continuity of individual identity is tied to his physical brain).

The brain of a patient whose corpus callosum is severed suddenly pops a new CBS with a portion of his overall experiences migrating to the new one.

It would be interesting to find out what causes a new instance of the CBS to form in the first place. Is it classical or QM phenomena? Or is it some kind of objective reduction "OR" postulated by Penrose and Hameroff?

With advances made in cognitive neuroscience and brain mapping, we may get close to an answer. Not that we would have an answer to the hard problem, but we might inch a bit closer to the problem of how physical processes relate to identity.

Sunday, July 1, 2007

Physics and qualia

I was reading Roger Penrose's "The Road to Reality", and was glad that he addressed the philosophical issue of how physics, mathematics, and perhaps even our consciousness interface, in the very first chapter.

In that chapter, he has an interesting diagram of three different worlds, the Platonic mathematical, the physical, and the mental, and how they relate to each other.

I think the majority of physicists, though using completely mathematical methods in attempting to explain the universe, still hold the belief that the stuff they are dealing with is somehow "real" as compared to pure mathematical objects (in other words, the Platonic world, that has an exact correspondence with the real world, obeying the final laws of physics in the same manner).

Thus, the physicist sees concepts like mass, charge, and so on as being something real, and mathematics can only describe "how" they behave, but never "what" they ultimately are. It is almost that the physicist treat these concepts similar to qualia, to use the term loosely.

While a mathematician who programs a computer that simulates the universe may declare mass, charge, and so on, as nothing more than predefined data types , physicists may suggest that these concepts are not just zeros and ones residing in the computer, but might have a deeper meaning that, while not making any material difference to the execution of the program, is nevertheless essential for actually making the program translate to reality, instead of just a simulation of reality.

While many physicists would avoid the qualia/hard problem debate, they unwittingly hold spacetime itself to be something "real", as opposed to being some mathematical structure. Thus, a physicist might not try to explain what "red" and "blue" really are and might even dismiss them, but he would most likely balk at any suggestion that their own perception of space and time as they seem exists only in their minds, and may just be an array of zeros and ones in an ongoing simulation. The physicist is getting duped by his own subjective experience of spacetime and therefore holds it in reverence compared to platonic mathematical objects.

But one cannot blame him for that. All of physics is based on observations of physical phenomena as they happen in our three dimensional universe which flows along time. No one can even imagine a fourth dimension. String theorists have broken this mould, but at present, they are more concerned with trying to explain reality as they happen in our real three-dimensional world. The rest of the dimensions are apparently "curled up" tightly on the order of the Planck length (some 10^-35 m) , so we cannot perceive them.

But then, why cannot we even imagine a fourth or higher dimension? If you are familiar with my previous posts, you probably have guessed where I am headed. Yes, you were right! It is tempting for me to suggest that the platonic qualia space has more than three dimensions, but we have access to only three.

But I choose not to. For the perception of spacetime, in my opinion, is not on the same footing as other qualia, such as the color red or the taste of beer. The access concept doesn't apply to spacetime, as it does for sensory qualia which are bound to the common binding space (CBS) (see this post for an explanation). Here we are dealing with the underpinnings of the CBS itself.

More on this in a future post.

What is reality?

How does one define reality? Is it supposed to be certified by a conscious agent? Well, if the conscious agent is a result of processes in the world that it is trying to certify as real, does that validation have any merit to it? Doesn't the whole argument become circular?

I suppose that when I am dreaming, the world in the dream is in every way as authentic as the world in my waking state, at least for the duration of the dream. But the moment I wake up, I realize that it was an unreal world, a product of my own consciousness. Now can the same be a possibility of the world that I belong to in the waking state? Of course, this enigma is nothing new. It's been the subject of philosophical debates for millenia.

It is possible that my consciousness has nothing to do with the physical brain in my waking state. To give an analogy, in my dreams, I might be led to believe that my awareness is a product of the neural processes happening inside my head in my dream avatar, but the moment I wake up, I know that that isn't the case. This would then correspond to a Matrix-like scenario that I think David Chalmers likes to point out.

I guess the quest for solution for the hard problem assumes otherwise. If the above is true, then the whole issue is moot, for it would be a wild goose chase to try to come up with any explanation.

So then, what is reality? Does it still need a validation by a conscious agent? We saw that it doesn't always work.

I would say that the only definite reality is conscious entities themselves. A conscious agent is its own certificate. A conscious agent, of any form, spirit, or matter, does not need an external validating agent. If a conscious agent feels pain, it feels pain, period. No one (even in another universe) can deny it.

While us conscious beings can deride other parallel universes and basically claim that what that doesn't affect us and cannot affect us doesn't matter to us, if we come to know there are conscious entities in those universes that suffer, we might still empathize with them.

If we were to be asked a question "Is there suffering?", the answer to this question would include not just of beings in our universe, but of all possible fictional universes (from our point) that have conscious agents that undergo suffering.

This is because, all conscious agents spawn their own reality, and in the fraternity of conscious beings, suffering by one has to be acknowledged as suffering taking place by all other conscious beings of different universes. And even the time parameter may not be shared by all these universes, so the suffering experienced by one agent may not even correspond to a timewise progression in another universe. It's indeed a bizzare kind of acknowledgement of suffering which extends across the fraternal order of conscious entities.

I call this meta fraternity of conscious entities.

Tuesday, June 19, 2007

The structure of qualia space

I have already hinted at the idea of platonic versus access qualia spaces. The access qualia spaces are essentially windowed versions of access spaces where the windowing is carried out both with respect to the intensities as well as the dimensions, or rank-lowering projection operations. The former is a non-linear operation, the latter a linear one.

But one wonders about the structure of the platonic qualia space itself. This would be the mother of all qualia spaces. For example, we know that human vision is trichromatic. But does this mean there are only three different independent color axes in the platonic qualia space itself? As I had previously hinted at, many birds have tetrachromatic vision, so does this mean there is a fourth color axis that is not accessible by us humans? If that is indeed the case, then can there be a fifth, sixth, and so on? Are there a finite number or infinite? And do there exist operators between the various axes of the platonic color space?

The reason for hinting at operators is because, if we take the eigenhues of pitches, there exists a "pitch comparison" operator that orders the eigenhues (in the case of sound, any pure pitch is an eigenhue, and there are an infinite number of them accessible to us humans), and we can also, by corollary, construct eigenhues out of existing ones (like an octave above, a semitone below and so on). The relational operator forms the basis of music theory, and we will not have any sense of melody if this operator were not accessible to us. I call this "operator access", since it is an operator (which should also be present in the platonic pitch space) which is accessible to us on "this" side. I wonder if the eigenhues corresponding to colors have some relational operator on the platonic side, but which is inaccessible to us. Without the operator access of pitch comparison, any melody would be akin to a light show without much meaning.

The very fact that we have the accessible pitch operator implies that the platonic qualia space for pitches is infinite since we can have an infinite number of octaves either way by applying the pitch operator successively. In terms of standard pitch theory, pitches can be viewed as a helix that is a function of frequency that, because of human limitations, run out at the limits of 20Hz and 20KHz. But the mere presence of the operator implies that the platonic helix is infinite in extent, both up, and down.

The pitch operator is akin to a real number operator like multiplication. If an operator were to exist for colors, depending on the exact mathematical structure of the color eigenhues, it may be a discrete one like for modulo arithmetic. But we don't know, since access of such operators, if any, is forbidden, and we don't have any clues at our disposal.

Sunday, June 3, 2007

Can deterministic computing produce consciousness?

In this post, I had shown that two or more physically separate computers executing the same program trace can produce one consciousness at the most. Now the question remains as to whether even one consciousness can be produced as a result of a program execution.

According to the "strong AI" hypothesis, a computer running a program produces consciousness. This statement is admittedly vague, since one cannot really define what one even means by "running a program", except perhaps in the view of strong AI advocates.

If one considers a computer's state at any time to be comprised of N bits (that is, its memory), then the execution trace can be interpreted as a N-bit vector as a function of each clock cycle.

Let us now assume, for argument's sake, that a computer running a (finite) deterministic program does indeed produce consciousness. If we store the N bits for each clock cycle on the hard disk and replay them (on the same digital nodes as the original execution), does the act of replaying the trace produce consciousness again? If the strong AI advocates answer no, then they have some explaining to do as to why that's the case.

If on the other hand they assert that replaying the trace is no different from executing the program, then we need to look a bit more deeper into what constitutes "replaying" a trace.

The key issue here, I feel, is that an "external" conscious agent is necessary to even assign a meaning to the pattern of those N bits. For, being a chip designer myself, I have designed circuits where every other bit of a memory is flipped internally (to reduce the number of transistors). So if the execution is replayed with the even bits flipped, would it still produce the same consciousness?

What if the successive N bit vectors are hashed according to some hash table (which has entries for each bit for each clock cycle)? Now, without the hash table, the whole execution trace is garbage. But if the entries are taken in accordance with the hash table, then the execution would correspond to the original program. In that case, is it necessary to physically accomplish the dehashing step any more than it is necessary to physically re-invert the flipped bits in the previous example? If not, there always would correspond some hash table "out there" which would make any garbage bits correspond to a meaningful simulation. And since there are an almost infinite number of abstract hash tables available to do the dehashing (with only a small subset corresponding to meaningful simulations), which one(s) get chosen? Now the strong AI advocates cannot argue that it depends on which hash table the observer uses to interpret the bits, since that undermines their claim that the trace produces consciousness on its own with no external intervention.

Surely, assigning a meaning to the N bits seems to be a contentious issue. But even more contentious is what is meant by the bits themselves. To illustrate this point, let the N bits be transmitted into space as parallel light beams, with a '1' corresponding to a light pulse and a '0' corresponding to the absence of any. Let us assume that the light excites molecules in the gaseous medium, so that the molecules in a plane perpendicular to the direction of propagation can be used as a marker for the program trace. But wait, if we assume the light to travel a great distance, then different planes (an infinite number) will correspond to different times of the execution trace. So which plane should be selected to correspond to the actual conscious experience? What if someone chooses a plane of observation which is oblique to the direction of propagation?

It is pretty clear that the role of the observer is quite pivotal in interpreting the execution of the program. And we cannot accept the argument that qualia is observer dependent. For at a given physical time, I feel either hot or cold, not something that depends on who is reading off my mental states (as in the case of the thought experiment given above). If there is contention regarding that, then we are dealing with a different problem. Which is good, since I believe the problem we are supposed to be dealing with is itself something different.

I find the whole assertion of strong AI (as outlined above) rather silly and without merit.

Wednesday, May 16, 2007

Universal consciousness and meta ethics

In this post I had indicated that if there is only a single consciousness behind all living beings, then the question of justice and fairness are not relevant, since the perpetrator and victim are one and the same. Although this seems to be a fairly obvious conclusion, in reality it is not so straightforward.

Let's take criminal justice as an example. The two main reasons or punishing an individual for a crime committed by him/her are as follows-
1. Deterrence - To teach the individual (as well as others) that crime doesn't pay, so they don't commit it again.
2. Retribution - In this case, even if it certain that the individual will not repeat the offense, the law may seek a penalty from him/her just so as to make him/her suffer for the wrongdoing, even if it has got no further deterrence value either for the individual or for others.

Now let's take an example of a person who has been found guilty of a certain crime. But after committing the crime, let's say he suffers a severe head injury that either renders him insane or suffers permanent amnesia that makes him totally unaware of the crime he had committed. In most civilized societies, the individual would not be meted out the same punishment as he would be if he were fully aware of his wrongdoing. This is because, most societies require that a criminal be aware of what he is being punished for. Although this lessens the scope of deterrence (since the punishment is now less for the same crime), there is also an implicit belief that the individual now is "not the same" as the criminal who comitted the crime, and therefore should not get punished since it would be perceived as tantamount to punishing an innocent person.

But from a metaphysical perspective, is it really so? If we go solely by the retributive aspect of criminal justice, it should not make any difference whether he remembers the crime or not, provided we accept that it is the same consciousness as the one responsible for the crime that would suffer the punishment. If we start making the assumption that the loss of memory makes the individual different (from the perspective of the homuncular identity), then of course, we cannot ignore this aspect.

So it seems that society treats people as conscious individuals with identities that are determined more by access. Since society is not capable of reconciling the two different access identities (one before the accident and the other after), it can be hardly expected to do so in the case of different people or other life forms when it really turns out that there is a single consciousness operating behind them all.

For example, religious fundamentalists would still hold the belief that the pain felt by a human fetus in an abortion is somehow more tragic than (the same) pain felt by the fetus of a cow.

If we disregard access altogether, then if there is a single consciousness behind all living beings, then as I had mentioned in the earlier post, the question of criminal justice and ethics go away in a meta ethical sense. Of course, there are evolutionary reasons for having justice and punishment (solely determined on the access side), so one has to respect those. But these are mundane motivations rather than any meta ethical ones.

But let's assume for argument's sake that there are two consciousnesses operating behind two sets of people respectively. So if one person from one set has wronged the other set, then does it become fair to punish someone else from the offending set? My personal belief is that it should be ok (provided we are certain that it is the same consciousness operating behind everyone in each set). For the agent undergoing the suffering is not the person himself, but the consciousness operating behind him.

If the last paragraph is hard to digest, think of the two master consciousnesses as two people and the individuals in each set as bank accounts belonging to those two. When any transactions are made between banks belonging to the two, we only look at the net the first person owes the second or vice versa. We do not worry about details of which bank accounts were involved. In legal theory, when a statement like "John owes Peter" or "John has to repay Peter" is made, the details of which bank accounts are relevant are left out, since they do not matter in the larger picture. It is possible that entirely different bank accounts were used on both sides while repaying the loan, as opposed to while borrowing it.

I strongly believe that a similar argument holds in meta ethics too.

Wednesday, May 9, 2007

Evolution of qualia

In this earlier post I had alluded that evolution confers advantages to beings that perceive qualia. But how does evolution go about the process in the first place? It is rather striking that we perceive unique qualia, not only for the "standard" senses like sight, hearing, and so on, but also for functions which depend on morphology and biology, such as thirst, hunger, vomiting, defecating, and also such ones like water entering the nostrils, etc.

In every case, the qualia seem to be a "perfect match" to the stimulus or condition that we cannot think of an alternative. For example, while it may seem plausible that for the purpose of warning about water entering the nostrils, another unpleasant sensation like pain might be equally effective, it wouldn't have just "seemed right" as compared to what we all experience. So how did evolution settle on the various qualia which seem so fitting to the intended stimuli? Was it by trial and error? Were creatures which experienced pain instead of what we feel when water enters the nostrils (geez, is there a word for that?) at a disadvantage?

Also how did evolution pick out new qualia before it even let them play out the evolutionary game? Was it out of thin air? How many different qualia spaces does the bucket of platonic qualia spaces hold? If in the course of biological evolution, a new mutant needs a new sensory input/response mechanism, then will the appropriate qualia space automatically get tried as a normal part of evolution? If that's the case, we can think of an evolutionary battle between qualia spaces in serving a particular sense/response need.

I assume this is probably what happened when bats came up with echolocation. If we assume that before that, they relied on sight alone (and assuming that their sight corresponded to the same qualia space as ours), then echolocation would have initially groped for a new qualia space. It is also possible that after several tries, or in some species, the qualia which corresponded to their earlier vision hijacked echolocation, with a new, less efficient one for the original eyes.

But again, going back to the more fundamental question, how many different qualia spaces does the fundamental platonic qualia space hold? Did there exist abstract qualia spaces for biological mechanisms like hunger, or sex, even before the needs for them arose, like when the earth had only unicellular organisms like the amoeba? And in the future, if a creature needs a new biological mechanism, can it expect to garner appropriate qualia for that? If the number of qualia spaces is finite, do existing spaces need to be recycled?

Also what are the "hooks" that creatures use to access these abstract qualia spaces? Are they QM processes? Hmm.. that would be rather interesting to have a QM wavefunction for sexual desire! I guess we are headed in the direction of the hard problem already..

Monday, May 7, 2007

Renaming my conjecture

In this blog I had conjectured that the eigenhues perceived by two different individuals are exact. This conjecture cannot be either proved or disproved without the hard problem itself getting solved. I think that this conjecture (if it turns out to be true) would be a fundamentally important result that I wish to give it another name. I am calling it the "no tinted glasses conjecture" instead of "Shankar's color perception conjecture" after shedding my ego considerably. The new name actually conveys the meaning of the conjecture more deeply and dramatically.

For this not only implies that two normal individuals cannot have colors grossly inverted, but actually goes on to say the colors match to fine precision. Anyone who wears tinted sunglasses will initially notice the difference but will get used to it in no time. So two individuals who wear green and red tinted glasses would still "pass" according to the inverted spectrum principle, so an argument can be made that all individuals have this amount of hue variation to begin with. But my conjecture states that there is absolutely no variation whatsoever between individuals perceiving eigenhues due to direct stimulation of the neurons that are the "final link".

Again, I wish to caution that actual vision is subject to variations right from the lens and the cone and rod cells in humans, so the colors may not match. Indeed, in my own experience, seeing with only my left eye results in a slightly bluer (and cooler) sight compared to seeing with my right eye, though this is barely notiecable. Please refer to the earlier blog for a more detailed explanation.

Monday, April 23, 2007

Towards a formal model of qualia

I am sure that this is not the first attempt at it, but I wish to give a try at constructing a formal model of qualia. For starters, we first need to define what "qualia" means. Most of us know that this is the plural of "quale". But what is a quale? Is it the color red? Or is it the perception of some shape of the color red? (There is a difference of formal interest between the two.)

In this blog, I make the latter assumption. I call the color itself the "hue". And I term the gamut of all colors that can be perceived by a particular consciousness "qualette" (taken after palette, the range of colors). In terms of sound, a particular pitch is the "hue". An actual sound of the pitch is the quale corresponding to the pitch. And the set of all pitches that can be perceived by a consciousness is the qualette corresponding to sound. And I call different senses (hearing, vision, smell, and so on) just "senses". And I call the collection of senses at any given time along with the emotional state at that time, the "state". A non-zero trajectory of states is an "experience".

I want to clarify what I mean by "perceive". This is the equivalent of the term "access" I have used in the previous posts.

Now, the idea that a conscious state can be modelled as a point in some space is certainly nothing original. Let's not jump ahead and assume that this space is a Hilbert space now. But let me give my own view points of what this space is going to be like. I would also try to address the binding problem in the same breath.

Senses like sight, hearing, and touch have a 3-D "space" associated with them. We see objects in 3-D, because of our two eyes. Same holds for hearing (we can roughly determine the direction from where medium and high pitched sounds emanate. This is the reason we have surround sound systems. Of course the spatial resolution is much worse than that of sight.). And of course, if a portion of our skin itches, we know where exactly to scratch. The key point is, since the perceptions themselves are qualia, the aforementioned spaces are the "qualia spaces" corresponding to those senses. The binding problem (actually not a problem as much as an observation) states that the spaces corresponding to the different senses are "bound" together, so that the overall experience is consistent. For example, if we see a songbird in a particular direction, but its singing comes from a different direction, we would get confused. In the case of "out of body" experiences, the senses are bound to each other in a consistent way, but the "mind" moves around. This implies that the mind (or emotional qualia) also have a spatial relation in the same sense as sensory qualia but this might be a "spot" instead of a non-zero volume. I call this "spot bound". We can take the emotional qualia's center to be the coordinate reference, since this is the center of vision of the "mind's eye". I call the space the "common binding space" or CBS.

I think the senses of smell and hunger/nausea are also spot-bound, although the spots are obviously at different locations of the CBS. Please note that by "spot" I mean exactly that - I don't mean a very small area that can be approximately considered to be a spot from everyday experience. An actual way of confirming whether a sense is spot bound or not is to see if spatial information of the particular sense organ is processed/routed in the brain. In the case of smell, I don't think spatial information generated by the olfactory bulb is processed by the brain anyway. So we cannot really figure out from where a particular odor is coming unless we move around. I am not so sure about hunger or nausea. For example, if cells corresponding to hunger are activated in the lower region of the gut as opposed to the upper region, does the qualia of hunger also shift vertically?

So we can construct a space, and the whole experience at any time can be given as a point in this space. This point would move with respect to the "proper" time of the particular consciousness, which may be different from the physical time stream (and not to be confused with the proper time of the theory of relativity). Let us be clear on this. Let's assume two people A and B who both have the same qualia till they pass out (due to administration of general anesthesia) which puts them into deep dreamless state of unconsciousness. If A is revived after 5 minutes, but B after one hour, and there is no clock in the room, how exactly do their respective qualia points move in time? If after waking up, their experiences are exactly the same, they should not be able to tell for how long they were under the anesthesia. Their qualia trajectories should be identical. But this would not happen so simply if physical time is used to mark the points. If we parametrize the qualia trajectory as a function of the "proper time", it should be noted that in periods of total unconsciousnesses, proper time itself is undefined. Hence if proper time is used as the parameter, blackouts would correspond to the zero state of the qualia space, and every conscious stream of experience begins and ends at this state. In the example of the two people A and B, the trajectories would be identical in both cases for both before and after the period of anesthesia, in other words the total conscious experience. The "real time" spent at the zero point is meaningless when one uses the proper time for parametrization. Any attempt to relate "real" time to proper time suffers discontinuities at the zero point. Of course, this does not mean that we have to use proper time only. We can use real time, provided we accept that different qualia trajectories may correspond to the same experience if there are blackouts. Since the mapping of real time to proper time is one to one or many to one, never one to many, any meaningful trajectory with proper time as the parameter would lead to a continuous trajectory in real time without any stagnation points (multiple qualia states at the same real time). Also note that there is nothing that prevents a qualia trajectory (with whichever time parameter) from intersecting and coinciding with either itself or with others.

So how do we go about constructing this space? Since the CBS seems to be common to all senses (including emotional ones), we can annotate sight, hearing, touch, etc. data to each point of this space and construct one giant string. Note that we collapse the data over the entire CBS to a single point of our qualia space in doing so. For senses that are spot bound, we need to add their data along with only one coordinate in relation to the origin of the CBS. This would take care of even out-of-body experiences.

A word on emotional qualia states. While physical states can affect emotional states, it might seem that emotional states don't spill over into physical states. But there is an exception. This is the case of "imagination states". For example, A and B can be undergoing exactly the same physical qualia trajectory, but A can also be imagining a physical state different from B's at the same time. When A and B are looking at a green background, A can be imagining a big red disc in front of him while B can be imagining a blue square. These are different from hallucinating the same. But the imagined qualia can be as good as real ones when one performs operations in qualia space (see previous post) on them. For example, one could remember one's favorite song and start playing it in one's head. But when actually playing it on the CD player, one frequently realizes that the "imagined" version was pitch-shifted by one or two keys. What the person succeed in doing was apply an operator (comparing pitches) operating on two quales in qualia space (one corresponding to the physical state, and the other corresponding to the imagination state). One could also perform the same operations on quales existing solely in the imagination state. For example, I could determine which of the three spots I imagined was the brightest, or imagine a color between two colors which also I am imagining. Note that in the first instance the function result is a non-quale (a logic value) while in the second instance the output is a quale itself.

I wish to reiterate that imagination is different from hallucinations or dreams. If I imagine a red disc on a green background and actually end up seeing one, I would run scared! That would be a hallucination. The physical states of both hallucinations and dreams are indistinguishable from the "normal" physical states, and therefore considered as one. The imagination states are something that need to be included in the state vector, but separately from the classical state. So the entire "normal" physical state space is duplicated for the "imagination" state space. Also it should be noted that imagination states are bound to the CBS just like their physical counterparts. I can imagine only qualia, not the hues themselves (see the beginning of the post).

Does there exist an imagination counterpart of mental qualia? Speaking for myself, I couldn't come up with a decisive answer. I can imagine that I am angry, but I am not sure whether I really get angry at the moment! That would be similar to imagination turning into a hallucination in the physical realm.

Now coming to the representation of actual data. I would deal with only two, sight and sound, in this post. Although this is for the "normal" physical states, it applies equally well to the imaginary states.


For sight, for us humans with trichromatic vision, each point in the CBS has 3 independent quantities, namely the intensities of the eigenhues. This is all the information that is needed. It should be noted that this is a 3 dimensional space, and the operations the mind is able to perform on quales of sight are mixing operations only. In other words, the resultant quale would belong to a subspace of the input qualia. If someone has access to only two of the three eigenhues (due to a "back end" color blindness), then there is no way the person can come up with the missing eigenhue.


This is more complicated. At least theoretically, no two sounds are subjectively the same unless the complete Fourier spectrums of them are the same. So, in theory, we need an infinite dimensional vector space to represent the sound of a single point in the CBS!

There is one more complication, which I have discussed in the last post. This is, even though the pitches of all frequencies are orthogonal to each other (since the Fourier spectrum has to match for every frequency), there exists operators in qualia space where a single pitch can generate the entire gamut of pitches. Examples of such operators are "move up by a note" or "move down by a half note". So even though we have an infinite number of basis vectors in this space, fixing a single vector in this space fixes all of them! (One might wonder if two distinct pitches are required - after all, what one individual means by "moving up a note" might actually be the equivalent of "moving up by two notes" to another individual. But since pitches an octave apart have to sound the same, while pitches any closer should't do so, an individual would detect an inconsistency if "moving up by a note" meant a different ratio in qualia space- he would determine the matches come sooner or later than they are supposed to.)

Take the case of the inverted spectrum problem. In this case, even if we are sure that one of the eigenhues are the same for both individuals, that doesn't automatically imply that the other two are not swapped. But in the case of hearing, if we are certain that the pitches corresponding to a single tone are the same for two individuals, then we can be certain (at least theoretically) that all pitches between the two individuals match.

Access vs. platonic qualia spaces

As I had discussed in the previous post, the platonic qualia space for sound would have an infinite number of octaves. For sight, I am not sure if it is also infinite dimensional, or if its dimension is limited (certainly 3 or more though). Birds are tetrachromatic, so possibly the dimension is at least 4. It is possible that each species, even if only trichromatic, has totally different eigenspaces from humans, so one wonders what the dimensions of the platonic color space is. Note that the platonic space is at least as great as the combination of all access spaces (of whatever species). Note that the space refers to a single point of a particular sense bound to the CBS.

Of course, access spaces are restricted versions of platonic spaces, and in humans, for sound, access is limited to between roughly 20Hz and 20KHz. Same with the intensities (for both sight and hearing, and with all other qualia spaces too).

Now if we were to consider the echolocation of bats, it might form a new sense that is also bound to the CBS. So unless we are allowed access to this new sense, we would never know what it is like to be a bat. Of course, the platonic qualia space includes everything, including those of the bat or of any other creature in any galaxy far, far away.

Saturday, April 21, 2007

Operators in qualia space

Perception of qualia would be of no use if operations on them don't exist. For example, one can perform relational operators on qualia - for example, one could decide which light is brighter of two, or which sound is louder. One could also perform things like ordering pitches or hues. A tribal who has never come across printing or painting would still instinctively classify orange as being "between" red and yellow. What he does is apply an averaging function in the qualia space of hues.

However there is a fundamental limitation to operations on qualia whose result is qualia. This limitation is what I term "access limitation". This essentially states that the resultant qualia can sometimes be "out of bounds" for the access of a particular brain.

I will give two examples. The first one has to do with intensity. Intensity is the magnitude of different senses (vision, hearing, smell, pain, etc). At lower intensities, one can perform relational operations quite easily. (By performing operations, I mean, ordering sources according to different intensities, or even imagining or dreaming two sources of different intensities.) But at higher and higher intensities, the sense organs become saturated that further relational operations is not possible. Now one can dismiss this as just the limitation of the physical sense organs. But according to my previous post the limitation is built into the access pathway in the brain itself, and with a different brain architecture, a potentially infinite dynamic range can be realized for most, if not all, senses. This is the reason why we cannot even imagine or dream or hallucinate a greater dynamic range than our everyday experience.

The second limitation is even more illustrative. When I mentioned an averaging operator in the space of hues, the assumption was that the individual is not color blind. If an individual cannot experience an eigenhue (see this post for what I mean by it), then no relational or any other operation on the hues he perceives would give rise to that eigenhue. This is why soemtimes color blind people cannot even imagine the color they are missing. This is again an example of access limitation. This is not about intensity, but about the hue.

I will give another example of the second limitation that affects everyone. Take the sense of pitch. Now pitches corresponding to two frequencies which differ from each other by the twelfth root of two are adjacent notes. In fact, one can easily figure out the succeeding note from the current one. This is the basis of music theory. What we do is keep applying the same operator in qualia space ("one note above") starting from a low base note and we very soon find ourselves at the upper end of the hearing range. We can also go down as "one note below", and would then find ourselves at the lower end. In fact, when one crosses the limits (either lower or upper), one cannot even imagine notes beyond these. This is quite unusual because in pitch qualia space where neighboring notes are so beautifully related over several octaves with great consistency, the breakdown seems almost implausible. For in an abstract qualia space of pitches, it would seem that we should be able to carry out the determination of successive notes (either ascending or descending) ad nauseum. A platonic model of pitches should correspond to an infinite number of octaves. Logical reasoning dictates that. And yet that isn't the case. We should blame it on the access part of our brains. Our access is closed to pitches below 20Hz or beyond 20KHz (roughly).

I wish to reiterate that when I mean "access" I don't mean the ability to just sense such qualia (which can be tied to the ability of the sense organs). It means the ability of the mind to construct the qualia under question as a function of some operation in qualia space. In the pitch example given above, the ability of people to determine a pitch which is an octave higher than a pitch sounded to them is the access of the higher pitch. Most people would succeed if the sounded pitch were 1KHz. They would fail when the sounded pitch is 15KHz.

As I had mentioned earlier, the platonic space of qualia (which is post Cartesian theater) is ultralinear (infinite dynamic range), and the vagaries of the access limitations are due to the physical workings of the brain. It is possible that the brains of some other species of animals have different access limitations and may or may not overlap the regions reachable by the human brain.

Wednesday, April 18, 2007

On the linearity of qualia

I am wondering if qualia would lend themselves to a Hilbert space kind of formalism. But one of the main requirements is linearity. In our everyday experience, qualia are not very linear. If a spot of light is kept on made brighter, it would saturate our senses after a certain threshold. In fact, we cannot even imagine a brightness beyond a certain limit.

But I think that a fundamental distinction needs to be made between phenomenal and access consciousnesses. The latter is a result of processes in the brain (pre-Cartesian theater), and it doesn't surprise anyone that there are fundamental non-linearities built in the chain (which can be explained physically).

Imagining (as well as dreaming or hallucinating) anything is also subject to the same access chain, so this is the reason we cannot even imagine a bright light or a loud sound which is 10x what our sense organs are designed to withstand maximally.

But I think that p-consciousness (which is post-Cartesian theater) should be super-linear. This doesn't hold just true of physical qualia but also emotional ones. While emotional qualia (like anger, empathy, or even sex drive) may seem to be purely access driven and not as straightforward as physical qualia (like colors, pitches, and so on), I think they are as elegant and straightforward as the physical ones. A theory of qualia is incomplete if it leaves out emotional qualia solely to the physical workings of the brain. While the hook-ups to the emotional qualia are again access-driven and hence non-linear, the "other side" should be ultra linear. In fact, I think meta ethics should be of much importance as the color inversion problem. Some entheogenic drugs like Ecstasy in fact cause a heightened state of empathy. There is no reason to rule out, in theory, a super-high empathy state (> 1000x), which would solve the world's political problems! And imagine an orgasmic state which is 10000x the regular one!

Of course, one problem is how to quantify emotional qualia to begin with. What does it mean to say some one is having 453x the empathy of another person?

If we assume linearity of the p-qualia space, then the brain maps processes to a certain subspace of this space. The complementary space would have qualia which cannot even be felt or imagined or dreamed of. For example, we do not know what it is to be like a bat, whether they "hear" or "see" or do something else with their echolocation. If they use the Doppler effect to determine the speed of insects, how does this info get mapped? Would it be analogous to color of "our" vision?

I think we should assume linearity of p-consciousness as a first step towards a formal model of qualia.

Tuesday, March 27, 2007

A universal consciousness?

In Hinduism, there is this concept of brahman that refers to an all pervading consciousness. The individual souls (atman) are part of this brahman, and upon death, the atmans merge with the brahman.

Till a few years ago, I used to ridicule this concept. To me a unit of consciousness (you may call it "soul") was indivisible and also non-unifiable. Although I was plain aware of the fact that severing the corpus callosum in humans could lead to two individual consciousness in the same person, I still had problems reconciling that. But now, when I think about it, I do not think it is any more mysterious than the creation of a new consciousness when a woman gets pregnant. Physicalism is at the root of both and does have a bearing on consciousness, including creation, destruction, bifurcation, and unification of existing ones.

If bifurcation is possible, so should unification. I would say, re-attaching the nerve cells of the corpus callosum (at least in theory) should merge the two conscious streams back to one.

So does this mean consciousness is not conserved? Can a consciousness be destroyed without being conserved (as in rebirth) or getting unified with another stream? And what about ethics? If a consciousness is going to get permanently destroyed (as in death), does it matter if it is made to undergo a painless death or a painful one? Why do we care?

Fairly profound questions. But here is my take. I think that each conscious entity is nothing more than a physical console for a master consciousness on the "other" side. The "master consciousness", however, is not some omniscient supreme being. On the other hand, it is very limited in its epistemological capabilities. Its function is to provide instantaneous, memoryless qualia, nothing more. In other words, phenomenal consciousness. It interfaces itself to a console (a conscious entity) through some QM processes in the brain. Apart from feeling physical qualia (through the console), it can also undergo emotional qualia (like anger, grief, and so on), but even these processes are largely determined by the physical processes in the brain. Memories of past events, even behavior (access consciousness) are all stored locally in the physical brain. The master consciousness has no memory or personality other than that of the console it is currently plugged into.

This means that if there are two persons having two master consciousnesses, they can exchange them suddenly and they would not even know it. In fact, there could be a single master consciousness operating behind two individuals in a time multiplexed manner, similar to a multi-user operating system.

Now this would lead to an interesting ethical paradox. Let us suppose there are two people A and B. Suppose A harms B in some way. Now ethics would demand that A suffers some retribution because of that. But as soon as A harms B, let us assume that the master consciousnesses behind these two get switched. Now, in the interest of fairness, who would have to undergo punishment? A or B?

For a judge in the same physical world, there would be nothing in the behavior of either A or B that would give away the switching! In fact, there may be no theoretical way of distinguishing the change from a purely physical point of view. So it would be logical for A to undergo the punishment, as would be self-evident had no such switching taken place.

But given that the consciousnesses of A and B have switched, wouldn't punishing A now cause more suffering for the consciousness that was originally in B, while letting the other go scot-free? Although A would continue to believe that he is the one who harmed B, in reality its the other way round! So while A might still resign to whatever punishment he receives (because epistemologically his identity is that of A), in reality the consciousness that was sinned against is also getting punished for the same!

In dealing with ethics, I would like to think of joy/suffering undergone by any "master consciousness" as a scalar quantity. For example, in my life, I could keep a score of the pleasures and pains (both physical and emotional) and could tally the total over some period to give the "net" pleasure or pain I experienced. Although this is simplistic (for example, how does one assign weights to the various experiences?), I want to illustrate some points.

For example, do I assign points to my experiences in my dreams and treat them on par with the waking state? In my dream, I might get beaten by muggers, my loved one might be diagnosed with cancer, and so on, so I sure do suffer. But when I wake up, I feel relieved that it was all just a dream. But does that realization negate the subtotal in my dream? The answer is no. When I was dreaming, the pain (both physical and emotional) that I felt were every bit as real as they would have been in the waking state. Just realizing after waking up that it was all a dream does NOT make the suffering go away. If that were the case, it should not make any difference to me whether I get nightmares or pleasant dreams. In fact, there would be no need to wish "sweet dreams" to anyone then.

What if one has no memory of the bad dream on waking up? In this case too, it doesn't erase the suffering he underwent during the dream. Of course, if one remembers the dream, then thinking about it may cause more suffering, but this is a secondary effect. This is similar to reliving a tragic event or grieving over a loss after a long time since it happened. If a person undergoes a tragic or painful event, but suffers amnesia after that which removes the memory of the event completely from his mind, it still doesn't affect the fact that the person had the painful experience. What the amnesia does is, it prevents the event from having an effect on the pain score afterwards.

Now let's do this thought experiment. Imagine that for every misdeed a person commits during his waking state, the person suffers a negative consequence in his dream the same night. So if he beats someone up in the waking state, in his dream he gets beaten up by someone else! This might seem something like divine justice! If this happens a few times, the person would form the association and might stop beating people up! What a deterrence!

But let's add a twist to this scenario. Let's assume he gets beaten up in the dreams just like before, but has no memory of the dreams once he wakes up. In this case, he cannot form an association and might continue beating people up. But still he is brought to justice the same night every time that happens! Also let us assume that in his dream, he doesn't recollect that he had beaten someone up during the day, and therefore cannot link his being beaten up to what he did in the waking state. Some might call this unfair (since if someone is being punished, they would argue that the person needs to know for what), but I don't think so. Justice is when the consciousness undergoes some unpleasantness (like pain or grief), and no reason needs to be assigned. As long as the pleasure/pain score is altered in whatever manner to cause accountability, justice is being served. Of course, when someone knows why he is being punished, it may change his behavior which prevents him from getting himself into trouble in the future, but that's a separate issue.

In Hinduism, there is this concept of karma, which is akin to a score sheet for misdeeds. It is said that when someone gets reborn, the karma of his past lives would have an effect on his well-being or happiness in this life. Some people, even if they believe in rebirth, are not comfortable with the idea of someone getting punished for something they did in a past life of which they have no recall, for the same reasons as the thought experiment. But I think that if we just think of matters of justice, it is quite sensible. Actually, think of a scenario where between "rebirths", there is a transient state where they are aware of all the lives they have lived till then. In that case, they can sure form associations between their wrongdoings in one life and suffering in another, so not only is justice done, but there is also an opportunity for introspection. Of course, the same soul, on entering a new body, will lose all the wisdom since as I said, memories and identity are tied to the console once interfacing with the console. The console could be a human in one "birth" and an insect in the next one. And because I feel the person does not need to be made aware of why he is being punished for misdeeds of his previous birth, it is quite alright for the "person" undergoing the punishment to be an insect (since the only thing that matters is the ability to suffer pain qualia). This actually agrees with the rebirth aspect of Hinduism where one can be reborn as any other species.

But what if one consciousness commits some misdeed and unifies with another innocent one? Then how can justice be done? Is punishing the unified entity also entail punishing the innocent one to some extent?

I have no answer to this. This is a troubling question. It would be better to avoid this question in the first place if that could be possible. And here is where I am going to reach out for Occam's razor. The whole issue of retributive ethics can be completely avoided if we assume that ALL consciousnesses behind ALL consoles are effectively one and the same!

In this case, there is no question of justice, as the perpetrator and victim are one and the same! There is no need for retribution at the local level (console A vs console B). In fact there is no retribution at all! In reality we do not observe any kind of retributive justice in real life - evolution has always been predator vs. prey, society has seen tyrants who go scot free and so on. But in the grand scale, if we make the assumption that ALL conscious beings are ultimately the same, we need not look for local tit-for-tat justice in the first place!

For those who are unconvinced by the idea of a "dumb" soul behind a console that embodies the personality, think of yourself in dreams. When we wake up, a lot of the happenings in dreams make no sense whatsoever. But in the dream, even though our sensory experiences are quite realistic, mentally we appear to be greatly challenged in not being able to make out the inconsistencies which seem obvious in the waking state. This is because the soul is dumb (and able to only perceive physical qualia and basic mental ones). However congnitively and ethically, it is very challenged, and relies wholly on the physical aspect (the brain) for those. There are brain regions for empathy, criminal behavior and so on, its not the soul that is good or bad, contrary to what most religions say.

Of course, with the point made earlier, the whole question of ethics breaks down. Which is good since it appears to be a needless complication anyway.

The question is of course, how the consoles interface with this universal consciousness. Are QM processes responsible? I think so. If we find out, we could create our own non-biological consoles that can tap into this consciousness to experience any kind of qualia. We can even unify these with ourselves, so we get to share in the experiences.

May the Force be with us.

Saturday, March 24, 2007

The inverted spectrum problem (part 3)

In the previous post, I had asserted that the colors perceived by humans when the actual paths corresponding to different cone cells could be exact. But I also think there might be cases of mild and severe color inversions where the above may not hold true.

Let me explain why. In humans, there are 3 kinds of cones which correspond to blue, green and red (roughly speaking). Actually, it is not that for each monochromatic light, only one type of cone gets activated. All three types can get activated, but each type of cone is more sensitive to some wavelengths than others. The portion of the brain responsible for color perception decodes the information from the three types of cones to determine the actual hue perceived by the consciousness.

Human vision is trichromatic, meaning that the color perceived is a point in 3 dimensional color space. Typically we take red, green, and blue to be orthogonal components and any hue can be represented by a point in this space. If we normalize the intensity, all hues are on the positive octant of the unit sphere with origin at 0.

Note that the wavelength to color mapping is not one to one. Purple is a combination of red and blue (at opposite ends of the spectrum), but a monochromatic light having an average of red and blue wavelengths appears green and not purple.

There is nothing in theory that requires vision to be trichromatic. In fact, many birds have four types of cones, making their vision possibly tetrachromatic. It is quite likely that they perceive hues which cannot even be imagined by us (that is, outside of the qualia space of humans). In fact, the "white" perceived by birds might be different from our white and something that we cannot even imagine.

Now, it is true indeed that for a variety of reasons we consider red, green, and blue to be the primary colors. This has got to do printing, and CRT and LCD screens. In a monitor, there are R, G and B pixels and other colors and intensities are got by illuminating these at various levels.

But in principle, if we consider the color space to be 3-D, ANY set of three mutually orthogonal directions would do. But the main question is, is there a preferred set of reference hues which lead to invariance between different humans to exact precision? In other words, are there eigenhues that have a simple mathematical relationship so that all humans perceive the same color along these axes exactly? (It may turn out that these eigenhues may not even be orthogonal on the color sphere, but I suspect they would. Also, I think there would be an overdetermination with respect to the white point, which I believe would also exact for two individuals.)

Now, I wish to stress that these eigenhue axes are intrinsic to the "projector" of the Cartesian theater. Actual stimulation of the retinas of two individuals corresponding to these eigenhue axes will not lead to the same results because of the variability in the cone responses from individual to individual. I am talking about something a lot more fundamental.

Now lets take the case of color blindness. There are many types of color blindnesses and most have to do with the front end (the cones themselves). In some cases, the brain itself might be involved (as in the case of achromatopsia), where the subject sees only in black and white.

There is also evidence of some women having a fourth type of cone which allows them to differentiate hues better than other humans. This condition has been mistakenly quoted as tetrachromaticity, but unless the brain itself is wired for 4-D color space as opposed to 3-D, one cannot call it that (and there is no reason to believe that these women have such a radically different brain organization). They still would perceive the same range of hues as other normal humans, although the mapping to the actual visual spectral composition might be slightly different. (Actually, to tell the truth, I myself have not come across any content on the web establishing that birds indeed do have a 4-D color space, but I suspect this to be the case.)

So, we have seen that mix-ups can happen at the front end (the rods and cones), and the processing unit (the brain). What about the back end (the Cartesian projector)?

Now this question sure leads us to Cartesian dualism and the mind-body problem! But that doesn't mean we should get scared away and not attempt at conjecturing such conditions. We do know that our subjective experiences do depend on physical phenomena in the brain. After all, drugs like LSD can alter visual qualia and so no one can deny that there is a physical basis for our subjective experiences.

I think the color pathways offer an unique opportunity for a lot of such experiments compared to other senses like sound, touch, smell, etc. The reason is, assuming a 3-D color space for humans, there should be a great deal of identical brain processing for the three pathways except at the end of the chain, namely the colors of the lenses of the Cartesian projector. Note that these colors would be the eigenhues which I discussed earlier. An analogy can be found in the case of real life component video amplifiers. The component signals (R, G and B) undergo the same kind of processing in any cable chain and the amps can be exchanged as long as the inputs and outputs still correspond to one another.

Now we know why the front end (the cones) have different color sensitivity profiles. It has nothing to do with the mind-body problem and is in the purely physical realm. It has to do with the pigments photopsins and rhodopsins in the cone cells.

But what about the color lenses of the Cartesian projector? Now this is a totally different ball game! But I believe that the color lenses are due to simpler molecules (than photopsins and rhodopsins) and the quantum-mechanical wavefunctions of the excited states of these molecules correspond to the color perceived in qualia space. Well, I have not attempted to describe what QM has to do with perceived qualia, but I am certainly not Pinker to dismiss the consciousness-QM connection here. But at the same time, I am not sure if Penrose's argument is right here either.

So what does this imply? For one, I feel that there is a very restricted family of these molecules able to "project" on to the Cartesian screen. There should be three such in humans with possibly a fourth in the case of birds and other lower forms of life. Since I feel that these molecules aren't even proteins (which might have different allele-variants), but something much simpler, I feel that the hues of these would be the same for any two humans, because their eigenstates would be the same. These molecules would fail in their function with even the slightest mutation, and it is possible that some cases of brain achromatopsia might have to do with mutant forms of these molecules, rather than the wiring in the brain itself.

If my theory is right, this provides a new twist to the color inversion problem! For if, for the moment, we assume that the brain pathways themselves are the same for the three eigenhues, what would happen if these molecules get switched? Then we could indeed expect some people to be born with the classic "inverted spectrum" condition! I call this the "severe color inversion syndrome", since the subject indeed sees red different from a normal person. (Actually there would be many forms of this depending on which eigenhues get switched, but I lump them together for now. On top of that, there might also be color anomalies resulting from cone defects, but I do not want to discuss such complications which are unnecessary to the basic understanding.)

Now what happens if both the inputs and the outputs of the amps (read brain pathways) get switched together? If the amps are identical, it shouldn't matter. But I feel there might be minor differences in the amps themselves. I would term this condition "mild color inversion syndrome". This condition, if it exists, should not be discernible as easily as the severe one, even with subjective tests.

I think that most inversion syndrome conditions (if they indeed exist) would be the mild type. This is because, I think, any mutation that causes the eigenhue molecules to get switched also strongly causes the amp inputs to get switched. Perhaps because there might be a shared protein in the synthesis of both the eigenhue molecule and the "input selector". Evolution would have favored such a scenario.

I also think it is possible for a much rarer condition (which I term "alien color inversion syndrome") in which one of the normal eigenhue molecules in the human is replaced by the fourth one present in birds. I don't know of the possibility of this. But in that case, the colors perceived by someone from this condition would have no correspondence with that of normal people!

Monday, March 19, 2007

The inverted spectrum problem (contd)

In the last post, I had suggested that there might be minor variations in the colors perceived between two individuals, and the same might hold true of sound also. But let me elaborate on this a bit further.

I do believe that the absolute pitches heard by any two individuals might be off by a note or two. The reason is not because of any metaphysical mind-body interface, but might have to do with the mechanics of the inner ear itself. The part of the basilar membrane that vibrated with a particular pitch is very dependent on the mechanics of the ear which is subject to genotypic and phenotypic variations and also due to aging itself. So it is quite possible that a standard deviation of one or two notes is possible. There is no way the brain can calibrate out this source of error in the physical frequency<-> pitch qualia correspondence. But fortunately, this doesn't typically lead to any discernible changes in subjective preferences or sound pattern recognition. This might be one of the reasons pitches have geometric progression and a song played in a different base key still evokes the same subjective experiences and melody. Some forms of music (esp. Indian music) have no concept of absolute pitch, and the base note could depend on the performer.

But when we come to sight, I feel the match would be much closer, at least theoretically. If we take the human eye, it's got rods and cones. The rods respond to brightness while the three types of cones respond to red, green and blue colors. Of course, a red light might also stimulate the green cones, although only slightly. When they are equally stimulated, the resultant qualia is white. It might be argued as above that the actual hue perceived by two different individuals can differ because of the dynamics of the rod/cone activation which could show variations between individuals. It is possible for this to be the case.

But at a more fundamental level, the qualia correspondences may be much tighter, indeed exact. Let me explain this. How many of us have not experienced a bright flash when we had bumped our heads against something? Although very fleeting, it is of an absolute white, at least for me. My assumption here is that it is because of stimulation of the visual cortex, but only of the part that processes rod, and not cone information.

I now make the conjecture that any two people see the exact same white when only the "white" (read rod, not white matter) part of the brain is activated.

And similarly, if we could separately simulate the red, green and blue pathways, the color experiences corresponding to these stimulations would have an exact match between any two normal people (by normal, I mean those who don't have pathological problems like color blindness or genetic miswiring in the brain. In those cases, the differences in perception would not be a minor hue variation, but something really more drastic than that). Of course, this is just a conjecture, but I wish to call it "Shankar's color perception conjecture".

So one might ask, if in the case of sound, there could be minor variations, why not in the case of colors? The answer to this question is, in the case of sound, there is a continuum of auditory nerves for different frequencies, while for colors there are only three different types. In sound, the brain does not really know whether the nerve responsible for a pitch of 1KHz is indeed triggered by a sound of 1KHz, because there is no way of calibration. But in the case of color perception, there are only three different types of cones, and the distinction is clear.

Now, since this is only a conjecture, I'm not going to try to prove as to why two different people will have the same qualia when only a particular color pathway inside the brain gets activated. Well for now, I will assume Cartesian dualism, and then I believe that the color qualia are caused by the equivalent of mathematical eigenstates in qualia space. The qualia perceived will therefore be exact to mathematical precision, much the same way two different molecules of the same structure would have the same spectral lines.

Ok, I hope you didn't take the last paragraph too seriously :) For we have a long way to go before we can even perform these kind of experiments. But in the end, if this conjecture turns out to be true, I hope people remember the name of the conjecture :)