It's a neat analogy, but I wish you would have tried to give some arguments for the claims you made about qualia, even just explicit references to existing arguments.
I don't know why you think that the set of qualia should be finite or that qualia depend only on themselves.
After I put this on twitter, I was linked to an article which has the same argument with many details: https://www.academia.edu/22474275/Squalia_Qualia_like_Properties_of_Symbolic_Systems
Only set of possible letters is finite. I think that set of possible colors can be infinite.
Any syllogism which ends with something red, must have something red in its premises. Thus, redness itself can't be proved in any conclusion. Thus it depends only on itself. The mathematical objects which depends only on themselves are axioms. We can postulate the existence of class "colors" and object red in it.
Qualia are distributed representations in neural firing rates. They represent sensory experience in very high dimensional spaces. They contain a great deal of information, and shift rapidly before all of that information can be captured by other brain regions.
We know roughly what the brain is doing when people report different experiences. Rapidly shifting high dimensional representations match the reported properties of qualia and the causal effects on cognition they need to have.
If I see something red, there is no much information - 3 bits? - and also it is stable and not shifting.
There is no way to get your brain to reduce its bandwidth to just the redness. Information is always high even if it's supplies by guesses or priors. Dreaming is the ultimate example but sensory processing is always partly generative.
Qualia are atoms in experience and all complexity is relation between them. Atoms are simple but relations are complex.
Functional part for sure and for qualitative part it is only important that they are different from internal perspective.
The similar question is "Do you think that F=ma represent physical law?"
Moreover, if we take hidden variable in some computation, like x:=x+1, - here x has causal power, but we will not see x in the inputs and outputs.
I have absolutely no idea what you mean by any of this. And I'm trying to quit wasting time on consciousness discussions. They rarely go anywhere and there's no obvious payoff if they did. So: Leaving Orbit.
This distinction is a great crux. Red is a actually a very large amount of information! Why would you think it's only 3 bits? The brain does not use a 'color' slot with a compressed symbolic representation of color. Our representation of red is quite rich, containing information about associations (warmth, emotions, etc) and would be represented by a quite specific point in a complex high dimensional space.
Red itself is just one of rainbow's colors and can be encoded in 3 bits. But what you are speaking about is its functional role - its association with emotions etc.
In equation it is more obvious: letter T can denotes one of several physical variables - it an be used for time but also for leghth, energy etc. T as time appears in multiple equations.
Let me see if I understand what you're saying. Correct me if I'm wrong.
The same way symbols relate to formulas, so do qualia to experience. In essence, qualia are the symbols from which experience is constructed, and just like different symbols can be put together to create different formulas which mean the same thing, so can different qualia be put together to describe the same experience.
So for example if we say my 'red' is x and your 'red' is y then
"The cow is red" can be described both by
cow = x
and
cow = y
Different symbols, same meaning. This implies there exists some kind of universal equivalence relation reducing the space of all qualia formula to the space of all equivalent formula.
Let
Let a formula
We then define an equivalence relation
The problem is then reduced to how the equivalence relation works, i.e. the quesiton: "What is the mathematics of qualia?
Interesting post. Thanks for giving me something to think about.
I used to think it as following: there are three classes of objects:
1) numbers, like 10101
2) pure qualia, like redness
3) the tables of correspondence which connects numbers and pure qualia. Red is (10101----redness).
Physiological qualia are lines in the table of correspondence, and they combines both functional part (number) and qualitative part (redness).
The number of possible pure qualia is at first glance is very large and maybe unlimited, but the number of tables of correspondence is much larger as each pure qualia can be attached to any number, and also each table includes all colors - this drives combinatorial explosion.
The nature of qualia is relatively simple - they are just a type of mathematical objects which do not depend of anything except themselves. The real problem is the nature of table of correspondence.
Consider a simple example: E = mc². The law describes a relation between mass and energy, but notice that "E" isn't a physical object. It's a letter of the Latin alphabet, as are the other symbols in the equation. The Latin alphabet emerged at a particular moment in human history and reflects the features of human language (which decomposes into roughly thirty sounds), as well as the physical conditions of writing. Different alphabets evolved alongside different instruments and surfaces: cuneiform, for instance, was shaped by the practice of pressing a stick into wet clay.
If an alien were handed a book of mathematical equations, it could learn a surprising amount about human language and the materiality of human writing. The letters play a functional role inside the equations, but they're imported from somewhere else entirely.
In this post I want to suggest that qualia work the same way: they are objects from a different realm, conscripted by the human mind to serve as internal variables.
The "internal variable" part is the easier half. The feeling of red is needed to designate red objects in the world. We can't use red itself for that – red is just a wave frequency, and the brain has no way to process a frequency directly. In the same way, we can't use energy itself as the symbol for energy in Einstein's equation. We need to borrow from another realm, one that contains objects fit to serve as symbols. Mathematics borrows from written language.
What I'm suggesting is that qualia are borrowed objects too. This doesn't dissolve the hard problem - we still don't know what the realm of qualia actually is - but we can develop some intuitions about its properties by pushing the comparison with letters as far as it will go.
What the analogy gets us
1. The inverted spectrum is fine. If colorblindness involved a complete and consistent recoding of qualia, the system would still work – just as E = mc² remains functionally identical if we rewrite it as L = ub².
2. The set is finite but large. Humans have created a finite number of letters, though the count grows enormous once you include hieroglyphs and pictograms.
3. They come pre-structured for use. Letters were shaped to be easily combined and communicated. This doesn't require intelligence – DNA codons are also a kind of "letter," produced by evolution rather than design.
Where the analogy breaks
Qualia depend only on themselves, whereas letters can be built from simpler parts (dots, strokes, curves). And we can't easily create new qualia – perhaps only under strong psychedelics or direct brain stimulation.
A pet theory
My pet theory is that qualia are a special kind of mathematical object - one that depends only on itself. Because of this, no explanation can reach them. If something depends only on itself in order to exist, no further explanation of its existence is needed or even possible. But qualia also have a structural interface with the world, and that's what lets them function as symbols.
The knowledge argument, briefly
This view fits the knowledge argument neatly. We can know that we have functional qualia, but we can't describe their qualitative side - just as the relation between mass and energy is real but can't "know" which letters we happened to use to write it down.