Eight questions for computationalists

I don't know the answer to any of these questions, and I don't know which of them are confused.

Here's a way to make the statement "consciousness is computation" a little less vague, let's call the new version X: "you can simulate a human brain on a fast enough computer, and the simulation will be conscious in the same sense that regular humans are, whatever that means". I'm not completely sure if X is meaningful, but I assign about 80% probability to its being meaningful and true, because current scientific consensus says individual neurons operate in the classical regime, they're too large for quantum effects to be significant.

But even if X turns out to be meaningful and true, I will still have leftover object-level questions about consciousness. In particular, knowing that X is true won't help me solve anthropic problems until I learn more about the laws that govern multiple instantiations of isomorphic conscious thingies, whatever that means. Consciousness could "be" one instantiated computation, or an equivalence class of computations, or an equivalence class plus probability-measure, or something even more weird. I don't believe we can enumerate all the possibilities today, much less choose one.

There is too much vagueness involved here. A better question would be if there is any reason to believe that even though evolution could create consciousness we can not.

No doubt we don't know much about intelligence and consciousness. Do we even know enough to be able to tell that the use of the term "consciousness" makes sense? I don't know. But what I know is that we know a lot about physics and biological evolution and that we know that we are physical and an effect of evolution.

We know a bit less about the relation between evolutionary processes and intelligence but we do know that there is an important difference and that the latter can utilize the former.

Given all that we know, is it reasonable to doubt the possibility that we can create "minds", conscious and intelligent agents? I don't think so.

1. The distinction doesn't make sense to me. But then neither does the statement "Consciousness is really just computation." The only charitable reading I can give that statement is "Consciousness is really just and, as you will notice, the only really powerful or mysterious component of that system is computation". But even with that clarification, I really don't understand what you are getting at with the a vs b distinction. I get the impression that you attach a lot more importance to the (abstract vs concrete) distinction than I do.

2. It is probably responsive here to state that there is one aspect of consciousness that the Turing machine model of computation completely fails to capture. This is the fact that consciousness is inherently (essentially) embedded in time. One thinks conscious thoughts concurrently with ongoing processing of sense data. Google for the CompSci research papers of Peter Wegner and Dina Goldin to see how the Turing machine model of computation is inadequate for many purposes. Including, IMHO, a central role in the explanation of consciousness.

3. I'm not sure what you are getting at here, but yes, I do think that some of the more physical aspects of computation - such as that it takes time and produces entropy - may be relevant regarding its use in modeling consciousness.

4. I am unable to make sense of the concept of "experiencing red"! I am not just a 'qualia' agnostic. I favor the torture and burning of anyone who even mentions 'qualia'. Particularly color qualia.

5. Ah. Extensional functions vs intensional algorithms. You are flirting with the right ideas here, but not quite nailing the essential issues. As mentioned above in #2, the key question is how the computation is embedded in time rather than whether the individual steps of the computation are achieved intensionally or extensionally.

6. Interesting question. Just how fundamental is computation? I suppose you realize that a ToE might have a variety of axiomatizations, and that some of them might include AND gates as primitives, while others do not.

7. No. And take care lest ye be taken before the Inquisitor.

8. No computations are conscious. But all consciousnesses embed computations. And some computations (but no special kinds of computations) are embedded in consciousnesses, or, more generally, embedded in minds.

Now some questions for you. Somewhat rhetorical, so you only need respond to the overall implicit argument.

1. What is it like to be a bat?
2. What is it like to be a pocket calculator?
3. What would it be like to be an embedded controller for this thing? More like being a bat than being a pocket calculator?
4. Is your answer based more on extensional (how does it appear to behave?) or intensional (how is it implemented internally?) thinking?
5. Why is this appropriate?
6. Is your evidence regarding the nature of your own consciousness extensional or intensional?
7. Are you sure of that?

I think you're completely mistaken about what computationalism claims. It's not that consciousness is a mysterious epiphenomenon of computation-in-general; it's more that we expect consciousness to be fully reducible to specific algorithms. "Consciousness is really just computation" left at that would be immediately rejected as a mysterious answer, fake causality, attempting to explain away what needs only to be explained, and other related mistakes; 'computation' only tells us where we should be looking for an explanation of consciousness, it can't claim to be one itself.

(But my answers would be: (1) c, irrelevant; (2) that's not the level of abstraction where you'd be explaining consciousness, any more than you'd talk about Turing machines or register machines in explaining Photoshop; (4) no; (5) I'm leaning toward functions, but with a broad view of what should be considered "input" and "output" — e.g. your internal monologue serves as both; (6)(7) what's the relevance of a Theory of Everything here? (8) only certain kinds, obviously.)

Tentatively, my gut reactions are:

1. (c)
2. Any Turing, I expect.
3. To say that a machine computed 2+2 means that it had taken data representing "2" and "2" and performed an operation which, based on the same interpretation that establishes the isomorphism, is equivalent to addition of an arbitrary pair of numbers.
4. "computing red" makes as much sense as "computing 2", and for roughly the same reasons. "Red" is a symbol representing either emissive or reflective color.
5. Algorithm, at a guess, but the distinction is moot - the output of the algorithm will include references to consciousness in such detail that I find it implausible that any other algorithm implementing the same function will fail to share the relevant features.
6. I have no idea what this question means.
7. If you're talking about physics, the question makes no sense - a ToE in physics is no more likely to explain consciousness than it is to explain economics.
8. Consciousness appears to be a self-reflective behavior to me. At a minimum, any conscious algorithm would have to reflect this.

I think you will find this paper useful--Daniel Dennett answers some of these questions and explains why he thinks Searle is wrong about consciousness. Pretty much all of the positions Dennett endorses therein are computationalist, so it should help you organize your thoughts.

I feel that dfranke's questions make all kinds of implicit assumptions about the reader's worldview which makes them difficult for most computationalists to answer. I've prepared a different list - I'm not really interested in answers, just an opinion as to whether they're reasonable questions to ask people or whether they only make sense to me.

But you can answer them if you like.

For probability estimates, I'm talking about subjective probability. If you believe it doesn't make sense to give a probability, try answering as a yes/no question and then guess the probability that your reasoning is flawed.

1: Which of these concepts are at least somewhat meaningful?

a) consciousness

b) qualia

2: Do you believe that an agent is conscious if and only if it experiences qualia?

3: Are qualia epiphenomenal?

4: If yes:

a) Would you agree that there is no causal connection between the things we say about qualia and the actual qualia we experience?

b) Are there two kinds of qualia: the ones we talk about and the ones we actually experience?

5: Is it possible to build a computer simulation of a human to any required degree of accuracy?

a) If you did, what is the probability that simulation would be conscious/experience qualia?

b) Would this probability depend on how the simulation is constructed or implemented?

6: What is the probability that we are living in a simulation?

a) If you prefer to talk about how much "measure of our existence" comes from simulations, give that instead

7: What is the probability that a Theory of Everything would explain consciousness?

8: Would you agree that it makes sense to describe a universe as "real" if and only if it contains conscious observers?

9: Suppose the universe that we see can be described completely by a particular initial state and evolution rule. Suppose also for the sake of simplicity that we're not in a simulation.

a) What is the probability that our universe is the only "real" one?

b) What is the probability that all such describable universes are "real"?

c) If they are all "real", are they all equally real or does each get a different "measure"? How is that measure determined?

d) Are simulated universes "real"? How much measure do they inherit from their parent universe?

10: Are fictional universes "real"? Do they contain conscious observers? (Or give a probability)

a) If you answered "no" here but answered "yes" for simulated universes, explain what makes the simulation special and the fiction not.

11: Is this entire survey nonsense?

I would describe myself as a computationalist by default, in that I can't come up with an ironclad argument against it. So, here are my stabs:

1) I'm not sure what you mean by an abstract machine (and please excuse me if that's a formal term). Is that a potential or theoretical machine? That's how I'm reading it. If that's the case, I would say that CIRJC means both a and b. It's a computation of an extremely sophisticated algorithm, the way 2 + 2 = 4 is the computation of a "simple" one (that still needs something really big like math to execute).

2) I don't know if there needs to be a particular class of models; do you mean we know in advance what the particular human consciousness model is? I'd probably say we'd need several models operating in parallel, and that set would be the "human consciousness model".

3) To me, that just means that a simple state machine took in an input, executed some steps, and provided an output on a screen. There was some change of register positions via electricity.

4) Computing red: here's where qualia is going to make things messy. In a video game, I don't have any problem imagine someone issuing a command to a Sim to "move the red box" and the Sim would do so. That's all computation (I don't think there's "really" a Sim or a red box for that matter living in my TV set), but the video game executed what I was picturing in my head via internal qualia. So it seems like there would be an approximation of "computing" red.

5) I don't have any problem saying the algorithm would be very important. I can put this in completely human terms. A psychopath can perfectly imitate emotions, and enact the exact same behavioral output as someone else in similar circumstances. The internal algorithm, if you will, is extremely different however.

6) I would say this is an emphatic yes. Neurons, for instance, serve as some sort of gate analog.

7) I think it would mention qualia, in as much as people would ask about it (so there would at least be enough of an explanation to explain it away, so to speak).

8) I don't think computations are conscious in and of themselves. If I'm doing math in notebook, I don't think the equations are conscious. I don't think the circuitry of a calculator or a computer are conscious. That said, I don't think individual cells of my brain are conscious, and if you were to remove portion of a person's brain (surgery for cancer, for example) that those portions remain conscious, or that person is less conscious by the percentage of tissue removed. Consciousness, to me, may be algorithmically based, but is still the awareness of self, history, etc. that makes humans human. Saying CIRJC doesn't remove the complexity of the calculation.

I haven't read that other thread; can I ask what your opinions are? Briefly of course, and while I can't speak for everyone else, I promise to read them as thumbnails and not absolute statements to be used against you. You could point to writers (Searle? Penrose?) if you like.

1. I'm not sure of what exactly you're after with this question, or what the question would even mean.
2. Any Turing-equivalent model seems equally valid.
3. In my mind, "a machine computed X" means that we can use the machine to figure out the answer to X. For instance, John Searle claims that any physical process can be interpreted to instantiate any computation, given a complex enough interpretation. According to this view, e.g. an arbitrary wall can be said to be computing 2+2 as well as 583403 + 573493. But the flaw here is that you cannot actually use the wall to tell you the answer to 583403 + 573493. If you already know the answer, you can come up with a contrived mapping of the wall's atoms to a computation giving the result, but then you cannot use this mapping to tell you the result to any other calculation. So "the machine computed 2+2" means that after the computation, the machine was in such a state that you could somehow read "2+2 = 4" from its state.
4. "Computing red" means that a system has an internal representation of the external world, where a specific kind of sensory data produced by the eyes (or equivalent sensors) is coded as being that specific type. This coding is subjectively experienced as the color red.
5. The intermediate steps matter. A giant look-up table wouldn't be conscious, though the process that originally produced the table could be.
6. I have no idea of what a physical theory explaining consciousness would be like. So I don't know.
7. See above.
8. Only certain kinds, though I'm unsure of the exact properties required.

I suppose I can consider myself a weak computationalist. I think a computer running a human mind will generate qualia, if it's a simple enough computer. After all, you could interpret a rock in such a way that it's a computer running a human mind.

It's the algorithm that matters.

1. c, or at least I don't understand the distinction.
2. Any sufficiently simple Turing machine. Since there's nothing that can clearly be called the output, if you didn't limit it in some way, you could say that a clock is a Turing machine if you map each time to the state the Turing machine would have at that time.
3. A function was given two inputs that map to two by a sufficiently simple mapping. The result of the function tends to be the sum. In this case, it maps to four.
4. You could have an image-recognition program that involves computations about the color red. It would generate a qualia distinct from what it calls "green". I very much doubt it would resemble the qualia of red you feel. In fact, I doubt we even have the same qualia for red.
5. Algorithms, although at some point you get to steps where it's just functions.
6. What do you mean by "consciousness"? If you mean that it generates qualia, yes. If you mean intelligence, of course not. You could run an intelligent program on Conway's Game of Life.
7. Yes.
8. I'd say all, but not all equally conscious.

I'm currently having an exchange with Massimo Pigliucci of Rationally Speaking who might be known here due to his Bloggingheads debate with Eliezer Yudkowsky where he was claiming that "you can simulate the 'logic' of photosynthetic reactions in a computer, but you ain't gonna get sugar as output." I have a hard time to wrap my mind around his line of reasoning, but I'll try:

Let's assume that you wanted to simulate gold. What does it mean to simulate gold?

According to Wikipedia to simulate something means to represent certain key characteristics or behaviours of a selected physical system.

If we were going to simulate the chemical properties of gold, would we be able to use it as a vehicle for monetary exchange on the gold market? Surely not, some important characteristics seem to be missing. We do not assign the same value to a simulation of gold that we assign to gold itself.

What would it take to simulate the missing properties? A particle accelerator or nuclear reactor.

In conclusion, we need to create gold to get gold, no simulation apart from the creation of the actual physically identical substance will do the job. Consequently, in the case of gold at least, substrate neutrality is false.

1) I don't know. I also think there is a big difference between c) "nonsensical" and c) "irrelevant". To me, "irrelevant" means all possible worlds are instantiated, and those also computed by machines within such worlds are unfathomably thicker.

2) I don't know.

3) Probably causation between before and after is important, because I doubt a single time slice has any experience due to the locality of physics.

4) Traditionally I go point at things, a stop sign, a fire truck, and apple, and say "red" each time. Then I point at the grass and sky and say "not red". Red is a relational property within the system of: me plus the object. Each part of the system can in principle be replaced by a different, potentially Rube-Goldberg part with identical output without affecting the rest of the system. The computation is the part inside my brain. Whether the stop sign is real or I am blind and my nervous system is being stimulated by mad scientists makes no difference in that respect.

5) In the red system consisting of me and the stop sign, generally the stuff outside my skull can be replaced by functions, the inside stuff needs specific algorithms to produce sensations.

6) Note to self: when giving a list of questions, include something that doesn't actually mean anything and see what the answers to it are like. My best guess is that you're not doing that, but I have no idea what this means.

7) Why would it have to? Meaning no, any patterns larger than the smallest are explained by their components.

8) I can't think of any output that in principle couldn't be produced by a conscious computational process. But not all computational processes are conscious.

Hm. I am not a 100% computationalist, but let me try.

1. b) 80% c) 15% a) 5% (there should be a physical structure, but its details probably don't matter. I can imagine several intuition pumps supporting all answers).
2. Don't know.
3. There is an isomorphism between instantaneous physical states of the machine and (a subclass of) mathematical formulae, and the machine went from a state representing "2+2" to a state representing "4".
4. There is an isomorphism between the physical states of the machine and colors (say represented by RGB) and the machine has arrived to the state whose partner (as given by the isomorphism) is close to (255,0,0).
5. Algorithms. I can learn that a ball is round by seeing it or by touching it and it certainly feels different. However among the algorithms there may be equivalence classes with respect to consciousness.
6. Don't know. I am not even convinced that axiomatic logic would not need to be replaced by something more general before arriving to the said Theory of Everything, or whether such Theory can be constructed.
7. (If such a Theory exists, then) no 75%, yes 25%. Partly depends on what "explain consciousness" means: if by "explanation" we mean a set of statements which, when properly communicated, cause people to feel that there is nothing mysterious with consciousness, there may be some need for qualia. Strongly depends on meaning of "qualia": the definition presently used by philosophers will probably be useless for any axiomatisation.
8. Consciousness isn't a binary property, so, in some sense, yes (90%).

By the way, upvoted for asking interesting questions.

Here is another attempt to rephrase one of the opinions hold within the philosophy camp:

Imagine 3 black boxes, each of them containing a quantum-level emulation of some existing physical system. Two boxes contain the emulations of two different human beings and one box the emulation of an environment.

Assume that if you were to connect all 3 black boxes and observe the behavior of the two humans and their interactions you would be able to verify that the behavior of the humans, including their utterances, would equal that of the originals.

If one was to disconnect one of the black boxes containing the emulation of a human and store it within the original physical environment, containing the other original human being, the new system would not exhibit the same behavior as either the system of black boxes or the genuinely physical system.

A system made up of black boxes containing emulations of physical objects and genuinely physical objects does not equal a system made up of only black boxes or physical objects alone.

• Emulations only exhibit emulated behavior.
• The black boxes only exhibit a representation of the behavior of the physical systems they are emulating.
• The black boxes are only able to emulate a representation of behavior given an equally emulated environment.

The representations of the original physical systems that are being emulated within the black boxes are one level removed from the originals. A composition of those levels will exhibit a different interrelationship.

Once you enable the black box to interact with the higher level in which it resides, the system made up of the black box, the original environment and the human being (representation-level / physical-level / physical-level) will approach the behavior exhibited in a context of emulated systems and the original physical system.

You can equip the black box with sensors and loudspeakers yet it will not exhibit the same behavior. You can further equip it with an avatar, still, the original and emulated human will treat an avatar differently than another original, respectively emulated human. You can give it a robot body. The behavior will still not equal that of the behavior that a system consisting of the original physical systems would exhibit and neither the behavior that would be exhibited in the context of a system made up of emulations.

You may continue to tweak what was once the black box containing an emulation of a human being. But as you approach a system that will exhibit the same behavior as the original system you are slowly reproducing the original human being, you are turning the representation into a reproduction.

(2) Humans can manually compute any algorithm that a TM compute (this is just the Church Turing conjecture in reverse), so a human has to be at least a UTM. The significant part of the computationalist claim is that humans are at most a UTM.

(4) No.

(5) If intermediate steps matter, the Turing Test is invalidate, since a Giant Lookup table could produce the same results with trivial intermediate steps. However, computationalists do not have to subscribe to the TT.

(7) An "And gate" looks like a piece of hardware, but it is really anything that computes a certain abstract function. Computationalism requires that a mind is essentially a class of programmes. Computationalism probably does not require a very fine grained description of the Consciousness Programme, since that would make it hard to explain how numerous different people with different brains and life expreiences could all be conscious. (Computationalism has to retrodict human consciousness as well as predict AI). That being the case, computationalism can stop short of a description of computation that does not go all the way down to primitive elements. (Computation is of course not essentially tied to the binary system. You could have a decimal UTM).

(6) Either qualia don't exist at all, even as mere appearances, or they have to be mentioned. I go for the latter. (A complete theory of optics has to be able to explain mirages!)

(8) I don't think any computaitonalist thinks all computations are conscious. Consciousness, for computationalists, cannot be any programme, or just one programme, but must be a set of programmes each embedding a UTM.

1. (b) Consciousness is something that a concrete machine does, as in "My calculator computed 2+2".

2. Instructed to skip.

3. Unpack what "the machine computed 2+2" means. (I'll try.) A machine computes 2+2 if it has an algorithm (perhaps a subroutine) that accepts two inputs a and b (where a and b are some set of numbers containing at least the natural numbers through 5) and generally (almost always) outputs the sum a+b. The machine may output a+b by any means whatsoever -- even just using a look up table or appending two strings of symbols. (In contrast, an algorithm that always outputs '4' does not compute 2+2.)

4. Unpack what 'computing red' means. At the first level, computing red means identifying that a set of wavelengths are within a certain range. At the subjective, qualia level, computing red means identifying the range of wavelengths "red" with a network of information about that range (possibly including past experience with that range). The experience of the quale is observing the association of the range of wavelengths with the network of related associations; it is the observation that "red" is passed through a node and redirected to a set of other nodes. (This is why consciousness is required to experience qualia.) I observe that I have a little bit of control over what associations red is passed to (different subsets of the network of associations) and asking myself 'what does red feel like?' or 'what is red?' is an exercise in lingering around this locus of control; associating, pulling back, reassociating, etc. When I actually look at something red, the shape and texture dominate my associations so I don't think 'red' is a very strong quale for me, or not a very good way to divide up my experience of it.

5. At this level of questioning, I'm not sure what 'feel' means. Feelings about mental processes depend upon associations with physical feelings, including immediate or remembered physical sensations that the brain produces while thinking, whatever those are. So if I'm on drugs, thinking should feel different ... is this functional or algorithmic?

6. Don't think so..

7. No, I don't imagine qualia are an essential ingredient of consciousness.

8. I agree with RobinZ, consciousness requires self-reflective behavior -- which I see as an algorithm modeling itself to some unspecified extent, though not necessarily containing any component of self-awareness.

I just remembered that I wrote up my thoughts about consciousness is this post titled Hypotheses for Dualism. There are likely to be some comments relevant to this discussion there.

My own answers, before reading anyone else's, were:

1. (b)
2. The calculator processes information. In the same system that gives the interpretation of inputs and outputs as rational numbers, the information processing of the calculator can be seen to be isomorphic to addition.
3. I can make many senses of the phrase, depending on the context in which it is used. Here's one: light with wavelength around 650 nm was reflected off the petals and entered the two-year-old's eyes; electrochemical signal processing occurred in her brain such that she reported, "The rose is red!".
4. I originally answered algorithms, but I find RobinZ's answer persuasive.
5. I don't know, but I doubt it. I expect consciousness has something to do with self-reflection, and Gödel showed that self-reflection is pervasive even if you don't build it in explicitly at the start.
6. I don't know, but I doubt it.
7. Only certain kinds.

Okay, here's my answers. Please take note that full answers will be too big, so expect some vagueness:

1) B 3) Big topic For me, It can use result of "computation". 4) Invoking memory or associations? Mostly no. 5) Hard to say yet. I'll take a guess that it's mostly functions, with maybe some parts where steps really matter. 6) I think it's possible. 7) I guess so. 8) They have something in common, but I think it depends on your definition of "conscious". They are most certainly not self-conscious, though.

I think the logic behind this argument is actually much, much simpler.

Let us suppose that consciousness is not a type of computation.

Rational argument, and hence rational description IS a type of computation - it can be made into forms that are computable.

Therefore consciousness, if it is not a type of computation, is also not describeable within, or reducible to, rational argument.

I call this type of thing the para-rational - it's not necessarily against rationality to suppose that something exists which isn't rationally describable. What doesn't make sense is to go on to either

a) Attempt to rationally describe it in detail afterwards. or b) Use it as an excuse to avoid thinking rationally about things you CAN think about in a rational way. c) Try and use its properties in a logical argument - all this gives you on the whole is an illogical argument.

So yes, there might be an aspect of consciousness which is beyond the rational, and which is always associated with certain types of existent being. But I would prefer the proposition that this is para-rational - alongside the rational realm, rather than irrational - joined to the rational realm, and making it non-rational after all.

This is a difficult area - as one should necessarily believe para-rational things for para-rational reasons (whatever THAT means). But I can't see how we could rule out other types of 'existence'. However, I can see good reasons not to make it a subject of too much rational discussion - if you can't rationally describe something, don't attempt to....

1. There is no such thing as an abstract machine, nor an abstract computation. If you imagine a machine adding two and two, the computation is implemented in your brain, which holds a representation of the operations. Physics is information; information is also physics. There is no information without a physical embodiment; there is no computation without physical operations.

2. Humans don't have infinite memory, and thus are less-powerful than Turing machines.

3. "Computing red": Please put more words into that phrase. It's too ambiguous to deal with.

4. Functions vs. algorithms: This is a good question. Can a lookup table be conscious? I said no. Therefore I must choose 'algorithm'.

5. A theory that explains consciousness should be statable in abstract terms using mathematical operations.

6. Yes, a theory that explains consciousness must explain qualia.

7. Answering that question would mislead people more than it would inform.

Either "qualia" are ultimately a type of experience that can be communicated to a conscious being who hasn't had the experience, or they cannot. If they can be, they cease to have any distinction from any other communicable fact. If they cannot, you can't actually use them to determine if something is conscious, because nobody can communicate to you their own individual qualia. Either way, qualia by necessity drop out of any theory of consciousness that can classify whether something as inert as a brick is a conscious being or not. And if a theory of consciousness does not predict, either way, whether or not a brick is conscious, then it is a waste of time.

1. c. The abstraction wouldn't be a very good abstraction if it fails to be similar to real machines except in what it abstracts away.
2. Tautologically, all equivalent models of computation are equivalent for this purpose.
3. The portion of the machine which is responsible for that computation was in a state which is isomorphic to "2+2" and is now in a state which is isomorphic to "4".
4. The phrase “computing red” is too vague/lacking context to interpret.
5. Functions. Your report of how your algorithm feels from the inside is part of the output of the algorithm, and therefore of the function; a mind made of modules with no side-outputs would not have the corresponding “feelings”.
6. Neither consciousness nor computation exists in the axioms of a sensible Theory of Everything; both are descriptions of certain sorts of systems which are possible in any sufficiently complex universe, just as "7" occurs in descriptions of some states of any universe containing at least 7 objects.
7. No.
8. Consciousness is not a sharp-edged category. More usefully-described-as-conscious computations are less frequent in the space of all possible computations.

My $0.02, without reading other answers:

\1. I'm not sure, but I lean towards (b).

Unpacking a bit: As it is used in the sentence "the sum of 1 and 1 to yield 2 is a computation", my intuition is that something like (a) is meant. That said, it seems likely that this intuition comes from me reasoning about a category of computations as a cognitive shortcut, and then sloppily reifying the category. Human brains do that a lot. So I'm inclined to discard that intuition and assert that statements about 1+1=2 are statements about an abstract category in my mind of concretely instantiated computations (including hypothetical and counterfactual instantiations).

I'm perfectly comfortable using "machine" here as a catchall for anything capable of instantiating a computation, though if you mean something more specific by the use of that word then I might balk.

\2. N/A

\3. Oh, hey, look at that! (I wrote the above before reading this question.)

A couple of caveats: It's not saying anything terribly precise about the physical state of the machine, but I suppose we can speak very loosely about it. And there's an important use-mention distinction here; I can program a computer to reliably and meaningfully compute "blue" as the result of "2+2" by overriding the standard meanings of "2" and "+". Less absurdly, the question of whether 2+2=4 or 2 + 2 = 4.00000 actually can come up in real life.

Waving all that stuff aside, though, it's saying that prior to performing that computation the machine had some data structure(s) reliably isomorphic to two instances of values at a particular (identical) point along a number line, and of an operation that given a pair of such values returned a third value with a particular relationship to them. (I don't feel like trying to define addition right now.)

\4. Sure.

It means different things for different kinds of computing devices. For example, for the Pantone-matching software on my scanner, computing (a particular shade of) red means looking up the signals it's getting from the scanner in a lookup table and returning the corresponding code, which downstream processes can use for other purposes (e.g., figuring out what CMYK values to display on my monitor).

For my eye and visual cortex, it means something very roughly similar, though importantly different. The most important aspects of the difference for this discussion have to do with what sorts of downstream processes use the resulting signal for what sorts of operations.

\5. Either the question is confused, or I am.

Unpacking: How it feels to be a particular computation is an artifact of the structure of that computation; changing that structure in a particular way might change how it feels, or might not, depending on specifics. I'm not sure how to map the labels "outputs", "inputs", "inside", and "intermediate" in your question to that answer, though.

\6. That hinges a bit on how precisely we define "computational devices"; there are no doubt viable definitions for which I'd answer "yes," although my answer for an AND gate is "no".

Come to that, it also hinges on what axiomatization you're using; I suppose you could construct one that did, if you wanted to. I would just consider it unnecessarily complex.

Having said all that: No, I wouldn't expect a "simplest possible axiomatization" of a "theory of everything" to contain any "computational devices." (Scare quotes used to remind myself that I'm not sure I know what those phrases mean.)

\7. As above; it might, much as it might mention AND gates, but I would look askance at one that did. (Also as above, this hinges a fair bit on what counts as a quale, but my answer for "the perception of red" is "no".)

\8. Mostly, I think this question is a question about words, rather than about their referents.

There are computations to which my intuitive notion of the label "conscious" simply does not apply. But I suppose I could accept for the purposes of discussion a definition of "conscious" that applies in some sense to all computations, if someone were to propose one, though it would be a counterintuitive one.

Would an axiomatization of a Theory of Everything that can explain consciousness mention qualia?

LessWrong User:Mitchell_Porter has made some headway on this very interesting question. See his submissions How to think like a quantum monadologist and Consciousness.

My answers:

1. Your terminology is confused and the question is ill-formed. There is a difference between mathematically abstract computation and implementation. Implementation usually requires energy to carry out, and (based on concerns around reversible computing) it will always take energy to communicate the output of an implemented computation to some other physical system.

2. The Church Turing Thesis is probably correct. Moreover, any one of these formalisms can emulate any other with a runtime hit of some constant plus a scalar multiplier.

3. That a calculator "computes 2+2" means that something in its environment put it into a configuration where these three symbols were represented within its machinery and set its symbol manipulation rules chug along deterministically until its machinery represent the symbol four.

4. Saying something "computes red" is non-idiomatic and demonstrates confusion. If I was being generous, I would say that this involves a physical system having part of itself manipulated by light at a certain freq