Hi Florin,
I am grateful for your willingness to put your cards on the table with regard to the computationality, or lack thereof, of nature. I am a (fervent) believer that computation is a core feature of nature, and I will now make a few observations that I hope at least somewhat weaken your conviction to the contrary.
Your first objection is that "computability is a concept invented by humans billions of years after the Big Bang." This is a reincarnation of an old philosophical argument against mathematical realism. The fact that computability did not enter the sphere of human knowledge until billions of years after the Big Bang merely means that computability is billions of years old, and supremely indifferent to whether we're aware of it. One could easily make the "X is a concept invented by humans billions of years after the Big Bang" argument against the reality of, say, calculus, or arithmetic, or geometry; yet it doesn't take a Eugene Wigner to point out that this just does not jive with how uncannily isomorphic and therefore useful those things are to virtually all our attempts at understanding nature.
I am not sure where you stand on ideas like Tegmark's ultimate ensemble -- you cite one of his papers, but in passing, as a way of forestalling potential objections to the actual point you're about to make -- but to me computability can be thought of as, along with what you call the "dual objects" of math and physics, the newest member of a "triality." Each of the three, math, physics, and computability, is isomorphic to the other, and also incomplete; the three incompletenesses are the junction points at which the three objects should be bolted together to produce a single apparatus of understanding.
So, the way I see it, you are free to be a "computational Platonist" (which, according to Wikipedia at least, seems to be opposite view from what RLO keeps calling "Platonist") or, as I am, a "computational realist," but your verdict on that computational case must be consistent with your verdict on the corresponding mathematical case. I do not understand a world view that admits mathematical realism but forbids computational realism. But maybe that isn't your position after all, in which case, I'm cool with disagreeing if you are too.
I am not sure what to make of your comments about the Turing test, which seems to imply a diversion into artificial intelligence. For purposes of this discussion I am completely uninterested in AI (and consciousness for that matter), and my paper's proposal of "computational ontology" is restricted purely to the physical. I realize that a possible implication of computational ontology would be a link between consciousness and physicality, but tossing about such conjectures seems disproportionately fashionable (at least on the FQXi forum) given how crackpottish it makes one sound. So, I try to keep any latent sympathies toward such views firmly in the closet, at least for the time being. Let's just say that, although I might not follow your argument in that paragraph, I agree with the conclusions of unpalatability and unlikeliness to which it led you.
"The stuff physics tries to describe is ubiquitous all around us: space, time, elementary particles, electromagnetic waves, etc. Computation is not. . . . [but] there is a loophole in my argument and it comes from quantum mechanics which can be understood in an information setting framework, and therefore the jury is still out on this." I would like to try to draw an analogy between this stance and a frequently-debated stance in the neverending battle between atheists and religious believers: "the god of the gaps." The idea being, science can provide a reasonably thorough (and ever-improving) account of reality, but even that account contains nontrivial gaps, and so a good many religious moderates simply shrug their shoulders and attribute the unknown mechanisms that lurk in those gaps to God. To me, your statement can be interpreted as saying that mathematics can provide a reasonably thorough (and ever-improving) account of reality, but even that account contains nontrivial gaps that can only (or best) be understood computationally (e.g. quantum mechanics), and so a good many "physics moderates" simply shrug their shoulders and attribute the unknown mechanisms that lurk in those gaps to "better math." Religious moderates sublimate their ignorance of the gaps into faith in God; physics moderates sublimate their ignorance of the gaps into faith in mathematics. In both cases the moderate sublimates ignorance into faith in future revelation; only the source of revelation differs.
Perhaps there is a heuristic lurking in this discussion that corresponds somewhat to yours. Just as your heuristic mediates the relationship between mathematics and reality, perhaps a fruitful heuristic could be proposed that mediates the relationship between mathematics and computation. That is, just as yours asks "What behaviors exist in reality that cannot be accounted for using mathematics?" perhaps this heuristic could ask "What behaviors cannot be accounted for in mathematics that _can_ be accounted for using computation?" To me the most fundamental answer to this question is, as I said to Ray Munroe Jr. in another post on this thread, conditional branching -- if/then/else statements. I think computation is the set of everything possible when you take mathematics and augment it with natural, seamless mechanisms for handling conditionality. To put it differently, computers are used all the time to model complex systems by figuring out what computational behaviors will exhibit regularities that fit existing equations; but nobody ever uses the behavior of equations to exhibit regularities that fit purely computational models. Hence, to paraphrase kids during recess, my computation-dad can beat up your equation-dad. :)
At one point, RLO flatly declared (as he is wont to do): "Nature does not use numbers. It does not need them. It does need geometry, but that can be done without absolute numbers." I replied: "It is an interesting claim that nature does not need numbers but does need geometry, especially coming from someone whose paper is titled 'The Infinite Fractal Universe.' Isn't fractal geometry the only type of geometry that canNOT 'be done without absolute numbers'? Fractals need numbers. If nature is a fractal, then nature also needs numbers."
I think that line of reasoning can be redeployed in our context as follows: It is an interesting claim that nature does not admit computation but does admit fractals, especially coming from someone who has agreed that the appearance of fractals in nature "is a fruitful idea in a rather large region of validity." Isn't fractal geometry the only type of geometry that cannot be separated from computation? Fractals need computation. If nature is fractal, then nature also needs computation.
(Note that aside from the obvious changes, I also changed "if nature is _a_ fractal" to "if nature is fractal," switching "fractal" from a singular, all-encompassing noun to an indefinite, less intrusive adjective that can be applied with whatever degree of broadness one wants. I worded it the first way with RLO since the one thing he and I agreed on is that nature is indeed "_a_ fractal," which I understand is part of the point I'm trying to make here. Begging the question can be tricky to avoid, but I think I managed to avoid it here.)
The last thing I want to leave you with in this message is the following metaphor. Computation plays the same role in modern Western civilization that beasts of burden did in preindustrial agrarian societies. Whether at home, in the field, or en route to/from the market, a preindustrial farmer's beasts of burden were never far from his side. Likewise, whether at home, at work, or on the daily commute, a modern Westerner's devices of computation are never far from his side.
Beasts of burden had (and have) innate behaviors, intrinsic tendencies, but preindustrial agrarian societies were justifiably uninterested in them; to the extent they thought about beasts of burden, it was from the perspective of answering the question "What can they do for us? To what concrete, productive uses can we apply them?" And that's why cattle and donkeys and horses were always fully laden with goods, or hitched to carts and wagons full of goods. Nobody needed to wonder what they would do if they were unyoked from their carts and wagons, set free and allowed to execute their innate behaviors, because we knew already -- they'd just sort of wander around aimlessly, eating, crapping, and reproducing.
I invite you to think about computation's role in the universe by wondering what computation would look like if we, modern Westerners, unyoked it from the oxcart of binary von Neumann architecture and allowed it to wander around aimlessly, executing on its innate behavior. If we weren't always forcing computation to do our grunt work for us, how would it spend its time? I tried to use this thought experiment as a guide in designing computational ontology. The "Object" class is computation in its pure, elemental form, undoped by notions of polynomial time or the desirability of algorithmic halting.
Sorry to slap you with this enormous bit of rambling before you've even read the paper. Again, I really do think highly of your contest submission and appreciate your willingness to discuss these issues with me.
Thanks very much,
Owen
