Discussion Computational Irreducibility

[Superdeterminist]

In his 2002 book A New Kind of Science, computer scientist Stephen Wolfram proposed the principle of "Computational Irreducibility" (CI). This is an alleged property of systems (e.g. the weather, or water molecules in water) achieved once they hit a certain threshold of complexity. If a system is computationally irreducible, it means that it's impossible to capture all of its future behaviour with a single equation or theory, and the only way to find out what it will do is to actually run the system and observe what happens.​

Above is an example of a system (cellular automaton rule 30) displaying CI. The vertical axis = time (t=0 at top). There are several recurring motifs (Wolfram calls these pockets of reducibility - he claims science essentially is the study of the pockets of reducibility in our universe). Overall though, the structure as a whole displays no discernible pattern (it is irreducible).

Wolfram suspects that the human brain, being so complex, possesses CI. If true, this would mean that it's impossible to predict anyone's future thoughts or behaviour with any single theory, equation, or set of equations; brains will always produce unforeseen results. Wolfram seems to subtly try to make a case for free will using this argument (thought I think he would probably deny it):​

And it is this, I believe, that is the ultimate origin of the apparent freedom of human will. For even though all the components of our brains presumably follow definite laws, I strongly suspect that their overall behavior corresponds to an irreducible computation whose outcome can never in effect be found by reasonable laws.

However, I think that CI brains would only be unpredictable, they would not be any more "free" than predictable/computationally reducible brains (what exactly can "free" even mean?). Brains may be unpredictable, but they're still fully determined by their constituent parts, all obeying physical laws.

Wolfram opines that a CI universe is "a good thing" because it means that we avoid the boredom of a world where everything could be predicted and people could calculate their exact futures. Personally I disagree, because CI is a barrier to knowledge (it reveals the limitations of science - theories and their predictions will never capture all behaviour), and I think that the less we know, the less able we are to solve problems, = more suffering, and that is a terrible thing. I would rather be bored than ignorant, and moreover, I see boredom as just another human problem with a potential solution. Yes it is nice to have pleasant surprises, but this would come at the cost of being unable to predict and prepare for misfortune, which in my opinion isn't worth it.

All of this is still unverified and highly theoretical of course. And, perhaps Wolfram is extending computer science into domains where it doesn't belong. But it seems scarily solid as a theory. If you ask me though, I hope it isn't true.​

 

[KuriGohan&Kamehameha]

The universe runs off entropy, and that is what is scary about trying to predict human behavior. What compels our motivations, do they always lead to chaos? I am studying a neuroscience degree and yet there is still barely anything I nor my lecturers know when it comes to the vast expanse of the mind. Difficult things to think about. You may enjoy the book Algorithms to Live By, where several computer scientists try to apply mathematical problems to human dilemmas.

 

[Life sucks]

Any theory that tries to generalize isn't true. There is no one theory that could describe everything and this theory is no exception.

Theory of everything is impossible for any type of science and not only physics. The root is mathematical (incompleteness theorem, Entscheidungsproblem, halting problem and other related problems).

But its important to understand how it works, for every theory, there is something bigger than it and it expands infinitely (theoretically and practically, because arbitrarily large is practically infinite). Logically speaking, if someone wants to prove this theory or any universal theory, the proof must check and verify the whole universe, it will take forever and then its impossible to prove and its also possible that some instances disprove the theory. (Note that even the universe itself is incapable of proving a universal theory).
On the other hand, if we assume one theory to be true, it might work for some instances, however, will fail on others. A new theory will either expand or replace it. The process of developing theories and changing them will take forever. Its practically an infinite loop, the good side is there is always some room for improvement but the bad side is there is no end. There is nothing like "Theory of everything", "All the math, physics or chemistry". People would be disappointed because there is no end and thats why they hide this fact. David Hilberts's Entscheidungsproblem is enough to disprove any theory claiming to be universal.


Finally I want to say that humans always overestimate themselves and try to misuse science to support prolife or give themselves more importance. Humans are tiny compared to the universe, its like 0 to infinity. Its possible to develop and advance (although its endless process) but don't fall into the trap of prolifers and start fearing and believing in something irrelevant because of their propaganda. If something is still unachievable, that doesn't mean it doesn't follow some kind of a rule, it means that humans are still incapable of finding it.

 

[Deleted member 1465]

Everything in the universe (if we assume the universe to be a closed system) tends toward irreduciblity because of a constant increase of entropy.
Matter/energy appears to attempt to organise itself into increasingly complex structures based on profound deterministic patterns.
It is possible that the tendency towards growing complexity occurs due to the negative pressure of increasing entropy over time.
If all matter/energy was originally contained within an infinitesimal area and remained entangled after inflation, this implicate order is constantly unfolding into every single explicate Cartesian subspace location in the universe, whilst at the same time being constantly enfolded back into the implicate order.
If this is true, then this may happen precisely because of the tendency for entropy to always increase within an enclosed system, and that the two principles occur in a paradoxical relationship resulting in a dynamic effect.
It is that paradoxical effect that drives everything.
So one could say that rising complexity & therefore computational irreduciblity is potentially what causes and is also caused by the universe's tendency over time towards entropy.

NB. Just ideas. That may have been a bit rambley due the contradictory nature of talking about paradox. It may also be bollox.
Edit: it took me a while to gather my thoughts to respond to this. When I read it back though it looks like word vomit LOL.

 

[262653]

Edit: it took me a while to gather my thoughts to respond to this. When I read it back though it looks like word vomit LOL.

Oh yeah? That sounded very insightful to me. Probably because I don't know any better.

 

[Deleted member 1465]

Oh yeah? That sounded very insightful to me. Probably because I don't know any better.

LOL either that or it was word salad. TBH I'd say there is little to choose between the two when discussing such odd things.

 

[ForcedLifeResistant]

I think there's bound to be some form of irreducibility that precludes a Laplacian kind of predictability of behavior. That, of course, doesn't mean that there can exist no theory that might have any measure of predictive power, re: behavior. You might asymptotically approach perfect predictive power, after refining some theory's laws or showing the extant laws to only hold under certain conditions, yet never actually achieve it.

The unattainability of perfect predictive power doesn't necessarily preclude the attainability of better predictive power. Perhaps we'll reach some Asimovian point at which something indistinguishable (to us moderners) from psychohistory is within our grasp. We won't know if we'll ever achieve that kind of predictive power without already having something approaching that kind of predictive power.

 

[signifying nothing]

this implicate order is constantly unfolding into every single explicate Cartesian subspace location in the universe, whilst at the same time being constantly enfolded back into the implicate order.
If this is true, then this may happen precisely because of the tendency for entropy to always increase within an enclosed system, and that the two principles occur in a paradoxical relationship resulting in a dynamic effect.
It is that paradoxical effect that drives everything.
So one could say that rising complexity & therefore computational irreduciblity is potentially what causes and is also caused by the universe's tendency over time towards entropy.

And 'bollox' is an excellent imperfect palindrome that summarises what's potentially happening.