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Comment by im3w1l | Hacker News Reader

Your perspective is a popular one, but a lot of people also think there is a "true" theory that will perfectly explain how the universe evolves.

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>a lot of people also think there is a "true" theory that will perfectly explain how the universe evolves

Doesn't Godel's incompleteness theorems make this doubtful? Logic was not my area of focus but I thought the basic idea was that there is always going to be some un-answerable question(s) or un-provable answers in any consistent theory[1]? I'm pretty sure there is not significant work using non-axiomatic math, I'm honestly not even sure what that looks like. I'd actually be quite interested to find out about some theoretical physics work that did not fall under the auspices of the incompleteness theorem.

[1] There are certainly caveats to "theory" but I believe all those caveats are satisfied by any version of String Theory be actively researched.

No, for instance you can perfectly describe the rules of Conway's Game of Life, and if you were an artificial intelligence living in the Game of Life you could presumably figure out the rules quite easily through experimentation. You wouldn't be able to prove those are the rules though, you'd have to make some assumptions that the rules didn't change in space and time, and that they weren't a manifestation of some more complex rules.

> you can perfectly describe the rules of Conway's Game of Life, and if you were an artificial intelligence living in the Game of Life you could presumably figure out the rules quite easily

I'm not so sure about this. It reminds me of the quote "If our brains were simple enough for us to understand them, we'd be so simple that we couldn't".

Conway's Game of Life is Turing complete, so if it is possible to build an artificial intelligence in a regular computer then it is possible to build one within the Game of Life. Also, understanding the basic rules of the game of life is not the same as understanding how an artificial intelligence within it functions. The rules that determine how patterns of pixels change in the game can be written down on a single sheet of paper, a description of an artificial intelligence built within the game would probably be absurdly complex.

>No

I asked multiple questions, I'm not sure which one you are responding to.

In the context of the incompleteness theorem a 'theory' consists of a formal language to describe theorems, some primitive axioms and some rules that can be used to prove theorems from the axioms. Godel's incompleteness theorem states (loosely speaking) that if a theory is rich enough to describe the arithmetic of the natural numbers, is consistent and is 'effectively axiomatized', then there are statements that can be expressed within the theory and that are true, but that cannot be proven using the rules of deduction in the theory. In short, this is a totally different meaning of the word 'theory' to the one you are thinking of.

Sure, I'm not saying the "theory" in String Theory is the same "theory" in the incompleteness theorems but is there any mathematics or logic that are employed by string theorists that do not fall under the auspices of the incompleteness theorems?

Presburger arithmetic is a decidable theory. "This means it is possible to algorithmically determine, for any sentence in the language of Presburger arithmetic, whether that sentence is provable from the axioms of Presburger arithmetic."

If you don't understand what the incompleteness theorems say, be wary of citing them.

Not sure why I should be "wary." I was asking a question. If one should be wary of asking questions about something how could they ever learn?

Sorry, yes, good point

A lot of people think that but a lot of people think that at any given time in human history.

There will - let there be no doubt - be a final theory of physics (Humanity will end at some point), but determining whether that theory is truly "perfect" is probably impossible within the bounds of measurements known to us at the moment.

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