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The Universe Is Made of Mathematics

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Re: The Universe Is Made of Mathematics

#51

Post by kazinator »

DCKing wrote: post #16
kazinator wrote: post #2

Every result in physics hitherto has been some sort of mathematics: an equation or a constant (measured or otherwise established to some digits of precision). What is a particle? A collection of mathematical properties. So is a wave. If we extrapolate from the past to the future, we can expect more of the same: no "non-mathematical bottom" will be found. Nobody is even looking; the researchers expect all new results…

You're just describing the fact that we can make up descriptions of physics all the way down. If current mathematics is unable to describe physics, then new mathematics is invented [1]. Just because the descriptions work rather well does not mean that those descriptions are somehow more than mere descriptions. It just means that they are very good descriptions. You're making the same category error as mentioned in th…

> If current mathematics is unable to describe physics, then new mathematics is invented

Now suppose that this process stops. One day, mathematics describes physics. What does that mean? It means that some pencil-and-paper mathematics descriptions hint at an abstraction, and that abstraction is physics.

The mathematics which was used prior to that point was not the right one. That mathematics still corresponds to a universe, just not this one.

The idea is that every mathematical object is a universe (not to be confused with some representation of that object, like a definition in plain language, or a diagram, equation).

The world may be exactly the same category of thing as dodecahedron or pi. (Not in the category of pencil-and-paper description of such things; the category of those thing themselves.)

Re: The Universe Is Made of Mathematics

#52

Post by zbyte64 »

DCKing wrote: post #45
zbyte64 wrote: post #40

Earlier quoted context omitted.

>I'm not sure I follow. What does "transform into new situations" really mean? Emergence as a side-effect. >If this is really what he meant, I appreciate the correction. If it would have been clear from the text, I would have proceeded with pointing out with pointing out the dodgy assumptions that underly the finetuning problem, but that would be even more like arguing against a deist/theist. Yes, I am probably putti…

Talking about "side effects", "transformation" or "emergence" seems to assign properties to mathematics that I can't really wrap my head around. I thought that all we could be certain of when it comes to math is that it is a self-consistent set of axioms and rules. A set, of infinite size or not, that would be static and fixed.

A set is fixed but you have an infinite number of sets. We could imagine a (infinitely large) set that contains all primes. But how was that set constructed? To construct such a set an iterative process has to be continuously applied to the prior set. I consider this akin to emergence because physical processes act much the same way and result in novel configurations (sets).

Re: The Universe Is Made of Mathematics

#53

Post by goldenkey »

westoncb wrote: post #37
goldenkey wrote: post #31

Earlier quoted context omitted.

But aye..that's the rub. Is there any difference between meat that appears to operate _EXACTLY_ the same as different meat (constructed using the symbols)? Computationally, no. But if two things in an information-theoretic world, are informationally equivalent, then for all intensive purposes, they are equivelent. Quantum physics says this with regard to quantum states, there's no meat to differentiate electrons, onl…

I think you have a mistake here: > ...the same as different meat (constructed using the symbols)? Your answer is talking about a comparison between, e.g., a human and an essentially identical human /constructed/ using a set of symbols that encodes our understanding of the human's constitution. The original question is comparing, e.g. a human and a set of symbols which describes the human. I consider each of the follo…

True reality is ineffable. The subjective does not equal the objective.

The nature of consciousness is a black box. Therefore the nature of measurement, of assurance that mathematics matches reality, is only within the context of conscious observation, which is therefore subjective.

The objective truth will not be found within subjection.

Re: The Universe Is Made of Mathematics

#54

Post by ursus_bonum »

kazinator wrote: post #51
DCKing wrote: post #16

Earlier quoted context omitted.

You're just describing the fact that we can make up descriptions of physics all the way down. If current mathematics is unable to describe physics, then new mathematics is invented [1]. Just because the descriptions work rather well does not mean that those descriptions are somehow more than mere descriptions. It just means that they are very good descriptions. You're making the same category error as mentioned in th…

> If current mathematics is unable to describe physics, then new mathematics is invented Now suppose that this process stops. One day, mathematics describes physics. What does that mean? It means that some pencil-and-paper mathematics descriptions hint at an abstraction, and that abstraction is physics. The mathematics which was used prior to that point was not the right one. That mathematics still corresponds to a u…

Now suppose that it doesn't stop. Suppose it can't stop.

Suppose no mathematical system is sufficient to describe any universe. It's always just a rough approximation.

Either could be true, I guess.

Re: The Universe Is Made of Mathematics

#55

Post by ursus_bonum »

jameshart wrote: post #41
nemo1618 wrote: post #35

Earlier quoted context omitted.

Hmm. That's an interesting counterpoint. Suppose we discover our universe is a simulation. This would imply that the universe is Turing-computable. Would there not therefore exist a "Grand Unified Theory" that simply described, with absolute precision, the operation of the simulator? Or would it be impossible to produce such a specification?

So if you Gödelized the universe - mapped every conceivable state to a number (proving that that is possible left as an exercise for the reader) - then created mathematical operations on those numbers that transitioned the universe from one state to another 'physically possible' successor state.. I guess Gödel would be able to give you a number representing a universe such that you could not prove whether its state w…

420?

Re: The Universe Is Made of Mathematics

#56

Post by zbyte64 »

goldenkey wrote: post #53
westoncb wrote: post #37

Earlier quoted context omitted.

I think you have a mistake here: > ...the same as different meat (constructed using the symbols)? Your answer is talking about a comparison between, e.g., a human and an essentially identical human /constructed/ using a set of symbols that encodes our understanding of the human's constitution. The original question is comparing, e.g. a human and a set of symbols which describes the human. I consider each of the follo…

True reality is ineffable. The subjective does not equal the objective. The nature of consciousness is a black box. Therefore the nature of measurement, of assurance that mathematics matches reality, is only within the context of conscious observation, which is therefore subjective. The objective truth will not be found within subjection.

> The nature of consciousness is a black box. Therefore the nature of measurement, of assurance that mathematics matches reality, is only within the context of conscious observation, which is therefore subjective.

Consciousness has a track record of taking a black box and deducing what is going on inside.

> The objective truth will not be found within subjection.

Wouldn't you need to understand the nature of subjective processes in order to stipulate such a limit? If you don't understand consciousness then you do not understand its limits.

Re: The Universe Is Made of Mathematics

#57

Post by thaumasiotes »

kazinator wrote: post #48
thaumasiotes wrote: post #17

Earlier quoted context omitted.

> facts like that two is the smallest prime and the only even one I see the fact that two is the only even prime brought up from time to time as if it's inherently interesting. Why is it more interesting than the identical observation that 37 is the only prime which is a multiple of 37? I guess this bothers me because 2 being the only even prime isn't a consequence of the definition of "prime"... it's part of the def…

You're right in that evenness is divisibility by two by definition. For any P which is prime, P is the smallest divisible by P. It is probably that divisibility by two (evenness) is interesting. For example, it has the property that if we know the evenness of two integers, then we know the evenness of their sum or product. Division of cases by even versus odd occurs regularly; in few circumstances do you have to sepa…

As regards your third line, I feel compelled to note that if we know the equivalence class of two integers (mod 37), we also know the equivalence class (mod 37) of their sum and product. ;)

Re: The Universe Is Made of Mathematics

#58

Post by kazinator »

thaumasiotes wrote: post #57
kazinator wrote: post #48

Earlier quoted context omitted.

You're right in that evenness is divisibility by two by definition. For any P which is prime, P is the smallest divisible by P. It is probably that divisibility by two (evenness) is interesting. For example, it has the property that if we know the evenness of two integers, then we know the evenness of their sum or product. Division of cases by even versus odd occurs regularly; in few circumstances do you have to sepa…

As regards your third line, I feel compelled to note that if we know the equivalence class of two integers (mod 37), we also know the equivalence class (mod 37) of their sum and product. ;)

Indeed, it just the mod 37 congruence doesn't correspond to nice Boolean:

  odd(x + y) = odd(x) XOR odd(y)
  odd(x * y) = odd(x) AND odd(y)
There.

Re: The Universe Is Made of Mathematics

#59

Post by goldenkey »

zbyte64 wrote: post #56
goldenkey wrote: post #53

Earlier quoted context omitted.

True reality is ineffable. The subjective does not equal the objective. The nature of consciousness is a black box. Therefore the nature of measurement, of assurance that mathematics matches reality, is only within the context of conscious observation, which is therefore subjective. The objective truth will not be found within subjection.

> The nature of consciousness is a black box. Therefore the nature of measurement, of assurance that mathematics matches reality, is only within the context of conscious observation, which is therefore subjective. Consciousness has a track record of taking a black box and deducing what is going on inside. > The objective truth will not be found within subjection. Wouldn't you need to understand the nature of subjecti…

Yes, but it all rests on a foundation that the inside of the black box is similar to the outside of the black box. And that, may be totally false.

Re: The Universe Is Made of Mathematics

#60

Post by outofcuriosity »

ursus_bonum wrote: post #55
jameshart wrote: post #41

Earlier quoted context omitted.

So if you Gödelized the universe - mapped every conceivable state to a number (proving that that is possible left as an exercise for the reader) - then created mathematical operations on those numbers that transitioned the universe from one state to another 'physically possible' successor state.. I guess Gödel would be able to give you a number representing a universe such that you could not prove whether its state w…

420?

My money's on 69.

Rudy Rucker had some interesting conversations with Gödel about a deterministic universe in which (because time is illusory) backward time travel exists: http://www.rudyrucker.com/blog/2012/08/01/memories-of-kurt-g...

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