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Are space ships in game of life invented or discovered? I've come to believe that's ultimately exactly the same question. We're talking about rich structures t

by svara 3y ago

Are space ships in game of life invented or discovered? I've come to believe that's ultimately exactly the same question. We're talking about rich structures that emerge from simple rule sets. That's really all there is to mathematics. We started from structures that provide helpful abstractions for things in real life, which might lead some to believe that mathematics points to some hidden reality behind things, but that's ultimately just spiritual thinking in rational sounding clothing. It is sometimes said that it is surprising that nature follows laws that are mathematical, but that's the wrong way around. Mathematics just provides helpful abstractions that we can apply to whatever we like. Saying nature is mathematical is just saying that nature is consistent in the laws it follows.

mensetmanusman 3y ago
Nature being consistent to 10 significant digits in an abstraction means that math is more than a language.
- turtledragonfly 3y ago
  Why is that? (genuine question) Just because an approximation is really good in some cases doesn't mean it's more than an approximation, does it?
  - mensetmanusman 3y ago
    I believe because all other domains of low entropy information exchange (language) are incredibly imprecise, contradictory, and incomplete. That the universe chose to stick with a set of axioms that are minimal entropy and maximally predictive about the non-existent future means that some approximations are so arbitrarily close to the truth that they become indistinguishable.
cscheid 3y ago
I 100% agree with everything you said, I just wanted to make this point even more forcefully: > Saying nature is mathematical is just saying that nature is consistent in the laws it follows. It's more like "wherever nature isn't mathematical, we don't think about it as being mathematical", so saying "nature is mathematical" is very strongly tautological. It's the same kind of situation as "why is everything linear?", or "why is everything an oscillator". The answer is more like "the things that aren't can't be easily described mathematically, and so we don't. What shakes out is mostly linear or quadratic (oscillators)".
- LanceH 3y ago
  Physics is just one (non-)choice of axioms. Math that works in the world is physics, it's all discovered. You can't invent math and expect physics to follow. Other math is invented through the choice of axioms and then we discovery the theorems that follow from those.
hurryer 3y ago
But why is nature consistent?
- hackinthebochs 3y ago
  Is it intelligible that it might not have been? What would it mean for nature to be inconsistent? What would a universe look like that didn't follow laws?
  - hurryer 3y ago
    Random stuff happening? Pockets of local consistency?
    - greiskul 3y ago
      There probably wouldn't exist any type of inteligent animal to wonder about it, since life and the evolution of life kind of requires chemestry to be a thing.
      - esahione 3y ago
        The anthropic principle doesn't explain why it is, in actuality, intelligible. It's only a constraint on what couldn't be the case given we exist. It's clearly a much deeper question, given even Wigner wrote a paper about it. He called it a miracle. Look, ultimately, mathematics is abstract and the physical world is material. The fact that an abstract condition is able to affect material conditions is literally a miracle that can only be explained metaphysically.
    - hackinthebochs 3y ago
      Random stuff happening for no reason with no pattern or constraint runs afloul of the principle of sufficient reason. The PSR is a basic assumption of intelligibility. Events happening with no cause can't be made sense of. Everything that happens is brute in the worst way possible. By the standards of reason, it is maximally unintelligible. We must rationally give higher credence to any other explanation, i.e. an order and law-based universe. One might say the universe has no obligation to be intelligible to us, and perhaps that true. But we have an obligation to intelligible beliefs. In being able to ask the question of why the world is law-based, we're rationally constrained in the answer we can accept. You can see it as an application of the anthropic principle, but I think it's more basic than that. If there is sense to be made of anything (in a logical sense that is prior to the universe), then the universe must also make sense.
timeagain 3y ago
My favorite Daniel Dennett quote: “People don’t build ships, the ocean builds ships.”
jablongo 3y ago
This is a compelling way of looking at things for sure; to me it seems like you're saying math is just a language (like English) that we can use to describe the world. English is no more "right" than some other made up language, so same goes for math, and thats certainly seems true in some cases. However there are things that are intrinsic to mathematics that also seem intrinsic to existence, like prime numbers. Many things about prime numbers are 'discovered' as if they were elements of nature that need to be revealed through study. For example, the distribution of primes and the distribution of twin primes are things likely to have been discovered by an alien intelligence, assuming one exists. What would their math look like? Different for sure, but I think it's likely they still studied the primes, hypothetically.
- svara 3y ago
  I agree with you that what I'm saying is that maths is ultimately a kind of language that we use to describe the world. I wouldn't agree with calling it "just" language or "like English". It's different in that consistency is strictly enforced, such that simple rules can lead to rich emergent structures. That's what I was getting at with the game of life metaphor. So, if you follow my argument, the fact that there are prime numbers is not 'intrinsic to mathematics', it's the other way around -- we use rules that lead to rich structures, because those provide useful, consistent abstractions to talk about things. Prime numbers are among those rich structures. To respond to a sibling comment that seems somewhat related -- The fact that we can calculate some physical constants with high precision is not a counter argument to that. What we are doing is fitting a mathematical abstraction to data; once we have done that, we can find more physical truths by assuming consistency and performing logical inference. The fact that a constant can be calculated then just means that we have a consistent theory for the physical structures from which that constant arises.
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by svara 3y ago

mensetmanusman 3y ago

Nature being consistent to 10 significant digits in an abstraction means that math is more than a language.

turtledragonfly 3y ago
Why is that? (genuine question) Just because an approximation is really good in some cases doesn't mean it's more than an approximation, does it?
- mensetmanusman 3y ago
  I believe because all other domains of low entropy information exchange (language) are incredibly imprecise, contradictory, and incomplete. That the universe chose to stick with a set of axioms that are minimal entropy and maximally predictive about the non-existent future means that some approximations are so arbitrarily close to the truth that they become indistinguishable.

cscheid 3y ago

I 100% agree with everything you said, I just wanted to make this point even more forcefully: > Saying nature is mathematical is just saying that nature is consistent in the laws it follows. It's more like "wherever nature isn't mathematical, we don't think about it as being mathematical", so saying "nature is mathematical" is very strongly tautological. It's the same kind of situation as "why is everything linear?", or "why is everything an oscillator". The answer is more like "the things that aren't can't be easily described mathematically, and so we don't. What shakes out is mostly linear or quadratic (oscillators)".

LanceH 3y ago
Physics is just one (non-)choice of axioms. Math that works in the world is physics, it's all discovered. You can't invent math and expect physics to follow. Other math is invented through the choice of axioms and then we discovery the theorems that follow from those.

hurryer 3y ago

But why is nature consistent?

hackinthebochs 3y ago
Is it intelligible that it might not have been? What would it mean for nature to be inconsistent? What would a universe look like that didn't follow laws?
- hurryer 3y ago
  Random stuff happening? Pockets of local consistency?
  - greiskul 3y ago
    There probably wouldn't exist any type of inteligent animal to wonder about it, since life and the evolution of life kind of requires chemestry to be a thing.
    - esahione 3y ago
      The anthropic principle doesn't explain why it is, in actuality, intelligible. It's only a constraint on what couldn't be the case given we exist. It's clearly a much deeper question, given even Wigner wrote a paper about it. He called it a miracle. Look, ultimately, mathematics is abstract and the physical world is material. The fact that an abstract condition is able to affect material conditions is literally a miracle that can only be explained metaphysically.
  - hackinthebochs 3y ago
    Random stuff happening for no reason with no pattern or constraint runs afloul of the principle of sufficient reason. The PSR is a basic assumption of intelligibility. Events happening with no cause can't be made sense of. Everything that happens is brute in the worst way possible. By the standards of reason, it is maximally unintelligible. We must rationally give higher credence to any other explanation, i.e. an order and law-based universe. One might say the universe has no obligation to be intelligible to us, and perhaps that true. But we have an obligation to intelligible beliefs. In being able to ask the question of why the world is law-based, we're rationally constrained in the answer we can accept. You can see it as an application of the anthropic principle, but I think it's more basic than that. If there is sense to be made of anything (in a logical sense that is prior to the universe), then the universe must also make sense.

timeagain 3y ago

My favorite Daniel Dennett quote: “People don’t build ships, the ocean builds ships.”

jablongo 3y ago

This is a compelling way of looking at things for sure; to me it seems like you're saying math is just a language (like English) that we can use to describe the world. English is no more "right" than some other made up language, so same goes for math, and thats certainly seems true in some cases. However there are things that are intrinsic to mathematics that also seem intrinsic to existence, like prime numbers. Many things about prime numbers are 'discovered' as if they were elements of nature that need to be revealed through study. For example, the distribution of primes and the distribution of twin primes are things likely to have been discovered by an alien intelligence, assuming one exists. What would their math look like? Different for sure, but I think it's likely they still studied the primes, hypothetically.

svara 3y ago
I agree with you that what I'm saying is that maths is ultimately a kind of language that we use to describe the world. I wouldn't agree with calling it "just" language or "like English". It's different in that consistency is strictly enforced, such that simple rules can lead to rich emergent structures. That's what I was getting at with the game of life metaphor. So, if you follow my argument, the fact that there are prime numbers is not 'intrinsic to mathematics', it's the other way around -- we use rules that lead to rich structures, because those provide useful, consistent abstractions to talk about things. Prime numbers are among those rich structures. To respond to a sibling comment that seems somewhat related -- The fact that we can calculate some physical constants with high precision is not a counter argument to that. What we are doing is fitting a mathematical abstraction to data; once we have done that, we can find more physical truths by assuming consistency and performing logical inference. The fact that a constant can be calculated then just means that we have a consistent theory for the physical structures from which that constant arises.

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