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You can't make that bet. Mathematics is just a language; if there were phenomena that couldn't be explained by mathematics, they could not be explained at all.

by Retra 8y ago

You can't make that bet. Mathematics is just a language; if there were phenomena that couldn't be explained by mathematics, they could not be explained at all. And we probably couldn't communicate about them in any consistent manner or conceive of them in a useful way. That doesn't mean these things can't exist, only that we could never be rationally justified in saying that they do. Thus it is possible that the true nature of reality is forever beyond the reach of human understanding. Of course, that's almost irrelevant to anyone who's trying to advance human understanding rather than, say, command complete mastery over the universe.

naasking 8y ago
> You can't make that bet. Mathematics is just a language I surely can make that bet! Calling it "just a language" is seriously understating the implications of language. A language is a structured organization of symbols forming a grammar. So basically, mathematics is a description of structure. Everything has structure except a true random number generator. Given the regularity of existence, the unreasonable effectiveness of mathematics, and the fact that a form of mathematical monism adequately explains all of these facts in the most parsimonious fashion, either we are in an exceedingly unlikely zone of stability of a random process (13 billion years running!), or I'm making a pretty safe bet.
- Retra 8y ago
  A true random number generator definitely has structure. That's the structure in the definition of randomness. And I would not take it as a given that the effectiveness of mathematics is in any way unreasonable.
  - naasking 8y ago
    > A true random number generator definitely has structure. That's the structure in the definition of randomness. True randomness has no structure because that's what makes it inherently unpredictable. Don't confuse pseudo-randomness with randomness. The fact that the output may conform to a distribution over many samples does not necessarily entail it has structure. Whether true randomness actually exists is an open question. The things we model as random variables could easily be pseudo-random variables whose internals we are simply ignorant of, like how quantum uncertainty is eliminated in Bohmian mechanics. > And I would not take it as a given that the effectiveness of mathematics is in any way unreasonable. https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...
    - Retra 8y ago
      True randomness has the structure of randomness. You can measure and identify it. A random number generator will generate numbers at random. That's structure. If you want to think about something without structure, think about what happens inside models that assume a contradiction. >https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness.. https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness.... Oh, argument by meme. I would believe you if maybe you had an XKCD of it.
      - naasking 8y ago
        > True randomness has the structure of randomness Stating it as a tautology doesn't make your sentence coherent. Randomness having structure would entail that it's compressible, but randomness is incompressible by definition. > Oh, argument by meme I have no idea what you're talking about. I pointed you to the book written by an eminent physicist explaining precisely why mathematics is unreasonably effective if mathematics were not somehow intrinsic to existence. This addresses not only your assertion that mathematics is not unreasonably effective, but it also supports my point that mathematics is in some way intrinsic.
        Retra 8y ago
        A random signal is incomprehensible. The fact that the signal is random is not. The medium is not. And you can't have a signal without a medium, so there is always structure. Mathematicians study randomness, and what they study about it is the structure that it has. >I have no idea what you're talking about. I pointed you to the book written by an eminent physicist [...] You pointed me to a wikipedia article which contains right inside it reasonable people who disagree with that point of view. So read what you link.
        naasking 8y ago
        > A random signal is incomprehensible. The fact that the signal is random is not. I said incompressible not incomprehensible. > Mathematicians study randomness, and what they study about it is the structure that it has. They study the structure of its distribution. That's not the kind of structure that's relevant to the question we're debating here, which is the structure of the process generating the output. True randomness would need infinite structure to describe its infinitely unpredictable output corresponding exactly to its output. Such a hypothesis should never be preferred over other hypotheses with more concise structure. Therefore, I continue to assert that I would take that bet, and further, that it's a very safe bet. > You pointed me to a wikipedia article which contains right inside it reasonable people who disagree with that point of view. So read what you link. Reasonable people whose arguments are unconvincing. You should read some more philosophy of mathematics. There's a reason why Platonism and other forms of mathematical realism are still predominant.
Koshkin 8y ago
> Mathematics is just a language Perhaps, for some definitions of the word 'language,' but by and large this is a gross misconception propagated by (theoretical) physicists and other heavy users of more or less abstract mathematics. (In contrast with those who use mathematics to perform computations, such as engineers; unfortunately, this has also been happening within mathematics itself in regards to the relationship between its different branches.)
- Retra 8y ago
  Mathematics being a language does not preclude it from being a computational or physical process, so I don't know what you're objecting to. Nothing I would assert, anyway.
fmihaila 8y ago
> You can't make that bet. Mathematics is just a language Not just any language. It is an ever-changing, ever-growing language, which always expands along with our understanding of the universe. There is no a priori limit to either the language, or our understanding. Together, they comprise the infinite sequence of learning, converging towards its limit. Since we live in time, we can only access the approximations, so it will always be true (in this plane of existence) that we cannot know everything, even while our knowledge continues to increase.

by Retra 8y ago

naasking 8y ago

> You can't make that bet. Mathematics is just a language I surely can make that bet! Calling it "just a language" is seriously understating the implications of language. A language is a structured organization of symbols forming a grammar. So basically, mathematics is a description of structure. Everything has structure except a true random number generator. Given the regularity of existence, the unreasonable effectiveness of mathematics, and the fact that a form of mathematical monism adequately explains all of these facts in the most parsimonious fashion, either we are in an exceedingly unlikely zone of stability of a random process (13 billion years running!), or I'm making a pretty safe bet.

Retra 8y ago
A true random number generator definitely has structure. That's the structure in the definition of randomness. And I would not take it as a given that the effectiveness of mathematics is in any way unreasonable.
- naasking 8y ago
  > A true random number generator definitely has structure. That's the structure in the definition of randomness. True randomness has no structure because that's what makes it inherently unpredictable. Don't confuse pseudo-randomness with randomness. The fact that the output may conform to a distribution over many samples does not necessarily entail it has structure. Whether true randomness actually exists is an open question. The things we model as random variables could easily be pseudo-random variables whose internals we are simply ignorant of, like how quantum uncertainty is eliminated in Bohmian mechanics. > And I would not take it as a given that the effectiveness of mathematics is in any way unreasonable. https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...
  - Retra 8y ago
    True randomness has the structure of randomness. You can measure and identify it. A random number generator will generate numbers at random. That's structure. If you want to think about something without structure, think about what happens inside models that assume a contradiction. >https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness.. https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness.... Oh, argument by meme. I would believe you if maybe you had an XKCD of it.
    - naasking 8y ago
      > True randomness has the structure of randomness Stating it as a tautology doesn't make your sentence coherent. Randomness having structure would entail that it's compressible, but randomness is incompressible by definition. > Oh, argument by meme I have no idea what you're talking about. I pointed you to the book written by an eminent physicist explaining precisely why mathematics is unreasonably effective if mathematics were not somehow intrinsic to existence. This addresses not only your assertion that mathematics is not unreasonably effective, but it also supports my point that mathematics is in some way intrinsic.
      - Retra 8y ago
        A random signal is incomprehensible. The fact that the signal is random is not. The medium is not. And you can't have a signal without a medium, so there is always structure. Mathematicians study randomness, and what they study about it is the structure that it has. >I have no idea what you're talking about. I pointed you to the book written by an eminent physicist [...] You pointed me to a wikipedia article which contains right inside it reasonable people who disagree with that point of view. So read what you link.
        naasking 8y ago
        > A random signal is incomprehensible. The fact that the signal is random is not. I said incompressible not incomprehensible. > Mathematicians study randomness, and what they study about it is the structure that it has. They study the structure of its distribution. That's not the kind of structure that's relevant to the question we're debating here, which is the structure of the process generating the output. True randomness would need infinite structure to describe its infinitely unpredictable output corresponding exactly to its output. Such a hypothesis should never be preferred over other hypotheses with more concise structure. Therefore, I continue to assert that I would take that bet, and further, that it's a very safe bet. > You pointed me to a wikipedia article which contains right inside it reasonable people who disagree with that point of view. So read what you link. Reasonable people whose arguments are unconvincing. You should read some more philosophy of mathematics. There's a reason why Platonism and other forms of mathematical realism are still predominant.

Koshkin 8y ago

> Mathematics is just a language Perhaps, for some definitions of the word 'language,' but by and large this is a gross misconception propagated by (theoretical) physicists and other heavy users of more or less abstract mathematics. (In contrast with those who use mathematics to perform computations, such as engineers; unfortunately, this has also been happening within mathematics itself in regards to the relationship between its different branches.)

Retra 8y ago
Mathematics being a language does not preclude it from being a computational or physical process, so I don't know what you're objecting to. Nothing I would assert, anyway.

fmihaila 8y ago

> You can't make that bet. Mathematics is just a language Not just any language. It is an ever-changing, ever-growing language, which always expands along with our understanding of the universe. There is no a priori limit to either the language, or our understanding. Together, they comprise the infinite sequence of learning, converging towards its limit. Since we live in time, we can only access the approximations, so it will always be true (in this plane of existence) that we cannot know everything, even while our knowledge continues to increase.