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You are asking a question that does not have an answer, because "exist" is not well-defined. But if you want to know whether an arbitrary JavaScript in your bro

You are asking a question that does not have an answer, because "exist" is not well-defined. But if you want to know whether an arbitrary JavaScript in your browser will stop or not, well you can not know that for all scripts people can throw at you. In this sense uncomputable functions do exist. BTW - The field trying to deal with defining what exist means is called ontology: https://en.wikipedia.org/wiki/Ontology https://en.wikipedia.org/wiki/Ontology

CrazyStat 5y ago
The JavaScript argument doesn't really get at the point I was trying to make (poorly, probably). The parent was arguing that since almost all functions are uncomputable, "some aspects of reality might only be accurately described by uncomputable functions." This seems unlikely to me. Functions are a mathematical abstraction. Almost all of those functions are uncomputable, but what does the universe care? In what manner could the universe be organized in such a way as to depend on an uncomputable function? Perhaps a better question for my above post would have been: Can we imagine any empirical experiment to distinguish between a universe that depends on uncomputable functions and one that does not? Edit: And if not, in what sense can the universe actually depend on an uncomputable function if we can't distinguish?
- Isinlor 5y ago
  Universe depending on all real numbers would be uncomputable, because most real numbers are uncomputable. This follows from the fact that set of all Turing machines is countable (you can write an algorithm that lists all Turing machines), but set of real numbers is uncountable. So, by Cantor's diagonal argument you can prove that there are real numbers that can not be computed. My guess is that universe can not depend on real numbers (i.e. real numbers are not real) because real numbers introduce infinity related breakdowns in physical models. For example, if there exist a physical state can encode arbitrary real number then that would allow to store infinite amount of information. But it is not possible to prove that something does not exist, see arguments related to Russell's teapot. https://en.wikipedia.org/wiki/Computable_number https://en.wikipedia.org/wiki/Computable_number https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument https://en.wikipedia.org/wiki/Russell%27s_teapot https://en.wikipedia.org/wiki/Russell%27s_teapot
  - CrazyStat 5y ago
    I have similar feelings though I would allow all computable numbers, which would still exclude almost all the reals (while including all rationals and important real numbers like e and pi). Thanks for the interesting discussion!

CrazyStat 5y ago

The JavaScript argument doesn't really get at the point I was trying to make (poorly, probably). The parent was arguing that since almost all functions are uncomputable, "some aspects of reality might only be accurately described by uncomputable functions." This seems unlikely to me. Functions are a mathematical abstraction. Almost all of those functions are uncomputable, but what does the universe care? In what manner could the universe be organized in such a way as to depend on an uncomputable function? Perhaps a better question for my above post would have been: Can we imagine any empirical experiment to distinguish between a universe that depends on uncomputable functions and one that does not? Edit: And if not, in what sense can the universe actually depend on an uncomputable function if we can't distinguish?

Isinlor 5y ago
Universe depending on all real numbers would be uncomputable, because most real numbers are uncomputable. This follows from the fact that set of all Turing machines is countable (you can write an algorithm that lists all Turing machines), but set of real numbers is uncountable. So, by Cantor's diagonal argument you can prove that there are real numbers that can not be computed. My guess is that universe can not depend on real numbers (i.e. real numbers are not real) because real numbers introduce infinity related breakdowns in physical models. For example, if there exist a physical state can encode arbitrary real number then that would allow to store infinite amount of information. But it is not possible to prove that something does not exist, see arguments related to Russell's teapot. https://en.wikipedia.org/wiki/Computable_number https://en.wikipedia.org/wiki/Computable_number https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument https://en.wikipedia.org/wiki/Russell%27s_teapot https://en.wikipedia.org/wiki/Russell%27s_teapot
- CrazyStat 5y ago
  I have similar feelings though I would allow all computable numbers, which would still exclude almost all the reals (while including all rationals and important real numbers like e and pi). Thanks for the interesting discussion!