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I am to really glad to hear commentary like this coming from physicists. (read: glad to see others siding with my biases). Ceteris paribus there is one signifi

by ukj 7y ago

I am to really glad to hear commentary like this coming from physicists. (read: glad to see others siding with my biases). Ceteris paribus there is one significant distinction between Mathematics and Computer Science: state. The Mathematical Universe is immutable/stateless/timeless. The Computational Universe is mutable/stateful/time-bound. The observer effect in physics can be trivially expressed and evaluated as a mutating getter in any programming language. It cannot be expressed in any Mathematical grammar.

davidivadavid 7y ago
It seems likely that anything that can be expressed in "any programming language" is isomorphic to something that exists in math and can be expressed in that language (automata theory, type theory, category theory, pick your poison).
- ukj 7y ago
  That is probably because you think expression end evaluation are isomorphic. They aren't. Not all functions are referentially transparent. All Mathematical functions are assumed to be.
  - deleted 7y ago
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- deleted 7y ago
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andrepd 7y ago
>The observer effect in physics can be trivially expressed and evaluated as a mutating getter in any programming language. >It cannot be expressed in any Mathematical grammar. What on earth are you trying to say...? There is a whole mathematical treatment of quantum mechanics, measurement effect included (several treatments). More to the point, any algorithm can be formalised in e.g. a Turing machine, or any other equivalent universal model of computation. So there's literally nothing in "computer science" that you cannot express in mathematics. This reeks of Dunning-Kruger: you don't even know enough about what you're talking about to realise how badly little sense you're making. I strongly suggest you familiarise yourself with a topic before opining about it. I'll be hard-pressed to believe you ever opened a physics textbook in your life after high school. Why then do you feel the need to talk blindly about it? I never opened a book about aeronautics in my life, therefore I would never presume to lecture anybody about plane-building... That would just be arrogance.
- jshevek 7y ago
  >This reeks of Dunning-Kruger: you don't even know enough about what you're talking about to realise how badly little sense you're making. I strongly suggest you familiarise yourself with a topic before opining about it. I'll be hard-pressed to believe you ever opened a physics textbook in your life after high school. Why then do you feel the need to talk blindly about it? You can just address their ideas, this extra stuff isn't helpful.
- ukj 7y ago
  >Any algorithm can be formalised in e.g. a Turing machine, or any other equivalent universal model of computation Quoting http://math.andrej.com/2006/03/27/sometimes-all-functions-are-continuous/ http://math.andrej.com/2006/03/27/sometimes-all-functions-ar... >>The lesson is for those “experts” who “know” that all reasonable models of computation are equivalent to Turing machines. This is true if one looks just at functions from N toN. However, at higher types, such as the type of our function m, questions of representation become important, and it does matter which model of computation is used. Mathematics only proves things up to isomorphism. Two things that are theoretically equivalent are not necessarily empirically equivalent. Or, just the good ol' adage: in theory there is no difference between theory and practice, but in practice there is. >So there's literally nothing in "computer science" that you cannot express in mathematics. In addition to the examples in the blog post linked above, you cannot express a mutating getter in Mathematics. Go ahead. I'll wait.
  - jshevek 7y ago
    Please don't use that style of quotation for non-code. It is awful on mobile.
  - Jenz 7y ago
    > In addition to the examples in the blog post linked above, you cannot express a mutating getter in Mathematics. Neither can you express foobarish bamboozles...
    - ukj 7y ago
Koshkin 7y ago
> Computational Universe is mutable/stateful/time-bound A bunch of functional programmers would like to have a word with you.
- ukj 7y ago
  A bunch of functional programmers continue to insist that the Turing Machine has no ticker tape which stores state? Yeah. I know ;)
  - Koshkin 7y ago
    https://gabrielsw.blogspot.com/2012/04/purely-functional-turing-machine.html https://gabrielsw.blogspot.com/2012/04/purely-functional-tur...
    - ukj 7y ago
      Yeah! So you know that read:T call that you have implemented in Scala? You know that it could produce a different result on consecutive calls, right? Because the notion of a mutex/lock doesn’t exist in Math. Mathematics doesn’t allow that, because it is not a “pure function”. https://en.wikipedia.org/wiki/Pure_function https://en.wikipedia.org/wiki/Pure_function Non-determinism is the norm in distributed systems. e.g any networked Turing machine.
      - davidivadavid 7y ago
        You seem to imply that there's no mathematical model/theory of non-deterministic/distributed systems. Surely you don't believe that?
        ukj 7y ago
        I am implying that Mathematical semantics are broken/incomplete. Mathematics uses denotational semantics. It implies pass by-value and pass-by-reference are equivalent. They are in theory, they aren't in practice. That is why Haskell's lazy evaluation leaks time. Engineers/physicists intuitively rely at least on operational semantics. It's a higher order logic, and since Linear Logic time is localized. https://ncatlab.org/nlab/show/Geometry+of+Interaction https://ncatlab.org/nlab/show/Geometry+of+Interaction

by ukj 7y ago

davidivadavid 7y ago

It seems likely that anything that can be expressed in "any programming language" is isomorphic to something that exists in math and can be expressed in that language (automata theory, type theory, category theory, pick your poison).

ukj 7y ago
That is probably because you think expression end evaluation are isomorphic. They aren't. Not all functions are referentially transparent. All Mathematical functions are assumed to be.
- deleted 7y ago
  [deleted]
deleted 7y ago
[deleted]

andrepd 7y ago

>The observer effect in physics can be trivially expressed and evaluated as a mutating getter in any programming language. >It cannot be expressed in any Mathematical grammar. What on earth are you trying to say...? There is a whole mathematical treatment of quantum mechanics, measurement effect included (several treatments). More to the point, any algorithm can be formalised in e.g. a Turing machine, or any other equivalent universal model of computation. So there's literally nothing in "computer science" that you cannot express in mathematics. This reeks of Dunning-Kruger: you don't even know enough about what you're talking about to realise how badly little sense you're making. I strongly suggest you familiarise yourself with a topic before opining about it. I'll be hard-pressed to believe you ever opened a physics textbook in your life after high school. Why then do you feel the need to talk blindly about it? I never opened a book about aeronautics in my life, therefore I would never presume to lecture anybody about plane-building... That would just be arrogance.

jshevek 7y ago
>This reeks of Dunning-Kruger: you don't even know enough about what you're talking about to realise how badly little sense you're making. I strongly suggest you familiarise yourself with a topic before opining about it. I'll be hard-pressed to believe you ever opened a physics textbook in your life after high school. Why then do you feel the need to talk blindly about it? You can just address their ideas, this extra stuff isn't helpful.
ukj 7y ago
>Any algorithm can be formalised in e.g. a Turing machine, or any other equivalent universal model of computation Quoting http://math.andrej.com/2006/03/27/sometimes-all-functions-are-continuous/ http://math.andrej.com/2006/03/27/sometimes-all-functions-ar... >>The lesson is for those “experts” who “know” that all reasonable models of computation are equivalent to Turing machines. This is true if one looks just at functions from N toN. However, at higher types, such as the type of our function m, questions of representation become important, and it does matter which model of computation is used. Mathematics only proves things up to isomorphism. Two things that are theoretically equivalent are not necessarily empirically equivalent. Or, just the good ol' adage: in theory there is no difference between theory and practice, but in practice there is. >So there's literally nothing in "computer science" that you cannot express in mathematics. In addition to the examples in the blog post linked above, you cannot express a mutating getter in Mathematics. Go ahead. I'll wait.
- jshevek 7y ago
  Please don't use that style of quotation for non-code. It is awful on mobile.
- Jenz 7y ago
  > In addition to the examples in the blog post linked above, you cannot express a mutating getter in Mathematics. Neither can you express foobarish bamboozles...
  - ukj 7y ago

Koshkin 7y ago

> Computational Universe is mutable/stateful/time-bound A bunch of functional programmers would like to have a word with you.

ukj 7y ago
A bunch of functional programmers continue to insist that the Turing Machine has no ticker tape which stores state? Yeah. I know ;)
- Koshkin 7y ago
  https://gabrielsw.blogspot.com/2012/04/purely-functional-turing-machine.html https://gabrielsw.blogspot.com/2012/04/purely-functional-tur...
  - ukj 7y ago
    Yeah! So you know that read:T call that you have implemented in Scala? You know that it could produce a different result on consecutive calls, right? Because the notion of a mutex/lock doesn’t exist in Math. Mathematics doesn’t allow that, because it is not a “pure function”. https://en.wikipedia.org/wiki/Pure_function https://en.wikipedia.org/wiki/Pure_function Non-determinism is the norm in distributed systems. e.g any networked Turing machine.
    - davidivadavid 7y ago
      You seem to imply that there's no mathematical model/theory of non-deterministic/distributed systems. Surely you don't believe that?
      - ukj 7y ago
        I am implying that Mathematical semantics are broken/incomplete. Mathematics uses denotational semantics. It implies pass by-value and pass-by-reference are equivalent. They are in theory, they aren't in practice. That is why Haskell's lazy evaluation leaks time. Engineers/physicists intuitively rely at least on operational semantics. It's a higher order logic, and since Linear Logic time is localized. https://ncatlab.org/nlab/show/Geometry+of+Interaction https://ncatlab.org/nlab/show/Geometry+of+Interaction