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If it's first step was to enumerate the machine which computed Pi, then this enumerating machine would never take a second step. Geometry isnt computable, and

If it's first step was to enumerate the machine which computed Pi, then this enumerating machine would never take a second step. Geometry isnt computable, and all physical ontology is geometric.

tsimionescu 4y ago
Pi is very much computable, and I don't know what aspect of geometry you think is not computable.
elil17 4y ago
Is it true to say that geometry isn’t computable? You can symbolically compute geometry. You wouldn’t be able to compute the decimal circumference of a circle, for example, but you can represent it as 2pir in a symbolic system. You can then use that to do things like symbolically derive other geometric properties (e.g. surface area of a sphere). It’s not clear that the universe “computes” the circumference of a circle to infinite precision. The best candidate I can think of would be the event horizon of a black hole, which is not composed of particles as I understand it, but I believe the jury is still out on whether the Plank length means that the shape of such a thing is still quantized at some level. Plus, humans can’t compute pi either. We can conceive of it, though, and I don’t see an argument for why an AI agent can’t conceive of it too (or at least behave like it conceived of it).
naasking 4y ago
First, all of physics is computable to arbitrary precision. Continuous quantities in physics are being systematically removed because they almost inevitably introduce absurdities [1]. Measures lose all meaning below Planck length anyway. Second, the point of enumerating all Turing machines is not to run them to completion, it's simply to create them, so your objection is inapplicable. The Turing machine itself defines an ontology. The claim was that algorithms do not have access to novel ontologies, which conflicts with the basic construction of recursively enumerable functions that defines computation. Third, even if it were true that geometry is not computable, don't mistake the formalism we currently use as somehow necessary. Geometry is powerful enough to model physics, but it could also be too powerful, ie. there could be some formalism less powerful than geometry that would also suffice for physics. For instance, we use real numbers in physics for convenience, but real numbers almost certainly don't really exist as we define them. [1] Baez's, Struggles with the Continuum, https://arxiv.org/abs/1609.01421 https://arxiv.org/abs/1609.01421
- mjburgess 4y ago
  QA is non-linear when discretised, so no, no one is "replacing" anything. There is no "digital physics", it's a PR term of a hype industry, not the title of any, eg., textbook on area of physics. Physics is not computable to arbitrary precision, both chaos and qm require physics to use non-computable numbers.
  - naasking 4y ago
    > QA is non-linear when discretised, so no, no one is "replacing" anything. I don't know what any of this is referring to as I never mentioned "replacing" anything. > There is no "digital physics", it's a PR term of a hype industry, not the title of any, eg., textbook on area of physics. Incorrect: A Computable Universe, https://www.worldscientific.com/worldscibooks/10.1142/8306#t=aboutBook https://www.worldscientific.com/worldscibooks/10.1142/8306#t... > Physics is not computable to arbitrary precision, both chaos and qm require physics to use non-computable numbers. Also incorrect, and put most succinctly by Peter Shor [1]: Because of quantum mechanics and the uncertainty principle, the value of a physical constant can't be defined to more than 60 or 70 digits. And any finite-precision number by definition is computable. See also [2] for alternative conceptions. [1] https://physics.stackexchange.com/questions/16889/non-computable-numbers-in-physics#comment40236_16893 https://physics.stackexchange.com/questions/16889/non-comput... [2] https://arxiv.org/abs/1003.5831 https://arxiv.org/abs/1003.5831
    - mjburgess 4y ago
      That's a textbook on the idea, not a text book on an area of physics using that idea. Of course there are many books professing the idea, there are none, eg., providing a computable formalism for classical mechanics. The value of a physical constant can be defined to abitarily many digits, that's a misunderstanding of QM which limits the measurement precision in conjugate variables. But even were our measurement limited to finite precision, the world certainly isnt.
      - naasking 4y ago
optimalsolver 4y ago
Compute the first step of the first machine. Compute the second step of the first machine and the first step of the second machine. Compute the third step of the first machine, the second step of the second machine... http://www.amirrorclear.net/academic/ideas/simulation/index.html http://www.amirrorclear.net/academic/ideas/simulation/index....
- mjburgess 4y ago
  Good article. The issue is that his parallel computation isn't itself a Turing machine. If you build a system which can "keep pace with the diagonalization argument", necessarily, it isnt a computer. No computer can process at the rate real numbers require, this is another way of stating the Cantor result. If you build a computer (here, note, computer = an abstract mathematical formalism over discrete numbers), you cannot compute fast enough. I happen to think reality, esp. spacetime, is geometric (ie., real-valued) though empirical measures of it are, of course, just a discrete approximation.

If it's first step was to enumerate the machine which computed Pi, then this enumerating machine would never take a second step. Geometry isnt computable, and all physical ontology is geometric.

tsimionescu 4y ago

Pi is very much computable, and I don't know what aspect of geometry you think is not computable.

elil17 4y ago

Is it true to say that geometry isn’t computable? You can symbolically compute geometry. You wouldn’t be able to compute the decimal circumference of a circle, for example, but you can represent it as 2pir in a symbolic system. You can then use that to do things like symbolically derive other geometric properties (e.g. surface area of a sphere). It’s not clear that the universe “computes” the circumference of a circle to infinite precision. The best candidate I can think of would be the event horizon of a black hole, which is not composed of particles as I understand it, but I believe the jury is still out on whether the Plank length means that the shape of such a thing is still quantized at some level. Plus, humans can’t compute pi either. We can conceive of it, though, and I don’t see an argument for why an AI agent can’t conceive of it too (or at least behave like it conceived of it).

naasking 4y ago

First, all of physics is computable to arbitrary precision. Continuous quantities in physics are being systematically removed because they almost inevitably introduce absurdities [1]. Measures lose all meaning below Planck length anyway. Second, the point of enumerating all Turing machines is not to run them to completion, it's simply to create them, so your objection is inapplicable. The Turing machine itself defines an ontology. The claim was that algorithms do not have access to novel ontologies, which conflicts with the basic construction of recursively enumerable functions that defines computation. Third, even if it were true that geometry is not computable, don't mistake the formalism we currently use as somehow necessary. Geometry is powerful enough to model physics, but it could also be too powerful, ie. there could be some formalism less powerful than geometry that would also suffice for physics. For instance, we use real numbers in physics for convenience, but real numbers almost certainly don't really exist as we define them. [1] Baez's, Struggles with the Continuum, https://arxiv.org/abs/1609.01421 https://arxiv.org/abs/1609.01421

mjburgess 4y ago
QA is non-linear when discretised, so no, no one is "replacing" anything. There is no "digital physics", it's a PR term of a hype industry, not the title of any, eg., textbook on area of physics. Physics is not computable to arbitrary precision, both chaos and qm require physics to use non-computable numbers.
- naasking 4y ago
  > QA is non-linear when discretised, so no, no one is "replacing" anything. I don't know what any of this is referring to as I never mentioned "replacing" anything. > There is no "digital physics", it's a PR term of a hype industry, not the title of any, eg., textbook on area of physics. Incorrect: A Computable Universe, https://www.worldscientific.com/worldscibooks/10.1142/8306#t=aboutBook https://www.worldscientific.com/worldscibooks/10.1142/8306#t... > Physics is not computable to arbitrary precision, both chaos and qm require physics to use non-computable numbers. Also incorrect, and put most succinctly by Peter Shor [1]: Because of quantum mechanics and the uncertainty principle, the value of a physical constant can't be defined to more than 60 or 70 digits. And any finite-precision number by definition is computable. See also [2] for alternative conceptions. [1] https://physics.stackexchange.com/questions/16889/non-computable-numbers-in-physics#comment40236_16893 https://physics.stackexchange.com/questions/16889/non-comput... [2] https://arxiv.org/abs/1003.5831 https://arxiv.org/abs/1003.5831
  - mjburgess 4y ago
    That's a textbook on the idea, not a text book on an area of physics using that idea. Of course there are many books professing the idea, there are none, eg., providing a computable formalism for classical mechanics. The value of a physical constant can be defined to abitarily many digits, that's a misunderstanding of QM which limits the measurement precision in conjugate variables. But even were our measurement limited to finite precision, the world certainly isnt.
    - naasking 4y ago

optimalsolver 4y ago

Compute the first step of the first machine. Compute the second step of the first machine and the first step of the second machine. Compute the third step of the first machine, the second step of the second machine... http://www.amirrorclear.net/academic/ideas/simulation/index.html http://www.amirrorclear.net/academic/ideas/simulation/index....

mjburgess 4y ago
Good article. The issue is that his parallel computation isn't itself a Turing machine. If you build a system which can "keep pace with the diagonalization argument", necessarily, it isnt a computer. No computer can process at the rate real numbers require, this is another way of stating the Cantor result. If you build a computer (here, note, computer = an abstract mathematical formalism over discrete numbers), you cannot compute fast enough. I happen to think reality, esp. spacetime, is geometric (ie., real-valued) though empirical measures of it are, of course, just a discrete approximation.