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Cake day: October 20th, 2024

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  • Pointing that A is like B regarding the aspect X is often treated as a “comparison” between A and B, but it doesnt imply that A is as great, as important, or as bad as B. It doesnt imply that A is like B in any way other than in the aspect X.

    Why not focus on the point that is being made instead of freaking out over the angles from which the analogy breaks down. Every analogy breaks down from some angle.











  • Turing machines can’t exist, either.

    Oh no! You got me there!

    Why do you need uncountable infinities for hypercomputers, though?. I see that Martin Davis criticism has to do with that approach, and I agree this approach seems silly. But, it doesnt seem to cover all potential fronts for hypercomputers. Im not talking about current approaches to quantum computing either. What if some yet unknown physical law makes arrangements of particles somehow solve the first order logic validity problem, which is also not in R? Doesnt involve uncountable infinity at all. Again, im not saying its possible, just that theres no purely logical proof of impossibility, thats all.



  • church-turing is a a thesis, not a logical theorem. You pointed me to a proof that the halting problem is unsolvable by a Turing Machine, not that hypercomputers are impossible.

    The critic Martin Davis mentioned in wikipedia has an article criticizing a kind of attempt at showing the feasibility of hypercomputers. Thats fine. If there was a well-known logical proof of its unfeasibility, his task would be much simpler though. The purely logical argument hasnt been made as far as i know and as far as you were able to show.




  • …I never said they are not.

    The incompleteness theorem says that a consistent axiomatic formal system satisfying some conditions cannot be complete, so the universe as a formal system (supposed consistent, complete, expressive enough, …) cannot be axiomatized.

    external oracles

    What do you mean external?

    The possibility of using physical phenomena as oracles for solving classically uncomputable problems in the real world is an open question. If you think this is logically as impossible as a four sided triangle you should give sources for this claim, not just some vague statements involving the incompleteness theorem. Prove this logical impossibility or give sources, thats all im asking.

    Who says you cant take a first order logic sentence, codify it as a particular arrangement of certain particles and determine if the sentence was valid by observing how the particles behave? Some undiscovered physical phenomenon might make this possible… who knows. It would make possible the making of a real world machine that surpasses the turing machine in computability, no? How is this like a four sided triangle? The four sided triangle is logically impossible, but a hypercomputer is logically possible. The question is whether it is also physically possible, which is an open question.



  • I took this interpretation to the “existence of uncomputable functions” because of course they exist mathematically, but we were talking about the physical world, so another meaning of existence was probably being used.

    You say you studied, but still your arguments linking incompleteness and the physical world did not make sense. To the point that you say things like the universe already is a formal system to which we can apply the incompleteness theorem. Again, expressivity of arithmetic isnt the only condition for using incompleteness. The formal system must be similar to first order logic, as the sentences must be finite, the inference rules must be computable and their set must be recursively enumerable, … among others. When I asked this, you only mentioned being able to express natural numbers. But can the formal system express them in the specific sense that we need here to use incompleteness?

    Then, what do you do with the fact that you cant effectively axiomatize the laws of the universe? (which would be the conclusion taken from using incompleteness theorem here, if you could) What’s the point of using incompleteness here? How do you relate this to the computability of brain operations?

    These are all giant holes you skipped, which suggest to me that you brushed over these topics somewhere and started to extrapolate unrigorous conclusions from them.