6 ms·

Smart people can be cranks. In fact they are far more likely to be so, perhaps because they overestimate their own ability. See e.g. http://lesswrong.com/lw/j8/

Smart people can be cranks. In fact they are far more likely to be so, perhaps because they overestimate their own ability. See e.g. http://lesswrong.com/lw/j8/the_crackpot_offer/ http://lesswrong.com/lw/j8/the_crackpot_offer/ In any case I didn't call him a crank, but many actual mathematicians do. >Does he just "claim" or does he give proof? Because if he has the proper system, and he proves his theorems based on his axioms... I might be misremembering this, but I think his argument was just that "computers have tested all possible counterexamples up to some big number, therefore it's true. All this talk of different axiom systems is giving ultrafinitism vastly more credit than it's due. It's not a different but coherent mathematical system. It's a "philosophy" based entirely on refusing to accept a result because it feels counterintuitive. And then coming to vastly more counterintuitive and absurd results as a consequence of trying to resolve it. I mean they really believe that there exists a biggest number and there are no numbers bigger than that. Even regular finitists are kind of absurd, denying the existence of pi or the square root of 2.

pbhjpbhj 9y ago
Under some interpretations of physics there is a finite number of objects in the universe, hence a largest possible cardinality of things that is finite. Even sets like the number of possible states of the Universe appear to me to be finite, though so large as to be intractable to my imagination. A conceptual circle and a real circle differ markedly because of the lumpiness of matter, quantisation, uncertainty. Every real circle is an approximation (yay Plato!). Pi doesn't appear to me to be real, as in writ in matter/energy -- it's a ratio of measurements of an imaginary article, circles don't exist in our experiential 4-space. Irrational numbers like root-of-2 just fall out of basic maths though, there's not going to be a real line with that measure just as there's no line with a predefined unit measure (ie unless you define that line at that point in time as your unit, but a real line isn't even straight). I'd be really interested in refutation of this -- it's one of those positions I've held since Uni, at least, but never explored as I've never seen it challenged/supported nor named.
- revelation 9y ago
  What do you mean "refutation"? This is making you look as much of a crank as they are. There is no imaginary requirement to have a direct counterpart in the physical world, in "matter/energy". Infinity, axiom of choice, .. are all tools. We use them because their presence gives us other helpful results. None of it has anything to do with "lumpiness of matter", "matter/energy", "experiental 4-space", "real line".
  - pbhjpbhj 9y ago
    Perhaps I am a "crank". Refutation as in "you overlooked this standard point that undermines your position", like maybe "polarised light describes a perfect circle", or "the gravitational field of a black-hole (when shaved) is a sphere". AFAIK there's nothing truly infinite, nor perfectly geometric, that we can experience in our physical spacetime -- I'd like to hear from those who can show me that's wrong. The world itself isn't axiomatic, if certain theories/systems that are unfalsified show parts of it are infinite/etc. -- despite that just being a model -- that's an interesting result.
  - coldtea 9y ago
    >There is no imaginary requirement to have a direct counterpart in the physical world, in "matter/energy". No, but there's no requirement that the useful/only way to do math is with "platonic" / ideal math objects either.
- wolfi1 9y ago
  sounds like you belong to the pythagoreans[0] [0] https://en.wikipedia.org/wiki/Pythagoreanism https://en.wikipedia.org/wiki/Pythagoreanism
  - pbhjpbhj 9y ago
    I'm certainly sympathetic to some Platonic ideas.
- Houshalter 9y ago
  As far as we know the universe isn't discrete like a cellular automata. So it's state contains infinite information for starters. I'm not sure what the current theories of physics say, but I don't believe the universe is finite in time or space either. And who knows what new discoveries physics might make in the future and what weird math it might require. There's no a priori reason to expect the universe to be modelled by finitist math. But even if we knew for sure it was, so what? Theorems about real numbers apply perfectly well to finite approximations. You don't gain anything by restricting yourself to finite math, and you lose quite a bit and make a lot of things much harder.
roenxi 9y ago
We've entered fuzzy-definition territory; but I'd say it is a stretch of the language to imply Wildberger is a crank. Which you have now done twice with no references. He is unorthadox in his pushing of rational numbers, sure, but he gets through an extremely large amount of maths correctly. It is well within his job domain reflect on odd academic questions about what happens outside the world of human measurement.
deleted 9y ago
[deleted]

pbhjpbhj 9y ago

Under some interpretations of physics there is a finite number of objects in the universe, hence a largest possible cardinality of things that is finite. Even sets like the number of possible states of the Universe appear to me to be finite, though so large as to be intractable to my imagination. A conceptual circle and a real circle differ markedly because of the lumpiness of matter, quantisation, uncertainty. Every real circle is an approximation (yay Plato!). Pi doesn't appear to me to be real, as in writ in matter/energy -- it's a ratio of measurements of an imaginary article, circles don't exist in our experiential 4-space. Irrational numbers like root-of-2 just fall out of basic maths though, there's not going to be a real line with that measure just as there's no line with a predefined unit measure (ie unless you define that line at that point in time as your unit, but a real line isn't even straight). I'd be really interested in refutation of this -- it's one of those positions I've held since Uni, at least, but never explored as I've never seen it challenged/supported nor named.

revelation 9y ago
What do you mean "refutation"? This is making you look as much of a crank as they are. There is no imaginary requirement to have a direct counterpart in the physical world, in "matter/energy". Infinity, axiom of choice, .. are all tools. We use them because their presence gives us other helpful results. None of it has anything to do with "lumpiness of matter", "matter/energy", "experiental 4-space", "real line".
- pbhjpbhj 9y ago
  Perhaps I am a "crank". Refutation as in "you overlooked this standard point that undermines your position", like maybe "polarised light describes a perfect circle", or "the gravitational field of a black-hole (when shaved) is a sphere". AFAIK there's nothing truly infinite, nor perfectly geometric, that we can experience in our physical spacetime -- I'd like to hear from those who can show me that's wrong. The world itself isn't axiomatic, if certain theories/systems that are unfalsified show parts of it are infinite/etc. -- despite that just being a model -- that's an interesting result.
- coldtea 9y ago
  >There is no imaginary requirement to have a direct counterpart in the physical world, in "matter/energy". No, but there's no requirement that the useful/only way to do math is with "platonic" / ideal math objects either.
wolfi1 9y ago
sounds like you belong to the pythagoreans[0] [0] https://en.wikipedia.org/wiki/Pythagoreanism https://en.wikipedia.org/wiki/Pythagoreanism
- pbhjpbhj 9y ago
  I'm certainly sympathetic to some Platonic ideas.
Houshalter 9y ago
As far as we know the universe isn't discrete like a cellular automata. So it's state contains infinite information for starters. I'm not sure what the current theories of physics say, but I don't believe the universe is finite in time or space either. And who knows what new discoveries physics might make in the future and what weird math it might require. There's no a priori reason to expect the universe to be modelled by finitist math. But even if we knew for sure it was, so what? Theorems about real numbers apply perfectly well to finite approximations. You don't gain anything by restricting yourself to finite math, and you lose quite a bit and make a lot of things much harder.

roenxi 9y ago

We've entered fuzzy-definition territory; but I'd say it is a stretch of the language to imply Wildberger is a crank. Which you have now done twice with no references. He is unorthadox in his pushing of rational numbers, sure, but he gets through an extremely large amount of maths correctly. It is well within his job domain reflect on odd academic questions about what happens outside the world of human measurement.

deleted 9y ago

[deleted]