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That's just because you use the word "exact", though. Exactitude doesn't exist in the universe as we understand it. There's a difference between something not

by snet0 5y ago

That's just because you use the word "exact", though. Exactitude doesn't exist in the universe as we understand it. There's a difference between something not being instantiated in this universe and being unscientific, though. If we produce a model of the universe that doesn't make a single incorrect prediction given all data available, and it predicts infinities to exist in some strange but quite real cases, is it unscientific?

tsimionescu 5y ago
> Exactitude doesn't exist in the universe as we understand it. Of course exactitude exists. For example, two electrons have exactly the same charge. A photon has exactly 0 charge. > There's a difference between something not being instantiated in this universe and being unscientific, though. Well, science is a particular way of studying what exists. Studying something that doesn't exist is unscientific (of course, you can use science to try to determine IF something exists). But there are also things that are outside the reach of the methods of science, so they are unscientific in this sense. Questions such as "did some god create the universe" are unscientific because it is simply impossible to apply the methods of science to arrive at an answer to this question. Similarly, asking "is the universe infinite in size" is unscientific, because it is impossible to apply the methods of science and arrive at a definite answer to this question. > If we produce a model of the universe that doesn't make a single incorrect prediction given all data available, and it predicts infinities to exist in some strange but quite real cases, is it unscientific? If it predicts actual infinities exist in certain conditions, than it is not going to be a testable theory in those conditions. It may still be a perfectly workable model, just as GR is perfectly workable despite predicting singularities at the center of black holes. That doesn't mean that the singularities exist, it means that GR breaks down at certain points. But even if you had a physical theory that relied on something like a Banach-Tarski construction, you could never distinguish between an actual infinity of points, leading to two perfectly solid, perfectly identical spheres; and an arbitrarily large number of points, leading either to two perfectly solid but slightly different-sized spheres; or two identically-sized spheres with small holes. Of course, without some need to specify the number of points, you would be well positioned to use the infinite variant. But if someone asked you if this means that the sphere really has an infinite number of points, the answer would have to be that you can't be sure.
- canjobear 5y ago
  > Of course exactitude exists. For example, two electrons have exactly the same charge. A photon has exactly 0 charge. Aren't claims like this unscientific according to your standard? You will never be able to measure that two electrons have the same charge to infinite decimal precision. You might have a theory that says they should have the same charge, but you won't be able to test that theory to infinite precision either.
  - tsimionescu 5y ago
    Hmm, actually you may be right. I'm not entirely sure how powerful the 'requirement' in QM for these quantities to be quantized is though, but most likely you are right - the theory wouldn't be able to distinguish between identical charges and veeeeery slightly different charges.
- rytill 5y ago
  As the other comment implied, infinity and exactitude are two sides of the same coin. Exactitude is infinite precision. No finite amount of empirical evidence can afford infinite precision, so you’re back in math-land.
  - tsimionescu 5y ago
    That's true, though I have a hard time squaring that with observations of classical objects. Would it make sense to say that I have approximately 2 legs, or can I actually be confident in saying I have exactly two legs? Even with things like MWI, in any particular world I would still have an exact integer amount of legs, as far as I understand. Perhaps the problem here is one of mixing intuition (the idea of 'an object') with rigorous physics and mathematics, perhaps this is where I am going a bit wrong.
    - snet0 5y ago
      We have a very precise (although one might struggle to describe it) idea of what qualifies as a human leg. The number 2 is basically defined (at least in common usage) as the number of things you have when you have one thing and then another thing. I'd point out that, as you mentioned, this is a different level of abstraction to physics and mathematics.

by snet0 5y ago

tsimionescu 5y ago

> Exactitude doesn't exist in the universe as we understand it. Of course exactitude exists. For example, two electrons have exactly the same charge. A photon has exactly 0 charge. > There's a difference between something not being instantiated in this universe and being unscientific, though. Well, science is a particular way of studying what exists. Studying something that doesn't exist is unscientific (of course, you can use science to try to determine IF something exists). But there are also things that are outside the reach of the methods of science, so they are unscientific in this sense. Questions such as "did some god create the universe" are unscientific because it is simply impossible to apply the methods of science to arrive at an answer to this question. Similarly, asking "is the universe infinite in size" is unscientific, because it is impossible to apply the methods of science and arrive at a definite answer to this question. > If we produce a model of the universe that doesn't make a single incorrect prediction given all data available, and it predicts infinities to exist in some strange but quite real cases, is it unscientific? If it predicts actual infinities exist in certain conditions, than it is not going to be a testable theory in those conditions. It may still be a perfectly workable model, just as GR is perfectly workable despite predicting singularities at the center of black holes. That doesn't mean that the singularities exist, it means that GR breaks down at certain points. But even if you had a physical theory that relied on something like a Banach-Tarski construction, you could never distinguish between an actual infinity of points, leading to two perfectly solid, perfectly identical spheres; and an arbitrarily large number of points, leading either to two perfectly solid but slightly different-sized spheres; or two identically-sized spheres with small holes. Of course, without some need to specify the number of points, you would be well positioned to use the infinite variant. But if someone asked you if this means that the sphere really has an infinite number of points, the answer would have to be that you can't be sure.

canjobear 5y ago
> Of course exactitude exists. For example, two electrons have exactly the same charge. A photon has exactly 0 charge. Aren't claims like this unscientific according to your standard? You will never be able to measure that two electrons have the same charge to infinite decimal precision. You might have a theory that says they should have the same charge, but you won't be able to test that theory to infinite precision either.
- tsimionescu 5y ago
  Hmm, actually you may be right. I'm not entirely sure how powerful the 'requirement' in QM for these quantities to be quantized is though, but most likely you are right - the theory wouldn't be able to distinguish between identical charges and veeeeery slightly different charges.
rytill 5y ago
As the other comment implied, infinity and exactitude are two sides of the same coin. Exactitude is infinite precision. No finite amount of empirical evidence can afford infinite precision, so you’re back in math-land.
- tsimionescu 5y ago
  That's true, though I have a hard time squaring that with observations of classical objects. Would it make sense to say that I have approximately 2 legs, or can I actually be confident in saying I have exactly two legs? Even with things like MWI, in any particular world I would still have an exact integer amount of legs, as far as I understand. Perhaps the problem here is one of mixing intuition (the idea of 'an object') with rigorous physics and mathematics, perhaps this is where I am going a bit wrong.
  - snet0 5y ago
    We have a very precise (although one might struggle to describe it) idea of what qualifies as a human leg. The number 2 is basically defined (at least in common usage) as the number of things you have when you have one thing and then another thing. I'd point out that, as you mentioned, this is a different level of abstraction to physics and mathematics.