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There's a good general (mathematical) sense to what something "infinite" is: a thing able to contain something the same size as itself. As an example, the natu

There's a good general (mathematical) sense to what something "infinite" is: a thing able to contain something the same size as itself. As an example, the natural numbers are infinite because they contain the even numbers and the even numbers are the same "size" (or cardinality) as the natural numbers themselves. As a second example, the real numbers are infinite because they contain the interval (-1, 1), which has the same "size" as all of the real numbers.

paganel 10y ago
Yeah, I'm aware of this (especially the second example, ever since my Calculus teacher in high-school used a very similar definition to it in order to make us understand what real numbers are), what I was trying to say is that, at the end of it all, the science of Physics should be about making sense of the real world (using mathematical concepts, if the need arises, but not to see those concepts as reality itself). More exactly, I say that translating the concept/idea of infinity from mathematics to physics is not idempotent (not sure if this it's the correct term, but you get the idea), saying that infinity "exists" in the physical world the same as it does in mathematics is kind of tricky when you think of the consequences through and through. To take your second example, applied to Physics that would mean that no matter what two small particles we choose as being "fundamental" there will always be an infinity of (presumably even more small) particles separating the two, and so on and so forth (it's "turtles all the way down", so to speak). Like I said, I'm not a specialist, just a programmer, but I think we should be aware of the presumptions we implicitly make when discussing about different topics but using the same language (in this case the of concept of "infinity" in maths vs physics). Hume explained it better than me (maybe in an "An Essay Concerning Human Understanding" ?!) when he said that the mathematical idea of a straight line (I'm talking about the geometrical line) is just that, an human-constructed idea, there's no absolute straight line in the real world (not sure what he thought about the idea of infinity, probably not much, judging by his being critical against mathematical induction).

paganel 10y ago

Yeah, I'm aware of this (especially the second example, ever since my Calculus teacher in high-school used a very similar definition to it in order to make us understand what real numbers are), what I was trying to say is that, at the end of it all, the science of Physics should be about making sense of the real world (using mathematical concepts, if the need arises, but not to see those concepts as reality itself). More exactly, I say that translating the concept/idea of infinity from mathematics to physics is not idempotent (not sure if this it's the correct term, but you get the idea), saying that infinity "exists" in the physical world the same as it does in mathematics is kind of tricky when you think of the consequences through and through. To take your second example, applied to Physics that would mean that no matter what two small particles we choose as being "fundamental" there will always be an infinity of (presumably even more small) particles separating the two, and so on and so forth (it's "turtles all the way down", so to speak). Like I said, I'm not a specialist, just a programmer, but I think we should be aware of the presumptions we implicitly make when discussing about different topics but using the same language (in this case the of concept of "infinity" in maths vs physics). Hume explained it better than me (maybe in an "An Essay Concerning Human Understanding" ?!) when he said that the mathematical idea of a straight line (I'm talking about the geometrical line) is just that, an human-constructed idea, there's no absolute straight line in the real world (not sure what he thought about the idea of infinity, probably not much, judging by his being critical against mathematical induction).