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I have a general question about math and infinity which really bothers me as a math student - can we actually divide every length by two?

I would like to believe the answer is yes, because it settles with the mathematics. and Then I heard about Planck length.
I read that Planck length is the smallest meaningful length, and I would like to know what does it mean. In some places it is said that Planck length is like the resolution of the universe, and nothing with a smaller length can exist, and in some other places it is said that Planck length is just the smaller length which can be measured.

Can you please explain to me this subject?

Stella Biderman
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D. Hershko
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  • As far as I know, there's no sensible use in physics for P.L.... yet . Besides, even if it really was "the smallest meaningful length" , we in mathematics doesn't give much of a darn about "meaningful", reality and stuff like that, so yes: you can divide by two any positive mathematical length. Let us now take a rest out of worries... – DonAntonio Jan 14 '18 at 16:30
  • Math and Reality are two different things. – XRBtoTheMOON Jan 14 '18 at 16:31
  • I disagree with the closure of this question, although I understand it; I think that even though the question of what "physical possibility" is and how it interacts with mathematics is somewhat philosophical, it is mathematical enough (and specific enough in this case) to belong here as opposed to at philosophy.stackexchange. I've voted to reopen. – Noah Schweber Jan 19 '18 at 18:23
  • thank you very much, this is really important for me. – D. Hershko Jan 20 '18 at 21:02

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The explanation is very simple: math is not reality.

Even if the amazing mathematical models of the reality we can measure are very detailed and have surprising predictive power, they are nothing but mathematical models.

The canonical reference for this is Wigner's The Unreasonable Effectiveness of Mathematics in the Natural Sciences.

Martin Argerami
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  • Mathematics can be used to model physical systems. I'm not sure why we have to conclude that math which does not correspond to physics is "not reality." – daniel Jan 14 '18 at 16:39
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    I think you are playing with words. In a question about physics, "reality" means "what we can measure". – Martin Argerami Jan 14 '18 at 16:40
  • In particular, any time you use math to model the world you’re implicitly evoking a philosophical thesis that basically says that you’re not unjustified in doing so. In the philosophical fields of Epistemology and Metaphysics, how precisely to phrase these theses and how to determine if they’re justified is a major topic. One of the most prominent examples of this is what’s known as the Physical Church-Turing Thesis, which asserts that computer science formalisms approximately describe the way actual computers work. – Stella Biderman Jan 14 '18 at 16:41
  • I think that math does descries our reality. but it wasn't my question. the question was about the meaning of the "meaningless" of every thing smaller than P.L, – D. Hershko Jan 14 '18 at 16:57