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Why mathematicians want to destroy infinity – and may succeed
(www.newscientist.com)
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this post was submitted on 06 Aug 2025
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At a certain point, I realized that from another perspective, the big divide seems to be between those who see continuous distributions as just an abstraction of a world that is inherently finite vs those who see finite steps as the approximation of an inherently continuous and infinitely divisible reality.
Since I’m someone who sees math as a way to tell internally-consistent stories that may or may not represent reality, I tend to have a certain exasperation with what seems to be the need of most engineers to anchor everything in Euclidean topography.
But it’s my spouse who had to help our kids with high school math. A parent who thinks non Euclidean geometry is fun is not helpful at that point.
How about neither? Math is a formal system (like a game). It has no inherent relationship to "reality" or physics. There are only a few small areas of math that have been convincingly used in physical models, while the vast majority of mathematics is completely unrelated and even counter to physical assumptions (eg tarski paradox). Questions about the finiteness or divisibility of "reality" are scientific, not mathematical. Etc.
Yeah there is an important difference there. I think though that it's not clear whether the world is fundamentally discrete or continuous. As far as I know there is no evidence either way on this (though I remember reading that space and time must have the same discreteness/continuousness).
Or both, neither, something else, etc.
Not sure what that would even mean.