Re:Surprise Computer Science Proof Stuns Mathematicians
by claytongulick on Wednesday March 22, 2023 @01:27AM
(#35257181)
Neat point, but I do think the abstraction of "one" fails us regularly.
Even in the supposedly simple idea of counting apples.
To continue to (ab)use the apple example, tell me how many apples this is [1].
Sure, there's a problem with the "apple" category/symbol (to your point) but similar exceptions and confounding examples are abundant throughout messy physical reality.
So I think my point stands, "one" is an imperfect model of reality. Useful, but inexact.
Given that "one" may be the most basic fundamental axiom of mathematics, as more abstractions are built upon it the accuracy with which those concepts reflect the physical world declines.
Even in the supposedly simple idea of counting apples.
To continue to (ab)use the apple example, tell me how many apples this is [1].
Sure, there's a problem with the "apple" category/symbol (to your point) but similar exceptions and confounding examples are abundant throughout messy physical reality.
So I think my point stands, "one" is an imperfect model of reality. Useful, but inexact.
Given that "one" may be the most basic fundamental axiom of mathematics, as more abstractions are built upon it the accuracy with which those concepts reflect the physical world declines.
Hence the invention of fractions, etc...
[1] https://www.dailymail.co.uk/news/article-2433619/Siamese-app...