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I'm not sure what you mean by the universality of math. There exist different algebras which define addition differently. In the case of 2+2=4, this is formali

I'm not sure what you mean by the universality of math. There exist different algebras which define addition differently. In the case of 2+2=4, this is formalized by the Peano axioms [1], which define addition of natural numbers. However, in tropical geometry [2], addition returns the minimum of the numbers, not their sum. The author of the original tweet makes this point, and I strongly agree with it: https://twitter.com/ConceptualJames/status/1288957167844962306/photo/1 https://twitter.com/ConceptualJames/status/12889571678449623... As for 2.4 + 2.4 = 5, I think the tweet author is being a bit sloppy there in his explanation. But consider 0.1 + 0.2. Ask a human, and they'll tell you it's 0.3. Ask a computer, and it'll likely tell you it's 0.30000000000000004. The point is that in both scenarios, 0.1, 0.2, and addition are defined differently. [1] https://en.wikipedia.org/wiki/Peano_axioms https://en.wikipedia.org/wiki/Peano_axioms [2] https://en.wikipedia.org/wiki/Tropical_geometry https://en.wikipedia.org/wiki/Tropical_geometry

CyberRabbi 5y ago
> I'm not sure what you mean by the universality of math. There exist different algebras which define addition differently. Yet each one is self-consistent and potentially independently discoverable by sentient life forms light years away from us, even though these different algebras have no material form. > But consider 0.1 + 0.2. Ask a human, and they'll tell you it's 0.3. Ask a computer, and it'll likely tell you it's 0.3000000000000004 Just because the computer performs imprecise arithmetic does not make .1+.2=.300000004 a meaningful statement from which an entire self-consistent arithmetic system can be derived. The computer’s result is in error. It’s called floating point error.