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Comment by chunky1994 | Hacker News Reader

chunky1994

It's rather amusing that the author assumes that non-associtiave objects are "weird" for physicists (or at least that was my reading), since the velocity addition formula is in general non-associative and that has been extensively studied.

(I remember three separate occasions in my undergrad particle physics class where we actually went through all the calculations involved with the velocity addition formula and finally saw that SOL was wacky).

https://en.wikipedia.org/wiki/Velocity-addition_formula

I wonder if that is uncommon or if the article is just a bit ungenerous towards our understanding of non-associative objects.

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To be fair, one never talks of relativistic "velocities" beyond undergrad physics. It is much easier to talk about Lorentz "boosts", and as members of a Lie Group, they are associative, though not commutative.

This. It's better to just make the full leap into spacetime geometry (4-vectors and 4-tensors) than keep trying to slice it into annoying 3-vectors.

The other thing that contains non-associative elements is logic. Due to the Curry-Howard correspondence, that means functional programming too.

So this quote about mathematicians seems a bit off. Baez is talking about mathematical physicists, I guess, not logicians and computer scientists. I know he is not a functional programmer from various online remarks he has made. So maybe it's more of a personal perspective that we shouldn't take too seriously.

'“Nonassociative things are strongly disliked by mathematicians,” said John Baez, a mathematical physicist at the University of California, Riverside, and a leading expert on the octonions. “Because while it’s very easy to imagine noncommutative situations — putting on shoes then socks is different from socks then shoes — it’s very difficult to think of a nonassociative situation.” If, instead of putting on socks then shoes, you first put your socks into your shoes, technically you should still then be able to put your feet into both and get the same result. “The parentheses feel artificial.”'

Not to mention operator calculus. Operators do not, in general, associate. Feynman developed his own notation for operator calculus.

How do operators in general fail to associate? Usually the "multiplication" operation for operators is function application, which is a paradigmatic example of a thing that is associative.

Operator calculus is much more general than multiplication. It can involve exponentiation, differentiation, integration, etc.

Under what conditions is velocity addition not associative? In 1d they are associative right, but cant think in 3d

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