7 ms·

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 additi

by chunky1994 8y ago

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 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.

ssivark 8y ago
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.
- throwaway37585 8y ago
  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.
smaddox 8y ago
Not to mention operator calculus. Operators do not, in general, associate. Feynman developed his own notation for operator calculus.
- gjm11 8y ago
  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.
  - smaddox 8y ago
    Operator calculus is much more general than multiplication. It can involve exponentiation, differentiation, integration, etc.
sk_hazratali 8y ago
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pnutz 8y ago
Under what conditions is velocity addition not associative? In 1d they are associative right, but cant think in 3d
theoh 8y ago
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.”'

ssivark 8y ago

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.

throwaway37585 8y ago
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.

smaddox 8y ago

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

gjm11 8y ago
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.
- smaddox 8y ago
  Operator calculus is much more general than multiplication. It can involve exponentiation, differentiation, integration, etc.

sk_hazratali 8y ago

You are right http://www.sherekhudahazratali.com/2018/07/hai-chati-aaj-khwaja-piya-ki-manqabat-lyrics.html http://www.sherekhudahazratali.com/2018/07/hai-chati-aaj-khw...

pnutz 8y ago

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

theoh 8y ago

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.”'