Le 13/04/2019 à 14:29, Joachim Durchholz cites Richard O'Keefe :

I would
be astonished if you had been told that
    a ** b ** c
was defined to be
    a ** (b ** c)
back in 1950-something,

Actually we were told, with the reasoning that (a ** b) ** c is the same as a ** (b * c), I recall that that was presented as "nothing new there so not worth defining it that way).

Truth be told, that was the 1970-something for me.

'70?? Even worse...

I began my school in '50-something, and I was duly taught that. And without "nothing new here", which I find rather unpleasantly surprising. My teacher pointed out that (a**b)**c is equal to a**(b*c), so the left associativity would not be extremely clever.

Joachim says in his previous posting:

I guess my intuition is more based on math, where associativity is an irrelevant detail

In Lie algebras maybe? Well, add the associativity to it, and kill all the quantum theory.

Good luck.

There are many people, mainly young (e.g. my students) who have a tendency to "see mathematics" through "computer lenses" - parsing, implementable data structures, recursion as an implementation detail, etc. For the mathematical culture this is harmful.

Jerzy Karczmarczuk