learnteach

Written as a comment by

[Error: Irreparable invalid markup ('<lj-username="polkamadness">') in entry. Owner must fix manually. Raw contents below.]

Written as a comment by <lj-username="polkamadness"> in mertuil's journal:

You're looking at this all wrong; you just need to reframe things a bit. Operator precedence is all about dominance and submission. The very word "precedence" should have given you a hint -- it's a polite word for dominance.

Mr. addition and Mr. subtraction are submissives; Mr. multiplication and Mr. division are dominants. Hence in expressions like 2+3*4 and 4*3+2, Mr. addition submissively allows Mr. multiplication to have his way with the three before he does. We also say that Mr. multiplication binds tighter than Mr. addition.

What about when two submissives want to have their way with the same number? Being polite types, they agree to let whomever got there first go first. I.e., in 2-3-4 the first Mr. subtraction on the left goes first and has his way with the two and three. The second Mr. subtraction is left with the sloppy leavings and the four.

Dominants also have a first come, first served rule, although they're not very polite about it.

Mr. exponentation is an ultra-dominant; all the dominances and submissives defer to him.

Ultra dominants are far from polite -- "no, *you* go first!" -- and are so macho that they force the second ultra-dominant to go first. I.e., in 2^3^4, the second Mr. exponentation goes first.

Mr. Negation, perhaps because he only gets to have his way with one number, is dominant not submissive like you would expect. Thus, in -2+3 he gets to have his way with the two before Mr. addition.