If an addition result comes first and gets exponentiated, the changes from the addition are exaggerated. It makes addition more powerful than it should be. The big stuff should happen first, then the more granular operations. Of course, there are specific cases where we need to reorder, or add clarity, which is why human decisions about groupings are at the top.

[–] Mango@lemmy.world 2 points 11 months ago

Yeah, but that's why I like to buff my base attack before I invest in multipliers and armor penetration!

[–] SmartmanApps@programming.dev 1 points 7 months ago (1 children)

The big stuff should happen first, then the more granular operations

The "big stuff" is stuff that is defined in terms of something else. i.e. exponents are shorthand for repeated multiplication... and multiplication is shorthand for repeated addition, hence they have to be done in that order or you get wrong answers.

[–] AdrianTheFrog@lemmy.world 1 points 7 months ago* (last edited 7 months ago) (1 children)

"Wrong answers" only according to our current order of operations, math still works if you, for example, make additions come first (as long as you're consistent about it).

OFC it is a convention and to change it you would have to change all expressions ever written all at the same time, to avoid confusion between competing standards. I'm not arguing that it should be changed, only that there is no 'high truth' behind it.

[–] SmartmanApps@programming.dev 1 points 7 months ago

“Wrong answers” only according to our current order of operations

No, according to arithmetic.

math still works if you, for example, make additions come first

No, it doesn't - order of operations proof. The only way it could work with addition first is if we swapped the definitions of addition and multiplication around... but then we still have the same order of operations, all we've done is swapped around what we call addition and multiplication!

there is no ‘high truth’ behind it.

There is when it comes to order of operations.