My question wasn’t rhetorical btw. I’m curious where PEMDAS is leading you astray.
As far as that NYT essay goes, I’d ignore it. That notation is ambiguous and not worth thinking about. For the very specific question of “does 2(2+2) mean 2*(2+2)?” The answer is yes, but with the caveat that you generally think of it as grouped together, like you would 2x. So I would disagree that the question boils down to 8/2*4.
It’s a convention.
For the same reason that a period means the sentence ends. It’s just how we have chosen to write things. It’s convenient.
Here’s another way to look at it; have you ever heard the phrase “the map is not the territory”? A model doesn’t necessarily properly reflect the thing it’s designed to model. Including mathematical models.
In this case, “One frisbee plus zero frisbees equals zero frisbees” makes no sense because there’s no way you can physically add a “zero frisbees” to anything. But you can physically add a frisbee to no frisbees, so the opposite formulation does work. When modelling a physical system or object you need to pick the right mathematics for the job and then make sure they are applied in a way that fits what you are modelling, or you get a nonsensical result.
That’s not the only reason it doesn’t make any sense.
Here’s another way of looking at it.
Addition and subtraction answer the question, “And then what happened?” 5 plus 5 means that I have five frisbees in my hand, and then, after a certain period of time, I add another five frisbees and now I have ten frisbees in my hand.
Multiplication and division answer the question, “So how many are there?” 5 times zero means that frisbees come in 5-packs, so how many 5-packs are in my hand right now? Well, actually, none of them are in my hand. I have zero frisbees in my hand. I never had any frisbees to begin with.
So, (1+1) x 0 means, “Ok, I can take frisbees from the pile, tape then together in pairs, and give them to you. How many times do you want me to do that? None? You don’t want me to do that? OK, but that means you won’t have any frisbees.”
Given their participation in this thread, I think it was more a rant than actually wanting an explanation.
I disagree. Stoid has some basic misunderstanding of mathematical concepts and freely admits it. But when one of their incorrect concepts meets the reality of how math works, the response is, “But that doesn’t match my concept. I don’t understand.”
It would be like everyone telling me not to eat linoleum, but I say, “I don’t understand. Linoleum is food.”
Yes, but how many times did they want to rant?
0 x rant = no ranting.
5 x rant = diatribe.
4 x rant = quadrant
The dad joke thread is over there.