1y ago

PEMDAS is technically correct, but morally wrong

If we're supposed to be able to understand math as easily as a language, we should be able to read it from left to right like a language.
Yes, I know there's lots other languages that go right to left or top to bottom, but the point is you don't have to go jumping around the page or sentence figuring out which word should be read first based on which characters it contains.
We put the first word first, then the second word second, etc.
Why can't we just write equations in the order they were meant to be solved?

28 comments

we can if we want, its called Polish notation
https://en.m.wikipedia.org/wiki/Polish_notation
instead of x + y we write + x y
then 2 + 3 * (3 + 7) + 6 becomes + 2 + * 3 + 3 7 6
no order of operations to remember, but good luck parsing it.

Some of you have never read a Choose Your Own Adventure book and it shows.

Morally wrong? What does morality have to do with any of this?
This is a matter of conventions. Which way we do it doesn't actually matter that much as long as we all agree on a way. Maybe you think PEMDAS is counterintuitive, maybe others disagree. That doesn't make it morally wrong.

Is it just me or people actually writing and using math daily never complain about this stuff? Only "it's been a while I forgot the rules" crowd.
- But it said that 98% of people will get this wrong! I have to prove to my Facebook friends that I'm smarter than them and the rules of math keep ruining it for me!!!!

Reverse Polish Notation works almost like you describe. You put the operands first, then the operation. For example:
3 + 4 --> 3 4 +
3 • (5 + 2) --> 5 2 + 3 •
Probably the reason why we are not using it is because most tools today use algebraic notation, and it would be a lot of effort to switch
- I loved my HP48GX calculator with RPN.
- Best system for calculators IMO. Especially if you need to add many numbers together (eg doing price calculations)—just enter all the numbers to the register, double-check for errors, then add together. Way less error prone than traditional calculators.
- It's just less readable for humans, great for programs though
- I have no doubt that your link goes to urban dictionary.

PEMA is technically correct. Division and subtraction are illusions.
- Actually multiplication and division are shorthand notations for addition and subtraction - e.g. 2x3=2+2+2 - so everything boils down to addition and subtraction.

Why can’t we just write equations in the order they were meant to be solved?
I mean, you can. No one is stopping you.

My guess is that in real world applications, it makes more sense to think about things in terms of multiplying values together and then adding the total. Like if you have a list of products, with prices and quantities for each, to get the total value you multiply each quantity by its price and then add them all together.

Not all equations have a solution right away. PEMDAS, or BEDMAS as I was taught, helps you navigate these novel equations. It's a natural way to think when exploring problems outside of a textbook.
- Bedmas > Xmas
  
  My Xmas starts and ends with a good old bedmas

Could you give an example of how you think it should be written? I'm having trouble envisaging it.

Yes having equations written in a more straightforward way might make it easier for laypeople to understand but I think that the people who use their head for anything more complicated than a+b and don't just use a calculator can probably figure it out fine.
- Also don't understand the "morally wrong" argument. Just because something is slightly more complicated than it could be doesn't make it "morally wrong".

A more fun variation on this would be to contest mathematical notation. PEMDAS is one thing, but mathematical notation? Not only might you get lost in the order of operations, now you're lucky if you can even read it without committing yourself to the maths cubicles.
Yeah, they don't get dungeons, they get cubicles because it's a geometrically appropriate hell.

read it from left to right like a language
A number of languages are not left-to-right, BTW.

Maybe just stick to using a calculator?

You can if you wrote everything as just addition and subtraction, but then we made some shorthand notations for that, such as 2x3=2+2+2, and so now you have to do multiplication before addition otherwise you get a wrong answer, and if you wrote all multiplications before all additions there'd still be no problem, but as someone else pointed out, there are cases where it's easier to have a different order, and so voila! Order of operations rules.

28 comments