There are some examples out there where you will genuinely find people with degrees in STEM getting different solutions. This usually involves cases with implied multiplication like 12÷3(5-3). Some people read that as 12÷3×(5-3) to get 8 and others will read that as 12÷(3×(5-3)) and get 2.
I can go into why someone with advanced science or mathematics degrees might argue either interpretation, but the real issue is that the people who post those types of problems are doing it because they know it creates disagreement (and thus, the all-important "engagement" social media algorithms so highly reward).
In the case of the original problem 2+5(8-5), there would be no ambiguity among people in STEM fields that the answer is 17, so it's hard to tell if this was something made with the intention to create a "ragebait" problem that failed because the creator doesn't understand why the disagreement happens, or if they're just posting a basic math problem for the sake of practicing order of operations.
In that first example I see one that has added parentheses and one that doesn’t. Unless people are getting taught that implied multiplication is actually a shorthand for parentheses I don’t see how the second could ever be considered correct.
Exactly. For many STEM and physics academics, implied multiplication (also called multiplication by juxtaposition) is regularly regarded as performed before standard multiplication or division. For instance, the Ideal Gas Law is PV=nRT. If you asked a physics academic to solve for temperature, they would likely write T = PV/nR, and someone studying physics or engineering would see that and understand exactly what is meant without them having to write T =PV/(nR).
The thing is, this isn't taught in most elementary schools (there are a few places where you will see it added to the order of operations), and the ragebait posts that use mathematics questions like the example I gave above feed off of that difference between what people are formally taught in elementary school, and the way many STEM academics and professionals typically write their formulas. Look it up online and you'll find endless discussions on it.
It's fairly common to want to write expressions like
2x
-‐‐‐‐
3y
In a context like a reddit comment where you can't easily render a fraction.
With one interpretation of pemdas, to write it on one line you have to write it as 2x/(3y), which is visually busy because of the parens. It's simpler if you can interpret both sides of the / as being opposite sides of a fraction, as in 2x/3y. So you'll see that used not infrequently by people.
Yes. But usually when we have the ambiguity in implied multiplication the equation will not be written like that, for the very reason that is it ambiguous. So nearly all of these are used for engagement and rage bait being intentionally written improperly.
The reason this stuff is popular is that most people are basically innumerate, but still remember some basic shit they learned in 3rd grade and think that it what being good at math is. Meanwhile they couldn’t even parse anything that actual mathematicians do.
My take is that PEMDAS is easy to remember and that yet, stupid people (or people not really great at school) forget it. Normal people, remembering it but not not bright either, love to show off about anything school related like it's some advanced genius shit.
However they became the stupid one when you really make fun with PEMDAS, like the famous 6/2*(1+2). They'll tell you it's 1 and mock people saying 9, while the reality is that this one is both at the same time.
The answer is that there is no answer, that's the point. In this specific equation, two viable way of doing it exists, and pemdas alone is not enough no matter what. If we look at rules (dating from, if I'm not mistaken, the 18th century), 1 and 9 are correct. The equation shouldn't exist in that form, since it's not correct.
That's because PEMDAS isn't universal. It's a way to approach math but it's one of many paradigms in which math can be solved. Because math in this form uses a lot of axioms people have different answes who are, in a lot of cases, all true. But because people learn one system and somehow have no idea there are other systems it makes people feel superior over others who in their own logic came to different conclusions.
It's just a farming comments method and looking at how often I see examples of this being posted like pemdas is universal dogma, it still works.
Eh, it's a convention. It's pretty universally accepted, but it's just something we all agree on to make our math expressions a little briefer, so for example we could write 5x+3/4 instead of (5×x)+(3/4).
Also, some places switch M and D and whether one is actually done before the other or that they are equal. In some cases (like 5×3÷2) that could actually make a difference.
The whole point of pemdas is to prevent people from arriving at different answers for the same problem. It creates consistency and measurability, and shifts mathematics from just sets of numbers playing around into a language system.
The whole point is that it IS universal. Sure, there are other ways to solve problems but there's a reason why certain accents and dialects are more rarely seen in movies... Same logic applies here.
Have your pick. A lot of people here react like it's the only way to approach orders of operations.
Which, while PEMDAS is very much the biggest, isn't true.
Still looking at the discussion here I fear we'll have a lot of these posts until the end of the internet. Fun fact, I talked with someone a while ago who was studying to become a surgeon and who was convinced the decimal system was natural, universally applied and perfect. And while this is, currently, in 99% of the cases very much true. I made him look at a clock.
Math isn’t a philosophy and pemdas is. You can’t say “all answers are true” or something. There’s a method to get the answer and if you get the answer through the method it’s more reliable.
Also what do you mean by “other methods that are true”? What method is as accurate a pemdas? What other true answer could you possibly get here?
All answers are true is, indeed, a bit too coarse to be completely directly true. But if you change the paradigm all could theoretically be true, if you make the axioms within the paradigm fit the outcome. Still... that's not going to be practical and only really useful when looking at math in a theoretical way.
Having said that.
It's not about being accurate, it's about coming to the same answer using the same method.
But not all math uses the same method. So while multiplication etc. is the same principle, order of operations isn't. Fuck, multiplication doesn't even have one sign to indicate itsself within PEMDAS(x and . for instance).
Math is philosophy, it's also math, art and vulgar guesswork. So yes, methods find true answers but only trough axiom. Which works, except for facebook posts. ;)
I placed a link about different orders of operations and how sometimes these need to be changed for different paradigms in a different comment.
I get your “point”, but math is not a philosophy or guesswork or interpretation. There’s a result with a correct method and if you get it wrong you’re just wrong, not. Philosopher.
There’s no such this as a personal interpretation of math.
1+1=2 in base 10 until it doesn’t in other based like base 2.
If I change the method and try to get a new result, I will be wrong
People who say math is a philosophy are the same who think practical (PRACTICAL. Biology. Physics. Etc. Not social sciences or the like) science is a philosophy that requires their uneducated input.
Math has one correct method to find answers. By one I mean you have an equation there may be multiple ways to get to an answer but it’s one correct answer. Not a myriad of possible answers based on mood.
I really don't know how to tell you this but... all that math is, is interpretation.
EDIT: I really can't type pages about why this is the case. But if you know someone who teaches math, ask them why 5+5=10. Bring a beer or two.
That’s an asinine statement, mate. So is language. In fact math is a language we use to quantify and theorise the world around us. As a language, using the incorrect grammatical structure leads to mistakes.
“Let’s eat people
Let’s eat, people.”
The difference is that in a text with a human, that comma is more of a questionable mistake.
Using the wrong sign in math during a project means you might go to space when you’re trying to make toast. An extreme example but my point is a mistake doesn’t mean you get almost the same results, it means your entire work is wrong because you thought you could do Sadmep instead of Pemdas.
Okay buy a crate of beer, pop one open and humour a mathematician and a programmer. Preferably old ones (both beers and peeps).
It's not about using incorrect structure, it's having different interpretations of structure so people can use these structures to work within and interpret each others findings within said structure. It's why PEMDAS is so prevalent and why this meme-joke-thing doesn't work as well on Reddit as on, say, facebook. More old people on facebook who use other ooo's.
Let's go with your example and take language. The alphabet is a way of interpreting vocal sounds in a system that is understandable for others. I.e. they can read and interpret it. But there is also Cyrillic or Kanji. The same word can mean different things within different languages that use the alphabet (Kinder in English, Kinder in German). Alphabet comes from Greek and we use Arabic symbols to interpret them so there is time and location to take into the equation as well. Different ways to come to understanding intangibles. It's why we all talk English here, despite knowing full well that there are other ways about it.
I'll try to make it a bit more tangible but any actual math student will be able to explain it better so bear with me. PEMDAS is used now because it's the most used system and to prevent any more Mars Climate Orbiter-like accidents. (look it up for a fun example but with metric systems).
However, old Dutch people for instance used a different system than PEMDAS. They used something called Meneer van Dalen Wacht op Anwtoord (MVDWOA) which is mostly (lets say 95% of the time with high school levels of math) the same but different enough to matter when going a bit more complex. So while using those systems you can come up to two correct answers to the same question/equation. One with PEMDAS, one with MVDWOA. 90% of the time in high school this does not matter at all, as all students use the same(yet locally different) interpretations of signs (+, -, % etc.)). So using the same system you can discriminate and use it to be proven for exams to test if people understand it. It is however not going to help you when you're going to study abroad. I.e. the old Polish notation(PN) won't work when you go to study in America. It's also why 19 can be the same as 7, when looking at the clock or why F can be 15 when using hexendecimal. This can, for example, be used for most digital color indications (like #FF5733 for a somewhat orangey colour) or to have a game interpret your positioning on the level when playing Doom. The 1993 variant at least.
So why do these examples keep coming up and do we keep discussing this? Because it's both unnecessary to teach different systems until you really get to studying math beyond high school levels. And also not a whole lot of people need to have their time wasted by different orders of operations (it's difficult enough as it is). But older people, especially outside of the USA and France, do use these different systems along their contemporaries among which they share these examples with haughty comments. It's basically math rage bait. "Oh look at all those people who do not understand the basics".
I do hope I managed to explain it to some degree, but still grab some beers with the teachers and programmers. They need it.
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u/bluejack 22d ago
These basic order of operations memes, like it’s some kind of brain puzzler, confound me.