I wrote a (very long) blog post about those viral math problems and am looking for feedback, especially from people who are not convinced that the problem is ambiguous.
It’s about a 30min read so thank you in advance if you really take the time to read it, but I think it’s worth it if you joined such discussions in the past, but I’m probably biased because I wrote it :)
@Prunebutt meant 4.5! and not 4.5. Because it’s not an integer we have to use the gamma function, the extension of the factorial function to get the actual mean between 1 and 9 => 4.5! = 52.3428 which looks about right 🤣
I think you got hit hard by Poe’s Law here. Except it’s more like people couldn’t tell if you were jokingly or genuinely getting your math wrong… Even after you explained you were joking lol
If one doesn’t realize you’re op, the entire thing can be interpreted very differently.
Then “Not sure if sarcastic and woosh, or adding to the joke ಠ_ಠ” could be interpreted as something like “I’m not sure if you are adding to the joke and I’m not understanding it”.
🤣 I wasn’t even sure if I should post it on lemmy. I mainly wrote it so I can post it under other peoples posts that actually are intended to artificially create drama to hopefully show enough people what the actual problems are with those puzzles.
But I probably am a fool and this is not going anywhere because most people won’t read a 30min article about those math problems :-)
The answer realistically is determined by where you place implicit multiplication (or "multiplication by juxtaposition") in the order of operations.
Some place it above explicit multiplication and division, meaning it gets done before the division giving you an answer of 1
But if you place it as equal to it's explicit counterparts, then you'd sweep left to right giving you an answer of 9
Since those are both valid interpretations of the order of operations dependent on what field you're in, you're always going to end up with disagreements on questions like these...
But in reality nobody would write an equation like this, and even if they did, there would usually be some kind of context (I.e. units) to guide you as to what the answer should be.
Edit: Just skimmed that article, and it looks like I did remember the last explanation I heard about these correctly. Yay me!
Exactly. With the blog post I try to reach people who already heared that some people say it’s ambiguous but either down understand how, or don’t believe it. I’m not sure if that will work out because people who “already know the only correct answer” probably won’t read a 30min blog post.
Unfortunately these types of viral problems are designed the attract people who think they "know it all", so convincing them that their chosen answer isn't as right as they think it is will always be an uphill challenge
yeah, our math profs taught if the 2( is to be separated from that bracket for the implied multiplication then you do that math first, because the 2(1+2) is the same as (1+2)+(1+2) and not related to the first 6.
if it was 6÷2x(2+1) they suggested do division and mult from left to right, but 6÷2(2+1) implied a relationship between the number outside the parenthesis and inside them, and as soon as you broke those () you had to do the multiplication immediately that is connected to them. Like some models of calculatora do. wasn’t till a few yeara ago that I heard people were doing it differently.
Thank you very much 🫶. No it’s not annoying at all. I’m very grateful not only for the fact that you read the post but also that you took the time to point out issues.
What’s especially wild to me is that even the position of “it’s ambiguous” gets almost as much pushback as trying to argue that one of them is universally correct.
Last time this came up it was my position that it was ambiguous and needed clarification and had someone accuse me of taking a prescriptive stance and imposing rules contrary to how things were actually being done. How asking a person what they mean or seeking clarification could possibly be prescriptive is beyond me.
Bonus points, the guy telling me I was being prescriptive was arguing vehemently that implicit multiplication having precedence was correct and to do otherwise was wrong, full stop.
Without any additional parentheses, the division sign is assumed to separate numerators and denominators within a complete expression, in which case you would reduce each separately. It’s very, very marginally ambiguous at best.
👍 That was actually one of the reasons why I wrote this blog post. I wanted to compile a list of points that show as clear as humanity possible that there is no consensus here, even amongst experts.
That probably won’t convince everybody but if that won’t probably nothing will.
When I went to college, I was given a reverse Polish notation calculator. I think there is some (albeit small) advantage of becoming fluent in both PEMDAS and RPN to see the arbitrariness. This kind of arguement is like trying to argue linguistics in a single language.
Btw, I’m not claiming that RPN has any bearing on the meme at hand. Just that there are different standards.
Ambiguity is fine. It would tedious to the point of distraction to enforce writing math without ambiguity. You make note of conventions and you are meant to realize that is just a convention. I’m amazed at the people who are planting their feet to fight for something that what they were taught in third grade as if the world stopped there.
You’re right though. We should definitely teach different conventions. But then what would facebook do for engagement?
It’s hilarious seeing all the genius commenters who didn’t read the linked article and are repeating all the exact answers and arguments that the article rebuts :)
I’m still not used to having combined image and text posts so I usually don’t notice the text portion if it isn’t a big ol’ wall and I hope I’m not the only one.
❤️ True, but I think one of the biggest problems is that it’s pretty long and because you can’t really sense how good/bad/convining the text is it’s always a gamble for everybody if it’s worth reading something for 30min just to find out that the content is garbage.
I hope I did a decent job in explaining the issue(s) but I’m definitely not mad if someone decides that they are not going to read the post and still comment about it.
You probably missed the part where the article talks about university level math, and that strong juxtaposition is common there.
I also think that many conventions are bad, but once they exist, their badness doesn’t make them stop being used and relied on by a lot of people.
I don’t have any skin in the game as I never ran into ambiguity. My university professors simply always used fractions, therefore completely getting rid of any possible ambiguity.
You lost me on the section when you started going into different calculators, but I read the rest of the post. Well written even if I ultimately disagree!
The reason imo there is ambiguity with these math problems is bad/outdated teaching. The way I was taught pemdas, you always do the left-most operations first, while otherwise still following the ordering.
Doing this for 6÷2(1+2), there is no ambiguity that the answer is 9. You do your parentheses first as always, 6÷2(3), and then since division and multiplication are equal in ordering weight, you do the division first because it’s the left most operation, leaving us 3(3), which is of course 9.
If someone wrote this equation with the intention that the answer is 1, they wrote the equation wrong, simple as that.
There has apparently been historical disagreement over whether 6÷2(3) is equivalent to 6÷2x3
As a logician instead of a mathemetician, the answer is “they’re both wrong because they have proven themselves ambiguous”. Of course, my answer would be RPN to be a jerk or just have more parens to be a programmer
The calculator section is actually pretty important, because it shows how there is no consensus. Sharp is especially interesting with respect to your comment because all scientific Sharp calculators say it’s 1. For all the other brands for hardware calculators there are roughly 50:50 with saying 1 and 9.
So I’m not sure if you are suggesting that thousands of experts and hundreds of engineers at Casio, Texas Instruments, HP and Sharp got it wrong and you got it right?
There really is no agreed upon standard even amongst experts.
Hi, expert here, calculators have nothing to do with it. There’s an agreed upon “Order of Operations” that we teach to kids, and there’s a mutual agreement that it’s only approximately correct. Calculators have to pick an explicit parsing algorithm, humans don’t have to and so they don’t. I don’t look to a dictionary to tell me what I mean when I speak to another human.
Thanks for putting my thoughts into words, that’s exactly why I hate math. It was supposed to be the logical one, but since it only needs to be parsed by humans it failed at even that. It’s just conventions upon conventions to the point where it’s notably different from one teacher/professor to the next.
I guess you can tell why I went into comp-sci (and also why I’m struggling there too)
No, those companies aren’t wrong, but they’re not entirely right either. The answer to “6 ÷ 2(1+2)” is 1 on those calculators because that is a badly written equation and you(not literally you, to be clear) should feel bad for writing it, and the calculators can’t handle it with their rigid hardcoded logic. The ones that do give the correct answer of 9 on that equation will get other equations wrong that it shouldn’t be, again because the logic is hardcoded.
That doesn’t change the fact that that equation worked out on paper is absolutely 9 based on modern rules of math. Calculate the parentheses first, you then have 6 ÷ 2(3). We could solve from here, but to make the point extra clear I’m going to actually expand this out to explicit multiplication. “2(3)” is the same as “2 x 3”, so we can rewrite the equation as “6 ÷ 2 x 3”. All operators now inarguably have equal precedence, which means the only factor left in which order to do the operations is left to right, and thus division first. The answer can only be 9.
If you’d ever taken any advanced math, you’d see that the answer is 1 all day. The implicit multiplication is done before the division because anyone taking advanced math would see 2(1+2) as a term that must be resolved first. The answer still lies in the ambiguity of the way the problem is written though. If the author used fractions instead of that stupid division symbol, there would be no ambiguity. It’s either 6/2 x 3 = 9 or [6/(2x3)] = 1. Comment formatting aside, if someone put 6 in the numerator, and then did or did NOT put all the rest in the denominator underneath a horizontal bar, it would be obvious.
TL;DR It’s still a formatting issue, but 9 is definitely not the clear and only answer.
Kinda. You can’t define a name, but you can get the compiler to interpret literals as a function. If you have a Num instance for (Integer -> Integer) where,
fromInteger i = x -> x * i
the compiler can interpret integer literals as functions like so
I always hate any viral math post for the simple reason that it gives me PTSD flashbacks to my Real Analysis classes.
The blog post is fine, but could definitely be condensed quite a bit across the board and still effectively make the same points would be my only critique.
At it core Mathematics is the language and practices used in order to communicate numbers to one another and it’s always nice to have someone reasonably argue that any ambiguity of communication means that you’re not communicating effectively.
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