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 :)
Seems this whole thing is the pedestrian-math-nerd’s equivalent to the pedestrian-grammar-nerd’s arguments on the Oxford comma. At the end of the day it seems mathematical notation is just as flexible as any other facet of written human communication and the real answer is “make things as clear as possible and if there is ambiguity, further clarify what you are trying to communicate.”
Pretty much. While it’s worth knowing that not everyone agrees on how implicit multiplication is prioritised, anywhere that everyone agreeing on the answer actually mattered, you wouldn’t write an equation as ambiguous as this one in the first place
It’s not ambiguous. People who say it is have usually forgotten The Distributive Law or Terms, or more commonly both!
Seems this whole thing is the pedestrian-math-nerd’s equivalent to the pedestrian-grammar-nerd’s arguments on the Oxford comma.
Not even remotely similar. Maths rules are fixed. The order of operations rules are at least 400 years old.
mathematical notation is just as flexible as any other facet of written human communication
No, it isn’t. The book “A history of mathematical notation” is in itself more than 100 years old.
Wow neat, and yet the thread was full of people going back and forth about how the equation can be misinterpreted based on how the order of operations can be interpreted. Thanks for your months later input though.
I only just found the thread yesterday. There’s only 1 “interpretation”, and the only back and forth I’ve seen about interpretations is about implicit multiplication, which isn’t a thing, at all - it’s people conflating The Distributive Law and Terms dotnet.social/@SmartmanApps/110925761375035558
So you are saying exactly what I said; people can misinterpret things that other people have written. Good job. Thanks again for stopping by a 3 month old thread about a dumb meme.
So you are saying exactly what I said; people can misinterpret things that other people have written
No, I’m not. They’re “misinterpreting” something that isn’t even a rule of Maths. There’s no way to misinterpret the actual rules, there’s no way to misinterpret the equation. There’s no alternative interpretations of the notation. Someone who didn’t remember the rules literally made up “implicit multiplication”, and then other people argued with them about what that meant. 😂
You look like a real idiot here. I really suggest you actually read the article instead of “scanning” it. You clearly don’t even understand the term “implicit multiplication” if you’re claiming it’s made up. Implicit multiplication is not the controversial part of this equation, which you would know if you read the article and understood what people in this thread are even talking about. Stop spamming your shitty blog and just. Read. The. Article.
read the article instead of “scanning” it.
I stopped reading as soon as I saw the claim that the right answer was wrong. I then scanned it for any textbook references, and there were none (as expected).
You clearly don’t even understand the term “implicit multiplication” if you’re claiming it’s made up
Funny that you use the word “term”, since Terms are ONE of the things that people are referring to when they say “implicit multiplication” - the other being The Distributive Law. i.e. Two DIFFERENT actual rules of Maths have been lumped in together in a made-up rule (by people who don’t remember the actual rules).
BTW if you think it’s not made-up then provide me with a Maths textbook reference that uses it. Spoiler alert: you won’t find any.
Implicit multiplication is not the controversial part of this equation
It’s not the ONLY controversial part of the equation - people make other mistakes with it too - but it’s the biggest part. It’s the mistake that most people have made.
shitty blog
So that’s what you think of people who educate with actual Maths textbook references?
Read. The. Article.
Read Maths textbooks.
I agree with your core message, that the issue is caused by bad notation. However I don’t really see why you consider implicit multiplication to be the sole reason. In my mind, a/bc is equally as ambiguous as a/b*c. The symbols are not important.
You don’t even consider this in your article, instead you seem to take the position that the operations are resolved from left to right. This idea probably comes from programming languages, as they commonly use this convention, but I haven’t seen this defined in mathematics anywhere. I’m open to being wrong here, so if you can show me such a definition from an authoritative source (maybe ISO) I’d be thankful.
As it stands, you basically claim “the original notation is ambiguous, but with explicit × the answer is obviously nine, because my two calculators agree”, even though you just discounted calculator proofs. By the way, both calculators explicitly define this left-to-right order in their documentation.
The ISO section 7.1.3 you quoted is very reasonable and succinct, and contradicts your claim that explicit multiplication sign removes ambiguity. There would be no need for this section if a left-to-right rule existed.
Standards are as mentioned in the article often extra careful to prevent confusion and thus often stricter than widespread conventions with things they allow and don’t allow.
a/b*c is not ambiguous because no widespread convention would treat it any other way than (a/b)*c.
But you can certainly try to proof me wrong by showing me a calculator that would evaluate 6/2*3 to anything but 9.
So if there is not a single calculator out there that would come to a different result, how can it be ambiguous?
Update: Standards are rule-books for real projects to make it simpler to work together. It’s a bit like a Scrabble dictionary. If a word is missing in the official Scrabble dictionary, it doesn’t automatically mean that it’s not a real word, it just means that it wouldn’t be allowed to play that word in official Scrabble tournaments.
Same with (ISO) standards. Just because the standard forbids it doesn’t mean it’s not widespread or forbidden generally. It’s only forbidden in a context where all participants agreed to follow the standard.
All of the programming languages I can think of apply operator precedence as noted in the first reply. That’s the only standard I ever learned, and I’ve never seen any ambiguity in that.
a/bc is equally as ambiguous as a/b*c
It’s not ambiguous at all. By the definition of Terms - ab=(axb) - a/bc is 2 terms and a/bxc is 3 terms. If we were to write it in fraction form (to illustrate the difference), in the former c is in the denominator, but in the latter it’s in the numerator, hence a different answer. dotnet.social/@SmartmanApps/110846452267056791
you seem to take the position that the operations are resolved from left to right… but I haven’t seen this defined in mathematics anywhere
It applies to operators, or more precisely division. When doing the divisions, you have to do them left-to-right, but other than that each of the operators can be done in any order. i.e. it doesn’t matter what order you do the multiplications in, as long as you do them before the additions and subtractions. Unfortunately I’ve seen many people misremember left-to-right as an overarching rule, rather than only applying to division.
Don’t forget math with fruits! https://imgur.com/JOuRhQ3
Just saw the image you posted and it’s awesome :-) I’m part of the group that can’t solve it, because I don’t know the 🌭 function from the top of my head. I also found the choice of symbols interesting that 🌭 is analytical continuation of 🍔 and not the other way round 🤣
I don’t see the problem actually.
- Everything between ()
- Exponents
- multiply and devision
- plus and minus
- Always work from left to right.
==========
-
1+2= 3
-
No exponents
-
- 6 devised by 2 (whether a fraction or not) is 3
- 3 times 3 is 9
-
Nothing remains
The meme refers to the problem of handling implicit multiplication by juxtaposition.
Depending on what field you’re in, implicit multiplication takes priority over explicit multiplication/division (known as strong juxtaposition) rather than what you and a lot of people would assume (known as weak juxtaposition).With weak juxtaposition you end up 9 just as you did, but with strong juxtaposition you end up with 1 instead.
For most people and most scenarios this doesn’t matter, as you’d never encounter such ambiguous equations outside of viral puzzles like this, but it is worth knowing that not all fields agree on how implicit multiplication is handled.
Humans…
Can agree over a universal charging cable, but not over simple math rules…
Truly the dichotomy of man
The meme refers to the problem of handling implicit multiplication
There’s no such thing as implicit multiplication. dotnet.social/@SmartmanApps/110925761375035558
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I don’t see the problem actually.
Everything between ()
You recreated the problem right there - ignored The Distributive Law. a(b+c)=(ab+ac). i.e. 2(1+2)=(2x1+2x2). After step 1 - solving brackets - all that’s left is 6/6. dotnet.social/@SmartmanApps/110819283738912144
I love that the calculators showing different answers are both from the same manufacturer XD
In the blog post there are even more. Texas Instruments, HP and Canon also have calculators, and some of them show 9 and some 1.
I tried explaining this to people on facebook in 2010 or so.
“You must be fun at parties!”
Bitch, i dont want to attend your lame ass party where people think they know how math works.
If you are so sure that you are right and already “know it all”, why bother and even read this? There is no comment section to argue.
I beg to differ. You utter fool! You created a comment section yourself on lemmy and you are clearly wrong about everything!
You take the mean of 1 and 9 which is 4.5!
/j
🤣 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 :-)
Actually the correct answer is clearly 0.2609 if you follow the order of operations correctly:
6/2(1+2)
= 6/23
= 0.26🤣 I’m not sure if you read the post but I also wrote about that (the paragraph right before “What about the real world?”)
I did read the post (well done btw), but I guess I must have missed that. And here I thought I was a comedic genius
I did (skimmed it, at least) and I liked it. 🙃
Right, because 5 rounds down to 4.5
@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 🤣
Ackshually, the answer is 4
6÷2*(1+2)
6÷(1+2)*2
6÷(3)*2
2*2
4
You’re welcome
psychopath
Psychomath
If there are rules about which dot comes first then you are not allowed to do this.
You aren’t allowed to do this because division isn’t transitive.
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I would also add that you shouldn’t be using a basic calculator to solve multi part problems. Second, I haven’t seen a division sign used in a formal math class since elementary and possibly junior high. These things are almost always written as fractions which makes the logic easier to follow. The entire point of working in convention is so that results are reproducible. The real problem though is that these are not written to educate anyone. They are deliberately written to confuse so that some social media personality can make money from clicks. If someone really wants to practice math skip the click and head over to the Kahn Academy or something similar.
basic calculator to solve multi part problems
This isn’t a multi-part problem, and any basic calculator other than Texas Instruments gets it correct.
These things are almost always written as fractions
Fractions are always written as fractions - they are 1 term - 2 separate terms are always separated by an operator, such as a division sign, like in this case.
the Kahn Academy or something similar.
Good advice! In particular look up what they say about The Distributive Law.
Typo in article:
If you are however willing to except the possibility that you are wrong.
Except should be ‘accept’.
Not trying to be annoying, but I know people will often find that as a reason to disregard academic arguments.
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.
I just fixed it, should be live in a few minutes.
A person not knowing the difference in usage between except and accept sounds like a perfectly reasonable reason to disregard their math skills.
Especially when said person keeps making incorrect statements about Maths and ignores completely what is taught in high school.
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.
The blog post is fine
Except that it’s wrong. Read this instead.
Great read! Easy for everyone to understand, but also thorough. I loved the breakdown into the calculators functionality
Thank you for taking the time reading it.
I disagree. Without explicit direction on OOO we have to follow the operators in order.
The parentheses go first. 1+2=3
Then we have 6 ÷2 ×3
Without parentheses around (2×3) we can’t do that first. So OOO would be left to right. 9.
In other words, as an engineer with half a PhD, I don’t buy strong juxtaposition. That sounds more like laziness than math.
How are people upvoting you for refusing to read the article?
as a half PhD
Go read the article, it’s about you
Go read the article, it’s about you
The article is wrong dotnet.social/@SmartmanApps/110897908266416158
Yeah, but implicit multiplication without a sign is often treated with higher priority.
Is it though? I’ve only ever seen it treated as standard multiplication.
as an engineer with half a PhD
As an engineer with a full PhD. I’d say we engineers aren’t that great with math problems like this. Thus any responsible engineer would write it in a way that cannot be misinterpreted. Because misinterpreted mathematics can kill people…
Without parentheses around (2×3)
But there is parentheses around (2x3). a(b+c)=(ab+ac) - The Distributive Law. You can’t remove them unless there is only 1 term left inside. You removed them when you still had 2 terms inside, 2x3.
6/2(1+2)=6/2(3)=6/(2*3)=6/6=1
OR
6/2(1+2)=6/(2+4)=6/6=1
i didn’t fully understand the article, but it was really interesting reading summaries & side discussions in the comments here!
i enjoy content like this that demonstrates how math is at its heart a useful tool for conceptualizing things vs some kind of immutable force.
Very cool article on an aspect of math that I’ve never thought too deeply about before 👍
