6÷2(1+2)

zeta.one/viral-math/

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 :)

octesian, (edited )

I don’t remember everything, but I remember the first two operations are exponents then parentheses. Edit: wait is it the other way around?

wischi,

Yes it’s the other way round. Parentheses are top priority.

wischi,

The full story is actually more nuanced than most people think, but the post is actually very long (about 30min) so thank you in advance if you really find the time to read it.

usernamesaredifficul,

bidmas

brackets, index (powers), division, multiplication, addition, subtraction.

brackets are always first that’s the whole point of brackets

Samsy, (edited )

I really hate the social media discussion about this. And the comments in the past teached me, there are two different ways of learning math in the world.

wischi, (edited )

True, and it’s not only about learning math but that there is actually no consensus even amongst experts, about the priority of implicit multiplications (without explicit multiplication sign). In the blog post there are a lot of things that try to show why and how that’s the case.

Prunebutt,

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

SpaceNoodle,

Right, because 5 rounds down to 4.5

Lionel,

…Because 4 rounds up to 4.5

wischi,

@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 🤣

Prunebutt,

Not sure if sarcastic and woosh, or adding to the joke ಠ_ಠ

Redjard,
@Redjard@lemmy.dbzer0.com avatar

The mean of 1 and 9 is 5

Prunebutt,

woosh

Sidhean,

Stop it Patrick, you’re scaring them!

stu,

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

Prunebutt,

I thought the “/j” tone-tag was enough ;_;

Redjard,
@Redjard@lemmy.dbzer0.com avatar

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”.

SpaceNoodle,

jarcasm?

Prunebutt, (edited )
wischi,

🤣 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 :-)

Prunebutt,

I did (skimmed it, at least) and I liked it. 🙃

relevants, (edited )

Actually the correct answer is clearly 0.2609 if you follow the order of operations correctly:

6/2(1+2)
= 6/23
= 0.26

wischi,

🤣 I’m not sure if you read the post but I also wrote about that (the paragraph right before “What about the real world?”)

relevants, (edited )

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

MrVilliam, (edited )

Nah man, distribute the 2.
6/2(1+2)
= 6/2+4
= 3+4
= 7

This is like 4st grayed maff.

Th4tGuyII,
@Th4tGuyII@kbin.social avatar

@relevants you truly are the smartest of all men

TokyoMonsterTrucker,

The order of operations is not part of a holy text that must be blindly followed. If these numbers had units and we knew what quantity we were trying to solve for, there would be no argument whatsoever about what to do. This is a question that never comes up in physics because you can use dimensional analysis to check to see if you did the algebra correctly. Context matters.

kogasa, (edited )
@kogasa@programming.dev avatar

It’s not ambiguous, it’s just that correctly parsing the expression requires more precise application of the order of operations than is typical. It’s unclear, sure. Implicit multiplication having higher precedence is intuitive, sure, but not part of the standard as-written order of operations.

wischi,

I’d really like to know if and how your view on that matter would change once you read the full post. I know it’s very long and a lot of people won’t read it because they “already know” the answer but I’m pretty sure it would shift your perception at least a bit if you find the time to read it.

kogasa,
@kogasa@programming.dev avatar

My opinion hasn’t changed. The standard order of operations is as well defined as a notational convention can be. It’s not necessarily followed strictly in practice, but it’s easier to view such examples as normal deviation from the rules instead of an implicit disagreement about the rules themselves. For example, I know how to “properly” capitalize my sentences too, and I intentionally do it “wrong” all the time. To an outsider claiming my capitalization is incorrect, I don’t say “I am using a different standard,” I just say “Yes, I know, I don’t care.” This is simpler because it accepts the common knowledge of the “normal” rules and communicates a specific intent to deviate. The alternative is to try to invent a new set of ad hoc rules that justify my side, and explain why these rules are equally valid to the ones we both know and understand.

wischi,

What is the correct answer according to the convention you follow?

kogasa,
@kogasa@programming.dev avatar

I have a masters in math, please do not condescend. I’m fully aware of both interpretations and your overall point and I’ve explained my response.

wischi,

I still don’t see a number ;-) but you can take a look at the meme to see other people with math degrees shouting at each other.

kogasa,
@kogasa@programming.dev avatar

Sorry your article wasn’t as interesting as you hoped.

onion,

The difference is that there are two sets of rules already in use by large groups of people, so which do you consider correct?

kogasa,
@kogasa@programming.dev avatar

There aren’t.

Th4tGuyII,
@Th4tGuyII@kbin.social avatar

They weren't asking you if there are two sets of rules, we're in a thread that's basically all qbout the Weak vs. Strong juxtaposition debate, they asked you which you consider correct.

Giving the answer to a question they didn't ask to avoid the one they did is immature.

kogasa, (edited )
@kogasa@programming.dev avatar

Ah yes, simply “answer the question with an incorrect premise instead of refuting the premise.” When did you stop beating your wife?

That’s not what they asked me. I have no problem answering questions that are asked in good faith.

Th4tGuyII, (edited )
@Th4tGuyII@kbin.social avatar

I can't have stopped because I never started, because I'm not even married... See, even I can answer your bad faith question better than you answered the one @onion asked you.

But I will give it to you that my comment should've stipulated avoiding reasonable questions.

The difference is that there are two sets of rules already in use by large groups of people, so which do you consider correct?

However I still think you need your eyes checked, as the end of this comment by @onion is very clearly a question asking you WHICH ruleset you consider correct.

Unless you're refusing the notion of multiplication by juxtaposition entirely, then you must be on one side of this or the other.

kogasa,
@kogasa@programming.dev avatar

“Which ruleset do you consider correct” presupposes, as the comment said, that there are 2 rulesets. There aren’t. There’s the standard, well known, and simplified model which is taught to kids, and there’s the real world, where adults communicate by using context and shared understanding. Picking a side here makes no sense.

Th4tGuyII,
@Th4tGuyII@kbin.social avatar

When the @onion said there were two different sets of rules, you know as well as I do that they meant strong vs. weak juxtaposition.

You're right that in reality nobody would write an equation like this, and if they did they would usually provide context to help resolve it without resorting to having to guess...

But the point of this post is exactly to point out this hole that exists in the standard order of operations, the drama that has resulted from it, and to shine some light on it.

Picking a side makes no sense only if you have the context to otherwise resolve it... If you were told to solve this equation, and given no other context to do so, you would either have to pick a side or resolve it both ways and give both answers. In that scenario, crossing your arms and refusing to because "it doesn't make sense" would get you nowhere.

In all honesty, I think you're acting like the people who say things like "I've never used algebra, so it was worthless teaching me it as a kid" as though there aren't people who would learn something out of this.

kogasa,
@kogasa@programming.dev avatar

You are literally so far removed from this conversation I don’t know what to do with you. Good luck.

Th4tGuyII,
@Th4tGuyII@kbin.social avatar

That's rich considering what sparked this conversation was you refusing to answer a simple question.

Good luck to you too - with reading comprehension like your's, you might just need it.

kogasa,
@kogasa@programming.dev avatar

with reading comprehension like your’s

Man.

Th4tGuyII,
@Th4tGuyII@kbin.social avatar

I'll just say it again, you're the one saying this problem is completely unambiguous, with your only explanation as to why being that real people communicate as though that solves every edge case imaginable.

I'm just saying, if you really believe that to be the case, Good luck.

Aussiemandeus, (edited )
@Aussiemandeus@aussie.zone avatar

I guess if you wrote it out with a different annotation it would be

‎ ‎ 6

-‐--------‐--------------

2(1+2)

=

6

-‐--------‐--------------

2×3

=

6

–‐--------‐--------------

6

=1

I hate the stupid things though

velox_vulnus,

Markdown fucked your comment. Use escape symbols.

Aussiemandeus,
@Aussiemandeus@aussie.zone avatar

Escape symbols?

onion, (edited )

Lemmy interprets some symbols as formatting commands, for example putting a # at the start of a line turns it into a header:

header

You can tell it to not do that by putting a backslash before the symbol:

# not a header

The backslash is called the escape symbol.

Aussiemandeus,
@Aussiemandeus@aussie.zone avatar

Cheers mate

velox_vulnus, (edited )

Never mind, here’s another better way to do this:

^6^⁄2(1+2) ⇒ ^6^⁄2*3 ⇒ ^6^⁄6 ⇒ 1

Works on the web page, but looks weird on some mobile app. Markdown is a fucking mess. Some implementation has MathJax support, some have special syntaxes.

Rustmilian, (edited )
@Rustmilian@lemmy.world avatar

Lemmy* markdown is a fuckin mess. It’s way better elsewhere. & <>

Aussiemandeus,
@Aussiemandeus@aussie.zone avatar

Yeah connect for lemmy didn’t sort the out very well.

Brak,
@Brak@hexbear.net avatar

oooh this looks very pretty on hexbear, thanks friend!

Aussiemandeus,
@Aussiemandeus@aussie.zone avatar

I guess if you wrote it out with a different annotation it would be

‎ 6

–‐--------‐-------------- 2(1+2)

= 6 –‐--------‐-------------- 2×3

= 6 –‐--------‐-------------- 6

=1

I hate the stupid things though

Th4tGuyII, (edited )
@Th4tGuyII@kbin.social avatar

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!

wischi,

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.

Th4tGuyII,
@Th4tGuyII@kbin.social avatar

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

BCsven,

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.

Th4tGuyII, (edited )
@Th4tGuyII@kbin.social avatar

So you were taught strong juxtaposition then, where the implicit multiplication takes priority?

BCsven,

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.

sverit,

Yeah, that’s why fractions are good thing.

original_reader,

I read the whole article. I don’t agree with the notation of the American Physical Society, but who am I to argue that? 😄

I started out thinking I knew how the order of operations worked and ended up with a broader view of the subject. Thank you for opening my mind a bit today. I will be more explicit in my notations from now on.

wischi, (edited )

Thank you so much for taking the time. I’m also not convinced that APS’s notation is a very good choice but I’m neither american nor a physisist 🤣

I’d love to see how the exceptions work that the APS added, like allowing explicit multiplications on line-breaks, if they still would do the multiplication first, but I couldn’t find a single instance where somebody following the APS notation had line-break inside an expression.

baggins,

That’s cool and Imma let you finish but I’m not a mathematician and the answer is 9.

wischi,

That’s the correct answer if you follow one of the conventions. There are actually two conflicting but equally valid conventions. The blog explains the full story but this math problem is really ambiguous.

baggins, (edited )

I read it. And I’m not a mathematician, so the answer is 9.

E: The salty mathematicians down-voting this can get fucked lmfao

wischi, (edited )

Ooh now I get you, sry. True. But sadly you now know the truth and you have to be careful with the implicit multiplications on your tax forms from now on ;-)

dgmib,

You state that the ambiguity comes from the implicit multiplication and not the use of the obelus.

I.e. That 6 ÷ 2 x 3 is not ambiguous

What is your source for your statement that there is an accepted convention for the priority of the iinline obelus or solidus symbol?

As far as I’m aware, every style guide states that a fraction bar (preferably) or parentheses should be used to resolve the ambiguity when there are additional operators to the right of a solidus, and that an obelus should never be used.

Which therefore would make it the division expressed with an obelus that creates the ambiguity, and not the implicit multiplication.

(Rest of the post is great)

wischi, (edited )

In this case it’s actually the absence of sources. I couldn’t find a single credible source that states that ÷ has somehow a different operator priority than / or that :

The only things there are a lot of are social media comments claiming that without any source.

My guess is that this comes from a misunderstanding that the obelus sign is forbidden in a lot of standards. But that’s because it can be confused with other symbols and operations and not because the order of operations is somehow unclear.

dgmib,

What is your source for the priority of the / operator?

i.e. why do you say 6 / 2 * 3 is unambiguous?

Every source I’ve seen states that multiplication and division are equal priority operations. And one should clarify, either with a fraction bar (preferably) or parentheses if the order would make a difference.

wischi, (edited )

Same priority operations are solved from left to right. There is not a single credible calculator that would evaluate “6 / 2 * 3” to anything else but 9.

But I challenge you to show me a calculator that says otherwise. In the blog are about 2 or 3 dozend calculators referenced by name all of them say the same thing. Instead of a calculator you can also name a single expert in the field who would say that 6 / 2 * 3 is anything but 9.

dgmib,

Will you accept wolfram alpha as credible source?

mathworld.wolfram.com/Solidus.html

Special care is needed when interpreting the meaning of a solidus in in-line math because of the notational ambiguity in expressions such as a/bc. Whereas in many textbooks, “a/bc” is intended to denote a/(bc), taken literally or evaluated in a symbolic mathematics languages such as the Wolfram Language, it means (a/b)×c. For clarity, parentheses should therefore always be used when delineating compound denominators.

wischi,

Did you read the blog post? I also quoted the exact same thing.

amio, (edited )

Forgot the algebra using fruit emoji or whatever the fuck.

Bonus points for the stuff where suddenly one of the symbols has changed and it's "supposedly" 1/2 or 2/3 etc. of a banana now, without that symbol having been defined.

wischi, (edited )

This meme is specifically about the implicit multiplication because the article it links to is about that too.

But you are right there are a lot more “viral math” things than just the implicit multiplication problems 🤣

bouh,

This is not a math problem but a calculator engineering problem. Some solve the sub operations from right to left while other do it from left to right.

wischi, (edited )

It’s not really a calculator engineering problem. If you don’t have time to read the entire blog you should definitely check out the section “But my calculator says…”. It’s actually about order of operations regarding implicit multiplication.

Tartas1995, (edited )

I feel like if a blog post presents 2 options and labels one as the “scientific” one… And it is a deserved Label. Then there is probably a easy case to be made that we should teach children how to understand scientific papers and solve the equation in it themselves.

Honestly I feel like it reads better too but that is just me

wischi,

I’m not sure if I’d call it the “scientific” one. I’d actually say that the weak juxtaposition is just the simple one schools use because they don’t want to confuse everyone. Scientist actually use both and make sure to prevent ambiguity. IMHO the main takeaway is that there is no consensus and one has to be careful to not write ambiguous expressions.

Tartas1995,

I mean the blog post says

“If you are a student at university, a scientist, engineer, or mathematician you should really try to ask the original author what they meant because strong juxtaposition is pretty common in academic circles, especially if variables are involved like in $a/bc$ instead of numbers.”

It doesn’t say scientific but…

atomicorange,

I’m a scientist and I’ve only ever encountered strong juxtaposition in quick scribbles where everyone knows the equation already. Normally we’re very careful to use fraction notation (or parentheses) when there’s any possibility of ambiguity. I read the equation and was shocked that anyone would get an answer other than 9.

Tartas1995,

My comment was directed to the blog post and the claims contained in it.

The blog post claims it is popular in academy, if that is a deserved label, then I don’t understand how the author of the post lands on “there is no good or bad way, they are all valid”. I am in favor of strong juxtaposition but that is not the case that I am making here. Sorry for the confusion.

ConfusedPossum,

Who gives a shit about order of operations. In a real world scenario you'll know what to do

MrVilliam,

This is why you’re a confused possum.

youngalfred,

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.

wischi,

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.

Iamdanno,

A person not knowing the difference in usage between except and accept sounds like a perfectly reasonable reason to disregard their math skills.

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