https://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 :)

  • Prunebutt@feddit.de
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    11 months ago

    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

    • wischi@programming.devOP
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      11 months ago

      🤣 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 :-)

      • relevants@feddit.de
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        11 months ago

        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@programming.devOP
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          11 months ago

          🤣 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@feddit.de
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            11 months ago

            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

      • wischi@programming.devOP
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        11 months ago

        @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 🤣

  • Alcatorda@lemmy.world
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    11 months ago

    Hi! Nice blog post. Since you asked for feedback I’ll point out the one thing I didn’t really understand. You explain the difference between the calculators by showing excerpts from the manuals and you highlight that in the first manual, implicit multiplication is prioritised. But the text you underlined only refers to implicit multiplication involving special expressions(?) like pi, e, sqrt or log, and nothing about “regular” implicit multiplication like 2(1+3). So while your photos of the calculator results are great proof that the two models use a different order of operations, to me the manuals were a bit confusing since they did not actually seem to prove your point for the example math problems you are discussing. Or maybe I missed something?

    • only refers to implicit multiplication involving special expressions(?) like pi, e, sqrt or log, and nothing about “regular” implicit multiplication like 2(1+3)

      That was a very astute observation you made there! The fact is, for the very reason you stated, there is in fact no such thing as “implicit multiplication” - it is a term which has been made up by people who have forgotten Terms (the first thing you mentioned) and The Distributive Law (the second thing you mentioned). As you’ve noted., these are 2 different rules, and lumping them together as one brings exactly the disastrous results you might expect from lumping different 2 rules together as one…

      See here for explanation of all the various rules, including textbook references and proofs.

  • be_excellent_to_each_other@kbin.social
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    11 months ago

    I am so glad that nothing I do in life will ever cause this problem to matter to me.

    The way I was taught in school, the answer is clearly 1, but I did read the blog post and I understand why that’s actually ambiguous.

    Fortunately, I don’t have to care, so will sleep well knowing the answer is 1, and that I’m as correct as anyone else. :-p

  • Captain Aggravated@sh.itjust.works
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    11 months ago

    I think this speaks to why I have a total of 5 years of college and no degree.

    Starting at about 7th grade, math class is taught to every single American school child as if they’re going to grow up to become mathematicians. Formal definitions, proofs, long sets of rules for how you manipulate squiggles to become other squiggles that you’re supposed to obey because that’s what the book says.

    Early my 7th grade year, my teacher wrote a long string of numbers and operators on the board, something like 6 + 4 - 7 * 8 + 3 / 9. Then told us to work this problem and then say what we came up with. This divided us into two groups: Those who hadn’t learned Order of Operations on our own time who did (six plus four is ten, minus seven is three, times eight is 24, plus three is 27, divided by nine is three) Three, and who were then told we were wrong and stupid, and those who somehow had, who did (seven times eight is 56, three divided by nine is some tiny fraction…) got a very different number, and were told they were right. Terrible method of teaching, because it alienates the students who need to do the learning right off the bat. And this basically set the tone until I dropped out of college for the second time.

  • cobra89@beehaw.org
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    11 months ago

    While I agree the problem as written is ambiguous and should be written with explicit operators, I have 1 argument to make. In pretty much every other field if we have a question the answer pretty much always ends up being something along the lines of “well the experts do this” or “this professor at this prestigious university says this”, or “the scientific community says”. The fact that this article even states that academic circles and “scientific” calculators use strong juxtaposition, while basic education and basic calculators use weak juxtaposition is interesting. Why do we treat math differently than pretty much every other field? Shouldn’t strong juxtaposition be the precedent and the norm then just how the scientific community sets precedents for literally every other field? We should start saying weak juxtaposition is wrong and just settle on one.

    This has been my devil’s advocate argument.

    • While I agree the problem as written is ambiguous

      It’s not.

      the answer pretty much always ends up being something along the lines of “well the experts do this” or “this professor at this prestigious university says this”, or “the scientific community says”.

      Agree completely! Notice how they ALWAYS leave out high school Maths teachers and textbooks? You know, the ones who actually TEACH this topic. Always people OTHER THAN the people/books who teach this topic (and so always end up with the wrong conclusion).

      while basic education and basic calculators use weak juxtaposition

      Literally no-one in education uses so-called “weak juxtaposition” - there’s no such thing. There’s The Distributive Law and Terms, both of which use so-called “strong juxtaposition”. Most calculators do too.

      Shouldn’t strong juxtaposition be the precedent and the norm

      It is. In fact it’s the rules (The Distributive Law and Terms).

      We should start saying weak juxtaposition is wrong

      Maths teachers already DO say it’s wrong.

      This has been my devil’s advocate argument.

      No, this is mostly a Maths teacher argument. You started off weak (saying its ambiguous), but then after that almost everything you said is actually correct - maybe you should be a Maths teacher. :-)

    • wischi@programming.devOP
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      11 months ago

      I tried to be careful to not suggest that scientist only use strong juxtaposition. They use both but are typically very careful to not write ambiguous stuff and practically never write implicit multiplications between numbers because they just simplify it.

      At this point it’s probably to late to really fix it and the only viable option is to be aware why and how this ambiguous and not write it that way.

      As stated in the “even more ambiguous math notations” it’s far from the only ambiguous situation and it’s practically impossible (and not really necessary) to fix.

      Scientist and engineers also know the issue and navigate around it. It’s really a non-issue for experts and the problem is only how and what the general population is taught.

  • Adkml [he/him]@hexbear.net
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    11 months ago

    The ambiguous ones at least have some discussion around it. The ones I’ve seen thenxouple times I had the misfortune of seeing them on Facebook were just straight up basic order of operations questions. They weren’t ambiguous, they were about a 4th grade math level, and all thenpeople from my high-school that complain that school never taught them anything were completely failing to get it.

    I’m talking like 4+1x2 and a bunch of people were saying it was 10.

  • Duncan Murray@fosstodon.org
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    9 months ago

    @wischi “Funny enough all the examples that N.J. Lennes list in his letter use implicit multiplications and thus his rule could be replaced by the strong juxtaposition”.

    Weird they didn’t need two made-up terms to get it right 100 years ago.

    • Indeed Duncan. :-)

      his rule could be replaced by the strong juxtaposition

      “strong juxtaposition” already existed even then in Terms (which Lennes called Terms/Products, but somehow missed the implication of that) and The Distributive Law, so his rule was never adopted because it was never needed - it was just Lennes #LoudlyNotUnderstandingThings (like Terms, which by his own admission was in all the textbooks). 1917 (ii) - Lennes’ letter (Terms and operators)

      In other words…

      Funny enough all the examples that N.J. Lennes list in his letter use

      …Terms/Products., as we do today in modern high school Maths textbooks (but we just use Terms in this context, not Products).

  • Aussiemandeus@aussie.zone
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    11 months ago

    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

          • 6⁄2(1+2) ⇒ 6⁄2*3 ⇒ 6⁄6 ⇒ 1

            You’re more patient than me to go to that trouble! 😂 But yeah, looks good. Just one technicality (and relates to how many people arrive at the wrong answer), the 2x3 should be in brackets. Yes if you had a proper fraction bar it wouldn’t matter, but that’s what’s missing with inline writing, and is compensated for with brackets (and brackets can’t be removed unless there’s only 1 term inside). In your original comment, it does indeed look like 6/(2x3), but, to illustrate the issue with what you wrote, as soon as I quoted it, it now looks like (6/2)x3 in my comment.

  • LittleHermiT@lemmus.org
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    11 months ago

    I would do the mighty parentheses first, and then the 2 that dares to touch the mighty parentheses, finally getting to the run-of-the-mill division. Hence the answer is One.

  • Portosian@sh.itjust.works
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    11 months ago

    Honestly, I do disagree that the question is ambiguous. The lack of parenthetical separation is itself a choice that informs order of operations. If the answer was meant to be 9, then the 6/2 would be isolated in parenthesis.

    • chuckleslord@lemmy.world
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      11 months ago

      It’s covered in the blog, but this is likely due to a bias towards Strong Juxtaposition rules for parentheses rather than Weak. It’s common for those who learned math into advanced algebra/ beginning Calc and beyond, since that’s the usual method for higher math education. But it isn’t “correct”, it’s one of two standard ways of doing it. The ambiguity in the question is intentional and pervasive.

      • Portosian@sh.itjust.works
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        11 months ago

        My argument is specifically that using no separation shows intent for which way to interpret and should not default to weak juxtaposition.

        Choosing not to use (6/2)(1+2) implies to me to use the only other interpretation.

        There’s also the difference between 6/2(1+2) and 6/2*(1+2). I think the post has a point for the latter, but not the former.

        • chuckleslord@lemmy.world
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          11 months ago

          I don’t know what you want, man. The blog’s goal is to describe the problem and why it comes about and your response is “Following my logic, there is no confusion!” when there clearly is confusion in the wider world here. The blog does a good job of narrowing down why there’s confusion, you’re response doesn’t add anything or refute anything. It’s just… you bragging? I’m not certain what your point is.

          • your response is “Following my logic, there is no confusion!”

            That’s because the actual rules of Maths have all been followed, including The Distributive Law and Terms.

            there clearly is confusion in the wider world here

            Amongst people who don’t remember The Distributive Law and Terms.

            The blog does a good job of narrowing down why there’s confusion

            The blog ignores The Distributive Law and Terms. Notice the complete lack of Maths textbook references in it?

        • atomicorange@lemmy.world
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          11 months ago

          I originally had the same reasoning but came to the opposite conclusion. Multiplication and division have the same precedence, so I read the operations from left to right unless noted otherwise with parentheses. Thus:

          6/2=3

          3(1+2)=9

          For me to read the whole of 2(1+2) as the denominator in a fraction I would expect it to be isolated in parentheses: 6/(2(1+2)).

          Reading the blog post, I understand the ambiguity now, but i’m still fascinated that we had the same criticism (no parentheses implies intent) but had opposite conclusions.

      • But it isn’t “correct”

        It is correct - it’s The Distributive Law.

        it’s one of two standard ways of doing it.

        There’s only 1 way - the “other way” was made up by people who don’t remember The Distributive Law and/or Terms (more likely both), and very much goes against the standards.

        The ambiguity in the question is

        …zero.

  • RickyRigatoni@lemmy.ml
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    11 months ago

    My years out of school has made me forget about how division notation is actually supposed to work and how genuinely useless the ÷ and / symbols are outside the most basic two-number problems. And it’s entirely me being dumb because I’ve already written problems as 6÷(2(1+2)) to account for it before. Me brain dun work right ;~;