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 :)

  • CarbonScored [any]@hexbear.net
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    1 year ago

    A fair criticism. Though I think the hating on PEDMAS (or BODMAS as I was taught) is pretty harsh, as it very much does represent parts of the standard of reading mathematical notation when taught correctly. At least I personally was taught its true form was a vertical format:

    B

    O

    DM

    AS

    I’d also say it’s problematic to rely on calculators to implement or demonstrate standards, they do have their own issues.

    But overall, hey, it’s cool. The world needs more passionate criticisms of ambiguous communication turning into a massive interpration A vs interpretation B argument rather than admitting “maybe it’s just ambiguous”.

    • wischi@programming.devOP
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      1 year ago

      The problem with BODMAS is that everybody is taught to remember “BODMAS” instead of “BO-DM-AS” or “BO(DM)(AS)”. If you can’t remember the order of operations by heart you won’t remember that “DM” and “AS” are the same priority, that’s why I suggested dropping “division” and “subtraction” entirely from the mnemonic.

      It’s true that calculators also don’t dictate a standard but they implement what conventions are typically used in practice. If a convention would be so dominating (let’s say 95% vs 5%) all calculator manufacturers would just follow the 95% convention, except maybe for some very special-purpose calculators.

  • Adkml [he/him]@hexbear.net
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    1 year 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.

  • Prunebutt@feddit.de
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    1 year 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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      1 year 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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        1 year 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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          1 year 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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            1 year 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

  • Captain Aggravated@sh.itjust.works
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    1 year 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.

    • Yes, unfortunately there are some bad teachers around. I vividly remember the one I had in Year 10, who literally didn’t care if we did well or not. I got sick for an extended period that year, and got a tutor - my Maths improved when I had the tutor (someone who actually helped me to learn the material)!

  • Alcatorda@lemmy.world
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    1 year 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.

  • MiDaBa@lemmy.ml
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    1 year ago

    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.

  • Aussiemandeus@aussie.zone
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    1 year 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.

  • 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

  • cobra89@beehaw.org
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    1 year 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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      1 year 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.

  • youngalfred@lemm.ee
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    1 year ago

    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.

  • Tartas1995@discuss.tchncs.de
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    1 year ago

    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@programming.devOP
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      1 year ago

      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@discuss.tchncs.de
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        1 year ago

        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@lemmy.world
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          1 year ago

          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.

          • I read the equation and was shocked that anyone would get an answer other than 9

            As a Maths teacher, I’m shocked whenever anyone ever gets an answer other than 1. I’m not sure how you came up with 9 when you previously said you’ve only ever seen strong juxtaposition? You can only get 9 with so-called “weak juxtaposition” (which is wrong).

          • Tartas1995@discuss.tchncs.de
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            1 year ago

            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.

              • Tartas1995@discuss.tchncs.de
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                9 months ago

                So I shouldn’t use text written by the author to understand the pov of the author and critic his pov because it is “only” a blog post, noted.

                • Not sure how you came up with that conclusion. I never said anything about it being “just a blog post”.

                  You said…

                  I don’t understand how the author of the post lands on “there is no good or bad way, they are all valid”

                  And I’m pointing out he arrived at that by ignoring what’s taught in high school, which is where it’s taught (not in academia). It’s like saying “It’s ambiguous if there’s such a thing as rain” if you present weather evidence which has omitted every single rainy day that has happened. i.e. cherry-picking. Every single blog which says it’s ambiguous has done the exact same thing. You can find what actually is taught in high school here

      • I’d actually say that the weak juxtaposition is just the simple one schools use

        Schools don’t teach “weak juxtaposition” - they teach the actual rules of Maths! As per what’s in Maths textbooks. It’s adults who’ve forgotten the rules who make up the “weak juxtaposition” rule. See Lennes.

  • TokyoMonsterTrucker@lemmy.dbzer0.com
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    1 year ago

    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.

    • The order of operations is not part of a holy text that must be blindly followed

      No, it’s in Maths textbooks, and must be… blindly followed. :-)

      If these numbers had units

      …it wouldn’t matter at all. The order of operations comes from the very definitions of the operators themselves. e.g. 2x3 is shorthand for 2+2+2.