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 :)

  • I think weak juxtaposition is more easily taught

    Except it breaks the rules which already are taught.

    the PEMDAS ruleset

    But they’re not rules - it’s a mnemonic to help you remember the actual order of operations rules.

    Just let one die. Kill it, if you have to

    Juxtaposition - in either case - isn’t a rule to begin with (the 2 appropriate rules here are The Distributive Law and Terms), yet it refuses to die because of incorrect posts like this one (which fails to quote any Maths textbooks at all, which is because it’s not in any textbooks, which is because it’s wrong).

    • The_Vampire@lemmy.world
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      8 months ago

      Except it breaks the rules which already are taught.

      It isn’t, because the ‘currently taught rules’ are on a case-by-case basis and each teacher defines this area themselves. Strong juxtaposition isn’t already taught, and neither is weak juxtaposition. That’s the whole point of the argument.

      But they’re not rules - it’s a mnemonic to help you remember the actual order of operations rules.

      See this part of my comment: “To note, yes, PEMDAS is a teaching tool and yes there are obviously other ways of thinking of math. But do those matter? The mathematical system we currently use will work for any usecase it does currently regardless of the juxtaposition we pick, brackets/parentheses (as well as better ordering of operations when writing them down) can pick up any slack. Weak juxtaposition provides better benefits because it has less rules (and is thusly simpler).”

      Juxtaposition - in either case - isn’t a rule to begin with (the 2 appropriate rules here are The Distributive Law and Terms), yet it refuses to die because of incorrect posts like this one (which fails to quote any Maths textbooks at all, which is because it’s not in any textbooks, which is because it’s wrong).

      You’re claiming the post is wrong and saying it doesn’t have any textbook citation (which is erroneous in and of itself because textbooks are not the only valid source) but you yourself don’t put down a citation for your own claim so… citation needed.

      In addition, this issue isn’t a mathematical one, but a grammatical one. It’s about how we write math, not how math is (and thus the rules you’re referring to such as the Distributive Law don’t apply, as they are mathematical rules and remain constant regardless of how we write math).

      • It isn’t, because the ‘currently taught rules’ are on a case-by-case basis and each teacher defines this area themselves

        Nope. Teachers can decide how they teach. They cannot decide what they teach. The have to teach whatever is in the curriculum for their region.

        Strong juxtaposition isn’t already taught, and neither is weak juxtaposition

        That’s because neither of those is a rule of Maths. The Distributive Law and Terms are, and they are already taught (they are both forms of what you call “strong juxtaposition”, but note that they are 2 different rules, so you can’t cover them both with a single rule like “strong juxtaposition”. That’s where the people who say “implicit multiplication” are going astray - trying to cover 2 rules with one).

        See this part of my comment… Weak juxtaposition provides better benefits because it has less rules (and is thusly simpler)

        Yep, saw it, and weak juxtaposition would break the existing rules of Maths, such as The Distributive Law and Terms. (Re)learn the existing rules, that is the point of the argument.

        citation needed

        Well that part’s easy - I guess you missed the other links I posted. Order of operations thread index Text book references, proofs, the works.

        this issue isn’t a mathematical one, but a grammatical one

        Maths isn’t a language. It’s a group of notation and rules. It has syntax, not grammar. The equation in question has used all the correct notation, and so when solving it you have to follow all the relevant rules.

        • The_Vampire@lemmy.world
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          8 months ago

          Nope. Teachers can decide how they teach. They cannot decide what they teach. The have to teach whatever is in the curriculum for their region.

          Yes, teachers have certain things they need to teach. That doesn’t prohibit them from teaching additional material.

          That’s because neither of those is a rule of Maths. The Distributive Law and Terms are, and they are already taught (they are both forms of what you call “strong juxtaposition”, but note that they are 2 different rules, so you can’t cover them both with a single rule like “strong juxtaposition”. That’s where the people who say “implicit multiplication” are going astray - trying to cover 2 rules with one).

          Yep, saw it, and weak juxtaposition would break the existing rules of Maths, such as The Distributive Law and Terms. (Re)learn the existing rules, that is the point of the argument.

          Well that part’s easy - I guess you missed the other links I posted. Order of operations thread index Text book references, proofs, the works.

          You argue about sources and then cite yourself as a source with a single reference that isn’t you buried in the thread on the Distributive Law? That single reference doesn’t even really touch the topic. Your only evidence in the entire thread relevant to the discussion is self-sourced. Citation still needed.

          Maths isn’t a language. It’s a group of notation and rules. It has syntax, not grammar. The equation in question has used all the correct notation, and so when solving it you have to follow all the relevant rules.

          You can argue semantics all you like. I would put forth that since you want sources so much, according to Merriam-Webster, grammar’s definitions include “the principles or rules of an art, science, or technique”, of which I think the syntax of mathematics qualifies, as it is a set of rules and mathematics is a science.

          • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.dev
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            8 months ago

            That doesn’t prohibit them from teaching additional material

            Correct, but it can’t be something which would contradict what they do have to teach, which is what “weak juxtaposition” would do.

            a single reference

            I see you didn’t read the whole thread then. Keep going if you want more. Literally every Year 7-8 Maths textbook says the same thing. I’ve quoted multiple textbooks (and haven’t even covered all the ones I own).

            mathematics is a science

            Actually you’ll find that assertion is hotly debated.

            • The_Vampire@lemmy.world
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              8 months ago

              Correct, but it can’t be something which would contradict what they do have to teach, which is what “weak juxtaposition” would do.

              Citation needed.

              I see you didn’t read the whole thread then. Keep going if you want more. Literally every Year 7-8 Maths textbook says the same thing. I’ve quoted multiple textbooks (and haven’t even covered all the ones I own).

              If I have to search your ‘source’ for the actual source you’re trying to reference, it’s a very poor source. This is the thread I searched. Your comments only reference ‘math textbooks’, not anything specific, outside of this link which you reference twice in separate comments but again, it’s not evidence for your side, or against it, or even relevant. It gets real close to almost talking about what we want, but it never gets there.

              But fine, you reference ‘multiple textbooks’ so after a bit of searching I find the only other reference you’ve made. In the very same comment you yourself state “he says that Stokes PROPOSED that /b+c be interpreted as /(b+c). He says nothing further about it, however it’s certainly not the way we interpret it now”, which is kind of what we want. We’re talking about x/y(b+c) and whether that should be x/(yb+yc) or x/y * 1/(b+c). However, there’s just one little issue. Your last part of that statement is entirely self-supported, meaning you have an uncited refutation of the side you’re arguing against, which funnily enough you did cite.

              Now, maybe that latter textbook citation I found has some supporting evidence for yourself somewhere, but an additional point is that when providing evidence and a source to support your argument you should probably make it easy to find the evidence you speak of. I’m certainly not going to spend a great amount of effort trying to disprove myself over an anonymous internet argument, and I believe I’ve already done my due diligence.

              • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.dev
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                8 months ago

                Citation needed.

                So you think it’s ok to teach contradictory stuff to them in Maths? 🤣 Ok sure, fine, go ahead and find me a Maths textbook which has “weak juxtaposition” in it. I’ll wait.

                Your comments only reference ‘math textbooks’, not anything specific

                So you’re telling me you can’t see the Maths textbook screenshots/photo’s?

                outside of this link which you reference twice in separate comments but again, it’s not evidence for your side, or against it, or even relevant

                Lennes was complaining that literally no textbooks he mentioned were following “weak juxtaposition”, and you think that’s not relevant to establishing that no textbooks used “weak juxtaposition” 100 years ago?

                We’re talking about x/y(b+c) and whether that should be x/(yb+yc) or x/y * 1/(b+c).

                It’s in literally the first textbook screenshot, which if I’m understanding you right you can’t see? (see screenshot of the screenshot above)

                you have an uncited refutation of the side you’re arguing against, which funnily enough you did cite.

                Ah, no. Lennes was complaining about textbooks who were obeying Terms/The Distributive Law. His own letter shows us that they all (the ones he mentioned) were doing the same thing then that we do now. Plus my first (and later) screenshot(s).

                Also it’s in Cajori, but I didn’t find it until later. I don’t remember what page it was, but it’s in Cajori and you have the reference for it there already.

                you should probably make it easy to find the evidence you speak of

                Well I’m not sure how you didn’t see all the screenshots. They’re hard to miss on my computer!

                • The_Vampire@lemmy.world
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                  8 months ago

                  So you think it’s ok to teach contradictory stuff to them in Maths? 🤣 Ok sure, fine, go ahead and find me a Maths textbook which has “weak juxtaposition” in it. I’ll wait.

                  You haven’t provided a textbook that has strong juxtaposition.

                  So you’re telling me you can’t see the Maths textbook screenshots/photo’s?

                  That’s not a source, that’s a screenshot. You can’t look up the screenshot, you can’t identify authors, you can’t check for bias. At best I can search the title of the file you’re in that you also happened to screenshot and hope that I find the right text. The fact that you think this is somehow sufficient makes me question your claims of an academic background, but that’s neither here nor there. What does matter is that I shouldn’t have to go treasure hunting for your sources.

                  And, to blatantly examine the photo, this specific text appears to be signifying brackets as their own syntactic item with differing rules. However, I want to note that the whole issue is that people don’t agree so you will find cases on both sides, textbook or no.

                  Lennes was complaining that literally no textbooks he mentioned were following “weak juxtaposition”, and you think that’s not relevant to establishing that no textbooks used “weak juxtaposition” 100 years ago?

                  You are welcome to cite the specific wording he uses to state this. As far as I can tell, at least in the excerpt linked, there is no such complaint.

                  • You haven’t provided a textbook that has strong juxtaposition

                    I told you, in my thread - multiple ones. You haven’t provided any textbooks at all that have “weak juxtaposition”. i.e. you keep asking me for more evidence whilst never producing any of your own.

                    At best I can search the title of the file you’re in that you also happened to screenshot and hope that I find the right text

                    I didn’t “just happen” to include the name of the textbook and page number - that was quite deliberate. Not sure why you don’t want to believe a screenshot, especially since you can’t quote any that have “weak juxtaposition” in the first place.

                    BTW I just tried Googling it and it was the first hit. You’re welcome.

                    What does matter is that I shouldn’t have to go treasure hunting for your sources.

                    You don’t - the screenshots of the relevant pages are right there. You’re the one choosing not to believe what is there in black and white, in multiple textbooks.

                    with differing rules

                    Yeah, I wrote about inconsistency in textbooks here (also includes another textbook saying you have to expand brackets first), but also elsewhere in the thread is an example where they have been consistent throughout. Regardless of when they remove brackets, in every single case they multiply the coefficient over what’s inside the brackets as the first step (as per BEDMAS, and as per the screenshot in question which literally says you must do it before you remove brackets).

                    people don’t agree

                    People who aren’t high school Maths teachers (the ones who actually teach this topic). Did you notice that neither The Distributive Law nor Terms are mentioned at any point whatsoever? That’s like saying “I don’t remember what I did at Xmas, so therefore it’s ambiguous whether Xmas ever happened at all, and anyone who says it definitely did is wrong”.

                    no such complaint.

                    So what do you think he is complaining about?

        • 💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱@programming.dev
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          8 months ago

          P.S. if you DID want to indicate “weak juxtaposition”, then you just put a multiplication symbol, and then yes it would be done as “M” in BEDMAS, because it’s no longer the coefficient of a bracketed term (to be solved as part of “B”), but a separate term.

          6/2(1+2)=6/(2+4)=6/6=1

          6/2x(1+2)=6/2x3=3x3=9