https://zeta.one/viral-math/ [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 :)
Attached: 1 image 4/7 There are 4 mnemonics - BODMAS, BIDMAS, BEDMAS, and PEMDAS. The mnemonics aren't the rules, they are just a way to remember the rules, and, as per screenshot, it doesn't matter whether you do Division or Multiplication first, hence there is no conflict between the last and the first 3 (only in the mind of people who think they are the actual rules, and one or the other HAS TO be done first). This also debunks "it depends where you learnt" - the mnemonics aren't universal, but the rules are!
Hi, I’m stupid, is it 1+2 first, then multiple it by 2, then divide 6 by 6?
Or is it 1+2, then divide 6 by 2, then multiple?
I think it’s the first one but I’ve got no idea.
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.
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.
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.
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.
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.
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.
with reading comprehension like your’s
Man.
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
Neither of which is a rule in Maths, as had already been pointed out. The 2 relevant rules, both of which never got mentioned in the whole discussion, are The Distributive Law and Terms.
You’re right that in reality nobody would write an equation like this
No, that was wrong - they really would. 2(1+2) is the standard way to write a factorised term. i.e. a(b+c).
hole that exists in the standard order of operations
There’s not a hole in the order of operations - there’s a hole in people’s memories where The Distributive Law and Terms used to be. You’ll notice no students ever get this wrong, because they remember all the rules.
given no other context to do so, you would either have to pick a side
That “side” being follow the rules of Maths - works every time. :-)
The standard order of operations is as well defined as a notational convention can be.
If it was so well defined, then how did two different sets of rules regarding juxtaposition even come to be?
A well-defined order of operations shouldn't have a hole that big.
Also, @wischi asking you to give the answer as defined by your convention isn't condescending, they're asking you to put your money where your mouth is...
Your response certainly felt condescending though, especially since your "explanation" was essentially that anyone who disagrees with the convention you follow is wrong and should feel stupid, and that you needn't even consider it.
There aren’t two different sets of rules. There’s the simple model that’s commonly understood and taught to kids, and there’s the real world where you have context and the dynamics of a conversation and years of experience with communication. One is well defined, the other isn’t.
Them asking me to solve the arithmetic problem is condescending, yes.
My response didn’t say “anyone who disagrees with the convention is stupid.” Here’s condescension for you: please don’t make your reading level my problem. What I said was, there’s an unambiguous way to parse the expression according to the commonly understood order of operations, but it is atypical to pay that much attention to the order of operations in practice. If you think that’s a value judgment, that’s on you-- I was very clear in my example about capitalization, “strictly adhering to the conventional order of operations” is something reasonable people often just don’t care about.
There aren’t two different sets of rules. There’s the simple model that’s commonly understood and taught to kids, and there’s the real world where you have context and the dynamics of a conversation and years of experience with communication. One is well defined, the other isn’t.
And that simple model, well-defined model didn't properly account for juxtaposition, which is how different fields have ended up with two different ways of interpreting it, i.e. strong vs. weak juxtaposition.
In the real world you simply wouldn't write any equation out in such a way as to allow misinterpretation like this, but that's ignoring the elephant in the room...
Which is that the reason viral problems like this still come about and why @wischi went through the effort of writing a rather detailed blog on this is because the order of operations most people are taught doesn't cover juxtaposition.
Them asking me to solve the arithmetic problem is condescending, yes.
Considering your degree specialisation is in solving arithmetic problems, I don't see the issue with them asking you to put your money where your mouth is and spit out a number if it's so easy.
My response didn’t say “anyone who disagrees with the convention is stupid.” Here’s condescension for you: please don’t make your reading level my problem.
Ironic that you tell me to check my reading comprehension right after you misquote me, but nonetheless that is the impression your responses have given off - and you haven't done anything so far to dispel that impression.
What I said was, there’s an unambiguous way to parse the expression according to the commonly understood order of operations, but it is atypical to pay that much attention to the order of operations in practice.
Yes, and the question everyone is asking you is what is that unambiguous way? Which side of weak or strong juxtaposition do you come out on?
If you think that’s a value judgment, that’s on you-- I was very clear in my example about capitalization, “strictly adhering to the conventional order of operations” is something reasonable people often just don’t care about.
The value judgement was actually more to do with your choice of example, and how you applied that example to this debate. It gave me the distinct impression that you view this debate as not worth having, as anybody who does juxtaposition differently from you is wrong out the gate - and again, your further responses only reinforce my impression of you.
And that simple model, well-defined model didn’t properly account for juxtaposition, which is how different fields have ended up with two different ways of interpreting it, i.e. strong vs. weak juxtaposition.
No, that’s just not what happened. “Strong juxtaposition,” while well-defined, is a post-hoc rationalization. Meaning in particular that people who believe that this expression is best interpreted with “strong juxtaposition” don’t really believe in “strong juxtaposition” as a rule. What they really believe is that communication is subtle and context dependent, and the traditional order of operations is not comprehensive enough to describe how people really communicate. And that’s correct.
Considering your degree specialisation is in solving arithmetic problems
My degree specialization is in algebraic topology.
I don’t see the issue with them asking you to put your money where your mouth is and spit out a number if it’s so easy
The issue is that this question disregards and undermines my point and asks me to pick a side, arbitrarily, that (as I’ve already explained) I don’t actually believe in.
Ironic that you tell me to check my reading comprehension right after you misquote me, but nonetheless that is the impression your responses have given off - and you haven’t done anything so far to dispel that impression.
I didn’t misread, you’re in denial.
Yes, and the question everyone is asking you is what is that unambiguous way? Which side of weak or strong juxtaposition do you come out on?
Hopefully by this point in the comment you understand that I don’t believe the question makes sense.
The value judgement was actually more to do with your choice of example, and how you applied that example to this debate. It gave me the distinct impression that you view this debate as not worth having, as anybody who does juxtaposition differently from you is wrong out the gate - and again, your further responses only reinforce my impression of you.
Again, that’s your fault-- you’ve clearly misinterpreted what I said. If I didn’t think this conversation was worth having I wouldn’t be responding to you.
No, that’s just not what happened. “Strong juxtaposition,” while well-defined, is a post-hoc rationalization. Meaning in particular that people who believe that this expression is best interpreted with “strong juxtaposition” don’t really believe in “strong juxtaposition” as a rule. What they really believe is that communication is subtle and context dependent, and the traditional order of operations is not comprehensive enough to describe how people really communicate. And that’s correct.
I think you're putting the cart before the horse here - there is definitely a communication issue around juxtaposition, but you're acting as though strong juxtaposition is some kind of social commentary on the standard order of operations rather than the reality that it is an interpretation that arose due to ambiguity, just as weak juxtaposition did.
If it were people just trying to make a point, then why would it be so widely used and most scientific calculators are designed to use it, or allow its use. This debate exists because so many people ascribe to one or the other without thinking.
My degree specialization is in algebraic topology.
One - that does sound kind of cool
Two - You still have a mathematics degree do you not? You said this was an easy "unambiguous" problem to solve, so I don't see how you're prohibited from solving it...
The issue is that this question disregards and undermines my point and asks me to pick a side, arbitrarily, that (as I’ve already explained) I don’t actually believe in.
God saying stuff like that, you sound just like an enlightened centrist...
Anyways, even if you don't want to comment on the strong vs. weak juxtaposition debate, unless you simply intend on never solving any equation with implicit multiplication by juxtaposition ever again, then you must have a way of interpreting it.
That is what you're being asked to disclose, since you seem to be very certain that there is a correct way of resolving this. You've brought the question upon yourself.
If you don't want to take a side, simply saying the rules are ambiguous and technically both positions are correct depending on what field you're in is also a valid position...
But denying the problem all together is not productive.
I didn’t misread, you’re in denial.
In the first place I don't think you've proven me wrong. As far as I can tell your comments still boil down to that you think the whole debate is wrong, and that engaging in the debate is dumb.
But I can say for certain that you either misread or deliberately misconstrued at least part of my reply, because when responding to me you removed the "you follow" from it, which changes the interpretation.
If you think that wasn't what I said, feel free to go back and look.
Hopefully by this point in the comment you understand that I don’t believe the question makes sense.
I understand you don't believe the question makes sense, you've said that enough times...
But I'll just refer you to my earlier comment - unless you intend on never solving any equation involving implicit multiplication ever again, then you must ascribe to one way or the other of resolving it.
Again, that’s your fault-- you’ve clearly misinterpreted what I said.
Then tell me how I've misinterpreted what you said, because I stick by what I said as far as your example goes.
Your choice of example is not only a much more clear cut issue, being that most kids are taught by primary school (or the US equivalent) how and where to capitalise their letters, and to me it also demonstrates that you've not understood that the whole reason this debate is a thing is directly because there's no "wrong way" of doing this.
If I didn’t think this conversation was worth having I wouldn’t be responding to you.
I understand you see this conversation with me as worth having, but I suspect this is more to do with wanting to resolve this conversation in your favour than it is to do with the underlying debate.
most scientific calculators are designed to use it
They don’t. They use The Distributive Law and Terms.
why @wischi went through the effort of writing a rather detailed blog on this is because the order of operations most people are taught doesn’t cover juxtaposition.
The order of operations rules do cover it. Did you not notice that the OP never referenced a single Maths textbook? Because, had that been done, the whole house of cards would’ve fallen down. See my Fact Check posts doing exactly that.
If it was so well defined, then how did two different sets of rules regarding juxtaposition even come to be?
They didn’t - neither of them is a rule of Maths.
It actually looks trivial as a problem
Because it actually is.
that’s why the article is so long
The article was really long because there were so many stawmen in it. Had you checked a Maths textbook or asked a Maths teacher it could’ve been really short, but you never did either.
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
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!
if it was 6÷2x(2+1) they suggested do division and mult from left to right, but 6÷2(2+1)
Correct! Terms are separated by operators and joined by grouping symbols, so 6÷2x(2+1) is 3 terms - 6, 2, and (2+1) - whereas 6÷2(2+1) is 2 terms - 6 and 2(2+1), and the latter term has a precedence of “brackets”, NOT “multiplication”. Multiplication refers literally to multiplication signs, which are only present in your first example (hence evaluated with a different order than your second example).
Also noted that the OP has ignored your comment, seeing as how you pointed out the unambiguous way to do it.
2(1+2) is the same as (1+2)+(1+2)
You nearly had it. 2(1+2) is the same as (2x1+2x2). The Distributive Law - it’s the reverse process to factorising.
implicit multiplication
There’s no such thing as “implicit multiplication”
Some place it above explicit multiplication and division,
Which is correct, seeing as how we’re solving brackets, and brackets always come first.
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
Which is wrong.
Since those are both valid interpretations of the order of operations
No, they’re not. Treating brackets as, you know, brackets, is the only valid interpretation. “Multiplication” refers literally to multiplication signs, of which there are none in this problem.
But in reality nobody would write an equation like this
Yes they would. a(b+c) is the standard way to write a factorised term.
Attached: 1 image 1/7 This week for #MathsMonday we are going to debunk the "implicit multiplication" (IM) claims (and also look at the mnemonics). I say claims, because there is actually no such thing as IM in #Mathematics. I find invariably the people who say there is have forgotten The Distributive Law (TDL) and/or Terms, but most often both! As we have already seen, these are both rules of #Maths, taught in many #Math textbooks, so that right away debunks any claims that "there is no convention in Maths"...
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.
I don’t agree with the notation of the American Physical Society
I clicked on the link to see what you were talking about, and the quotes which are used in the blog aren’t in there at all. i.e. I searched the whole document, not just the referenced page, and, for example, the expression “multiplication before division” isn’t in there at all. On the other hand the stuff about not inserting multiplication signs into terms is 100% correct, because you are breaking up one term into two, and dropping the precedence from Terms to Multiplication, which changes the answer.
Direct quote from the article:
the American Physical Society state in their Style and Notation Guide on page 21 that they do “multiplication before division”, but you must be careful to not take that out of context
That’s the correct answer if you follow
…the rules of Maths.
I’m not a mathematician and the answer is 9
I’m a Mathematician and the answer is 1.
1/3 #MathsMonday Order of operations thread index #Mathematics #Maths #Math Introduction https://dotnet.social/@SmartmanApps/110807192608472798 1 The Distributive Law #DontForgetDistribution https://dotnet.social/@SmartmanApps/110819283738912144 2 Terms #MathsIsNeverAmbiguous https://dotnet.social/@SmartmanApps/110846452267056791 3 Factorising<->The Distributive Law https://dotnet.social/@SmartmanApps/110886637077371439 4 implicit multiplication, mnemonics https://dotnet.social/@SmartmanApps/110925761375035558 5 1917 (i) - Left Associativity https://dotnet.social/@SmartmanApps/110965810374299599 6 1917 (ii) - Lennes' letter (Terms and operators) https://dotnet.social/@SmartmanApps/111005247356655843 ...
It was incredibly thorough and well researched
It never mentions the 2 relevant rules of Maths, nor any textbooks, nor speaks to any Maths teachers. You can find all those thing here
1/3 #MathsMonday Order of operations thread index #Mathematics #Maths #Math Introduction https://dotnet.social/@SmartmanApps/110807192608472798 1 The Distributive Law #DontForgetDistribution https://dotnet.social/@SmartmanApps/110819283738912144 2 Terms #MathsIsNeverAmbiguous https://dotnet.social/@SmartmanApps/110846452267056791 3 Factorising<->The Distributive Law https://dotnet.social/@SmartmanApps/110886637077371439 4 implicit multiplication, mnemonics https://dotnet.social/@SmartmanApps/110925761375035558 5 1917 (i) - Left Associativity https://dotnet.social/@SmartmanApps/110965810374299599 6 1917 (ii) - Lennes' letter (Terms and operators) https://dotnet.social/@SmartmanApps/111005247356655843 ...
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