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 :)
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
Right, because 5 rounds down to 4.5
@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 🤣
🤣 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 :-)
I did (skimmed it, at least) and I liked it. 🙃
Actually the correct answer is clearly 0.2609 if you follow the order of operations correctly:
6/2(1+2)
= 6/23
= 0.26🤣 I’m not sure if you read the post but I also wrote about that (the paragraph right before “What about the real world?”)
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
Nope it’s bedmas since everything is brackets
What the heck are you all fighting about? It’s BODMAS.
They’re arguing about whether Distribution is Multiplication or not. Spoiler alert: it isn’t, it’s Brackets.
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So what does BODMAS sound like to the other side?
samdob
I’d would be great if you find the time to read the post and let me know afterwards what you think. It actually looks trivial as a problem but the situation really isn’t, that’s why the article is so long.
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 was being facetious. I will try to find the time to read the post, but I know already that the problem isn’t trivial. It involves, above all else, human comprehension, which is a very iffy thing, to say the least.
What if the real answer is the friends we made along the way?
That’d be good, but what I’ve found so far here is a whole bunch of people who don’t like being told the actual facts of the matter! 😂
I’ve seen a calculator interpret 1 ÷ 2π as ½π which was kinda funny
An e-calculator I’m guessing? (either that or Texas Instruments) Desmos USED TO interpret that correctly, but then they made a change with automatically turning division into fractions and broke it (because if you’ve specified division then it’s not a fraction) dotnet.social/@SmartmanApps/111164851485070719
I believe it was a app , yes
All calculators that are listed in the article as following weak juxtaposition would interpreted it that way.
And they’re all wrong dotnet.social/@SmartmanApps/111164851485070719
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.
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.
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.
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
why that’s actually ambiguous.
It isn’t actually ambiguous. You have remembered what you were taught in school, unlike the author of the blog post, who manages to write the whole thing without ever once checking a Maths textbook (which would reveal the only correct answer to be 1).
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.
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
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Escape symbols?
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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.
@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.
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)!
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.
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
We do teach children how to solve this. It’s not children who get it wrong - it’s adults that get it wrong! Cos they’ve forgotten the rules of Maths (in this case The Distributive Law and Terms).
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.
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.
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…
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).
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.
The blog post claims it is popular in academy
The blog post also completely ignores what is actually taught in high school - as found in Year 7-8 Maths textbooks - which indicates how much credibility you should attach to the blog post - none.
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
