6÷2(1+2)
6÷2(1+2)
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 :)
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Why would I read something that I know is wrong? #MathsIsNeverAmbiguous
Mathematical notation however can be. Because it's conventions as long as it's not defined on the same page.
Mathematical notation however can be.
Nope. Different regions use different symbols, but within those regions everyone knows what each symbol is, and none of those symbols are in this question anyway.
Because it’s conventions as long as it’s not defined on the same page
The rules can be found in any high school Maths textbook.
Let's do a little plausibility analysis, shall we? First, we have humans, you know, famously unable to agree on an universal standard for anything. Then we have me, who has written a PhD thesis for which he has read quite some papers about math and computational biology. Then we have an article that talks about the topic at hand, but that you for some unscientific and completely ridiculous reason refuse to read.
Let me just tell you one last time: you're wrong, you should know that it's possible that you're wrong, and not reading a thing because it could convince you is peak ignorance.
I'm done here, have a good one, and try not to ruin your students too hard.
unable to agree on an universal standard for anything
And yet the order of operations rules have been agreed upon for at least 100 years, possibly at least 400 years.
unscientific and completely ridiculous reason refuse to read
The fact that I saw it was wrong in the first paragraph is a ridiculous reason to not read the rest?
Let me just tell you one last time: you’re wrong
And let me point out again you have yet to give a single reason for that statement, never mind any actual evidence.
you should know that it’s possible that you’re wrong
You know proofs, by definition, can't be wrong, right? There are proofs in my thread, unless you have some unscientific and completely ridiculous reason to refuse to read - to quote something I recently heard someone say.
try not to ruin your students too hard
My students? Oh, they're doing good. Thanks for asking! :-) BTW the test included order of operations.
Just read the article. You can't prove something with incomplete evidence. And the article has evidence that both conventions are in use.
You can’t prove something with incomplete evidence
If something is disproven, it's disproven - no need for any further evidence.
BTW did you read my thread? If you had you would know what the rules are which are being broken.
the article has evidence that both conventions are in use
I'm fully aware that some people obey the rules of Maths (they're actual documented rules, not "conventions"), and some people don't - I don't need to read the article to find that out.
Notation isn't semantics. Mathematical proofs are working with the semantics. Nobody doubts that those are unambiguous. But notation can be ambiguous. In this case it is: weak juxtaposition vs strong juxtaposition. Read the damn article.
Read the damn article.
Read it. Was even worse than I was expecting! Did you not notice that a blog about the alleged ambiguity in order of operations actually disobeyed order of operations in a deliberately ambiguous example? I wrote 5 fact check posts about it starting here - you're welcome.
Look, this is not the only case where semantics and syntax don't always map, in the same way e.g.: https://math.stackexchange.com/a/586690
I'm sure it's possible that all your textbooks agree, but if you e.g. read a paper written by someone who isn't from North America (or wherever you're from) it's possible they use different semantics for a notation that for you seems to have clear meaning.
That's not a controversial take. You need to accept that human communication isn't as perfectly unambiguous as mathematics (writing math down using notation is a way of communicating)
Look, this is not the only case where semantics and syntax don’t always map
Syntax varies, semantics doesn't. e.g. in some places colon is used for division, in others an obelus, but regardless of which notation you use, the interpretation of division is immutable.
they use different semantics for a notation that for you seems to have clear meaning
They might use different notation, but the semantics is universal.
You need to accept that human communication isn’t as perfectly unambiguous as mathematics (writing math down using notation is a way of communicating)
Writing Maths notation is a way of using Maths, and has to be interpreted according to the rules of Maths - that's what they exist for!
Notation isn’t semantics
Correct, the definitions and the rules define the semantics.
Mathematical proofs are working with
...the rules of Maths. In fact, when we are first teaching proofs to students we tell them they have to write next to each step which rule of Maths they have used for that step.
Nobody doubts that those are unambiguous
Apparently a lot of people do! But yes, unambiguous, and therefore the article is wrong.
But notation can be ambiguous
Nope. An obelus means divide, and "strong juxtaposition" means it's a Term, and needs The Distributive Law applied if it has brackets.
In this case it is: weak juxtaposition vs strong juxtaposition
There is no such thing as weak juxtaposition. That is another reason that the article is wrong. If there is any juxtaposition then it is strong, as per the rules of Maths. You're just giving me even more ammunition at this point.
Read the damn article
You just gave me yet another reason it's wrong - it talks about "weak juxtaposition". Even less likely to ever read it now - it's just full of things which are wrong.
How about read my damn thread which contains all the definitions and proofs needed to prove that this article is wrong? You're trying to defend the article... by giving me even more things that are wrong about it. 😂