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Why Twitter can't agree on a simple math equation

uberman 6y ago
The notion that something as simple as: AB/CD Could have multiple "valid" interpretations boggles my mind. It is clear to me at least that AB/CD is the "lazy way" of writing A x B / C x D where the "dots" between A and B have been omitted by the typesetter/author. I find it somehow disturbing that some would rather interpret this as the "lazy way" of writing (A x B) / (C x D). I find it even more disturbing that two different modules of Cassio calculators interpret this differently. https://twitter.com/DavePunFun/status/1327327770750271488 https://twitter.com/DavePunFun/status/1327327770750271488
- naniwaduni 6y ago
  As a human, if you write AB/CD, you either mean (AB)/(CD), or you're writing a trick question. You do not mean (AB/C)D, because if you did, you could write the equally short ABD/C. If you're appending a multiplication by D after AB/C, you could write AB/C×D. Meaning is borne by contrast. In any case, the practice of writing "/2π" is pervasive enough that asserting that "PEMDAS" implies ordering explicit division left-to-right with implicit multiplication is at wrong at best.
  - uberman 6y ago
    I guess we can agree to disagree on the validity of implicit multiplication. My larger point though is if we as an "advanced society" cannot agree on what this very basic notation means then how many times have we implemented something wrong. Check the link above for images of two Cassio calculators producing different answers for a dead simple grade 5 math problem. Just to also be clear, are you saying that E = MC^2 is actually E = (M x C)^2 since implied multiplication suggests that: MC === (M x C) rather than MC === M x C and by your argument above, if you thought otherwise you would simply rearrange the formula to be: E = C^2 x M
    - chrisfosterelli 6y ago
      Prioritizing implicit multiplication prioritizes it over other multiplications / divisions (during the "MD" part of PEMDAS). Since exponents still come before any multiplication / division, E = MC^2 is interpreted the same.
dvtrn 6y ago
>Of course the vagueness is deliberate in this case Which is why I Hate a vast majority of these types of “viral math” problems. There’s enough math-anxiety that these problems, with their intentionally poor notation really don’t do anything but add noise.
bradknowles 6y ago
PEMDAS. 1. Done.
- dekhn 6y ago
  Not really; the question switches between two different notations (explicit division and implicit multiplication) so it's not clear why those rules would apply.
db48x 6y ago
There is plenty of ambiguity in the common math notation, and it's not limited just to arithmetic. Some of the worst ambiguities are in calculus. If we wanted to, we could teach a notation that is completely unambiguous. Consider (* (/ 6 2) (+ 1 2)) instead.
AndyPatterson 6y ago
I don’t see how it can be both 1 and 9 though. In my mind it can only be 1 because anything to right of the division sign should be fully evaluated first before using the result in the division operation.
- naniwaduni 6y ago
  It cannot be 9. Answering 9 requires you to see notation you recognize as unintuitive (if you are not a calculator, in any case), shut up and multiply, and discard that provenance. Possible answers are 1 and "the question is ill-formed".
deleted 6y ago
[deleted]
1970-01-01 6y ago
The problem isn't mathematics. The problem is the operation "÷" is not well defined. Note how this looks when variables are substituted: 6÷2(1+2) x=6, y=2 x÷y(1+y) ... is x÷y(1+y) A) x/y(1+y) ... 6/2(1+2) = 6/6 = 1. or B) x(1+y)/y ... 6(1+2)/2 = 6(3)/2 = 9. or C) x/y+(y+1) ... 6/2+(2+1) = 6. I'm going with 6. Without a formal definition for "÷" 6 is just as reasonable as 1 and 9.

The notion that something as simple as: AB/CD Could have multiple "valid" interpretations boggles my mind. It is clear to me at least that AB/CD is the "lazy way" of writing A x B / C x D where the "dots" between A and B have been omitted by the typesetter/author. I find it somehow disturbing that some would rather interpret this as the "lazy way" of writing (A x B) / (C x D). I find it even more disturbing that two different modules of Cassio calculators interpret this differently. https://twitter.com/DavePunFun/status/1327327770750271488 https://twitter.com/DavePunFun/status/1327327770750271488

naniwaduni 6y ago
As a human, if you write AB/CD, you either mean (AB)/(CD), or you're writing a trick question. You do not mean (AB/C)D, because if you did, you could write the equally short ABD/C. If you're appending a multiplication by D after AB/C, you could write AB/C×D. Meaning is borne by contrast. In any case, the practice of writing "/2π" is pervasive enough that asserting that "PEMDAS" implies ordering explicit division left-to-right with implicit multiplication is at wrong at best.
- uberman 6y ago
  I guess we can agree to disagree on the validity of implicit multiplication. My larger point though is if we as an "advanced society" cannot agree on what this very basic notation means then how many times have we implemented something wrong. Check the link above for images of two Cassio calculators producing different answers for a dead simple grade 5 math problem. Just to also be clear, are you saying that E = MC^2 is actually E = (M x C)^2 since implied multiplication suggests that: MC === (M x C) rather than MC === M x C and by your argument above, if you thought otherwise you would simply rearrange the formula to be: E = C^2 x M
  - chrisfosterelli 6y ago
    Prioritizing implicit multiplication prioritizes it over other multiplications / divisions (during the "MD" part of PEMDAS). Since exponents still come before any multiplication / division, E = MC^2 is interpreted the same.

dvtrn 6y ago

>Of course the vagueness is deliberate in this case Which is why I Hate a vast majority of these types of “viral math” problems. There’s enough math-anxiety that these problems, with their intentionally poor notation really don’t do anything but add noise.

bradknowles 6y ago

PEMDAS. 1. Done.

dekhn 6y ago
Not really; the question switches between two different notations (explicit division and implicit multiplication) so it's not clear why those rules would apply.

db48x 6y ago

There is plenty of ambiguity in the common math notation, and it's not limited just to arithmetic. Some of the worst ambiguities are in calculus. If we wanted to, we could teach a notation that is completely unambiguous. Consider (* (/ 6 2) (+ 1 2)) instead.

AndyPatterson 6y ago

I don’t see how it can be both 1 and 9 though. In my mind it can only be 1 because anything to right of the division sign should be fully evaluated first before using the result in the division operation.

naniwaduni 6y ago
It cannot be 9. Answering 9 requires you to see notation you recognize as unintuitive (if you are not a calculator, in any case), shut up and multiply, and discard that provenance. Possible answers are 1 and "the question is ill-formed".

deleted 6y ago

[deleted]

1970-01-01 6y ago

The problem isn't mathematics. The problem is the operation "÷" is not well defined. Note how this looks when variables are substituted: 6÷2(1+2) x=6, y=2 x÷y(1+y) ... is x÷y(1+y) A) x/y(1+y) ... 6/2(1+2) = 6/6 = 1. or B) x(1+y)/y ... 6(1+2)/2 = 6(3)/2 = 9. or C) x/y+(y+1) ... 6/2+(2+1) = 6. I'm going with 6. Without a formal definition for "÷" 6 is just as reasonable as 1 and 9.