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I opened the video in the background and immediately recognized the person: the author behind the 3Blue1Brown YouTube channel. It has a long series of video reg

by hashar 3y ago

I opened the video in the background and immediately recognized the person: the author behind the 3Blue1Brown YouTube channel. It has a long series of video regarding various mathematical topics which are rather accessible. My favorite by far is a "proposal" for an alternate notation which makes much more sense and, if adopted, would make mathematics way less intimidating (Triangle of Power (2016), 3Blue1Brown - https://www.youtube.com/watch?v=sULa9Lc4pck https://www.youtube.com/watch?v=sULa9Lc4pck ). I'd give him a Fields medal (or at least an honorary mention of some sort) :-]

smokel 3y ago
Note that the alternate notation was suggested by someone named "2'5 9'2" on the Mathematics Stack Exchange [1], and not by 3Blue1Brown. Obviously, this should not take away from the amazing educational work that 3Blue1Brown has achieved, but the honorary mention would probably suffice :) [1] https://math.stackexchange.com/questions/30046/alternative-notation-for-exponents-logs-and-roots https://math.stackexchange.com/questions/30046/alternative-n...
- pranavjoneja 3y ago
  He mentions in the video that he saw the idea in "a math exchange post" and he also has a link to the exact post in the video description. Doesn't that count?
  - emiliobumachar 3y ago
    It does count as properly attributing the idea, yes. It doesn't count as having it. Possibly the Fields Medal suggestion assumed it was his?
  - simiones 3y ago
    The point was that it's just not his invention. He attributes it extremely clearly, no one is accusing him of theft. But you don't get math prizes for presenting someone else's ideas.
    - hgsgm 3y ago
      Fortunately, you do. https://en.m.wikipedia.org/wiki/Leroy_P._Steele_Prize https://en.m.wikipedia.org/wiki/Leroy_P._Steele_Prize
- a1o 3y ago
  I agree with the comment that says this removes the personality of each function
  - hgsgm 3y ago
    Why doesn't subtraction need personality?
    - Tainnor 3y ago
      I don't think there are many deep theorems about subtraction, but there are a lot of very deep theorems about powers (and polynomials), the exponential function and logarithm functions (especially in complex analysis).
raverbashing 3y ago
> immediately recognized the person: the author behind the 3Blue1Brown YouTube channel Yes, that is noted by the 3B1B in the title But yeah the asymmetry of operators in math is exhausting.
Turneyboy 3y ago
I'm a fan of his work but that's just not what Fields medals are for.
hfkwer 3y ago
I'm a math professor with about a decade of teaching math. On the list of things that make math intimidating, for undergrads at least, the notation for powers, roots, and log, is very low. The "proposal" also ignores that 1. The kth root of x is often denoted x^(1/k); 2. We have convenient shortcuts for the square root and the natural logarithm; 3. Parentheses become a mess; 4. The notation for squares, cubes, etc. is deeply entrenched; does anyone really think that write "x triangle 2 above" (yup, it's a mess to write in ASCII) instead of x² or x^2 would make mathematics less intimidating to everyday people? 5. Having symbols, subscripts, prescripts, and superscripts above the symbol all strewn together is much more intimidating to anyone. 6. How do you nest them? Try to write down log_a(log_a(x)) to see what I mean. I enjoy 3B1B's videos in general, but this one really only makes sense if you don't think too much about it.
- agumonkey 3y ago
  I'm no math professional, and my struggled around some math topics was rarely notation, but 1) a bit of hidden information/culture (which can show in notation too) 2) a misalignment on what the topic was trying to achieve. The last bit which I can't describe clearly is 'maturity'. Sometimes an idea just eludes you for years, until it doesn't. Changing maths would probably not have fixed this. Oh, and the underlying human feelings behind the problem solving made by others. It seems that a lot of maths is lowering energy required to express or find a solution, no matter what subfield you work on, that seems to be the goal.
- simiones 3y ago
  1. The kth root of x being x^1/k would be written as this: k 1/k △x = x△ 2. I don't think these are as important. Also, ln x / log x is still the same or more symbols than `e△x`. 3. Not significantly more than parens in exponents. You also get rid of one level of parens from log. 4. Notation change is often a huge hassle, this is absolutely true. 5. Isn't this a problem for current notations as well? Especially if you ever want to put a complex expression for k in the k'th root notation. 6. log_a(log_a(x)) would be `a△(a△x) `. Still, I don't personally like the symbol. The biggest problem to me is that it requires smaller letters (subscripts/superscripts) all the time, which makes it more annoying to write than the regular notation for the base of an exponentiation and the argument of a log or root. Complex expressions in small letters are very annoying to me, and this notations makes it necessary to use them in all cases, where the normal notation at least has some cases where this is not needed.

by hashar 3y ago

smokel 3y ago

Note that the alternate notation was suggested by someone named "2'5 9'2" on the Mathematics Stack Exchange [1], and not by 3Blue1Brown. Obviously, this should not take away from the amazing educational work that 3Blue1Brown has achieved, but the honorary mention would probably suffice :) [1] https://math.stackexchange.com/questions/30046/alternative-notation-for-exponents-logs-and-roots https://math.stackexchange.com/questions/30046/alternative-n...

pranavjoneja 3y ago
He mentions in the video that he saw the idea in "a math exchange post" and he also has a link to the exact post in the video description. Doesn't that count?
- emiliobumachar 3y ago
  It does count as properly attributing the idea, yes. It doesn't count as having it. Possibly the Fields Medal suggestion assumed it was his?
- simiones 3y ago
  The point was that it's just not his invention. He attributes it extremely clearly, no one is accusing him of theft. But you don't get math prizes for presenting someone else's ideas.
  - hgsgm 3y ago
    Fortunately, you do. https://en.m.wikipedia.org/wiki/Leroy_P._Steele_Prize https://en.m.wikipedia.org/wiki/Leroy_P._Steele_Prize
a1o 3y ago
I agree with the comment that says this removes the personality of each function
- hgsgm 3y ago
  Why doesn't subtraction need personality?
  - Tainnor 3y ago
    I don't think there are many deep theorems about subtraction, but there are a lot of very deep theorems about powers (and polynomials), the exponential function and logarithm functions (especially in complex analysis).

raverbashing 3y ago

> immediately recognized the person: the author behind the 3Blue1Brown YouTube channel Yes, that is noted by the 3B1B in the title But yeah the asymmetry of operators in math is exhausting.

Turneyboy 3y ago

I'm a fan of his work but that's just not what Fields medals are for.

hfkwer 3y ago

I'm a math professor with about a decade of teaching math. On the list of things that make math intimidating, for undergrads at least, the notation for powers, roots, and log, is very low. The "proposal" also ignores that 1. The kth root of x is often denoted x^(1/k); 2. We have convenient shortcuts for the square root and the natural logarithm; 3. Parentheses become a mess; 4. The notation for squares, cubes, etc. is deeply entrenched; does anyone really think that write "x triangle 2 above" (yup, it's a mess to write in ASCII) instead of x² or x^2 would make mathematics less intimidating to everyday people? 5. Having symbols, subscripts, prescripts, and superscripts above the symbol all strewn together is much more intimidating to anyone. 6. How do you nest them? Try to write down log_a(log_a(x)) to see what I mean. I enjoy 3B1B's videos in general, but this one really only makes sense if you don't think too much about it.

agumonkey 3y ago
I'm no math professional, and my struggled around some math topics was rarely notation, but 1) a bit of hidden information/culture (which can show in notation too) 2) a misalignment on what the topic was trying to achieve. The last bit which I can't describe clearly is 'maturity'. Sometimes an idea just eludes you for years, until it doesn't. Changing maths would probably not have fixed this. Oh, and the underlying human feelings behind the problem solving made by others. It seems that a lot of maths is lowering energy required to express or find a solution, no matter what subfield you work on, that seems to be the goal.
simiones 3y ago
1. The kth root of x being x^1/k would be written as this: k 1/k △x = x△ 2. I don't think these are as important. Also, ln x / log x is still the same or more symbols than `e△x`. 3. Not significantly more than parens in exponents. You also get rid of one level of parens from log. 4. Notation change is often a huge hassle, this is absolutely true. 5. Isn't this a problem for current notations as well? Especially if you ever want to put a complex expression for k in the k'th root notation. 6. log_a(log_a(x)) would be `a△(a△x) `. Still, I don't personally like the symbol. The biggest problem to me is that it requires smaller letters (subscripts/superscripts) all the time, which makes it more annoying to write than the regular notation for the base of an exponentiation and the argument of a log or root. Complex expressions in small letters are very annoying to me, and this notations makes it necessary to use them in all cases, where the normal notation at least has some cases where this is not needed.