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A better user interface for math (2011)

47 points by kevin 11y ago

yang140 11y ago
Thanks for sharing this post. Bret mentioned this in his "Media for thinking unthinkable" talk that Mathematical notation itself is a great tool for making mathematical structure visible. They are like user interface, it tell things that language can't express. The birth of mathematical notation is considered to be birth of modern mathematics. With dynamic media provided by computer, there should be a better way to dynamically represent mathematical structure. With that in mind, I would also recommend Evan Miller's comment's on Bret Victor's "Kill Math" article called "Don't Kill Math". Evan empathize that besides dynamic simulation, we should also embrace "theory and calculation" to see the underlying structure. http://worrydream.com/MediaForThinkingTheUnthinkable/ http://worrydream.com/MediaForThinkingTheUnthinkable/ http://www.evanmiller.org/dont-kill-math.html http://www.evanmiller.org/dont-kill-math.html
- jordigh 11y ago
  > The birth of mathematical notation is considered to be birth of modern mathematics. What does this mean? We've had some kind of mathematical notation ever since we've had mathematics. The Babylonian tablets with Pythagorean triplets had to use some sort of notation for the actual numbers: http://www.researchhistory.org/2012/10/24/earliest-evidence-of-pythagoras-theorem/ http://www.researchhistory.org/2012/10/24/earliest-evidence-... https://en.wikipedia.org/wiki/Babylonian_numerals https://en.wikipedia.org/wiki/Babylonian_numerals What do you consider notation and what is not notation?
  - alphydan 11y ago
    I think you're right that there was always notation. But perhaps he is referring to the birth of algebraic notation (the manipulation of symbols to represent unknown quantities). Although the roots of Algebra start in the middle east around the VIIIth century, the current notation doesn't really develop until the XIIIth or XIVth [0] [0] http://cerebro.xu.edu/math/math147/02f/algebra/algebra.html http://cerebro.xu.edu/math/math147/02f/algebra/algebra.html
    - jordigh 11y ago
      I don't know, I think that dismissing Diophantus or the Greeks as not being modern enough is a bit strange. After all, we still use the exact algorithm as Euclid for finding gcds. We simply don't state it in geometric terms like he did. I suppose if by modern mathematics one means algebra, then it's fair to place it somewhere in the 12th century.
tomsmeding 11y ago
Sounds like an awesome idea. I think that you're not the only one "good at math" that "sucks at arithmetic"; I think it's a common thing. :) For this to work out, there has to be someone with a real, intuitive vision on numbers who can actually explain it to someone else. I suppose that's the hard part. To start something, we've been using the decimal system for such a long time; would it maybe be interesting to research how other bases work out when taught to people, preferably children? That would quite hinder their progression in "normal", decimal arithmetic, though, so it would be quite unethical...
- mkesper 11y ago
  Maybe its effects would be vaguely comparable to bilinguality?
pdm55 11y ago
Nice video. I create similar diagrams with Geogebra, https://www.geogebra.org/ https://www.geogebra.org/. What I like about Geogebra is (1) it's free and (2) I can build interactive diagrams without having to do any computer coding. I encourage students in my Calculus and Statistics classes to use it to explore ideas for themselves.

47 points by kevin 11y ago

Thanks for sharing this post. Bret mentioned this in his "Media for thinking unthinkable" talk that Mathematical notation itself is a great tool for making mathematical structure visible. They are like user interface, it tell things that language can't express. The birth of mathematical notation is considered to be birth of modern mathematics. With dynamic media provided by computer, there should be a better way to dynamically represent mathematical structure. With that in mind, I would also recommend Evan Miller's comment's on Bret Victor's "Kill Math" article called "Don't Kill Math". Evan empathize that besides dynamic simulation, we should also embrace "theory and calculation" to see the underlying structure. http://worrydream.com/MediaForThinkingTheUnthinkable/ http://worrydream.com/MediaForThinkingTheUnthinkable/ http://www.evanmiller.org/dont-kill-math.html http://www.evanmiller.org/dont-kill-math.html

jordigh 11y ago
> The birth of mathematical notation is considered to be birth of modern mathematics. What does this mean? We've had some kind of mathematical notation ever since we've had mathematics. The Babylonian tablets with Pythagorean triplets had to use some sort of notation for the actual numbers: http://www.researchhistory.org/2012/10/24/earliest-evidence-of-pythagoras-theorem/ http://www.researchhistory.org/2012/10/24/earliest-evidence-... https://en.wikipedia.org/wiki/Babylonian_numerals https://en.wikipedia.org/wiki/Babylonian_numerals What do you consider notation and what is not notation?
- alphydan 11y ago
  I think you're right that there was always notation. But perhaps he is referring to the birth of algebraic notation (the manipulation of symbols to represent unknown quantities). Although the roots of Algebra start in the middle east around the VIIIth century, the current notation doesn't really develop until the XIIIth or XIVth [0] [0] http://cerebro.xu.edu/math/math147/02f/algebra/algebra.html http://cerebro.xu.edu/math/math147/02f/algebra/algebra.html
  - jordigh 11y ago
    I don't know, I think that dismissing Diophantus or the Greeks as not being modern enough is a bit strange. After all, we still use the exact algorithm as Euclid for finding gcds. We simply don't state it in geometric terms like he did. I suppose if by modern mathematics one means algebra, then it's fair to place it somewhere in the 12th century.

tomsmeding 11y ago

Sounds like an awesome idea. I think that you're not the only one "good at math" that "sucks at arithmetic"; I think it's a common thing. :) For this to work out, there has to be someone with a real, intuitive vision on numbers who can actually explain it to someone else. I suppose that's the hard part. To start something, we've been using the decimal system for such a long time; would it maybe be interesting to research how other bases work out when taught to people, preferably children? That would quite hinder their progression in "normal", decimal arithmetic, though, so it would be quite unethical...

mkesper 11y ago
Maybe its effects would be vaguely comparable to bilinguality?

pdm55 11y ago

Nice video. I create similar diagrams with Geogebra, https://www.geogebra.org/ https://www.geogebra.org/. What I like about Geogebra is (1) it's free and (2) I can build interactive diagrams without having to do any computer coding. I encourage students in my Calculus and Statistics classes to use it to explore ideas for themselves.