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Instead of isolated examples that happen to use math, would it make sense (or even be possible) to start a platform for visualization of mathematics? Something
by vinchuco 10y ago
Instead of isolated examples that happen to use math, would it make sense (or even be possible) to start a platform for visualization of mathematics? Something like context-augmented LaTeX. Not a computation engine (like mathematica or sage), but something closer to a github for math (visualization and exploration).
Consider how much time it took you to learn Gaussian elimination from a book or lecture vs how long it would take to see an animated example and then pick up the details.
Or consider how ambiguous mathematic notation can be [1].
So much of mathematics (purportedly the most structured knowledge produced by humankind) sleeps in mountains of unread journals and inside the brains (software) of mathematicians that are trained to do these visualizations on wetware.
It is a feature of math that these aren't hard-coded, as in the abstract one can conjure up any edits the imagination desires without the complex implementation details typically required by a computer. And in some cases a visualization (such as geometry) can be misleading and reduce generality [2].
However, there could be much to be gained by the majority from the hypothetical platform. Computation packages like mathematica only incidentally help visualize, as a byproduct.
Take for instance the videos by 3blue1brown [3]. Their appeal (and those in the parent link) is that they reduce the individual mental overhead and that a carbon copy of the visual is imprinted in the learner.
There is no punchline to this comment. And I'm certainly not an expert on the matter. I still find the 'movement' fascinating.
[1] https://jeremykun.com/2013/02/08/why-there-is-no-hitchhikers-guide-to-mathematics-for-programmers/ https://jeremykun.com/2013/02/08/why-there-is-no-hitchhikers...
[2] http://math.stackexchange.com/questions/743067/visually-deceptive-proofs-which-are-mathematically-wrong http://math.stackexchange.com/questions/743067/visually-dece... (not what I had in mind but this will do)
[3] http://www.3blue1brown.com http://www.3blue1brown.com
- deleted 10y ago[deleted]
- rawnlq 10y agoI think mathbox fits what you're describing: http://acko.net/files/pres/siggraph-2014-bof/online.html http://acko.net/files/pres/siggraph-2014-bof/online.html http://acko.net/blog/mathbox2/ http://acko.net/blog/mathbox2/
- dyarosla 10y agoWas just about to link that.