from Hacker News

Learning advanced math by drawing, playing with beach balls and knitting

by lebanon_tn on 7/17/18, 12:11 PM with 41 comments

  • by dmreedy on 7/17/18, 3:37 PM

    If this subject is interesting to you, and you haven't read Mindstorms yet, I cannot recommend it enough. The entire book is an exploration of the significance of mental models in learning.

    A quote from the opening:

    'BEFORE I WAS two years old I had developed an intense involvement with automobiles. The names of car parts made up a very substantial portion of my vocabulary: I was particularly proud of knowing about the parts of the transmission system, the gearbox, and most especially the differential. It was, of course, many years later before I understood how gears work; but once I did, playing with gears became a favorite pastime. I loved rotating circular objects against one another in gearlike motions and, naturally, my first "erector set" project was a crude gear system. I became adept at turning wheels in my head and at making chains of cause and effect: "This one turns this way so that must turn that way so..." I found particular pleasure in such systems as the differential gear, which does not follow a simple linear chain of causality since the motion in the transmission shaft can be distributed in many different ways to the two wheels depending on what resistance they encounter. I remember quite vividly my excitement at discovering that a system could be lawful and completely comprehensible without being rigidly deterministic. I believe that working with differentials did more for my mathematical development than anything I was taught in elementary school. Gears, serving as models, carried many otherwise abstract ideas into my head. I clearly remember two examples from school math. I saw multiplication tables as gears, and my first brush with equations in two variables (e.g., 3x + 4y = 10) immediately evoked the differential. By the time I had made a mental gear model of the relation between x and y, figuring how many teeth each gear needed, the equation had become a comfortable friend.'

  • by nabla9 on 7/17/18, 5:16 PM

    I can learn to understand basics of many advanced concepts outside engineering math to the level where I can read/skimp some research papers and understand the thinking behind it. But it's very hard to recognize the concept on my own and the utility 'on the wild' unless someone else is pointing it out and explains it.

    Take for example Sheaf[1]. The basics are not that hard if you spend some time. But once you have learned it in abstract. Can you see use for it [2] in data analytic, signal processing, or machine learning? How long you have to work for it to really click to the point where you can see and utilize the concept?

    I think this is the reason why mathematicians are needed more in every area. They should walk around pointing things out.

    [1]: https://en.wikipedia.org/wiki/Sheaf_(mathematics)

    [2]: http://www.drmichaelrobinson.net/20131024_overview.pdf

  • by rrherr on 7/17/18, 1:07 PM

    “Me before #strangeloop: I'm not a real programmer unless I know Haskell

    Me after #strangeloop: I'm not a real programmer unless I knit”

    https://twitter.com/adam_chal/status/914207020215042048

  • by stared on 7/17/18, 3:33 PM

    Yes, learning by playing!

    A collaborative science-based games list: https://github.com/stared/science-based-games-list/ (and its discussion: https://news.ycombinator.com/item?id=14661813)

  • by dharma1 on 7/17/18, 2:11 PM

    Is there a book full of this type of stuff that would be useful with young children?

  • by danharaj on 7/17/18, 1:36 PM

    I knew a grad student who used a ball of yarn to learn knot theory.

  • by Someone on 7/17/18, 2:45 PM

  • by mar77i on 7/17/18, 4:19 PM

    I liked mathematics, but nobody got me to crave it like Vihart. That Youtube legend covers complex mathematics like no one else. The teaching method introduced in the article spontaneously reminded me of her chaotically creative ways...

  • by User23 on 7/17/18, 8:20 PM

    Dirac independently rediscovered the purl stitch. https://books.google.com/books?id=Su-k9Kld5ooC&pg=PA232&lpg=...

  • by internetman55 on 7/17/18, 4:21 PM

    I think the way you learn advanced math is going to class, reading a textbook, reading a paper, going to a talk, talking to a friend, etc.

  • by PebblesRox on 7/17/18, 2:40 PM

    Reminds me of this Richard Feynman story: https://thinkingwiththings.wordpress.com/2012/03/16/richard-...

  • by geoalchimista on 7/17/18, 6:33 PM

    Title is clickbait. Whatever you can learn from "drawing, playing with beach balls and knitting" is most likely not advanced math. (Otherwise professors in a math department would all be playing knitting and beach balls to get tenure.) Advanced math is hard. It is like toiling in the field under a scorching sun.

    Edit: Didn't see that the author of the article is a math professor. This method seems to work in a liberal arts college, but I doubt it would work in a STEM curriculum.