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

https://www.smithsonianmag.com/innovation/what-knitting-can-teach-you-about-math-180969637?no-ist

by lebanon_tn • 8 years ago

209 39 8 years ago

smithsonianmag.com

rrherr• 8 years ago

“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

vanderZwan3• 8 years ago

Same, but #joyofcoding. And apparently, Jon Skeet agrees[0].

[0] https://twitter.com/jonskeet/status/1005458230401748992

agumonkey2• 8 years ago

This depresses me, because there's a strange .. loop in society where people thinks advance means unaccessible and university lab only. Where in fact most concepts are uber 'simple' in form and can be explored quite easily. Similarly there was an article about J. Bose early radio research where you could see polarizing filters made out of a book with metal foil interspersed. I really feel bad about the distorted reality people live in.

wallflower2• 8 years ago

where you could see polarizing filters made out of a book with metal foil interspersed

A tangent. In case you missed the amazing documentary "Magic, Art, and Scanimation", it is all about the iterative process of "making" magic through hard work, creativity, and insight.

https://news.ycombinator.com/item?id=17271786

https://www.youtube.com/watch?v=JLfLSjbm4s8

s-shellfish• 8 years ago

We all live in distorted realities. Lots of people in laboratories think for part of the time, you need to be in those environments to be in sync with the research, because it's an active movement of pieces playing out and involves a dynamic that goes deeper than what research comes out through the surface, what gets published.

Many concepts are super simple once they've been absorbed by culture to the point that you can learn by osmosis. It's not the same clarity as coming to a conclusion without the awareness existing initially.

My dilemma often is, for some concepts such as math, computation, you can't really prove where such concepts originate from, or whether they exist independent of the human mind and are instead, discovered over time. The obvious implication being that some concepts may exist in some minds outside of the laboratory, and then what is the purpose of doing such research?

The reason often comes down to the fact that someone is funding you to be there 40-80 hours (or more, depends on how much sleep you need) a week doing nothing else. That's a lot of time to focus on just those things, and I honestly think that makes, not just a big difference, but THE difference, between who gets there first. Because otherwise, you have to be focused on other things, that might not be directly tied to whatever research concepts you may want to discover independently.

Concepts become uber simple because people work hard to spread them out and make them easily understood. There's a counter argument to this that you should also be able to decide whether you want to be influenced by those concepts, but that's just living life. I imagine a lot of people who are not interested in super simple concepts have some aversion to them that could be very valid. It doesn't make them less intelligent, it's just something you wouldn't understand unless you experienced the particular dynamic. Distorted realities indeed. We all have them.

contravariant• 8 years ago

Every so often I'm reminded of why the first computers were based on weaving machines.

kolpa4• 8 years ago

Obviously a place called Strange Loop is going to biased towards knitting and biased away from Haskell.

https://en.wikipedia.org/wiki/Loop_knitting

https://stackoverflow.com/questions/21505192/haskell-program...

danharaj• 8 years ago

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

vanderZwan3• 8 years ago

It is quite interesting how our brains tend to deny the role of the rest of our body in the process of thinking. After seeing Alan Kay's "Doing With Images Makes Symbols", and his TED Talk "a poweful idea about ideas", I realised how silly that line of thinking was[0].

Using the right things to fiddle with physical manifestations of an idea lets "my hands" think along the more "abstract" parts of my brain. And doing that kind of parallel work is actually very useful.

[0] https://archive.org/details/AlanKeyD1987_2

[1] https://archive.org/details/AlanKay_2007

kolpa4• 8 years ago

Brains think brains are the best problem-solvers.

Eyes see eyes as the most beautiful part of the body.

Skin feels that skin is the best part to touch.

dharma1• 8 years ago

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

wallflower2• 8 years ago

Not exactly but YES!

One of my favorite books is Steven Caney's "Play"

https://www.amazon.com/Steven-Caneys-Playbook-Caney/dp/09111...

From an older edition, one of many projects was making a hammock out of old 6-pack rings. For many years, the plastic used in these rings is designed to degrade, but at the time the book was written it would have worked.

http://3.bp.blogspot.com/_Zkz9la3e96c/SmyCb2oFfvI/AAAAAAAABt...

iak8god• 8 years ago

Matt Parker's "Things to Make and Do in the Fourth Dimension" is a good one too: https://www.amazon.com/Things-Make-Do-Fourth-Dimension-ebook...

kolpa4• 8 years ago

https://csunplugged.org is not exactly but might be nice.

j2kun3• 8 years ago

not a book, but Tadashi's Toys http://www.msri.org/web/msri/public/tadashis-toys

vanderZwan3• 8 years ago

https://naturalmath.com/

(The PDFs are pay-what-you-want and Creative Commons licensed)

PebblesRox• 8 years ago

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

Someone• 8 years ago

For knitting, I expected links to https://www.americanscientist.org/article/adventures-in-math..., http://scientificamerican.com/article/the-stunning-symbiosis..., or http://www.toroidalsnark.net/mathknit.html

jcl• 8 years ago

Reminds me of crocheted hyperbolic surfaces, which make it easier to visualize some less-intuitive properties of hyperbolic geodesics:

http://www.theiff.org/oexhibits/oe1e.html

stared• 8 years ago

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)

dmreedy• 8 years ago

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.'

tmaly• 8 years ago

Who is the author of the Mindstorms book? I see several different books with this title.

ragazzina• 8 years ago

I think it's Seymour Papert. Mindstorms: Children, Computers, and Powerful Ideas, 1980, ISBN 0-465-04674-6

mar77i• 8 years ago

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...

internetman55• 8 years ago

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.

nabla9• 8 years ago

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

j2kun3• 8 years ago

Oh, if only I could make a career of pointing math things out :)

Joking aside, I think a lot of researchers will oversell the applications of their technology, so it's just as important to be able to recognize when a particular math thing will help, and when it's more harm than good. The first rule of statistics is: if the decision maker already has their heart set on a particular action, you shouldn't waste your time and money designing a statistical study with fancy tests and inference techniques.

geoalchimista3• 8 years ago

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.

kolpa4• 8 years ago

I'll defer to the math professor on this one.

geoalchimista3• 8 years ago

I'd be curious to see what a math prof would have on this.

But IMHO, math is learned by writing proofs. That is the only solid way for building an understanding.

j2kun3• 8 years ago

It depends on your goals. Much of mathematics is training for specific goals (often narrow), while if your goal is simply to be exposed to many different things, you can get quite a lot of the intuition with knitting needles and drawings.

As a mathematician and engineer, I bet this class is more like a "film history" class than a "principles of optics" or "CGI techniques" course.

sitkack• 8 years ago

Otherwise professors in a math department would all be playing knitting and beach balls to get tenure.

Your hyperbolic statement is not an argument.

User23• 8 years ago

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

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

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