
Learning advanced math by drawing, playing with beach balls and knitting - lebanon_tn
https://www.smithsonianmag.com/innovation/what-knitting-can-teach-you-about-math-180969637?no-ist
======
dmreedy
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
Who is the author of the Mindstorms book? I see several different books with
this title.

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

------
nabla9
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)](https://en.wikipedia.org/wiki/Sheaf_\(mathematics\))

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

~~~
j2kun
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.

------
rrherr
“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](https://twitter.com/adam_chal/status/914207020215042048)

~~~
agumonkey
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.

~~~
wallflower
> 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://news.ycombinator.com/item?id=17271786)

[https://www.youtube.com/watch?v=JLfLSjbm4s8](https://www.youtube.com/watch?v=JLfLSjbm4s8)

~~~
agumonkey
never heard of it, thanks

------
stared
Yes, learning by playing!

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

------
dharma1
Is there a book full of this type of stuff that would be useful with young
children?

~~~
wallflower
Not exactly but YES!

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

[https://www.amazon.com/Steven-Caneys-Playbook-
Caney/dp/09111...](https://www.amazon.com/Steven-Caneys-Playbook-
Caney/dp/0911104372)

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...](http://3.bp.blogspot.com/_Zkz9la3e96c/SmyCb2oFfvI/AAAAAAAABtE/lWrkQ1IRKaU/s1600-h/six+pack+001.jpg)

~~~
iak8god
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...](https://www.amazon.com/Things-Make-Do-Fourth-Dimension-
ebook/dp/B00O2LM3LW)

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

~~~
vanderZwan
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](https://archive.org/details/AlanKeyD1987_2)

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

~~~
kolpa
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.

------
Someone
For knitting, I expected links to
[https://www.americanscientist.org/article/adventures-in-
math...](https://www.americanscientist.org/article/adventures-in-mathematical-
knitting), [http://scientificamerican.com/article/the-stunning-
symbiosis...](http://scientificamerican.com/article/the-stunning-symbiosis-
between-math-and-knitting-slide-show1/), or
[http://www.toroidalsnark.net/mathknit.html](http://www.toroidalsnark.net/mathknit.html)

~~~
jcl
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](http://www.theiff.org/oexhibits/oe1e.html)

------
mar77i
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...

------
User23
Dirac independently rediscovered the purl stitch.
[https://books.google.com/books?id=Su-k9Kld5ooC&pg=PA232&lpg=...](https://books.google.com/books?id=Su-k9Kld5ooC&pg=PA232&lpg=PA232&dq=paul+dirac+purl+stitch&source=bl&ots=dOJ0LRsoaR&sig=hc9ndZRxogoMhT1iEXttCK6Alpk&hl=en&sa=X&ved=2ahUKEwj03eS6-qbcAhUMUa0KHQnkDt8Q6AEwDHoECAMQAQ#v=onepage&q=paul%20dirac%20purl%20stitch&f=false)

------
internetman55
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.

------
PebblesRox
Reminds me of this Richard Feynman story:
[https://thinkingwiththings.wordpress.com/2012/03/16/richard-...](https://thinkingwiththings.wordpress.com/2012/03/16/richard-
feynman-and-womens-invisible-skills-22/)

------
geoalchimista
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.

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

~~~
geoalchimista
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.

~~~
Jtsummers
The author of the linked article _is_ a math professor.

Additionally, not all math is writing proofs. It's also applying their results
(a student doesn't need to _prove_ 2+2=4 to _use_ 2+2=4 in some computation)
and developing intuitions about the nature of mathematical objects (which can
then be used to guide future development by helping to discover new hypotheses
to prove).

~~~
geoalchimista
Fair enough. I didn't see the last line. I retract what I said earlier.

Still I am not very convinced that it is a good idea to teach STEM students
that way. The author of the article works at a liberal arts college.

~~~
adenadel
Lots of people falsely equate the liberal arts with the humanities. This is a
misconception that I try to fight in my in-person conversations with people.
Math, chemistry, physics, and biology are all liberal arts. Business,
engineering, nursing, and other types of professional training are not liberal
arts.

