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.
Learning advanced math by drawing, playing with beach balls and knitting
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Re: Learning advanced math by drawing, playing with beach balls and knitting
#22“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
I remember watching my girlfriend and friend crocheting together once then they explained to me how the patterns work. I was blown away, it was exactly like programming, different stitches formed groups that were used as bigger pieces to create the finished product. Each stitch was kind of like the basic types of a programming language, the different stitch groups were like functions and the pattern itself was the finished program. Even the most complicated designs could be broken down into different repeating combinations of stitches. It also reminded me a bit of writing music. The way groups of notes are used to form chords or riffs which are grouped into repeating bars to form a song.
Re: Learning advanced math by drawing, playing with beach balls and knitting
#23“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
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 real…
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.
Re: Learning advanced math by drawing, playing with beach balls and knitting
#24I 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.
Re: Learning advanced math by drawing, playing with beach balls and knitting
#25Is there a book full of this type of stuff that would be useful with young children?
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...
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...
Re: Learning advanced math by drawing, playing with beach balls and knitting
#26“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
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...
Re: Learning advanced math by drawing, playing with beach balls and knitting
#27Title 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.
Re: Learning advanced math by drawing, playing with beach balls and knitting
#28I knew a grad student who used a ball of yarn to learn knot theory.
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…
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.
Re: Learning advanced math by drawing, playing with beach balls and knitting
#29Is there a book full of this type of stuff that would be useful with young children?
https://csunplugged.org is not exactly but might be nice.
Re: Learning advanced math by drawing, playing with beach balls and knitting
#30Title 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 liber…
I'll defer to the math professor on this one.