My Perspective On Category Theory: Past and Future

Рет қаралды 2,031

Күн бұрын

I reflect on how I got here, some exciting recent developments, and what I hope is going to happen in applied category theory over the next few years. Particularly, I give my view on the importance of visualization software and gamifying category theory for education in the future. Here are links to a few things I mention:
www.appliedcat...
disi.org/
www.theguardia...
discopy.org/
arrowtheory.co...
planting.space/
dragonbox.com/

Пікірлер: 24

@chineduecheruo8872 3 ай бұрын

I 100% agree, your visual explanations opened up Category theory for me. Thank you!

@RichardSouthwell 3 ай бұрын

I'm sure there are lots of other great pieces of software for visualizing category theory that I didn't mention. Catlab.jl for one. Please let me know about others in the comments

@factoral2645 Ай бұрын

your videos are great!

@RichardSouthwell Ай бұрын

@@factoral2645 thank you. So are you!

@CTMUSINGULARITY 3 ай бұрын

Hey Richard. Are you still interested in meeting?

@thomashall659 3 ай бұрын

This is welcome news! I've been thinking of ways to represent categories in a 3d game engine, where the player does their homework in an immersive setting. Originally I created some mock environments for representing concepts from the field of cognitive linguistics, where player does their linguistics homework with the help of machines in the environment. I would like to do this for categories as well. After watching your videos last year I was inspired for sure. The chalk board is great. My reference books are Lawvere/Schanuel and Awodey. My goal is to make accessible the insights from modern linguistics and mathematics. So thank you for posting this today and I will ping you back when I have something tangible deployed to Unreal or Unity game engines. Keep up the good work. Cheers, Thomas

@RichardSouthwell 3 ай бұрын

@@thomashall659 That sounds like it will be absolutely amazing

@RichardSouthwell 3 ай бұрын

Please send me an email richardsouthwell254@gmail.com if you want to discuss this idea further. A few people have expressed interest, so it'd be great for us all to virtually meet

@kamilziemian995 2 ай бұрын

Maybe one day I will learn category theory on the level that satisfy me. But, I still have problems with all concepts that cannot be formalized in standard set theory, because I want to have some good foundations for math. Maybe we will find such foundation in coming years?

@Absomet 3 ай бұрын

Richard where are you??? It's Jesse the crazy French guy! I've tried to contact you several times but non of my old adresses work! I have some really incredible stuff I wanted to tell you, and from the subject of this video, it even sounds like you're waiting for it! Please give me a link!

@RichardSouthwell 3 ай бұрын

Hey Jesse, I missed you man ! Here are a couple of email addresses richardsouthwell254@gmail.com and richard@planting.space Drop me an email, I look forward to chatting again

@moshecallen 3 ай бұрын

I've not YET worked through your videos on category theory. I fully intend to do so because they should help in the way I see my own research going, but first I need to actually get my Ph.D. in hand, which I'm expecting to get after this current term.

@RyanIsHoping 2 ай бұрын

Congrats!

@양익서-g8j 3 ай бұрын

재밌다

@dcmicore 3 ай бұрын

A big thanks for you videos, help a lot. Your book too. Sad I lost it in the train, silly me. Need to buy another one, but it really worth it. Even understanding how use category product, in real life, not for me. Maybe I'm to dumb, lol. Thank you.

@RichardSouthwell 2 ай бұрын

You can understand everything mate

@dcmicore 2 ай бұрын

@@RichardSouthwell Thank you.

@ayan849 3 ай бұрын

Many thanks Richard for teaching Category theory. I have been thinking on Category theory's possible applications in theory of evolution in general. There is a lot of ambiguity about what is the entity upon which natural selection works, many-to-one genotype to phenotype mappings etc.; degenerate mappings are at the heart of living systems in many ways. I feel that the relational perspective of category theory, especially the possibility of generalizing our singular notions of truth and false -- is the natural language in which theory of evolution must be written. On another note, I also feel that Categorical ideas can make a model of the 'subject' or 'observer' in science, which has been historically put outside the realm of science; through making the equations in physics "objective" or "frame invariant". This is the project envisioned by Jacques Lacan in his theory of subject and it's relation to language acquisition; we need a new language in science to talk about the subject, bringing in the role of history it it. I would love to get comments on these thoughts; whether they make sense at all.

@RichardSouthwell 2 ай бұрын

A lot of that makes a lot of sense to me

@444haluk 3 ай бұрын

Do you love math because someone gamified the math for you in the past? No. You love math because someone in the past cared about the nature of things like you do and did the most of the job for you.

@RichardSouthwell 3 ай бұрын

I hadn't thought of it that way. I played a lot of chess as a teenager, and I think it helped prepare me for maths. I could say school education or university research could be viewed as some kind of complex gamifications of maths, but your point is taken. Maybe the focus should not be so much on introducing kids (as in dragonbox), but just to introduce category theory in a systematic purely picture based way. There is too much expectation of mathematical maturity in current category theory teaching, and a self contained game based approach would help. It would allow many more people to get in to the subject who are less used to high abstraction. Think of the difference between playing suduko and learning the mathematics of latin squares

@avi3681 3 ай бұрын

@444haluk I didn't think Richard's main point was about gamification. He did talk about Dragon Box towards the end, but the main thread of it was the idea of making math more visual. A huge part of our brain is devoted to visual processing, so if we can harness this for mathematics it will definitely help. The experiment he mentioned from Bob Coecke seems to provide some direct evidence of this. Teaching high school students quantum mechanics using pictures, led them to perform as well on an Oxford QM exam as a graduate student in physics. I think many of the people who have enjoyed Richard's channel are people who might not have ever gotten into category theory if it wasn't for his many many pictures on the blackboard.