Hi, thank you for all your Category Theory videos/talks. Comment about the arrow composition notation that had me confused a bit, then realised that when using “fat semi-s” as in f ; g, they should be read as “g follows f” instead of “f follows g” . Which is how I initially learned to read composition notation from other resources, when combining arrows using circle notation f o g. Seeing the Unital identity composition rule (44:35) using fat semi-s and I thought it had mistakenly been written backwards, but it was my thinking that was reversed. I suppose, one example of many ways Category Theory is great for exercising mental agility. Thanks again 👍
I know it's an old video, but I just wanted to thank you for posting it. Got me to understand a little more about CT. One thing though: Whenever it's about commutativity you'd say "communitive".
@2:45 no mate. That is a common misconception . What separates humans from other animals (by a huge chasm) is higher order symbolic reference language, which is totally different to primitive language. Terrence Deacon ham-fisted wrote about this, but ordinary people can grok the gist of it if I say it is about mental capacity to think in terms of abstractions, that is, "objects" (and relations between them) that have absolutely no physical meaning (or need not have any physical meaning). _No other species we know_ can do this. But _every_ moderately intelligent species on Earth can associate symbols to physical objects or material needs or desires (first-order symbolic reference).
There are two sets that are both standardly called the natural numbers: the positive integers and the non-negative integers. Depending on the context, 0 may or may not be included.
This is really good. I love that there is a bit of history, and well explained motivations. PS. Could have even more history of category theory, or maybe there is a separate talk about that?
I've watched a few videos about category theory, and for the first time, I feel like I have a glimmer of understanding. Thank you!
I have never learned this much in one sitting. EVER. Super basic and super good. :) This is pure gold.
Kant said of Hume that he wakened him from his dogmatic slumber. David... you awakened me from my dogmatic blunder.
Hi, the equivalent of Kant
David, thank you so much! Best CT intro I’ve seen. Off to part 2...
Hi, thank you for all your Category Theory videos/talks. Comment about the arrow composition notation that had me confused a bit, then realised that when using “fat semi-s” as in f ; g, they should be read as “g follows f” instead of “f follows g” . Which is how I initially learned to read composition notation from other resources, when combining arrows using circle notation f o g. Seeing the Unital identity composition rule (44:35) using fat semi-s and I thought it had mistakenly been written backwards, but it was my thinking that was reversed. I suppose, one example of many ways Category Theory is great for exercising mental agility. Thanks again 👍
I know it's an old video, but I just wanted to thank you for posting it. Got me to understand a little more about CT.
One thing though: Whenever it's about commutativity you'd say "communitive".
@2:45 no mate. That is a common misconception . What separates humans from other animals (by a huge chasm) is higher order symbolic reference language, which is totally different to primitive language. Terrence Deacon ham-fisted wrote about this, but ordinary people can grok the gist of it if I say it is about mental capacity to think in terms of abstractions, that is, "objects" (and relations between them) that have absolutely no physical meaning (or need not have any physical meaning). _No other species we know_ can do this. But _every_ moderately intelligent species on Earth can associate symbols to physical objects or material needs or desires (first-order symbolic reference).
holy moly. you just opened a rabbit hole for me
Do you have pdf notes or slides that we can refer to?
Part 2: Applied CT tutorial, th-cam.com/video/eIjPxaFbEeg/w-d-xo.html
Great lecture, thanks, David. Is there a way to get a copy of the slides?
I would love to have them too. I agree with J. Williams that this is a really good intro to CT.
They are here:
www.dspivak.net/talks/FRA-Tutorial--part1.pdf
www.dspivak.net/talks/FRA-Tutorial--part2.pdf
Amazing video!
On slide 9 you refer to the number 0 as a natural number. But the natural numbers begin at 1. What’s up with that?
There are two sets that are both standardly called the natural numbers: the positive integers and the non-negative integers. Depending on the context, 0 may or may not be included.
This is really good. I love that there is a bit of history, and well explained motivations. PS. Could have even more history of category theory, or maybe there is a separate talk about that?