Awesome panel! Wish it went on a bit longer, but maybe it could be a more periodic thing? It would be really cool to watch something like a "Category Theory Show". i.e. listening to energetic people talk about various aspects of category theory (and answering questions from chat). Maybe even some friendly debate? I would definitely tune in for something like that!
Paul Dancstep is spot on. As a non-mathematician learning category theory speaking to different category theory mathematicians is like speaking to multiple language teachers. You need to research many sources and like Paul says 'triangulate' all the information to get to a point where you can peice it together to understand the key concepts.
This is a fantastic panel. I was introduced by stumbling to Pauls Universal library talk and have been able to apply it to my work in Artificial Intelligence and Computer Science where I think of relationships between entities. I would describe myself as very weak in Math, but find Category theory the most interesting subjects in Math and it has driven me to learn other maths. Thank you to all the panelists.
My exposure to "Category Theory" was from Algebra, Third Edition by MacLane and Birkhoff. Didn't understand a goddamn thing. Still don't understand a goddamn thing. I guess because my degrees are in molecular biology and not math.
I had done an undergraduate degree in math, and I didn't understand any of it until I did category theory ... and then I suddenly understood the whole of it 😝
missed it ... (navely ... ) Just an afterthought ... is what is being modeled here part of mathematical behavior or part of human behavior? add-ons: I think I see a 'C' connection in the sense that if there are existing libraries in C that do for all manner of things then it makes sense to track where these libraries are formally useful?
Mathematics is used to refine generalizations about human behavior which are not mathematical. It can also be used for models. A hot thing is networks and simplicial complexes. Anyways, What is being made when the model is made is a hom-set between concept and reality. Let’s say your model is genuinely replicating human behavior. while it is a mathematical object which models humans it is a product of your labor. It is not surprising that the characteristics required to model humans are transferred to the structure of models by labor. These ultimately come from humans and their actual activity. These models are just a fancy way of talking about ourselves, plural inclusive. So it is really up to the modeler how good it will be. I know this isn’t a direct answer and is more of a philosophical rant. Hope its not annoying.
@@aaAa-vq1bd Yes, this I understand. What was in my mind regarding my comment is the tactic "if you need to prove something just find an isomorphism" And so any analysis of mathematical models is likely to highlight a strategy of "finding an isomorphism' And yes, Math is a human construct. Does math exist where humans do not exist?
@@aaAa-vq1bd It definitely is not received as a rant and it is comforting that a person other than myself considers such things as wonders if wonders are what they are. Some ponderings: does ai (or maybe iterative ai) have the potential to de-humanize the analysis and conclusions? And if so, what philosophical and/or mathematical basis is the ai iterating to? Can this step be considered evolutionary? Plus! a random thought thrown in based on uncanny events in math such as Leibniz and Newton discovering a land round about the same time. Is the universe telling us what is important and humans are ready to research into? Maybe like the way the universe (okay local universe) influences hunters to hunt in certain directions and places. Really a dialogue with what humans perceive is not one sided monologue but a many sided dialogue. For example: can I say I found something on an internet search engine or is it better to say "look what an internet search engine regarded as worthy of my attentions?"
Awesome panel! Wish it went on a bit longer, but maybe it could be a more periodic thing? It would be really cool to watch something like a "Category Theory Show". i.e. listening to energetic people talk about various aspects of category theory (and answering questions from chat). Maybe even some friendly debate? I would definitely tune in for something like that!
Bartosz Milewski had also made a great contribution to getting into the area, through his blog, book, and videos ... Category Theory for Programmers.
I'd say he's had the most impact!!!!
Amazing that he can make it accessible while still retaining rigor.
Yes he has, really influential, to me at least shout out to Bartosz
34:00 I agree that the people on math stackexchange are absolutely hostile.
15:30 "One doesn't so much learn Category Theory, as absorb it over a period of time". Richard Bird. 🔥
Paul Dancstep is spot on. As a non-mathematician learning category theory speaking to different category theory mathematicians is like speaking to multiple language teachers. You need to research many sources and like Paul says 'triangulate' all the information to get to a point where you can peice it together to understand the key concepts.
Thanks for posting this video. It’s great that you guys are trying to grow category community.
Mathematicians are the most susceptible to ideological possession.
It's worrying how much Eugenia wants mathematics to be political.
Yeah. I cought on to that as well.
More Category Theory and less Calculus! 😝
This is a fantastic panel. I was introduced by stumbling to Pauls Universal library talk and have been able to apply it to my work in Artificial Intelligence and Computer Science where I think of relationships between entities. I would describe myself as very weak in Math, but find Category theory the most interesting subjects in Math and it has driven me to learn other maths. Thank you to all the panelists.
My exposure to "Category Theory" was from Algebra, Third Edition by MacLane and Birkhoff. Didn't understand a goddamn thing. Still don't understand a goddamn thing. I guess because my degrees are in molecular biology and not math.
I had done an undergraduate degree in math, and I didn't understand any of it until I did category theory ... and then I suddenly understood the whole of it 😝
Thank you!!
A lot of good people on Twitter too, with maths / maths adjacent areas of interest (for following and / or asking qns)
missed it ... (navely ... )
Just an afterthought ... is what is being modeled here part of mathematical behavior or part of human behavior?
add-ons: I think I see a 'C' connection in the sense that if there are existing libraries in C that do for all manner of things then it makes sense to track where these libraries are formally useful?
Mathematics is used to refine generalizations about human behavior which are not mathematical. It can also be used for models. A hot thing is networks and simplicial complexes. Anyways,
What is being made when the model is made is a hom-set between concept and reality.
Let’s say your model is genuinely replicating human behavior. while it is a mathematical object which models humans it is a product of your labor.
It is not surprising that the characteristics required to model humans are transferred to the structure of models by labor. These ultimately come from humans and their actual activity.
These models are just a fancy way of talking about ourselves, plural inclusive. So it is really up to the modeler how good it will be.
I know this isn’t a direct answer and is more of a philosophical rant. Hope its not annoying.
@@aaAa-vq1bd Yes, this I understand. What was in my mind regarding my comment is the tactic "if you need to prove something just find an isomorphism"
And so any analysis of mathematical models is likely to highlight a strategy of "finding an isomorphism'
And yes, Math is a human construct. Does math exist where humans do not exist?
@@aaAa-vq1bd It definitely is not received as a rant and it is comforting that a person other than myself considers such things as wonders if wonders are what they are.
Some ponderings:
does ai (or maybe iterative ai) have the potential to de-humanize the analysis and conclusions?
And if so, what philosophical and/or mathematical basis is the ai iterating to?
Can this step be considered evolutionary?
Plus! a random thought thrown in based on uncanny events in math such as Leibniz and Newton discovering a land round about the same time. Is the universe telling us what is important and humans are ready to research into? Maybe like the way the universe (okay local universe) influences hunters to hunt in certain directions and places. Really a dialogue with what humans perceive is not one sided monologue but a many sided dialogue. For example: can I say I found something on an internet search engine or is it better to say "look what an internet search engine regarded as worthy of my attentions?"
!!