The joy of abstract mathematical thinking - with Eugenia Cheng
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- Опубликовано: 2 июл 2024
- Category theory is an abstract branch of mathematics - but did you know it can be both fun, and extremely useful for everyday life?
Watch the Q&A here: • Q&A: The joy of abstra...
Buy Eugenia’s book here: geni.us/GBfELuE
Watch this clear and engaging talk on category theory, as Eugenia sheds light on how her speciality can be applied to many different areas of life, including inequalities, current events, and day to day living.
This talk was recorded at the Ri on 5 April 2023.
00:00 Introduction
06:54 What is category theory?
18:30 What is abstraction?
25:41 Why is context important in mathematics?
33:04 Relationships between things
41:21 Categories - history and definition
50:08 Conclusion
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Dr Eugenia Cheng is a mathematician, educator, author, public speaker, columnist, concert pianist and artist. She is Scientist In Residence at the School of the Art Institute of Chicago. She won tenure in Pure Mathematics at the University of Sheffield, UK and is now Honorary Visiting Fellow at City, University of London. She has previously taught at the Universities of Cambridge, Chicago and Nice and holds a PhD in pure mathematics from the University of Cambridge. Alongside her research in Category Theory and undergraduate teaching her aim is to rid the world of “math phobia”.
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Erik Meijer's talk on using computer programming as an abstraction layer for mathematics was enlightening, showing how it can turn abstract mathematical concepts into interactive lessons for children. This method not only cultivates a deeper understanding of mathematics but also sparks interest and motivation in learning the subject.
Could you provide a link or a title? He has done a lot of talks!
Was it a Royal Institute talk or was it giving for another organization?
I love hearing someone competent coherently express ideas that have been stewing less coherently in my own mind for years. I disliked math until someone taught me elementary algebra somewhat as the speaker suggests, and when I learned more about the general idea of a function, lots of other things started making sense. I learned a bit about what a number is from Strang's lecture proving that e is a number. Linear algebra helped with all kinds of things, including the concepts of distance, metrics, norms, the triangle rule, and inductive proofs. When I started realizing that students learn better when you start introducing some of these concepts at an earlier stage in their education, I began teaching my 9th grade class in ancient history about the nature of abstraction, using the examples they were learning in their class in geometry, as well as things like logic gates, art, and scientific simulations. I am sure some of it was not absorbed by all of them, but they all got some of it, and some got a lot. I wish my teachers had known what the speaker knows and taught the way she teaches. Brava!
Thanks for making mathematics live, Dr. Cheng!
Dr. Eugenia Cheng is such an impressive communicator of what is a difficult subject that she actually makes it intuitive. Complexity is difficult to understand, such as biology that can be difficult to explain. When we consider biological systems the function of a cell is often regarded as the starting point to understand complexity of biology, as opposed to the relations of the cell to other biological components that make up the whole organism. For example, most of us are wired to consider the function of the immune system as a discrete binary activity that identifies what is ok and what is a pathogen and therefore "bad" - but what if as philosopher Thomas Pradue suggests, we consider the relations that the immune system has with other things like the microbiome, and its role in immunology - are the relations more important or the functions? The ability to abstract the relations to unravel the complexity associated with immunology and other complex systems is unbounded. Abstraction as philosopher William James promoted is an approach to progress science as long as we are aware that we are abstracting. Very thought provoking presentation - thankyou Eugenia.
Love the info. this channel brings all the time!
The way she talks is mesmerizing, I could listen to another three hours of this
She is a very compelling speaker. I think this is the second or third talk by her and every time its educational and enjoyable
Loved this lecture so much! More like this please ♥️
this was superb! thanks
TED Talks back on track :)
Sometimes I believe learning has more to do with a personal connection with the teacher. I have failed a few courses in my time. The material just didn't make sense to me when I was learning it. Somehow I would do much better in the same course after retrying it with a new teacher. Teachers come with their own problems and personalities, too. Perhaps I was simply a bad student. I won't rule out that possibility.
Most teachers are honestly pretty bad. It's not easy and we don't appreciate great teachers enough.
@@infectedrainbow And the system makes it difficult for teachers to be good - they don't provide the resources necessary heh
Yes. I've been saying for years, as an educator but not as a mathematician, that we teach mathematics not because it applies to daily life, but because it doesn't. The ability to step out of concrete reality into abstract reasoning is a uniquely human skill. While someone might not use the formulae they learned in secondary school, they can use the skill of thinking logically, constructing proofs, rejecting false answers and so on.
Thanks for this much more sophisticated take from an actual mathematician's perspective.
Thank you, RI. I really appreciate your videos.
Found this talk to be informative, enlightening, witty and engaging. Thank you from Wisconsin, USA.
Amen! Lori Park from BOSTON. ✝👌
Cudahy Wisconsin...hi!
That was wonderful, thankyou.
This video was very illuminating to me. Thank you, Eugenia Cheng and the Royal Institute!
‘There is only truth relative to context ..’ .. Fantastic! 👍
Absolutely. 'And which I will demonstrate by showing these familiar relationships in a new context..'
Wittgenstein would be amused I'm sure.
Incredibly satisfying in a slightly weird way.
I sometimes wonder whether having mathematical abstract thinking skills is a curse in today's world.. Thanks for the great lecture.
I find most people don't understand the advantages of viewing real processes through an abstract lens.
They think it's too vague and detached from the real processes - but they don't realise that because they're so focused on the details they can't see the forest for the trees, while the abstract approach provides a bird's eye view from which you can delve into the details while maintaining a clear concept of the whole system.
In programming particularly, from the abstract view it becomes clear that it's all just functions transforming information - objects and arrows between objects
@@orterves a dumb question: is category theory a object oriented mathematics ?
Wow! This talk was just AMAZING! I am studying math in grad school right now and I can't even describe how she opened my eyes to so many possibilities. I might change fields lol Thank you so much Dr. Cheng!
Well, trigonometry helps a lot in daily life. Most of the time intuitive. Math to me it the lenguage of nature and the only lenguage where a monologue makes sense.
i disagree with the monologue thing, i think monologues make sence in every language, and i think mathematics is maybe the most colleberative language of all, because it is the only language where we extensively fiddle with the natural way the language is created together to make it more intuitive. in a sense mathematics is a self awere language, wich in my eyes makes it more colleberative because it is something we are willingly participating in.
this idea of mathematics as a lonesome activity is a bit harmfull to it i believe, because it plays into the steriotype of the loner mathematician person
What a terrific lecture. R.I. at its best.
Loved 42:00 onwards, genius.
And no notes.
(Also - fonts where uppercase I and lowercase l are the same, seriously should be illegal.)
This is why I have always loved math but I didn’t like math in school. I have been engaging in these things without a name for them all my life. This is my first intro with Eugenia and she seems amazing.
Off topic, I know, but I liked the optical illusion at 30:28 where, if you scan the black dots, some seem to transiently have white centres.
great talk
What a fantastic speaker!
Agreeable abstractions are the soul of every peace treaty.
Love it!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
I had the same problem. Complex number were 11th in one board and 12th in another board and learning by yourself was not allowed. Did not understand why.
What an important lecture.
After seeing this... I think category theory is the best discipline in mathematics that exists for I love to think in analogies👌
Charming and illuminating. I would like to be able to take a maths course from someone who could help you bump up a level or two in your understanding of this beautiful field.
How if the past present and future determine to the flow of seconds, how do we measure it ? It by its shape and size?
I just bought her book and started reading it as part of my research I am doing to develop a graphical Universal Modeling Language that I am calling UniML.
As I read through her book it is becoming clear to me that what I am attempting to do with UniML is not all that different from Category theory, only is approaching it from the direction of developing a graphics notation that can be used by things like category theory to describe itself.
BTW, I have made a number of videos on UniML and uploaded them to my RUclips channel that describes it in more detail, albeit that this is still a work in progress and not a finished product in that the design is still in a state of flux.
But I am finding her book really helpful in providing many good Use cases to examine as well as providing concepts that are helpful in refining its design. And that is one of the reason I bought it to begin with, thinking that might turn out to be the case, which I am glad to see, that it indeed is!
It is never trig or calc that is the problem. A teacher digressed into baseball stats, causing loss of interest immediately,
as i was interested in the physical dynamics of surfing, ballet, and actual kinetic sports, which require a lot of appraisal - thinking about energies and vectors.
Complex dynamical systems occur in every observable association, and some mathematical understanding of this is essential.
Should you pursue Eugenia's processes you WILL find that you learn physical, social, and other skills more quickly.
And, recognizing her name just now, i realize she authored a book - "The Art of Logic in an Illogical World" , which sounds like an important read; I found it lying on my bed, neglected in the arousals of war and dispute!
I KNEW I was right that there have to be book like this
Those circle drawing compasses were weapons because of the pointy side
I agree that the progression of how we teach math is very, very flawed and with the wrong teacher, amazing scholars can get turned away from subjects that they would be great at.
I love this topics and will keep it to explain others what I do in my job. Very simple explanation! By the side, that we do not use trigonometry in daily life, or some other aspects of school maths, I'd like to disagree with this. We always try to apply all new concepts in our home to support our children. The sad thing is that teachers should actually do it.
Can I buy tickets to attend these talks, or are they invite only? They always seem half-empty. Amazing talk
You can certainly buy tickets to come to our historic Theatre, and we'd love to see you! You can book tickets to all of our in-person and livestreamed events here on our website: www.rigb.org/whats-on
Wow, Eugenia is just a breath of fresh air to me. Loved this!
The cultist infecting math with propaganda is refreshing?
Hi Eugenia Cheng. Please use more hand gestures as you deliver. I observed hand gestures less than 20% of the time. Try for 90% of the time - smaller varied gestures work well.
as or more fun than any game you can play i can atest at times.
This lady should be employed by the government of the day. To inspire kids to enjoy maths.
She is the joy
It is not what I expected, the title is about abstraction but rarely explains abstraction, rather than some mathematical problems.
I wish i saw this 15 years ago
Lucid. Tempted to buy that yellow book but scared it will be lot of work to understand
She’s talking about the truth but without accepting the lies
In maths ther are only two numbers zero and one and only two oprations addition and division ..and that is true in daily life .. all others are theories
I differ. Everytime a kid solves a word problem they should be told they actually conducted a physics experiment. Then they do not have to read books like unreasonable effectiveness of mathematics in universe.
Cool way to think about imagination .
I still don't understand why the super rich non male is seen as below the super rich male? Surely it could be reversed and show super rich non male to super rich male below if we abstract the terms as A,B,C? This example seems subjective rather than objective.
Yes you can. The point of category theory is you can replace any example with another with equivalent structure. The subject matter is irrelevant. But it is clever teaching to nudge people into coming up with alternatives when they don’t like the example. I’m sure she does that with her students.
@@numericalcode It's postmodern propaganda infecting math
Fun way of thinking! Not to directly bash this talk, so many talks now are just powerpoint and lecture. I was fully focused and absorbing but I feel the human mind needs props to really set thoughts in memory. I applaud the gray jacket at the beginning that had a pouch. She attended a conference, mars? with really intelligent attendants and she spung it into a Cat theory exercise.
I used to give the 2 bananas and 2 apples example from a decade
I've never heard it called Taxi-cab distance. I've always known it as the manhattan distance.
One of the things Manhattan is known for: taxis.
You learned something new
Volume was low on this video.
In the words of Public Enemy: "turn it up!"
No two points have same characteristics
Latency exists between the knowledge attained, and the knowledge yet to be obtained, which create microscopical waves of knowledge which propagate from the origin points created through communication lanes.
The intersection of category theory and set theory = modern politics.
This is what the British students need, really great scholars who actually understand UK students, their understanding that all of us are different is amazing.
None of those i, i ,i or you don’t understand because I’m so more intelligent are present, not condescending but just really really interesting.
Even the word maths is pronounced correctly instead of that awful bastardisation.
We require more and more to be as infused and interested in this amazing science such as this wonderfully gifted and honoured speaker....
I like how you ignored all the political propaganda. amazing
Carpenters use trig all the time.
You should tell that to the kids who ask, “When are we ever going to use this?”
@@numericalcodebut what about the kids who don't want to be carpenters?
She’s right. Not sure about her woke examples though. If anything, her examples only indicate that even in category theory your bias can distort your conclusion but with a veneer of authority
Great, but the number of adverts I had to sit through! Good grief.
abstract mathematical thinking categorizes men and women explicitly.....never let the popular forces to delude you
no, you’re just a loser. hope this helps xx
Ads after 3m30s shame on whoever did that.
Excellent! just a couple small suggestions, maybe slow it down a little - allow for longer pauses for thought. and perhaps a little less of your personal views on the world, I agree with them, but many of them seem unnecessary, they move my thoughts from math to politics. Thanks heaps though, you're ace.
Would it be correct to substitute "Non-male" with "female" ? Or is that no longer accepted?
If there are only two genders, then "non-male" means "female". If there are more than two genders then "non-male" means "female, NB, etc". Using the word she did allows it to work with anyone's worldview.
@@bryan__m So basically postmodern infection of society while pretending to teach math. Uselessidiots go first you know right
💻she's using a #Dell laptop. 🤔
Do you really need to put adds in this video ?
COVID always was what it is. It is peoples' perception of it that has changed.
This is really cool. Just watching. What she calls category theory is what I call "Snowflake Logic."
Awesome, but show us how this helped you fold the jacket into the pocket!!
there’s math all over the universe it’s how Sacred Geometry works 💜💜
If all truth is context related, than this "truth" is also context related...
Nice self reference
🤯🤯🤯
never thought of it that way u should publish this
You’re conflating fact with truth.
@@tXoddXk Is me conflating fact with truth, a fact or a true statement?
It’s observed, so factual.
The problem with academic is that they like to invent new subjects and fancy names, and then explain them for hours and hours. Amazingly, they have audiences.
Luddites 😢
Hard to listen to and follow what she was on about, might be my brain. But nice lecture all the same. Thankyou.
She’s an auto-bot 🫶🏼
This fell apart about 35 minutes in
To have the posh, string quartet playing, brown woman who is an academic tell me I have too much privledge as a member of the set of humans with an X chromosone and genetically derived low skin pigmentation was less entertaining and educational on category theory than i'd hoped when I pushed play. I think I'll go back to set theory where my personal characteristics didn't seem so mateserial.
at last a non apple laptop.
Math*
This was very interesting, but unfortunately it was extremely long-winded. It was literally, 'yap yap' 4 times, and 'relevant info' 1 time. skip the first 25 minutes..
Was enjoying the lecture until she decided to go all Communist on us, talking about white privilege and how women are more oppressed than men (missing the irony that as a mathematician she’s one of the most privileged humans that ever existed). It’s like, what’s the matter with people? Even if true, and it’s not, how does that do anything other than create hate?
I think the point of the example is to show that polarizing topics can be abstracted to make clearer its nuances which can provide middle grounds for engaging in productive conversations. And besides, the diagram is just that: a diagram. Its accuracy depends on the context in which we are measuring privilege.
Also what does this have to do with communism? This seems a lot like her example of seat belts and fascism where it looks like y'all are both thinking in different levels of abstraction.
@@SantiagoRodriguez-hq4ik Intersectionality, which is what she is talking about, has it's origins in cultural Marxism. The privledged class is the oppressors and the under privledgded is the oppressed. Communists since the
French revolution have been trying to judge one group as oppressed and another group as privledged so the adminstrative state can redistritute everything to make it more "just". Plus, I doubt this method of abstraction will convince anyone with half a brain, it only obfuscates the issue with a straw man argument.
@@SantiagoRodriguez-hq4ik No the point of the example is to infiltrate academia and shove postmodernism into it. She's been doing this. And what does postmodernism have to do with communism? Lol
Edit: Didn't notice the "y'all" at first. Good job at disarming the enemy, comrade
Why spoil maths with propaganda and political ideology?
Genuinely a shame you can't have a lecture without racist or sexist devisive undertones now other than that really informative, really good 👍
The entire talk in one word, egocentric.
No ... do YOU think?
I found her very interesting and thought-provoking, except when she got into that goofy neo-marxism.
wasn't she all the time? I watched two random pieces to see if I want to watch the whole thing, and she got to that bs in both...
Why is an asian women speaking about math. I thought math was racist? lol
Watch the show. She spoke about racism. .... it's all related ...
Sure it is (sarcasm), and asians do better than others (stats). So how uninclusive of the RI to invite an asian to speak about math... Should they be cancelled?
Maths is one of the subjects I studied at the uni, but sorry her uptight speech is too annoying to listen to.