How to Think Like a Mathematician - with Eugenia Cheng
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- čas přidán 2. 06. 2024
- How does pure mathematics apply to our daily lives?
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For thousands of years, mathematicians have used the timeless art of logic to see the world more clearly. Today, truth is buried under soundbites and spin, and seeing clearly is more important than ever. In this talk, Eugenia Cheng will show how anyone can think like a mathematician to understand what people are really telling us - and how we can argue back. Taking a careful scalpel to fake news, politics, privilege, sexism and dozens of other real-world situations, she will teach us how to find clarity without losing nuance.
Watch the Q&A: • Q&A: How to Think Like...
Eugenia Cheng 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, where she is now Honorary Fellow. 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”. Her first popular math book, How to Bake Pi, was published by Basic Books in 2015 to widespread acclaim including from the New York Times, National Geographic, Scientific American, and she was interviewed around the world including on the BBC, NPR and The Late Show with Stephen Colbert. Her second book, Beyond Infinity, was shortlisted for the Royal Society Science Book Prize.
This talk and Q&A was filmed in the Ri on 2 July 2018.
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So I hope nobody missed the part where she said category theory is much about looking at a subject from the perspective of its relationship with other subjects or how it fits together with other subjects in order to gain a deeper understanding of it. The METHOD of applying mathematics to (insert any subject other than sociopolitics here) is all she trying to illustrate. If you couldn't use the method she illuminates to abstract that much out of the talk then it went right over your head.
It certainly did that.
Precisely!
I like to think that throughout the lecture, she was subtly showing us that mathematicians stick to facts when working on problems. She used several facts that many people would find uncomfortable to use, such as the privilege hierarchy. She was sticking to facts over feelings and opinions (unless she explicitly mentions that what she said was her opinion), and not caring if people will get offended, cuz I think she knows people will get offended, but proceeds to state facts, which I feel like is key to think like a mathematician.
The speaker points out that because they set up their problems carefully and use logic to reach their conclusions, mathematicians generally find it easy to reach consensus. I'd encourage anyone who feels that this video has gone too far in the support of any political agenda to use the same method and demonstrate its error.
The problem in this talk, as I see it, was not that she supported any political agenda but that she assumed the modelling and simplifications done here are sufficient to argue anything as complex as human interactions.
Mathematicians find it easier to reach consensus where such clear definitions of operations and objects are possible without loss of generality (or even of usefulness). This is very clearly not the case in almost every topic touched on here. The most basic reading of sociology, anthropology, philosophy (or even musicology, for that matter!) will show that the objects studied by those disciplines, which she is tackling through maths here, very strongly resist such a bare-bones epistemological approach. In other words: while she is *technically* correct in her operations to obtain those diagrams, she is doing so by silently ignoring nearly every crucial aspect of the problems she's addressing. She is misunderstanding and/or misinterpreting the situations she's addressing.
Sure, the diagrams "work", but you won't say anything meaningful with them. Just the platitudes we saw here.
As for any political agenda present here (because there is one, and that is absolutely not a problem), this kind of approach is pretty much a disservice, as I see it. I tend to agree with her positions, with what she is trying to say and convince her audience of. But the way of going about it is infuriatingly poor from any epistemological point of view I can think of (not to mention super cringe-worthy), and undoes the whole project.
@@GuilhermeCarvalhoComposer I agree with you when you say that her method for convincing her audience of her political agenda is not good. In some cases her diagrams assume beliefs (--beliefs which many would considered controversial--) without sufficient evidence or justification. With that said, I do not believe that convincing us of her political opinion is the primary point of her talk. Towards the start of the lecture, she says that she's not going to tell us what to think but how to think. As a mathematician, a high standard of evidence and justification is the norm. So if her main goal had been to persuade an audience of her beliefs, she would have given more evidence than she did. Instead, the main point of the lecture was that using these diagrams helps organize complex scenarios in a way that allows us to reason about them more effectively.
You say that these diagrams oversimplify the situation. First, the diagrams can readily be made arbitrarily complex by adding more branches and more dimensions, as you see fit. However, in any attempt to understand a real-world scenario, we must limit the complexity at some point and therefore sacrifice some accuracy. The key is to find the right level of complexity for your needs, given that there is usually an inverse relationship between the ease of understanding/application of a model and the accuracy of a model. (This is true for a mathematician's model as much as it is for a sociologist's or any other person for that matter.)
Honestly, I am a bit confused about what you are saying in your second paragraph, and I'd rather not comment on it until I understand what you are saying. What makes her "technically correct"? How do you know that she is "silently ignoring nearly every crucial aspect of the problems she's addressing"? What does she do to show that "she is misunderstanding and/or misinterpreting the situations she's addressing"?
Looking forward to your response!
Time Code
3:34 Pure mathematics is a framework for agreeing on things
4:35 Science hierarchy pure math > applied math > science...
5:56 Plan 1. Analogies 2. Interconnectedness 3. Relationships 4. Pivots 5. Intelligence
6:18 1. Analogies
13:18 2. Interconnectedness
26:54 3. Relationships
35:27 4. Pivots
40:51 5. Intelligence
Finally I see a lecture where someone makes a case that mathematics is about learning how to think. For someone with abstract enough cognition it's obvious and even sometimes frustrating, seeing everybody arguing instead of thinking, getting carried away with emotion and misinterpreting or cherry picking data that fits someone's worldview.
If your worldview consists of large, general ideas that you don't have a definition of then you don't know where you are. And those large, general ideas make you stay ignorant and feel safe at the same time.
It's quite possible to think without understanding anything about mathematics
And your response is a great example of that.
I said: "mathematics is about learning HOW to think" not "mathematics is about learning TO think".
@@henrykkaufman1488 Thanks for your reply.
I know HOW to think, only not in that way. Maths is learning how to think in a particular way, it's a system of reasoning, and many people just don't "get it". Fortunately it's quite possible to live a successful life without maths. A great many people are perfectly intelligent yet helpless when it comes to maths so they choose a career and a life without it. Mine was in journalism.
And no other subject that I know of triggers such strong reactions of loathing in so many people. They (we) may in a minority yet their (our) number is still signiificant. All those people know HOW to think.
A friend with whom I get on very well is passionate about maths. Two years ago she tried to explain certain points to me, and for 6 weeks we exchanged FB messages and emails. Then she told me she was very sorry (and she was) but she couldn't help me because she didn't understand how my brain worked. But she readily acknowledges that it does. We often have some interesting exchanges on all sorts of topics (NOT maths!) and she values my judgement on them.
@@xavierkreiss8394 None of my comments here suggested that someone without mathematical knowledge doesn't know how to think at all, or that mathematical, rational thinking is the only way to think. I mostly pointed out that it is only rational thinking that makes communication possible. A fact that, I suspect not incidentally, this conversation is an example of.
All cognition is emotional first and rational second. You are also sometimes carried away by emotion and are unable to see how that is affecting your rationality. Happens to everyone.
This woman is an excellent speaker. I don't necessarily agree with everything she says, and I also think she prioritises some things over others that I would not, but I found her talk very insightful.
Spoons make us fat because they make food easier to eat,scooping the last of the ice cream,gravy etc from the bowl.
Mathematics is not only about numbers, .mathematicians are also human being.I am really impressed how she explained society issues, thinking by concept of mathematics, and trying to understand by everyone point of view. The people of world really needs this type of knowledge to understand eachother, without creating hate.
I was panicking with my homework... I just needed to remember why I choose this career.
I was going to view this video for a minute or two but ended up listening to its entirety. This has opened me up to a much more in-depth way of processing information. Thank you Ms. Cheng.
The point was you can apply maths to understand different viewpoints in politics. Therefore thinking like a mathematician.
Thank you, Professor Cheng. I am a math spouse, and after 27 years I still look for insights into how my wife’s mind works. This will be helpful, I know.
4:39 What many people actually do is to conflate Mathematics (an umbrella term for a group of learning disciplines) with Arithmetic (A specific learning discipline under mathematics that has to do with numbers).
'Learning disciplines'?
Isn't that quite vague a term?
Please, if you will, elaborate on why you see the different mathematical disciplines this way.
@@xCorvus7x Because it's defined that way and has been commonly used that way for the last few thousand years. The word _Mathematics_ itself is Greek in derivation and means learning/knowing/studying. Biblio mathema (Books on Mathematics) have been written since ancient Greece and very few of them have to do strictly with numbers (mostly shapes, natural law, argumentative dialogues and postulates).
Because Mathematics is any methodology or set of systematic rules developed toward the ends of acquiring accurate new information in it's application (i.e. a learning discipline or a discipline that helps one learn).
So for example: Geometry deals with shapes. Arithmetic deals with numbers. Logic deals with what follows reasonably from a premise (irregardless of the validity of the premise). And these are all Disciplines under the header of Mathematics.
@@The1Helleri
Thank you very much for your response and this education (I feel that this should be at least mentioned in school, somewhere along the way).
I just realise that without mathematical tools, empirical studies don't make sense, so mathematics actually seems to incorporate all that is needed to learn, in some way or another.
If you are here reading the comments: Hi, Eugenia, and thanks for the talk! :]
2:00 fake fake news...the fact that this term somehow makes sense is perhaps one of the top 10 scary things in the world today.
One would think that 'fake fake news' is just 'news', but apparently some people make fake 'fake news' in order to see if people can distinguish between them and 'news'.
Please look at Tim Pools youtube channel, he is left of center but still a very intellectual honest person, focusing on objective facts and valid reasoning.
A combination that sadly is becoming less common with every passing day.
I think you will find some very interesting perspectives on the fake news allegation that often is tossed around today.
@@NetAndyCz Applying your logic something and I'm kinda thinking god made Trump as a test to determine how intelligent humans have evolved.
Fake news is not news. News is something that actually happened recently. There is a huge amount of censorship of news though.
@@MikeVeracity If I point to motorcycle and tell you that it's a secret portal through time and space that leads to the kingdom of spacelord Ubetere does not turn the motorcycle into a magic portal.
It simply a wrong, false, incorrect statement. The motorcycle still is a motorcycle, something that shouldn't even be questioned.
It's probably a much better use of time to question my mental health.
Now, if someone points their arm towards something and says #fakenews without presenting further evidence, it does not mean.....
Most accusations of fake news do not come with supporting evidence.
But as fake news is considered so evil, racist, sexistic, Islamophobic. So who dares to defend truth? You will only be next person found guilty of wrong thinking and rolled in tars and feathers by the media and Twitter mob, you will be fired from your job, your friends don't dare to speak to you, as the financial situation gets worse without a job your wife will divorce and your house sold in the process.
Quite a brilliant way to implement censorship, much more effective than the soviet union.
And we were prepared to nuke our planet to avoid the soviet union - but now we are allowing something much worse to poison the core of our free society, the freedom of speech.
So, please, fall in line and denounce fake news, who wants to be a racist?
This talk is, at its core, about communicating more effectively with each other. Regardless of whether or not you believe this talk is about mathematics, and regardless of your political or personal opinions and beliefs, the speaker is focused on how identifying and categorizing the world can help simplify extremely complicated situations such that the average person can understand them, with particular focus on being able to understand people on the opposing sides of binary arguments to facilitate productive conversations and solve the problems causing said arguments.
With that in mind, I suggest anyone outright dismissing or condemning the opinions of anyone else (including the speaker) in the comments might do well by themselves, and the people with whom they are arguing, to revisit the talk. You don't need to agree, bur that doesn't mean you shouldn't be respectful (if not considerate) and listen.
Your first paragraph sums it up perfectly.
The reason her approach and others like it are so important is because the issues are so explosive. You just have to say "Trump " or "gay marriage" and anger and hatred seethes and we need a solution for this because the alternative is too nasty for all of us.
I liked how you used basic fundamentals of logic and math to address real life issues. While some may find the examples potentially polarizing, i think that the choices made must have been thoughtful and I defer to your better judgment and find it brave and commendable. If we can look beyond the examples, the approach is something that I identify with and bears similarities to what I am trying to do, albeit you do it in a far more precise manner. I really respect and identify with what you are doing. Keep up the good work. First time, I've come across your name and video but already, I can see the caliber and dedication. Kudos. Gambatte ne.
As a fellow mathematician I find emotions to be natural. Emotions are categorical syllogisms of reality thus born into existence is an afterthought.
And sometimes they aren't about reality at all.
wtf ? lost me...
"born into existence" ???
I suggest "Using Category Theory to Analyze Society - with Eugenia Cheng" as a more precise title that would bring a more interested and receptive audience. People with differing political views will relate "How to Think" with the political views of the video, causing them to think more negatively about all the contents of the video.
Great feedback, thanks!
At the time you have commented, has the title not specified that the talk was about how the think like a mathematician?
Love the way you think - very helpful.
It's putting set theory into more better use.
@@xCorvus7x It did and still does at the time of writing this late response.
Also one of THE MOST important things I found missing in her talk, was the weights on the arrows of her diagrams. It's a very crucial point.
If a thing has many factors that doesn't mean all those factors are equally probable, or equally important/relevant.
If someone X says, A -> B --> C
And then she comes in and says oh, it's actually, A, B, C, D, E, F, G, H .... all interconnected like a graph. Hence, it's all a very complicated interconnected system. Well we'll have to do a probability/relevance/importance analysis of all those pathways in her graphs. And if in the end, it turns out that the path: A --> B ---> C accounts for let's say 95% of the probability or everyday occurrences, then that someone X is not far off, and her analysis is farther from the practical truth.
This is I feel where her analogies of a social system to a mathematical system, can be improved. But her analogies are a very good starting points.
A brilliant speech. I particularly like her conclusion where she applies logic and empathy to feelings.
The common factor of logic and empathy is that both are non-judgemental. So is pure mathematics.
So to bake a perfect pi, just take judgement out of the recipe and let people choose whether they want to eat their pi with apple sauce, chocolate pudding, powdered sugar, pink icing or even just the pure pi.
But - dammit - let them choose later on and only for themselves. Do not let them stuff their particular version down your throat.
To everyone complaining about the wokeness: she used those examples to explain the interconnectedness/relatedness, you could just as easily use other "non-woke" examples if you disagree with the assumptions she made. The whole point was about the power of generality and abstraction, not that you should be woke because math tells you to.
It's ironic, because the point is to analogize your thinking, which includes replacing the examples she gave that you may not have liked with examples you more agree with.
Or you could just dismiss the mode of thinking that invented the internet, computers, and now AI. I would be weary of wandering to close to the "stupid" quadrant, though.
The philosopher in the room is asking what is the meaning of two? How does two relate to the human condition? How can we possibly concern ourselves with such trivialities as chairs, apples and bananas until we answer the more fundamental question? After all, if a banana or apple is made of large bolts of cloth and filled with beans they are all chairs.
"Three types of priviledge"
I've been tricked.
The title is misleading.
Right. Cause how to think would be too inviting.
What is math not useful for? Would be my question to my younger self
You are so welcome! Thank you too! Illuminating!😺
In the overabundance of potentially good stuff to hear, I think I'll trust the comments and stop what in the intro seemed a good lecture about how to *avoid* identity politics in the public discourse.
The danger of theory without quantification, well demonstrated here. You can let yourself feel like you are being logical and justified when all you are doing is hiding your prejudices in a logical framework. The true power of logic is to take your hypothesis, eg. That “the people in power should be the ones to make the changes.” And see if that can work out logically in a wider system, given the other observable facts like human nature. If your hypothesis requires a fallacy to work out or ends in a contradiction then you should rework the hypothesis and retest.
Yes, the dumbest things I've ever heard have come from smart people who have devised complex logical systems, but have neglected to adequately test them against reality.
this is the dark side of the mind it self because, this elements characteristic can create new frame depending the non count hable characteristic elements bring ups so any divergent arrows bring up changes bring downs many arrows. and convergent arrow circuntance is when phenomenon of values happens. this is on godel hard problem. and hard math paradox problems. everything become wrong if before wholes of essential stuff was right , maybe just because a butterfly fisics particle theorem. math not necessary have meaning until you put it in the model some says.
R.B. Nice way of putting it. It is either happening more or I’m becoming more aware of it.
@@jamesmaybury7452 You put it pretty well to begin with mate.
My favourite example is when William Lane Craig said there are 3 meta levels to suffering. Then he applied this logic to animal suffering. Of course he is a Christian so he has to somehow justify the belief that we have dominion over the animals and can do whatever we want to them, anyway...
He said the top layer of suffering is meta-awareness of the suffering, so while a pig may suffer, it doesn't realise that it's suffering and thus does not really suffer.
I'm paraphrasing of course, but essentially he used logic to disprove the fact that animals can suffer. Of course a SCIENTIST would just do some brain scans and compare behaviour between us and other animals and INSTANTLY conclude that it's all the same shit and we probably suffer in much the same way.
Smart people >.
@@r.b.4611 We do have dominion over animals that's just a fact.
However to say a animal does not suffer is idiotic, and easily testable.
that was a talk beyond my expectations
The point about power depending on context deserves more attention than just a classroom vs. street analogy. In certain contexts (e.g. social media, a college campus) a perceived lack of "global" privilege (i.e. privilege outside that context) gives you maximal "local" privilege.
🎯 Key Takeaways for quick navigation:
00:22 🧮 The Value of Mathematics
- The speaker, Eugenia Cheng, introduces her love for mathematics and its creative and imaginative aspects.
- She addresses the question of math's usefulness in our daily lives.
01:20 🌍 Mathematics for Clarity of Thought
- Eugenia highlights the usefulness of mathematics in helping people think more clearly.
- She emphasizes the importance of clear thinking in the current sociopolitical climate.
03:32 📐 Pure Mathematics as a Framework
- Eugenia discusses how pure mathematics can serve as a framework for agreement and clear thinking.
- She contrasts mathematicians' ability to agree in their field with the lack of agreement in other subjects.
04:57 🔍 Beyond Traditional Applications of Mathematics
- Eugenia argues that pure mathematics is not just abstract but directly applicable to how we think.
- She challenges the conventional view that mathematics is solely about numbers.
06:15 🧩 Analogies in Mathematics
- The speaker explores the concept of analogies in mathematics, which involve finding commonalities between different situations.
- She explains how abstraction in math helps us understand broader concepts and relationships.
09:50 🔄 Levels of Abstraction in Mathematics
- Eugenia delves into different levels of abstraction in mathematics and how they help us understand various situations.
- She uses examples like 1+2, 2+3, and 1*2, 2*3 to illustrate the concept of abstraction.
11:38 ⚖️ Understanding Complex Issues through Interconnectedness
- The speaker discusses the importance of interconnectedness in understanding complex issues and relationships.
- She provides examples related to relationships and police violence to highlight the concept.
16:20 🤝 Flexibility in Thinking
- Eugenia emphasizes the importance of flexibility in thinking and how it allows for a more intelligent approach to understanding complex problems.
- She likens it to the flexibility in materials that makes them stronger.
18:33 🔄 Breaking Vicious Cycles
- The speaker addresses the idea of breaking vicious cycles by understanding the interconnectedness of actions and feelings.
- She uses examples related to relationship breakdown and police violence to illustrate the concept.
21:43 🔍 Understanding the chain of events in an airline incident
- Analyzing the reasons behind an airline incident involving passenger removal,
- Identifying factors contributing to the situation,
- Examining the consequences of overbooking and its impact.
22:40 💭 Factors contributing to weight gain
- Exploring the various factors contributing to weight gain,
- Considering the influence of metabolism, genetics, and emotions,
- Discussing external factors, such as societal norms and the food industry's role.
25:44 📊 Complex interconnections in life and decision-making
- Demonstrating the complexity of interconnected factors in various life situations,
- Encouraging a comprehensive understanding of the underlying factors,
- Highlighting the importance of not oversimplifying complex issues.
26:31 💡 Using mathematical thinking to analyze complex situations
- Applying mathematical thinking to analyze complex real-world situations,
- Discussing the 2016 US election as an example of using mathematical reasoning,
- Emphasizing the value of mathematical thinking in understanding multifaceted issues.
28:50 🌐 Understanding hierarchical structures and privilege
- Illustrating hierarchical structures using factors of numbers and privilege categories,
- Exploring the concept of privilege and its different dimensions,
- Promoting empathy and understanding through pivoting between points of view.
30:40 🔄 Shifting perspectives to understand privilege
- Demonstrating the ability to shift perspectives and understand privilege,
- Encouraging empathy and acknowledging varying degrees of privilege,
- Highlighting the importance of considering multiple viewpoints.
34:43 🧐 Recognizing power dynamics in different situations
- Discussing power dynamics in contexts related to privilege and oppression,
- Emphasizing the need to understand the different experiences of privilege,
- Promoting constructive conversations about power imbalances.
36:34 🧑🤝🧑 Fostering empathy and understanding
- Fostering empathy and understanding by examining various perspectives,
- Encouraging individuals to consider their privilege and the privilege of others,
- Promoting effective communication and empathy in discussions.
42:04 🧠 Eugenia Cheng on the nature of intelligence
- Eugenia discusses her perspective on intelligence, highlighting that it's not solely about being logical but also about being powerfully logical and helpful.
- She emphasizes the importance of making long chains of deductions, having a framework for testing oneself, and being able to engage emotions to be truly intelligent.
43:55 🤓 The importance of having a framework for being reasonable
- Eugenia elaborates on what it means to be reasonable, emphasizing the significance of having a framework for testing the truth of theories.
- She distinguishes scientific theories from baseless claims by highlighting the presence of a framework for admitting when one is wrong.
45:18 🧐 Emotions and logic in education and reasoning
- Eugenia discusses the role of emotions in education, highlighting that learning is more effective when emotions are engaged.
- She challenges the idea of pitting emotions against logic and emphasizes that they can work together to foster understanding and meaningful conversations.
46:37 🤔 Carlo Cipolla's theory of stupidity
- Eugenia introduces Carlo Cipolla's theory of stupidity, explaining the four categories of people based on self-benefit and harm to others.
- She discusses the significance of benefiting both oneself and others to be considered intelligent.
48:25 🌍 Logic, empathy, and a virtuous circle
- Eugenia explores how logic can help people empathize with others and understand different perspectives.
- She promotes a virtuous circle where feelings and actions work together to create a more harmonious and understanding world.
Made with HARPA AI
@38:28 "we all feel everyday sexism all the time" - really?
Very nice discussion about the effectiveness of Pure Mathematics
the video is about how to think. though some may not like the way she presented the concept, i think its a good way to describe it. cool video.
Lovely lecture. Thanks Ri.
Awesome presentation!
I couldn't bear watching this until the end.
Thank you Eugenia for having formalized clairvoyance in its pure state!
Very Interesting approach of the talk. Pure mathematics involves abstraction which sounds like moving from subjectivity to objectivity.
She gets political because that is an area of society that seriously needs more logic instead of emotional argument and opinion entitlement...I am skeptical about the optimism claim though.
Those who come to here can understand mathematics is useful. If you could persuade the people who hate maths, then you are great.
Thank you for this video, This is how I think all the time and now I know I'm not alone. Y personal mantra has become "It's hard to be open minded in a narrow minded world" .
Yes. Intelligent thinking is three dimensional problem solving. I can look at my own and someone else's needs, and rotate, translate, and/or reflect them around within the larger environment that we are both operating within, to find a single solution that helps us both get something that we need. Maybe not exactly what we were expecting, but something positive towards our goals.
Physical thinking is 1D and is just focusing on one's own body's needs.
Emotional thinking is 2D and focuses on one's own body's needs plus another's body's needs.
But intellectual thinking is 3D and solves the problem of getting both of our needs met in a way that truly works, given the goals of the community/environment that we're in, so that we can effectively get our needs met in a way that helps the third, larger group, get its needs met too.
She I so good, even stand-up quality. This is so an important subject, to introduce mathematics to ordinary life topics. We can find the answers by taking into concern the complexity, not find answers just by simplifying all the time. The best answers can activate the acting of reducing a problem, not activate the blaming as it was the only goal from the beginning.
You're happy with this post? It's incoherent.
This lecture wins the award for packing the most flame-war inducing topics into the shortest time. Brilliant! Well done Eugenia! Enjoy reading the comments. 😉 (seriously though, as a “cis” white rich male, I learned a new perspective on category theory from this. Ordering the book! Thanks!)
She constantly disregard basic logic, you can't use any part of your assumption as a part of the proof of the assumption, that's called circular logic.
Also, other times her political views are treated as axioms and the results will of course be in line with the axioms used. Compare classical vs non Euclidean geometry to understand why that methodology is bullocks.
Please go ahead and subscribe to whatever dangerous political views that want to destroy the western civilization you wish to subscribe to.
Our society is still free, or at least until the neo marxists like this lady have taken over.
But please don't blame your views on mathematics, as correct math had next to no part in this lecture.
@@NomenNescio99 She didn't use assumptions to prove assumptions. She didn't prove anything. She talked about frameworks of thinking. She also stopped and recognized that someone with an opposing view could take things a different way, but with a framework people with opposing views can have a more thoughtful discussion. All I'm seeing you do is get angry and cling to your views, not really unpacking things and providing thought or substance.
It's really good talk. Got to learn so many things.....
I loved this lecture, I am currently reading her book and examining my own ways of thinking and the ones that surround me. The sportsman black rich man example is something I hear everyday. "Is classism, not racism". When it's both. Thank you!
You speak so wise. Thank you.
np
The LOGIC-EMPATHY isomorphism! AWESOME TALK.
I think she is trying to show that maths is not some abstract thing that lives in a bubble on the top of an ivory tower. It's intrinsic in how the world works, even how we think about things. She is making abstract mathematics something you can feel. I don't think there was anything wrong in what she said. Politics, the economy, social structures ... understanding these with mathematics is part of being human, whether you know it's there or not. Sometimes you feel something and you don't know why. She just thinks that maybe you can try to figure out why you feel that way, organise the ideas.
Without abstractions we aren't human. We can't relate. We can't communicate. Language is the first abstraction. Learning language is doing mathematics. Your mind FEELS the rules, when a sentence makes sense and when it won't, when words go together and when they can't.
Ditto music. You feel it.
Ditto morality. You feel it.
Ditto fish swimming. They feel it. They understand fluid dynamics at a different level, by feel. It's like feeling the wind when riding a bicycle.
There is a sense in which our minds are just computers, but instead of number crunching, human minds crunch ideas.
She just trying to show that mathematics is THE basis that allows us to model ideas. It's THE meta-idea.
There is Mathematics behind everything. Everywhere you look, the world, the planets, the stars, the atom, the cell, the eye, we see patterns, and that's all we can see. Is it because there are patterns out there in the world? Or, is it that our limited minds can only see patterns? If something isn't a neat, simple pattern we can't even see that thing. At least I can't.
It's the matrix. Pun intended.
Fantastic, dr. Cheng! Thank you!
It helps me a lot.Thank you
She learned well from her time in Chicago. She talked so much about Black men...lead me to think she has a black spouse.
@@reggaefan2700 Nope ... she is married to a regular Chinese.....
She is a sociologist /social psychologist, who also happens to be a theoretical mathematician.
Unless, you require that a person with those titles have experience and knowledge of the literature, results, and ideas of the field. Actual psychologists use evidenced results to reason about things (maybe a patient). She just helps people to build a logical framework to reason with the results.
Can we talk about math, and not politics?
"No."
The point was you can apply maths to understand different viewpoints in politics. Therefore thinking like a mathematician.
She was pushing propaganda all along, and we all saw it, we all felt it, and here we are, denouncing it. That's it. If there was a point to it, it vanishes the moment you realize she has a political agenda. [at @@101yayo]
Absolutely brilliant!
The beauty of maths is that there are no boundaries to your imagination.
Dear Dr. Cheng I love your mind. Dr. Cheng I have had a problem with the commutative property of multiplication for 46 years when I argued my point when: A=1apple and B =0 for example, so I say yes B X A = 0, but not A X B = 0 (sorry I do not have the not equal to symbol in my keyboard) or rather A X B = C and B X A = C exept when B = 0. as you have a apple and you multiply it zero times you still have a apple. I would greatly appreciate explaining how I am wrong or hopefully agreeing with me. Thank You! anxiously awaiting your reply.
Nope; if you have an apple and multiply it by zero, in the end you still get zero. Any number multiplied by zero gives you zero, no matter the order. So not AxB and BxA are indeed equal to zero. You say that if you have an apple and multiply it by zero you still get an apple. That’s not true: it would be true if you multiplied that apple by one, not zero.
Let me know if it is clearer.
Nope
Think it as that:
There ist a box with an infinite number of apples owned by Frutana. You can take out as many you need for your math.
4*2 you take out 4 apples, 2 times. You now have 8 apples.
Put them back.
4*0 you Take out 4 Apples, 0 times.
You now have 0 Apples.
She lost me at "Broccoli is delicious..."
Is there anywhere that we can find the slideshow she used? I want to print some of those graphs and post them around my room. I supposed I could go on and make them myself.
Loved this. Eugenia was brave talking about her professional skills and showing how they help her personally, because we learn a little about her. We don't know everything about her. That makes her in part, vulnerable. Just remember the stupidity graph at the end though. Eugenia is aiming for you to benefit as well as herself. If like me you disagree with some of the conclusions and assumptions made during the talk, it is up to you to be more intelligent in discussing those issues. I really liked this talk because it is a challenge to grow stronger, not just have an opinion. That's exactly what healthy societies need.
To people calling her a racist: you and I probably agree on a fair number of political issues. I disagree with some assumptions she made in this talk. But if you watch this video and your only takeaway is that she is a racist, I think you you might have missed the forrest for the trees here...
The new way of “winning “ arguments is to call your opponent a racist. That way nobody has to think.
Just amazing content! So I pressed!
"Math is the language of the universe" (myself or somente else that I dont know), and this is probably the deepest phrase anyone can make
Thankyou.
Her logic was fabulous and listening to her arguments was really a treat. Some people can argue that the added politics kind of ruined the talk in some way, but I did not feel that she came here to mathematically prove that any point of view is better or worse than any other (liberal vs conservative) that some viewers might have thought so according to the comment section. I can see such arguments amongst all people around me. It is important to not forget that we all feel that we are being reasonable, but with different starting assumptions.
Really? I couldn't find the way you think!
Very true and a great logical way to think about it, but the privilege thing was way off mark and factually wrong as well as police violence so one can see why people would have an ich to scratch in correcting those errors. All the other opinion based political stuff was fine and id agree that arguing against them under minds the point of the lecture.
@@gonnaenodaethat6198 yes in most of these talks I see a bit of politics which honestly I do not like one bit, because no matter what is the subject it always polarises people into groups, but the Logic part of the talk was really a treat to me. I noticed that All of the talkers that I have watched have the same liberal world view ... but so be it. As long as it will not get too political and focuses mainly on the Topic i will keep enjoying these
It's prejudice to just someone by their color. I didn't get through the 2nd chapter of her book and I refuse to read it. It's not logic, it's politics!!
Although Cheng in this talk (and book) and other books is about applying category theory, she seems to only use the arrow-theoretic aspects all of which is just graph theory that long predates category theory. The new concepts in CT are universality (universal mapping properties) and naturality (natural transformations) which I don't see being used.
Love the way you think Kenneth Studstill - really helpful! Need more comments like this - lateral thinking.
Great talk. Initially I thought it was going to be one of those contrived talks that some people give just because they are more interested in giving a talk than actually talking about something interesting that people could benefit from. It got more interesting as it went and it all coalesced really well the definition of stupid. I liked the numbers part also. Her delivery was very good also - kept your attention. She is proof of her own pre-talk statement about how maths can bring clarity of thought.
Thank you! Now I have got the explanation how a very strong logic and a very strong empathy can be in the same person. Most tests put that on the opposite sides, so you either logician or empath. I am both!
Great deduction
Great talk
Thanks for sharing👍😀
Great Talk. I wish I can work with people who has a similar vision instead of fearing about not submitting enough leetcode problems.
Just like walking forward takes numbers of steps lol i used to live right across my place of work and would count my steps from my doorstep to the time clock at work and it was always 48 steps 😄 i tried counting my step here and there just to see if i get a different number and for 2 years i finally realized stopped. Btw, the number didn't change 😃what an amazing world full of numbers.
I find it interesting.. why werent people applauding?
They applauded at the end. What do you want cheerleaders lol
I love maths.... even though I don't get it sometimes😅😅
One element that you have forgotten to add in every mathematical situation in stillness of brain.
@46.19 When you‘re emotional you cannot be reasoned with? There‘s no framework for you to accept that you might be wrong?.. emotions are ‚right‘.. hmmm.. there are times when one might feel ‚justified‘ to take action because of how one feels.. but i find it a bit far fetched/absolutist to claim that emotions are right.. however put so, that they point to a kind of truth that needs to be weighed up/discovered that may provide insight then yes.. good luck with your interconnected diagrams and applied maths Miss Cheng. I liked the way you mashed up maths and emotions 😀
when a video finally confirms that you are, indeed, Unfortunate
That hair-pin tho :) Tongue in cheek!
You could make a very similar video, with these kind of concepts concepts supporting very different positions. (Right wing positions, for instance.)
She uses concepts from math/logic to elucidate certain political situations, but since she doesn't prove any positions to be true, or refute any positions, this type of thing really doesn't change the political conclusions ppl come to.
A lot of this is pretty intuitive to people as well - they know it but might have a hard time explaining it.
I've read that people don't often make logical mistakes, outside of specially created puzzles. Most often our mistakes are due to perceptual errors: not having the correct information, missing key details, etc.
Your comments stand out for being coherently expressed. Most commenters in support of the lecture seem to have suffered a lot of blows to the head. Thanks.
Historically, British society has been structured around social hierarchies, with the aristocracy and upper classes holding significant privilege and power. Contemporary discussions around privilege in Great Britain often center on issues of class, race, gender, and other aspects of identity that impact social mobility and access to opportunities. The presentation by this speaker shows how much she has let this social hierarchy permeate her otherwise logical mind. She describes her situation, and then believes that it applies across the world.
Not everything in mathematics is equal. Some things are greater than, or less than.
That is only when other factor or conditions or values are varying or not the same for example: 2+2=4 or 2 feet of iron rod plus 2 feet of iron rod equals 4 feet of iron rods at 4 degrees Celsius but are not equal to 4 feet at 60 degrees Celsius.
Excellent session
I came here to have a voice to read her book in, stayed because her talk was interesting!
What I am thinking about you is to ask you how and where to start my maths education from and would you teally cate to guide me. on that and Iremember I am 43. I relly loved your presentation. 👌👌
This sounded like a TED talk extended format....
This is a great presentation!!!!!!
Love it!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What is that factors of 30 cube diagram thingy called?
I come from a computer science space but a "hamming cube" seems fitting. You just would have to think of each bit corresponding to a prime factor.
Parallelogram
You can call it a Hasse Diagram.
Miss Eugenia Cheng is the best. I never listened to a better speech of a mathematician. I feel very impressed. Brilliant!
Bravely bang on. Sadly most will miss the nuances of what she is saying.
Supposedly rational people proving that they're not... the talk is basically about being neutral - prioritizing logic over emotions, she mentions e.g. how Oprah is more privileged than a poor white man, but they get instantly offended at the mere sight of "privilege" and similar political terms.
In my own discipline (Business Systems Analysis) we have "the 5 whys" for trying to understand why something went wrong. I liked the breakdown of the United Express Flight 3411 incident. Now I have to think about how to use the lattice. Liked this lecture -- in spite of all the other comments (a rich, white man wouldn't have been criticised so harshly). The second time I watched it with my wife and 10yo daughter.
Where is the mathematical proof a white man wouldn't be criticized so harshly?
YOU AND Eugenia Cheng criticize white males harshly on the basis of a hateful paradigm of "white privilege" -- as if the civilization that white men created from scratch with no help from the likes of you over the past 1000 years had fallen down out of the sky and white men had merel;y got there first and hogged it all -- so your own words prove conclusively that you're a liar.
Wonderful and noble!
I don't think anyone will be against the usefulness of a subject with the surplus of interesting matters. I think a lot of that is related to how we educate young people in the current system .Mathematicians are also human, so they have story. If we tell more stories of them to the students, we can for sure trigger more of their interest towards science and maths. For instance, the competition between Leibniz and Newton in terms of who actually invented calculus would be a very interesting story to tell.
Exactly, the system is completely upside down, instead of stoking fires of interest first then teach the methods educational systems just teach the methods and leave you be to figure out the story for yourself, causing kids to think they are an "anti talent" at something they might have a passion for.
This is brilliant, it's like an entry-level guide to systemic critique. 10/10
Analogy interconnected relationship pivot inteligence.
So what is the nature of mathematical reasoning: reduction, deduction, induction.. .?
She learned well from her time in Chicago. She talked so much about Black men...lead me to think she has a black spouse.
I love this question! It reminds me of Thomas Kuhn's stance on science. It cannot be defined!! Any definition would limit the methods, connections, and discoveries in the field. We have labeled these things in the past but then a paradigm shift (revolutionary idea) occurs and blows everything out of the water. That being said, I think it is important to distinguish between the nature of math reasoning and math proof. I think math proof is about manipulation of symbols via a logical structure that we trust to be accurate. This is like deduction since it builds on axioms and finds the consequences of the logical structure (axioms). Often the axioms of these structures are so basic and intuitive that they are hard to deny without changing our entire views of reality. As for math reasoning, I think abstraction is a better word than reduction in this case. Abstraction could be seen as "noticing a pattern". In practice these patterns might be hunches that we want to explore. Math is not ambiguous like words so we can reason about it better and explore it if we represent it (or something that resembles it) in math. Math (the developed logical rules) is symbolic so we can replace things with symbols to hide details and better expose patterns. I think mathematicians have many patterns stored in "muscle memory" of potential logical manipulations for specific situations to achieve some result from it. So if I were to choose a word I would choose abstraction but that's me...
@@reggaefan2700 what the actual f you twisted mind
There it goes... the Magnificent Math Ship to the bottom torpedoed by PC !
I assume liberals are not into math
❤️
What do the formulas mean? Relation?
You don’t get anything out of a logical system that you didn’t put into it. The same goes for ideological systems.