How does pure mathematics apply to our daily lives?

January 30, 2019 4:59 PM

How to Think Like a Mathematician - with Eugenia Cheng. 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.
posted by zengargoyle (24 comments total)

It's always frustrating as a philosopher when people from other disciplines try to crash your territory. 90% of this would fit in a regular critical thinking class. She also trots out the false cliche that philosophy doesn't progress.

However, it is nice when she uses diagrams specific to mathematics, so I'll try to quell my frustration.
posted by leibniz at 6:21 PM on January 30, 2019 [13 favorites]

Like leigniz, I thought this was a perfectly adequate intro to philosophy lecture (though I think her causation diagrams are way to complex and may scare off quite a few people who would be otherwise interested).

I didn't have the patience to watch the whole thing, is there anything in there that is not straightforward/typical philosophical ground (besides the notation system)?

More nitpicky, she is certainly big on thinking with more precision, I'm not sure that this always makes things more clear (and her discussion of being more intelligent to grasp more details at once didn't help me).

Most nitpicly, she kept saying "analogy" while it seems that she was thinking of abstraction (see the marriage bit). Did I misunderstand her point or was she really doing that?
posted by oddman at 6:44 PM on January 30, 2019 [2 favorites]

Leibniz -- as a philosopher, would you agree at all with the speaker that philosophers tend to get hung up arguing definitions more than mathematicians do?
posted by klausman at 7:44 PM on January 30, 2019

I appreciated the remarks about Carlo M. Cipolla’s Theory of Stupidity. I have never heard of this but it’s a glorious and frightening peek at the current times and, given the theory, all times past, present, and future. Everywhere.

As to analogy, I agree that she meant abstraction. Analogy is this is kind of like that. Abstraction leaves out the details, which is how she described her thought.

The one thing that was maybe not typical philosophical grounds was she emphasized “feelings”.

On a more general note, I keep encountering people who think they have a great insight into something, an insight new and never before spoken. And then once spoken, you find that they are rehashing what was once an issue in philosophy that was dealt with ages ago. The amount of ignorance of philosophy and its content among the hard sciences, math, and especially computer science (read AI) is large.
posted by njohnson23 at 7:47 PM on January 30, 2019 [9 favorites]

Klausman, philosophers often do 'conceptual analysis' - that's part of the job description. And important concepts like 'justice' or 'happiness' or 'person' are inevitably going to be contested (there's even a theory about this). Unlike mathematicians, we often can't stipulate a logical definition and then get on with it- we have to deal with real world usage.

I have a favourite passage relating to this from R.G. Collingwood's book The Principles of Art (where in part he is trying to define art):

"The proper meaning of a word (I speak not of technical terms, which kindly godparents furnish soon after birth with neat and tidy definitions, but of words in a living language) is never something upon which the word sits perched like a gull on a stone; it is something over which the word hovers like a gull over a ship's stern. Trying to fix the proper meaning in our minds is like coaxing the gull to settle in the rigging, with the rule that the gull must be alive when it settles: one must not shoot it and tie it there. The way to discover the proper meaning is to ask not, 'What do we mean?' but, 'What are we trying to mean?' And this involves the question 'What is preventing us from meaning what we are trying to mean ?' "
posted by leibniz at 8:22 PM on January 30, 2019 [16 favorites]

@leibniz That's a great metaphor. I'm a lawyer, instead of a philosopher (a patent lawyer, even!) and what I spend my time doing could easily be described as trying to stretch the boundaries of where the gull might be hovering, with the added problem of convincing other people that not only is the gull where I say it is, but it is in fact perching on a rock that just happens to be there.

English is a wonderfully flexible tool, but you'd never know it from US education (at least through college). I twigged to it while teaching the language in Japan, but it took years of law practice to really get it through my skull. If I had any imagination, I could totally write a great novel.
posted by spacewrench at 8:56 PM on January 30, 2019 [2 favorites]

As for abstraction vs analogy: I had the advantage of reading these comments before watching, and I notice that Eugenia did use the word abstraction right away in her first examples. I think the key is that an analogy between two situations (such as island:sea::mountain:air) exists precisely when the two situations share a common abstraction.
posted by TreeRooster at 9:20 PM on January 30, 2019 [5 favorites]

I enjoyed the talk and found the examples illuminating and I hope I'll remember them. But ultimately the argument is in a sense privileged, to suggest that people fighting/arguing should instead a) understand their conflict better and b) work together to resolve it, is really old advice. (To be fair, what this talk does is suggest some ways that people could go about doing so.) The same with the suggestion that all things being equal it's people with the power who should take responsibility... Except that people in positions of privilege aren't motivated to do that precisely because of privilege.
posted by polymodus at 11:34 PM on January 30, 2019 [1 favorite]

though I think her causation diagrams are way to complex and may scare off quite a few people who would be otherwise interested

I think somewhere by the end of section 1 or section 2 of Eugenia's talk, she was implicitly referring to the Yoneda lemma which is a fundamental result of category theory. Apparently it's like, foundational similar to how Godel's theorems have been for mathematical logic, or the importance of the Church-Turing thesis for computer science. I thought it was funny and but also kind of disturbing in terms of philosophical implications.
posted by polymodus at 11:52 PM on January 30, 2019 [3 favorites]

IIRC Eugenia Cheng’s specialism is Category theory, which you could describe as the mathematics of taking abstraction to it’s absolute limit?

leibniz: It is a truism I’ve read elsewhere that as soon as any part of current Philosophical study becomes useful, it stops being regarded as Philosophy & gets assigned somewhere else, perpetuating the idea that Philosophy is the study of the useless.
posted by pharm at 12:31 AM on January 31, 2019 [2 favorites]

Because it's easily missable, there's a Q&A: How to Think Like a Mathematician - with Eugenia Cheng that takes questions from the audience.

I probably should also have mentioned more about The Royal Institution lectures (in general). They're often just general public lectures that don't go that deep or specific. There are kids and non-scientist-ish people. Often a condensed version of a new book geared towards the general public. It's not an academic presentation to others mostly in the same field.
posted by zengargoyle at 12:35 AM on January 31, 2019 [1 favorite]

I saw the keynote talk she did at HaskellX in 2017, which was in similar territory (essentially applications of category theory to the real world). One example she gave was explaining intersectionality and privilege using category theory.
posted by acb at 3:19 AM on January 31, 2019 [2 favorites]

I didn't know "pure math" meant "lots of arrows".
posted by runcibleshaw at 5:15 AM on January 31, 2019

(10:34) a better way to do it is to become more intelligent and as you become more intelligent you find ways of packaging things together as one concept

let me tell you, as a cognitive scientist I love it when mathematicians do philosophy to tell me how the brain works, especially such simple concepts like becoming more intelligent
posted by nicodine at 6:44 AM on January 31, 2019 [4 favorites]

LOL -> Grothendieck  
            ↑
       dancing goats
            ↑
     silly obscure comment  <-  category of silly comments

posted by sammyo at 6:44 AM on January 31, 2019

She also trots out the false cliche that philosophy doesn't progress.

I'd be curious to know what you think are a few examples of philosophy making progress.
posted by thelonius at 7:44 AM on January 31, 2019

My last comment was kind of threadshitty so I wanted to expand on it. I think there's a lot to like about her ideas about categories and abstract relationships. She's clearly brilliant. This brief video encapsulates a nice way to formalize some aspects of critical thinking in an intriguing way. That she's a woman of color succeeding in communicating abstract mathematics ideas to the public is so, so rad! But I think a lot of the ugh-y responses in this thread are coming from a common locus of frustration because it's hard from this video to see whether she's refined these ideas with the philosophy community. I'm all for big, bold ideas! But to make intellectual progress, these big, bold ideas must be vetted by those who know what ideas existed before ours. We can't stand on the shoulders of giants and build upward if we don't first find our footing on those shoulders.

(It's totally possible she has done this -- hard to tell from skimming her publications. But in the sciences, when we do bold interdisciplinary work, we try to be clear about who our collaborators are precisely to demonstrate that we know of our own limitations and blind spots.)
posted by nicodine at 8:11 AM on January 31, 2019

Holding up a trash can lid to fight off the brickbats... Back in 1933 Alfred Korzybski, in his book Science and Sanity, outlined an analysis of thought based on the process of abstraction. He defined abstraction as leaving out the details more or less. Our thoughts lie on different levels of abstraction. He also states that abstractions though useful have no real ontological state. They just live in the mind. Class terms such chair, Republican, etc. are of value but we have to be very careful in how we use them. For Korzybski, the problem lies in confusing levels of abstraction. In this talk she talked about this problem in just this way. The difference though was she promoted abstraction as a tool, and then pointed out that you have to be careful in how far up you go. Korzybski said that abstraction is how our mind works already, and that you need to be aware of it and have tools to control it to make you aware of it. As a mathematician, she knew the power and usefulness of abstraction when doing math and this talk predicates that the same approach is useful in general. Maybe so, but there are caveats that need to be pointed out.
posted by njohnson23 at 9:23 AM on January 31, 2019

"It's always frustrating as a philosopher when people from other disciplines try to crash your territory. 90% of this would fit in a regular critical thinking class. She also trots out the false cliche that philosophy doesn't progress."

You must hate Russell and Wittgenstein.
posted by klangklangston at 5:46 PM on January 31, 2019 [1 favorite]

@Thelonius- There's the claim mentioned above that philosophical areas get turned into sciences when they hit solid results. I think there's some truth in that, but we don't really need it to defend philosophy.

My experience of working in philosophy over the last 20 years is of agreeing far more than disagreeing. Even where someone holds an opinion diametrically opposed to mine, there's usually at least some insight in there, and I have to recognize it and incorporate it into any further work.

In my specialist field of philosophy of emotions I see significant progress over the last 30 years, such that I read sources older than that mainly for historical interest rather than much argumentative support. It's not the purest case, since we draw on data from the sciences, but my impression is that psychology is lagging behind philosophy here rather than the reverse, e.g. in notions such as embodied cognition.

In other areas I won't deny that you will often find debates preserved for centuries, but I will claim that the options in these debates get ever more sophisticated over time.

You must remember that for really deep questions, everything is connected- your answer to a value theory question may well have implications for your theory of knowledge and vice versa. This means that the opposing options often involve vast sets of interlocking theories. It also means that final settled answers to these questions ultimately rely on complete models of the world. This by the way, is also the case in physics and other sciences, and these sciences are much more limited in scope than philosophy.

@klangklangston- I don't really see what you're getting at. It may be worth noting that (early) Wittgenstein at least was pretty hostile to philosophy.
posted by leibniz at 6:29 PM on January 31, 2019 [1 favorite]

Thanks! It is an interesting question, and, I think, one that different philosophers would answer very differently , both today, and over history. Schopenhauer, for example, would undoubtedly reply that the most significant progress in philosophy was Kant's critical revolution, whereas Wittgenstein or many others in the 20th century would probably say that the most important development was in a correct understanding of logical or linguistic form. I'm not trying to prop up a relativist position arguing that there is no progress; I just think it's interesting to consider how people would answer this differently.
posted by thelonius at 7:19 PM on January 31, 2019 [1 favorite]

"@klangklangston- I don't really see what you're getting at. It may be worth noting that (early) Wittgenstein at least was pretty hostile to philosophy."

Arguing that a mathematician, especially a "pure mathematician" (as she calls herself), is "crashing" the discipline of philosophy is implying both that they are inherently distinct and that exploring the rules of symbolic logic is a philosophical pursuit, not a mathematical one.
posted by klangklangston at 11:21 AM on February 1, 2019

This was an interesting talk, and I appreciate being introduced to it here.

That said, I have a lot of individual complaints about the specific examples. I'm not convinced that gay marriage can be represented as a single binary tree. Where do "any number of sentient beings with any relationship who can give credible consent should be allowed to marry" fit in? The airline example is missing several higher level steps: "corporate managers are required to maximize revenue to shareholders," "selling empty seats while simultaneously charging people who are late for planes provides extra unearned revenue," and "capitalist institutions are always as exploitative of customers as possible, while remaining profitable." There's also another dimension where personal ethics and professional directives compete. The police example makes no effort to claim that distrust of cops among the Black community leads to short-timescale events in which individuals are less compliant. That seems to be the implicit assumption, but it's exactly the opposite of every police interaction I've ever observed. The examples are so simplified, they make it hard to take seriously the idea that this approach can be useful.

I spend a fair part of my life lecturing to humanities students in the last quantitative class they will ever take. My goal is, essentially, to convince them that a quantitative analysis is a fun and useful thing to do when reading a sensational news story, hiring an insurance agent, or voting for a legislator. I pretend it's all about black holes, to keep people interested. I appreciate any attempt to bring a quantitative world view to people who aren't used to thinking that way.

But. . . is systematization really the thing to champion? My friends in the humanities have far more detailed charts and rubrics for characterization than anything we in the math and physical sciences division could come up with. Most of them are going great work. But, it's not solely because they're systematic. Detailed decision trees are also common to film critics, bird-watchers, and lawyers. (And phrenologists, alchemists, and eugenicists.) Others have noted that everything here could pretty easily be cast as philosophy. Math does such things too, but it's hardly unique, and its application to the real world depends critically on the choice of definitions, which is entirely absent in this presentation.

If you ask me, the only thing that makes math and science unique in the academy, or useful as an analogy for interacting with the human world, is our cultural tradition of only saying things that could be proven wrong. There are lots of valuable and interesting questions that can't fit into that scheme, and I'm grateful people study them. But, as an approach to evaluating the world, "don't make factual statements unless you can explain what would convince you that you are wrong," seems like an important concept. I'd argue that it's more useful than systematic thinking, which every train-spotter does.
posted by eotvos at 11:36 AM on February 1, 2019 [4 favorites]

the mathematics of taking abstraction to it's absolute limit?

fwiw...
What does it mean to understand a piece of mathematics? "I first really appreciated this after reading an essay by the mathematician Andrey Kolmogorov. You might suppose a great mathematician such as Kolmogorov would be writing about some very complicated piece of mathematics, but his subject was the humble equals sign: what made it a good piece of notation, and what its deficiencies were."[1]

John Baez on Research Tactics: "Grothendieck came along and gave us a new dream of what homotopy types might actually be. Very roughly, he realized that they should show up naturally if we think of 'equality' as a process—the process of proving two thing are the same—rather than a static relationship."[2,3,4]
posted by kliuless at 3:22 PM on February 2, 2019 [3 favorites]