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November 3, 2015

Cakes, Custard, Categories and Colbert

Posted by John Baez

As you probably know, Eugenia Cheng has written a book called Cakes, Custard and Category Theory: Easy Recipes for Understanding Complex Maths, which has gotten a lot of publicity. In the US it appeared under the title How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics, presumably because Americans are less familiar with category theory and custard (not to mention the peculiar British concept of “pudding”).

Tomorrow, Wednesday November 4th, Eugenia will appear on The Late Show with Stephen Colbert. There will also be another lesser-known guest who looks like this:

Apparently his name is Daniel Craig and he works on logic—he proved something called the Craig interpolation theorem. I hear he and Eugenia will have a duel from thirty paces to settle the question of the correct foundations of mathematics.

Anyway, it should be fun! If you think I’m making this all up, go here. She’s really going to be on that show.

I’m looking forward to this because while Eugenia learned category theory as a grad student at Cambridge, mainly from her advisor Martin Hyland and Peter Johnstone, Hyland became interested in n-categories and Eugenia wound up doing her thesis on the opetopic approach to n-categories which James Dolan and I had dreamt up. I visited Cambridge for the first time around then, and we wound up becoming friends. It’s nice to see she’s bringing math and even category theory to a large audience.

Here’s my review of Eugenia’s book for the London Mathematical Society Newsletter:

Eugenia Cheng has written a delightfully clear and down-to-earth explanation of the spirit of mathematics, and in particular category theory, based on their similarities to cooking. Sometimes people complain about a math textbook that it’s “just a cookbook”, offering recipes but no insight. Cheng shows the flip side of this analogy, providing plenty of insight into mathematics by exploring its resemblance to the culinary arts. Her book has recipes, but it’s no mere cookbook.

Among all forms of cooking, it seems Cheng’s favorite is the baking of desserts—and among all forms of mathematics, category theory. This is no coincidence: like category theory, the art of the pastry chef is one of the most exacting, but also one of the most delightful, thanks to the elegance of its results. Cheng gives an example: “Making puff pastry is a long and precise process, involving repeated steps of chilling, rolling and foldking to create the deliciously delicate and buttery layers that makes puff pastry different from other kinds of pastry.”

However, she does not scorn the humbler branches of mathematics and cooking, and there’s nothing effete or snobby about this book. No special background is needed to follow it, so if you’re a mathematician who wants your relatives and friends to understand what you are doing and why you love it, this is the perfect gift to inflict on them.

On the other hand, experts may be disappointed unless they pay close attention. There is a fashionable sort of book that lauds the achievements of mathematical geniuses, explaining them in just enough detail to give the reader a sense of awe: typical titles are A Beautiful Mind and The Man Who Knew Infinity. Cheng avoids this sort of hagiography, which may intimidate as often as it inspires. Instead, her book uses examples to show that mathematics is close to everyday experience, not to be feared.

While the book is written in bite-sized pieces suitable for the hasty pace of modern life, it has a coherent architecture and tells an overall story. It does this so winningly and divertingly that one might not even notice. The book’s first part tackles the question “what is mathematics?” The second asks “what is category theory?” Unlike timid people who raise big questions, play with them a while, and move on, Cheng actually proposes answers! I will not attempt to explain them, but the short version is that mathematics exists to make difficult things easy, and category theory exists to make difficult mathematics easy. Thus, what mathematics does for the rest of life, category theory does for mathematics.

Of course, mathematics only succeeds in making a tiny part of life easy, and Cheng admits this freely, saying quite a bit about the limitations of mathematics, and rationality in general. Similarly, category theory only succeeds in making small portions of mathematics easy—but those portions lie close to the glowing core of the subject, the part that illuminates the rest.

And as Cheng explains, illumination is what we most need today. Mere information, once hard to come by, is now cheap as water, pouring through the pipes of the internet in an unrelenting torrent. Your cell phone is probably better at taking square roots or listing finite simple groups than you will ever be. But there is much more to mathematics than that—just as cooking is much more than merely following a cookbook.

Posted at November 3, 2015 10:03 PM UTC

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Re: Cakes, Custard, Categories and Colbert

Well, that’s pretty strong incentive to catch the show tomorrow! I was a big fan of the Colbert Report while it lasted, and caught just a bit of the new Late Night during its first week (during all the hoopla), but haven’t tuned in recently for fear of being disappointed…

Could it be that Stephen Colbert is a fan of mathematics? He’s also interviewed Terence Tao and Edward Frenkel.

Possible nitpick: does Eugenia spell it ‘pastry’, or ‘pastery’? I see two places where pastry is puffed up with an extra ‘e’, so was just wondering.

Posted by: Todd Trimble on November 4, 2015 2:32 AM | Permalink | Reply to this

Re: Cakes, Custard, Categories and Colbert

I only have the American version of her book on hand, and there it (unsurprisingly) says “pastry”. The spelling “pastery” may have been a weird slip of my own… so I’ve corrected that.

Posted by: John Baez on November 4, 2015 4:00 PM | Permalink | Reply to this

Re: Cakes, Custard, Categories and Colbert

Colbert also interviewed Art Benjamin:

who, unlike Tao, did have a favorite number when Colbert asked. =)

Posted by: Alissa Crans on November 4, 2015 6:04 PM | Permalink | Reply to this

Re: Cakes, Custard, Categories and Colbert

If Colbert should interview John Baez, would he get three favorite numbers?

Posted by: Todd Trimble on November 4, 2015 7:24 PM | Permalink | Reply to this

Re: Cakes, Custard, Categories and Colbert

I would give him one: 24.

By the way, I’m giving a public lecture at the winter meeting of the Canadian Mathematical Society, in Montreal, on Saturday December 5th. The title is The answer to the ultimate question of life, the universe, and everything.

Just how over-the-top is that? I wasn’t sure the organizers would like it, but it turns out they love it and even hope it attracts clueless people expecting the mysteries of the universe to be revealed. I hope not too many audience members are disappointed. It will be essentially a fourth installment of ‘My favorite numbers’.

Speaking of digressions: for fans of category theory, Prakash Panagaden will be having a session on Logic, Category Theory and Compuation at that conference. There will be talks by André Joyal, Robert Seeley, Richard Blute, Robin Cockett, Peter Selinger, Phil Scott, Pieter Hofstra and others. I’ll be there too.

Posted by: John Baez on November 4, 2015 9:41 PM | Permalink | Reply to this

Re: Cakes, Custard, Categories and Colbert

Sounds like a lot of fun, and wish I could be there (not so far from where I live). But it seems that I have become a part of the annual Nutcracker performance put on by my daughter’s dance studio, which is that weekend, and this year I am an understudy for Herr Drosselmeyer, so I really must stay put. :-) Hopefully your talk will be recorded.

Posted by: Todd Trimble on November 5, 2015 2:57 AM | Permalink | Reply to this

Re: Cakes, Custard, Categories and Colbert

If something is recorded I’ll let you know. Otherwise, happy Nutcracker!

Posted by: John Baez on November 5, 2015 3:01 AM | Permalink | Reply to this

Re: Cakes, Custard, Categories and Colbert

Awesome alliteration.

Posted by: Emily Riehl on November 4, 2015 7:03 PM | Permalink | Reply to this

Re: Cakes, Custard, Categories and Colbert

beat only by a conversation on cartesian closed categories and computation on the n-cat cafe (continued in the comments):

Posted by: Trent K on November 8, 2015 7:30 AM | Permalink | Reply to this

Re: Cakes, Custard, Categories and Colbert

YouTube: Dr. Eugenia Cheng Gives Paula Deen A Run For Her Butter (on the “The Late Show with Stephen Colbert” channel).

(is she over caffeinated here?)

Posted by: RodMcGuire on November 5, 2015 2:05 PM | Permalink | Reply to this

Re: Cakes, Custard, Categories and Colbert

(is she over caffeinated here?)

I don’t think so. You see the same kind of exuberance in some other video recordings of her. (For example, there’s one where Eugenia is explaining the exact proportions for making a perfect scone, or something like that.)

I thought she was great! There’s not much time to make a few points (that were probably also made in her book) that are well worth making: (1) math is fun, (2) math puts together a few simple ingredients to make something yummy, (3) by iterating a few smallish rules or steps one can build up to something complex (exponentially so), (4) mathematicians aren’t just people who deal with numbers and calculations, (5) there is freedom in mathematics to “make up your own rules”. She had a kind of fun madcap energy and Stephen played well off of that (loved the swordplay with rolling pins!). Also found funny the seconds of dead silence as they were enjoying their pastries together with cream on their faces, before interlocking their arms for a final bite.

Posted by: Todd Trimble on November 6, 2015 2:09 AM | Permalink | Reply to this

Re: Cakes, Custard, Categories and Colbert

I’m not too happy with her analysis of mille-feuille.

If you count the layers of butter then there are only 3 n3^n of them and thus 3 n+13^{n}+1 layers of dough. Maybe if she had brushed butter over the dough while folding then adjacent dough layers wouldn’t coalesce and her analysis would be closer.

Posted by: RodMcGuire on November 6, 2015 1:58 PM | Permalink | Reply to this

Re: Cakes, Custard, Categories and Colbert

Eugenia has always been funny and a bit hyperactive in her Catster videos, and I expect that planning out this show with Colbert brought out that side of her even more. The alternative would be to play the ‘straight man’ — a serious, earnest mathematician — and let Colbert do all the jokes, but once you’re on late-night TV making mille-feuille in front of a blackboard that alternative becomes a bit difficult. And she knows the world has already seen too many images of earnest mathematicians unable to joke around.

Posted by: John Baez on November 6, 2015 5:46 PM | Permalink | Reply to this

Re: Cakes, Custard, Categories and Colbert

Especially in american comedy shows I observed that automatized laughing audios are often used - probably to give the audience an indication that there was supposed to be a joke - ? Such audios could eventually also be used for the canonical deadpan mathematician, even if the deadpan mathematician wasn’t joking.

Posted by: nad on November 11, 2015 4:19 PM | Permalink | Reply to this

Re: Cakes, Custard, Categories and Colbert

Laugh tracks are not yet completely obsolete, but I think they are largely obsolescent (nowadays I think their use would verge on “campy”; it’s hard to find just the right word, but “retro” might also fit).

Late Show is recorded before a live audience of course.

Posted by: Todd Trimble on November 11, 2015 4:38 PM | Permalink | Reply to this

Re: Cakes, Custard, Categories and Colbert

Never mind Craig’s interpolation theorem—a surprisingly little-known fact is that Daniel Craig is a descendant of Brouwer. Once you know it, you can see it:

L.E.J. Brouwer and Daniel Craig

Posted by: Tom Leinster on November 11, 2015 12:16 AM | Permalink | Reply to this

Cakes, Custard, Categories for WAGs

I love the book and cannot imagine anyone else writing it besides Eugenia. One possible audience for it is spouses, siblings, parents and friends of category theorists, to explain to them “what we do at the office”. I wonder whether anyone has had any reaction from this audience.

Posted by: Paul Taylor on December 15, 2015 7:12 PM | Permalink | Reply to this

Re: Cakes, Custard, Categories and Colbert

There’s another review of Eugenia’s book, by Jeremy Martin, in the Notices of the AMS. It’s quite nice, go read it.

There are one or two things he says that I disagree with. For instance, he writes

the writing gives the impression that category theory is necessary to distinguish between different kinds of sameness. I disagree. Working mathematicians can distinguish between homeomorphism and homotopy equivalence without explicit knowledge of category theory.

I would argue that a mathematician distinguishing between homeomorphism and homotopy equivalence is using category theory, whether they realize it or not.

However, I think I’m with him in being confused about the triangle on page 196. Eugenia says that “logic” in this triangle “deals with making arguments about things”. That seems to me to be so general as to encompass all mathematicians. (Likewise with her description of “algebra” as “where we manipulate symbols”.) On the other hand, I don’t know where on the triangle to put combinatorics or analysis. Does anyone know the origin of the “theory” Eugenia is referring to here?

Posted by: Mike Shulman on September 24, 2016 10:03 PM | Permalink | Reply to this

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