From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8691 Path: news.gmane.org!not-for-mail From: John Baez Newsgroups: gmane.science.mathematics.categories Subject: Re: Chen review Date: Tue, 1 Sep 2015 09:46:08 +0800 Message-ID: References: Reply-To: John Baez NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: ger.gmane.org 1441202109 16245 80.91.229.3 (2 Sep 2015 13:55:09 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 2 Sep 2015 13:55:09 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Wed Sep 02 15:55:02 2015 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.7.22]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1ZX8VB-0000Fs-4K for gsmc-categories@m.gmane.org; Wed, 02 Sep 2015 15:55:01 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:50275) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1ZX8U6-0001CG-Ue; Wed, 02 Sep 2015 10:53:54 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1ZX8U7-00075r-Dr for categories-list@mlist.mta.ca; Wed, 02 Sep 2015 10:53:55 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8691 Archived-At: Hi - While we're at it, here is my own review of Cheng's book, which should eventually appear in the notices of the London Mathematical Society. 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 a mere cookbook. > I'm not sure "exacting" is the right word to describe category theory, but there's probably *something* difficult about it that it shares with making pastries. Obviously I couldn't say "abstract". Best, jb On Sat, Aug 29, 2015 at 10:36 PM, pjf wrote: > > Free Press Journal (India) > > August 28, 2015 > > Cakes, Custard & Category Theory - Culinary approach to maths > > LENGTH: 482 words > > New Delhi: Cooking can be an answer to simplifying mathematics, says a > new book which tries to whet the appetite of maths whizzes and > arithmophobes alike with recipes and puzzles. > > > From simple numeracy to category theory ('the mathematics of > mathematics'), maths crusader Eugenia Cheng prescribes easy recipes for > understanding complex arithmetic in her book "Cake, Custard and Category > Theory". > > Calling on a baker's dozen of entertaining, puzzling examples and > mathematically illuminating culinary analogies - including chocolate > brownies, iterated Battenberg cakes, sandwiches, Yorkshire puddings and > Mobius bagels - Cheng tells readers why everyone should love maths. > > So what on earth does a recipe have to do with maths? "You might think > that rice cookers are for cooking rice. This is true, but this same > piece of equipment can be used for other things as well: making clotted > cream, cooking vegetables, steaming a chicken. Likewise, maths is about > numbers, but it's about many things as well - getting the right answer, > putting ideas together and so on," she says in the book, published by > Hachette India. > > According to Cheng, a senior lecturer in Pure Mathematics at the > University of Sheffield, many people are either afraid of maths, or > baffled by it, or both. > > "Or they were completely turned off it by their lessons at school. I > understand this - I was completely turned off sport by my lessons at > school, and have never really recovered. I was so bad at sport at > school, my teachers were incredulous that anybody so bad at sport could > exist. And yet I'm quite fit now, and I have even run the New York > marathon," he writes. > > She says 'category theory' which can be thought of as the 'mathematics > of mathematics' is about relationships, contexts, processes, principles, > structures, cakes and custard. > > "Yes, even custard. Because mathematics is about drawing analogies > including custard, cake, pie, pastry, doughnuts, bagels, mayonnaise, > yoghurt, lasagne and sushi." > > Maths, according to Cheng, like recipes, has both ingredients and > method. "And just as a recipe would be a bit useless if it omitted the > method, we can't understand what maths is unless we talk about the way > it is done, not just the things it studies," she says. > > Citing examples of cottage, shepherd and fishermen pies, she says all > these are more or less the same with the only difference being the > filling that is sitting underneath the mashed potato topping. In all > these cases, the recipe is not a full recipe but a blueprint and one can > insert own choice of fruit or meat or fillings. > > "This is also how maths works. The idea of maths is to look for > similarities between things so that you only need one 'recipe' for many > different situations. The key is that when you ignore some details, the > situations become easier to understand, and you can fill in the > variables later," she writes. > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]