Chen review

Chen review

[pjf]

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/ ]

Re: Chen review

[John Baez]

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 <pjf@seas.upenn.edu> 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/ ]