# Category of scones

(This post is completely unrelated to the category of cones. Apologies if you were mistakenly directed here by a fuzzy search engine.)

In May 2013, the category theorist Dr Eugenia Cheng (whom you may recognise from her quotations on the Imre Leader Appreciation Society) wrote a paper on the ideal cream tea. This received a lot of media attention, including from the Daily Mail, Telegraph and The Aperiodical (in increasing order of accuracy).

The paper discusses the optimal proportions of cream, strawberry preserve and scone for an ideal cream tea. Unlike most academic papers, this one has an accompanying video:

I was slightly disappointed that there was no category theory in the paper, despite the author being a category theorist. It did, however, explicitly mention that the preserve should be added before the cream, in the style of the Cornish. By comparison, residents of Devon advocate the reversed approach of adding the cream first. The fact that these are genuinely different outcomes can be neatly abstracted into the statement that this diagram in the category of scones does not commute:

The other shortcoming of Eugenia Cheng’s otherwise brilliant paper is that it doesn’t mention that cream teas can be augmented by the addition of a bisected strawberry, as in the image below. The left-hand scone has been prepared using the Devonian order of morphism composition, whereas the right-hand scone has been prepared using the (strictly superior) Cornish method:

Jacob Aron mentioned on Twitter that if the scone has a diameter of 2 centimetres, the clotted cream would need to be infinitely tall, distributed in the form of a Dirac delta function† $V \delta(x) \delta(y)$, where V is the desired volume of cream.

† Disclaimer: This is not a function in the pure-mathematical sense.

### Flexagons

There have been other recent examples of gastronomical mathematics in the last year. I presume that you’ve seen the integral banana I posted several months ago. Additionally, Evelyn Lamb has reviewed a multitude of videos involving both mathematics and food, including the culmination of Vi Hart’s flexagon series of videos.

Evident from the construction of the simplest hexaflexagon is that we are dealing with a Möbius strip, which is folded to form a multiple cover of the hexagon. The automorphisms of the Möbius strip (C18) quotiented by the automorphisms of the resulting hexagon (C6) gives the group of flexations (C3).

With three of the strips used to build a hexaflexagon, one can also construct a Boerdijk-Coxeter helix. Twenty cyclic Boerdijk-Coxeter helices of 30 tetrahedra each are obtained by partitioning the 600-cell (a four-dimensional regular polytope) according to a discrete Hopf fibration.

This entry was posted in Uncategorized. Bookmark the permalink.

### 0 Responses to Category of scones

1. thejoemoose says:

Reblogged this on Ramblings, shamblings, and other grooves and commented:
Did I just read a blog entry on scone morphology??

2. Simon Tatham says:

Gastronomical mathematics: I have long thought that it ought to be possible to serve an entire meal consisting of nothing but foodstuffs mentioned in well known mathematical theorems or constructions. The Ham Sandwich Theorem, Conway’s game ‘Sprouts’, and the Blancmange Function approximate a balanced diet between them, but surely there must be ways to make it more interesting.

(I suppose the real question is whether Zorn’s Lemon gets disqualified.)

• Sam Cappleman-Lynes says:

If anyone suggests eating the chocolate bar from ‘Chomp’, I’m leaving.

• wojowu says:

We can share this chocolate, if you let me take first turn 😛

• apgoucher says:

Here are some more of which I can think:

1. The Sausage Catastrophe: arrange n spheres in d-dimensional space to minimise the volume of the convex hull. For d = 3, a collinear ‘sausage’ is optimal when n is below around 58, beyond which a three-dimensional arrangement is optimal. For d = 4, the cut-off point is believed to be 375769. For d = 5 and above, it is believed that sausages are always optimal.

2. The Cookie-Cutter Problem: it’s easy for me to confuse myself, since it was one of the topics Vishal Patil, Emily Bain and I used in the Trinity Mathematical Society edition of Call My Bluff (where we present three conflicting definitions, only one of which is correct, and the opponents have to guess). Hence, I suggest you Google it.

3. Gingerbreadman Map: a particular chaotic map from R^2 to itself.

4. Apples and lemons: Keplerian surfaces obtained by revolving an arc about the line connecting its endpoints.

Of course, this is excluding puns such as the Croissant Distribution, Leech Lettuce and Real Lime. Presumably you’re using the blancmange function to get the dairy component of your balanced diet? I don’t think that it’s complete yet, until we have some mathematical seafood to provide the iodine quota.

• ggendler says:

A paper which has been discussed multiple times at UKMT camps is ‘Lion and Man – Can Both Win?’ by Bollobas, Leader and Walters. Therefore if any of the guests at your meal are lions, feeding them a man would be very mathematical.

• apgoucher says:

That’s assuming that the man hasn’t already been mauled by an angry ursine for trespassing in a Baire space…

3. cloudswrest says:

Regarding gastronomical mathematics, have you ever had a Klein bagel, https://en.wikipedia.org/wiki/Klein_bottle#The_figure_8_immersion ?