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mathematician, composer, photographer, fiddler

29 Jul 2012 | categories: Speeches

Existential Angst

My toast to my sister at her wedding

I’m not very good at speaking in public. I mean, it’s my job—I’m a university lecturer—but that’s different. There’s a blackboard and if I speak into it then the sound waves reflect to the audience, and if I wait long enough then by the time I turn round everyone’s gone.

When I started thinking about giving a wedding toast, I thought of something a friend of mine, a very grand man, the Professor of Algebraic Surgery at the University of Edinburgh, once told me about his father’s wedding. His father is the German literary critic Marcel Reich-Ranicki. Most of you have probably never heard of him, but in Germany he’s a household name. Think of him as the German Harold Bloom, except that in Germany, as hard as it may be to believe, literary critics are A-list celebrities.

In 1940 Reich-Ranicki and his entire family found themselves in the Warsaw Ghetto. Two years later he learned that his life would be spared but his fiancée’s would not, unless he married her immediately. At the hastily organized wedding, he was suddenly struck by the words:

Ward je in dieser Laun’ ein Weib gefreit?

That’s an archaic German translation of a line from Shakespeare’s Richard III:

Was ever woman in this humour wooed?

A recent BBC radio program began with a speech by Reich-Ranicki about his wedding, and went on to explore Shakespeare’s ability to speak across so many cultures and ages. That made me wonder what Shakespeare might have to say to us on this occasion.

Parents rofling

Unfortunately I’m no literary genius so the first words which struck me were:

To be, or not to be

Seeing my little sister get married before me does affect my outlook in various ways. But it doesn’t throw me into existential angst. Even if my parents wish it would.

Actually, the reason I thought of that quotation first was because in thinking about Nazis and Shakespeare, I immediately thought of Ernst Lubitsch’s 1942 film To Be or Not to Be. It’s about a troupe of actors in Nazi-occupied Warsaw who use disguise and acting to fool the occupying troops. Jack Benny plays a Shakespearean actor whose wife instructs her secret lover to wait in the audience until Benny begins Hamlet’s famous soliloquy, at which point he is to walk out and come to her dressing room, as this will assure their privacy. The scene recurs throughout the film with a very funny twist in the final scene, which I won’t spoil for you. The film is hilarious and clearly influenced Quentin Tarantino’s Inglorious Basterds in many ways. But I digress.

The next Shakespeare quotation I thought of was:

See, how she leans her cheek upon her hand!
O, that I were a glove upon that hand,
That I might touch that cheek!

Sister & husband clapping

The bride is indeed exceedingly gorgeous today, but what an incestuous thing for a brother to say in a wedding toast!

Finally I thought of Sonnet 116:

Let me not to the marriage of true minds
Admit impediments. Love is not love
Which alters when it alteration finds,
Or bends with the remover to remove:
O no! it is an ever-fixed mark
That looks on tempests and is never shaken;
It is the star to every wandering bark,
Whose worth’s unknown, although his height be taken.
Love’s not Time’s fool, though rosy lips and cheeks
Within his bending sickle’s compass come:
Love alters not with his brief hours and weeks,
But bears it out even to the edge of doom.
If this be error and upon me proved,
I never writ, nor no man ever loved.

Stunning and very appropriate for this couple today. [And isn’t it wonderful that in Shakespeare’s English, “prove” rhymed with “love”?]

But there is a higher authority than Shakespeare, at least for this particular audience, and I want to close with some of his words.

Love:

Humans do claim a great deal for that particular emotion.

The man who said those words, as many of those gathered here today probably already know, was:

Spock

Stardate 5725.6

To the bride and to love!


2 Jul 2012 | categories: Coordinates

Baltimore

I’m exceedingly happy to be joining the topology group at Johns Hopkins University. Please note my new address.


22 Jun 2012 | categories: Talks, Mathematics

Euler Calculus in Edinburgh

I’m looking forward to speaking about A New Approach to Euler Calculus for Continuous Integrands at ATMCS 5 in Edinburgh on Monday 2 July 2012.

I will generalize Euler calculus from constructible integrands to continuous integrands in a way which is additive & functorial, satisfies a Fubini theorem, and is defined within any O-minimal theory.


24 May 2012 | categories: Music

In Medias Res

I’ve uploaded In Medias Res, a player piano piece I composed for my concert at the Centro Nacional de las Artes in Mexico City.


17 Mar 2012 | categories: Bookbinding

How to Optimize a Codex

Coptic Samizdat

The best way to print a book is in signatures—that is, as a sequence of nested bifolia to be sewn together through their folds to form a codex. (See Wikipedia for definitions of these terms.)

Traditionally, a book is printed with the same number of bifolia in each signature. This is because a signature is traditionally made by folding a single large sheet of paper in half repeatedly and then trimming.

However, if one prints bifolia individually then there is a priori no reason for the number of bifolia in each signature to be the same. In fact, there is good reason for them not to be.

Landmark page placed at beginning of signature

Indeed, in many forms of bookbinding (e.g. Coptic binding), great prominence is given to pages at the beginnings, middles & ends of signatures. The presentation of a book can therefore be greatly enhanced by varying the number of bifolia in each signature to place landmark pages of the book (e.g. beginnings of chapters) in these prominent positions.

This isn’t entirely straightforward to do, so I’ve written a program to do itthe Signature Optimizer.

I’ve been using it myself for some time and am very pleased with the results.

I even use it when printing short papers I don’t intend to sew. (I usually trim margins first using Briss so that the text in the resulting A5 booklet isn’t much smaller than the intended full-sized A4 sheets, saving lots of paper.)

I wrote the Signature Optimizer in JavaScript so it can easily be used by anyone with a web browser. The source code is all inline so you can simply save the page source to your disk to use it offline. (In fact, it’s easy to install as a standalone app on an iPhone or iPad: just navigate to the Signature Optimizer in Safari, tap the bookmark button and then tap “Add to Home Screen”.)

The Signature Optimizer also generates a LaTeX script which transforms a given PDF file into a PDF file which, when printed, produces bifolia which are ready to fold and sew. To do this, simply save the generated LaTeX script as a file, replace your-file.pdf with the name of the PDF file you want to print, and run pdflatex. You may want to experiment with the scaling factor and the value of delta (the distance between pages within a bifolium).

How did the signature optimizer come about? How does it work?

London Topological Tube Map Diary

In October 2011 I found myself couch surfing in London. I was taking the tube a lot so was thinking a lot about shortest paths through its famous topological map (compare Harry Beck’s radical original 1933 topological tube map, and his early sketch, on which the current map is based and which Beck completed as an uncommissioned spare time project, as well as GH Davis’s 1927 three-dimensional drawings of the London Underground and the London Sound Survey’s Soundmap of London Canals and Minor Rivers). One day while gazing mesmerized at the stunning model-train-set-like view of tangled roads & railways from some friends’ 17th story apartment, it struck me that arranging a book into signatures is quite like finding a short path through the underground. The stations are all the pages divisible by 4 and the underground links are all imaginable signatures linking these pages. The nicer a signature—the more landmark pages it exhibits and the closer the number of its bifolia to the ideal number for a given paper weight—the shorter the link. Finding a good sequence of signatures, then, is the same as finding a short path from the first page to the last through this network. I read about Dijkstra’s algorithm (see also Dijkstra’s original 1959 paper) for finding a “shortest path tree” within a directed metric graph, but I eventually realized that the situation is far simpler since the graph in question is acyclic and the page numbers in fact give a topological sorting of the graph’s nodes. This topological sorting makes it easy to inductively construct a shortest path tree. The main task, then, is to define the length of a signature in this graph. I took this to be the sum:

length(signature) = λ · ( #{ landmark pages in signature } – #{ landmark pages given prominence } ) + (1-λ) · p ( #{ bifolia in signature } )

where 0 ≤ λ ≤ 1 is a constant and p is a polynomial with various properties. Specifically, I wanted p(4) < p(3), p(6) < 2·p(3) and p(3) + p(4) < p(7) < p(2). To find such a polynomial, I fit a degree-2 polynomial to the points (2,4), (3,2), (4,1), (5,1), (6,2), (7,7/2). This gave:

p(x) = 10.4643 – 4.16964 x + 0.455357 x2

Experimenting then showed that taking λ=½ strikes a good balance between fitting landmark pages into prominent positions and using reasonable signature lengths. (Taking λ=1 gives signature arrangements with most landmark pages in prominent positions but with impractical signature lengths. Taking λ=0 gives signature arrangements indifferent to the placement of landmark pages.)

Afterword

I later realized I had essentially rediscovered the Knuth–Plass algorithm for breaking lines in TeX, which was itself first developed for typesetting music:

“The idea of applying dynamic programming to line breaking occurred to DE Knuth in 1976, when Professor Leland Smith of Stanford’s music department raised a related question that arises in connection with the layout of music on a page. During a subsequent discussion with students in a problem-solving seminar, someone pointed out that essentially the same idea would apply to the texts of paragraphs as well as to music.” —Knuth & Plass, Breaking Paragraphs into Lines, 1981.

All this suggests implementing the optimizer as a TeX package which, when loaded in the preamble of a TeX document, would result in a PDF of optimized bifolia, the landmark pages having been determined automatically by TeX. Even better, it could be integrated into TeX’s layout engine so that, for example, a document otherwise typeset on just over 16 pages would be squeezed onto 4 bifolia.

References


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