Arrangement and Re-arrangement
Lying abed this morning I finished reading Ivar Ekeland’s book “The Best of All Possible Worlds: Mathematics and Destiny” and, while brushing my teeth, alighted on Leah Price’s review of William Sherman’s book “Used Books: Marking Readers in Renaissance England” in the 9th October 2008 edition of the London Review of Books.
I have written before about sometimes being present at the crossroads of the universe when two ideas arrive from different directions, coalesce and drive off together up the hill. Let me try to explain my surprise this time.
Ekeland’s book is really two books. Both are good and well worth reading and, by buying “The Best of All Possible Worlds” (C$14.00 when I bought my copy just before Christmas) you get the two bound into one volume. The first book is a fascinating exploration of the least-action principle from Pierre Louis Maupertuis, a chap of whom I had never heard but who was, apparently, the origin of Voltaire’s Doctor Pangloss, to Poincaré. This book requires no mathematical maturity from the reader and the couple of theorems needed for the argument (including a geometric argument for the existence of a second (non-maximal) diameter of a convex closed curve) are relegated to appendices. It also raises the concept of playing billiards on non-rectangular tables. I have always thought billiards and snooker fairly boring to play and extremely boring to watch but the idea of having different (but convex) table shapes would certainly make them more interesting. Imagine snooker competitions where the competitors didn’t know the (irregular but convex) shape of the table until the start of the match.
Ekeland’s second book deals with human behaviour. He writes in the final chapter “There is a general feeling that science has given us longer and better lives, but has not taught us how to live them.” The last two or three chapters should be compulsory reading for all politicians and university administrators.
Science seems to raise more questions than it provides answers, but human beings are in quest of certainties, and if science will not provide them, then others will—religions and ideologies. And indeed, the first half of the last century was the era of ideologies, which ended with the bloody clash of fascism and communism, while the second half has seen religions emerge as the main actors, and may yet lead us to another conflagration between the Abrahamic creeds…
I find a confusion in this part of the book between science and technology (I don’t, for example, think that there was much science beyond Newton’s Laws of Motion involved in getting men to the moon) but this does not detract from Ekeland’s cri de coeur for sanity and rationality in our thinking. We are in the classical games theory dilemma of needing everyone to act rationally for the good of all. Ekeland believes that the application of mathematics and logic to human and well as scientific problems could, indeed, result in the “best of all possible worlds” in the sense that Voltaire mocked.
The two parts of Ekeland’s book are bound together by that phrase and play on the word “best”: in the first part in its scientific sense selecting our universe from all of those available in the multiverse and in the second part in its societal sense. This is, of course, the very confusion between what “Dr Pangloss” was really saying and what Voltaire was (deliberately?) confusing.
So, where does the article from the London Review of Books come in? The book being reviewed deals with the things that people wrote in the margins of books. Apparently 17th century marginalia now adds to, rather than detracts from, the value of old books. However, the part that interested me was
Even after the invention of printing, aids like tables of contents and indexes were added by hand by individuals. Readers would interleave blank pages, rearrange sections, and could even combine sections from different volumes. The printed page was seen as merely a starting place…
If this was so in the 16th century, how much more should it be the case now. With more and more books becoming available in soft copy (pdf) and with really useful tools like pdftk capable of splitting and recombining pdf files in all sorts of ways (as it says in the pdftk documentation “If PDF is electronic paper, then pdftk is an electronic staple-remover, hole-punch, binder, secret-decoder-ring and X-Ray-glasses”), we are free to build precisely the books we need. If I had a soft copy of Ekeland’s book, I could split it into two and combine the first part with some sections from Voltaire’s Candide (perhaps the world’s most tedious book in its entirety but OK in chunks) and thereby build a new, personalised book. I could then take the second part of Ekeland’s book and combine it, perhaps, with some of Grayling’s essays to build another new book personalised for me.
As an author, I would actually feel quite comfortable about people doing this with my books. I wonder about other authors.