Here’s the piece on Trefethen’s Index Cards I talked about recently.

The idea of an intellectual carrying around a notebook, filling it with the thoughts that arise in his mind from day-to-day, has been capitalised on in recent years by various companies. The market for serious-looking notebooks confronts us in every bookshop. Many people buy notebooks with this purpose in mind but not many have them published. And historically, famous thinkers whose notebooks have ended up being published, such as Quine, Samuel Butler and Georg Lichtenberg, have only managed twenty or thirty years worth of notes at best.

These facts make Balliol’s Nick Trefethen, University Professor of Numerical Analysis, quite unique. Since 1970 when he was 14, Trefethen has been typing down his thoughts onto index cards, initially at 3”x5”, at some point switching to 4”x6” which he has used ever since, now writing roughly two or three per month. After fourty years of writing cards, Trefethen has made a selection of them public as Trefethen’s Index Cards, published by World Scientific this year.

There is a striking consistency of quality throughout the cards: they all show that Trefethen is a master of concise expression. While the index card format was initially just a convenient way to store the cards, it became a constraint, forcing a training in conciseness. Trefethen writes, ‘Once I’ve put an idea on a card, it becomes a piece of my mental framework, a principle I will refer to for the rest of my life.’ This consistency is also striking. Trefethen characterises the development of his thought as additive: there are very few cards containing opinions he has now turned his back on. It is thus that Trefethen’s Index Cards gives us a unique opportunity to see the complete, systematic structure of a modern scientific mind, that we can all learn something from, and will probably all find places to disagree with.

The book is organised into chapters titled by card topic, beginning with Ego, and moving through Kids, Living with Others, the Meaning of Life and then onto Politics and Society, Education, The Life of the Professor, Writing and Literature, Memory, Science, Mathematics and Computers, and more besides. Within each chapter the cards are arranged in chronological order, so when reading it’s interesting to compare the development of thought across chapters.

Trefethen’s initial motivation for the cards came from The Glass Bead Game by Hermann Hesse. This work of science fiction is set in a fictional European province dedicated to intellectual pursuits, in which economic and other material pursuits are kept to the minimum necessary. The pinnacle of scholarly pursuit within this country is playing a game with glass beads, through which all the knowledge and belief mankind has gathered through the arts, humanities and sciences is brought together. Deep connections hitherto unknown are uncovered through the process of playing.

Trefethen hoped that he might make a start on collating all knowledge in this way with his cards. He explains that as he grew older he realised that not only is it unfeasible for one man ever to collect all knowledge like this, but also that various philosophical results suggest that the task is impossible even for all humanity banded together to create a glass bead game. But the inspiration remained.

This awareness of the intellectual nature of his project is visible in other places. And the best example of this draws upon Trefethen’s profession, mathematics. On page twenty-four Trefethen says, ‘As the years go by and memory becomes less reliable, I think the habit of writing takes on a special significance. In interacting with the written page, we can edit and adjust and keep on track even at an age when on the hoof, our thoughts would ramble and we’d be at a loss to recall every third name.’

Anyone who does any kind of advanced maths recognises that a lot of work is done by the notation that has taken centuries to develop; without the ease of doing simple, routine moves purely symbolically, our minds would be too cluttered to work on the more interesting things. The thought from this index card is that this seems to apply to all other kinds of thought too, and more as one gets older. Through his cards Trefethen aims to both construct his world, and keep it safe from the ravages of time. And by publishing some of these cards he has enabled us to engage with that carefully constructed world too.