On growth and form

In my mid teens, my family were for a while in a small city close to the border between England and Wales. I have, in general, little good to say about the school I attended there; but two of the teachers were inspirational and played a large part in shaping my life.
Also critical to what I would become was the Municipal Public Library.
It's difficult, now, to explain how wonderful libraries in the UK used to be. They are still immeasurably valuable, of course; without them, minds would be infinitely poorer; but their wings have been successively clipped by rounds of financial cutbacks and by changes in social outlook over the years. Back then, a fourteen year old with his head full of ideas planted by one of those inspirational teachers could walk down to the library and ask for ... anything at all. For free.
One of the things I asked for was Erik Pontoppidan's 1755 The natural history of Norway. Luckily for me (I hadn't realised that the original would be in Danish), the library actually obtained a copy of the 1855 English translation instead. It arrived within the week, brought down for me from the British Library: a huge, old book, printed in archaic type on thick paper pages which I turned in awed reverential amazement. I couldn't take it home; it had to be read in the library itself, brought into a side room where a librarian engaged on administrative tasks could keep a discreet eye on me; but I didn't care. I cycled from school to the library each day and immersed myself in it, reading it twice before it had to be returned.
Another request was for D'arcy Thompson's On growth and form. It came in the second, larger (over a thousand pages) edition from 1942, and it took me a full year to read. I didn't have to read it at the library this time; I could take it home with me, though I had to renew it every two weeks and return it to the shelves every six before (it was on local stock, not on loan from elsewhere like Pontoppidan) booking it out again the following day.
On growth and form was perfectly designed to penetrate my fourteen year old (fifteen year old by the time I finished it) psyche. The two inspirational teachers happened to be in maths and biology, and On growth and form was a meeting of those two fields, a revelation which entranced me in itself. It had at least two other tricks up its sleeve as well.
First, it was written in a beautiful way. The English Literature teacher at school was not one of the inspirational ones, in fact he seemed to have a talent for treading on any youthful interest he encountered (unlike the later Mr Abbot), but he was unable to stamp out the love of language and literature which my parents had kindled in me. The syllabus included plenty of material into which I could disappear, hiding in the undergrowth beyond his reach. And On growth and form was literature in the same way: a lyrical and beautiful landscape in which I could wonder and wander.
Second, it spoke to another discovery which I had made and was exploring at that time: that mathematics and the visual plastic arts were intimately linked. I had recently discovered (in the classroom) the magical alchemy of transformational geometry and the way it could be elegantly encoded in the four or nine digits of a matrix. Thompson's chapter IX, "On the theory of transformations, or the comparison of related forms", showing how this idea could be extended to variable physical identities, took my breath away.
Nowadays, anyone can play with his concepts in a few seconds, using a visually intuitive warp mesh in a graphics package like PaintShop Pro or the more rigorous symbolic methods of a computer algebra language like Mathematica, but in 1966 they were well beyond my (or even my teacher's) analytical scope. That inability to emulate, however, did nothing to take away the sheer awe inspiring beauty of seeing Thompson transform for me on the page one fish or one skull into another. One of the central messages of On growth and form is nature's economy, reusing a simple idea over and over again, and this chapter encapsulated it in way which drew art, biology, language and mathematics in one beautiful gift wrapped package. I have since discovered as an adult that this same chapter is his best known and most widely quoted; but at the time it belonged to me alone.
The reason On growth and form took me a year to read was not just those thousand plus pages; I would have covered them fairly swiftly, slowed down only by the wish to savour them and think about their content. No; what took me a year was laboriously decoding (dictionaries on one side, grammar guides on the other) all his untranslated passages quoted from French, German, Greek, Italian and Latin. I had none of those languages (I still have none in any functional sense), but kept worrying at them until I extracted at least some partial sense from them. Then there were the casual references to Buffon, Democritus, Kant, Maxwell, Plateau (of those five I had heard only of Buffon, and that through his eponymous needle) and others, all of whom I had to look up .
I now (again as an adult) see that Thompson was both brilliant and blinkered, also of a classically educated class which was already beginning to disappear as he wrote. Nobody could write a book like his now, and hope to sell it. And yet, I don't regret the difficulty of reading it. I was, at the time, going for a cross country run every morning (although I told nobody at school and avoided games afternoons if possible): forcing aching muscles beyond common sense for the endorphin rush and the pleasure of early light on dew laden landscape had a lot in common with pushing through unknown linguistic thickets for fuller understanding of Thompson's lucid English. And muscles develop with use; when, a couple of years later on an English literature course, I had to study Chaucer, the same mental muscles stirred, remembered themselves, and didn't let me down; in fact they carried me on through chunks of Dante's Inferno and Vita Nuova, Bocaccio's Decameron, not to mention T S Eliot's relatively trivial scatterings of a lines, couplets, quatrains.
Another two or three years down the line, as an undergraduate, I returned to Thompson, and to chapter IX in particular. Then, though I never forgot him, I didn't see him again for decades. But recently I have been gradually, little by little, here and there, gathering again the books which influenced me as I grew. Many of them arrive thanks to the love of my life who hears me mention a book and goes off to find it for me: so it was with On growth and form, which she gave me on my most recent birthday in an abridged version (a mere 345 pages) perfect for reacquaintance.
By coincidence, whilst writing this I have received an email from a talented social sciences student with whom I am currently working, in which she mentions the effect of seeing a documentary:

"…while I was never good at physics or chemistry … a friend of mine sat me down in front of a documentary ... Basically a lot of talking head quantum physicists talking about quantum physics, but in a very accessible way. But it totally blew me away. ... Once it had finished, my friend and I went and sat outside in the night air, barely talking, just sitting there and breathing, and looking at the world in an entirely new way."

I recognise that feeling; and it is one of the things which Thompson gave me, all that time ago when England was winning the soccer world cup. Science too often takes a po-faced view of itself, demanding to be taken very seriously and feeling belittled if it is treated as a launch pad for general, nonscientific cultural growth. But science and general culture are mutually dependent; neither can exist without the other, each can inform and infuse the other, and they should celebrate any bridge between them, whatever its nature or extent and however tangential.
And, to come back to where I started, free public libraries are a vital investment in cultural completeness - even in the wonderfully empowering days of the world wide web.

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• Erik Pontoppidan, The Natural History of Norway [English translation by Andreas Berthelson] 1755, London: A. Linde.
• D'Arcy Wentworth Thompson, On growth and form. (Abridged) 1992, Cambridge: Canto. 9780521437769 (pbk.). [Originally 1917 and1942, Cambridge: Cambridge University Press.]