Henrietta Midonick

My reading is not very focused. I'm trying to improve this, trying to arrange things so that I might know a reasonable amount about something rather than knowing the minimus of everything. For the moment, though, I have a cupboard full of books that I picked up from charity shops for almost nothing because they looked, you know, kind of interesting. My friend has a new girlfriend, and when I met her she saw this book and said "Ah, so you're a numbers person, are you?" which I suppose was a reasonable enough assumption. Fortunately, I happened to have a copy of Jan Tschichold's "Illustrated History of Writing and Lettering" with me so I could prove that I liked numbers and letters.

So I'm no expert, and can say nothing about the value of this collection of excerpts from primary texts (ancient Babylon to 14th century Immanuel Ben Jacob Bonfils) may have for the student of mathematical history. As a lay reader, I'm not really here for the maths, anyway (some of it is over my head, and much of the rest is simply uninteresting). In the first part, which deals with various ancient civilisations - Babylonian, Egyptian, Indian and so on - I get some fun from Mayan glyphs (number represented by key characteristics in the drawing of little faces) and Incan quipu (number represented by a sophisticated kind of string-knotting - there are line drawings of some; one looks like a terrifying hundred-legged spider on the ceiling over your bed). The appeal is not in witnessing the manipulation of number, but the emergence of number (indeed, of writing itself - not only in algebra do numbers and letters meet).

There are purely literary pleasures, too: the fragmentary quality of one Babylonian tablet results in a satisfying piece of absurd poetry:

I found a stone, but did not weigh it; ...
I weighed it: 1 ma-na. What was the original weight of the stone? ...
I found a stone, but did not weigh it; ...
one-eleventh and ... , I weighed it: 1 ma-na.
What was the original weight of the stone? ...
I found a stone, but did not weigh it; ...
I weighed it: 1 ma-na. What was the original weight of the stone? ...
I found a stone, but did not weigh it; after ...
I weighed it: 1 ma-na. What was the original weight of the stone? The original weight of the stone was ...
I found a stone, but did not weigh it

...and so on. I think of Molloy sucking his pebbles.

The second part of the book deals with early eastern mathematics, much of it a seemingly endless collection of tiresomely practical arithmetical problems. Yet here, too, there are bright spots, moments to make us realise how little we understand of people. Following this passage from the Arithemetical Classic of Hsia-Hou Yang (sixth century):

Now 2,000 packages of cash much be carried to the twon at the rate of 10 cash per bundle. How much will be given to the mandarin and how much to the carrier? Answer: 1,980 packages and 198-2/101 cash to the mandarin; 19 packages and 801-98/101 to the carrier.

...is a dry footnote stating that "there is no reason given for the division of 2,000,000 by 1,010".

The third and final part is on Greek geometry (it ends, appropriately enough, with Proclus in the 5th century summarising the history of Greeks maths). There's a feeling of homecoming here as familiarly systematic, organised, logical reasoning breaks in. Proposition 3 from Archimedes' "On Spirals": "Given any number of circles, it is possible to find a straight line greater than the sumo f all their circumferences." I pause to think of a proof. It's annoying, it seems something both impossible to prove and not in need of proof - the idea of the infinite. "We have only to describe polygons about each and then take a straight line equal to the sum of the perimeters of the polygons." Well, there you go. Archimedes was cleverer than I am.

The editing is frustrating. Each writer gets a short contextualising introduction, which is fine; but the excerpts themselves have been lifted verbatim from earlier editions, complete with cryptic references back to works already cited (but not in this edition), unexpanded abbreviations, and so on. There is no bibliography and no index. Still, it's alright for browsing.… (más)