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Tuesday, October 25th, 2011

Time Event
4:53p
Counting on it ...
This book found its way into my hands via the LibraryThing.com “Early Reviewers” program, having been matched with my on-line library by the LTER “almighty algorithm” in the July batch. Unfortunately, the book did not arrive until early October, sort of missing the “early” in “Early Reviewers” for a book that came out the first week of July! Oh, well, I had plenty of other things to read.

Anyway, I was somewhat surprised to have been matched up with Keith Devlin's The Man of Numbers: Fibonacci's Arithmetic Revolution, not having a lot of mathematical books in my collection, although, I suppose, quite a number of biographical books on figures in science and philosophy. This is very much more a look at the man (and a piecing together of his history), rather than the mathematics, per se, so I guess that makes sense.

Leonardo Pisano, filius Bonacci, was from Pisa (of the famed leaning tower), and from the Bonacci family, an attribute which eventually became condensed to “Fibonacci” over time. It appears that his father was a Customs official there, and had, in this role, much contact with the merchant classes, and the business communications of the day. At one point (around 1180-85 CE), Leonardo's father was posted to a North African city, Bugia (presently in Algeria), and, once established there, he sent for his teenage son to join him.

One of the points the author makes early on is how numbers and counting are so intrinsically intertwined with our modern existence that it hard to imagine a world where dealing with numbers was something of a specialty, the tools of certain trades. In the world that Leonardo Pisano grew up in, every major trade center was likely to have its own sets of weights, measures, and currency, and the calculations were done with either complex finger computations (leading to the term “digit” surviving as a number notation) or worked out on a abacus … neither of which lent themselves to preserving the details of the math. Also, in the European world, any written numbers were expressed in Roman numerals, which, due to their structure, were not very useful for anything other than addition and subtraction.

In Bugia, young Leonardo was exposed to the Islamic system of numbers, which had absorbed influences from India, including the concept of the place-keeping “0”, and the three-place separations that we still use today (ie. 1,000,000). While this was not unknown in Europe (having come across with the Islamic invaders into Spain, etc. some centuries before), Leonardo saw the utility of this in the context of trade.

Frankly, he almost was forgotten to history, but his name survived in later math books that referred back to his publications. A great deal of The Man of Numbers is tracking down the historical threads which lead back to Fibonacci and what survives of his books, and looking at the nature of these books from what remains. His main product, Liber Abbaci or “Book of Calculation” was a book of how to do calculations, and examples of these, and problems to be solved, a familiar format for math books ever since. However, the problems in his book were all “word problems”, as modern “symbolic” notation hadn't been developed, so what we'd write as x²=40x-4x² would be a whole paragraph of descriptive text.

The book tries to piece together the fragmented bits of Leonardo's biography and work, and fit these into the cultural milieu of his time, and the years following. It is fascinating that a figure like Leonardo, who is so well known for the mathematical entities that have come down from “Fibonacci”, has been so little known in terms of his biography and bibliography. This reads something like a mystery, trying to prise this information out of surviving material (much of which sits untranslated in late medieval sources in various Italian cities) to get a clear look of the man and his work.

Obviously, this being out only a few months, The Man of Numbers should be available in the more comprehensive brick-and-mortar book vendors. Of course, the on-line guys have it, with both of the big boys currently offering it at a 43% discount (with used copies coming in at right about the same price point so far). This was certainly an fascinating read, and anyone interested in math, the medieval world, or a story about researching obscure topics, should find this quite enjoyable.


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