Software Musings

Working Back

Posted on: 02/01/2011

I have always known that mathematics teaching in high schools is generally disastrous. I suspect that almost all non-specialists and even a majority of specialists could leave a high-school mathematics course with the idea that most mathematicians are dead, those who are alive spend their time doing arithmetic of enormous complexity and that mathematics was complete sometime around the time of Pythagoras (say about 1850). When one points out that most mathematicians who have ever lived are still alive, that one can do a mathematics degree without meeting a number other than 0 and 1 and that there are important mathematical problems that have remained unsolved since the 19th century there is a feeling of incredulity. And, I hope, a feeling of having been cheated by the school system.

Well, over the past few months I’ve had a similar road to Damascus experience with history and feel a great sense of having been cheated. I’ve recently read two sources:

  1. “Anaximander and the Origins of Greek Cosmology” by Charles H Kahn (ISBN 978-0-87220-255-9)
  2. “The Official History of Heraclius’ Persian Campaigns” by James Howard-Johnston (included in his book “East Rome, Sasanian Persia and the End of Antiquity”, ISBN 978-0-8607-8992-5)

The former I bought myself, the latter was recommended by Greg Fisher when I had lunch with him at the beginning of December. I await his book on the Sasanians with interest.

What the two books have in common is that they both deduce the existence and contents of documents that have been lost. As Kahn says: “Since the written work of Anaximander is known to us only by a single brief citation in a late author for whom the original was already lost, it may well seem an act of folly to undertake a detailed study of his thought”. But by a process somewhat akin to ded reckoning (“ded” for “deduced” is a term used by pilots) Kahn shews how the analysis of the output of later authors presupposes a common origin for much of the cosmological thought and traces that origin back to Anaximander. A fascinating intellectual journey built on a remarkable knowledge of the later literature.

Howard-Johnston makes a similar journey to deduce the existence of a lost prose/poem created by George of Pisidia from Heraclius’ official dispatches from the battlefield back to the citizens of Constantinople. His deductions start from Theophanes’ Chronographia and work backwards, demonstrating the links in the chain and holding them up for the reader to test their strength, to George of Pisidia. Another intellectual tour de force.

I had a good history teacher at school. All teachers were expected to read some inspirational text in our morning assemblies and I still remember his (he was not invited to do so again and was eventually sacked for his behaviour with a 6th form girl at the end-of-term dance and we had a collection to buy him a crate of beer): “Cromwell said, ‘put your trust in God; but mind to keep your powder dry'”. He was good (I remember his graphic account of what the crowd did with the bodies of Mussolini and his mistress) but not good enough to tell me that history was also the type of deduction that Kahn and Howard-Johnston were doing.

And if we’re misled about mathematics and history, what about the other subjects? Perhaps even biology isn’t totally mind-numbingly boring. Although that seems unlikely.


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January 2011
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The author of this blog used to be an employee of Nortel. Even when he worked for Nortel the views expressed in the blog did not represent the views of Nortel. Now that he has left, the chances are even smaller that his views match those of Nortel.
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