That was occasioned by the 200th anniversary of the birth of the Scottish mathematician Edward Sang, who, working with his daughters,
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I must have been one of the last people in Britain taught to use logarithm tables. I'm not sure why our maths teacher bothered; at school in the mid 1980s, everyone already had an electronic calculator. The tatty book of numbers, sitting ignored on the desk while I punched buttons, held no appeal. But what I didn't know was that for hundreds of years this had been the most sophisticated computer available, and making it had consumed peoples' lives.
January 30th marks the 200th anniversary of the birth of one such individual: Edward Sang, a Scottish mathematician and engineer who, with his daughters' help, produced the finest log tables ever. Sang's monumental effort ended unhappily — one part Don Quixote to two parts King Lear — but he deserves to be remembered, both for his achievement and for what his story tells us about our relationship with technology.
Logarithms turn complex multiplication into simple addition. For example: the log of 10 is 1, and the log of 100 is 2; 1+2=3, which is the log of 1,000. But producing log tables was a lot harder than using them, and required human calculators to work through a vast number of repetitive and tricky calculations.The first volumes of log tables were used mainly by mathematicians and astronomers. This changed in the 19th century, when the growth of engineering and finance created a vast crop of sums needing to be processed. It had also become clear that the original tables, compiled around 1620, were riddled with errors.
Sang was both a gifted mathematician and a practical man. While working in Constantinople in the 1840s, he came to despair of the inaccuracies in the available tables. He envisaged a complete set of tables that would allow just about any useful calculation to be performed easily, including trigonometric and astronomical calculations as well as logs — a Victorian personal computer.
On moving to Edinburgh in 1854, Sang began the task, aided by his daughters Flora and Jane, who he had taught his calculating skills. For the next 25 years, while Edward earned a living teaching and consulting on matters mathematical, the three of them worked on the tables in their spare time. They eventually produced more than 50 volumes of calculations of unmatched accuracy, each containing several million digits.
The problem was, nobody wanted them. Only one volume of log tables, covering the numbers between 1 and 200,000, was ever published, in 1871. Sang sought funding from learned societies the government to publish tables up to a million, but they all turned him down. He died, disappointed and in debt, in 1890.
In 1907, his two surviving daughters — Flora, then 69, and Anna, who had not worked on the tables —gave the work to the Royal Society of Edinburgh in return for a pension to ease their genteel poverty. The Society hailed the work as a "great national possession", but the First World War interrupted its publication plans. None of Sang's four daughters married, and his one son died in a lunatic asylum; it's easy to suspect, although impossible to tell, that the family's obsessive mathematical quest blighted their lives.
Machines, and the ability to use them, come and go. Young folk can't understand why their elders find programming a VCR so difficult. The next generation won't know what a VCR is. Sang's story is a reminder that intellectual obsolescence is just as prevalent, and powerful.
The Sang family devoted their lives to making their own mathematical expertise redundant. Their chosen medium, the logarithm, reigned for centuries, but electronic calculators made using log tables seem like a chore, and mental arithmetic came to seem as arcane a skill as conjugating Latin verbs.
No future computational technology will endure as long as log tables. The trend of getting machines to do our thinking is accelerating all the time. Satellite navigation lets us find our way without taking a compass bearing, or even reading a map. Translation software, although crude, will give you the gist of most foreign texts.
Now technology is replacing even more basic mental attributes — knowledge and memory. An electronic personal organizer will make sure you never forget to go to a meeting or send a birthday card. And now, when I rack my brains (When was the Origin of Species published? What was the Blue Peter tortoise called?), a search box pops into my mind's eye, and I imagine what I should type into Google. Phrase your search enquiries right, and you can retrieve something from the web almost as quickly as from your brain.
This is clearly a good thing. GPS navigation saves lives, and online information would be arduous or impossible to obtain by other routes. But the incapacitation I feel when my web connection goes down — and the flood of information that engulfs me when it doesn't — suggests that we may have swapped intellectual resourcefulness for convenience. Perhaps learning times tables, or tracts of poetry, or how to use logarithms, wasn't so useless after all. Perhaps it equipped us to think for ourselves in a way that Google can't.
It's like that philosopher said. What was his name? Greek bloke, or possibly German. Hang on a minute, I'll just look it up…
