Exponents

It was a Golden Age: the mid-'60s, the sun shining down on the smart little suburban cul-de-sac of detached houses and semis less than a decade old, the flowers growing in the front, the immaculate grass lawn at the back so long and so green under the massive, ancient oak-tree.   I was still at primary school, and had barely a care in the world.

And so it was one bright morning that I was doing sums, sitting in the front room with its smell of wax from the polished red tiles under the window-sill.  At some point my father must have looked on benignly, perhaps puffing on his pipe - for in those far-off halcyon days there were no cancers caused by smoking.  He noted perhaps how I was trying to multiply quite large numbers together, and not always successfully. 

"Here, have a look at this, son," he said.  And digging deep in his own childhood memories, and using an old book of tables from somewhere, he proceeded to expound the theory of logarithms.

They seemed to work in a mysterious way beyond the ken of the child: just by converting two numbers using the tables to these logarithms, then adding the latter together and looking up the answer in the same tables, you obtained the answer to horrendously complex problems.  This was real adult magic.  Soon, with his halting but essentially correct explanations of exponents and mantissas, I found myself master of this new skill. 

I have always been grateful to my father for passing on to me that knowledge, especially as it probably represented the limit of his mathematical education, and so possessed an almost symbolic value as a final gift from one generation to the next.  But I later found out that there was something rather disturbing about logarithms which my father had not told me - perhaps had not known, since it was a well-kept secret.

The rows and columns of figures to be found in log tables are factual and inarguable.  For a given accuracy every publisher's set of tables should be identical.  However, this being the case, there is no need for other publishers to go to the trouble of calculating their own; they could simply use everyone else's, which should all be identical. 

But they are not.  Precisely to prevent this occurrence, every set of log tables published differs very slightly from its rivals.  In this way a publisher can demonstrate conclusively if its numbers have been filched.  The consequence of this is shocking: every set of logs is wrong at some point - but you do not know where.  So it is possible that your crucial calculation - for a bridge, say - is wrong, simply to enable a publisher to claim copyright in its tables. 

When my father taught me about logs, I had not known that he was presenting me with a cankered rose, the mathematical equivalent of a tragic hero with a fatal flaw.  And I had not realised that logs were actually a paradigm for something far larger than numbers: the whole capitalist system, and its insouciant disregard for truth in the pursuit of profit.  An Age of Innocence indeed. 

(27.12.91)

See also Moody Sonnets - The Third Eye

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