Converting units - done badly

In February 1968, I wrote my first computer program.  It is a little scary to realise that I have been doing that for nearly fifty years.  I was in my "gap year" before going to university and had a job attached to a team of physics researchers working on new semiconductors.  Their analysis and model building was done in the computer language Algol, which provided the basis of many later and more powerful languages; it was a very good language as my first.  However, Algol in its original form did not have input/output routines as standard, which was a bit of a handicap.  The computer staff we worked with in 1968 had devised their own, and included a feature which I have never seen since.  Data could be read in as exact or to the accuracy of the number of significant decimal digits in the input stream.  The program offered this choice to the modeller.  So if the data read 1968, that might mean 1968.000000000 or somewhere in the range 1967.5 to 1968.5 (all this was converted to binary of course).  Then calculations used the data to the accuracy selected.  There were reasons for this, of course.  If calculations lost significant decimal digits then one had to beware of attaching spurious accuracy to the results.  And so one learnt to structure calculations to retain accuracy - a very useful discipline.  It has stood me in good stead as a journal referee when I have drawn attention to the dubious accuracy of some tables of results in a submitted paper.

But comprehending the limits of significant digits is not a universal skill.  In the UK, readers of books and newspapers are expected to know both metric and imperial units.  But the editor who converts them can forget what significant digits mean.  A walking book I read recently instructed: "When you reach about 500 feet above sea level (about 152.4 metres) ... "  and a gardening book described a grass verge as being about three feet (91.44 cm). 

Newspapers make the same mistake when they convert currencies using the daily exchange rate "the mansion cost over 10,000,000 euros (8,790,000 pounds)".

A recent book fell into this sort of trap in a spectacular way.  The author was quoting the value of items at different times; "in 1696 ... meadow land was valued at 8shillings and 8pence an acre (roughly £1214 in today's terms)" (I love that word "roughly").  Not only is that absurdly precise, it is a snapshot at a moment in time, affected by inflation as soon as the book is published.  And it doesn't really compare like with like, as the author demonstrated in the same book: "In 1696 ... his ten pewter dishes, two pots, four brass pans, warming pan, two skillets, a kettle and three plates were valued at £3 11s 0d (£9952)"  In 1696, those were handmade items, and valuable as such.  The equivalent today would be with machine made items, mass produced and therefore cheap,  The conversion makes no sense at all.

  • think about accuracy; 
  • don't claim more accuracy than the data deserves;
  • convert between units with common sense!


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