The peculiarly British compromise between the metric and the imperial systems is the most lasting monument to this country's bitterest culture war in living memory, the one between scientists and humanities graduates in the 30 or 40 years after the Second World War.
The question of turning away from the Old Empire and towards Europe was also in the mix, but it was secondary. Much of the Old Empire was going metric at the time, and almost all of it has now done so. Rather, this was and is about whether the weights and measures used in everyday life, and taught in schools, should be the ones used in science, or the ones named in Shakespeare.
Only named, of course. The imperial system dates only from 1824, making it not yet 200 years old. It suppressed numerous customary weights and measures across these Islands and the Empire, replacing them with ones that often bore the same names, as certain customary units on the Continent still have names such as livre, but which had most definitely been devised by a committee. Scottish pints and gallons were more than halved.
The reason why the American system is different, despite using much of the same vocabulary, is because it is older. Meanwhile, the metric system was invented by a Church of England bishop who died as long ago as 1672. It is not a product of the French Revolution.
Why not teach both the metric and the imperial systems? Have you ever met British scientists and my lot, British humanities graduates? In any case, who could possibly teach the imperial system these days? But at popular level, a remarkably enduring compromise has indeed taken hold. The only problem was the legal ban on selling certain items in imperial measures by name, a piece of domestic legislation enacted by a Conservative Government. By all means let that ban be repealed. In practice, that repeal would change nothing very much at all.
I hate to advocate for the other side, but Britain is in fact rather good at science. Yet imagine that the imperial system really were to be reincorporated into school Maths. Would you fail if you could not do it? That would be most people these days, deprived of the Maths certificate necessary to progress to further scientific education, for want of competence in a system that was not used for such purposes anywhere in the world. If you could find anyone to do so, then by all means teach it. But even those of us who probably quoted Shakespeare in our sleep ought not to wish to make anything else conditional on it. It is not as if it is anything important like Classics.
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