Imperial vs Metric Measurements

From time to time I still hear people complaining about the metric or imperial measurement systems. Usually allying themselves to an extraordinary extent with one or the other side. A while ago, for example, I heard a Today programme item concerning a hedge-layer who was supposed to charge by metric lengths, but wanted to continue to use the old imperial units. What frustrated me, beyond the obvious, was that neither he nor the presenter realised how absurd the particular position was. The hedge-layer wanted to continue to charge by the chain - a chain is 22 yards long. He was objecting to having to switch to metric units for billing.

Now the properly numerate amongst you who are versed in both measurement systems (which probably means about 100 people in the UK, all around my age) will already have seen where this is going, but let's work it out the hard way:

1 chain is 22 yards is 66 feet (3 feet = 1 yard) which is 66*12 inches, i.e. 792 inches. One inch is 2.54 centimetres. So 1 chain is 792*2.54 cm which turns out to be (after some simple arithmetic) 2011.68 cm

So 1 chain is 20.1168 metres. Now, remember the context. We're talking about a hedge here. The guy is charging for the amount of hedge he either plants or restructures. In a 20 metre length of hedge, does anyone think he cares about 12 centimetres error in the length? That's an error of four and a half inches in a chain length. A margin of error of less than 1%.

So what was the fuss about? Given the lack of people versed in the old measures, is there really any harm in thinking in terms of the "metric chain", a length of 20 metres?

The other thing is, before people start complaining about pointless old-fashioned units that no-one (except a few people practising old crafts) uses anymore, that the chain is deeply embedded in our culture and practices. A cricket pitch is 22 yards long - yes, there it is again, the chain. And an acre is 22 yards by 220 yards. 1 chain by 10 chains (note the 10, this is a decimal measure!). So if an acre is 1 chain by 10 chains, that means (using our new metric chain) that it is 20 metres by 200 metres, i.e. 4000 square metres. And a hectare is 100 metres (5 chains) by 100 metres (5 chains) giving 10,000 square metres in all, which means (as hopefully we all know) that a hectare is 2.5 acres, or 4 hectares are 10 acres.

And 220 yards, or 10 chains, is a furlong. A mile is 8 furlongs, a furlong is 10 chains. We have powers of 2 and 10 mixing up yet again. Especially since 5 furlongs is approximately 1 kilometre, so 10 furlongs is 2 kilometres.

The point is that if we want a measurement system that is based on a combination of decimal (powers of 10) and binary (powers of 2), we've already got one. It's just that most people don't realise it. And that scheme is the hybrid of metric and imperial that we mostly use today in the UK.

To be continued...

In case anybody cares: a speed of one furlong per femto-fortnight means travelling approximately 201.2 metres in 1.21 * 10^{-9} seconds. This is equivalent to approximately 166,300,000 metres per second. The speed of light in a vacuum is approximately 299,800,000 metres per second. So the speed of light in a vacuum is not only approximately one foot per nanosecond, it's also roughly 1.8 furlongs per femto-fortnight; or 9 furlongs per 5 femto-fortnights. Another way to think of this is that light travels a mile plus a kilometre through a vacuum in 10 femto-fortnights. And don't forget that, entirely coincidentally, 9/5 is the multiplication factor when moving between centigrade and fahrenheit for temperatures.

Since light is slowed by about 30% in an optical fibre, the speed of light in modern communication backbones is just under 1.4 furlongs per femto-fortnight.