Last September I fired off a letter to the Guardian phrasing the EU's decision to stop forcing changes to our weights and measures system (Take Pride in our Mongrel Measures). Surprisingly enough this got published. Its theme, that of praising plurality in our measurement systems seems to have been out of fashion for a long time, but really does need to be re-visited if bureaucrats and the arithmetically challenged are not to make our life even more sterile than it is.

When it comes to number systems, I am always reminded of what my Maths lecturers used to grind into us: if your choice of units of measurement makes a difference to the outcome of a calculation, then you have got something wrong. Units of measurement are no more than arbitrary baselines in a given dimension and can only affect the values of constants.

On the face of it, the metric system seems entirely logical and rational. What could be simpler than a measurement system based on decimals. Unfortunately, it is neither logical, nor rational, nor useful.

The only *logical* system is one that is based on base two - and perhaps arguably related bases such as eight and sixteen. Computers are logical; they work in base two. Humans aren't good in base 2 - although base 8 or 16 is not an unreasonable choice if you want to be logical.

The SI units of measurement are an example of a rational system. It has a single unit of measurement for each dimension and all measurements are expressed in that unit. The SI system uses the *metre, kilogram and second* for length, mass and time, but it could equally well have used the *centimetre, gramme and second*, or the *foot, pound and second*. All would have resulted in a total rational measurement system.

As for useful - well usefulness depends on the purpose. I would argue that for a measurement system to be useful to humans, its measurements should be expressed in small integer values. We find it hard to visualise large integers.

Here's an example of how large integers don't work. Last year, I employed builders to build an extension to my house. They got two of the windows muddled up and put the frames in the wrong location - swapped over. The size of these frames was written on the plans and the frames in millimetres (four digit values) and even though the builders were used to measuring in millimetres, they can't visualise a four digit measurement and so the lengths were no more than "names" to them. They got the names muddled up.

Now, if the frames had been labelled as *four foot* and *four foot six* (inches) -which is what they were when measured in English, there would have been no confusion. The builders can visualise this easily (to a man they would tell you their height in feet and weight in stones), and would not have made such a silly mistake.

The problem exhibited here is that while there are also examples where the metric system can be useful, it is a one size fits all approach that can never be generally useful. If the window frame had been measured in centimetres, it would still have been a three digit value, decimetres would have yielded a two digit value, and metres would given you an awkward one and a bit measurement.

Using ten as your multiplier does not give you sufficient granularity of measurement to have the choice given to you by the imperial system. The yard and the metre are about the same length and fill the same niche, but there is no equivalent to the foot in the metric system. Perhaps that's why after forty years of metricated teaching we still use feet and inches to measure our height.

The rationale for the metric system is that base ten is easy - but that is the flip side to a major complaint of teaching of mathematics today, that the subject is dumbed down. Before metrication and decimalisation, British children had to learn mental arithmetic in base 12 (inches and pennies), base 8 (pints to the gallon), base 16 (ounces to the pound) and base 3 (feet to the yard), if they were to master all the different conversion units.

The sad thing is that while the teaching of number bases seems to have been lost along with the 12 times table, base 12 is still very much needed in *time* (5 x 12 seconds to the minute, 12 months to the year) and in *navigation* and *geometry*. All subjects for which base 10 simply complicates your calculation. 100 degrees to a right angle may sound logical, but when a 3-4-5 right angled triangle then ends up with angles of 66.66666 recurring and 33.33333 recurring, you realise that something has gone wrong. And how do you fit ten months to the year around four seasons?

The original rationale for metrication really came from the mistaken practice with the Imperial System of trying to rationalise all measurements down to integer measures in a succession of different units. For example, the Victorians would measure the length of a railway line in so many miles (8 furlongs), furlongs (220 yds), chains (22 yds) and yards. Computing with such mixed measurements required the labourious *practice* method, repeatedly applying the awkward conversion units. As my lecturers would have said, your choice of measurements has made your calculation difficult, therefore you have done something wrong.

The error in the analysis was then to try and make the conversion units easy (i.e. base 10) rather than the more rational approach of only working in one unit. If you measure the railway line as 18.5 miles rather than 18 miles and 4 furlongs, life is suddenly much easier. The rule is choose the correct units for the job and stick with them.

So, back to the original letter to the Guardian. There is no need for a sterile debate about the different measurements systems. Each has its own domain of use. The Imperial System evolved over time to suit many day to day uses and is on a human scale. The metric system is now widely used for Engineering. Each works well in its domain. Let the people decide which units of measurement they want to use, and the bureaucrats can make life difficult for themselves rather than the rest of us.