Somehow, I missed the bonfires and the dancing In the streets. All the same. I am assured that the Royal Mint invited us a few days ago to celebrate 21 years of decimalisation.

The Mint apparently thinks 21 still marks a coming of age. It would be nice to think that somewhere in that organisation there is still a hankering after guineas. Decimalisation can now be ranked with so much else, as one of the disasters of the Sixties and Seventies. (Please do not write in saying it caused inflation too - it didn't).

The excuse for decimalisation was simplicity. But simple systems breed simple minds. And the inability of so many younger people today to cope with figures of any complexity owes a lot to decimalisation.

A great advantage of the old and "difficult", system was that children learnt it quickly.

Money, as ever, mattered. Multiplying and dividing by 12 and 20, knowing now many threepenny bits there were in a shilling, how many in a florin and how many half-crowns made a pound became routine.

There is always something to be said for the difficult. I have long suspected that one reason for the apparent high intelligence of the Japanese
is the complexity of their vocabulary and its characters.

Children have to
master it from an early age and mental agility is automatically stimulated.

As if decimalisation was not bad enough - and only some tourists actually seemed stumped by the old system -we added the abomination of metrication.

Those who believe that metrication, being simple, is in some way "natural" overlook the sheer unnaturalness of that system. Inches, feet and yards are based on human measurements.

By contrast the metre was supposed to be 1/10,000,000 of a quadrant circle of the Earth measured around the poles of the meridian passing through Paris.

It would be difficult to imagine a more grotesque basis for daily mensuration.

The metre has no human dimensions at all. No man has such a stride. Nor has the centimetre any relationship to the human hand.

An acre is also a homely measure. The hectare is far too large.

One grumble about the kilometre. Britain has been 'allowed' by Brussels - such a kindness don't you think? - to keep the mile. Yet news reports constantly refer to distances In kilometres.

The reason may well be that where the original distance was given In kilometres, the reporter is incapable of turning it into miles. That simply bears out my point about the collapse in numeracy and mental agility.

The manifestation of this is particularly pathetic in shops. Young Noyleen stands at her cash register slowly ringing up 25p and 35p and 10p - and is awed to find that old codgers like me have put down 70p and are getting impatient.

Calculators should also be rationed for the young. Apart from eliminating mental exercise, they rob people of a sense of size. Results ten or 100 times too large or too small are not immediately seen as obviously wrong.

Even business graduates are affected. "That's about 1,000 square feet," I told one when we were looking at a space about 18 feet by 52 feet. "How did you know?" he asked after fiddling with his calculator. Oh dear.

The lesson we should draw is surely one of disciplined flexibility: **we must recognise natural constraints and patterns**, simple proportions and efficient styles of measurement.

We can see that different tasks may require different scales, and so should avoid falling into the doctrinaire trap of blindly imposing a single, rigid basis to all situations.

The decimal-metric system, being a product of revolutionary zeal (and zealots are notorious for their puritanism), permits no units which are not powers of ten: no secondary or auxiliary bases are allowed, even when mathematics itself demands them.

The people of earlier times** counted **in tens, but were wise enough not to let that impede their mensuration: binary, ternary, duodenary and sexagenary scales were used where appropriate; no-one felt threatened by them.

It was realized that powers of ten, though perhaps good enough for mere counting, raised unnecessary barriers to sensible working practices; and so such numbers were largely rejected for units of measurement. Decimal **currency**, even, was abandoned c.130 BC. (The denarius, as its name suggests, was originally ten As, but was made worth sixteen As at this time. Some assert that this was merely devaluation of the As; but in that case why choose sixteen?)

There is another irony here because our forebears (not frightened of fractions) were happy with 8-pint gallons, 3-foot yards and so on; they were free of the stifling Influence of the denary base (used solely for simple arithmetic) and so did not bother about changing it;
**decimal numeration survived by being marginalized.**

Had there been some sort of cosmic law which ordained a match between number-base and measures, we should have had a twelve-based numeration from time immemorial (especially once it was found that it made calculations easier, too!)

Yet... We all recognize the convenience afforded, particularly to the scientific world, by
measuring-units which fit the number-base: a match between the two schemes, whereby successive units of measure correspond to successive powers of the radix, so permitting standard-form calculations and fraction-point transformations, is highly desirable to laboratory workers and accountants alike.

It promises coherent systems and hence elimination of troublesome conversion-factors. It was this promise which seduced - and still seduces - academics and politicians (for different reasons) into uncritical acceptance of the decimal-metric idea.

They have been sold a pup.

What looks so good on paper, with its elegant unit names and inspired series of power-prefixes, fails to accommodate natural ratios, often imposes problems where there were none before and has a marked propensity for expanding simple fractions into strings of decimal digits.

Instead of grasping the nettle of decimal incompatibility with natural mensuration and arithmetic, L'Institut National shrank away from the chance of basing their system on the dozen and went for a quick denary fix.

Our dozenal base** is **amenable to true rationality: a twelve-based weight system equals and sometimes betters the binary; linear, areal and cubic measure, using feet-and-inches and the almost miraculous yard, are elegantly served.

Accepting secondary bases where appropriate (so avoiding the disastrous rigidity of the metric system) we can have, for example, our inches divided-down dozenally in a power-of-twelve system, yet leave the other edge of the rule with the binary subdivisions which are so useful; we can leave the clock-dial alone (apart from the re-numbering it always needed anyway); we can have a thermometric scale from 0 (freezing water) to *130 (boiling water) using Fahrenheit degrees; and - underlying it all - we can have the most efficient and (if I may use the expression) user-friendly arithmetic it is possible to devise.