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We propose and support the adoption of base twelve as the most suitable of all possibilities for man's numbering scale. It can allow a concise representation of the primary and secondary ratios which are frequently required in mathematics and scientific work, weights and measures, coinage, time, packaging and social exchanges.
Our immediate concern however is to retain the use of traditional human orientated measures, with their natural divisions, which have been developed down the ages for our convenience and have counterparts in all national units. These have thereby become the most appropriate for practical and social purposes. and allow a proper perspective towards our material environment.
If our measures were to be put into a rational numerical framework that will also allow a size-order progression for scientific and technical work, the two usages would be compatible with one-another in a manner not possible with the present conflicting patterns of thought.
By comparison, the metre and its derivatives are artificial and arbitrary, concepts; French logic nodded a little when defining a straight line by the arc of a circle. By being a system integrated with a numbering scale metric is used for scientific purposes which has allowed the false assumption to arise that it is based on scientific principles. Locked into a rigid framework not allowing any diversion to more appropriate sizes, a ritualised progression of anonymous shadowy units tramples on several well-used sizes. This compression of facts into immutable form detaches the subjects, and the user, from reality and requires interpretation by a self appointed priesthood to a bemused congregation.
A somewhat poetical presentation, but it has been rightly noted that a majority now live in complete ignorance of, and certainly without any control over, the means and processes upon which they are completely dependent. Decimal metrication, with its abstract subservience to numbers, is part of the cause. A Ministry spokesman, defending the criminalisation of the use of all our normal, and natural, measures for all retail use, remarked that people do not now purchase items by size or weight, but cost; a cynical admission from those who seem to know the price of everything but the value of nothing.
The replacement of our flexible and user-friendly monetary system by a more rigid structure, for which we have to carry about a greater weight of coins, was to the sole advantage of money counters at the expense and inconvenience of money users. With its binary and ternary divisions, a handful of coins could be added up at a glance, and fewer were needed for payment and change giving. Decimalisation was, in part forced on us by inflation, when the ordinary unit of exchange, the shilling with its twelve pennies, was slipping off the lower end of the scale. This did not cause the inflationary spiral, but certainly allowed it free rein. Propaganda at the time had a refrain "Decimals are easy, you just move the point". And so it was - for the price raisers.
Not so easy for school children it seems. Recent reports admit that about a third of school leavers still have little or no understanding of place-value methods and happily revert to whole numbers and simple fractions when out in the real world away from officialised calculations. A dozen scale would allow them to combine both with understanding. Infant primers introduce the idea of division by sharing twelve apples or sweets between friends, But the hapless young mind is soon brought back to the less accommodating dividend, ten, with which seemingly simple relationships explode into rows of figures.
Mis-understanding of modern calculation methods is not confined to children. The Science Editor of an international magazine is on record as declaring: "Yet we count by tens, by the decimal system, because 10 is the only number that creates multiples of itself by changing the first digit. We know what he was trying to say, and many still believe it, despite some teaching of arithmetic in other bases for computer work (though even this little seems to have been dropped, except for base two). All manner of numbers can, and have been used as radices for different purposes. even transcendental such as e or pi, negative or complex. One mathematician suggested a prime number, such as eleven or thirteen, so that no one fractional would be "more equal than others". i.e., all would be irreducable and thus no preference for those forming aliquot parts; which would hardly be of use in everday life.
It is ordinary folk who would benefit from dozenal arithmetic, as it is simple to represent in dozenals the most frequent relationships they need, and will help them become more numerate. There seems to be a studied avoidance of base twelve in arithmetic curricula now; I recall learning tables up to twelve times with no more than normal difficulty. Could it be that Authority realises that a populace, ignorant in literacy as well as in numeracy, would be a more manageable one, and, moreover, drop out of the political process ? When not docile it could be easily fed with all sorts of promises, and reasons as to why they know best. The down grading and overall reduction of educational facilities, if not deliberate, has its advantages for some.
Decimalisation of time is still a gleam in the eyes of the CGPM in Paris, which pontificates on what we should be thinking metrologically. Several otherwise responsible Journals have also noted that there would be 100,000 x 0·864 seconds in a day, and once a pig gets its snout through a hole in the fence, the whole animal follows as a matter of course. A proposal by the Canadian Metric Association printed an interesting diagram with the ten hour day divided into three sections showing when the good citizen is expected (allowed?) to work, play and rest. Perhaps anything not forbidden will be compulsory. Decimal transmogrifiers must realise that any change in the unit of time will alter all time-related constants, not to mention the billions (Anglo-German) of phonic motors controlled by mains frequency, but do not seem bothered by the need to replace these and/or generator speed. They do that sort of thing because that is the sort of thing they do.
We recognise the extreme difficulty, if not impossibility, of changing well established practices, yet it is important to continue to discuss the fallacies and foibles of the present scene, also the hypocrisy of technical sycophants, for the comfort of those who realise they are losing something valuable but do not know why it is so, and the benefit of many who, thinking they have reached the ultimate of numerical and metrological excellence now reject any possibility of further advance. No amount of fiddling with ten-based arrangements will result in any improvement or resolution of difficulties. The dispute over measurement is, at heart, one over arithmetical notation which will not be resolved until the arithmetical notation has acquired the merit granted by divisibility formerly achieved out of necessity by the measuring systems. On an optimistic note, Professor A C Aitken, one of our founder members, said that nothing, even relatively inefficient, will last for ever.
In the case of the now preferred numerical-measurement system, entrenched usage is backed by it having acquired political support since it is so useful in organisational and controlling roles. Hence active opposition to any change can be expected. Indeed, the extension of decimetric methods to areas in which there can be no technical advantage is motivated by a desire for uniformity at all costs. When my Laboratory was metricated, and previously simple relationships appeared as rows of figures, the admin type to whom I complained said: "I like it, it makes things easy for me". All he ever had to do was add up, and never got his hands wet or dirty!
For communication of ideas and publication, we adopted Sir Isaac Pitman's inverted two and three as used in his Phonetic Journal, which stemmed from the reversion or inversion of standard type faces to represent differing phonemes. The Dozenal Society of America adopted the Bell Telephone symbols (the "star" and "hash") on the grounds of public familiarity. De-facto 'numerals' for ten and eleven are A and B for hexadecimal input computers, and in the International Standard Book Numbering System, X is used as a single symbol for a base eleven check on the validity of a book number. But letters are not suitable for general use as numbers, so the DSA and the DSGB continue with their respective choices until pressure of events determine otherwise. It is the principle that matters, and Professor Aitken advised that Duodecimalists should not prescribe over much what is desirable.
Progress is an important thing, which all lay claim to, but results often turn out to be no more than a mining of existing resources with greater intensity, or, more likely, a transfer of difficulties to areas less able to object or defend themselves, with benefits claimed by the victors as always. Genuine improvement is an evolutionary process, whereby the most suitable variants are encouraged. Social and economic systems are biological in behaviour, requiring redundancy to ensure stability against unknown factors in unforeseen circumstances. Market forces are now allowed to create economically non-redundant structures, the ultimate being one in which the failure of any one part will cause a collapse of the whole (to draw on a mechanical analogy). Monoculture in food production has its obvious dangers, but with ideas, risks sterility of thought and inhibition of action, creating a cultural desert and calling it progress as Tacitus would have put it. For the unification of Germany under Bismark, each state having its own version of Roman measures, metric measures were imposed, but did not Kaiser William II say that the success of the British was due to their superior measuring system?