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Dear Dozenalists:
I just came across your two Web sites for the first time, although I've been a dozenalist for a long time. In my opinion, nobody who has ever given the matter much thought would not concede that twelve would have been a better choice of base than ten turned out to be.
But very few of those people would go on to agree that the advantages justify the enormous cost and effort of conversion: not just the re-education of young and old, but also calculators and keyboards, fonts and banknotes, an enormous amount of written material and digital data, and even speed limit signs and automobile speedometers, for example.
In my opinion, we dozenalists have to offer much more benefit than we now do, and we have to offer a system that can coexist with the old system for a long time – at least a generation. I have in mind a package consisting not just in the reform of our number system, including the change to base 12, but also in the reform of our metric system. This would provide us with a motivated initial user base of scientists and their vendors and students, and from there the new system could percolate outwards.
There are numerous small problems with the current metric system, but the oddest is how poorly it is integrated with scientific notation, given its foundation in decimal powers. Practicing scientists would prefer to express quantities with an explicit magnitude, rather than embed the magnitude in the units as we do now. In other words, they would rather express the speed of light as 3x10¹º cm/s than as 300 megameters/second or 0.3 gigameters/second. That’s why the Système International rejects the metric prefixes in favor of using only meters, kilograms and seconds (MKS).
A better alternative would be to write all real numbers in the form exponent-unit-mantissa, so that for example the speed of light would be 8m/s3 (in decimal units). “3m” replaces kilometer, since kilo- means “ten to the third”. This notation – let’s call it dozenal notation – replaces the decimal point, scientific notation and even the e-notation used in computer languages. Of course, in our new metric system the exponent would be the smallest power of twelve greater than the quantity, and presumably our metric system would also include a base unit for speed, which the SI system curiously omits.
In addition to units for distance, time, speed, weight (mass), etc. – there are a total of about 30 such measures – we would offer a unit for plain old numbers, so that we could express the population of China, for example, as 9z3 in dozenal, with the z read as zy (pronounced “zee”). This saves us from having to invent new words like tenty and eleventy; instead, a number like three hundred sixty five would be read threezy three six five (since 10³ is the smallest power of ten greater then 365). Putting the exponent first also brings the magnitude of a number to our attention, to a far greater degree than tossing around terms like million, billion and trillion (on whose interpretation we Yanks and Brits can’t even agree). Lastly, the leading exponent would mark numbers as dozenal.
Many English speakers may not realize how much of a benefit it is to be able to read numbers as they are “spelled”, since our language is fairly logical on this count (although we do say seventeen hundred instead of one thousand seven hundred). But French, for example, has no words for seventy or ninety (and only a paraphrase for eighty), so French people have to wait for the next digit before writing or dialing. In German, the digits are read in reverse order, in pairs, so that 24 is vier-und-zwanzig, or four-and-twenty. And pity the poor Russians. So being able to read numbers aloud by spelling out the digits is a benefit in itself.
Finally, let’s continue the reform by addressing even picayune irritations, on the theory that while we’re changing numbers and units, we might as well fix everything else, too. Here are a few more things that need fixing:
I came to my dozenalism as part of a project called Shwah to reform all writing: not just numbers but also letters and the rest of written language. If you’re interested in seeing the Shwah implementation of the program I describe above, one based on an entirely new set of symbols and on natural metric units, then I refer you to www.shwah.net/numbers.htm and metrics.htm. One advantage of this radical approach is that there is no ambiguity between decimal and dozenal.
But there is no need for all dozenalists to embrace Shwah – most of the benefits of the reform could be realized just as easily by standardizing usage and a few symbols: the two missing digits, the magnitude and ordinal signs, and a few more. Given the number of fonts in use, I urge you to choose symbols from the Unicode 00XX range, so that they will be widely available.
But the key to success is the new metric system, along with the tools to support it, including a web-based calculator and conversion utility.
Peter Cyrus (pcyrus@shwah.net)