Alex's Adventures in Numberland - Alex Bellos [21]
Michael de Vlieger’s youthful infatuation with base 12 was not a passing phase; he is the current president of the DSA. In fact, he is so committed to the system that he uses it in his job as a designer of digital architectural models.
While base 12 certainly makes times tables easier to learn, its greatest advantage is how it cleans up fractions. Base ten is frequently messy when you want to divide. For example, a third of 10 is 3.33…, where the threes go on for ever. A quarter of 10 is 2.5, which needs a decimal place. In base 12, however, a third of 10 is 4 and a quarter of 10 is 3. Nice. Expressed as a percentage, a third becomes 40 percent, and a quarter 30 percent. In fact if you look at how 100 is divided by the numbers 1 to 12, base 12 provides more concise numbers (note that the semi-colons in the right column stand for the ‘dozenal’ point).
It is this increased precision that makes base 12 better suited to Michael’s needs. Even though his clients supply him with dimensions in decimal, he prefers to translate them into dozenal. ‘It gives me more choices when dividing into simple ratios,’ he said.
‘Avoiding [messy] fractions helps ensure things fit. Sometimes, because of time constraints or late-breaking changes, I will need to quickly apply a lot of change at a location that doesn’t jive with the grid I initially set up. Thus it’s important to have predictable simple ratios. I’ve got more and cleaner choices with dozenal, and it’s faster.’ Michael even believes that using base 12 gives his business an edge, comparing it to cyclists and swimmers who shave their legs.
The DSA used to want to replace decimal with dozenal, and its fundamentalist wing still does, but Michael’s ambitions are more modest. He wants simply to show people that there is an alternative to the decimal system, and that perhaps it suits their needs better. He knows that the chances of the world abandoning dix for douze are non-existent. The change would be both confusing and expensive. And decimal works well enough for most people – especially in the computer age, where mental arithmetic skills are less required generally. ‘I would say that dozenal is the optimum base for general computation, for everyday use,’ he added, ‘but I am not here to convert anybody.’
An immediate goal of the DSA is to get the numerals for dek and el into Unicode, the repertoire of text characters used by most computers. In fact, a major debate in dozenal society is which symbols to use. The DSA standard and were designed in the 1940s by William Addison Dwiggins, one of the US’s foremost font designers and the creator of Futura, Caledonia and Electra. Isaac Pitman preferred and . Jean Essig, a French enthusiast, preferred and . Some practical members would prefer * and # since they are already on the 12 buttons of a touch-tone phone. The number words are also an issue. The Manual of the Dozen System (written in 1960, or 1174 in dozenal) recommends the terms dek, el and do (with gro for 100, mo for 1000, and do-mo, gro-mo, bi-mo and tri-mo for the next highest powers of do). Another suggestion is to keep ten, eleven and twelve and continue with twel-one, twel-two, and so on. Such is the sensitivity over terminology that the DSA is careful not to push any system. Great care is needed not to marginalize devotees of any particular symbol or term.
Michael’s love of avant-garde bases did not stop at 12. He has toyed with eight, which he sometimes uses when doing DIY at home. ‘I use bases as tools,’ he said. And he has gone up to base 60. For this he had to design 50 extra symbols to add to the ten digits we have already. His purpose was not practical. He described working in base 60 as like going up a high mountain. ‘I can’t live up there. It is too big a grouping. In the valley it is decimal, and there I can breathe. But I can visit the mountain to see what the view is like.’ He has written out tables of factors in a base 60, or