物流配送新能源车将唱主角

Most people in the world count up to 10 like this:
0,1,2,3,4,5,6,7,8,9,10 Donald P Goodman, however, counts like this: 0,1,2,3,4,5,6,7,8,9,X,E,10

where X and E are single digits, and 10 is the number the rest of us know as twelve.

(Usually he writes X as an upside down 2, and E as an upside down 3, as you can see in the picture above, but these symbols are unavailable in this font).

You might think that the introduction of two new digits is an unnecessary complication to a system that works perfectly well, but Goodman argues that they make counting and calculating easier.

As president of the Dozenal Society of America (DSA), he believes that humanity would be better served if it switched from a base ten, or decimal, system to a base twelve, or "dozenal" one. And today, 12/12/12, is a good opportunity to get the message out.

"Dozenals make the beauty of mathematics easier to see and easier to understand, which makes it more likely that people, especially students, will give it the attention it deserves," he said.

And he is not alone. For the last four centuries, many eminent mathematicians, philosophers and social reformers have argued exactly the same: counting in twelves makes more sense than counting in tens. The Dozenal Society of Great Britain still flies the flag in the UK.

The DSA produces an excellent publication, the Duodecimal Bulletin, which contains many reasons why dozenal arithmetic is cleaner and simpler than decimal arithmetic. It all comes down to the fact that twelve can be divided into 2,3,4 and 6, whereas ten can only be divided into 2 and 5.

Telling the time is also more intuitive using dozenals.

Since five minutes is a twelfth of an hour, instead of saying five past one, we can say "one and a twelfth" hours, or 1;1, where ";" is the dozenal point.

Ten past one is 1;2, a quarter past one is 1;3, twenty past one is 1;4, and so on.

This means that on a dozenal clock face, as illustrated above, both the hour hand and the minute hand point to the precise time. In a decimal clock face, the minute hand inelegantly points to a number that has to be multiplied by five.

[In order to tell the time in smaller intervals than twelfths of an hour, the dozenal system requires a further division into 12. The dozenal minute is 25 seconds, and there are 144 of them in the hour.]

Goodman, a prosecuting attorney from Martinsville, Virginia, always uses dozenal time, and he has also made dozenal rulers so he can measure using dozenal at home.

The dozenal movement began in the 17th century when mathematicians began to question the appropriateness of a number system based on something as arbitrary as the fact that we have ten fingers.

Over the years there have been many suggestions for the new symbols for ten and eleven: Goodman prefers the upside down 2 and 3, which were originally suggested by Isaac Pitman, the Victorian intellectual who also invented a system of shorthand.

Also popular are the stylised X and upside down 3 designed by William Dwiggins in 1932 and popularised in the 1970s animated cartoon Little Twelve Toes, which features a great song by jazz hero Bob Dorough.

The names of the symbols are also much discussed. Goodman calls X "ten", E "elv" and 10 "unqua", based on the work of the British dozenalist Tom Pendlebury, who died in 1986. The dozenal point is pronounced "dit".

Thus the time E;3 is "elv dit three", and 1E;3 is "onequa elv dit three", since one unqua abbreviates to onequa.

Little Twelve Toes calls X "dek", E "el" and 10 "do", short for dozen. Enjoy it below (or click here if you're reading on the Guardian's mobile site):

I spoke to Goodman recently via email:

What do you hope to achieve with the DSA under your presidency?
I'd like to take us mainstream. We have a number of respected and accomplished mathematicians in our ranks, including professors at Rowan University and Hofstra University in the US. Dozenalists aren't cranks or crotchety anti-metric grouches. We just find the dozenal system easier, more efficient, and otherwise better than the decimal. This is a reasonable opinion well founded in the facts. In what way would the world be better if we abolished decimals?
I don't think any dozenalist would say that we should abolish decimals. There are doubtlessly fields of endeavour in which they are quite useful. We simply want dozenal to be the default base, just as decimal is currently our default base, but we use others (binary and octal, for example) when it's appropriate. Do you use dozenals in your daily life and how?
Constantly. I keep all my time in dozenal. I keep my calendar in dozenal. So, for example, 12/12/12 is simply 10/10/E8. Finally, I do just about all my counting and private figuring, except for money, in dozenals. I do this because it's easier. How would you suggest a change from decimal to dozenal takes place?
Well, that's a tricky business. But I believe that converting the currency would be the first and most crucial step. Once that was done, everything else would fall in line pretty quickly. There would also have to be organised education on the matter in the schools. One sort of tongue-in-cheek plan for the conversion is here.

That said, I doubt there's any one procedure that would work everywhere. It would have to be tailored to local circumstances.
Most dozenalists believe that we should let dozenals speak for themselves. As time goes on, and as more people learn about dozenals, more people will use them; after a while, people won't want to use decimals anymore. No official, top-down change is really needed, excep (eventually) for things like money and legal recognition for dozenal measurement systems. What do your kids think? Did you teach them dozenals too?
My children are very young yet; my oldest just turned eight. After consideration, we're teaching them decimal arithmetic, since that's what they'll need for communication with most others. Once they've got that down, we'll show them the better way.