For the non-mathematicians here, a base in math is the number equal to the number of symbols used (in the positional system of numbers we now use, anyway) which dictates how all other numbers are written. For example, we now use base ten because we have ten symbols (0123456789) to represent our numbers. Forty-three is 43 because it is four times ten plus three. However, in base twelve, what we call forty-three is written 37 because it is twelve times three plus seven.
Base twelve (duodecimal) has some significant advantages over base ten (decimal). Twelve divides evenly into halves, thirds, fourths and sixths. Thus, most fractions of numbers are simpler. Decimal 0,33333… becomes 0,4 in duodecimal, and .166666… becomes 0,2 in duodecimal. For these and other reasons, twelve is the number of months in a year, hours on the clock, and the number of eggs in a carton.
And since there are twelve symbols instead of ten, large numbers (like the US national debt, the number of atoms in a planet, or the number of times a man thinks about sex in a day) can be expressed in relatively few digits.
Duodecimal requires twelve digits, which means the creation of two more digits would be necessary. Some have suggested X for ten and E for eleven, some propose * for ten and # for eleven, but I personally like a reversed 2 for ten and a reversed 3 for eleven, because letters of the alphabet are reserved for algebra and * and # already have uses in math (namely multiplication and signaling a number). I cannot show you the numbers here, but they can be viewed here.
Of course, it would be very costly and difficult to re-educate everybody in duodecimal, not to mention it would be necessary to read the old (decimal) numbers or else replace all decimal numbers with duodecimal ones. But despite these costs, some think the resulting labor and costs saved using duodecimal would pay for itself.
Early on in the French Revolution, there was a debate on whether or not to switch to duodecimal. Eventually, they decided it would be too costly and based their metric system on ten. Afterward, some of the revolutionaries had written in letters that they regretted not switching to base twelve.
I feel that base twelve is far superior to base ten, but it seems that under the current circumstances, it would be extremely costly to change, so I must settle for using it for personal calculations.
What do you think?
). Each “digit” consisted of a vertical stroke, which by itself stood for zero and could act as a place holder. The numbers 1-9 were indicated by 9 different strokes attached to the top of the zero and extending to the right. 10-90 were the same strokes to the top left, 100-900 were bottom right, and 1000-9000 were bottom left (I may have those mixed up, but so long as you remember which you put where, it will work anyway). This made the system in effect a base 10,000 system where any 4 digit decimal number could be written with one character. With two more strokes for decimal 10 and 11, you’d have a 12-based number system with amazing density, but still retain easy readability. Base 20,736. WHEEEEEEEEEEEEEE!!!
I, too, see problems with letters in a general context, but not in a limited one where their meanings are understood, such as hex. For a real treat, Hebrew uses its entire alphabet as its numerical system. Every word is a number and lots (but probably not all) numbers are words. Imagine grocery shopping: is that the brand name, or the price?
(Not that it would matter if we went to duodecimal, of course.)