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ARIES83 -> RE: What's *Your* Weather Like? (1/21/2013 1:59:25 AM)
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quote:
ORIGINAL: LadyPact
How can one argue against increments of ten?
I actually prefer a base 12 number system, I had
to invent new digits to try it out a while ago, I
found it to hard to adapt too being brought up
using metric.
But it's got a lot of good points, especially with
time keeping.
You asked...
-Aries
quote:
Counting in Base 12
I am furious that in the Middle Ages, Christian Europe adopted an Indian/Arabic, heathen, base 10 numerical system rather than a better base 12 system.
We are still stuck with base 10. But base 12 would have been possible. Base 12 fits the number of Christian Apostles. In a deeply Christian society, this should have been important. Base 12 fits the number of months in a Christian solar year. It also fits the number of signs in the pagan Zodiac. But I doubt this would have been an insurmountable problem in the high Middle Ages, eight gross of years after Christ.
Base 12 fits the number of eggs in a dozen. For those concerned with time, it fits number of hours in a day (counting from dawn to dusk, with variable length hours).
As a practical matter, people tend to divide groups into halves, thirds, and quarters. A dozen is the smallest number that allows you to do this.
Moreover, in base 12 it is easy to count on one hand.
Curl the fingers of your left hand so that you can see the tops of the parts closest to you. The four tips make up one row. The four knuckles closest to the tips make a second row. The next set of knuckles make a third row. (You cannot see the knuckles that merge into the back of your hand.)
All together you see three rows of four, which make twelve. Or you can count `by fingers': four fingers of three each. You can see the patterns of halves, thirds, and quarters within a dozen.
You can use the tip of your thumb and its two readily visible joints as markers for twice, three times, and four times twelve, or for the next three powers of twelve, which are 144, 1728, and 20736.
Base 10 is worse than base 12. You have to move to 100s to get a `quarter', such as 25 cents. Indeed, base 10 is more limited than programmers' base 16, which can be divided into quarters readily. Neither base 10 nor base 16 make it easy to mark thirds.
It would be much nicer for a `quarter' to be 0.3, which it is in base 12, and a `third' to be 0.4. These are nice round numbers (albeit round number fractions).
Also many people dislike fractions. It takes a while for children to learn them. Instead, they use smaller, but integral measures. Thus people think of a dozen eggs as the larger unit, and one egg as the smaller unit. Four eggs are one third of a dozen.
While ten allows you to divide a larger entity into halves, only twelve easily allows for thirds and quarters.
It goes without saying that some people would be confused that a third is 0.4 (or four) and a quarter is 0.3 (or three).
Understanding and remembering the difference would be one of rites of childhood.
I blame Fibonacci, who wrote a famous book in 1202, Liber abaci, in which he discussed base 10 numbers.
Fibonacci was not the first Christian European to mention base 10 numbers. They appear in the Codex Vigilanus copied by a monk in Spain in 976.
But Fibonacci was more influential. Not only did he write when enough people were ready to accept the new idea, he gained support from the Holy Roman emperor. Even so, several more centuries passed before base 10 numbers caught on.
Among other hindrances, people found it hard to understand how `nothing' — a zero — could cause the value of a number to jump by 10 when it was placed after it in writing.
There are arguments against base 12. In particular, it is easy to determine whether a base 10 number can be divided by 2 and 5. Thus, in base 10, we can tell that 148 is divisible by two, since it is an even number. Similarly in base 12, for which the expression of the same number is 104.
We can tell whether a base 10 number is divisible by 5 by asking whether the number ends with a 5 or a 0? Base 12 does not handle 5 at all. But it does handle 3, which I think is much more important.
Quick, is 141 in base 10 divisible by three? (Yes, it is divisible by 47.)
How about base 12? If you count in base twelve, then decimal 141 is duodecimal B9, or 11 times 12 plus 9. The number ends in 9, which is one of a zero, three, six, or nine, so it is divisible by three. This determination is easier than dividing by 47.
(Another conundrum for school children: 3, 6, and 9 are the quarter parts of 12, yet they are used to find divisors of three....)
Unfortunately, base 10 numbers are entrenched into our society. Even though a better base exists, I doubt we shall ever switch to it.
It is easier to change hardware, for example, to switch from wood to oil, than it is to change the cultural conventions that are our `software'.
Put another way, if you are going to do something that changes the world, and you do it in the realm of ideas, please choose the better path...
http://www.rattlesnake.com/notions/base-12.html
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