Smaller numbers are simply used more frequently. Zero is almost synonymous for none or No. One, besides being the base for counting it often serves for an answer of Yes.
Two, is the next common number. We see it in major animal body parts, where it serves for more than just useful, it also serves for redundancy when one is required.
Three is not common in life forms. I am hard pressed to find an example where an animal or plant has three of anything. The best I can do is point out: It is the minimal number of legs for a table. Three also defines a triangle. It is almost like it is a key for things we build.
Four is the norm for the number of legs of warm blooded animals.
Five seems to be an almost useless number.
Nature comes back with 6 legs on most insects. And when we draw a circle and step around it with the compass, we get exactly 6 equilateral triangles.
Seven, mostly because it is awkward to deal with, is frequently found in mysticism. Thus, it is used for the number of days in a week.
Eight is the number of legs on a spider, I really don't know why nature likes 8 legs for a spider. Being a power of 2 gives it use in the computer world to write binary numbers shorter. Base 16 is predominant because it makes them even shorter. Both have little advantage over ten for a number system base.
Nine, like seven, gets some awkwardness play. I think because it doesn't divide by two.
For writing larger numbers humans need a reasonably large base to keep to keep values short, but not too big for us to memorize addition and multiplication tables.
There are several things that are far from optimal, with base ten. The principal fault is that it only has two divisors: 2 and 5. From that point of view it is no better than 14 which has two divisors 2 and 7. I believe ten has been used for counting mostly because we have ten fingers.
Incidentally, six has two divisors; and we use 3 much more than 5 especially when dividing things or fractions. Six, however most of us would consider too small for a number base. (Computer people have more or less rejected Octal because of its small size, and have gone to base 16 which suits the needs of electronics to count in binary.)
Base twelve has many advantages, not the least is that twelve has divisors of: 2, 3, 4 and 6. In base twelve just looking at the last digit of an integer will let you know if it is divisible by any of the divisors of twelve. In our familiar base ten the last digit only tells one if the number is divisible by either 2 or 5.
Also, because twelve has so many divisors, it makes the base twelve simple multiplication table moor symmetric, hence much easier to memorize. I will not go into more explanation of why a number system base twelve would be a significant improvement.
The next thing to improve would be to make our measurements consistent with the number system and the way we count. For a Decimal counting system Metric has pretty well made other measurements consistent counting system. This alone has convinced all the civilized world to use Metric, except USA which is dumbly not doing so for the lay public; however even in the USA almost all scientific work uses metric.
The optimal world would use base twelve and have its units of measurement consistent in base twelve, as metric has done for base ten.
To reduce confusion, from here on I am going to refer to base twelve as: Dozenal. This name is quite standard among those who have thought about a better number base. For fractional values: In decimal we use a "Decimal point" and refer to "Decimals" following it. This will be called the "Dozenal point" with "Dozenals" following it. Examples with this notation: A twelfth would be .1 a sixth is .2 a quarter is .3 a third is .4 and a half is .6
While "cleaning up" counting, and measuring, there are two areas even Metric has not addressed. The measurement of: Time and Angles. Angles should be measured in Revolutions, which would be abbreviated "Revs"; with Dozenal fractionals following the Dozenal marker. Because this is probably new, for angles, let me point out a few examples. A straight line would be .6 Revs. A right angle would be .3 Revs. A right triangle would have angles of .1 .2 and .3 Revs.
Time should be measured in Days and Dozenal fractional parts following the dozenal point. The start of a Day would be kept at midnight. This would make noon at .6 what we now call 6AM would be .3 and what we call 6PM would be .9 Yes, until we get used to it there would be some change over confusion. But, arithmetic on time would all be simple standard Dozenal arithmetic from a year down to billionths of a day. Of course there would still be 265.3 dozenal days in a year. Which could be divided in to a dozenal number of months, but like we have now not all months would have exactly the same number of days. (I would hope that all months would only differ in length by one day.)
Most of us who have dabbled, and written selling articles about changing to a base twelve system have secretly known: It is never going to happen.
I feel too much effort has been spent reminiscing about the old British system of measurements and even money; and bitching about Metric. Anyone who has seriously used Metric knows it is vastly superior to the old British system.
Back in 1958 I lived in England, and felt at the time, it was crazy to have to have special calculators to simply add up a grocery bill. It was so confusing small retailers often had to hire an accountant to figure out what price he need to charge to make a profit on the goods he was selling. I erroneously imagined that because of this the British would be good with fractions. I was totally wrong. They were neither competent with fractions or decimals.
Correctly, I predicted that England would eventually go Metric with their money at least, then after seeing the benefit would convert to Metric across the board. I incorrectly believed that if Britain went Metric the United States would follow.
A feeble attempt was made in the US around the very early 1970, and then it was given up. I shake my head in disbelief. No single country with such a confusing and awkward system of measure can hope to be an industrial world leader--they will become the laughing stock of the world. We are seeing this today as I type this today Sun 2010-10-10 09:28:16
The sad thing is: The people born and raised with a terrible system cannot recognize the system's faults. As a lady I met in England a half century ago, very seriously said to me: "Your money is terribly confusing isn't it?" Americans are equally blind today and will resist any change.
But maybe all is not lost. Outside the USA there has to be thousands who can appreciate a bad system, and may be willing to make a moderate improvement in the system(s) they use.
In my next page I will give my idea of how that next change could possibly occur.
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