The Queen Of Numbers

Here is something to really think and talk about. Have you ever stopped to ponder just how inefficient our basic counting system is, the one that we have taken for granted since early childhood? In my book, "The Patterns of New Ideas", I suggested that our present system of counting by tens is woefully inefficient and we began using this system only because we have ten fingers and people in ancient times used their fingers to count. This is surely the supreme example of how we can be technologically forward but system backward.

For ancient people, using their ten fingers to count worked just fine. But the world was to get far more complex. The four basic arithmetical operations are: addition, subtraction, multiplication and, division. Basing our counting system on any number, such as the tens that we use now, will do very well with the first three.

However the last of the four, division, is the tricky one. Division is very important in the flow of daily life, just as are the first three. The difference with division is that not all of the convenient numbers that we could possibly base our counting system on are equally divisible.

I maintain that, for maximum efficiency, the number on which we base our counting system should be as divisible as possible. It does not make sense to base the system on too high of a number because that would mean that more symbols (1,2,3,...) would have to be use and that would hinder communication. However, we have made a really great mistake by counting by tens simply because ten is so poorly divisible.

Consider that by far the most important and most frequent measurement that human beings take is that of time. In fact, we take measurements of time many times more often than all other entities that we measure such as distance, weight, temperature, etc. Now notice when you look at a clock or watch that we base our measurement of time not on the number ten, but on twelve and multiples of twelve. There are twelve hours in a day, sixty seconds in a minute and, sixty minutes in an hour.

You may notice that there was once ten months. The sept- of September means seven in Latin, just as oct- means eight, nov- means nine and, dec- means ten (as in "decimal", for example). But the logic of counting by twelves, rather than by tens, prevailed. Two more months were added to make twelve, July is named for Julius Caesar and August is named for Augustus Caesar.

The truth is that when measuring time, division is very important and people instinctively adapted a system based on twelve, rather than the conventional ten. This is also why eggs are sold by the dozen, rather than by tens, twelve eggs are more likely to be evenly divisible by the members of a family.

Time is not the only measurement in which twelve is very obviously a better base to use than ten because of it's easy divisibility. A complete circle, such as the circumference of the earth, is divided into 360 degrees. This is a nice, round, easily divisibly multiple of twelve.

The Metric System is an absolutely brilliant idea that was conceived at the time of the French Revolution. But yet something is still missing about it. The Metric System is superior to the old English system of feet, yards and, miles.

However, here we are in the Twenty-First Century and that old system still has not gone away and the Metric System usually has to be forced on people by law. The reason is very clear, the Metric System is far better with regard to multiplication and the easy convertibility of units, but the old system still has the advantage of divisibility. Twelve inches are a foot, 36 inches are a yard and 5,280 feet are a mile. Notice that measurement of time was never metricized.

The Metric System is at the mercy of the number base that we use and will never reach it's full potential as long as we count by tens, rather than twelves. Fractions are still as useful as they are because ten is such an awkward number to divide, basing our number system on twelve would change this by incorporating much of the useful divisibility of fractions.

Just think how convenient it would be if we could express time in decimal form based, of course, on twelve, rather than ten. Consider a decimal such as 1.63 hours. It is difficult for us to grasp quickly because it straddles the two number systems.

By using a grid, we can easily express any point on the grid by using cartesian coordinates. What if we could do this with the entire planet? We can, but expression in terms of latitude and longitude are based on twelve but we will have to express the coordinates in base-ten decimal form and it makes for an awkward and inefficient arrangement. Latitude and longitude are getting ever-more important in these days of GPS but we cannot effectively express the coordinates of a point in decimal for and will not be able to most-effectively do so until we count by twelves.

Our number system plainly and simply revolves around twelve but we try to make it revolve around ten because we happen to have ten fingers. This is certainly one of the greatest mistakes ever made. We do not still write in hieroglyphics yet we still count by tens.

THE EXPRESSION OF TIME IN DEGREES

While we are on the subject of counting and measurement systems, let's consider the units of hours and minutes. Hours and minutes are completely arbitrary units and were adapted due to the easy divisibility of the units which we use for time.

We cannot actually measure time but only motion, which is a function of time. Our measurement of time is based on the motions of the earth. The earth rotates 360 degrees in one day. Thus, one degree of the earth's rotation corresponds to 240 seconds or what we would now refer to as four minutes. An hour is fifteen degrees.

Since humans are now spending quite a bit of time in space, in earth orbit, why not express time in degrees? This would base the passage of time on how far the earth has rotated during that interval of time. I am certain that this would be much more convenient and efficient, hours and minutes were merely convenient everyday units in the pre-space age.