Part 1 Introduction- Ying-Yang: The Theory of Everything

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Ancient Chinese philosophers believed that everything contained two energies called “ying” and “yang”. Yang represented birth, light, heat, and strength; it was very active and virulent. Ying represented death, darkness, cold, and weakness; it was very passive and showed strength only when confronting yang. The symbol on the left shows these two forces intertwined, ying is black and yang white. Neither ying nor yang can exist without the other. There is no birth without death or death without birth. Perfection is when these two forces are in balance as the symmetry of the symbol shows. There is a tendency to see yang as good and ying as bad. This is a huge mistake! Too much of a good thing is bad, whether it is caloric intake, economic growth, population, or wealth. This is the lesson of the ancient Chinese philosophers.

One can use the theory of ying-yang to described processes as grandiose as the big bang and as small as the microscopic beginnings of life. In the big bang, the dense, hot, radioactive stars represent yang. This yang is the creator of life as these atomic furnaces produce the very stuff that we are made from. Ying is the void of space, cold, dark, and dead. Our earth maintains a delicate balance of ying and yang, not too dense or sparse, not too hot or cold, not too light or dark, with birth and death in a delicate balance. The same theory can be used on the microscopic level. Life begins with the exponential growth of the fetus, sustainable by the death of individual cells. We will examine this in the next of several articles, that we will call, “The Ying-Yang Articles.” They will all be marked with the ying- yang symbol above.

Many of the ying-yang processes, like the two above, are beyond human control. We will pay special attention to those that can be influence by man and show the importance of maintaining the balance of perfection, advocated by ancient Chinese. An important advantage we have, that was not availed to the ancient Chinese, is the invention of calculus. With this valuable tool, we can formulate yang in a precise mathematical form. In fact, a single deferential equation can describe yang. The solution to this equation is the exponential function. Ying is much harder to describe. It takes many different forms, and, in most cases, its ability to control yang is the only measure we have of its power. Knowledge of calculus is not a prerequisite to understanding of the process of yang. Paradoxically, it makes our calculations easier. Anyone able to calculate interest on a loan or investment will be able to understand the basic process.

Here are the ying yang articles currently planned:

Part 1 Introduction- Ying-Yang: The Theory of Everything
Part 2 Understanding Yang and Ying’s Defense
Part 3 Get the Most Yang for the Buck
Part 4 The Tale of Two Taxes
Part 5 Retirement Troika
Part 6 Riding the Exponential Curve
Part 7 The Disaster of Excessive Yang

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DICK

Backward Numbers

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I read with great interest a statement by an elementary teacher, “Developmentally, children will write numbers backwards until they are 8 years old “

No! These children write numbers, as they should be! The rest of us write numbers backwards! For example, the number 6154 should be written 4516. (In the Scandinavian countries, it is common usage to speak of numbers under 100 in the reverse order. They say the number “24” is four and twenty. “56” is spoken of as six and fifty, but they still write numbers backwards like the rest of us.) Justification for my claim requires the consideration of the way we developed written words and numbers.

The languages of the Western world were derived from Latin, which is read and written from left to right. There is no particular advantage in doing it this way. We could just as well read from right to left, top to bottom, or from bottom to top, but whatever we do, it is vital that we be consistent. When one finishes reading a line of text, the beginning of the next line must be easily located. To facilitate this, almost all written text is left justified. Our typewriters and computers do this for us automatically.

The Latin languages work very well for words, but are an abomination when it comes to numbers. Try adding the numbers, MCX XIII and MCCXI. the correct answer is MMCCCXXIV. There is a very good reason we limit Roman numerals to clocks and Super Bowl games. While our written words come from the Hellenic civilization, our written numbers come from the Arabic civilization, and as you might guess, the Arabic-based languages are written and read from right to left, and are right justified.

Try adding up the numbers, 8045, 24, 906, 5, and 83. I think that everyone would agree that the job would be made easier by arranging these numbers in a column.

8045
24
906
5
83

____

?????

This is still not the best way. Try:

8045
24
906
5
83

_____
9063

Much easier!

Now try writing the numbers backwards and adding left to right (the same direction we teach our children to read and write):
--2 1 1
5408
42
609
5
38
____

3609

5+4+6+5+3 = 32 (23); put down the 3 and carry the 2
2+4+2+0+8 = 61 (16); put down the 6 and carry the 1
1+0+9 = 01 (10); put down the 0 and carry the 1
1+8 = 9; put down the 9. The answer is 3609 (9063).

I first became aware of the problem, when using an old key punch machine. These were the machines that one used to punch little holes in IBM cards, which were read by computers. The cards contained words of written instructions as well as numbers. The machines automatically left justified everything, which worked quite well for entering words. However, there was a real problem when entering numbers. Each number was placed in a field of fixed length, and needed to be right justified. The operator had to stop, and count the number of digits in the number and subtracted it from the length of the field, in order to know the precise place to start typing the number so that would be right justified.

The handheld calculator illustrates the modern version of this problem. Calculators automatically right justify all numbers even though we enter them from left to right. Observe that when entering a digit all of the previous entered digits march magically to the left. One can observe this phenomenon by setting your word processor to right justify, and start typing.

You
you get
you get something
you get something just
you get something just like
You get something just like this!

Bizarre!

I certainly do not plan a crusade to have everyone write numbers in the correct direction, but I hope that you will better understand a young student’s dilemma.

DICK