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f ig. 2. Pi and the simple number series for computing its value to any degree oi accuracy, The curve shows that greater and greater accuracy is approached as more terms are used.

appearance in equations apparently far removed from the geometry of a circle Be that as it may, one would like to think that, because of the simplicity and symmetry of circles, pi would turn out to be a nice integral number, or, at least, one that comes out "even."

For ham calculations, we are accustomed to using the value 3.14 for pi. If you consult a handbook of math tables, you can find that pi to ten places is 3.1415926536 But even this is an approximation, in the sense that the last place has been "rounded off." In fact, pi has been calculated to at least twenty thousand places in the digital computer, and that twenty-thousandth place must still be rounded off' To make matters worse, no one has been able to discern any rhyme or reason to these endless decimal places. Suppose, OM. that you were making the initial discovery of pt by using a compass and ruler Would you readily accept that the relationship between such elemental dimensions could be so wild? Or, would you blame your measuring instruments for pi's persistent remainder?

Although we would not fault the mathematicians for labeling pi an "irrational" number, in what follows we shall see that the endless numbers cannot be construed as a random fallout, as though the digits had been recklessly cast from a giant pepper shaker.

Surprisingly, pi can be calculated by merely performing simple arithmetical operations indicated by a sequence or series of numbers. And, each decimal place so calculated is accurate, except, of course, the last one, because this is rounded off. Such a number series is depicted in Fig 2. Why should the sum of these alternate positive and negative fractions produce pi accurate to any number of dozens, hundreds, or even thousands of decimal places? As may be suspected, there are academically-acceptable answers Whether these answers completely resolve one s natural amazement over the situation is a question on another level of consciousness. Although number series are old hat to the mathematical ly-versed, many have long forgotten their own gasps of astonishment when first introduced to therm Actually, we have merely scratched the surface—it w ill be rewarding to inspect other manifestations of such "scientific numerology/'

Another constant that asserts itself whenever we use mathematics to indicate the connection between cause and effect or between states of being is epsiloriF or e. This strange number, as with pi, never comes out even regardless of the number of decimal places calculated Epsilon to ten places is 2 7182818285. Although epSilon is not simply related to a geometric figure, as is pi, there is nothing arbitrary or artificial about its value. Indeed, it is entrenched in virtually everything going on in the universe This is because this old universe of ours ¡is dynamic rather than static; it turns out that epsilon tikes to get invoked in anything that changes Included are such measurabtes as temperature, radioactivity, pressure, biological aging, energy in electric and magnetic fields, and even bank interest and population growth, Again, intuition would suggest that such a universal number should be a nice simple one. But, again, nature, with her majestic overview of these processes, has thought otherwise.

Just the same, epsilon is unique, for it, too, can be expressed as a simple number series. Now, don't invest magical qualities m these number series —they cannot be used to produce just any string of numbers It is truly amazing that epsilon can also be calculated to any number of decimal places by carrying out the easy arithmetical operations of a certain number series!

Epsiion is most intimately associated with any process that undergoes so-called organic growth or decay, The word "organic" stems from the fact that biological species tend to modify their populations in a manner readily stipulated by some exponential power of epsilon. For example, the bugs depicted in Fig. 3(a) are reproducing in such a way that their number at any grven time < an be calculated by a simple growth" equation involving epsilon We may sav that these critters are expanding straightforwardly according to N^= N0ext, where Nf rs the number of bugs present at any time, and N0 'S the number of bugs originally present.

Assuming an Adam-Eve situation, we might start with just a pair of am bilious bugs. Then, N0 would equal 2. The value of x describes the effective birthrate of these bugs and determines how fast the population curve rises with passing time. Finally, t represents the time elapsing from the fall from grace of the original buglet duo. Generally, x and t have to be derived from measurement or observation. It may well be that x can be gleaned from a biological handbook covering the antics ot various types of bugs, In any event, once we deduce x and t, we find ourselves able to predict the consequences of one particular entomological romanr e-(Such a relationship is very close to electrons s, as evidenced by the inevitable appearance of "bugs" in breadboarded circuits!)

Another, and perhaps more mundane, manifestation of epsilon is shown in Fig. 3(b). Suppose you have not nearly been pauperized by inflation and manage to start a savings account with one thousand dollars. Assume that while this account draws simple interest, you patiently await the great day when your money has doubled to two thousand bucks You propose to remove it at that time in order to buy an improved version of a two thousand dollar rig you had set your heart on when you deposited the kilo-buck (We know lull well that the rig will cost four thou by then, but that is not the point) When, at





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