The Master .Plan

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September 16, 1999 - Part One: Mathematics (Two)

Note: This is part one of a three part series. They're all connected, in a rather "connections" kind of way. Bear with me :-)

I was rereading Contact, by Carl Sagan, and was stuck by a passage early in the first chapter:

In the seventh grade, they were studying something called "pi". If you measured the circumference and then divided it by the diameter of the circle, that was pi. At home, Ellie took the top of a mayonnaise jar, wrapped a string around it, straightened the string out, and with a ruler measured the circle's circumference. She did the same with the diameter, and by long division divided the one number by the other. She got 3.21. That seemed simple enough.

The next day the teacher said that π was about 22/7, about 3.1416. But, actually, if you wanted to be exact, it was a decimal that went on and on forever without repeating the pattern of numbers. Forever, Ellie thought...

The book said something else: π was called a "transcendental" number. There was no equation with ordinary numbers in it that could give you π unless it was infinitely long... And π wasn't the only transcendental number. In fact there was an infinity of transcendental numbers. More than that, there were infinitely more transcendental numbers than ordinary numbers, even though π was the only one of them that she had ever heard of. In more ways than one, π was tied to infinity.

She had caught a glimpse of something majestic. Hiding between all the ordinary numbers was an infinity of transcendental numbers whose presence you would never have guessed unless you looked deeply into mathematics. Every now and then, one of them, like π, would pop up unexpectedly in everyday life. But most of them--an infinite number of them, she reminded herself--were hiding, minding their own business, almost certainly unglimpsed by irritable Mr. Weisbrod.

Every now and then, mankind has had to face something of this magnitude. A thought so large it is hard to hold in one mind. Infinity is a tricky thing to think about, since it indicates something that cannot be comprehended in the limiting terms of spoken language. Except in the arcane language of mathematics.

The fascanation for me in π is the simple fact of it's infinity. Something that goes on forever, never repeating. Hidden in the measurements of a measurable, finite circle.

I've always had trouble with math. As a computer programmer, that comes as a shock to a lot of people, but it's true. I suck at math :-) And yet, I can find something beautiful and meaningful in a subject that drives me crazy. This kind of mathematics fascinates me since you can find something philisophical in the concept of infinity.

Zero is a similar subject. The abscence of value is not really thought about, but since much of our society is based on haves and have-nots in a financial way, zero becomes quite understandable :-)

If you like Science Fiction at all, Contact is a fascinating book. A bit difficult at times, but the ending is incredibly philisophical. The movie is very good as well, but doesn't have the same ending as the book, which in a way is a shame.

Till next time...