@@@@@ @ @ @@@@@ @ @ @@@@@@@ @ @ @@@@@ @@@@@ @@@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @@@@@ @@@@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @@@@@ @ @ @ @ @@@@@ @@@@@ @@@Mt. Holz Science Fiction Society
08/10/01 -- Vol. 20, No. 6
Table of Contents
The Appeal of Mathematics (comments by Mark R. Leeper):
I am finding myself with a little more spare time than I have had until recently and I am thinking of going back and studying mathematics. For years I have promised myself if I had time I would do some math. Not that I expect to discover anything new or earn money by doing mathematics or improve the world. It just seems to me that working with mathematics is the natural thing to do. There is little in life that is so worthwhile. I do not think I have ever put on paper why I feel the way I do about mathematics.
When I was in high school I loved mathematics and was somewhat puzzled that more people did not just love mathematics. Mathematics was this thing to play with that was always there. I thought that they had somehow missed the point of mathematics and that if they saw it, they could not resist it any more than I could. Later Rubik's Cube became a craze. It is basically a plastic embodiment of a complex problem in group theory. I remember little kids on the street having fun working on what they did not realize was a problem in advanced algebra. Today I know a little more about the world. I can understand why some people do not love mathematics or at least think they do not love it, but I still think it is all because they have missed the point.
To me there is almost nothing more basic and elemental than mathematics. Imagine if you will a universe that has no matter in it. It is a total vacuum. But even in this universe mathematical logic still must be true. If "A is false or B is true", and if "A is true" then it follows B must be true, even in this empty universe.
Add just one particle to the universe and arithmetic kicks in. The particle is in a place or not. You have zero and one. From those you have all the integers.
To this space add another particle. The two particles have to interact. They either attract or repel. They start moving in mathematical courses around each other. Calculus kicks in if you want to describe their motion.
Add one more particle and you have the three-body problem whose mathematics is so complex it is not fully understood. But if it ever comes to be understood, it will be understood in the language of mathematics.
Mathematics is so basic because the particles would be matter, and matter loves mathematics. Matter obeys the laws of mathematics. Perhaps there is a God who can override the laws of mathematics and make matter obey His laws. There may or may not be such a God. But if there is one, He has to intervene to stop matter from obeying the laws of mathematics. When He stops intervening matter faithfully goes back to obeying mathematics. Matter may, if forced, obey God. It is the mathematics that the matter loves and returns to if it is free to. And matter's love song to mathematics has a name. It is what we call "physics." The study of physics is a search for the mathematics that matter has chosen to obey.
There are those who believe that the world of mathematics is coldly rational. Nothing could be further from the truth. Mathematics is the one realm where some form of magic really exists and works. Does that sound like an overstatement? Hold your judgment for a moment. Let me explain what I mean.
In the time of Shakespeare it was thought that the world was filled with beautiful spirits that mortals could not see. One could conjure to do magic. The conjurer could make a little incantation and then see the magic done but could not see the spirits who were fulfilling the conjurer's wishes. If he could he would be beguiled by the beauty of the spirits.
That or something very like that can actually happen with mathematics. At one point I wanted to write an equation that would just graph as the points (1,0) and (-1,0). Easily done. A curve that just graphs as (1,0) is (((X-1)^2)+(Y^2))=0. A curve that graphs as (-1,0) is (((X+1)^2)+(Y^2))=0. A curve that graphs as just the two points is (((X-1)^2)+(Y^2))*(((X+1)^2)+(Y^2))=0. Like the conjurer I had made a minor spell and got the desired effect. I had created an equation that did what I wanted. But I asked myself what kind of a curve was doing this. I graphed in three dimensions the curve (((X-1)^2)+(Y^2))*(((X+1)^2)+(Y^2))=Z. When Z=0 this was my original equation. What I got was something that looked sort of like a parabola rotated around its axis of symmetry. But at where we would expect the point it breaks into two points. It really was a beautiful shape. It touched the plane Z=0 at just the two points I had requested. My little incantation had created this beautiful curve whose only purpose for existence was to touch the two points I had requested in the plane.
To do most science these days you need expensive equipment. You do not have too many physicists who can afford to go off and work by themselves. And it is pretty tough for a loner to go off and do physics or chemistry by himself. What does the mathematician need? He needs paper and a pencil.
People have noted about me the manic behavior that I always seem to have a pencil or pen. It is less obvious, but I also always carry paper with me. Why? I hate to be bored. As long as I knew mathematics, I never had to be bored. I could always pull out paper and do a little mathematical fooling around. It is like having a Rubik's Cube in my pocket, but it was a much more interesting and diverse puzzle. For ten or so years after I got out of school I did a lot of mathematics in my spare time. Later I did less since there was nobody to discuss it with. Now with more time, I want to go back to do more mathematics. It is the most fundamental study of all.
And that I what I see in mathematics. [-mrl]
Correction (comments by Mark R. Leeper):
Last issue I was looking at the AFI top ten list and said that only two had nudity and one had sex. I did not list THE GRADUATE in either category. That was a true statement. But if one applies the same standards, neither really did CLEOPATRA, the film on which I was commenting. THE GRADUATE probably was on as much a sexual theme as CLEOPATRA. It seems to me that the sex was not the reason people were seeing the film; it was more a film of protest. But it is a fine line of distinction and that should be acknowledged. [-mrl]
Mark Leeper
mleeper@optonline.net
Quote of the Week:
So far as I can remember, there is not one word in the
Gospels in praise of intelligence.
-- Bertrand Russell
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