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© Copyright 2002, Jim Loy
On a Mork and Mindy episode, Mork discovered that he was an alien, and as such, had to register with immigration. Upon being tested by a psychologist, he was found to be somewhat strange. In fact, he put the square peg in the round hole, ruining the psychologist's peg board, and driving the psychologist crazy. You see, on Ork, a square peg is supposed to go into a round hole.
New age folks seem to think that the laws and formulas of science and mathematics are figments of our imaginations, that we have invented them, that they are not truly derived from nature.
I once asked a mathematician how he might respond to a student who suggested that maybe, way out there in a distant galaxy, 1+1 did not equal 2. He seemed to think that that was a stupid question, which it is, in a way. But it offers a little insight into mathematics. Let's look at it, just a little.
I say, why wonder about some distant galaxy? Why not wonder about just across the street? I go across the street and 1+1=2. At least my calculator says so. Your calculator says so. Counting your fingers tells you so. A Hindu in India will tell you that 1+1=2. So will a Chinese person. New age folks distrust western mathematics, but the basics do not seem to differ from culture to culture.
Set theorists know why 1+1=2 does not vary from culture to culture. It is because it is based upon much simpler and more basic concepts of sets. In a way, these ideas are more basic than anything physical.
Certainly, we cannot know much about way out there in some distant galaxy. So it seems safe to theorize that maybe 1+1 does not equal 2, out there, maybe.
But astronauts went to the Moon. Robot spacecraft have exited the solar system. And their computers still worked, out there. Stars and galaxies contain hydrogen and helium, identical to hydrogen and helium right here on earth. Gas clouds way out there have hydrogen gas, two hydrogen atoms bonded into a molecule: 1+1=2, way out there. The spectrums say so.
Addendum:
Let's perform an experiment. You and I watch as someone puts one marble into an empty box. Then we watch as that person puts another marble into the box. I predict that there are now two marbles in the box. Maybe that prediction is based upon cultural bias or not. But my prediction will be accurate. We can verify that by performing this experiment over and over. It turns out that I am always right.
Besides that, I predict that you will predict that there are two marbles in the box. I cannot be quite as sure about your prediction. Maybe you are from Alpha Centauri or from some distant galaxy. Maybe you are insane or a joker. Nonetheless, I predict that you will predict that there are two marbles in the box. And I find, by doing this experiment over and over, that you and other people do (almost always) predict that there are two marbles in the box. Unfortunately, we are both from Earth. We probably share the same language, and many of the same cultural experiences. So maybe some of these things have colored our predictions. But we don't see how that can be. How does culture change something which seems so basic? And we always get the same prediction, two.
Well, what if I am a joker or am insane, and I predict three? And when we open the box, I say "You see, there are three marbles in the box." You look and see two marbles. Your reaction is, "Jim, you are either joking or insane; there are two marbles." Is my statement (that there are three marbles) as valid as yours (that there are two marbles)? Science would demand tests, and we would find that almost everyone agrees that there are two marbles. Further tests show that I am indeed a joker who cannot always be trusted (this is hypothetical, remember). We have evidence that there really are two marbles in the box.
See Occam's Razor, where we find that science prefers the simpler solution. If two explanations cover the facts, and one is bizarre or perverse (like our three marbles above), and one is simple, then we prefer the simpler explanation. The more complicated explanation may indeed be true. But we cannot choose it without stronger evidence.