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Mathematicians are Trained to Value Simplicity


I ran into an old friend from grad school the other day, who told me about an experience he had recently while attending a mathematics meeting at an Ivy League university.

During the lunch break, my imaginary friend recounted, I ran into two mathematicians who were debating the results from a talk just given by Dr. A. “Dr. C here believes he has found an error on page 17 of the proof of my main theorem,” explained Dr. A. I looked at the theorem a while, then pointed out that if you transform everything into another coordinate system things are much simpler, and in the new coordinate system it is obvious that the theorem is false. “Oh” said Dr. A, “I hadn’t thought to look at things from that point of view, things are much simpler and clearer in that framework.”

Later that same day, my friend continued, I ran into two biologists who were debating Darwinism. “Dr. B here believes he has found an irreducibly complex molecular machine in the cell that falsifies Darwinism. I have shown how this machine could have been constructed by co-opting features from other similar, previously existing structures,” explained Dr. D. I didn’t bother looking at his diagrams of the co-opted structures, but inquired, “are you one of those biologists who believes the origin and evolution of life, and of human intelligence, can be explained entirely by natural causes, without design?” “Well, yes, of course,” replied Dr. D. “So you believe that four fundamental, unintelligent forces of physics alone can rearrange the fundamental particles of physics into Apple iPhones and nuclear power plants?” I asked. “Well, I guess so, what’s your point?” he replied. “When you look at things from that point of view, it’s pretty obvious there must be an error somewhere in your theory, don’t you think?” I said.

Dr. D looked at me and sneered, “Do you have any idea how many books have been written, how many journal articles have been published, which support Darwin’s theory? How much biochemistry do you know, by the way?” I had to admit that I was just a mathematician and knew little biochemistry. “But it’s hard to imagine anything simpler and more obvious in all of science than the fact that unintelligent forces of physics alone cannot construct iPhones,” I added. He snapped back, “Many of the greatest minds in history, from the top universities in the world, have carefully studied the origin and evolution of life, and nearly all agree with me. And you think you can overturn their theories with such a simple argument, that doesn’t even look at the details of biochemistry or evolutionary theory?” And the two biologists went back to arguing about irreducible complexity and co-option.

I guess I did look pretty ignorant, I thought as I left. But I soon ran into Dr. A again. “Did you two ever decide if there was an error on page 17 of your theorem proof, as Dr. C suspected?” I asked. “Oh, we didn’t bother looking further at the details on that page,” he answered. “Once you showed how clear and simple everything is when you look at it from a different point of view, we realized that there had to be errors somewhere in my long complicated proof. That was really brilliant, by the way.”

I guess I should stick to mathematics, my friend thought, as he walked away. In mathematics, if you find a simple, clear way of looking at a complicated problem you are applauded, not sneered at.

In the video below, I have attempted to take my ficticious friend’s simple argument and make it a bit more complicated and sophisticated, so that evolutionary biologists may be able to understand it.

[youtube 2Ea5s1pnigk]