Friday, May 14, 2010

The Unreasonable Ineffectiveness of Mathematics in The Social Sciences

Sometimes I get mad at psychology. The psychologists have had a hundred years to get us figured out and for what? What have the chemists, biologists, physicist and mathematicians given us over the past hundred years? Well, they have reshaped the earth. We have become a space faring species with instant global communication. But we still have serious behavior dysfunction. We can build remote controlled weapons that fire with murderous accuracy as we view on our American monitors. But we still fire the weapons. There is a grand little article, The Unreasonable Effectiveness of Mathematics in the Natural Sciences, (Wigner , 1960). Wigner notes that mathematics is a human construct but it remains exact description of the natural world even as it is extended to more abstract and counterintuitive domains. I contrast this to the unreasonable ineffective of mathematics in the social sciences. While I have certainly not scaled the commanding heights of the social sciences, I do have a PhD in mathematics education. I find I have a great tool kit for responding to the immediate questions of mathematical pedagogy but I have no clue how to deal with a 13 year old coming out of a home in chaos. Children come in angry and hungry and I have no theory of response. I listen and I hand out a granola bar. I have my little psychic bandages and I find I care about these children. I see little science in this. I have no mathematics for predicting, engineering or creating the mental state of security, acceptance, motivation and curiosity. I have my craft, but it has been abstracted from years of experiences and I have no algorithms to pass on. I suppose that is the core of it. Like Joseph Campbell’s description of the Hero’s Journey,(Campbell, 1973) the scientist journeys to a mystical land of abstractions and expertise and finds the great boon. Then the hero has to return to the land of the mundane. The hard sciences can package their boon – their great insights – into machines that respond to the touch of the novice. We can effectively use machines with no understanding of their internal workings. We use formulas routinely with no grasp of their derivation. The natural sciences can package their knowledge in devices. The social sciences have found no way to do this. The effective practitioner has to slowly self-construct over years of experience and there is no algorithm for controlling human behavior. I suppose we will lose some of our humanity when we find such a tool of manipulation. So I am not really mad at the psychologists. I just bemoan the unreasonable ineffectiveness of mathematics in the social sciences.

Wigner, E. P. The unreasonable effectiveness of mathematics in the natural sciences, Comm. Pure Appl. Math., 13 (Feb. 1960)

Joseph Campbell, The Hero with a Thousand Faces, 3rd printing (New Jersey: Princeton University Press, 1973) 11.

Monday, March 15, 2010

I was at Starbucks last Saturday and stumbled into a Coffee Party meeting. I asked if I could join in the conversation and that opened an interesting discussion. Now I find the idea of a grassroots movement to recalim civility and effective government compelling. How do you answer someone who asks you why you hate America? Who come up with that one? I could only respond as reasonably as I could, “Probably for the same reasons as you.” That would be the unexpected response. Stating a thing does not make it true. You can say I hate America I can say you hate America. That accomplishes nothing but is the strategy is to create impasse, it is effective. I suspect that I am in a fool’s paradise here. I expect a rational response. A more probable reaction is strident voices would be to become even more strident. I do like the idea of printed messages of civility and invitation to talk. We cannot shout down those who gather to shout us down. Actually, no one has tried to shout me down. I have seen media images of that behavior but I have not yet seen it on the streets of Casper. I hope the Coffee Party movement can focus on civility. It is hard to be mad at someone who is trying to listen to you.

Do we see ourselves as a compassionate people? How do compassionate people act? There is something about the two coat rule in the bible. If you have two coats and your neighbor has none, then give him one of yours. How hard is that? From the Book of Matthew, 3:11 He answereth and saith unto them, He that hath two coats, let him impart to him that hath none; and he that hath meat, let him do likewise. So, do you have two coats?