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.

No comments: