Solving A Problem

Daniel Defay’s paper on Numbo presented in Hofstadter’s book provides an interesting look into some of the logic that is used in creating a computer representation of what the human brain might try to do when solving problems using mathematics. In Numbo, Defay explains the use of codelets, the pnet, and the cyto-net in trying to solve a given mathematical problem based on some random big target number and only using a random amount of smaller numbers with addition, subtraction, and multiplication.

Although Defay readily explains the basics of the architecture, the reasoning behind his methods used, and the fact that in many respects Numbo is similar in design to Hofstadter’s Jumbo, Seek-Whence, and Copycat programs, I thought that the best part of Defay’s paper was in the concluding sections, more importantly the section that describes his human test subjects and the methods that the test subjects used to solve the a stated Numble problem and how they compared to Numbo’s solving of a Numble problem. I believe that this is important because it shows the parallels to the human brain and the Numbo computer program as well as showing the difficulties a programmer, or cognitive scientist might have in recreating brain function in a computer program.

“Another factor that would certainly complicate any comparison between Numbo and people is the highly questionable nature of human protocols. I was repeatedly told by solvers that it is difficult, if not impossible, to keep track of everything going on when one is solving a problem.” (Hofstadter, 151)

I think that this statement by Defay sums up the main problem of analyzing the way the human brain solves problems, nicely.