I have been re-reading Seymour Papert's Mindstorms, perhaps the seminal work on the use of computers in children's education. Papert trained originally as a mathematician, which heavily influenced his thinking on the use of computers in education. Papert states in the book that much of his thinking was influenced by another famous mathematician, George Polya. Polya is famous for his thinking on problem solving and heuristics in mathematics. Naturally I had to start reading about Polya. Polya's writings helped me to resolve two questions about myself that have troubled me for over thirty years:
- Why is it that I can listen to a company problem and come up with an excellent new strategy in 5-10 minutes; I see my ability to develop strategies as somewhat akin to the way some people can do bar tricks.
- Why is it that I can solve certain kinds of problems but I can not solve large, complex conceptual problems; I appear to specialize in solving concrete problems that are suitable for a zen like approach--focused and simple.
The answer to the first question comes from a quote from George Polya:
"In order to solve this differential equation you look at it till a solution occurs to you."
If Polya can just look at a math problem and solve it, why can I not just look at a business problem and develop a new strategy. While solving differential equations may be a different kind of problem from developing a business strategy, I think both Polya and I have developed heuristics. In the case at least of Polya, the heuristics are quite profound in their own right. This recognition of the role of heuristics gives me additional motivation to clarify my thinking on my formal concept of business model, which is clearly an heuristic. (My original thinking on business model is here.)
The second question was answered by a description of Polya in The Random Walks of George Polya by Gerald L. Alexanderson:
"It was not given to him to solve very difficult problems or to build vast conceptual structures. Yet he could perceive the significance, the beauty, and the promise of a rather concrete, not too large problem, forsee the possibility of a solution, and work at it with intensity. And, when he had found the solution, he kept on working at it with loving care, till each detail became fully intuitive and the connection of the details in a well-ordered whole fully transparent."
If a thinker as profound as Polya can have limitations in problem solving, so can I. Somebody else can solve the difficult conceptual problems.
If you are interested in problem solving, education or artificial intelligence, you should read both Papert and Polya. The applications to artificial intelligence will become apparent after you read the books. Papert also discusses epistemology in the context of learning, but Polya dismisses philosophy in this famous quote:
"I am too good for philosophy and not good enough for physics. Mathematics is in between."
Now I am off to see if Polya ever wrote about Bertrand Russell or whether Godel's Proof, developed in thirty minutes (obviously using a heuristic) was sufficiently elegant to settle the matter. Godel, arguably the greatest mathematician of the 20th century, mathematically proved that the basic principle in Russel's Principia Mathematica--mathematics was grounded in logic --(therein lies the link to philosophy) was incorrect. (The other candidate for the greatest mathematician of the 20th century was John von Neumann, a student of Polya.)
If I had studied math with a teacher trained by Papert, maybe I would have pursued math instead of philosophy in college. One interesting thing is how Papert and Polya show that epistemology is perhaps the link between mathematics and philosophy :)
If you are wondering how any of this relates to management or finance, learn about heuristics for problem solving.Image credit George Polya