On a recent drive to and from a GIPS(R) (Global Investment Performance Standards) verification client, I began to listen to a book on Einstein and some of his friends, which included Kurt Gödel. I don’t recall hearing of Gödel before, but do recollect his “incompleteness theorems.”
According to Wikipedia, “The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics.” It further reports that “The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an ‘effective procedure’ (e.g., a computer program, but it could be any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic).”
Does this not hold for performance attribution? Recall that I recently touched on the question as to whether or not attribution answers the questions we wish it to. Perhaps even the best model will leave something out. Might Gödel’s theorem hold here, too?
You know the saying, “a little knowledge is dangerous,” and it definitely applies here, as I’ve only lightly scratched the surface of this topic, and would need to devote several hours to have any real understanding of it. But the brief statement above seems to hold some truth.
Perhaps this might be a good topic for Jose Menchero, PhD to address, given that his PhD is in physics, and he is no doubt familiar with Gödel. Interesting subject, I think.
By the way, Gödel is an interesting subject, himself.