The Fundamental Theorem of Human Ignorance

The following "theorem" was first proposed by Professor Zhu on August 6, 2003 in a speech delivered during the Stanford Statistics alumni dinner held in San Francisco, CA, USA. Professor Zhu spoke as a representative of students in the 1990's, while others spoke on behalf of those in the 1980's, 1970's, and 1960's. Everybody at the dinner seemed to agree that the theorem was correctly stated, but to date somebody has yet to provide a complete and rigorous mathematical proof for it.

Theorem (Zhu 2003)   Let X be a randomly selected individual from a population of size n and Y, a random topic selected independently from X from a population of size m. Then,

(i) (weak law) P(X knows Y) → 0 as min(n,m) → ∞;

(ii) (strong law) under mild regularity conditions, X will almost surely not know Y as min(n,m) → ∞.