[math-fun] Proofs that computers cannot have a sense of humour

Theorem: It is impossible for a computer to have a sense of humour. Proof 1: Note that computers cannot determine whether general Diophantine equations have solutions. For a general Diophantine equation given by D(x_1, ..., x_n) = 0, consider the following sentence J: J = "Why is 6 afraid of 7? Because 7 min{8 + D(x_1, ..., x_n)^2 | x_1, ..., x_n in Z} 9." Then J is humorous if and only if D(x_1, ..., x_n) = 0 has a solution. Proof 2: It is undecidable to determine whether a group with presentation P is the trivial group. Now apply the same proof to the following sentence K: "What's purple and has presentation P? The trivial grape." Then K is humorous if and only if P is a presentation for {e}. Sincerely, Adam P. Goucher