We present a ball game that can be continued as long as wewish. It looks as though the game would never end. But byapplying a result on trees, we show that the game nonethelessends in some finite number of moves. We then point out somedeep results on the natural number system connected withthe game.
We revisit a problem faced by all programmers. Can one write a program that determines whether any given program is the shortest program? How does one prove that a given program is the shortest? After answering these questions, we discuss very briefly the Kolmogorov complexity of a string of zero and one, which leads to a barrier on any axiomatic system, known as Chaitin’s barrier.
