Turing's fundamental result is that the halting problem is unsolvable. Chaitin's fundamental result is that the halting probability is algorithmically random, i.e. the digits of the number Omega expressing the halting probability form a binary random sequence. The use of the Bible, the Koran and the I Ching for divination and the tradition of the secret books of Hermes Trismegistus, and the medieval Jewish Cabala exemplify this belief or hope. Such sources of universal wisdom are traditionally protected from casual use by being hard to find, hard to understand when found, and dangerous to use, tending to answer more questions and deeper ones than the searcher wishes to ask. The esoteric book is, like God, simple yet undescribable.
Omega is in many senses a cabalistic number.
It can be known of, but not known, through human reason. To know it in detail, one would have to accept its uncomputable digit sequence on faith, like words of a sacred text. We won't go any further into this, but quote a review of Chaitin's work stating that Chaitin's article makes the world shake just a little. I then discuss recursive and recursively enumerable sets, and the undecidability of the Halting Problem. This will lead to computable real numbers, computable decimal expansions, computable functions on the computable real number line, the recursive failure of the Heine-Borel theorem, and the recursive Lebesgue measure of the recursive unit interval.