Chaitin's constant $\Omega$ is a constant whose digits are defined to encode the solution to the halting problem which is undecidable and hence $\Omega$ is uncomputable. I am not particularly familiar with the field of algorithmic information theory, and I have a question about a statement which I once read (by a physicist) in a paper by David Deutsch:
If the dynamics of some physical system did depend on a function not in $C(T)$ [the set of computable functions], then that system could in principle be used to compute the function. Chaitin (1977) has shown how the truth values of all ‘interesting’ non-Turing decidable propositions of a given formal system might be tabulated very efficiently in the first few significant digits of a single physical constant [Emphasis mine].
I have read the paper referenced, and I think I understand (a fair bit of) it, but I still do not understand exactly where the italicized statement comes from; I could not seem to find relevant results in the paper. Would anybody be able to explain exactly where the statement that all of a formal system's ‘interesting’ undecidable propositions can be efficiently tabulated in a real number's first few significant digits comes from, how such tabulation would proceed, and what (if any) is the relation of this to $\Omega$ and Chaitin's work?