[ad510]

When I wrote "predict" there, I was referring to whether the predicted probabilities approach the true underlying probabilities, and Solomonoff induction can "predict" a true random number generator in that sense because its predicted probabilities will approach those of the random number generator. [1] However, if you tried to use it to predict a halting oracle, the halting oracle would be deterministic but Solomonoff induction would never be able to predict it with complete confidence, and this is what I was referring to in that paragraph.

But you're right that random numbers are inherently unpredictable; maybe I should add another footnote explaining what I meant there. (Edit: I added a clarification to the paragraph you quoted.)

[1] http://twistedoakstudios.com/blog/Post5623_solomonoffs-mad-s... in the "Thinking with Programs: Random Data" section

[goldenkey]

One of the principles of turing machines is that they are deterministic. In that vain, there exists no programmable RNG except for pseudo random ones. One has to ask oneself if piping a transform of the digits of a transcendental real number is a violation to this rule -- thus what is random really? Is random the lack of ability to find a correlation or program to reproduce it -- or is it something more like Komogrolov complexity? These are tough and inscrutable questions. Shannon, Turing, Curry, Church, Post, and others explored them deeply. Information theory gets extremely existential and esoteric. Is randomness a monad of our universe? Or is physicals and natural chaos just extremely leathery when it comes to extracting the generating program? Our lives depend on it. But either way, we'll carry on. Nature you goddamn enigma.