Yes, I know that Solomonoff induction is completely impractical for real life machine learning. My point was that if you can survive in the simulation to the point where you see either the 0 or the 1, we don't have any way even in theory (let alone in practice) to guess the probabilities of seeing a 0 or 1, unless you use some sort of learning algorithm. You can use any learning algorithm for this; it doesn't have to be Solomonoff induction.
Well, I must say that I'm pleasantly surprised with the comments so far. I was actually expecting that this would be quickly shot down as either unoriginal or fundamentally flawed. But instead it seems no one has caught on to what this post is actually claiming, so I suppose I should now be very blunt about it.
At the beginning of the blog post, it claims that it explains 2 things:
1. where exactly might you be able to use learning algorithms where you can't just use existing physics theories instead
2. a hands on guide to applying learning algorithms in these situations
This is physicist code for "this blog post claims that it solves a major unsolved problem in physics." Let me explain.
Currently, we have the standard model and general relativity, which have been experimentally verified to extreme precision but are fundamentally incompatible with each other. So people have proposed theories of everything such as string theory, loop quantum gravity, and information/digital physics (which I'm obviously a fan of) to resolve these incompatibilities.
One of the biggest problems in fundamental physics right now is that the standard model and general relativity have been verified to such precision that it's hard to think of a practical experiment to show how they are wrong. The conventional wisdom is that this is only possible if we do things like measure the Planck scale or what happens inside a black hole, which are completely impractical on human timescales.
What this post proposes is that you actually don't need to measure the Planck scale or what happens in a black hole in order to test the proposed theories of everything, and instead you can do it with a sufficiently powerful computer simulation and a sufficiently good brain-computer interface. If our technology keeps improving exponentially, this may be possible in the next several decades.
So yeah, I made a bit of a white lie when I framed this post as a summary of recent research in information physics. I can back up almost everything in the post with the sources I linked to, but the part about the 0 or 1 experiment and predicting its outcome using Solomonoff induction is actually original research on my part, and I suspect it would actually be a very big deal if this works the way I think it does.
So here are the possible outcomes for this blog post:
1. The problem in physics I just described is actually already solved.
2. The blog post is fundamentally flawed, and/or it actually doesn't solve the problem that I'm claiming it solves.
3. The blog post actually does solve a major unsolved problem in physics, and this is a huge deal.
This is why I am so surprised at the comments I'm getting so far, since this proposal for experimentally testing theories of everything seems to be passing the internet commenter test. So if no one on HN finds anything seriously wrong with the blog post, can we get people like Scott Aaronson, John Baez, Juergen Schmidhuber, Stephen Hawking, or people of that caliber to look at it so we can get a more definitive answer to whether this actually solves an unsolved problem in physics?
Also, kudos to Xcelerate's comment, which is the closest to the point I was trying to get at with the blog post.
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.)
general relativity: http://www.feynmanlectures.caltech.edu/II_42.html
quantum electrodynamics: "QED: The Strange Theory of Light and Matter" or http://vega.org.uk/video/subseries/8
standard model: http://quantumdiaries.org/2010/02/14/lets-draw-feynman-diaga...
conceptual core of quantum mechanics: http://scottaaronson.com/democritus/lec9.html
history of quantum mechanics: "The Second Creation" and "The Infinity Puzzle"