In the world of computation any unpredictable infinite series of numbers, bits, or whatever is a Turing Machine that can compute anything a human can compute. I don't like this even though it may be true. As Borges suggests.
What I do like is Steven Wolfram's physics that basically reality is a computation over a fixed number of space-time particles on the order of 10^100 of them. The computation can change their arrangement based on rewrite-rules that are not limited in span over the particles. The solution to physics is then, to figure out the rewrite rules which then constitutes a perfect analysis of all physical laws. These particles are far finer than Planck lengths or times.
He's actually making headway here.
There is no God here, just the rules. Wolfram is arguably one of the greatest mathematicians of our time, and arguably not crazy. Just like Borges is also arguably not crazy. At the base of Wolfram's thinking is exactly such a library, except he thinks first it is not infinite to provide infinite products (an infinite time and space), and you can figure out the re-write rules needed to prove everything we know (by math) in modern Physics ... including the 'grand unification.' P.S. rewrite rules are mirrors that change the nature of reality. Time marches forward as the rewrite rules apply.
Now, if a rewrite rule applied probabalistically,
based on a random infinite number, you might have some trouble I think. But neither Borgas nor Wolfram, hoping for the best, believe that, for now, anyway. Quantum Mechanics says otherwise and just gives up. Too soon?