I do appreciate what you are saying, but in this discussion of splitting rocks, it must be noted that there is no such thing as a table of random numbers – since all the numbers are the effect of a cause, whatever that might be – algorithm, tossing of die, your ingenuity, even Brownian motion. (based on Wolfram’s response to Chaitin’s Omega)
From the frog’s perspective (Tegmark) that observation makes no difference – the table of evidently random numbers could just appear in his timeline. But from the bird’s perspective, there is nothing random at all.
Yours is a tipping point example, much like Schrödinger’s cat with greater obscurity. Schrödinger gives us two choices, dead cat/live cat – but you suggest a tipping point in the eye of the beholder.
I counter that at the root, what is obscure or distinctive is a mathematical structure to the observer, i.e. the answer depends on whether the observer is a frog or a bird. The bird would see a distinctive tipping point which the frog could not see.
Nevertheless, frog or bird, I would suggest that the question the frog could ask is: what is the Kolmogorov complexity of the unaltered table? If it is a low complexity, then what he would observe to be a range of tipping possibilities is knowably false from his frogness view. If it is a high complexity, he’ll have to ask the bird.
OK, "this big gap between certainty and naive experience" would then be the distance between said frog and bird.