An objection to the idea that everything is a computation.
Form Rudy’s book, LLS, page 401, Suppose that R is some very simple computation that is everywhere defined – to be specific, suppose that, given any input In, the computation R_In simply stays in the In state for ever. Any computation at all can emulate R, but we don’t expect that the do-nothing R can emulate all the other computations. For this reason, we say that R represents a minimal degree of unsolvability.

I want to challenge this seemingly most fundamental of notions. In particular I want to challenge the underlined statement.



The truth of the assertion I believed depends on the domain and range of the computation, and therefore can be said to depend on the nature of the multiverse. That is if In and R_In are continuous valued then all bets are off, because any computation M (we could say experiment) that tries to measure R can be fooled by some other approximate R^’, and in fact there an infinite number of such R^’. Furthermore, there is an infinite set of these R^’ that are uncomputable! That is, even though M tells us that in our universe that R has some constant value we do not know this to be true and therefore we can only emulate R to some measure M, and R would in fact be able to emulate other computations if we know the “inner” workings of R.

This is just a way of saying that there is no computational method of determining that the universe is infinite valued. I.e. if the universe is continuous valued it can “fool” any M that tries to show that it is not, but so can a universe that is merely countably infinite. OTOH, if the universe if finite any experiment E is contained in that universe and therefore can only come up with answers contained there in. That is, for all E contained in a finite universe there is no way of arriving at a proof that the universe is not infinite because this proof would require infinite resource but E is in the universe and therefore would be a contradiction to the assertion that the universe is finite.

We are therefore left with a chicken and egg problem when we try to assert that everything is a computation. If the universe is infinite valued then computation must truly be something more subtle than a finite sequence of rules, see. And if the universe is finite we know that we can therefore never measure to what degree it is finite, that is what are its limits compared to the imagined, non-existent, continuity. So the proposition everything is a computation is inherently unverifiable, and at the same time any such universe generating computation has infinitely many emulations. We can’t have it both ways.

The deeper problem is that all attempts by awareness to ask, “What am I?,” immediately involves infinite recursion, a recursion that wants to grow into the Ubër Infinite. Yet our assertion everything is a computation rejects the infinite, so that in accepting the assertion we appear to be saying our thoughts are outside the universe, and if not then we are saying that our thoughts about infinity are false.




I suspect RR goes on to say this better than I have but I wanted to get my head around this argument before proceeding.