- In the last chapter of FOR, DD infers - given various assumptions (e.g. that the universe will recollapse) - that "intelligence will

survive, and knowledge will continue to be created, until the end of the universe." The amount of knowledge created, and the

subjective time of survival, would be infinite. This inference appears to be based on the fact that the Turing Principle is our best

theory of the foundations of computing, and the TP implies that there is no upper bound to the number of computational steps that

are physically possible. Otherwise, DD argues, we are left with a sort of "approximate Turing Principle" which would be correct,

given worlds enough and time, but which isn't correct because the universe only allows a very large but finite number of

computational steps to be performed. For comparison he says that "the theory that the world is *half*-comprehensible explains

nothing and could not possibly fit in with explanations in other fields unless *they* explained *it*. It simply restates the problem

and introduces an unexplained constant, one-half. In other words, what justifies assuming that the full Turing Principle holds at

the end of the universe, is that any other assumption spoils good explanations of what is happening here and now."

Leaving aside the evidence that the universe may continue to expand forever (which also possibly disallows the full Turing

Principle, but for other reasons), isn't this a circular argument? The equivalent of the "constant, one-half" in this case would be

the maximum possible number of steps any possible computer - say, for the sake of argument, one spontaneously assembled from all the

matter in the universe at the instant of the Big Bang and run at full speed until the Big Crunch - could perform. This constant

would, however, not be arbitrary, but would emerge from the structure of the universe. The resultant "modified Turing Principle"

would imply that a computer could only be universal within certain limits in a given universe. Or to put it another way, because

Turing envisaged an infinite paper tape in order to simplify matters (rather than bothering with practical details), this doesn't

necessarily imply that, in a collapsing universe, any real computer will *necessarily* run for an infinite amount of (subjective)

time.

Or does it?

(I haven't read the last few pages yet, and it's a few years since I last read FOR, so I don't actually remember where DD is going

with this...)

Charles

[Non-text portions of this message have been removed] > There are many options for what could happen inside a black hole, but

Fair enough. I still wonder whether the Turing Principle is sufficient to cause the existence of a suitable universal computer to come into existence *everywhere* in the multiverse, or just *somewhere*. DD was also unsure about this in FOR, although he plumped for everywhere IIRC. I wonder if he's revised that opinion in the intervening 7 years...?

> nobody knows which of them actually happens. One is that the black hole

> gives rise to a daughter universe separated from ours by the event horizon

> in which the Turing Principle is respected. Another is that the black hole

> either evaporates or as in the Omega Point and presumably Barrow's

> alternative a future civilisation gets rid of the event horizon and the

> informtion inside is let out. Or...?

Charles