What about Dyson's work on the infinite survivability of sophontic life
in an indefinitely expanding, cooling universe? It's been a long time
since I read this, and I haven't read Tipler's recent book yet either,
but it doesn't seem to me that making an assumption of the possibility of
infinite computation settles the question one way or the other.
The Heat Death (I use the term with irony) is approached just as
asymptotically as the Big Crunch, and it would be approached *much* more
slowly, which would give more time for life forms to adapt to the changes
in their physical environment. In the Heat Death scenario, computation
would gradually but inexorably slow down, but it would have a future that
is, for all practical purposes, infinite. It's not as if one day God is
going to flip a big switch that wipes out all the remaining negentroy in
the universe. The point of exactly zero negentroy is infinitely far off in
the future. Computation approaching the Big Crunch, on the other hand,
would have a sharp future time limit, but would speed up "infinitely" as
it approached that limit.
Either future would require continuous steady adjustment of our "natural
time scale", but I think we could adapt just as well to either one.
And then there's always the possibility advocated by the Alfvenite
steady-state heretics. At the moment, the Alfvenite/Lernerite stuff
doesn't seem plausible to me, but I think the certainty with which we know
Big Bang theory to be true is greatly exaggerated. Such exaggeration about
the certain truth of theories that are poorly understood by the general
population is usually to the advantage of those who do understand those
theories, especially when seeking funding for further research.