p.1 Computers are physical systems: what they can and cannot do is
dictated by the laws of physics. In particular, the speed with which a physical device can process information
is limited by its energy and the amount of information that it can process is limited by the number of degrees of freedom
it possesses.
p.5 Parallelization can help perform certain computations more efficiently,
but it does not alter the total number of operations per second.
p.15 If the latter picture is correct, then black holes could in principle
be ‘programmed’: one forms a black hole whose initial conditions encode the information to be processed, lets
that information be processed by the Planckian dynamics at the hole’s horizon, and gets out the answer to the computation
by examining the correlations in the Hawking radiation emitted when the hole evaporates. [JLJ - you know, I was just beginning
to understand this guy, and then he writes something like this. Certainly, it takes a different kind of perspective to talk
about programming evaporating black holes.]
p.17 Physical systems that can be programmed to perform arbitrary digital
computations are called computationally universal.
