Darwin's Dangerous Idea - Evolution and the Meaning of Life

448 THE EMPEROR'S NEW MIND, AND OTHER FABLES
seem to organize themselves somewhat better than they 'ought' to, just on
the basis of blind-chance evolution and natural selection. It may well be
that such appearances are quite deceptive. There seems to be something
about die way that die laws of physics work, which allows natural selection
to be a much more effective process than it would be with just arbitrary
laws. [Penrose 1989, p. 416.]
There could not be a clearer, more heartfelt expression of the hope for
skyhooks than this. And though we cannot yet rule out "in principle" the
existence of a quantum-gravity skyhook, Penrose has not yet given us any
reason to believe in one. If his theory of quantum gravity were already a
reality, it could well turn out to be a crane, but he hasn't got that far yet, and I
doubt that he ever will. At least he's trying, however. He wants his theory to
provide a unified, scientific picture of how the mind works, not an excuse for
declaring the mind to be an impenetrable Ultimate Source of Meaning. My
own opinion is that the path he is now exploring—in particular, the possible
quantum effects occurring in the microtubules of the cytoskeleton of
neurons, an idea enthusiastically promoted in Abisko by Stuart Hamer-off—
is a nonstarter, but that is not a topic for this occasion. (I can't resist raising
one question for Penrose to ponder: if the magnificent quantum property
lurks in the microtubules, does that mean that cockroaches have
noncomputable minds, too? They have the same kind of microtubules we
have.)
If a Penrose-style quantum-gravity brain were truly capable of nonalgorithmic
activity, and if we have such brains, and if our brains are themselves
the products of an algorithmic evolutionary process, a curious inconsistency
emerges: an algorithmic process ( natural selection in its various levels and
incarnations) creates a nonalgorithmic subprocess or subroutine, turning the
whole process (evolution up to and including human mathematician brains)
into a nonalgorithmic process after all. This would be a cascade of cranes
creating, eventually, a real skyhook! No wonder Penrose has his doubts
about the algorithmic nature of natural selection. If it were, truly, just an
algorithmic process at all levels, all its products should be algorithmic as
well. So far as I can see, this isn't an inescapable formal contradiction;
Penrose could just shrug and propose that the universe contains these basic
nuggets of nonalgorithmic power, not themselves created by natural selection
in any of its guises, but incorporatable by algorithmic devices as found
objects whenever they are encountered (like the oracles on the toadstools).
Those would be truly nonreducible skyhooks.
The position is, I guess, possible, but Penrose must face an embarrassing
shortage of evidence for it. The physicist Hans Hansson came up with a good
challenge in Abisko, comparing a perpetual-motion machine to a truthdetecting
computer. Different sciences, Hansson noted, can offer different
The Phantom Quantum-Gravity Computer 449
reliable shortcuts to verdicts about projects. If someone were to go to the
Swedish government with a plan to build a perpetual-motion machine (at
government expense), Hansson would unhesitating testify, as a physicist,
that this would be—would have to be—a waste of government money. It
could not succeed, because physics has proven that a perpetual machine is
flat impossible. Did Penrose think that he had offered a similar sort of proof?
If some AI entrepreneur were to go to the government asking for money to
build a mathematical-truth-detecting machine, would Penrose be similarly
willing to testify that such money would be wasted?
To make the question more specific, consider some rather special varieties
of mathematical truth. It is well known that there can be no all-purpose
program that can examine any other program and tell whether or not it has
an infinite loop in it, and hence will not stop if started. This is known as the
Halting Problem, and there is a Gödel-style proof that it is insoluble. ( This
is one of the theorems Turing alluded to in his 1946 comment quoted at the
beginning of the chapter.) No program that is itself guaranteed to terminate
can tell of every (finite) program whether or not it will terminate. But it
might still be handy—worth some serious money—to have a program
around that was very, very good (if not perfect) at this task. Another class of
interesting problems are known as Diophantine Equations, and it is known
that there is no algorithm guaranteed to solve all such equations. If our lives
depended on it, should we spend a nickel on a program for solving Diophantine
Equations "in general" or for checking for halting "in general"? (Remember:
we shouldn't spend a nickel on perpetual-motion machines, even to
save our lives, since it will be money wasted on an impossible task.)
Penrose's answer was illuminating: if the candidates for truth-checking
"just somehow bubble up out of the ground," then we would be wise to spend
the money, but if some intelligent agent is the source of the candidates and
gets to examine the program in our truth-checker, then it can foil our
algorithmic truth-checker by constructing just the "wrong" candidate or
candidates—an equation unsolvable by it, or a program whose termination
prospects will confound it. To make the distinction vivid, we can imagine
that a space pirate, Rumpelstiltskin by name, is holding the planet hostage,
but will release us unharmed if we can answer a thousand true-false
questions about sentences of arithmetic. Should we put a human mathematician
on the witness stand, or a computer truth-checker devised by the best
programmers? According to Penrose, if we hang our fate on the computer
and let Rumpelstiltskin see the computer's program, he can devise an
Achilles'-heel proposition that will foil our machine. (This would be true
independendy of Godel's Theorem, if our program was a heuristic truthchecker,
taking risks like any chess program.) But Penrose has given us no
reason to believe that this isn't just as true of any human mathematicians we
might put on the witness stand. None of us is perfect, and even a team of