Notes for the Lifebox, the Seashell, and the Soul - Rudy Rucker

Notes for The Lifebox, the Seashell, and the Soul, by Rudy Rucker
the decimal positions n! and 0 in all the other places. Someone might readily say that a
number like this is unlikely to occur in any real context.
Analogy. In 1956, Richard Friedberg and Albert Muchnik carried out a complex and
artificial construction of a computation of intermediate degree for one notion of solvability
degrees and logicians such as J. C. E. Dekker did similar constructions for other notions of
degrees.
History. In 1874, Georg Cantor constructed a specific enumeration of the countable
set of algebraic reals and produced a transcendental number by having it differ in the i th digit
from the i th member of his enumeration of the algebraic numbers. Again, someone could say
that Cantor’s number isn’t a number that would naturally occur, that it is artificial, and that it
depends in an essential way upon higher-order concepts such as treating an infinite
enumeration of reals as a completed object.
Analogy. In the 1960s, the logician Gerald Sacks and his colleagues streamlined the
techniques of Friedberg and Muchnik to produce a bewildering variety of computations of
intermediate degree. Yet all of their constructions remained somewhat artificial.
History. But in 1873 Charles Hermite proved that the relatively non-artificial number
e is transcendental, and in 1882 Ferdinand Lindemann proved that the downright gardenvariety
number pi is transcendental as well.
Analogy. Hasn’t happened yet ⎯ and may never happen. But my guess is that
eventually someone will prove that a natural and familiar computation like CA Rule 30 is a
non-universal computation that has an unsolvable halting problem.
Weinberg’s Zinger
And of course Turing machines and two-state CAs are, for instance, much slower
than a PC. As the physicist Stephen Weinberg remarks, “This is why Dell and Compaq don’t
sell Turing machines or rule 110 cellular automata.” Stephen Weinberg, “Is the Universe a
Computer,” The New York Review of Books, October 24, 2002, pp. 43- 47. This was one of
the many smug and negative reviews which greeted the publication of Wolfram’s A New
Kind of Science. As John Walker remarked about the reviews, “Most of them were An Old
Kind of Envy.” Something I found particularly wrong-headed in Weinberg’s review was his
cavalier remark that we don’t really want to know the outcomes of complex processes like
medium energy particle collisions. But I have to admit Weinberg got off some good zingers,
as when he attributes Wolfram’s universal automatism to excessive time spent in
programming, and compares his world-view to that of a carpenter who looks at the moon and
wonders if it might be made of wood.
Joke About Cosmic Fry’s Electronics
If you do find your way to that Fry’s in the Sky, get me a slow-down ray! (Ignore
this, I’m slap-happy, punch-drunk, on the ropes. I’ve been thinking too hard about this stuff
for way too long.)
Everyone’s Different
It’s no accident that every single person in the world looks different. Even if two
fertilized eggs were to have the same DNA, the biochemical differences between the cells’
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