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

Notes for The Lifebox, the Seashell, and the Soul, by Rudy Rucker
All right!
Other people are the most interesting and beautiful entities you’ll ever see. Honor
them, talk to them, accept them, love them.
I’m sorry I’ve been hung up on this book so long, Sylvia. Let’s play.
This moment is the only moment you have.
I’m turning off the machine and going camping. Good bye!
[ And then I did go to the beach, and thought better of this ending and wrote a new
one on August 28, 2004, with some advice and this closing.]
Here I am preaching platitudes at you. How pompous, how fatuous, how annoying,
how old. I sound like my father.
Well, let’s say the advice is actually aimed at me. I need it. I forget the simplest
things.
And yes, I realize it’s a stretch to say that these slogans follow from my book’s long
class four chain of reasoning. But they’re a nice place to end up.
So now we’re done.
And thanks for riding along. It’s been fun.
[And then I saw this line in a book review of David Mitchell’s Cloud Atlas in the
New York Times: “Self-mockery as self-protection is a very old gambit, certainly but it is
beneath a writer as brilliant a Mitchell.” And I thought, whoah, I don’t want to use selfmockery
if it’s beneath a brilliant writer!]
Caption to Post Problem Illo
If the PCE were true, the region labeled “Universal” could be expanded to include
almost everything except the contents of the “Solvable” region. But this is impossible, as we
know there are very many unsolvable non-universal computations.
Remark on Gerry Sacks
As a historical aside, let me remark that Gerald Sacks is an utterly charming man, and
the only really sharp-dressed mathematician I’ve ever known.
Recursiveness as “Having a Solvable Halting Problem”
We sometimes use the name recursive for a computation that has a solvable decision
problem.
Definition. The computation P is said to be recursive iff it has a solvable halting
problem.
The reasons for the name “recursive” are historical. In the 1930s, logicians such as
Alonzo Church, Kurt Gödel, Jacques Herbrand, and Stephen Kleene ⎯ as well as Allan
Turing ⎯ were investigating various ways to define elementary computations. One class of
such computations was called the general recursive functions. General recursive functions
map integers into integers, but they can have the property of failing to return any output at all
for certain inputs. This is because the general recursive functions are allowed to use
unbounded searches in their definitions ⎯ and sometimes these searches fail. When some
particular input sets off an unsuccessful endless search, that means there’s never going to be
an output.
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