Contributed by
Dave Renfro
The Logic Pool deals with an intelligence that is similar
to the mememinds in Gregory Benford's Foundations Fear.
Mememind  I think this means some sort of intelligence whose
existence arises from abstract ideas, like beauty and morality
(but maybe more complex than these). As the ideas evolve and
become modified over time, the underlying mememind achieves
consciousness analogous to ordinary intelligences (biological and
machine) that achieve consciousness when certain matter/energy
things evolve and become modified over time (e.g. consciousness
from a human brain, consciousness from a Pentium 24 chip, etc.).
Anyway, Baxter's lifeform is a treein the mathematical sensethat
is a complex and evolving collection of axiomatic theories. Each chain
in the tree is an axiomatic theory and each branch grows by continuously
adding new axioms obtained by using Godel's technique to obtain
statements that are [undecidable  ak] in the theory generated by
the set of all statements preceding (in the latticeorder sense) the
axiom being added.

Contributed by
Kyle Ankeny
"'The
Logic Pool' definitely focus's on mathematics. As I said, math isn't my
favorite, so some of this was hard to grasp and understand for me. :)
Here's some passages from 'The Logic Pool':
(quoted from The Logic Pool)
"Marsden's data stores contain a fragmented catalogue of
mathematical
variants. All founded on the postulates of arithmetic, but differing in
their resolution of undecidable hypothesis."
"Undecidability. You're talking about the incompleteness theorems,"
"Right. No logical system rich enough to contain the axioms of
simple
arithmetic can ever be made complete. It is always possible to construct
statements that can be neither disproved nor proved by deduction from the
axioms; instead the logical system must be enriched by incorporating the
truth or falsehood of such statements as additional axioms..."
The Continuum Hypothesis was an example.
There were several orders of infinity. There were 'more' real
numbers,
scattered like dust in the interval between zero and one, that there were
integers. Was there an order of infinity between the reals and the
integers. This was undecidable, within logically simpler systems like
set theory; additional assumptions had to be made.
"So one can generate many versions of mathematics, by adding these
truefalse axioms."
"And then searching on, seeking out statements which are
undecidable in
the new system. Yes. Because of incompleteness, there is an infinite
number of such mathematical variants, spreading like the branches of a
tree...."

"Ok, don't get the wrong idea, it is not THAT dry. There is a plot
wrapped around this math. Essentially, they find a dead researcher, and
are trying to figure out how he died, this what he was working on. He
had evidently created sentient creatures that used these axioms and such,
they were like the 'tree'.

This story is just one of several related stories in the book Vacuum
Diagrams.
Contributed by
Kyle Ankeny
I think [Vacuum Diagrams] is an excellent Hard SF book. It spans 5 million
years of human history, through wars with the Xeelee, the fall of
civilization (sort of), and the final victory of Dark Matter life over
Baryonic life. It is an epic book, and the physics in it sometimes make
you just sit back and say 'wow'. It deals with all areas of science,
from biology to mathematics. I highly recommend you try to get this book
(I first read it from the library, and then bought it on EBay for
$1.00!), I believe there was a few copies on EBay, and there may be more
than when I got mine. So maybe the characterization in the book isn't
the greatest, but the book isn't about character development, it's about
epic ideas.

See also Godel's Sunflowers. 