Pointers to places in vast spaces

From: Tim May <tcmay.domain.name.hidden>
Date: Wed, 10 Jul 2002 10:23:56 -0700

On Wednesday, July 10, 2002, at 07:24 AM, Stephen Paul King wrote:
>
....
> I can't seem to get the idea out of my head that information can not
> just refer to information itself but merely can encode the "address" of
> where and when it can be found - this is how I think Goedelization
> works.

This is quite correct in many important respects.

Here's an example.

Consider the space of all strings (DNA, RNA) which make up living
things, from bacteria to reptiles to humans, and perhaps to other
organisms, past, present, and future. Even assume that this space
contains strings for beings which are "possible" (would be living if
they were instantiated, made, grown) but which have never existed in the
past and don't exist at present.

I usually draw this on a blackboard or sheet of paper as a
two-dimensional plot, with the x- and y-axes not explicitly labeled. If
it helps, consider the x-axis to be something like body size in cc, the
y-axis to be something like total number of neurons, and so on. Clearly
these axes are just extreme simplifications.

But what one can reasonably see is that in this space there are places
where the single-celled organisms live, "islands" for the reptiles and
birds, islands for the mammals, and some region where homo sapiens is
found.

Now humans have something like 4 billion base pairs in the genome. I
don't recall what the conversion is from ATCG sorts of base pairs to
bytes, but it's within a small factor, so something like 4 GB or 32
Gbits represents the human genome. Fits on a handful of CD-ROMs,
uncompressed.

But this is not the full story. This 32 Gbit sequence is effectively a
_pointer_ into a space of 2^ (32 Gbits) points, the space of all strings
of the same length as the human genome. (And the space of all living
things is even larger, as it includes all strings of our length, plus
all orderings of shorter strings. If we include beings with even longer
strings, it gets much bigger, of course.)

Where living things in this space can be found depends on many other
things, including the environment around the living thing (e.g., a
lizard in a desert which only eats wheat or rice cannot live, and did
not ever evolve).

In Bennett-type terms, the strings of living things have great logical
depth. They evolved, changed, got more "complex" (in the logical depth
sense) as the phenotypes competed, lived, reproduced, etc.

In a sense, the genome is a _pointer_ to a particular address in that
vast space of all possible living things. (Just as the library call
number of "War and Peace" is much shorter than the actual text of "War
and Peace.")

(Completely aside: We even have some ideas about the topology and
geometry of "life space": we know something about what "nearness" means,
through single-point mutations and their effects of organism viability,
and we are learning what rearrangements and insertions of string
sequences may mean.)

--Tim May
(.sig for Everything list background)
Corralitos, CA. Born in 1951. Retired from Intel in 1986.
Current main interest: category and topos theory, math, quantum reality,
cosmology.
Background: physics, Intel, crypto, Cypherpunks
Received on Wed Jul 10 2002 - 10:28:59 PDT