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 

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, 

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, 
Background: physics, Intel, crypto, Cypherpunks

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