I believe this question may have first bee inspired by a series of essays in
The Edge, from last month. Physicist Free Dyson wondered whether life had to
be digital or analog? One of the respondents was cosmologist Lee Smolin, who
said:
"Thus, even a moderately complicated graph may be knotted in a way that no
digital computer could classify in a physically relevant amount of time. So
it is certainly the case that the information contained in such topological
problems is not digital for all practical purposes."
Smolin appears to be endorsing the analog computer definition of life, or he
may be suggesting something that is neither digital, nor analog.
"Two other results of quantum gravity, the Bekenstein bound and the
holographic principle, require that only finite dimensional state spaces are
required to code the quantum information that can be extracted from any
region of the world with a finite area boundary. So it seems likely that
continuous variables play no role in nature, but at the same time, this does
not mean nature is digital in the ordinary sense. The problem is that these
finite dimensional state spaces have bases which are distinguished by solving
the problem of classifying embeddings of graphs. So while the holographic
principle says that no observer in the universe can access more than a finite
amount of information, that information may be stored in a way that cannot be
represented digitally by any computer that could be built inside the
universe."
So the physics behind a purely digital computer are self-limiting (if I
understand this) in Smolin's view. Smolin goes on to state a 'combinatoric'
type of process, which I suppose holds analog above the merely digital. Yet
this analog, as far as life goes seems impossible without cellular topology.
Sounds a bit like Penrose and Hameroff's digital function in the human
brain-except that its more, analog. Hmmm.
"The difference between combinatorial and digital coding of information is
that when information is coded digitally all the possible states of the
memory are equally accessible. When information is coded combinatorially, say
in the knotting of some graphs, this is not the case, the time required to
store or retrieve information depends very strongly on the state in which the
information is coded. But a cell is not a general purpose computer, and there
is no need that all possible configurations of the molecules where
information is stored be equally accessible. What is required is only access
to those states that are relevant for the functioning of the cell, and then
only at the time they are needed. (Similarly the protein folding problem does
not have to have a solution for arbitrary amino acid sequences, only for the
much smaller subset that are relevant biologically.) So I do wonder whether
the digital metaphor may be blinding us to ways in which information could be
stored in biological systems using the combinatorics and topology of
molecules."
Smolin uses this combinatoric concept to address Dyson's on life and the
future of the universe (Infinite In All Directions -1979).
"This seems relevant for Freeman's worry, for if information can be stored in
the topology of a system, then the system can be cooled or expanded
arbitrarily without degrading the information. At the very least, if the
universe has non-trivial topology, on either the large or small scale, there
are possibilities for storage of combinatorial information where the
discreteness of the states are maintained for arbitrarily low energies. At
worst life will be able to survive by coding itself into the quantum geometry
of space itself. " <--My underlining. For additional opinions on Dyson's
digital v. analog and life:
http://www.edge.org/documents/archive/edge82.html
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