On Sunday 14 October 2007, mjs wrote:
If information is not physical, and therefore governed by physical
principles, then what is its ontological status?
why any scientific notion should have a "physical ontological"
status?
the issue is never ontological, but "just" theoretical: which
theory, with its
own theoretical principles, can handle this or that notion? that
is the
question.
And, within theories of inert, within which physical (theoretical)
principles?
classical, relativistic, quantum?
Information is in signs and languages, it needs an interpreter, or
a compiler
as in operational semantics (in computers).
In some contexts, information may be formalised by the same
equations as
(neg-)entropy. But the coincidence of equations does imply the
formation of
the same invariants, the underlying "objects": the wave equation
applies to
water waves as well as to Quantum Mechanics (Schroedinger, modulo
the passage
to the complex field and Hilbert spaces). In no way a quantum
state yields
the same invariants or intended physical object as a water wave:
formalisms
may have very different (structural, physical....) meanings.
The connection between information and (physical) entropy is not
ontological;
indeed, not even theoretical, just formal: a theory requires both
a formalism
and the formation of invariants (like with Noether's theorems in
Physics:
invariance as symmetries defines the physical objects, by their
properties;
no common invariants between Shannon and Boltzmann)
There is no "purely physical" status of information, since a physical
structure yields no information, per se. Signs must be implemented in
physical ink or digits, of course, but this needs a writer and,
then, an
interpreter. This shows up clearly in the issue of finiteness.
In a finite space-time volume, typically, we can only put a finite
amount of
signs, thus of information.
But is there, per se, a finite amount of information in a finite
space-time
volume? What then about Riemann sphere, as a model of Relativity,
which is
finite, but illimited? how much information does it contain?
Infinite? The
question simply does not make sense, in absence of a specification
of a
writer and an interpreter (or compiler).
And in a finite space-time volume in Quantum Physics? one needs a
wave
equation in a, possibly infinite, dimensional Hibert space, to
talk of one
quanton within it; is this finite or infinite information?
A finite number of quanta may, of course, be represented by
finitely many
independent state vectors, n say, but quantum superposition allow
to obtain
any result, as measure, in R^d, an infinite space.
What is this mystic, absolute, reference to "physical
principles"? we just
have (current) theories.
Classical, relativistic principles or quantum mecanical happen to be
incompatible as entaglement or, more specifically, the quantum
field have no
classical nor relativistic sense, as physical principles.
Which is the "physical" connection between the (wild) DNA and the
(normal)
form of the nose? according to which physical theory can we relate
them?
The differential method, as used in molecular biology, radically
differs form
its use in physics (genes are difference makers: a mutation gives a
pathological nose - this is all what we know); we probably need to
develop a
notion of morphogenetic field, which may differ from the classical
one as
much or more than the quantum field. Based on "differences" and
this may be a
new, purely informational approach, with no meaning in current
physical
theories (science is not over, we still have a lot to do):
probably an issue
of a compiler to be discovered that "interprets" the DNA by and
within the
turbulent frame of the cell and the organized one of an organism.
Giuseppe Longo
http://www.di.ens.fr/users/longo
Laboratoire et Departement d'Informatique
CNRS et Ecole Normale Superieure
et CREA, Ecole Polytechnique
(Postal addr.: LIENS
45, Rue D'Ulm
75005 Paris (France) )
e-mail: [EMAIL PROTECTED]
(tel. ++33-1-4432-3328, FAX -2156, secr. -2059)
NOUVEAU LIVRE :
F. Bailly et G. Longo, Mathématiques et sciences de la nature.
La singularite' physique du vivant. Hermann, Paris, juillet 2006.
(English introduction downloadable: http://www.di.ens.fr/users/
longo )
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