(Following some requests, I include herewith the points of Section 4,
the theoretical core.
For recent subscribers--some pirates on board!-- the responses should
directly go to: fis@listas.unizar.es
Also, remember please that only two messages per week are allowed,
except the discussion chair, Terry, and my own maintenance work. For
instance, as a regular discussant I have only one shot left to respond
to Terry and Jeremy...
best---Pedro)*
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_
Steps to a theory of reference & significance in information_
*FIS discussion paper by Terrence W. Deacon (2015)*
[Section 4] Steps to a formalization of reference:*
A. General case: passive information medium near equilibrium [ e.g.
geological formation, crime
scene evidence, data from a scientific experiment, text, etc.]
1. Information (e.g. Shannon) entropy is NOT equivalent to thermodynamic
(e.g. Boltzmann-
Gibbs) entropy (or to the absolute statistical diversity of physical
states). [For convenience
these entropies will be provisionally distinguished as Shannon versus
Boltzmann entropy,
though recognizing that each includes multiple variant forms.]
2. However, for any physical signal medium, a change in Shannon entropy
must also
correspond to a change in Boltzmann entropy, though not vice versa
because the distinctions
selected/discerned to constitute the Shannon entropy of a given signal
medium are typically a
small subset of the possible physical variety of states---e.g.
statistical entropy---of that
medium. (See notes below.).
3a. The Shannon information of a received message is measured as a
reduction of signal
uncertainty (= a reduction of Shannon entropy).
3b. For a simple physical medium reduction of Shannon entropy must also
correspond to a
reduction of the Boltzmann entropy of that medium.
3c. This can be generalized as "any deviation away from a more probable
state" (which can
violate 3b in the case of media that are actively maintained in an
improbable state, such as
maintained far-from-equilibrium. See B below.).
4a. A reduction of Boltzmann entropy of any physical medium is exhibited
as constraint on its
possible states or dynamical "trajectories."
4b. The production of physical constraint requires physical work in
order to produce a decrease
of Boltzmann entropy, according to the 2nd law of thermodynamics.
5a. For a passive medium the physical work required to reduce its
Boltzmann entropy must
originate from some physical source extrinsic to that medium.
5b. Generalization: Constraint of the Shannon entropy of a passive
medium = constraint of its
Boltzmann entropy = the imposition of prior work from an external source.
6. An increase in constraint (i.e. deviation away from a more probable
state) in the information
medium literally "re-presents" the physical relationship between the
medium and the
extrinsic contextual factors (work) that caused this change in entropy.
(= what the information embodied
in the constraint can be "about.")
7. Since a given constraint has statistical structure, its form is a
consequence of the specific
structure of the work that produced it, the physical susceptibilities of
the information bearing
medium, and the possible/probable physical interactions between that
medium and this
extrinsic contextual factor.
8. The form of this medium constraint therefore corresponds to and can
indirectly "re-present"
the form of this work. (i.e. in-form-ation)
9. Conclusion 1. The possibility of reference in a passive medium is a
direct reflection of the
possibility of a change in the Boltzmann and Shannon entropies of that
medium due to a
physical interaction between the information bearing medium and a
condition extrinsic to it.
10. Conclusion 2. The possible range of contents thereby referred to is
conveyed by the form of
the constraint produced in the medium by virtue of the form of work
imposed from an
extrinsic physical interaction.
11. Conclusion 3. The informing power of a given medium is a direct
correlate of its capacity to
exhibit the effects of physical work with respect to some extrinsic factor.
12. Corollary 1. What might be described as the referential entropy of a
given medium is a
function of the possible independent dimensions of kinds of
extrinsically induced physical
modifications it can undergo (e.g. physical deformation, electromagnetic
modification, etc.)
multiplied by the possible "distinguishable" (see notes) states within
each of these
dimensions.
13. Corollary 2. Having the potential to exhibit the effects of work
with respect to some extrinsic
physical factor means that even no change in medium entropy or being in
a most probable
state still can provide reference (e.g. the burglar alarm that has not
been tripped, or the failure
of an experimental intervention to make a difference). It is thus
reference to the fact that no
work to change the signal medium has occurred.
In addition, since not all information media are physical structures or
otherwise passive systems
at or near thermodynamic equilibrium we need to modify certain of these
claims to extend this
analysis to media that are themselves dynamical systems maintained
far-from-equilibrium. This
yields the following additional claims:
B. Special case: non-passive information medium maintained far from
equilibrium [e.g. metal
detector or organism sense organ]
1. A persistently far-from-equilibrium process is one that is maintained
in a lowered probability
state. So certain of the above principles will be reversed in these
conditions. Specifically,
those that depend on extrinsic work moving a medium to a lower
probability, lower entropy
state.
2. Maintenance of a low Boltzmann entropy dynamical process necessarily
requires persistent
physical work or persistent constraints preventing an increase of
Boltzmann and Shannon
entropies.
3. Any corresponding increase in Shannon entropy therefore corresponds
to a disruption of the
work that is maintaining the medium in its lower entropy state. This can
occur by impeding
the intrinsic work or disrupting some dissipation-inhibiting constraint
being maintained in
that system.
4a. An increase in the Shannon entropy of a persistently
far-from-equilibrium information
medium can thereby "indicate" extrinsic interference with that work or
constraint
maintenance.
4b. A persistently far-from-equilibrium dynamical medium can be
perturbed in a way that
increases its entropy by contact with a passive extrinsic factor. Any
passive or dynamic
influence that produces a loss of constraint in such a system can
provide reference to that
extrinsic factor.
5a. Since work requires specific constraints and specific energetic and
material resources, these
become dimensions with respect to which the change in entropy can refer
to some external
factor.
5b. The dynamical and physical properties of a far-from-equilibrium
information bearing
medium determine its "referential entropy."
6. Corollary 3. This can be generalized to also describe the referential
capacity of any medium
normally subject to regular teleodynamic or teleological influences that
tend to cause it to be
in an improbable or highly constrained state. This therefore is
applicable to living systems
with respect to their adaptations to avoid degradation and also to far
more complex social and
cultural contexts where there is active "work" to maintain certain
"preferred" orders.
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--
-------------------------------------------------
Pedro C. Marijuán
Grupo de Bioinformación / Bioinformation Group
Instituto Aragonés de Ciencias de la Salud
Centro de Investigación Biomédica de Aragón (CIBA)
Avda. San Juan Bosco, 13, planta X
50009 Zaragoza, Spain
Tfno. +34 976 71 3526 (& 6818)
pcmarijuan.i...@aragon.es
http://sites.google.com/site/pedrocmarijuan/
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