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<big>(Following some requests, I include herewith the points of Section
4, the theoretical core. <br>
For recent subscribers--some pirates on board!-- the responses should
directly go to: <a class="moz-txt-link-abbreviated" href="mailto:fis@listas.unizar.es">fis@listas.unizar.es</a> <br>
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... <br>
best---Pedro)<b><br>
-------------------------------------------------------------------------------------------------------<br>
<u><br>
Steps to a theory of reference & significance in information</u><br>
</b>FIS discussion paper by Terrence W. Deacon (2015)<b><br>
<br>
[Section 4] Steps to a formalization of reference:</b> <br>
<br>
A. General case: passive information medium near equilibrium [ e.g.
geological formation, crime<br>
scene evidence, data from a scientific experiment, text, etc.] <br>
<br>
1. Information (e.g. Shannon) entropy is NOT equivalent to
thermodynamic (e.g. Boltzmann-<br>
Gibbs) entropy (or to the absolute statistical diversity of physical
states). [For convenience<br>
these entropies will be provisionally distinguished as Shannon versus
Boltzmann entropy,<br>
though recognizing that each includes multiple variant forms.]<br>
<br>
2. However, for any physical signal medium, a change in Shannon entropy
must also<br>
correspond to a change in Boltzmann entropy, though not vice versa
because the distinctions<br>
selected/discerned to constitute the Shannon entropy of a given signal
medium are typically a<br>
small subset of the possible physical variety of states—e.g.
statistical entropy—of that<br>
medium. (See notes below.).<br>
<br>
3a. The Shannon information of a received message is measured as a
reduction of signal<br>
uncertainty (= a reduction of Shannon entropy).<br>
3b. For a simple physical medium reduction of Shannon entropy must also
correspond to a<br>
reduction of the Boltzmann entropy of that medium.<br>
3c. This can be generalized as “any deviation away from a more probable
state” (which can<br>
violate 3b in the case of media that are actively maintained in an
improbable state, such as<br>
maintained far-from-equilibrium. See B below.).<br>
<br>
4a. A reduction of Boltzmann entropy of any physical medium is
exhibited as constraint on its<br>
possible states or dynamical “trajectories.”<br>
4b. The production of physical constraint requires physical work in
order to produce a decrease<br>
of Boltzmann entropy, according to the 2nd law of thermodynamics.<br>
<br>
5a. For a passive medium the physical work required to reduce its
Boltzmann entropy must<br>
originate from some physical source extrinsic to that medium.<br>
5b. Generalization: Constraint of the Shannon entropy of a passive
medium = constraint of its<br>
Boltzmann entropy = the imposition of prior work from an external
source.<br>
<br>
6. An increase in constraint (i.e. deviation away from a more probable
state) in the information<br>
medium literally “re-presents” the physical relationship between the
medium and the<br>
extrinsic contextual factors (work) that caused this change in entropy.
(= what the information embodied <br>
in the constraint can be “about.”)<br>
<br>
7. Since a given constraint has statistical structure, its form is a
consequence of the specific<br>
structure of the work that produced it, the physical susceptibilities
of the information bearing<br>
medium, and the possible/probable physical interactions between that
medium and this<br>
extrinsic contextual factor.<br>
<br>
8. The form of this medium constraint therefore corresponds to and can
indirectly “re-present”<br>
the form of this work. (i.e. in-form-ation)<br>
<br>
9. Conclusion 1. The possibility of reference in a passive medium is a
direct reflection of the<br>
possibility of a change in the Boltzmann and Shannon entropies of that
medium due to a<br>
physical interaction between the information bearing medium and a
condition extrinsic to it.<br>
<br>
10. Conclusion 2. The possible range of contents thereby referred to is
conveyed by the form of<br>
the constraint produced in the medium by virtue of the form of work
imposed from an<br>
extrinsic physical interaction.<br>
<br>
11. Conclusion 3. The informing power of a given medium is a direct
correlate of its capacity to<br>
exhibit the effects of physical work with respect to some extrinsic
factor.<br>
<br>
12. Corollary 1. What might be described as the referential entropy of
a given medium is a<br>
function of the possible independent dimensions of kinds of
extrinsically induced physical<br>
modifications it can undergo (e.g. physical deformation,
electromagnetic modification, etc.)<br>
multiplied by the possible “distinguishable” (see notes) states within
each of these<br>
dimensions.<br>
<br>
13. Corollary 2. Having the potential to exhibit the effects of work
with respect to some extrinsic<br>
physical factor means that even no change in medium entropy or being in
a most probable<br>
state still can provide reference (e.g. the burglar alarm that has not
been tripped, or the failure<br>
of an experimental intervention to make a difference). It is thus
reference to the fact that no<br>
work to change the signal medium has occurred.<br>
In addition, since not all information media are physical structures or
otherwise passive systems<br>
at or near thermodynamic equilibrium we need to modify certain of these
claims to extend this<br>
analysis to media that are themselves dynamical systems maintained
far-from-equilibrium. This<br>
yields the following additional claims:<br>
<br>
B. Special case: non-passive information medium maintained far from
equilibrium [e.g. metal<br>
detector or organism sense organ] <br>
<br>
1. A persistently far-from-equilibrium process is one that is
maintained in a lowered probability<br>
state. So certain of the above principles will be reversed in these
conditions. Specifically,<br>
those that depend on extrinsic work moving a medium to a lower
probability, lower entropy<br>
state.<br>
<br>
2. Maintenance of a low Boltzmann entropy dynamical process necessarily
requires persistent<br>
physical work or persistent constraints preventing an increase of
Boltzmann and Shannon<br>
entropies.<br>
<br>
3. Any corresponding increase in Shannon entropy therefore corresponds
to a disruption of the<br>
work that is maintaining the medium in its lower entropy state. This
can occur by impeding<br>
the intrinsic work or disrupting some dissipation-inhibiting constraint
being maintained in<br>
that system.<br>
<br>
4a. An increase in the Shannon entropy of a persistently
far-from-equilibrium information<br>
medium can thereby "indicate" extrinsic interference with that work or
constraint<br>
maintenance.<br>
4b. A persistently far-from-equilibrium dynamical medium can be
perturbed in a way that<br>
increases its entropy by contact with a passive extrinsic factor. Any
passive or dynamic<br>
influence that produces a loss of constraint in such a system can
provide reference to that<br>
extrinsic factor.<br>
<br>
5a. Since work requires specific constraints and specific energetic and
material resources, these<br>
become dimensions with respect to which the change in entropy can refer
to some external<br>
factor.<br>
5b. The dynamical and physical properties of a far-from-equilibrium
information bearing<br>
medium determine its “referential entropy.”<br>
<br>
6. Corollary 3. This can be generalized to also describe the
referential capacity of any medium<br>
normally subject to regular teleodynamic or teleological influences
that tend to cause it to be<br>
in an improbable or highly constrained state. This therefore is
applicable to living systems<br>
with respect to their adaptations to avoid degradation and also to far
more complex social and<br>
cultural contexts where there is active “work” to maintain certain
“preferred” orders. <br>
<br>
----------------------------------------------------------------------------------------------------<br>
</big><br>
<pre class="moz-signature" cols="72">--
-------------------------------------------------
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)
<a class="moz-txt-link-abbreviated" href="mailto:pcmarijuan.iacs@aragon.es">pcmarijuan.iacs@aragon.es</a>
<a class="moz-txt-link-freetext" href="http://sites.google.com/site/pedrocmarijuan/">http://sites.google.com/site/pedrocmarijuan/</a>
-------------------------------------------------
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