`(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)*`

------------------------------------------------------------------------------------------------------- _ 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.`

---------------------------------------------------------------------------------------------------- -- ------------------------------------------------- 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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