[Fis] How Molecules Became Signs. One Way Out

Sun Mar 13 13:03:28 CET 2022

Yes, Joseph, I agree! The alteration of the sign indicates whether 
information (entropy) or redundancy is generated.

Leydesdorff, L., Petersen, A. M., & Ivanova, I. (2017). 
Self-organization of meaning and the reflexive communication of 
information. Social Science Information, 56(1), 4-27. doi: 
10.1177/0539018416675074 .
We formulated on pp.  , as follows: I owe this to my coauthors:

Redundancy in three and four dimensions

For the three-dimensional case and using Figure 6, one can define, in 
addition to the two-dimensional values of Υ (in Eq. 3), a 
three-dimensional value including the redundancies (in the respective 
overlaps) as follows:

                                                  (5)

Figure 6: Overlapping uncertainties in three variables x1, x2, and x3:

two configurations with opposite sign of T123.

Using information theory, however, one would make the following 
corrections for double counting in the overlaps (by subtracting; see 
Figure 6):

                                             (6)

It follows that the difference between the uncertainty in the historical 
system (H123 in Eq. 6) and the system of expectations ( in Eq. 5) is:

                                                                  (7)

Furthermore, the mutual information in three dimensions can be derived 
in information theory using the Shannon formulas (e.g., Abramson, 1963, 
at p. 129; McGill, 1954; Yeung, 2008) as:

                                           (8)

Using Υ-values instead of H-values for the joint entropies in Eq. 8, one 
obtains the mutual redundancy in three dimensions as follows:

                              (9)

In the three-dimensional case, the mutual redundancy is thus equal to 
the mutual information in three dimensions. Furthermore, Leydesdorff & 
Ivanova (2014, at p. 392) show that in the case of four dimensions R1234 
= – T1234. The sign of the mutual redundancy alternates with the number 
of dimensions. This corrects for the otherwise inexplicable sign changes 
in the mutual information with increasing dimensionality. This sign 
change of the mutual information with dimensions is a well-known problem 
in information theory, but beyond the scope of the present study.[1] 
<#_ftn1> In other words, mutual redundancy is a consistent measure of 
negative entropy, while mutual information

is not, because of its sign changes with the dimensionality. We prove 
this claim in the next section by generalizing the formulation.

--------------------------------------------------------------------------------
[1] <#_ftnref1>Krippendorff (2009b, at p. 670) provided a general 
notation for this alteration with changing dimensionality—but with the 
opposite sign (which further complicate the issue; cf. Leydesdorff, 
2010: 68)—as follows:

                          (9)

In this equation, Γ is the set of variables of which X is a subset, and 
H(X) is the uncertainty of the distribution; |Γ| is the cardinality of 
Γ, and |X| the cardinality of X.Generalization

Eq. 8 can be rewritten as follows:

T123 = H1 + H2 + H3 - H12 - H13 - H23 + H123(8)
T123 = [(H1 + H2 - H12) + (H1 + H3 - H13) + (H2 + H3H23)] + [H123 - H1 - 
H2 - H3]
T123 = [T12 + T13 + T23] + [H123 - H1 - H2 - H3](10)

The second bracket in Eq. 10 makes a negative contribution, because of 
the subadditivity of the entropy: , which holds for any dimension n≥ 2. 
The terms in the first bracket of Eq. 10 are strictly positive. As 
noted, the sign of the resulting value of T123 depends on the empirical 
configuration (as indicated by the two configurations in Figure 6).

It follows (inductively) that for any given dimension n, one can 
formulate combinations of mutual informations corresponding to that are 
by definition positive (or zero in the null case of complete 
independence). For example (up to four dimensions) as follows:

(11)

where the sums on the right-hand side are over the permutations of the 
indices. This relation can be extended for general n as,

(12)

where the last term on the right-hand side is equal to . Returning to 
the relation between and , it now follows instructively that:

(13)

and the analogous relations for and follow in the same way from Eq. 
(12). More generally, in the case of more than two dimension, n > 2:

(14)

The left-bracketed term of Eq. 14 is necessarily negative entropy 
(because of the subadditivity of the entropy), while the configuration 
of the remaining mutual information relations contribute a second term 
on the right which is positive (see the set of Equations 11 above). In 
other words, we model here the generation of redundancy on the one side 
versus the historical process of uncertainty generation in relating on 
the other, as an empirical balance in a system that operates with more 
than two codes (e.g., alphabets; Abramson, 1963, pp. 127 ff.). When the 
resulting R is negative, self-organization prevails over organization in 
the configuration under study, whereas a positive R indicates conversely 
a predominance of organization over self-organization as two different 
subdynamics.

_______________

<https://www.springer.com/gp/book/9783030599508>Loet Leydesdorff

"The Evolutionary Dynamics of Discusive Knowledge" 
<https://link.springer.com/book/10.1007/978-3-030-59951-5>(Open Access)

Professor emeritus, University of Amsterdam

Amsterdam School of Communication Research (ASCoR)

loet en leydesdorff.net <mailto:loet en leydesdorff.net>; 
http://www.leydesdorff.net/

http://scholar.google.com/citations?user=ych9gNYAAAAJ&hl=en

ORCID: http://orcid.org/0000-0002-7835-3098;

------ Original Message ------
From: "joe.brenner en bluewin.ch" <joe.brenner en bluewin.ch>
To: christophe.menant en hotmail.fr
Cc: fis en listas.unizar.es; deacon en berkeley.edu
Sent: 3/13/2022 11:51:55 AM
Subject: Re: [Fis] How Molecules Became Signs. One Way Out

>Dear Friends and Colleagues,
>
>There is one way out of the dilemma which has not been directly 
>refuted. When Christophe and others ask if can we talk of information 
>in an a-biotic or pre-biotic world, if information means something 
>actual, present, the answer is no. If one asks instead did the 
>potential for  information as meaning exist, the answer for me is yes.
>
>An additional statement must be added, otherwise the above is no more 
>than a trivial tautology. It is that information is defined in the 
>process of its emergence from some energetic ground. Since no process, 
>nothing in process is complete, complete and incomplete parts of the 
>process are present simultaneously and dynamically. The locus of this 
>"nascent" information is the detailed physico-chemical structure of the 
>living entities involved and their non-living constituents. These or 
>parts of them move from actual to potential and vice versa and this 
>movement is what ultimately defines their meaning.
>
>One reading of the above is that I have given a new interpretation of 
>the nature of a sign. I would gladly accept this, provided it can be 
>subsequently decided whether or not the concept of sign adds further 
>information. It may not.
>
>Thank you and best wishes,
>Joseph
>
>
>
>>----Message d'origine----
>>De : christophe.menant en hotmail.fr
>>Date : 13/03/2022 - 00:02 (CEST)
>>À : deacon en berkeley.edu, fis en listas.unizar.es
>>Objet : [Fis] How Molecules Became Signs
>>
>>Dear Friends,
>>that war is a horrible drama for innocent civilians. And I agree with 
>>your comments.
>>Our FIS discussions cannot bring much help to that human drama, but 
>>our tentative analysis of what is “information” may somehow lead to a 
>>better understanding of human motivations guide behaviors.
>>Let me add another comment to Terry’s work.
>>
>>Dear Terry,
>>In addition to my Feb 23 post I would appreciate some information on 
>>parts of your paper I may not have understood that well.
>>Regarding the concept of information, you consider that information in 
>>a pragmatic-functional sense can be understood in terms of molecular 
>>evolution.
>>This brings to consider that “information” is present in an a-biotic 
>>or pre-biotic world (a purely molecular world). Such pre-biotic world 
>>has existed before the emergence of life in our universe. But can we 
>>talk of information and meaning, of signs, in such a world? How should 
>>they be understood in a purely material world devoid of living 
>>entities?
>>As said,  it would be nice if you could clarify these points by making 
>>available definitions for information, meaning and sign in such an 
>>a-biotic world. This would allow a better understanding of your 
>>starting point.
>>Also, I do not see that well using the Peircean term of “Interpretant” 
>>for an inert world. We know that the Interpretant (the meaning) needs 
>>an Interpreter (the meaning generator). So introducing Interpretants 
>>in your paper also brings to introduce Interpreters in an inert world. 
>>Your sentence “In Peircean terms, this amounts to asking what sort of 
>>molecular system is competent to produce the Interpretants” is 
>>equivalent to: “what sort of molecular system is competent to generate 
>>meanings”. I’m not sure that meaning generation by a molecular system 
>>in a purely material and inert world can be clearly understood by 
>>today science or philosophy. And I do not remember Peirce theory of 
>>sign being about inert matter. Could you tel us more about your 
>>position on these subject?
>>Thanks again for your time
>>Christophe
>>
>
>
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