[Fis] The unification of the theories of information based on the cateogry theory

[Sungchul Ji]

Hi  FISers,


On 10/8/2017, Terry wrote:


" So basically, I am advocating an effort to broaden our discussions and recognize that the term information applies in diverse ways to many different contexts. And because of this it is important to indicate the framing, whether physical, formal, biological, phenomenological, linguistic, etc.

. . . . . . The classic syntax-semantics-pragmatics distinction introduced by Charles Morris has often been cited in this respect, though it too is in my opinion too limited to the linguistic paradigm, and may be misleading when applied more broadly. I have suggested a parallel, less linguistic (and nested in Stan's subsumption sense) way of making the division: i.e. into intrinsic, referential, and normative analyses/properties of information."

I agree with Terry's concern about the often overused linguistic metaphor in defining "information".  Although the linguistic metaphor has its limitations (as all metaphors do), it nevertheless offers a unique advantage as well, for example, its well-established categories of functions (see the last column in Table 1.)

The main purpose of this post is to suggest that all the varied theories of information discussed on this list may be viewed as belonging to the same category of ITR (Irreducible Triadic Relation) diagrammatically represented as the 3-node closed network in the first column of Table 1.

Table 1.  The postulated universality of ITR (Irreducible Triadic Relation) as manifested in information theory, semiotics, cell language theory, and linguistics.

Category Theory

   f            g
   A -----> B ------> C
    |                           ^
    |                            |
    |______________|
   h

ITR (Irreducible Triadic Relation)

Deacon’s theory of information

Shannon’s
Theory of
information

Peirce’s theory of signs

Cell language theory

Human language
(Function)

A

Intrinsic information

Source

Object

Nucleotides*/
Amion acids

Letters
(Building blocks)

B

Referential information

Message

Sign

Proteins

Words
(Denotation)

C

Normative information

Receiver

Interpretant

Metabolomes
(Totality of cell metabolism)

Systems of words
(Decision making & Reasoning)

f

?

Encoding

Sign production

Physical laws

Second articulation

g

?

Decoding

Sign interpretation

Evoutionary selection

First and Third articulation

h

?

Information flow

Information flow

Inheritance

Grounding/
Habit

Scale   Micro-Macro?    Macro   Macro   Micro   Macro


*There may be more than one genetic alphabet of 4 nucleotides.  According to the "multiple genetic alphabet hypothesis', there are n genetic alphabets, each consisting of 4^n letters, each of which in turn consisting of n nucleotides.  In this view, the classical genetic alphabet is just one example of the n alphabets, i.e., the one with n = 1.  When n = 3, for example, we have the so-called 3rd-order genetic alphabet with 4^3 = 64 letters each consisting of 3 nucleotides, resulting in the familiar codon table.  Thus, the 64 genetic codons are not words as widely thought (including myself until recently) but letters!  It then follows that proteins are words and  metabolic pathways are sentences.  Finally, the transient network of metbolic pathways (referred to as "hyperstructures" by V. Norris in 1999 and as "hypermetabolic pathways" by me more recently) correspond to texts essential to represent arguement/reasoning/computing.  What is most exciting is the recent discovery in my lab at Rutgers that the so-called "Planck-Shannon plots" of mRNA levels in living cells can identify function-dependent "hypermetabolic pathways" underlying breast cancer before and after drug treatment (manuscript under review).

Any comments, questions, or suggestions would be welcome.

Sung

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