Hi,
In my 08/20/2015 Peirce-L post titled “Amount and meaning of information as
aspects of the Peircean sign: The Peircean Theory of Information” [10], I
utilized the so-called ur-category [1] to analyze the possible relation
between the constructor theory of information recently proposed by Deutsch
[6] and Peircean semiotics [7].
The ur-category [1] can be viewed as a geometric (or *iconic*)
representation of the ITR [2], which is its *symbolic* representation. The
origin of the concept of ITR may be traced to Peirce's definitions of the
sign, especially Definition #30 in [11]. The purpose of this post is:
(1) to re-affirm the universality of ITR and ur-category (see the figure in
Table 1),
(2) to use these theoretical principles to clarify several ambiguities that
often afflict the discussions on *information* and *communication* and
their relation to *physicochemical interactions, *and
(3) to suggest dividing information into "meaningless" (or Shannon)
information and "meaningful" (or Peircean) information.
(*1*) As evident in the figure in Table 1, the ur-category (and hence ITR)
can be applied to various processes in both natural (see Layers 3, 4, 5, &
6) and human sciences (see Layers 1, 2 and 3), layer 3 covering both
natural and human sciences. It is surprising that the ur-category can be
applied even to Einstein's general relativity theory of motion (see the
legend to Layer 6). Thus, if we can treat each of these disciplines as a
mathematical category, then ITR and the ur-category can be viewed as
“functors” discussed in the category theory [8, 9].
(*2*) The ur-category has three steps or "transformations", labelled f, g
and h. Steps f and g can be associated with physicochemical interactions
and hence with constructor-theoretic information or Shannon information,
the latter being characterized by selection processes. In contrast, Step h
does not involve any direct physicochemical interactions between the source
and the receiver nor between Object and Interpretant. In other words,
Steps f and g represent *interactions* while the combined effects of Steps
of f, g and h constitutes *communication*. Steps f and g are *dyadic* in
that they each implicate a 2-node network, i.e., "two nodes connected by
one arrow", whereas Steps f, g and h are parts of a *triadic* unit that
cannot be reduced to any networks with less than three nodes connected with
three arrows forming the so-called "commutative triangle [8, 9]. To the
extent that Steps f and g involve "selection" process, these steps can be
assigned Shannon information (to be denoted by I_S) whose amount can be
calculated, with some simplifying assumptions, based on the formula, I_S =
log_2 (N/n), where N and n are the numbers of the possible choices
available and the actual selection made, respectively. Please note that
the *meaning* of the message is determined by a combined effect of the
*triad* of Steps, f, g and h.
(*3*) Just as the ur-category provided a useful visual tool to distinguish
between "interactions" and "communications" in (*2*), so I claim that the
ur-category can help us distinguish between *meaningful* and *meaningless
informations *as first broached in [11]. According to the constructor
theory of information (CTI), any desired transformation in physical systems
requires "information" encoded in the constructor causing or 'catalyzing'
the transformation [6]. Thus Steps f and g can be associated with
"information" as defined by CTI. Also, since these steps are often (if not
always) associated with selection, they can be associated with Shannon
information. Steps f and g represent "interactions" and not
"communications" as pointed out in (*2*). Hence it would be logical to
conclude that the information associated with Steps f and g are
"meaningless". This contrasts with the information flow resulting from the
combined effects of Steps f, g, and h, which is "meaningful information" by
definition.
It is my opinion that some of the confusions that plague many discussions
involving "information" may be due to conflating these two types of
information. So, in order to help facilitate coherent and logical
discourses on information and related topics in science and philosophy
(e.g., communication, interaction, entropy, etc.), I recommend that we
recognize two kinds of information --(i) *meaningful* information and (ii)
*meaningless* information -- and further that the former be referred to as
the *Peircean information* (to acknowledge the fundamental role of Peirce's
definition of the sign in defining "meaning") and the latter as the *Shannon
information *(to acknowledge Shannon's information theory that quantifies
the amount of information, specifically excluding its meaning).
*Table 1.* The ITR (Irreducible Triadic Relation) [1, 2] as a Universal
Principle of physics (6, see the figure below) [3], biology (4, 5) [1, 4],
cybernetics (5, 6) [4,5], and semiotics (2) [7].
* f
g *
1: Source ------------> Message ---------- > Receiver
2: (Object) (Representamen)
(Interpretant)
3: {Input} {Constructor}
{Output}
4: <Evolution> <Genotypes> <Phenotypes>
5: |Nucleic acids| |Proteins| |Chemical
Reactions|
6: <|Mass|> <|Spacetime|>
<|Motion|>
|
^
|
|
|__________________________________|
* h*
*Communication *(1) and *semiosis *(2) as instantiations of ITR,
Irreducible triadic relations:
(1)* f* = encoding; *g* = decoding; *h* = grounding/correspondence.
(2) *f* = sign production; *g* = sign interpretation; *h* = correspondence
(3) *f *= Initial state of substrates; *g* = Information-caused transformer
of substrate; *h* = Construction
(4) *f = *phylogenesis; *g* = ontogenesis; *h* = genetic inheritance
(5) *f* = transcription/translation; *g = *enzyme catalysis*; h = *genetic
information flow
(6) *f* =”Matter tells spacetime how to curve”; *g* = “Curved spacetime
tells matter how to move” [3]; *h* = gravitation or action at a distance.
References:
[1] Ji, S. (2014). Ur-category accommodates Peirce’s tychism and
evolutionary cosmology. [biosemiotics:6360] dated 8/5/2014.
[2] Ji, S. (2015). The Irreducible Triadic Relation (ITR) as a
Universal Principle.
http://permalink.gmane.org/gmane.science.philosophy.peirce/16464 [3]
Misner, C. W., Thorne, K. S. and Wheeler, J. A. (1973). Gravitation. W.
H. Freeman and Company, New York.
[4] Ji, S. (2015). The Cell Language Theory: Evolution as Semiosis.
Imperial College Press, London (top appear).
[5] Brier, S. (2011). Cybersemiotics: A New Foundation for
Transdisciplinary Theory of Information, Cognition, Meaning, Communcation
and Consciousness. Sign 5: 75-120.
[6] Deutsch, D. (2012). Constructor Theory.
arXiv.org/ftp/arxiv/1210/1210.7439.pdf downloaded on 1/1/2015.
[7] https://en.wikipedia.org/wiki/Semiotics.
[8] Spivak, D. I. (2013) Category Theory for the Sciences. The MIT
Press, Cambridge, Massachusetts. Open Access HTML Version at
http://category-theory.mitpress.mit.edu/
[9] Brown R, Porter T (2006). Category Theory: an abstract setting for
analogy and comparison. PDF at
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.65.2083&rep=rep1&type=pdf
.\
[10] Ji, S. (2015). Amount and meaning of information as aspects of the
Peircean sign: the Peircean Theory f Information. Available at
http://comments.gmane.org/gmane.science.philosophy.peirce/16999,
[11] Marty, R. (xxxx). 76 Definitions of The Sign by C. S. Peirce.
http://www.iupui.edu/~arisbe/rsources/76DEFS/76defs.HTM.
All the best.
Sung
---
Sungchul Ji, Ph.D.
Associate Professor of Pharmacology and Toxicology
Department of Pharmacology and Toxicology
Ernest Mario School of Pharmacy
Rutgers University
Piscataway, N.J. 08855
732-445-4701
www.conformon.net
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