Hi,
(1) To the best of my knowledge, it was Volkenstein [1] who pointed out
that there are three basic aspects of information -- (i) amount (e.g., a
desktop computer can store more information measured in bits than a cell
phone), (ii) meaning (e.g., when a gene is mutated, its sequence loses
biological meaning and the cell cannot express it), and (iii) value (e.g.,
a short gene may encode a protein that is more critical for cell life than
the protein encoded by a long gene).
(2) There is no doubt that a sign can carry information, either meaningful
(e.g., a stop sign) or nonsensical to an observer or a receptor (e.g., a
Korean word to a non-Korean speaking person).
(3) The Peircean signs, when diagrammatically represented as a commutative
triangle (also called the ur-category) is rich enough to accommodate the
concepts of the amount and meaning of information as explained below:
f g
Source -------------> Message ------------> Receiver
(Object) (Representamen) (Interpretant)
|
^
|
|
|_____________________________________|
h
Figure 1. The ur-category representation of the relation between
*information* the *Peircean sig*n.
f = encoding; g = decoding; h = information flow/grounding. The
commutative condition is postulated to hold true, i.e., f
x g = h, or f followed by g leads to the same result as h.
(4) The ur-category used in Figure 1 was introduced and discussed in
detail in the biosemiotics list almost a year ago [2]. The ur-category can
be viewed as a visualization of ITR (irreducible triadic relation) which is
the simplest mathematical category [3, 4].
(5) In the past, as some of you may remember, I confined the concept of
"information" to Step h, but my recent reading of Deutsch's papers [3, 4]
broadened my perspective so that I now feel comfortable to implicate
"information" in all the three steps in the ur-category, i.e., Steps f and
g as well as h. But there may be important difference between the
information being transferred through Steps f and g and that through h --
the former has no "meaning" (e.g., *Shannon information *excludes meaning)
but the latter does (which hence may be called the *Peircean information *or
"meaningful" information). In other words, Shannon information is
"quantitative" but "meaningless" because it is not triadic but *dyadic*,
while Peircean information is "meaningful" because it is genuinely and
irreducibly *triadic*. Steps f and g represent the traditional "causality"
but Step h is suggested to represent what I elected to call "codality", or
information-based causality in contrast to energy-based causality [4a].
(6) If Figure 1 is right, it provides a coherent theoretical framework for
explaining the relations among a diverse set of concepts --- (i)
information, (ii) the Peircean sign, (iii) amount of information, (iv)
meaning of information, and (v) Shannon information (i.e., "meaningless
information in contrast to the Peircean information which is meaningful, by
definition).
(7) The ur-category representation of information shown in Figure 1 also
seems to agree with most of the elements of the so-called "constructor
theory of information (CTI)" recently proposed by Deutsch and Marletto [3,
4]. Before I attempt to connect CTI and what I am here taking the liberty
of referring to as the "Peircean theory of information" (PTI)*, i.e., the
theory of information depicted in Figure 1, let me first briefly review
some of the key elements of CTI:
*I am not unaware that some Peirceans may vehemently oppose my use of
Peirce's name in labeling this information theory because PTI may not be
completely consonant with Peircean semiotics. When and if this turns out
to be the case, I would not hesitant a moment to re-label PTI to something
else, including JTI !
(a) *constructor* = "anything that can cause transformation in physical
systems without undergoing any net change in its ability to do so", or "a
constructor is characterized by the effect it would have if it and its
substrates jointly constituted a closed system."
(1)
.
* constructor*
input state of substrate(s) -------------------------> output state of
substrate(s) (2)
Examples of constructors include the heat engine in thermodynamics and
enzymes in biology.
(b)* construction* = a transformation caused by a constructor, or a
constructor-caused transformation.
(c) *construction* *task *or* task* = "a set of pairs such as (2), each
designating a legitimate input state for the task and associating that with
a legitimate output state for that input"
(d) *possible task* = the task that a constructor can perform without
violating any known laws of nature
*impossible task* = the task that cannot be performed by any constructor
without violating the laws of nature.
(e) *constructor theory* = "the theory of which transformations can or
cannot be caused and why"
(f) *information* = "It is an abstract constructor."
(3)
" . . . it (i.e., CTI; my addition) does not regard information as an *a
priori* mathematical or logical concept, but as something whose nature and
properties are determined by the laws of physics alone." (4)
". . . information is not abstract in the same sense as, say, the set of
all prime numbers, for it only exists when it is physically instantiated.
So the laws governing it . . unlike those governing prime numbers, are
laws of physics."
(5)
" . . .despite being physical, information has a counter-factual character:
an object in a particular state cannot be said to carry information unless
it could have been in a different state." (6)
"In the theory we present here, the status of information in physics is
analogous
to that of (say) energy . . . "
(7)
(8) A quick comparison between CTI and PTI resulted in the "family
resemblances"
summarized in Table 1 below, indicating that CTI and PTI belong to the same
family of
categories called the ur-category [2, 3, 4].
______________________________________________________________
Table 1. An approximate comparison among the terms appearing in
the Constructor Theory of Information (CTI) and the
'Peircean
Theory of Information" (PTI)
______________________________________________________________
Items CTI PTI
______________________________________________________________
1 constructor sign (or
representamen)
______________________________________________________________
2 construction semiosis
______________________________________________________________
3 task communication
(?)
______________________________________________________________
4 information meaningless
information
meaningful
information
______________________________________________________________
If you have any questions, comments, or criticisms, let me know.
All the best.
Sung
References:
[1] Volkenstein, M. V. (2009). Entropy and Information. Birkheuser,
Basel.
[2] Ji, S. (2014). Ur-category accommodates Peirce's tychism and
evolutionary cosmology. [biosemiotics:6360].
[3] Spivak, D. I. (2013) Category Theory for the Sciences. The MIT
Press, Cam-bridge, Massachusetts. Open Access HTML Version at
http://category-theory.mitpress.mit.edu/
[4] 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
.\
[4a] Ji, S. (2012). Molecular theory of the Living Cell: Concepts,
Molecular Mechanisms and Biomedical Applications. Springer, New York. P.
93.
[5] Deutsch, D. (2015). Constructor Theory.
arXiv.org/ftp/arxiv/papers/1210/1210.7439.pdf. Downloaded on 1/1/2015.
[6] Deutsch, D. and Marletto, C. (2014). Constructor Theory of
Information. arxiv.org/ftp/arxiv/papers/1405/1405.5563.pdf
--
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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