Clark, lists,
Clark wrote today: "Someone just introduced me to Constructor Theory.
. . . Upon
reading it, the theory sounds very Peircean. I was curious if anyone here
has done any reading along those lines."
Sung: Yes. I have done a quick study of the Constructor Theory of
Information (CTI) early this year and came to the conclusion that CTI is an
instance of the Peircean semiosis (and hence an example of the mathematical
category; see Figure 1 below).
As some of you on these lists may recall, I introduced the concept of the
ur-category (see the biosemiotics post dated August 5, 2014 entitled
"Ur-category
accommodates Peirce’s tychism and evolutionary cosmology"), defined as the
category to which all other categories belong, representing it
diagrammatically as:
f g
A ------> B ------> C
| ^
| |
|_______________|
h
Figure A. The ur-category. A, B and C = objects; f , g, and h =
structure-preserving mappings that are related to one another through the
commutative condition, f x g = h, i.e., f followed by g leads tot he same
results as h.
The ur-category is related to ITR (irreversible triadic relation) first
articulated by Peirce (I believe) which may have led to the category theory
in mathematics. If my interpretation of CTI is right, what is called the
"universal construction" may turn out to be a mathematical category, as
depicted in Figure 1 below.
If you have any questions or comments, let me know.
All the best.
Sung
---------- Forwarded message ----------
From: Sungchul Ji <s...@rci.rutgers.edu>
Date: Sun, Jan 4, 2015 at 9:52 PM
Subject: ENERGY, INFORMATION, and the Principle of COMPLEMENTARITY
To: biosemiotics <biosemiot...@lists.ut.ee>
Cc: PEIRCE-L <peirce-l@list.iupui.edu>
(Undistorted diagrams are attached.)
The conclusion of this post given in Figure 1 at the end of the post may be
of some interest to the semiotics community, since it suggests that the
Universal computation described by Deutsch may be an instance of Peircean
semiosis. In other words, Deutsch's theory of information and Peircean
theory of sign or semiosis may be related, since both can be viewed as
mathematical categories represented as a commutative triangle.
The unabridged title of this email would read:
“Energy and Information may be the functors connected by the
(010515-1)
Principle of Complementarity acting as a natural transformation.”
The purpose of this post is to summarize the new theory of information
recently proposed by Deutsch [1] and Deutsch and Marletto [2] (to the
extent that I understand it, having just run into their papers only a few
days ago) and point out how their so-called “Constructor Theory of
Information (CTI)” may be consistent with (and hence supports) the validity
of Statement (010515-1).
(1) Although Deutsch never mentions the category theory in [1] and [2],
I think his ideas
(indicated in the parentheses in Table 1 below) fit nicely into the
three-level organization of the category theory discussed in [3]:
Table 1. The category theory of natural sciences [3].
Category Classes/Levels
*Nodes*
*Arrows*
*I*
OBJECTS
(electrons, protons, photons, molecules, cells, . . .)
MORPHISMS
(laws of physics, chemistry, biology, . . . )
*II*
CATEGORIES
(physics, chemistry, biology, . . . )
FUNCTORS
(energy*, information)
*II*
FUNCTORS
(energy, information)
NATURAL TRASNFORMATION
(Principle of Complementarity)
*includes matter
In [1, p.4], Deutsch and Marletto wrote:
“. . . In the theory (i.e., CTI; my addition) we present here, the status
(010515-2)
of information in physics is analogous to that of (say) energy . . . . “
I interpret (010515-2) as the indication that Deutsch and Marletto [1]
regard information and energy as being equally and independently
fundamental in physics, which idea I express in terms of their being
“complementary” to each other in the last row and column in Table 1, which
logically leads to the conclusion that the Principle of Complementarity [4]
is a natural transformation as defined in the category theory.
(2) The following two quotes explain what ”constructor theory” is:
(A) WHAT IS CONSTRUCTOR THEORY? (http://constructortheory.org/)
“The basic principle of constructor theory is that all fundamental laws of
nature are expressible entirely in terms of statements of which tasks (i.e.
classes of physical transformations) are possible and which are impossible,
and why. This is a new mode of explanation, intended to supersede the
prevailing conception of fundamental physics which seeks to explain the
world in terms of its state (describing everything that is there) and laws
of motion (describing how the everything changes with time). By
regarding counter-factuals ('X is possible' or 'X is impossible') as
first-class, exact statements, constructor theory brings all sorts of
interesting fields, currently regarded as inherently approximative,
potentially into fundamental physics. These include the theories of
information, knowledge, thermodynamics, life, and of course the universal
constructor.”
(B) From: http://en.wikipedia.org/wiki/Constructor_theory
“Constructor theory expresses physical laws in terms of the physical
transformations or
changes which the laws make possible. By allowing the existence of
counterfactuals <http://en.wikipedia.org/wiki/Counterfactual>, statements
about transformations which may prove false, it is also able to describe
information in terms of known physical laws.
The foundational element in the theory is the *constructor*, an entity
which can cause some change while retaining the ability to cause it again.
Examples of constructors include a heat engine (a thermodynamic
constructor), a catalyst (a chemical constructor) or a computer program
controlling an automated factory (an information constructor).
The theory was developed by physicists David Deutsch
<http://en.wikipedia.org/wiki/David_Deutsch> and Chiara Marletto
<http://en.wikipedia.org/w/index.php?title=Chiara_Marletto&action=edit&redlink=1>.
It draws together ideas from diverse areas including thermodynamics
<http://en.wikipedia.org/wiki/Thermodynamics>, statistical mechanics
<http://en.wikipedia.org/wiki/Statistical_mechanics>, information theory
<http://en.wikipedia.org/wiki/Information_theory> and quantum computation
<http://en.wikipedia.org/wiki/Quantum_computation>.
Quantum mechanics and all other physical theories are claimed to be
*subsidiary* theories and quantum information a special case of *super
information*.”
(3) In [2, pp. 2 & 9], Deutsch defines the important terms (i.e.,
‘constructor,’ ‘construction tasks,’ ‘substrates’, etc.) that appear in
CTI, using words and diagrams:
(010515-3)
“. . . a ‘constructor’, . . . I shall define as anything that can cause
transformations in physical systems without undergoing any net change in
its ability to do so. I shall call those physical systems the
constructor’s ‘substrates’:
constructor
input state of substrate(s) constructor -------------------> output state
of substrate(s).
A transformation, regarded as being caused by a constructor, I shall call a
‘construction’. “
“Chemical catalysis has natural generalizations. Carbon nuclei are
catalysts for (010515-4)
nuclear reactions in stars. A living organism is both a constructor and a
product of
the construction that is its life-cycle which, for single-celled
photosynthesizing
organisms, is simply:
cell
small molecules + light --------------> cell + waste
products (6)
Inside cells, proteins are manufactured by ribosomes, which are constructors
consisting of several large molecules. They function with the help of
smaller
catalysts (enzymes) and water, using ATP as fuel:
RNA+ribosome+enzymes+H2O
amino acids + ATP -------------------------------------------> protein +
AMP + waste products (7)”
I mention this reaction in particular because the RNA plays a different
role from the
other catalysts. It specifies, in a code, which protein shall be the
product on a given
occasion. Thus, the catalysts excluding the RNA constitute a programmable
constructor. The general pattern is:
program
||
v
programmable constructor
input state of substrates -------------------------------------> output
state of substrates (8)”
“Constructor theory is the ultimate generalization of the idea of
catalysis.” (010515-5)
Statement (010515-5) is of special interest to me because CTI seems to be
inspired by or consistent with molecular biology, just as the conformon-P
model of computation formulated by P. Frisco was inspired by molecular and
cell biology [8, 9, 10].
(4) In [2, p. 14], Deutsch classifies constructions into four groups, as
shown in Table 2. To the original table, I added the constructors enabling
the constructions in parentheses. Three of the four terms appearing in the
parentheses are from [2], and the fourth, i.e, the ‘living cells’ driven
by chemical reactions [5] and biopolymer mechanical forces called
conformons [6], is my conjecture based on previous publications [7, 8, 9].
Table 2. A classification of constructions
Output
I
n
p
u
t
*Abstract*
*Physical*
*Abstract*
COMPUTATION
(Mathematicians)
PREPARATION
(Experimenters)
*Physical*
MEASUREMENT
(Instruments)
OTHER CONSTRUCTION
(Living Cells ?)
(5) Since living cells ‘construct’ humans and humans ‘construct’
instruments, I am tempted
to suggest that these three entities constitute a mathematical category:
f g
Cells ---------> Humans ----------> Instruments
|
^
|
|
|__________________________________|
h
Figure 1. The universal construction as a mathematical category.
f = biological evolution; g = cultural evolution; h = natural constraints
(?)
If Figure 1 commutes, i.e., f x g = h, as I assume, this may provide the
necessary and sufficient conditions for the living cell being a Universal
Computer, along with the Universe itself.
With 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
References:
[1] Deutsch, D. and Marletto, C. (2014). Constructor Theory of
Information. Arxiv.org/ftp/arxiv/papers/1405/1405.5563.pdf.
[2] Deutsch, D. (2012). Constructor Theory.
arXiv.org/ftp/arxiv/papers/1210/1210.7439.pdf.
[3] Ji, S. (2012). Towards a Category Theory of Everything (CTOE).
Molecular Theory of the Living Cell: Concepts, Molecular Mechanisms,
and Biomedical Applications. Springer, New York. Pp. 633-642. PDF
at http://www.conformon.net under Publications > Book Chapters.
[4] Ji, S. (2012). Complementarity. Molecular Theory of the Living
Cell: Concepts, Molecular Mechanisms, and Biomedical Applications.
Springer, New York. Pp. 24-49. PDF at http://www.conformon.net under
Publications > Book Chapters.
[5] Ji, S. (1999). The cell as the smallest DNA-based molecular
computer. *BioSystem* *52*: 123-133. PDF at http://www.conformon.net
under Publications > Refereed Journal Articles.
[6] Ji, S. (2002). The Bhopalator: An Information/Energy Dual Model
of the Living Cell (II). *Fundamenta Informaticae **49*(1-3):147-165.
PDF at http://www.conformon.net under Publications > Refereed Journal
Articles [7] Ji, S. (2000). Free energy and Information Contents of
C*onformons* in proteins and DNA. *BioSystems* *54: *107-130. [8]
Frisco, P., and Ji, S. (2002). Conformons-P Systems, in: *DNA
**Computing, 8th International Workshop on DNA-Based Computers.
*Hokkaido University, Sapporo, Japan, 10-13 June, pp. 161-170. [9]
Frisco, P., and Ji, S. (2003). Towards a Hierarchy of Conformons-P
Systems. *Lecture Notes in Computer Science **2597:* 302-318. [10]
Frisco, P. (2010). Conformon P Systems and Topology of Information
Flow. *Lecture Notes in Computer Science
<http://link.springer.com/bookseries/558> **5957:
*30-53.
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