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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