Hi, (*1*) Information is triadic in that it has three mutually exclusive aspects --
(i) *amount* (how many bits of information can your USB store ?), (ii) *meaning* (What is the meaning of this series of DNA nucleotides ?), and (iii) *value *(What does this series of DNA nucleotides do for the living cell?). (*2*) Most definitions of information (e.g., Hartley, Shannon, von Neumann, 'Planckian information' [1], etc.) in the literature are in the form of *mathematical equations* and attempt to capture the *amount* of information and not the meaning or value. There are about 40 different such quantitative definitions of information discussed in [2]. (*3*) The main purpose of this post is to propose the following, diagrammatic, definition of "information" that is inspired by the definition of the sign given by Peirce as shown in (120815-2) and *Figure 1:* "Information is anything that is transferred from *B* to *C* mediated by *A*." (120815-1) Please note that the placeholders, *A*, *B*, and* C*, are generalizations of the A, B and C that appear in the definition of the sign given in (120815-2) below; hence the suggested name *Peircean information *(PI). The placeholders, *A*, *B* and *C* are analogous to the *free parameters* appearing in mathematical equations. Thus, (120815-1) can be viewed as a 'qualitative parametric' definition of information in contrast to the *parametric definition of information* given by Burgin in [2] which may be considered as a 'quantitative parametric' definition of information. If this view is correct, it would mean that 'information' is a complementary union of *quantity* and *quality*, in general agreement with the yin-yang doctrine of the Daoist philosophy. (Reproduced from yesterday's post) *"30 - 1905 - SS. pp. 192-193 - Letter to Lady Welby (Draft) presumably July 1905 . *(120815-2) So then anything (generally in a mathematical sense) is a priman (not a priman element generally) and we might define a sign as follows: A "sign" is anything, A, which, (1) in addition to other characters of its own, (2) stands in a dyadic relation Þ, to a purely active correlate, B, (3) and is also in a triadic relation to B for a purely passive correlate, C, this triadic relation being such as to determine C to be in a dyadic relation, µ, to B, the relation µ corresponding in a recognized way to the relation Þ." This definition of the sign can be diagrammatically represented as shown in *Figure 1, *which clearly shows that there are three *dyadic relations (or arrows) *(two of which are designated as Þ and µ and the third is not explicitly mentioned by Peirce but represented by me as g in *Figure A*). MOST IMPORTANTLY, the sign, A is related to object B in two ways -- (i) *dyadically through the relation **Þ*, and (ii) *triadically *through the relation µ *(*and the relation g, in my opinion*)*. * Þ g* Object ----------> sign ---------> Interpretant (*B*) (*A*) (*C* ) | ^ | | |____________________________| *µ* *Figure 1.* A diagrammatic representation of the Irreducible Triadic Relation (ITR) embodied in the Peircean sign. Þ = sign production; g = sign interpretation; µ= *information transfer.* (*4*) It is interesting to note that *Figure 1* that defines the Peircean SIGN simultaneously defines INFORMATION as well, the former emphasizing the *node*, *A* , and the latter emphasizing the *edge*, *µ*. (*5*) This leads me to suggest the following generalization: "Just as a *network* cannot exist without *nodes* and *edges*, so it is impossible to *communicate* without *signs* and *information *they carry." (120815-3) 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] Ji, S. (2015) Planckian information (IP): A new measure of order in atoms, enzymes, cells, brains, human societies, and the cosmos. In: *Unified Field Mechanics: Natural Science * *beyond the Veil of Spacetime* (R. Amoroso, P. Rowlands, and L. Kauffman, eds.), World Scientific, New Jersey, pp. 579-589. [2] Burgin, M. (2010). Theory of Information: Fundamentality, Diversity and Unification. World Scientific, New Jersey.
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