Dear Jerry, Pridi, and Colleagues, Thank you for the nice comments!
To answer to questions I have to present next step from the GIT (General Information Theory) we are developing. Let remember in words (below “Infos” is abbreviation from “Information Subject”, it is an intelligent natural or artificial agent (system)): Information is quadruple (Source, Recipient, Evidence, Infos) or formally i = (s, r, e, I) The nest step is to define elements of the quadruple: s and r are structured sets; e is a mapping from s in r which preserves (all or partial) structure of s and resolves any information expectation of I I expect new questions: - what is an “intelligent agent” - what is “information expectation” - ... If it is interesting, answers to these questions may be given in further letters. *** Now I want to make some comments to letters received (their full texts are given below my answers). Pridi: “information cannot be viewed in any absolute sense but as internal representations of "external patterns"” Kr.: Yes, the “reflection” is a property of Matter, “information” is a reflection for which the information quadruple exists. But information is not “internal representations of "external patterns" ”. It is result from resolving the subjective information expectation which is process of comparing of internal and external patterns. I know, this will cause new questions Pridi: In this framework then, it seems that "information" cannot be conceptualized without reference to the both "something out there" and the "internal structures" of the receptor/cognitive system. Kr.: Yes. Pridi: How can we really quantify meaningful (semantic) information ... ? Kr.: By distance between "external patterns" and “information expectation” (sorry to be not clear but it is long text for further letters). Pridi: All "objective" measures (entropy, negentropy,...) are actually totally dependant of I1 and I2 and can never be considered as "absolute". Kr.: Yes, but the world humanity is an Infos and its information expectations we assume as "absolute". Pridi: ... some researchers that posit that "information" may be more fundamental than the fundamental physical (mass, time, space, amps). Kr.: Yes, there are other paradigms which are useful in some cases, but in our paradigm “information” is not fundamental but “reflection” is the fundamental. Pridi: ... no "absolute truth" (whatever this means) is really gained. "Only" a richer more complete (subjective but coherent) world-view . Kr.: Yes. Jerry: ... assertion of a quadruple of symbols is rather close to the philosophy of C S Peirce (hereafter "CSP") Kr.: Our paradigm is nor opposite to what science has explored till now. All already investigated information theories (Shannon,Peirce, etc) have to be a part or intersection of a new GIT. Jerry: ... moves these 'definitions' of individual symbols into the subjective realm. (CSP's notion of "interpretation?) Different researchers have the freedom to interpret the evidence as they choose, including the relationships to engineering terms such as "bandwidth". Kr.: Yes. But not only researches, everybody has such freedom. Because of this there exist advertising processes ... but for this we have to talk in further letters. Jerry: Pridi's post appropriately recognizes the tension between objective scientific theories and subjective judgments about evidence by different individuals with different professional backgrounds and different symbolic processing powers. Kr.: Yes, there will be tension if we assume world as plane structure. But it is hierarchical one and what is assumed as “subjective” at one level is assumed as “objective” for the low levels. Jerry: ... to show that these definitions of symbols motivate a coherent symbol system that can be used to transfer information contained in the signal from symbolic representations of entities. It may work for engineering purposes, but is it extendable to life? Kr.: The goal of work on GIT is to create a coherent symbol system which is equal valid for life creatures and artificial agents. Jerry: ... this requires the use of multiple symbol systems and multiple forms of logic in order to gain the functionality of transfer of "in-form" between individuals or machines. Kr.: Yes, at least on three levels – Information, Infos, Inforaction (Information interaction) Jerry: Anybody have any suggestions on how this quadruple of symbols can be formalized into a quantitative coherent form of communication? Kr.: A step toward this I give above in the beginning of this letter but it is very long journey ... Thank you for creative discussion! Friendly regards Krassimir -----Original Message----- From: Jerry LR Chandler Sent: Wednesday, July 23, 2014 8:57 PM To: FIS Cc: Krassimir Markov ; Pridi Siregar Subject: Re: [Fis] Re to Pridi: infinite bandwith and finite informationcontent CS Peirce and Chemical Nomenclature Pridi, Krassimir, List: (In order to place this comment in context, and for reference, I have copied Krassimir's "definition" of information below. My comments follow the excellent post of Pridi.) > In physical world there exist only reflections but not information. > > Information “ i " is the quadruple: > i = (s, r, e, I) > where > s is a source entity, which is reflected in r > r is the entity in which reflection of s exists > e is an evidence for the subject I which proofs for him and only for him that > the reflection in r reflects just s , i.e. the evidence proofs for the > subject what the reflection reflects . > I is information subject who has possibility to make decisions in accordance > with some goals – human, animal, bacteria, artificial intelligent system, > etc. > > In other words, information is a reflection, but not every reflection is > information – only reflections for which the quadruple above exist are > assumed as information by the corresponded subjects. > > For different I , information may be different because of subjects’ finite > memory and reflection possibilities. > Because of this, a physical event with an infinite bandwidth may have finite > information content (for concrete information subject) . On Jul 23, 2014, at 6:45 AM, Pridi Siregar wrote: > Dear Krassimir, > > Thank you for your explanation. It does give me a better understanding of how > information (beyond Shannon) can be formalized! However, a closer look at the > formalism and its semantic does raise new questions: > > From the definition you have given, it appears that information cannot be > viewed in any absolute sense but as internal representations of "external > patterns" whose meaning depends on the subject capturing/interpreting/storing > the said patterns. In this framework then, it seems that "information" cannot > be conceptualized without reference to the both "something out there" and the > "internal structures" of the receptor/cognitive system. > > In other words the concept of "information" lies within some "subjective" > (albeit rational) realm. I'm sure that I'm stating the obvious for most of > FIS members but a question arised upon reading your formalism: How can we > really quantify meaningful (semantic) information beyond Shannon (that > disregards semantics) and his purely statistical framework? Or beyond > Boltzmann's entropy/Information based on micro-macro states ratios? > > When we formalize i = (s, r, e, I) there is a "meta-level" formalisation > that is only apparent since even (s,r) reflect our own (human) subjective > world-view. We could actually write (I1(s), I1(r), e, I2) where I1 and I2 are > two distinct cognitive systems and both of which lie at the OBJECT level of > the formalizing agent which is NEITHER I1 or I2. All "objective" measures > (entropy, negentropy,...) are actually totally dependant of I1 and I2 and can > never be considered as "absolute". > > > This leads me to a second question (sorry for the lengthy message): there are > some researchers that posit that "information" may be more fundamental than > the fundamental physical (mass, time, space, amps). This appears (and perhaps > only appears) to be at the opposite end of the above-mentioned view. Indeed, > in this framework some kind of "universal" or "absolute" notions must be > accepted as true. > > One apparent way out would be to demonstrate that information somehow > logically entails the fundemantal physical entities while accepting that we > are still within a human-centered world view. And thus no "absolute truth" > (whatever this means) is really gained. "Only" a richer more complete > (subjective but coherent) world-view . > > Am I making anys sense? Any thoughts? > > Best > > Pridi > Pridi's comment concur with many of my views wrt the concept of information. Krassimir's assertion of a quadruple of symbols is rather close to the philosophy of C S Peirce (hereafter "CSP") in one context. S as symbol represents an external source of signal, that which is independent of the individual mind and being. This is analogous to CSP's term "sinsign". R is a thing itself. That is, R generates S. E as evidence is a vague term which infers an observer (2nd Order Cybernetics?) that both receives and evaluates the signal (S) from the thing (R). CSP categorizes evidence as icon, index or symbol with respect to the entity of observation. I as Krassimirian information is a personal judgment about the evidence. (Correspondence with CSP's notion of "argument" is conceivable.) Krassimir's assertion that: > For different I , information may be different because of subjects’ finite > memory and reflection possibilities. > Because of this, a physical event with an infinite bandwidth may have finite > information content (for concrete information subject) . moves these 'definitions' of individual symbols into the subjective realm. (CSP's notion of "interpretation?) Different researchers have the freedom to interpret the evidence as they choose, including the relationships to engineering terms such as "bandwidth". Pridi's post appropriately recognizes the tension between objective scientific theories and subjective judgments about evidence by different individuals with different professional backgrounds and different symbolic processing powers. The challenge for Krassimirian information, it appears to me, is to show that these definitions of symbols motivate a coherent symbol system that can be used to transfer information contained in the signal from symbolic representations of entities. It may work for engineering purposes, but is it extendable to life? (For me, of course, this requires the use of multiple symbol systems and multiple forms of logic in order to gain the functionality of transfer of "in-form" between individuals or machines.) Pridi writes: > How can we really quantify meaningful (semantic) information beyond Shannon > (that disregards semantics) and his purely statistical framework? One aspect of this conundrum was solved by chemists over the past to two centuries by developing a unique symbol system that is restricted by physical constraints, yet functions as an exact mode of communication. Chemical notation, as symbol system, along with mathematics and data, achieves this end purpose (entelechy) of communication, for some entities, such as the meaning of an "atomic number" as a relational term and hence the meaning of a particular integer as both quantity and quality. This requires a dyadic mathematics and synductive logic for sublations. Pridi writes: > It does give me a better understanding of how information (beyond Shannon) > can be formalized! Can you communicate how this "better understanding... ... foramlized" works? It is not readily apparent to me how Krassimirian information can be formalized. Anybody have any suggestions on how this quadruple of symbols can be formalized into a quantitative coherent form of communication? Cheers Jerry
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