Karl did an interesting remark. Yes, "circle", "distance", "equal", etc. are terms understood by everybody. But it often happened that mathematicians attribute definitions to terms used in a non math context. E.g., a circle is a set of points in the Euclidean plan lying at a given distance from a point called the center. That definition recovers the ordinary one (i.e., the non math). The math definition of distance recovers the ordinary definition, too: this math definition is much more general than the ordinary one and it helps to clarify it. More tricky in the ordinary case is the definition of "equal", but thanks to the mathematicians, it is enlighted by the "equivalence relation" defined in set theory. The situation is different with "information": the math definition (includes some extensions: mutual information, information gain, Fisher information, etc.) recovers only a small aspect of the non math one(s). Much has been written about this latter. Question: should we find a much more general math definition in order to clarify the non math ones ?
Michel. 2011/10/3 karl javorszky <karl.javors...@gmail.com>: > On the existence of the term "information" > > Let me pick up the the idea expressed by a colleague that "... in fact, such > a thing as 'information' does not exist at all" (sorry, not a verbatim > citation). > > This is in fact true. The idea can be better understood if one states: "such > a thing as a 'circle' does not exist at all - that what exists is a > collection of points that are equally distant to a fixed point". This > approach shows that 'circle' is only a (romantic) abbreviation of things > that have an agreed-on existence, namely "fixed place", "point", "distance" > and "equal". These are words that every human who masters the ability of > speech will understand, therefore can be used as axiomatic; also one can > point at them and therefore make a diectic definition. > > The situation with 'information' is similar, if not analogous: > Such a thing as 'information' does not exist, but what exists is that > alternatives are there to connect matter-space complexes to other > matter-space complexes and pointing out one of the alternatives has a result > insofar as someone can understand that what I have pointed out". > Information is seen in this approach as a subjective, communicative result > of an interaction. That Na attaches to Cl is no information, that H2 and O > make a molecule is no information (these days, because we know that it can > not be otherwise). > > Information is always embedded in a social context. Today it is an > information (even within FIS, for some) that additions can be listed, and > that they can be listed in quite many sequences, and that each different > listing (sorting) yields a collection of differing inter-addition-distances. > (That is, 1+2=3 is sometimes a neighbour of 1+3=4 and sometimes 17 units > away while being 2 distant /find, when/). After this idea will have gained > ground, by being the basis of Physics and Chemistry, it will cease to be > information. For us it is no information that Pi is 3.14, because we have > already learnt it. > > Once we will have learnt that among the re-sortings of additions there are > standard re-sorts, and that the standard re-sorts construct two Euclid > spaces that are connected by two planes, it will cease to be an information > that biology uses two kinds of the same entity that are fused by means of > sequences (which we see under the microscope in the DNA), that is two > planes. We will have understood that it can not be otherwise. > > Presently, it is information that it helps if one understands the relation > between distances and additions. > > Karl > _______________________________________________ fis mailing list fis@listas.unizar.es https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis
