Quoting Loet Leydesdorff <[email protected]>: > > Because it is essentially a mathematical theory, information theory, > in my opinion, can be made relevant (that is, provided with meaning) > in all kind of contexts, and these various contexts can be used to > formalize mechanisms which can then be more abstractly translated > into other contexts by using information theory.
Dear Loet, Your opinion that IT can address meaning is refreshing, and I quite agree with you. Most feel that the Shannon approach cannot address meaning. I offer, however, the following example: Consider the following three random strings of 200 digits: Sequence A: 42607951361038986072061245134123237671363847519601557824849686201007746224524209371591449046940565604803389860720612451341232376713638475196015578248496862010077462245242093715914490469405656048033898 Sequence B: 03617746439242093715914490469405656048033898607206124513412323767136384751960155782484968620100774622452420937159144904694056560480338986072061245134123237671363847519601557824849686201007746224524209 Sequence C: 01475623843789694751743102380318185453848905236473225910906494173735504160210176853263006704607242470971896947517431023803181854538489052364732259109064941737795041102101768532630067046072424709708969 The values of the Shannon measure for each sequence are 3.298, 3.288 and 3.296 bits, respectively. That there exists no internal order in any of the sequences is shown by calculating the mutual information measures of adjacent pairs of digits in each of the three cases. These amount to 10.97%, 10.03% and 9.94% of the respective paired entropies, each of which is typical of a random distribution of these dimensions. Relationships between higher lagged pairs prove likewise to be random. Next the correspondences between pairs of sequences are examined. Looking at how each digit in A pairs with its corresponding location in B yields a joint entropy of 5.900 bits, 11.61% of which appears as mutual information i.e., random correspondence. Similar pairings between sequences A and C, however, reveal that fully 91.69% of the joint entropy consists of mutual information between the sequences. Obviously, sequences A and C are closely related. In fact, close scrutiny of sequence C shows it to be an arbitrary permutation of sequence A, along with a handful of mistaken permutations. While this may appear as a typical exercise in coding/decoding, its implications actually run far deeper. Instead of digits, one could have used symbols for codons in a genome (A,C,T,G) or monomers in a protein. In the latter instance, sequence A might represent the spatial sequencing on the outer surface of an antibody in the plasma of an organism, and B and C might describe the patterns on the surfaces of microbes present in the same plasma. While B appears to bear no relationship to A, C would engage A in a hand- in- glove match. The pattern in C would have ultimate meaning to A. It would signify the goal towards which A was created by the immune system, and the match would initiate a highly directed action (to eliminate the microbe). All of this significance can be gauged by the elevated value of mutual information between the sequences. So, whereas the raw Shannon measure by itself cannot convey meaning, it is obvious that the relative information conveyed by the AMI is capable of doing so. That meaning for antibodies is a pale representation of meaning in the human context only reflects how wanly quantitative models in general prefigure more complicated human situations. The basic elements of meaning, however, can indeed be captured by relativistic information measures. Greetings to all, Bob _______________________________________________ fis mailing list [email protected] https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis
