Abstract
We present a model of information processing which is based on two concurrent ways of describing the world, where a description in one of the languages limits the possibilities for realisations in the other language. The two describing dimensions appear in our common sense as dichotomies of perspectives: subjective - objective; diversity - similarity; individual - collective. We abstract from the subjective connotations and treat the test theoretical case of an interval on which several concurrent categories can be introduced. We investigate multidimensional partitions as potential carriers of information and compare their efficiency to that of sequenced carriers. We regard the same assembly once as a contemporary collection, once as a longitudinal sequence and find promising inroads towards understanding information processing by auto-regulated systems. Information is understood to point out that what is the case from among alternatives, which could be the case. We have translated these ideas into logical operations on the set of natural numbers and have found two equivalence points on N where matches between sequential and commutative ways of presenting a state of the world can agree in a stable fashion: a flip-flop mechanism is envisioned. By following this new approach, a mathematical treatment of some poignant biomathematical problems is allowed. Also, the concepts presented in this treatise may well have relevance and applications within the information processing and the theory of language fields.
Highlights
Sequences Versus StatesThere is an agreement in theoretical genetics that the genetic information is stored in a sequence, namely the DNA
That is the best image for the present work: we are offering a new explanational model on how the information stored in sequences gets translated into "states of sets" and, as importantly, back again
Summarising this section, we may restate that: Symbols pointing out identical elements of a set can be replaced by a natural number showing the cardinality of the subset generated such; If several symbols point to the identical object(s), all but one of these are redundant; Communicating an overlap structure by transmitting objects concurrently may lead to a sequence to evolve “by itself”; Individual objects can carry info by their sequence; Non-individuated objects can carry an info by pointing out characteristics of the place; A combination of both sequence and structure info is the total expectation space; Of this potential only that can carry info that can be otherwise
Summary
There is an agreement in theoretical genetics that the genetic information is stored in a sequence, namely the DNA. That is the best image for the present work: we are offering a new explanational model on how the information stored in sequences gets translated into "states of sets" and, as importantly, back again It may not be a direct model of the processes of the biological cell, but it offers a rational view of the functioning of numerous instances of autoregulation in the natural and social realms. If three index categories terminate with the same physical object on a shelf we shall use a 3-high book separator This would be the case if the last blue French book on gardening of that year were next to the first red book on gardening that had a different year of publication and were say, in German. If we have this technique, we are not at all far from deducing the concept of a periodic system of elements which we can regard as types (archetypes) of combinations (compositions) of logical properties
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