ITHEA^® International Journal

"Information Theories and Applications"

2022, Volune 29, Nimber 3

Abstract:

We propose to use a technique of counting ‘in stereo’, by using two counting systems concurrently. Research in number theory has brought up a very slight inner discongruence within the numbering system. The proposal is to root the definition of the term ‘information’ in properties of natural numbers, with the refinement that the extent of information is equal to the extent of being otherwise. The property of being otherwise can be numerically defined on a collection of pairs of natural numbers. An etalon collection of pairs (a,b) is used to demonstrate the concept of being otherwise. The property of being otherwise is based on the numeric fact, presented in oeis.org/A242615, according to which there are two upper limits of the number of logical relations existing among members of collections, namely sentences which state the existence of similarity, ‘n?’ contrasted to sentences that describe differences, ‘n!’, among the members of one and the same collection. The values f-1(number of different relations) point back to slightly differing values of n, and this in the form of Δ (f-1(n?), f-1(n!)) {=, <, =, >, =, <, <<} for n {1, 11, 32, 66, 97, 136, 140}. The numeric incongruences appear to play important roles in Physics, Chemistry, Theoretical Biology. Here, in the context of software design, the practical relevance of being able to switch between two methods of describing one and the same state of a set, becomes apparent in the increased efficiency in the transmission of messages. Recognition of forms and patterns in (eg optical) multitudes becomes possible by using the properties of cycles, which are an artefact of periodic changes which sender and receiver subject the collection of tokens to, in a pre-agreed (or, in Nature, a-priori existing) algorithm. The theoretical foundations for the possibility of recognition of Gestalts are presented to be implications of the inner incongruence of the numbering system, as shown by oeis.org/A242615. There exist shortcuts, abbreviated names for patterns. This is equivalent to a condensation of information.

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