Nature’s Little Accounting Tricks
The sentence ‘this has been defined such’ brings forth differing consequences in the technical sciences and in the humanities. The former will arrive at rules that regulate how the concept defined fits within the system of other concepts in a clean fashion, free of contradictions. In the latter, one will immediately question the social power of the ruling class, and investigate, what advantages have been achieved, and for whom, by de-legitimising alternative concepts to the definition imposed, and whether the elite presently ruling still maintains the credibility of monopolising the interpretation of phaenomena observed. The former will achieve a system of explanations that is logically homogenous and free of conflicts; the latter thrives on conflicts and works with the dialectic of alternatives.
Nature, of course, keeps her calm with respect to this controversy among humans. She just keeps doing her things, in her own fashion. We, as humans, are left with no choice other than having to align our understanding, and efforts of understanding, of what, and according to which rules, Mother Nature does, to the facts observed. The facts show that Nature ignores some of our definitions, and appears to work according to rules that do not obey some of our definitions. The insights resulting from not understanding some of Nature’s processes will lead us to experiencing cognitive dissonance and some resistance in following avenues of thoughts that lead us outside of the system of what has been termed traditionally as ‘rational thinking’, insofar as rational thinking means following age-honoured systems of definitions.
As a psychologist, one cannot – and will not want to – avoid thinking in a fashion that accepts the existence of logical conflicts and of contradictions. One of the explanations, why classical Greek tragedies are of an immortal cultural value is, that in these each participant acts according to well-reasoned and impeccable logic: that is, no one is at fault – or “logically wrong” – by pursuing his goals: the situation makes the conflict unavoidable.
Not shying away from dealing with logical conflicts opens up wider perspectives in dealing with Nature’s machinations. Once one is ready to disregard traditional definitions, one is free to construct explanatory models that do describe Nature in a simple, easy and comprehensive fashion and deliver the penny that drops while one cries “Aha!”.
Specifically, if one disregards the definition of commutativity and observes that (a,b)→c is indeed different to (b,a)→c, and one also overcomes the dichotomy (commutative) ↔ (sequential), one has passed important milestones in understanding the nuts and bolts of how the combinatorics of the interplay between the sequenced DNA and the commutative organism actually functions.
My lecture invites the audience to work with new ideas. The trouble lies in accepting cognitive dissonance regarding to the eternal truth of definitions and in understanding that definitions are man-made and can well turn out to have been time-honoured, sensually seductive but nevertheless false. The shock the audience will experience is comparable to the shocks our forefathers had experienced while being confronted with the ideas that the Earth is not flat, and, later, that it circles the Sun: both assertions having been fundamental definitions of truth.
The new idea is presented by using irrefutable arguments that show some properties of cyclic permutations. We use some properties of natural numbers to show that ordering and reordering logical tokens – actually, instances of a+b=c – allows us to recognise patterns that show where is what, and when. The numbers are beyond any discussions of being right or wrong, they are just numbers. What we can read out of the numbers can open the eyes, and give rise to discussions about whether the concept is practically applicable and how. It certainly seems useful as a tool of explaining how the transfer of genetic information is engineered by Nature. This lecture is an exercise in forensic accounting and will unveil some of the cute little accounting tricks Nature uses while managing the business of genetics (and of the memory and of pattern recognition and of learning, to point out the most obvious applications of the principles of information management).