11. Natural Order
Reminder: Step Ten
The circumstances under which genetics can take place are regulated by order rules that govern both places to, [kinds of] amounts and [kinds of] amounts to places. As there is a three way nonlinear relationship between [distinct] numbers of objects, the number of amounts-related logical relations and the number of places-related logical relations, Nature makes use of some accounting equivalences to allow for translating order, place and amount into each other.
Step Eleven
Aesthetics of Nature
The human nervous system processes neurological impulses according to a hard wired grammar of natural logic. Art succeeds in making us see, feel, hear the aesthetics that govern our perception. The biologic order that organizes our brain is the fundamental tautology on which our epistemology is based. It is not easy to speak in a logical fashion about the background, against which we observe the seemingly rational, rectangular, stable and predictable.
Looking at some of the strings connecting additions that are isolocated with respect to a reorder from αβ into γδ, as lines connecting points on a plane, one cannot escape a feeling of aesthetics. A biologic curve representing this is found in graphs and reminds one of small appendixes containing the essence of the whole and the origin of the world, according to Courbet; of helix-form relations. (Please see 11.g.1 )
In step one of these Twelve Easy Steps, we started off with the logical sentence a+b=c. We have received, at the quite impressionable age of 6 years, the traditional and relevant wisdom that the two summands, a and b, are distinct to each other. We have been trained to concentrate on the composite that results from joining the two summands. We have learned to not worry about the identity of the summands. By doing so, we have become trained to disregard the properties of the cuts that we wish away while conducting an addition.
In a+b=c we see two kinds of cuts, those of unit type that distinguish the units ‘1’ in ‘1+1+..+1’ that makes up the inside of a, b and c, and those of the summand type that distinguish a+b from c. In a+b we can imagine a cut after the end of the last unit in a and just before the first unit of b. This is the cut we wish away and see as not being there. It is demoted into a unit type cut as we regard c, which is 1+1+...+1, with no summand type cuts between the 1s. Reality teaches us that things that one wishes away usually come back to haunt one, because wishing things away creates an illusion which is deceptive. The moment of awakening does come and spurs some among us to cry out Aha!
Following the fate of the summand type cut, present in a+b and no more there in c and on a specific place between 1 and c-1, where we had wished it away, we see that both its existence and its placement do have consequences, which we had not calculated to be of any relevance. Conducting the additions with the enhanced attention to details spelled out in the Twelve Easy Steps, one will recognize that the cuts, which had traditionally been wished away, do influence our perceptions of what is a cavalier attitude to rounding errors and what is rational. The cuts specifically are delimiting between what can and what cannot be the case (constraint) and allow predicting what is where and when.
Specifically, the history of how things have become such as they are now is explained by means of the sequence of the evolution of order, or the sequence of re-orderings. In depence of which order had previously prevailed, the elements that are in a tie with respect to the current order, may or may not appear to be preordered with respect to a future order. (Please see step ten[A6] )
Self-Organization and Random Effects
How naturally does a natural order evolve, just by itself? You, the reader are invited to find your own opinion on this point, e.g. by generating random permutations of 136 additions and calculating the deviation of the random order to any and each of the 72 orders discussed here. There will always be one of the 72 orders catalogued here that is the closest to the random permutation. The intuitive prediction is that the random permutation is less deviating than an order that is maximally deviating to that one which is most close to the random permutation.[A7] That is, any random permutation could go through as a transient state between two of the 72 catalogued orders. This idea is supported by the findings of neurology, according to which the human nervous system perceives patterns in multitudes, independent of the existence of patterns. As genetics is quite opposite to stochastics, we shall look now in this last step at the natural properties of logical building blocks that arise from the hypothesis that the system is maximally ordered.
Seven Pillars of Triangles
The standard reorders connect three additions and create a triangle. We distinguish the three corners of the triangle as they have different coordinates. Each of the corners is an addition, and as such is included in chains that connect it with other additions. Now we classify the chains according to their properties of going through one, two or three of the corners of a specific triangle. The resulting seven classes of chains are, where X, Y and Z are names for the corners, {x,y,z,xy,yz,zx,xyz} which we name L1 to L7, respectively. (Please. see 11.g.2) The classes L1 through L7 are mutually exclusive and collectively exhaustive. The L7, XYZ, is to be compared to L7 values of other triangles with respect to other orders, and can serve as a logical accounting representation for the concept of mass, xy, yz, zx show the kinds and quantities of inner consistency and x,y,z show the bonding affinities of the logical entity. We shall discuss these interpretations of the order of natural numbers more deeply in step twelve.
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