12. Information

Reminder: Step Eleven

The accounting methods used by Nature while translating one- and more-dimensional logical descriptions into each other, while doing Genetics, are tautological. The mechanics of matching places and amounts becomes accessible after improving on methods one has learned in elementary school. The cuts separating the summands in a+b=c serve as tools to identify and distinguish logical entities with higher precision than found traditionally. We distinguish corners of triangles by their coordinates and by means of the strings that run through them.

Step Twelve

Standard Triangles as Implications of Order

No logical entity can exist without its logical surroundings, against which it is delineated and in which it receives its properties. By means of the strings going through one, two or three of its corners, each standard triangle is connected to a varied collection of elemental logical facts that set it in relation to each and every addition that is in the collection of the 136 additions discussed here. The unit reorders and the space relations they create are wholly integrated, and completely immersed in the totality of the logical statement a+b=c. The Euclid space is stable with rectangular axes that go in steps of 1 from 1 to 136. On a Venn diagram drawn on three sets, we distinguish and name the individual corners of the triangle. This brings forth a few dozen distinguishable logical entities that can match in differing ways – or not – to each other. The table  implicates a logical space with some furniture elements. To comply with neurological preferences in terms of units, we shall circumscribe a class of logical entities that can be visualized as solid bodies in a Newton space, like atoms and molecules.

Logical Archetypes: Spatially Referenced Standard Reorders

In the table there are 118 cases for which each holds that the sum of the lengths of two of its sides is at least equal to the length of its third side. (Please see 12.num.1) Please note that a differing permutation of the first level arguments {a,b,c,k,u,t,q,s,w}  may well bring forth a differing number of such standard reorders,  and the eight versions of the central element are for formal reasons included in this collection. We propose to call the geometrically representable standard reorders ‘logical archetypes,’ as they exist as an implication of the logical principles {+}, {<,=,>} on a multitude of natural numbers and they have a real, tangible existence in space, as they circumscribe a solid point with definite coordinates.

Periodic Table of Logical Archetypes

It appears that Logical Archetypes (LA) can be grouped according to several principles. We propose to use the level of iso-location on the plane K_Q, that is: b-2a vs. a-2b as one of the main ordering criteria for tabulating the LA . (Please see 12.num.2) The number of units being in this plane at any moment is comparable to the concept of atomic mass as a multitude of units. The duality of the LA is caused by their origin in the two Euclid-type spaces and mirrors concepts relating to ideas of protons and neutrons. There appear to be diverse kinds of missmatches between the amounts being connected to a spatial position and the spatial distances covered by the strings going through the triangles. We will call these ‘telecratic effects.’ The telecratic effects can be seen as a tendency of accounting consolidation into a collection of constraints on amount per distance with respect to distance per amount. If either {+} or {<,=,>} are not obeyed, the system breaks and we enter the subjects of physics and chemistry. Genetics works under ideal circumstances, where all logical relations are self referencing.

Logical Positivism

The Twelve Easy Steps continue the work of Wittgenstein by sharing the understanding that it is possible to create a picture of the world restricted by grammatical rules of the language, but still allowing for clear and complete emotional and artistic communication. Although nothing new and surprising can be said in a logical discourse, because it is by its nature tautological, that what can be said is coherent, clear and self-evident. The surprising revelation of understanding the Twelve Easy Steps is about ourselves, not about Nature or how well we were able to picture Nature, even without attention to the properties of the summands.The system worked quite well for all things but the living. May the introduction of the ‘Ordering Machine’ to applied sciences a productive tool for great works.

Information and the Eyes of the Beholder

The concept of information connects the emotional with the rational. Human neurology functions well if it is neither in sensory deprivation, nor under overload, and there is a degree of novelty within a relatively predictable continuity. We share many connotations of the word ‘information,’ but in logical language transmiting what composers, dancers, poets or painters communicate appears to be rather cumbersome.

Restricting the denotation of information to its technical core would kill an important aspect of information. The brain needs its rewarding effects of the emotional-neurological natural connection. The connotation of  ‘new  information’ makes this information deeply connected to an individual’s learning history. ‘this is new to me’ is equivalent to, ‘this is information for me.’ The rooting of the understanding of a concept in individual histories makes that concept unsuitable for logical discourse. There, a concept’s meaning and its properties are indifferent to the learning history of the individual. 

The usage of {+} and {<,=,>} concurrently on a collection of additions is information, as long as it is new to the user. The tautologies on which the accounting mechanism turns have always been there and have not been discovered, but have rather been uncovered. Being tautologies, the logical statements about what is where and when, are outside of time. They are timeless. The information content is not a description of the matter discussed, but of the person taking in this information. Information is suitable as a unit of experience, rather than a thought. The fact of the matter remains, information diminishes when predictions are present. They say: "There are no old jokes with long beards, only old men with long beards. For a newborn, every joke is new."