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The Universal Language

Written by Florin Colceag

Monday, 24 November 2008

Considering the cyclic general structure that is generated by the automorphisms of the projective line generated by the points 0, 1, and ½ we obtain numerous cycles that can be structured as a vocabulary (see the next attachment, cyclesorter). It is necessary to sort and classify considering arcs and orientations to obtain it. We obtain semantic cones formed by six letters, for example A1, A2, A3, A4, A5, A6, all described by the same pattern, and responding to a various situations with a different logic of tracing specific transformations given by automorphisms. These semantic cones can be considered as logic patterns.

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All these applications can be read in java 1.4

In this article I consider only one operation of the informational field. This operation associate three cycles by identifying the same line at two cycles, but on different positions (upper line, or lower line). This operation will be called concatenation . The table of association of this operation is called (matrix). On this table there are operations among semantic cones, that means sets of letters with similar patterns.

By considering each set of semantic cones identified by the matrix table we can find some elements that can be considered neutral, or uneven. Neutrality is given by the shape, and number 0 of arcs, uneven is the element that has a different pattern of arcs than the other two of the subsets formed by three cones.

The relationships given by the symmetries among the semantic cones identified my matrix are structured in cubes 0

They form the basic material to describe the behaviour of the algebraic fractal considering the semantic direction.

In the following material will be exploited only the operation of concatenation of cycles at upper levels of complexity.

The other operation of the informational fields that lead to other properties will be described in different articles. (see F. Colceag; Informational Fields; )

Conforming to this study the universal language can go at different levels of complexity of the algebraic fractal when there are three cycles in concatenation operation. This fact is convergent with various approaches in science, from quarks and colours theory to the three dermal leaves that form an embryo, and in all cases lead to complex manifestations.

letter

IIIB

IIB

IIA

IVb

IVA

IIIA

TV

TABEL 1

If we note (,,,,,) with ; (,,) with; (,,) with  and (,) with , we obtain the following sets table, without internal differentiating for operations:

*	d	^	_	z
d	d	_
^			d	_
_	^	z
z			^	z

TABEL 2

Figure 1 Graphs of connections among semantic fields

Explanation of signs

Taking the first two columns in one cycle we obtain a rectangle. A continuous segment is drawn when the same element can be found on the two ends of the segment in the rectangle.

The point evidentiate the position in the rectangle of the non-identical elements.

The semantic cones noted with letters at the end of the column present the same pattern and are considered to be conjugated. The bolded letters represent neutral elements, and the italic letters represent the uneven elements.

The table is useful in configuration the algebraic fractals, and the characteristic structures for any fractal dimension with specificity for dimension.

Rules of signs (grouping categories of partitioning of the semantic cones)are given by the following triplets:

For the upper left corner (the green corner)

(,, ), (,,), (, ,); (,, ), (, , )

(,, ), (, , ); (,,), (,,), (,,)

For the orange corner (right, down corner) we have:

(,,),or (,,) in conjunction for decision, and(,,)

PARTS OF THE TABLE WITH CORESPONDENCE ON THE CUBE

(Yzyz@&)*(Yzyz@&)= closed structure included in the algebraic fractal model, and creating a structure that can enter in the direct product with: (A,N,e,j,B,M,d,k,F,l,c,o,D,K,b,m,C,O,f,l,E,J,a,n)*(A,N,e,j,B,M,d,k,F,l,c,o,D,K,b,m,C,O,f,l,E,J,a,n), resulting complex product in strings manner

(A,N,e,j,B,M,d,k,F,l,c,o,D,K,b,m,C,O,f,l,E,J,a,n)*(A,N,e,j,B,M,d,k,F,l,c,o,D,K,b,m,C,O,f,l,E,J,a,n)=

closed structure included in the algebraic fractal model and replacing f1,f2, f3,f4, f5, f6

The other parts that don’t give internal operations can be seen into the Table2

The structure of semantic fields connections which permits the semantic transfer from a field to a different field can be seen on the Figure 1.This structure permits to apply the entire table 1 in modelling dynamic phenomena, with dynamism, adaptability, and possible communication among various objects from the informational fields.

This kind of semantic population permits to compare the operations in the informational fields with Turing machines, or to generalise them.

TABELE DE OPERARE PE MODULE MODUL I

Frame1

Frame2

Frame3

Frame4

Module IIA

MODULUL IIB

MODULUL IIIA

MODUL IIIB

MODUL IV A

MODUL IVB

MODUL V A

MODUL VB

MODUL VI

ALGEBRAIC FRACTALS

Funct.

letter

We can notice that the two tables are almost identical, the difference between them being f4, f5 and respective , , where in the second table there is a switch.

Because of this the new table permits creation of second degree cycles that are almost similar with the first degree cycles if we don’t refine the information to the second degree. The differences among the first degree and the second degree cycles that are at the first level of semantic for both are at the 3’th and 6’th positions of the cycle, where and differentiate the groups of semantic cones into a different manner.

The spin effect in the algebraic fractal

The figure below describes the rules of composition that lead to the spin effect. We can see that the difference between the spin created by authomorphisms composition and the composition of clusters of semantic cones is given by a change of poles. Two sides of the rhombus in the figure, and the not-axial diagonal form diagrams of composition. The sense of arrows indicates the sense of composition. We can notice that the spin difference between two consecutive dimensional cycles proves the repeatability of the general structure at every two new degrees of complexity. This is one of the most important detail that can assure general pattern’s transportation at different levels of complexity of the informational fields.

An example of first and second degree cycle

By looking at the traces drawn with the same colour in the previous table we can differentiate for A1 six patterns identified by the six colours (A11, A12, A13, A14, A15, A16) in the second degree of cycles complexity form. Each of these differentiations have a quadratic structure describing the symmetries of the structure. By considering this detail we obtain a separation of the informational field on a double or multiple riglated shape, in which can be determined complex structures of cyclic interconnected traces with 6 at power n elements.

The structure of a letter at the second dimension of the algebraic fractal development is more complex than a simple pattern repetition of the cyclic model. This fact leads to specific properties for any new algebraic fractal complexity level

THE SEMANTIC OF SHAPES

If we analyse the shape in which semantic cones are arranging in the composition matrices that are described in the tables attached to modules, we notice several patterns. These patterns suggest the chemical language of elements association, and is a new line of differentiating the information.. In general any new line of differentiating the information permits to identify new kinds of symmetries, and structure information on new structuring dimensions

Such structured information can be read only if all structuring lines are identified. These lines permits to identify new kinds of symmetries.

Considering the basic fact that the general pattern given by the table of composition repeats at any two level of complexity of the algebraic fractal, and that at any new level there are also specific properties we can conclude that the structure of symmetries described below will be enriched at the upper levels of complexity of the algebraic fractal, giving new logical properties specific to any level.

From the informational field specifics this fact gives a bridge with physics, and fields theories treated in a semantic way. The general conclusion of this superposition is convergent with the principle of an universe that is capable to communicate, because it has an basic alphabet , a basic grammar, and a basic semantic at any level of complexity of the algebraic fractal. These properties characterise the manifestations of the universe.

letter

TV

Symmetrical symbols (and ); (and )and ( and );

Self symmetric symbols

Triple non-commutative symmetry(, , ) In this case the symmetric ofis on diagonal symmetry given by * and the symmetric ofisin relating the sets (,,)and(,,) with(,,)and(,,)

ACKNOWLEDGEMENTS

My personal thanks to my friend and collaborator Adrian Colomitchi who wrote all the programs in Java, describing the mathematical phenomenon.

My personal thanks to Mr. Florin Talpes, general manager of the Softwin company, who financially supported part of this research.

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