Dimensional numbers

The scope of applications of dynamic numbers is unlimited because all objects have internal and external variable properties that can be regarded as internal deformations of that object. All accumulations, all sets are junctions of these numbers that form deformed continua. Junctions have a property that without simplifications they are not interchangeable because even equal numbers because of deformations are not equal. To manipulate them interchanging, dividing is impossible. This means that mathematics can occur only in resonance layers where we have structures of identical deformations.

The question is what can we do with such continua? Since the main concept is deformation, we can analyze this aspect, trying to find instruments for this purpose. The main operations go to number tables that are used to describe inhomogeneities or gradient maps of displacements. Also, there are such important concepts as “resonances”, “the same level”, “symmetry”, such operations as compression and extraction. These are the main processes and we need formalized methods of description.

It is convenient to express the dynamic number in a coordinate system as a dimensional number. Static, undeformed numbers are number axes, numbers of the first dimension. Deformations are described by the second-dimension axis, which shows internal oscillations of the number. The simplest form to show such inner oscillations is using internal fractions. Let us take natural two-dimensional numbers. This number means that there are no fractions and that oscillations inside and outside are possible by full numbers. This internal deformation may be outside or inside. 1 #2 is a two-dimensional number having internal deformation, which equals two units. According to the equation we have the correct equality 1 #2 = 1-11 =3. In other words, from the perspective of the first-dimension numbers, we have a unit which because of deformations equals 3, i.e., 1 = 3.

The drawn-out example shows the simplest dynamic number, in which we have the deformation system of number seven to the internal space of deformations. I have chosen the simplest natural number. Let us say that combining two dimensional numbers, we need to have the system of internal deformations and transform them into dynamical deformations of the result. The process should be defined by the rules of addition, according to the set properties of continua. The simplest possibility is when deformations are combined. Here we have natural numbers and there is no negative dimension, however we can introduce an additional condition, determining the direction in which the deformation moves - increases or decreases - and set out how to associate various possibilities: increases-increases, decreases-decreases, increases-decreases and so on.

The line of the graph shows that there is a concept of dynamical zero, which is nothing in the first dimension, while looking from the perspective of two dimensions, it may have an internal deformation which does not equal zero. That is 0 ≠ 0 #2. The remainder in the internal dimension means that zero is not absolute nothing. Therefore, zero is called dynamic, having internal oscillations.

The axes of numbers were marked above. Having applied this principle to space, we form space continuum from three axes of the first-dimension numbers that have at least one internal deformation. An interesting question is how different numbers are combined in this case. This method can be used to graphically illustrate arithmetical operations (?), where the first-dimension numbers and deformations are added separately.

We see that the intersection points of internal axes are eccentric, having a version of static numbers plus the difference or displacement. If you want to calculate it, you should combine the internal deformations according to set rules. Thus, you can add as many axes and internal deformations, as you wish, only you have to think through well the rules by which the deformations are combined. It is evident that it depends on the chosen properties of continuum.

I have already shown that all internal deformations can be pushed out into virtual external dimension. This is especially simple with natural two-dimensional numbers, as all numbers are positive, that is, not fractional. I have already shown how to do this - you simply take internal units outside. In this case one can expand all two-dimensional numbers into the junction of the first dimensional numbers and to transform the graph into their density table.

:Let us say there is the following junction 1 #2, 1, 1 #4, 1 #3, 1 #2 = 3, 1, 5, 4, 3. Then we combine this junction with 1, 2, 5, 3, 2, draw the number table adding natural densities and get the deformation system expressed by the table that can be included into the calculation of deformations in higher dimensions or simply create numeric density gradient where a static distribution of compressions and decompressions is marked. If we distribute the planes according to the principle of fractals, we could model the deformations from the point of view of a part and the whole. This system is very useful in graphical modeling and artificial intelligence, which should be able to move from the part to the whole and from the whole to the part. Tables-planes of dynamical numbers is a simple version of such movement. To create a more precise model, of course, you should give more effort.

To express a dynamical number of a higher dimension without generalization is very difficult. The simplest way to do this is to level out the dimensions of units, extracting outside all the virtual units. Let us say there is 7 with the following internal junction 1 #1, 1 #3, 1#2, 1 #1, 1#2, 1 #4, 1 #2. We get 7 with 15 virtual units. That is, we have a deformed 7 that equals 22. Thus, there is 7 with internal deformation 15, 7 #15. Now if we want to determine how this 15 is distributed inside we ought to know the matrix of deformations, if there is no matrix, we distribute equally, similarly to the water in a form.

There is no such continuum where 1 = 1. Mathematics that assumes this is not precise. Precise mathematics is the one that considers all deformations. For this purpose, we need numbers that can have internal deformations such as simple or complex dynamical numbers as an opposite of static numbers.

The text above is a way to raise the quality of consciousness into a higher level, expand the horizon of knowledge, better understand the world around us in its deepest root, where chaos and dynamical numbers rule.