The scale dimension – dimension, regarded as the degree of freedom in the theory of Infinite Hierarchical Nesting of Matter, which characterizes the location of all known objects in the Universe at large-scale ladder of levels of matter. With SPФ symmetry one can make the transition from a system on the level of matter to similar system at a different level of matter, with the change in size of the system is accompanied by at least two more parameters, for example, the mass and velocity of processes. 
This implies that the scale dimension differs from the usual three-dimensional spatial dimensions, and is a special degree of freedom. In the study of matter carriers, which embody the scale dimension, revealed fractality of space systems, their self-similarity, hierarchical structures and nesting of small systems into large systems, similarity of matter levels. The transition from a certain level of matter to an increasingly lower levels reveals the depth of the space-time – the objects are reduced in mass and size, and speed of the local time from the perspective of an outside observer increases.
In the research, which uses scale transformations and spatial dimensions, the scale dimension may be studied by geometrical methods, and thus beyond the scope of the geometry. The idea of the scale dimension finally took shape in the writings of Robert Oldershaw, Sergey Sukhonos and Sergey Fedosin.
Search and research prospects of new spatial dimensions involved many scientists and philosophers. Helena Blavatsky wrote:
The familiar phrase of the fourth dimension of space can only be reduced over the full form of: – the fourth dimension of matter in space ... The course of evolution may have to introduce us to the new characteristics of matter ... 
As can be seen Madame Blavatsky believed the fourth dimension is not just another spatial dimension, and dimension-mediated properties of matter that can become aware and approved in the future.
P. D. Ouspensky for describing the properties of the fourth dimension came from the fact that the motion of a point beyond itself leaves a trace as a line, a similar movement of the line gives the trace in the form of surface, movement of the surface in a direction not associated with the surface, gives a three-dimensional body. Hence, the displacement of three-dimensional body in non a three-dimensional direction should lead to a trace as a four-dimensional body. Ouspensky also drew attention to the fact that the line is a set of points, the surface – the set of lines, and the body can be represented as a set of surfaces related to each other. Consequently, the four-dimensional body shall consist of a set of related somehow to the whole three-dimensional bodies.
On the other hand, the line is limited to points at the ends and gives the distance between them, the surface is bounded by lines and dots, and determines the distance between these lines and points (an example is a circle with the center and circumference), and three-dimensional body is limited to surfaces, lines and dots with a certain distance between them. Then the boundaries of four-dimensional body can be three-dimensional bodies, and probably the surface, lines and points. Ouspensky also wrote:
Then – a point we consider as a section of line, the line as a section of surface, the surface of a section of the body. By analogy with this the three-dimensional body (a cube, sphere, pyramid) can probably be regarded as a section of the bodies of four dimensions, and all three-dimensional space as a section of four ... The Fifth Dimension should not be considered as lying outside the mind, but as a property of consciousness itself, – that line or what direction that should increase awareness. 
In physics, the idea of extra spatial dimensions is used in the theories of unification of fundamental interactions. One of the earliest theories was Kaluza–Klein theory (Theodor Kaluza, 1921), which tried to unite electromagnetism and gravity. Due to the unobservability of the fourth spatial dimension in our world Oskar Klein in 1926 suggested that this dimension compactified and has a very small size. In string theory used 10-dimensional and 26-dimensional space-time, and additional measurements are also subject to compactification.
Historic-philosophical analysis of concepts of spatial dimension shows,  that the earliest models of the universe were in the form of eggs (zero-dimension), replacing first band one-dimensional model of ancient Egypt – the universe as extended the Nile river, over which the pillars extend the sky in the form of a flat roof, to which the bottom nailed the stars. Then came the two-dimensional model of antiquity – Earth of Homer (VIII cent. BC) likened to a convex shield on all sides was surrounded by a river-ocean and covered with starry dome, and the medieval flat Earth was on the whales or elephants, and was also covered starry dome.
Ptolemy's model of the universe (II century AD.), was almost two-dimensional, in it around the Earth on epicyclical orbits rotating planets and stars (the latter are on a rotating spherical dome). At present, in science dominates the heliocentric model of the solar system and three-dimensional model of the universe of Western European civilization. Thus, there is increasing of space dimension in all models of the world and all areas of beliefs about it. This is confirmed by the history of painting, where the ancient paintings are one-dimensional, two-dimensional in the Middle Ages, and only in the Renaissance they acquire a third dimension.
Since the beginning of the twentieth century, artists began to attempt to show the new fourth dimension. The most impressive results are achieved in the paintings of M. C. Escher and Salvador Dali. The way from tape to three-dimensional space has done architecture, similarly to painting. One of the most famous attempts to break into the four dimension can be regarded as an architectural work of Le Corbusier. These examples of painting, cosmology and architecture conclusively proved that over the past five thousand years our civilization has evolved from a one-dimensional to three-dimensional space of consciousness, and is currently in the transition to the four dimension.
There are different points of view on the scale dimension, which underlying these or other properties of objects in it and thereby characterize the very scale dimension.
For example, Edmund Edward Fournier D'Albe believed,  that the ratio of linear dimensions of the stars and atoms, as well as the ratio of their durations of similar processes, expressed as the number 1022. Yong Pyo Young by comparing atoms and galaxies found for the coefficients of similarity in size and time of the order of 1030.  Thus the difference of time speeds at different levels of matter is emphasized, as a consequence of the properties of the scale dimension.
In terms of geometry that describes spatial forms, the concept of "scale dimension" is some interpretation of the concept "fourth spatial dimension". One can imagine some fourth axis of space, move along its three-dimensional body and assume that the four-body is the entire set of forms, which took three-dimensional body during moving along the fourth axis of space. Similarly, movement of a point (zero dimension) yields a line (one dimension), motion of a line parallel to itself delineates a plane figure (two dimensions), movement of a plane figure in direction of vector does not lie in the plane of the figure, leads to the bulk body. In contrast to this approach, scale dimension has the additional property – not just geometric objects move in space for formation of the fourth dimension, but it can still change its scale. That is, three-dimensional body can change its size (volume) when driving along scale axis, similar to the area can vary the shape and thickness of the line. As with any axis of the coordinate system in space-time, scale axis is different from all other axes in relation its direction, and that is enough for geometry. For physical systems is convenient to assume that the direction of the axis shows in the direction of increasing scale, and opposite direction – into the interior space.
The fourth dimension is very difficult for the imagination. One way to see its expression – imagine yourself shrinking in size and observing the surrounding space with objects in it. Another option – to draw a volume in space surveillance and permanently reduce its size. The process is endless, and despite the fact that outside of the scope, limited quantities beyond the Planck scale, quantum physics do not imagine what there happens, we can not say that there is no space. This decrease in the volume of observation reveals, moreover, special features of space, which are difficult to apperceive – namely, the infinity of space in an infinite number of points. Since all five visible (or represented figuratively) dimensions (including time) are of infinite length, then assume the finiteness of the fourth dimension at small scale there is no reason to.
In philosophy, the concept of space is defined as a form of existence of matter, having the property length, and time – as a form of existence of matter, having the property of duration of existence. In theory of relativity an elementary event is described by spatial coordinates and time at which the object in question is in the given spatial point. Consideration of time axis as equivalent axis of reference system was only possible due to the limited speed of light, because the length of the interval of the time axis is determined by the product of speed of light in space and time, must be finite. From this it follows that time axis in its origin is not identical to any one spatial axis, and physical spacetime is not equivalent to any n-dimensional space of geometry. Scale dimension, as well as time, occupies a special position in the determination of a complete physical frame of reference necessary in each case for the solution of theoretical and practical problems.
Robert Oldershaw considers a discrete self-similar scale relativity, which can be found in the scale dimension as a fundamental principle of symmetry of nature, which extends the principle of general relativity in the study of physical systems. The main levels in the observed world Oldershaw relates atomic, stellar and galactic levels of matter, and in nature must exist not yet observed levels of matter at the micro scale and on the mega scale.
Between the levels of matter according to Oldershaw connection can be established in the form of the same factors of similarity in size and time equal to Λ = 5.2 ∙ 1017, as well as the similarity coefficient in mass X = Λ D = 1.7 ∙ 10 56, where the exponent D = 3.174. This leads to a difference in the gravitational constant at different levels of matter – strong gravitational constant at the atomic level, the usual gravitational constant for the level of stars, and assumed to be essentially reduced the value of the gravitational constant for the level of galaxies: m3 • s–2 • kg–1. If to substitute these gravitational constant in the equation for the metric of the Einstein-Hilbert, different results are obtained – for example, depending on the matter level considered the black hole can be a proton or an appropriate stellar or galactic object.
Oldershaw considers it necessary to extend the principle of relativity in the sense that physical laws should be written so that they depended not only on the position in the geometrical three-dimensional space, from the time, of orientation, motion, and the position of the reference system on a discrete scale ladder matter, but also from the choice of the level of matter at the scale axis . According to him, if between the levels of matter holds the exact cosmological self-similarity (in the immutability of the coefficients of similarity for all levels), physical laws and relatively constant at these levels should be identical.
Sergey Sukhonos introduced into consideration the scale axis (M-axis) as a special, fourth spatial dimension, and disposes on it all the objects of the universe. In this case, he discovers that in the arrangement of groups of objects, there is order, corresponding to a logarithmic increase their size.  In connection with this Sukhonos makes the assumption that the observed distribution of groups of objects, has its cause harmonic oscillations in four-dimensional space, which generate nodes — three-dimensional stable systems. To substantiate this point of view are considered the natural oscillations in the form of standing waves in objects of different dimensions, when the length of an object always fits a whole number of waves.
One-dimensional case for a string, sandwiched on both sides, is shown in Figure 1. String is linear system, the excitation occurs in the plane, and standing wave node represents a point object. Next will be considered dimension of systems in accordance with the dominant length. If we denote Nд – the dimension of the motion of the system, Nc – the dimension of the system, Nу – the dimension of the system nodes, then for the string can be written:
Sukhonos suggests that (1) is satisfied for all values of Nc. Figure 2 shows two-dimensional (Nc = 2) case in the form of a circular flat membrane.
With vibrations of the membrane on the surface appear linear ring structure (the dimension of the nodes Nу = 1), which seemed to mark the places on the membrane, where there is no movement, representing linear " nodes" of standing waves on the plane. You can see that for a string in Figure 1 the oscillations occur perpendicular to the strings, and transverse vibrations in Figure 2 are also perpendicular to the plane of the membrane. On the membrane can be standing waves along the radius in the form of rings, and can assume the wave along the rings themselves. Space of excitation, which is seen in ring structures of antinodes vibrations, is three-dimensional.
We now turn from two-dimensional medium to three-dimensional medium (Nc = 3). In this case, the dimension of nodes equals two (flat wall of cell volumes in Figure 3), and the space of excitation must be four-dimensional.
In his early works Sukhonos analyzed the known idea that the fourth spatial dimension is orthogonal to three-dimensional space. He suggested that the forced pulsation of the three-dimensional volume (Fig. 3), its periodic compression-expansion should lead to a three-dimensional standing waves whose nodes are the walls of cells. To confirm this, he is considering an experiment in which a cubic volume of the liquid saturated with light particles (suspension) is compressed. An example is the cooling liquid metal alloy with different impurities. During the cooling the volume of casting will be compressed from all sides, providing compression orthogonal to three-dimensional space. This alloy during solidification is filled with so-called grains, two-dimensional boundary between which is formed by a suspension of (additives, pores, etc.). These boundaries are two-dimensional nodes of four-dimensional vibration in three-dimensional environment.
If to realize an increase in the dimension of the medium to a value of Nc = 4 and create some movement in it, is orthogonal to three-dimensional space, then in the medium will formed nodes whose dimension be equal to three (Nу = Nс – 1 = 4 – 1 = 3). Sukhonos suggests that such nodes can be three-dimensional body whose stability is caused only by the fact that they are nodes of five-dimensional oscillations in the four-dimensional environments. These nodes form a stable three-dimensional world of objects in the Universe, which is a complex superposition of vibrations four-dimensional space. The duration of the existence of systems of the universe, their stability is associated with power of nodes, with the energy of vibrations generating the systems. This implies that the description of the diversity of the universe can be accomplished using the theory of waves and vibrations, but in an environment of higher dimension than hitherto used traditional science.
Number of basic dimensions in physics is determined by the number of degrees of freedom or independent variables that determine the location of the physical body or its elements, considered as points in a given frame of reference. The number of dimensions or degrees of freedom gives the dimension of the used space-time. By adding of scale dimension to four-dimensional space-time, we obtain a five-dimensional manifold, which includes the usual space-time. According to the order of historical understanding it may be written in the form (3+1+1)-space, where in the first place reflects spatial dimensions, and then dimensions of the time and scale. In terms of geometry it is convenient for the axis of all the dimensions to be perpendicular each other.
According to Sergey Fedosin, scale dimension is a manifestation of nesting of matter and a consequence of the transformation of the fundamental forces at different levels of matter. Scale dimension includes a fourth spatial dimension (the transformation of an infinite set of objects by changing the size leads to a new similar set), but also requires conversion of mass and velocity of the processes (the rate of time) in objects when observer is moving from one level of the scale axis to another level. This follows from SPФ symmetry, whereby the physical laws of matter at different levels remain unchanged from the viewpoint of local observer. As a result, there is the scale invariance of physical laws, and the principle of general covariance expands, taking into account the fact that at different levels of matter are different in power of gravity fields. In addition, the relativity of scale dimension leads to what "correct" physical equations must be of such form that the scale conversion left them the same at every level of matter.
In four-dimensional space-time, simple four-dimensional body can be considered as a body consisting of a set of forms that takes a certain three-dimensional body for a certain period of time.
Model of a four-dimensional body with regard to the three spatial dimensions and the scale dimension is a set of three-dimensional bodies, located on a specific law on the scale axis. These three-dimensional bodies must change their dimensions in the appropriate size range, set the dimensions of the four-dimensional body. Incision of four-dimensional body at some point of the scale-axis shows three-dimensional body as the cross section of the scale-axis. More precisely, in point of the section should be three-dimensional image of half the three-dimensional body (to see the rest of the body is necessary to turn and look at it from the other side). In place of the cross section one can also imagine a projection of three-dimensional image of the half body on one side of the plane of the section. Similarly, a model of three-dimensional body is a discrete or continuous set of closely interrelated surfaces, together giving an image of this body, and the section of the body gives a surface. Relationship between three-dimensional bodies in this four-body can be defined by the similarity theory (see similarity of matter levels). Division by cutting three-dimensional body into pieces and carrying of these parts in space does not mean the loss of three-dimensional body, it begins to exist in a new form and even has the opportunity to build back to its original state. Four-dimensional body can be thought as a separated individual three-dimensional bodies, in various configurations or when an assembly take place, occurs one or another four-dimensional form.
The trivial case is possible when the scale axis is combined with one of the usual spatial dimensions. In this case, the instantaneous transfer of three-dimensional body along the axis of the spatial-scale dimension gives a trace in the form of a degenerate four-dimensional body. Outwardly, it looks as though three-dimensional body is disproportionately altered in some spatial direction, elongated, compressed, warping, bends, twists, etc. In painting, there are works that reflect similar experiments with three-dimensional space. Scale change can be represented as a contraction of three-dimensional body in a certain direction until the transformation of the body in the plane, with subsequent expansion in the opposite direction to the isomeric form of three-dimensional body. Thus it turns out the body, turned inside out, which left replaced by right.
Introduction of time increases the number of dimensions to five. If scale dimension is considered, taking into account the time in the volume of space where there is a three-, four-or five-dimensional body, we can trace the change of the scaling properties (volume, mass, material composition and other properties of the body) as a function of time.
From the physical point of view scale dimension can not come down simply to the spatial proportional changes in body shape and volume. If there is a small wooden model of a multistory building, then is constructed in the full-size building can not exist, because of its weight, it will crush the lower floors. The reason for this is that with the increase of size the mass increases in proportion to the cube of this size, that is much faster. This implies that similar to each other bodies at different levels of matter can not consist of one and the same substance in the same state. Properties of the material should be such that at every level of matter to ensure the existence of objects. As a rule, as the size of the objects in the transition from one level to another matter is increasing, there is a reduction of the density of objects and of the characteristic speed of its matter.  Latter can be understood as a slowing of speed of time of similar processes. For example, the larger-sized objects, the longer it takes them one revolution around its axis of rotation, longer lasting other typical processes.
When we moving deeper into the matter is found the opposite trend. Thus, the nucleons at the atomic level of matter are analogues of neutron stars in the star level of matter, and the average density of the nucleons over the matter density of neutron stars (6.1∙ 1017 kg/m3 and 3.7 ∙ 1017 kg/m3, respectively). Characteristic speed of the matter of the nucleons is the speed of light m/s, and for the matter of neutron stars, the characteristic speed is m/s. These speeds are determined so that with their help, according to mass–energy equivalence, it was possible to determine the full energy of the corresponding object: for a proton with the mass the absolute value of full energy is , and for a neutron star with the mass the same energy is . If neutron stars are composed of more dense nucleons then nucleons must consist of more dense particles of matter than the nucleons themselves.
In accordance with a change in physical properties of matter at different levels of matter there is also changing the existing forces. If at the level of planets and stars the main force is gravity, forming the spherical shape of bodies and control their motion near each other, then at the atomic level the same role is played by strong gravitation. In this case, strong gravitational constant is by many orders higher than the normal gravitational constant.
The hierarchy of space-based systems is that they are grouped in separate scales, located about equidistant from each other on a logarithmic scale sizes. This implies similarity of matter levels, when between the various levels similarity relations are derived not only in size but also in the masses, in the speed of similar processes and in other physical parameters. Consequence of the similarity are the stellar constants, discreteness of stellar parameters, hydrogen system, quantization of parameters of cosmic systems, gravitational model of strong interaction, the substantial models of neutron, proton and electron.
Thanks to the nesting of certain matter levels in another levels the more massive objects are composed of particles of lower levels of matter. This leads to the relationship of characteristics of objects and states of matter, as well as the symmetry between the properties of particles of matter and the properties of objects, which is manifested through the relationship of similarity. In this case may be found the basic and intermediate levels of matter. At the basic levels of matter current fundamental forces, gravitation and electromagnetic forces, reach a maximum. At the same time the density of matter objects increasing; the gravitational force of attraction at first oppose the electromagnetic force, and then strong interaction. Examples here include:
The role of weak interaction reduces to the fact that under the action of the fundamental forces and the strong interaction of objects after their formation take place a slow transformation of matter. For example, a neutron in a very large time by the standards of atomic processes turns into a proton, an electron and a neutrino. The transformation of the matter can be significantly accelerated by external factors. Thus, the incident on an elementary particle a neutrino can easily convert the matter of the particle and cause it to decay into other particles.
From the described is seen that the realization and manifestation of the scale dimension in nature can be represented as an infinite scaling ladders with steps – the levels of matter, which contain all known objects of the universe. In this case, similar objects at different levels are not simple enlarged or reduced copies of each other, as distinguished by their matter and its properties, and rate of the time. At the highest step of the scale space ladder we are seeing large galactic system and Metagalaxy, behind which must be placed even larger objects. At the bottom the elementary particles are discovered, still hypothetical partons and preons, as well as other smaller carriers of matter. In particular, the particles of which must consist of nucleons, is given the name praons.
The scale dimension characterizes the nesting levels of matter as a structural feature that specifies the order of material objects, adjusting their properties. There is a law of philosophy of breeding structures, which is formulated as follows: 
"Structures are contained in the essence of things and events and determined their quality, have mechanisms of reproduction, resulting in maintaining the integrity of these structures and distribution them through other things and objects. "
Another philosophical law describes the similarity of the carriers on different scale levels of the matter:
"Carrier distribution in mass (in size, while others related to the mass parameters) take place according to the law of geometric progression, highlighting at each step of the characteristic and dominant carriers, the major carriers and their satellites, and between carriers in separate steps, and between whole sets of steps are observed ratio similarity."
Stability of large-scale staircase of matter as a manifestation of the structure of nested levels of matter derives from the very method of formation of new material objects is dynamic in nature and is a consequence of multiple interactions of matter particles and field quanta. On the one hand, the disparate pieces of matter pulled together by gravitational forces and form a dense matter of new massive objects. With the growth of the mass of the objects in them is growing internal pressure increases the energy of the particles, which leads to a change in state of matter. At a basic level of matter occurs balance between the inflow and outflow of mass at the objects. This is illustrated by the massive main sequence stars, which are due to the high temperature emit huge amounts of energy and losing mass due to the expiration of the matter, thereby compensating inflow of matter from the outside. For neutron stars are also detected a slight variation of their mass, since the incident upon them matter "sprayed" in thermonuclear flashes. Apparently, neutron stars, as stellar analogs of the neutron, and magnetars, as analogues of protons have a maximum density which is attainable in stable objects under normal gravitation (the same should be for the nucleons and the strong gravitation).
On the other hand, the theory of infinite hierarchical nesting of matter predicts that the quanta of the gravitational field are produced mainly in the processes associated with the formation and transformation of matter of objects at the basic levels of matter. Thus, the formation of neutron stars in supernova explosion accompanies powerful neutrino emission. Neutron stars and magnetars can emit jets; they are sources of X-rays and gamma rays, as well as cosmic rays. The same is true for nucleons – they emit a neutrino, fluxes of matter and electromagnetic radiation. All these radiations may be part of gravitons, the carriers of the gravitational field in the Le Sage's theory of gravitation. Calculations show, based on the energy density flux of gravitons that the source of gravitons for normal gravity are the emission of particles at two or even three main levels lower than the star.
Thus, the fundamental fields forming objects at different levels of matter, and these objects in turn generate photons of fundamental fields, already operating at higher scale levels of matter. With regard to the objects of intermediate levels of matter, they are formed not only by the action of the fundamental forces, but also in the process of interaction of objects with each other or with the increase in mass, or the disintegration into smaller components. Thus, during the formation of planets of Solar System in numerous clashes occurred a separation between the planets, moons, asteroids, meteorites, comets, cosmic dust and micrometeorites, and these objects have taken some scale niches in mass and size. Analysis of these niches shows that the objects in them to the masses and sizes relate to each other in a geometric progression, and the transition between niches take place by the law of transition from quantity to quality.  In each niche can be allocated specific major carriers, standard carriers and the boundary points of action, in which objects become unstable under existing conditions.
Scale dimension describes not only the natural physical or chemical related objects, but also suitable for describing of the living beings. It turns out that living beings and carriers of life faithfully replicate key features of objects of different levels of matter, since arranged at the same levels of matter in relation to their size and mass.
Like other carriers of matter, living beings can form an infinite nesting of levels of living, so that in every organism, there are many levels with the appropriate living carriers at these levels. Living matter is a complex interplay of living and nonliving, and the living is clearly governs and dominates the inanimate. In turn, the inanimate has living inside, but apparently not in the manifest, in a weak form. Evolution of living in scale dimension is not only the progress in space and time, but also the transformation of the structure of the living in order to adapt to the changing conditions of existence of the new scales.
Study of scale dimension and objects belonging to it is engaged in the theory of Infinite Hierarchical Nesting of Matter. This theory presents itself as an interdisciplinary systems science and part of systems theory, which deals with the space systems of various scales. Discovering of scale dimension for scientific research is not just pushing the horizons of science, but also allows us to find previously unknown patterns in physics and mathematics.  The detection of direct links between micro, macro and mega-worlds of our universe allows us to understand its evolution as the evolution of hierarchically nested levels of matter, to clarify the picture of the world,  and to include in the scientific thinking new concepts and lines of development. From a practical point of view the substantial models of elementary particles built on the base of the theory of similarity, can make significant and necessary complement to the quantum mechanics and the theory of elementary particles, which can lead to useful results in physics and in technology.
New opportunities are created in biology as the science about life and living beings. Living beings can be understood as the active open systems with an infinite nesting of living systems inside and deep inner sources of ordering, which dictate behavior, and ensure the functioning of such systems. The expansion of the living can take place both within the same level of matter (moving in uninhabited territory), and by moving to new levels of matter. Last inevitably requires adjustment of the living forms of existence, since a large increase in the size of the habitat make problems with the integrity of the entire system in the environment and the slowdown resource allocation processes. Knowledge of the existence strategy and of the evolution of living is quite important for the development of humanity as a whole.
In medicine, science has come to ensure that at the genetic level to reproduce clones of living organisms from a single genetic material and correct gene to cure some diseases. It is also planned to use genetic methods to protect against dangerous micro-organisms and viruses. However, as it follows from the theory of infinite hierarchical nesting of matter, must exist such creatures whose size is much smaller than prions, the smallest of the currently known particles of the living. In this case, the disease may be associated with these creatures and finding of it is beyond the capabilities of modern medicine. To study these living particles now known nanotechnology should be replaced by even more powerful research methods.