Physics/Essays/Fedosin/Infinite Hierarchical Nesting of Matter
This page is an essay by Sergey Fedosin, a Russian physicist and academic, and represents his original research and personal opinions. It should not be taken as representing standard scientific understanding, but is presented here for discussion and review.
note by editor user:Derenek: While this is most definitely not a widely accepted scientific paradigm, it is an excellent example of the difference in the accepted methods of scientific writing and discourse between western scholars and Russian academics. The inclusion of historical, philosophical, and religious importance as integral parts of the theory are considered more acceptable and often found necessary by the typical Russian audience. This lies in stark contrast to the strict separation of disciplines usually found in standard western science literature.
- 1 Introduction
- 2 Core claims of the theory
- 3 Historical Background
- 4 Philosophical underpinnings
- 5 Scentific Analysis
- 6 Experimental Results
- 7 Well known supporters
- 8 Gaining popularity
- 9 Further research
- 10 Cosmology of Raël
- 11 Theory in pop culture
- 12 See also
- 13 References
- 14 External links
The proposed theory Infinite Hierarchical Nesting of Matter is a cosmological framework that suggests that matter can be divided or reduced infinitely, as opposed to atomism. As such it lies in stark contrast to the standard model making it an alternative philosophical, physical and cosmological theory. This concept is based on inductive logic and reaches conclusions about the structure of the observed universe. Metaphysical schools studying this theory focus on the fundamental organizing principles of nature. Initial versions of this theory were known as the Discrete Fractal Paradigm, and subsequently the Discrete Self-Similar Cosmological Paradigm .
Core claims of the theory
The Discrete Self-Similar Cosmological Paradigm focuses on nature’s fundamental organizing principles and symmetries. It emphasizes nature’s hierarchical organization of systems from the smallest observable subatomic particles to the largest superclusters of galaxies. It introduces a paradigm which also highlights the theory that nature’s global hierarchy is highly stratified into discrete scales or levels. Some of which we can currently observe, such as the Atomic, Stellar, and Galactic Scales. The third primary principle of the paradigm is that cosmological Scales are universally self-similar. Which indicates that for each class of objects or phenomena on any given Scale there is analogous class of objects or phenomenon on every other cosmological Scale. These parallel analogues from different Scales have strongly analogous morphologies, kinematics and dynamics.  From a purely physical point of view these similar relations lead to similarity of matter levels and SPФ symmetry, which asserts the invariance of physical laws operating on different levels of matter.
Individual observations and claims
- In this theory there are no elementary particles of matter (see preon, parton, electron, quark, Action/Reaction_Theory); instead it claims that matter is infinitely divisible. This claim lies in contrast to the theory of atomism, which assumes the existence of units of the matter that possess a minimum size.
- The Universe consists of an infinite number of enclosed levels of matter. Each level possesses characteristics similar to each preceding level. This leads to a similarity of cosmic systems; including the similarity of shapes, sizes, masses, rates of processes, and equations of motion.
- Each level of the matter includes carriers with a specific spectrum of sizes and masses. Additionally, matter is organized in stable conditions and are under the influence of fundamental forces and interactions with objects of different systems.
- Categorization of cosmic objects based on the levels of matter are the stepping stones of an infinite hierarchy of cosmic systems, similar to geometric progression.
- The progression of time regarding the rate of occurrences of similar events is much faster at a microlevel and progresses more slowly at a macrolevel.
- Each type of "elementary" particles (electrons, nucleons, etc.) does not depend on strictly identical mass nor the size of particles.
- The Universe is eternal, thus carriers of matter are constantly born and are then transformed into carriers of similar and disparate scales. This theory not only falls outside the limits of atomism, but also the Big Bang which limits the historical relevance of the Universe by claiming a moment of creation.
- The properties of space-time are determined by the structure of matter. Time is also denoted as an independent coordinate from space, which also is a derivative of velocity and development of matter. In addition to the widely used four-dimensional space-time construct, the theory of infinite nesting of matter claims the existence of a fifth, scale dimension.
- The behavior of forces such as gravitation and electromagnetism can be explained by modified Le Sage's theory of gravitation. Objects on different levels of matter generate radiation in the form of particle streams and field quanta, aggregating to form the fundamental forces acting on objects as well as other levels of matter. It is also possible that the gravitational field is ordered similarly to the electromagnetic field of an underlying level of matter. 
- There is a difference between the concepts of "quantity of matter" and gravitational mass, implying that under certain conditions, different amount of substance may possess the same gravitational properties. This follows from the dependence of gravitational forces on the velocity of bodies and the dependence of gravitational mass on mass density. It also claims bodies contribute to mass due to its gravitational and electromagnetic effects.
- Mass as a measure of inertia on the level of elementary particles is determined by strong gravitation, and at the macro level – standard gravitation.
- Distribution of systems consisting of living beings among cosmic systems have the same laws inherent to systems with non-living matter.
Quotations of famous philosophers and scientists
- That matter is divisible to infinity was claimed by Aristotle, Descartes, and also Gottfried Leibniz  in his monadology.
- Isaac Newton wrote: "Nature is very similar to itself and is very simple, performing all the great movements of celestial bodies with the help of attraction, gravity ... and every small particle motion of these bodies – with the help of other attractive and repulsive forces binding particles."
- In each particle, no matter how small it is, "there are the cities occupied by people, cultivated fields, and the sun, the moon and other stars like ours" – claimed the Greek philosopher Anaxagoras in his work on gomeomeriya in V century BC.
- Are the Worlds, where five continents,
- Arts, knowledge, wars, thrones
- And memory of forty centuries!
As Above So Below
Quod est inferius est sicut quod est superius
- This principle first uttered more than two thousand years ago, has been accepted as an axiom by followers of hermetic religious philosophy. From times of late antiquity, the Hermetic traditions began mystery schools from which, in Middle Ages alchemical science and other forerunners of modern mystery schools were born: notable groups being illuminatus, frank-macons, and rosicrucians.
- Many of the foremost scientists of the Middle Ages and present day have been connected with any of these movements, mainly because these organizations kept to themselves information inaccessible to any other. Hermetic scholars proposed the parallels between microcosm and macrocosm: in a religious sense, this analogy was understood as conformity to God with man created in his image and possessing similar divinity. However in science the statement about structural parallelism can be understood much more widely.
- Modern science increasingly confirms the truth of fundamental tenets set forth in ancient philosophical texts. In particular, the theory about similarity of processes occurring on both macro-and microlevels, is consistant with Hermetic belief. The study of extraordinary people's ideas lead to the same conclusions. Great researchers such as Leonardo da Vinci, possessed an uncanny ability to simultaneously perceive the whole and its parts; the principle of his research play prominently in the analysis of and division of phenomena into improbably small components then to their synthesis in new configurations.
Da Vinci designed the pyramid schema of mechanics, according to which: All natural forces – which he called the "four forces" – movement, mass, force and collision – are based on the system of the pyramids and follow naturally from one another. This principle of the pyramid in which energy gathers and is then lost in a geometrical proportion, has been made a basis of mechanics. "The uniform theory of field" of Albert Einstein was based on an establishment of conformity between principles of realization for all physical phenomena in the Universe – from space-time up to atom.
- On the other hand, inherent metaphorical qualities, in particular, the statement of Hermes about general parallelism, is the primary mode of thinking of pathbreakers and authors of ancient texts. “I wish to know ideas of the God, all rest – is details”, Einstein wrote. The central propositions on which the science is based, this aspiration to accuracy and unambiguity, also appear metaphorical.
This axiom regarding the similarity of all real communication between science, philosophy, and religion lies unchanged.
Kant and Lambert
In the cosmological representations of Immanuel Kant there was a recognition of the existence of uncountable sets of star systems which could be united into systems of a higher order. At the same time each star with their planets and satellites forms a system of subordinated order. "The Universe, hence, not only is spatially infinite, but also structurally diverse, as its structure includes space systems of different orders and the sizes." Putting forward this position, Kant came nearer to idea about structural infinity of the Universe which has received fuller development in cosmological doctrine of the contemporary of Kant, German scientist Johann Heinrich Lambert in 1761. Baruch Spinoza was an adherent of the Infinite hierarchical model of the Universe.
Irish scientist Edmund Edward Fournier D'Albe has made the assumption, that the scale of ranks reaches also into matter, by reduction.  According to Fournier D'Albe, a denominator of a progression, i. е. the attitude of the linear sizes of a star and atom or the sizes of a star, of supraworld and stars of "our" world, the atom of supraworld, is expressed by number 1022. Such parity of spatial sizes Fournier D'Albe distributed for the time too. One second in our world in the opinion of Fournier D'Albe – is equivalent to hundreds of billions of years in the life of infraworld, and a second in supraworld is equal hundreds billions of our years. Konstantin Tsiolkovsky was familiar with works of Fournier D'Albe.
Infinite Universes and photometric paradox of Olbers
Within the limits of classical cosmology, this paper tried to resolve the modeling of the hierarchical structure of the Universe developed by Carl Ludwig Charlier on the basis of idea of Johann Heinrich Lambert.  then attempted to solve the underlying paradox. In 1908 Charlier publisheded a theory of the structure of the Universe. According to which, the Universe represents an infinite set of systems escalating in order of complexity then entering each other. In this theory, individual stars form a galaxy of the first order, a set of galaxies of first-order forms a galaxy of second-order, and so on to infinity. On the basis of such a representation about a structure of the Universe Charlier came to a conclusion. That in an infinite Universe the photometric paradox is eliminated. If distances between peer systems are sufficiently large compared with their sizes it leads to continuous reduction of average density of substance during the process of transition to systems of a higher order. For the elimination of paradox it is required, that the mass density fall more quickly, than in inverse proportion to a square of distance from the observer. Such dependence of mass density in the Metagalaxy is not yet observed, therefore the modern explanation of Olbers paradox is based on other principles (for example, red shift, general relativity and so on). However the idea about a complex structure of the Universe and an enclosure of systems on different levels remains and develops. Albert Einstein and F. Selety discussed the hierarchical model of Charlier in 1922 - 1924 years. 
According to the fractal cosmology, the distribution of matter in cosmological systems occurs according to a certain law, depending on the size of systems, taking into account the principle of similarity occurring structures. Benoît Mandelbrot – in order to solve the mathematical theorem: infinite hierarchical (recursive) self-similar sets, for the description of the given systems creates a new term – fractal. The cosmological and philosophical views of Mandelbrot in historical aspect are well described in his unpublished paper " Two heirs to the Great Chain of Being "  and in the book written together with Yurij Baryshev and Pekka Teerikorpi .  Baryshev applies the fractal cosmological model with the fractal dimension D = 2 in order to interpret the redshift of galaxies as a result of gravity. This model with the help of dark matter can explain the observed large-scale distribution of matter and associate it with the background radiation. 
In 1937, Paul Dirac suggested that the parameters of large cosmological systems can be connected with the parameters of elementary particles with the help of some large coefficients.  The hypothesis of large numbers was also considered by Hermann Weyl,  Arthur Stanley Eddington,  Oskar Klein, Pascual Jordan and others.
Gérard de Vaucouleurs in 1970 used the hierarchical model to describe changes in the density of galactic systems, depending on their characteristic size.  The idea of nesting of matter was also considered by M.A. Markov  and D.D. Ivanenko (maximon - hadron - Metagalaxy). 
Well known supporters
The Hierarchical model of the universe is supported by large group of scientists: from Italy, among which Erasmo Recami, P. Caldirola, P. Castorina; Brazilian scientists W.A. Rodrigues, J.M. Martınez, V. Tonin–Zanchin, Slovak scientist M. Pavsic; A. Neil from U.K./Denmark; Indian scientists P. Ammiraju, K.P. Sinha, C. Sivaram, and others. They view elementary particles as microuniverses inside,  and outside such objects like black holes.   In this regard, the hypothesis of large numbers was again considered.  In addition to the application of general relativity as ideas to describe the objects of the microworld, there was another trend. The use of quantum approach for predicting the most probable orbits of planetary systems of stars. Overview of some results contained in Quantization of parameters of cosmic systems.
In the late 1970's and 1980's the idea had become so increasingly widespread that the infinite nesting of matter became suitable not only to explain certain phenomena and the guidance links between micro and macrocosm, but that it could become a new scientific paradigm.   
Another name for this paradigm — Discrete Self-Similar Cosmological Paradigm.  It implies similarity between infinite numbers of discrete matter levels, and this cosmological paradigm assumes a unified description not only of large cosmological systems (stars, galaxies, metagalaxies, etc.), but also of the smallest objects – molecules, atoms, elementary particles, etc. Due to this widespread support, in Russia, the theory of infinite nesting of matter is considered a full fledged theory in systems science and systems theory, which are intended to describe cosmic systems, their origin and evolution.
This cosmological paradigm completely abolished the formal restrictions of atomism in the theoretical and experimental study of the levels of matter such as elementary particles. Infinite hierarchical nesting of matter claims the unacceptability of the general theory of relativity to describe the entire Universe, and precludes the Big Bang as a likely scenario of the Universe's development. The theory is acquiring great importance in the study of universal mechanisms of formation of objects, the emergence of fields and forces, their origin and interaction at different levels, and of matter in an infinite universe. An important result was the justification of a fifth, scale dimension of space-time.
Compilation and systematization of facts substantially accelerated in the beginning of 21st century, thanks to artificial satellites, modern means of observation – infrared telescopes and computer analysis of accumulated material, and deepening knowledge in the field of elementary particles.
The focus of the authors specified below has been directed to the design of the theory of infinite nesting of matter as an independent and necessary step for further progress in scientific research.
Robert L. Oldershaw
Robert L. Oldershaw , the independent researcher of college Amherst (Massachusetts, USA) in a number of works since 1978 developed models of cosmological self-similarity (The Self-Similar Cosmological Model). He has allocated three basic levels of matter – nuclear, star and galactic levels. According to his work, matter is concentrated to the given levels, basically in the form of nucleons and stars, and stars also in the majority are a part of galaxies.   Oldershaw remarks, that the overwhelming quantity of matter in space contains in the lightest elements – hydrogen and helium, and at the level of stars – in dwarf stars with masses ranging between 0.1 – 0.8 solar masses. In addition examples of similarity exist in:
- Rotation of carriers near each other acting under the action of force, decreasing in inverse proportion to a square of distance.
- Often observable jets and emissions of matter of the identical types form in stars and galactic systems.
- The attitude of the sizes of the greatest atoms to the size of a nucleon of the same order, as the attitude of the size of greater star systems to the size of a neutron star.
- Dependencies between spin and mass, between the magnetic moment and spin have the identical form at nuclear and star systems.
- Rydberg’s atoms show dependence between radii and the periods of fluctuations electrons, very similar to Kepler's law for planets.
Definition of coefficients of similarity in mass, in size and in time of processes between nuclear and star systems. Oldershaw carries out comparisons of the Solar system and Rydberg’s atom with numbers of orbits n = 168. Concluding that compared to hydrogen there correspond stars with mass of the order of 0.15 solar mass. Additionally he claims the coefficients of similarity, in size and time are considered equal to each other and have the value of Λ = 5.2∙10 17 , and the coefficient of similarity in mass has the form ΛD = 1.7∙1056, where the exponent D = 3.174 . As a result of such comparison it begins to be possible to do exact predictions of mass and the sizes of stars, galaxies, the size of proton, the periods of rotation of galaxies, etc. Oldershaw believes that elementary particles should be treated as charged and rotating black holes, whose radius in the first approximation can be estimated from the Schwarzschild equation:
where is the constant of gravitation, acting on the given level of matter, and for the atomic level, for the level of stars, for the level of galaxies.
Assuming that strong gravitational constant m3•s–2•kg–1, Oldershaw calculates a matching radius of an electron being 4∙10-19 m, and the radius of the proton 0.81∙10-15 m. Stars and galaxies are assumed also to be objects like electrons and protons. In particular, at the level of stars, black holes are attributed to the electric charge with value of up to 1.5∙1018 C. At the level of galaxies globular clusters of stars correspond to an electron. Galaxies then correspond to the proton and the more massive atomic nuclei. To estimate the size of globular clusters and galaxies it then becomes necessary to multiply the radius of the electron and radii of atomic nuclei by the value of Λ2. As can be seen from this comparison, there is no complete parallel, since black holes are only suspected in some globular clusters and galaxies, but do not obscure these objects completely. Therefore, Oldershaw introduces for the electron, a concept of a halo consisting of tiny particles that form the matter of the electron. This halo surrounds the center of an electron, just as external stars in globular clusters surround the nucleus of the cluster. According to Oldershaw, dark matter should consist of black holes.
Sergey I. Sukhonos
Sergey I. Sukhonos  in a number of works  has shown existence of the separate material formations located on an axis by 13 discrete groups through equal intervals in a logarithmic scale. The greatest discovered size belongs to the Metagalaxy, the least – to a hypothetical particle called a maximon, some twenty orders smaller then nucleon. Metagalaxies, nucleons, and maximons belong to the basic levels of matter. Between them, are all known objects whose properties periodically repeat with the attitude of the sizes near 1022. Sukhonos highlights the fractal phenomena in nature, and also proves bimodality when objects show supplementary properties: spiral and elliptic galaxies; subdwarfs as primary stars of the Galaxy with deficiency of heavy elements, and usual stars of the main sequence; planets external and internal; processes of synthesis and division, monocentric and polycentric structures at different levels of matter. For an explanation of specified laws Sukhonos utilizes ideas about a fourth, scalar dimension and corresponding interaction, and also wave representations. He uses the term "wave of sustainability". Which refers to a scalar axis divided into three major intervals − microinterval, macrointerval and megainterval (the word micro here means small, rather than a millionth of the size).
Yun Pyo Jung
Yun Pyo Jung  from Korea criticizes the theory of the Big Bang in connection with logical contradiction – on greater scales nearby space objects never will make more than one orbit near each other because of the constant expansion of the Universe, despite of gravitational communication between them. Proceeding from idea of recursive cosmology, by comparison of the sizes between kernels of galaxies and nuclear kernels, galaxies and atoms, congestions of galaxies and molecules possessing a factor of similarity in size about 1030 can be defined. The same value is deduced for factors of similarity in time, connecting duration of the similar processes in nuclear and galactic systems. 
Sergey G. Fedosin
Sergey G. Fedosin , the physicist and the philosopher from Perm, Russia, mathematically has successfully calculated the basic features of the theory, having passed from qualitative conclusions to quantitative results in his monograph on the theory of similarity. 
Eighteen levels of matter from preons up to metagalaxies were divided into basic and intermediate stages in masses and dimensions, and between them can be derived relations of similarity. The main scales in this range of levels of matter are the level of elementary particles and the level of stars. At these levels there are many of the most stable and long-lived carriers; such as nucleons and the neutron stars containing a maximum quantity of composite particles and having a maximum density of matter and energy.
The matter of these carriers is degenerate, so their constituent particles are in quantum states with nearly the same energy, and therefore the states of such matter are described by the laws of quantum mechanics. In this case a neutron star contains about Φ = 1.62•10 57 nucleons, and by induction it can be assumed that the same quantum particles are contained in the nucleon. As a consequence of the similarity of the atomic level and the level of stars quantization of parameters of cosmic systems is found.
Determination of coefficients of similarity in mass Φ, in size P, and speed S, through the duration of similar processes Π is made by means of the hydrogen system. At the level of atoms the hydrogen system is a hydrogen atom, and at the level of main-sequence stars − the corresponding planetary system consists of a star of minimum mass and a planet as the analogue of the electron. Degenerate compact stars like white dwarfs and neutron stars possess their own coefficients of similarity, based on the ratio comparing the parameters of the proton. For magnetars as analogues of the proton the electric charge with value of 5.5∙1018 C and the magnetic moment of 1.6∙1030 J / T are predicted.
The ratio of radius of a neutron star to radius of a proton gives a factor of similarity of P = 1.4 •1019. Full energy of a neutron star without taking into account the energy of rest is defined by expression Es = MsC2, where C= 6.8•107 m/s – characteristic speed of particles of the neutron star, Ms – mass of the star. Similarly for a nucleon full energy En = Mnc2, where c = 2.9979•108m/s – speed of light and the characteristic speed of particles in the matter of nucleon, Mn – mass of a nucleon. The ratio of speed C to speed of light c gives factor of similarity on speed S = 0.23. The factor of similarity on time is Π = P /S = 6.1•1019. By calculation it then follows, that processes at the level of nucleon matter proceed in Π time more quickly, than at the level of neutron stars.
The theory of similarity predicts, that among stars the lightest are stars with mass of 0.056 solar mass. Such stars are now discovered and are called brown dwarfs or L-dwarfs. Solar systems possessing the mass and number of planets similar to atoms of oxygen, compares to the mass of the Sun and that mass exceeds the lightest stars in the same way as the mass of atom of oxygen exceeds mass of atom of hydrogen. The Milky Way galaxy, together with galaxies such as the Large Magellanic Cloud and Small Magellanic Cloud form a congestion of galaxies similar on a mass scale to a molecule of water H2O. Our Galaxy is considerably more massive then the Magellanic Clouds and parallels the role of an atom of oxygen (or may be fluorine). Around of the given congestion of three large galaxies are orbiting about 14 dwarf galaxies which can be named galactic analogues of the electron. The values of typical parameters of dwarf galaxies were confirmed, with the mass of 4.4 ∙ 106 solar masses and the radius of up to 371 pc. 
Just as on the axis of mass (and on the axis of the sizes), all natural bodies settle down into discrete groups. The attitude of mass between any of the next groups can be seen as the same number. Hence, mass increase of objects occurs on a geometrical progression, the same is true concerning the sizes of objects. It allows the observer to compare attitudes of similarity between various levels of matter and by that in advance to predict still more about investigated badly objects. As a consequence, SPФ symmetry similarity is generated between the basic levels of matter. An analogue of similar symmetry is CPT symmetry used in quantum field theory.
In addition, Fedosin found a connection between mass and energy of the space objects, corresponding to Einstein's formula (mass–energy equivalence), identified stellar constants, such as stellar Planck constant, stellar Dirac constant and stellar Boltzmann constant, calculated the angular momentum and the radius of the proton as well.   A comparison of the prevalence of stars of different masses with the prevalence of atomic nuclei proved discreteness of stellar parameters and one-one correspondence between the chemical elements and the stars.
The explanation of the red shift in spectra of remote galaxies and cosmic microwave background radiation from the concept of an expanding Universe seems inadequate, and invites other explanations. It leads to the idea of cosmic red shift and microwave background radiation as a consequence of interaction between photons and previously unknown particles – nuons. At the level of stars analogues of the nuons are white dwarfs, whose number exceeds the number of neutron stars. Fedosin shows that the overall mass of the nuons in the Universe of the same order as the mass of all the known nucleons. Thus the problem of invisible dark matter may be solved. The question must be raised about the need for the existence of dark energy. In particular, the effect of attenuation of radiation from the distant supernovas is considered to be the consequence of scattering of photons on the nuons, but not the result of the dark energy activity. 
Fedosin using Le Sage's theory of gravitation based on the notion of gravitons derived from the formula for Newtonian gravity, found the energy density and the penetrating power of gravitons in matter. 
In order to describe the nuclear forces in the gravitational model of strong interaction he introduces the concept of the gravitational torsion field and uses strong gravitation, as constituent parts of strong interaction between elementary particles. 
Strong gravitational constant which is equal to m3•s–2•kg–1, can be calculated through the coefficients of similarity between atomic and stellar systems. The idea of infinite nesting of matter was the basis for the construction of substantial electron model and explaining electronic spin. Model of quark quasiparticles shows that quarks can be represented as a combination of the two phases of hadronic matter and therefore, they are quasiparticles. In this case, the composition of hadrons can be reduced to quarks only for the formal description of properties of hadrons, but the actual reason for the idea of quarks is discrete. Therefore quantum properties of elementary particles and their resulting symmetry during interactions in the fundamental fields can be derived. In particular, in the substantial neutron model and substantial proton model it is found that the mass of the nucleons is in a narrow range of masses as a consequence of the equation of state of hadronic matter and its evolution in the field of strong gravitation.
The electric charge of the proton appears in the reactions of the weak interaction in neutron matter during beta decay and reaches a maximum when the density of zero electromagnetic energy becomes comparable to the energy density of strong gravitation.  Analysis of electric and magnetic polarizabilities of nucleons shows that they can be understood without invoking the idea of quarks.
In the concept of general field it is shown that the gravitational and electromagnetic fields, the acceleration field, the pressure field, the dissipation field, the fields of strong and weak interactions, and other force fields can be combined into one. The general field is universal in the sense that it operates at all levels of matter and allows us to describe the equation of motion of any object with the help of one tensor equation.
The detailed philosophical analysis of the theory of infinite nesting of matter was carried out by Sergey Fedosin in 2003.  At each level of matter, characteristic basic carriers and boundary points of measurement are allocated. Transitions from one level of matter to another are carried out under the law of transition of quantity and in quality when the quantity of carriers in object exceeds the admissible borders of the measurements typical for the given object. Examples of fractal structures at various spatial levels of matter are the result. Owing to hierarchical structure of the Universe consisting of objects similar each other, repeatability of elements of the natural phenomena, the unity and integrity of the Universe is supported, in addition symmetry of similarity is shown. The theory of infinite nesting of matter is justified by the law of similarity of carriers of different scale levels.
In addition to infinite nesting of physical material objects of different levels, an infinite nesting of life is found – inside the autonomous living organisms from one level: the smallest prions and ending with the whales are present in all other living structures of lower levels of scale. In this case there is an interpenetration of the living and nonliving matter, and a clear correlation between the size and mass of living carriers and the corresponding values of physical objects at different levels of matter. Thus, nesting of living matter in natural systems manifests as the distribution of organisms of different species scale or levels according to mass and size. Leading to an infinite nesting of levels living matter in each individual living organism.  As an illustration, it is known, that in the human body there is so much bacteria that their total mass may be up to two kilograms. 
The infinite nesting of living beings is in agreement with the living systems theory of James Grier Miller, which considered many living systems, in order of increasing size, and identifies his subsystems in each.  He concluded: nonrandom accumulations of matter-energy in physical space-time self-organizes into interacting, interrelated subsystems or components. In such complex structures, he identified eight "nested" hierarchical levels, including cells, organs, organisms, groups, organizations, communities, societies, and supranational systems. Nesting is defined that an organ is composed of many cells, and the body - of many organs, etc. In addition to such qualitative conclusions, in the theory of infinite nesting with the help of similarity of matter levels can determine some quantitative regularities. For example, there are coefficients of similarity in mass, to assess the critical number of living beings, delimiting between themselves different levels of the organization alive.
Max Tegmark classifies different types of simultaneously existing universes, depending on their possible properties. Under this universes he understands objects with dimensions close to the size of our Metagalaxy. It is assumed that such neighboring universes are autonomous and independent from each other, and they may have even other physical laws, or other elementary particles and physical constants. 
Leonard N. Plyashkevich, Mira L. Plyashkevich
Leonard N. Plyashkevich and Mira L. Plyashkevich in their work considered the basic postulates of a variant of cosmology, as an alternative hypothesis of the Big Bang.  Authors had made attempts to reveal a uniform principle of micro and macrocosms. For achievement of this purpose, methods of transformation between similarity and dimensions of physical quantities are used. The gravitational field equations are Faraday - Maxwell fields.
Denial of the Big Bang and interpretation of red shift in spectra of far galaxies as Doppler effect, allows this model to develop a hierarchical model of the Universe.
The problem of coexistence of usual matter and antimatter is mentioned.
The purpose of the work – to show, not plunging into chasms of metric theories, the right to existence and development of hierarchical model.
Boris M. Sirotenko (Boris Antsis)
A system of the Universe was published in the book "Rise of the Worlds" (2003).  The system covers Genesis of inert and living matter. The Universe is represented as a dynamic hierarchy of particular worlds. Subsidiaries of inert matter arise from elementary particles of the parent structure by their gravitational condensation in accordance with the theory of Jeans. It is proved that the condensation is involved only about half of the particles. Others particles with large escape velocity, remain dispersed in space and serve as material for a variety of potential fields. It is shown that the matte of all particular worlds, from the microworld, acquires the properties of superfluidity, superconductivity, etc. It seems macrocosm is the latest in the existing hierarchy. Large-scale constants connecting dimensions and mass of particles, and energy density and the relaxation time of particular worlds are calculated. It is found that, despite the infinite number of particular worlds, all the basic parameters of the Universe are finite. The theoretical possibility of the existence of life in each particular world is discussed and reviewed, what nature took to create highly intelligent beings.
The term Scalativity was penned by Leonard Malinowski to differentiate his efforts from, while paying respect to, Laurent Nottale and his work, Scale Relativity or Scalativity. The Scalativity means that absolute uniform scale cannot be detected. Human observers exist at the human scale whereby all measured properties of the Universe can be compared relative to an observer’s approximate mass, size, and awareness of time passage. It seems the human scale is arbitrary.
In Scalativity the currently observable Universe and all its contents such as particles (proton, neutron, electron, photon, neutrino), cosmic objects (galaxies, stars, planets and so on ) and electric field lines, are all presented as completely fractal. A truly Fractal Universe must incorporate infinity completely into Physics as well as Scale Relativity, with the understanding that there must exist self-similarity between scales. It is supposed that the neutron is composed of 1.2 x 1057 subquantum scale (sqs) Hydrogen atoms; an electron is composed of 1.2 x 1052 sqs-Iron atoms with an excess of 2.1 x 1040 sqs-electrons and a photon is composed of 4.5 x 1080 sqs-photons.
It is supposed that the vast majority of stars are cosmic scale nuclei in the process of cosmic scale (cs) beta decay. The sum of electromagnetic and neutrino radiation emitted by a star over its life time is one cs-antineutrino. Our Solar System is may be a cs-neutron in the process of cs-beta decay. The iron/nickel cores of the planets are expected to form one cs-electron of mass 1.084 x 1027 kg. The Sun will be left with 2.1 x 1040 positive ions on its surface. The 2.1 x 1040 ionized electrons will adhere to the cs-electron. The mass of mostly stable cosmic scale nuclei should range from 1 solar mass to 238 solar masses.
According to Malinowski, the Big Bang Universe is fractally self-similar to a cosmic scale 500 Megaton Uranium 235 fission explosion. Spiral galaxies are self-similar to nuclear explosion particles forming and Elliptical galaxies are self-similar to drops of water in the nuclear cloud capturing many cs-neutrons.
With just two postulates, that the pre-solar system mass is the mass of a cosmic scale neutron and that a cosmic scale neutron is composed of 100% Hydrogen atoms, Scalativity can calculate the fractal chemical compositions and binding energies of all nuclei. It is fascinating that to obtain the mass of the very stable nuclei Iron 56 by this method, one must fuse all the quantum scale Hydrogen and quantum scale Helium available in 56 separate protons and neutrons completely to 100% qs-Iron 56. There are many other quantum scale - cosmic scale self-similarities identified at www.scalativity.com.
José Díez Faixat
Fitting his ‘periodic table’ of rhythms to the date of the appearance of matter –the Big Bang– and of organic life, he find that every single instant of the emergence of successive taxonomic degrees of human phylogeny is marked out with absolute precision: Kingdom: animal, Phylum: chordata, Class: mammal, Order: primate, Superfamily: hominoid, Family: hominid and Genus: homo. The same then occurs with all the stages of maturation of our primitive ancestors: H. habilis, H. erectus, archaic H. sapiens, H. sapiens and H. sapiens sapiens. Once more, the precision of the hypothesis is repeated in the successive transformations that humanity has experienced in its more recent history: the Neolithic, Antiquity, the Middle Ages, the Modern Age and the emergent Postmodern Age. The ‘periodic table’ of rhythms may also provide the key to glimpse the successive phases yet to be deployed in the years to come in an ever-accelerating process that will eventually lead to a moment of infinite creativity –Omega– within a couple of centuries.
The same hypothesis that has behaved with utter precision when applied to the process of global evolution, also does so when cross-checked against the process of development of the individual human being. Within the same time frame, with the same pattern of folding and unfolding, and passing through the same stages, the ‘periodic table’ of rhythms periodically marks out –step by step– the successive phases embryologists, developmental psychologists and spiritual teachers talk of, thus confirming the old idea of phylogenetic-ontogenetic parallelism and pointing, very specifically, to an astonishing fractal and holographic universe.
Cosmology of Raël
Raelian cosmology is based on similar cosmological sights at the structure of the Universe.
Theory in pop culture
- YouTube|cNV9FEKi9FQ|Intro to cartoon serial Simpsons – The Ziff Who Came to Dinner. The episode the first time is shown 14.03.2004 (to the 125 anniversary from the date of Albert Einstein's birth).
- The ending of film of Steven Spielberg " War of the worlds " (War of the worlds, 2005) – http://www.imdb.com/title/tt0407304/
- Song Moby – We are all made of stars, 2002
- The Dark Tower – a series of novels of Stephen King
- Final in film " People in black " (1997) / Men In Black – one of the best screen versions of given article.
- The principles of fractal paradigm are presented according to the article «THE HIDDEN MEANING OF PLANCK'S CONSTANT» of Oldershaw R.L. in his letter dated 20.03.2008 and addressed to Fedosin S.G.
- Comments to the book: Fedosin S.G. Fizicheskie teorii i beskonechnaia vlozhennost’ materii. – Perm, 2009, 844 pages, Tabl. 21, Pic. 41, Ref. 289. ISBN 978-5-9901951-1-0. (in Russian).
- Gottfried Wilhelm von Leibniz, De materia prima, 1670 
- Newton I. Optics. 1954, pp. 301.
- Valery Bryusov, «The World of electron», 1922, in Russian.
- Fournier D’Albe, E. E. Two New Worlds: I The Infra World; II The Supra World, 1907, London: Longmans Green.
- Charlier C. V. L., Ark. Mat. Astron. Fys., 1908, Vol. 4, P. 1; Charlier C. V. L. Ark. Mat. Astron. Fys., 1922, Vol. 16, P. 1.
- Selety F. Ann. Phys., 1922, Vol. 68, P. 281; Einstein A. Ann. Phys., 1922, Vol. 69, P. 436; Selety F. Ann. Phys., 1923, Vol. 72, P. 58; Selety F. Ann. Phys., 1924, Vol. 73, P. 290.
- Mandelbrot B.B. — Fractals — W.H. Freeman, San Francisco (1977), and The Fractal Geometry of Nature, W.H. Freeman, New York (1983).
- Benoit Mandelbrot, "Two heirs to the Great Chain of Being", 1982 
- Baryshev, Y. and Teerikorpi, P. — The Discovery of Cosmic Fractals — World Scientific Press, London-Singapore, 2002, ISBN 981-02-4872-5.
- Baryshev, Y. Field fractal cosmological model as an example of practical cosmology approach. Practical Cosmology, 2008, Vol. 2, P. 60-67.
- Dirac P.A.M., Letters to the Editor: The Cosmological Constants, Nature, 1937, Vol. 139, P. 323; Dirac P.A.M., Physical Science and Philosophy, Nature Supplement, 1937, Vol. 139, P. 1001; Dirac P. Cosmological models and the Large Numbers Hypothesis. Proc.R.Soc. A, 1974, Vol. 338, P. 439-446.
- G. Gorelik: Hermann Weyl and large numbers in relativistic cosmology. In: Y. Balashov and V. Vizgin (eds) Einstein Studies In Russia (Birkhaeuser, Boston, 2002).
- Eddington A. New Pathways in Science. Cambridge University Press, Cambridge,1935, a 233-234.
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- Ivanenko D.D.: in Astrofisica e Cosmologia, Gravitazione, Quanti e Relativit`a – Centenario di Einstein, edited by M.Pantaleo and F.de Finis (Giunti-Barbera; Florence, 1978), p.131.
- Salam, A., and Strathdee, J. Confinement Through Tensor Gauge Fields. Physical Review D, 1978, Vol.18, Issue 12, P. 4596-4609.
- Recami E. Multi-verses, Micro-universes and Elementary Particles (Hadrons). arXiv:physics/0505149v123, May 2005.
- Recami, E. and Castorina, P. On Quark Confinement: Hadrons as «Strong Black- Holes». Letters Nuovo Cimento, 1976, Vol. 15, No 10, P. 347-350.
- Sivaram, C. and Sinha, K.P. Strong gravity, black holes, and hadrons. Physical Review D, 1977, Vol. 16, Issue 6, P. 1975-1978.
- P. Caldirola, M. Pavsic & E. Recami: “Explaining the Large Numbers by a Hierarchy of ‘Universes’: A Unified Theory of Strong and Gravitational Interactions”, Nuovo Cimento B48 (1978) 205-271.
- Chown, Marcus — Fractal Universe — New Scientist — 21 August, 1999.
- Gefter, Amanda — Is the Universe a Fractal? — New Scientist — 10 March, 2007: No 2594.
- Sergey Khaitun. «Ot ergodicheskoi gipotezy k fraktalnoi kartine mira: rozhdenie i osmyslenie novoi paradigmy», KomKniga, 2007, ISBN 5-484-00565-5 (in Russian).
- Robert L. Oldershaw. An Infinite Fractal Cosmos. arXiv:1001.2865v1, 17 Jan 2010.
- Robert L. Oldershaw. “Self-Similar Cosmological Model: Introduction and Empirical Tests”. International Journal of Theoretical Physics, Vol. 28, No. 6, 669-694, 1989. 
- R. L. Oldershaw. Discrete Scale Relativity. Astrophysics and Space Science, Vol. 311, No. 4, pgs. 431-433, October 2007 
- S. I. Sukhonos. (Structure of steady levels of the organization of material world), SPb.: Hydrometeoizdat, 1992., and also S. I. Sukhonos. (Scale harmony of the Universe), М.: Sofia, 2000, 312 pp, in Russian. ISBN 5-89117-096-5 .
- Yun Pyo Jung. «Infinite Universe In A Mote», Sagyejul Publishing Co., 1994, 290 pp.; «Infinity in a Speck» (Fractal Cosmology)
- Fedosin S.G. (1999), written at Perm, pages 544, Fizika i filosofiia podobiia ot preonov do metagalaktik, ISBN 5-8131-0012-1., https://payhip.com/b/wGPU
- Louis E. Strigari, James S. Bullock, Manoj Kaplinghat, Joshua D. Simon, Marla Geha, Beth Willman, Matthew G. Walker. A common mass scale for satellite galaxies of the Milky Way. – arXiv: Astrophysics (astro-ph), 27 Aug 2008.
- D. Adén, M. I. Wilkinson, J. I. Read, S. Feltzing, A. Koch, G. F. Gilmore, E. K. Grebel, I. Lundström. A new low mass for the Hercules dSph: the end of a common mass scale for the dwarfs? – arXiv: Galaxy Astrophysics (astro-ph.GA), 7 Oct 2009.
- Fedosin S.G. Sovremennye problemy fiziki: v poiskakh novykh printsipov. Moskva: Editorial URSS, 2002, 192 pages. ISBN 5-8360-0435-8.
- Fedosin S.G. The radius of the proton in the self-consistent model. Hadronic Journal, 2012, Vol. 35, No. 4, P. 349 – 363.
- Fedosin S.G. Cosmic Red Shift, Microwave Background, and New Particles. Galilean Electrodynamics, Spring 2012, Vol. 23, Special Issues No. 1, P. 3 – 13.
- Fedosin S.G. Model of Gravitational Interaction in the Concept of Gravitons. Journal of Vectorial Relativity, Vol. 4, No. 1, March 2009, P.1-24.
- Sergey Fedosin. The physical theories and infinite hierarchical nesting of matter. Volume 1, LAP LAMBERT Academic Publishing, pages: 580, ISBN-13: 978-3-659-57301-9.
- Fedosin S.G. Osnovy sinkretiki: filosofiia nositeleĭ. – Moskva: Editorial URSS, 2003, 464 pages. ISBN 5-354-00375-X. in Russian.
- Fedosin S.G. Nositeli zhizni : proiskhozhdenie i ėvoliutsiia. – S.-Peterburg: Dmitriĭ Bulanin, 2007, 104 pages. ISBN 978-5-86007-556-6.
- James Grier Miller, (1978). Living systems.New York: McGraw-Hill. ISBN 0-87081-363-3.
- Tegmark M. “Parallel Universes”, Scientific American,2003, Vol. 288(5), P. 41-51.
- L. N. Plyashkevich, M.L. Plyashkevich. To the question on similarity of atomic and galactic structures of matter, in Russian.
- Boris Antsis. Unified structure of Universe 
- Sirotenko, B. M. About similarity micro-and macrocosm, Hydrometeoizdat, 1990, 42 pp., in Russian.
- L. Salzman. Rise of the Worlds. – St. Petersburg, European House, 2003, 385 p. ISBN 5-8015-0154-1. in Russian.
- José Díez Faixat. ¡Bye-Bye, Darwin! The Hidden Rhythm of Evolution. Syntropy 2014 (1): 1-49.
- José Díez Faixat. Siendo nada, soy todo (Being nothing, I am everything). DILEMA, S.L. (2008), ISBN-13: 978-8498270969, in Spanish.
- José Díez Faixat. Entre la evolución y la eternidad (Between evolution and eternity). Editorial Kairos (1998), ISBN-13: 978-8472453340, in Spanish.
- José Díez Faixat. A hypothesis on the rhythm of becoming. World Futures: The Journal of New Paradigm Research, 1993, Volume 36, Issue 1, pages 31-56.
- The Scale of the Universe — Image of scale axis with objects on it.
- Film Cosmic Voyage
- Film Powers of Ten
- Turtles_all_the_way_down – Indirectly concerns to the questions on boundless division of the matter and occurrence of the world, by analogy. Various literary variations of very old philosophical question are described: If the Earth is flat also costs on the back of a huge turtle on what there is the turtle? The standard answer (or leaving from the answer?) says: the turtle on what it is not necessary, it simply below! Other question concerns origins of the world and the competence of its creator: If the world is created by the God then from whence the God has undertaken? If there is something, what by anything and is created by nobody (for example, the God) why world as those to not be nobody created?
- David Pratt – The Infinite Divisibility of Matter. The history of moving deep into levels of the matter – from atoms to elementary particles down to quarks is considered. Criticized modern theories of strings and representations about elementary particles, owing to presence of many artificial assumptions (gauge of a charge, pointness of electron and quarks, compactness dimensions of space, birth of particles only from itself (instead of from other free substance), lack of structure of some particles, refusal of intrinsic understanding of the physical phenomena).
-  Balashov I.F. The analysis of concepts of step-type behaviour, infinity, repeatability of the matter on different scales.
- Marcelo B. Ribeiro – The Apparent Fractal Conjecture.
- The Theory of Infinite Hierarchical Nesting of Matter as the Source of New Ideas. FQXi Essay Contest 2012.
- Many-worlds interpretation
- Topic:Philosophy of science
- Philosophy of infinity
- Theory of Everything Project
- Historical Introduction to Philosophy/Metaphysics
- Fizicheskie teorii i beskonechnaia vlozhennost’ materii
- Infinite Hierarchical Nesting of Matter in Russian