About this Book

This is the third volume in the Single Monad Model of the Cosmos series. In the first volume we introduced Ibn al-Arabi s eccentric conception of time and outlined the general aspects of his cosmological views. In the second volume, this fundamental insight was developed further into the Duality of Time Theory, which provided elegant solutions to many persisting problems in physics and cosmology, including the arrow-of-time, super-symmetry, matter-antimatter asymmetry, wave-particle duality, mass generation, homogeneity, and non-locality, in addition to deriving the principles of Special and General Relativity based on its granular complex-time geometry. In addition to explaining both quantum and relativistic phenomena, this theory can be extended further to describe the incorporeal worlds. In other words, whereas Relativity was able to explain gravity in terms of space-time curvature, the Duality of Time Theory explains all the five fundamental interactions between the physical (corporeal) microscopic particles and macroscopic objects, as well as the structure of incorporeal worlds, including the psychical, spiritual and divine realms; all based on the same discrete and genuinely-complex time-time geometry, whose spatial dimensions are dynamically being generated, in the inner levels of time, from one single metaphysical point, before they start evolving in the outer normal level that we encounter.

Therefore, in this third volume, we want to explore how the apparent physical and metaphysical multiplicity is emerging from the absolute oneness of divine presence, descending though four fundamental levels of symmetry: ultimate, hyper, super and normal. This is equivalent to understanding how the cosmos is perpetually and sequentially emerging from chaos, and then subsequently repairing back into it, at every instance of time. In reality, this is indeed the same acknowledged physical process of matter-antimatter pair creation and annihilation, but it is happening here between the corporeal and incorporeal worlds, on a global cosmological scale, every single instance of time. The reason why this creation and annihilation process is not causing any devastation or destruction, as we would normally expect from such extremely energetic fissile reaction, even when it happens on the slightest atomic scales, is because it is happening sequentially in the inner levels of time before the physical mass is generated. Rather, this process itself is the fundamental origin of the instantaneous generation of matter particles and antiparticles, which then simultaneously repair and vanish into the past, just to be re-created again, perpetually. This perpetual and sequential dynamic formation causes the illusion of motion and continuity of spatial dimensions, while in fact all this multiplicity is being created from one metaphysical point, which is the Single Monad that is the only entity described by real continuous existence.

In other words, while the spiritual world and divine presence are forming even higher levels of symmetry, the physical and psychical worlds are the two complementary folds of super symmetry, which is the same matter and antimatter symmetry already established in the Standard Model of Elementary Particles. In fact, this model also includes the hyper symmetry between fermions and bosons, or matter and energy, which are nothing but space and time, respectively. Therefore, we don t need to look further for any new particles to realize the super and hyper symmetries, but we need to introduce some fundamental modifications that will reveal the hidden discrete symmetry of space and allow exact mathematical derivation of the Equivalence Principle of General Relativity.

As a result of these essential modifications introduced by the complex-time geometry, super symmetry becomes the same established matter-antimatter symmetry of Quantum Field Theory, and hyper symmetry is the same established space-time diffeomorphism of General Relativity. Therefore, while normal symmetry governs the macroscopic objects, based on the familiar conservation laws of classical mechanics, super symmetry governs the elementary particles of matter and anti-matter, which are the fermions, based on Quantum Mechanics, and hyper symmetry governs the equivalence between these fermionic particles and energy waves, which are the bosons, thus converting between granular and continuous space, or particles and waves. However, because of the presence of mass and energy, this latter space is non-Euclidean, so the ultimate symmetry comes in the line to explain how this curved (Riemannian) space is emerging from the absolutely homogeneous Euclidean space of infinite number of dimensions, which is also equivalence to absolute Oneness.

This ULTIMATE SYMMETRY is a modern scientific interpretation of the same ancient mystical, and extremely controversial, theory of the Oneness of Being , that is often misinterpreted in terms of pantheism, or panentheism, but it is indeed the definitive gnostic knowledge of God and creation. This divine wisdom is usually experienced by many Sufi mystics, and also some other philosophers from earlier religions, but it is often expressed in a delicate poetical and highly metaphorical language, lest it can be easily misunderstood and reduced into the various confusing and inadequate philosophical and theological doctrines. For this reason, this virtuous knowledge was intentionally dispersed and widely scattered by Ibn al-Arabi over his numerous works and in different contexts within the various chapters of the Meccan Revelations, but he gave some crucial clues in his introduction on how to accomplish a comprehensive vision. Nonetheless, this critical reality may not be revealed to outsiders via any conventional language or other tools of expression, since it may only be personally experienced on the most profound spiritual levels, usually after extensive and conscientious meditation and contemplation.

As it has been clarified in the first two volumes, all the principles and essential details of the Single Monad Model and Duality of Time Theory are entirely based on Ibn al-Arabi s original view of creation and his intense interpretation of Islamic cosmology, outlined in the momentary Quranic descriptions of the world and other essential prophetic narrations. However, it must be clearly noted that, although these principles are divinely revealed by Allah, the Exalted, in Quran and through His Prophet Muhammad, peace be upon him, we are not merely relying on any innocent faith to describe physical and cosmological phenomena! Rather, we are applying the Islamic divine revelations to develop concrete logical investigations, supported by rigorous mathematical derivations of the most fundamental laws of nature. So, although we certainly believe that Allah is the One Who is ultimately creating every single thing at every instance of time, this book explains very clearly how this is being done, and not just a naive resorting to God did it .

The Duality of Time Theory exposes a deeper understanding of time, that reveals the ultimate discrete symmetry of space-time geometry, according to which the dimensions of space are dynamically being re-created in one chronological sequence at every instance of the outer level of time that we encounter. In this hidden discrete symmetry, motion is a result of re-creation in the new places rather than gradual and infinitesimal transmutation from one place to the other. When we approximate this discrete motion in terms of the apparent (average) velocity, this theory will reduce to General Relativity. This means that the semi-Riemannian geometry on  is a special approximation of this discrete complex-time geometry on . This approximation is implicitly applied when we consider space and matter to be coexisting together in (and with) time, thus causing the deceptive continuity of physical existence, which is then best expressed by the non-Euclidean Minkowskian space-time continuum of General Relativity, or de Sitter/anti-de Sitter space, depending on the value of cosmological constant. Therefore, the Correspondence Principle is fulfilled by the Duality of Time Theory, which goes much more deeper than just including General Relativity, and also far more deeper than simply reconciling it with Quantum Mechanics, but also opening the doors to the incorporeal worlds and explaining all natural and super-natural phenomena in terms the new dynamic and genuinely-complex time-time geometry.

As we have already introduced in Volume II of this series, the psychical entities have exactly the same structure as the physical objects, with the same kinds of elementary particles, atoms, crystals, and even rocks and mountains; but they are denoted as incorporeal because they exist in an orthogonal dimension of time. Therefore, the fermions in our physical world behave as bosons in the psychical world, and vice versa. The new genuinely-complex nature of time, where the dimensions of space are created dynamically in the inner levels, allows expressing super symmetry, through these two orthogonal arrows of time, without the need to introduce any super space which requires anti-commuting numbers.

With this unification between the two super symmetrical worlds, consciousness or knowledge is explained as the result of the instantaneous pairing between the two orthogonal time directions, producing a new spatial dimension whose points contain the information describing the various objects of awareness. Therefore, super symmetry is responsible for our passive recognition of the present moment of existence, which is perpetually turning into the past right after its instantaneous becoming. When these two physical and psychical arrows are complemented together with the encompassing spiritual dimension, hyper symmetry is achieved, which then adds the creative elements of living and ability . In other words, the hyper symmetrical geometry contains information about future possibilities before they are realized into the present moment, and the spirit provides the motivation and ability to choose and realize one of these possibilities. However, this ability is greatly constrained by the various current physical and psychical restrictions, and it becomes absolute only on the divine level of ultimate symmetry, which is acting from within each point of the absolute space, through the spin that is producing the magnetic field from which all other quantum fields are generated at each subsequent spatial dimension. The spin is the fundamental property that determines the final state to which the wave-function of every point of space is collapsing at every instance of time.

In simple mathematical terms, the physical dimensions, both as the space-time container and its contents of matter and energy, are defined by the complex-scalar field (of the genuinely-complex time): , and the psychical dimensions are described by the orthogonal number , so that . Separately, each one of these fields has its own Lorentzian symmetry, because they are hyperbolic complex numbers , with fractal time dimensions  and , but together they form the non-Euclidean space that we normally perceive, which is described by normal complex numbers , but with some diffeomorphism, or certain differentiable mappings of the manifold to itself, depending on its contents of matter and energy. The diffeomorphism group defines the hyper symmetry whose transformation is the same mass-energy equivalence relation , generalized to include mass and other quantum charges, while of course the group of super symmetry, being the symmetry of fermions, or physical particles, is defined by Lorentz transformation, but also with some essential modifications that reveal the granularity of the hyperbolic space where super symmetry is realized. The Duality of Time theory provides a clear transition, or symmetry breaking and restoring, between the continuous space of hyper symmetry  and the discrete space of super symmetry , based exactly on the same mass-energy equivalence relation or the principle of equivalence between the inertial and gravitational masses that is now derived mathematically without introducing any thought experiments that rely on plain induction.

In reality, the fractal dimension of time, in either the physical or psychical worlds, separately, is having a negative signature, thus reducing the number of dimensions rather than increasing them, but together they complement each other to make the three spatial dimensions that we feel living in. Therefore, quantum gravity can not be explained without understanding super symmetry that can be realized only with the two complementary physical and psychical worlds together, and then complementing them both with the spiritual world that defines the hyper symmetric space. Nonetheless, the picture can only be completed after understanding the ultimate symmetry that connects the manifested non-Euclidean space with the absolute homogeneous and infinite Euclidean, or Hilbert, space with infinite number of dimensions. This level of symmetry governs the divine realm of God and His Beautiful Names and Attributes, including also the Constant or Immutable Entities, that will be explained in Chapter IV. However, at the highest level, the Divine Ipseity or Quiddity is described by eternal Oneness beyond any symmetry or space nor time.

Therefore, there are five primordial realms, or levels of reality, each having its own distinctive symmetry that is defined with a certain type of geometry:

1. Oneness of God, conceived as abstract point beyond geometry.

2. Ultimate Symmetry of Constant Entities, defined in Euclidean space (without time).

3. Hyper Symmetry in the Spiritual World, defined in Riemannian space-time as normal complex numbers .

4. Super Symmetry between the Physical and Psychical Worlds, defined in two orthogonal Hyperbolic spaces (with time), as split-complex numbers .

5. Normal Symmetry in the Physical World, defined in Euclidean space and time as independent variables.

These nested symmetries are reflected on many fundamental levels of nature, including the five Divine Presences, the five regular polyhedra known as the Platonic solids, the four classical elements and their quintessence, the five Pillars of Islam and the five daily prayers. We shall discuss some of these fundamental fives in the Introduction.

After the revolutionary theory of Relativity and the discovery of Quantum Mechanics, and then the subsequent development of Quantum Field Theory that was able to describe the atomic structure of matter and explain some fundamental interactions through the Standard Model of Elementary Particles, thousands of physicists and cosmologists, from many pioneering universities around the globe, have been trying very hard to understand the micro-structure of space-time and gravity, by trying to reconcile Quantum Mechanics with General Relativity. The reason why none of these century-long extensive international efforts could ever explain the quantum nature of gravity is due to the fact that it is three-dimensional phenomena, and we are trying to explain it from the same level of existence that is also three-dimensional but only with its two physical and psychical domains together, while each one of them is only a two-dimensional world evolving in time.

In other words, our perception of the three spatial dimensions is occurring only instantaneously as a result of the sequential pairing between the two orthogonal and complementary physical and psychical worlds, while separately they are evolving only in two spatial dimensions, since we can only perceive one two-dimensional image at a time, that is then integrated, in our creative imagination, with the corresponding psychical image, to form a three-dimensional picture of the surrounding world, where gravity is encountered. For this reason, although it is essentially quantized, just as anything else in creation, gravity is always perceived as a continuous phenomena.

Perhaps this is the essential reason why many laypeople are still advocating the flat Earth model, assumed from its archaic shape as a plane or disk, as it is usually depicted in the early cosmography of most ancient civilizations. With the correct understanding of the fractal nature of time, all our direct perception of the (local) physical universe is two dimensional, and not only the Earth. When we extend this local view to the apparently infinite dome of the heavens, the dimensions become a whole three, but practically we are confined in a fractal time-dimension between two and three complete dimensions of space.

Consequently, there is no doubt that the ancient Sumerians and other later civilizations once had an extremely precise and detailed understanding of this crucial fact, and they built their profound mathematical model on it, using the sexagesimal system, with base 60, that is still being used for measuring time, angles, and geographic coordinates. What is less known, however, is that the absolute speed of light is implicitly operating in this system, from which the meter is also precisely defined! It is not by any chance that the speed of light is three hundred thousand meters per second, and that the distance between the north and south poles of the Earth is twenty thousand meters, because this is directly related to the apparent dimensions, which are two for the flat Earth and three for the dome of the Sky, or vacuum. Other fundamental constants and units can then be extracted from this system as briefly described at the end of Chapter VII of Volume II and we may also come back to this important subject throughout this book.