CHAPTER IV: ULTIMATE SYMMETRY

Ability and the Divine Presence
Euclidean Geometry and Space Transcendence
Abstract Mathematics and Number Theory

You should know that (divine) manifestations are of two types: the first is (eternally) endorsed by the Real, and that is none but the Perfect Human, while all other humans, animals, plants, orbs, angels, and everything else, are (temporal) manifestations that are not endured by the Real, because they are created for a specific purpose, while the Perfect Human (alone) is created for his own essence, since he is the (absolute) manifestation of divine Image. The reason why Allah created two pairs of all things is to remind them of the prominent rank of the Perfect Human, whose existence revealed the (outward) duality of the One Whose own Essence does not accept any (intrinsic) duality. The existence of the Perfect Human is endured because he manifested in the Image of the Real, so with this Image they became pair, just like the image of a person looking in the mirror; it is not himself nor any other! Ibn al-Arabi, paraphrased from the Meccan Revelations, III.109.16

Everything other than the Human are (imaginary) creations, while the Human alone is both creation and real (i.e. complex number with real and imaginary parts). The Perfect Human is in fact the real-through-whom-things-are-created, or because of him. Ibn al-Arabi, paraphrased from the Meccan Revelations, II.396.4

As illustrated in Figure IV.2 below, Ibn al-Arabi quoted the Pole of Spirits, who is Prophet Idris, known in the Bible as Enoch, who is the most knowledgeable of everything concerning the Natural World and the effects of the Higher World on it, as Ibn al-Arabi described him; thus he quoted him saying: the world exists between the circumference and the point [I.154.22]. Ibn al-Arabi then explained that the abstract point in the center of the circle meets any point in its circumference with its whole entity, without division or multiplicity. Similarly, all the creations are emerging from the Real, without affecting His unique Oneness or Unicity. The problem is that physical entities are different from the above abstract mathematical example of the circle and its center point, depicted in Figure IV.2. Nevertheless, with the correct understanding of the real flow of time according to the Single Monad Model and Duality of Time Theory, the ultimate purely-geometrical nature of creation is revealed in a unique manner that connects the multiplicity of creation with the ultimate Oneness and Unicity of the One and Unique God, Who is the Creator of all corporeal and incorporeal worlds, without being multiplied in Himself or composed of any other (sub)entities.

When we understand this essential issue of one-to-many relation, we will be able to solve many fundamental problems in philosophy, physics, cosmology, and mathematics, because this is the key that connects between discreteness and continuity which are reflected in various levels in Nature, such as: space-time, wave-particle, energy-mass, singularities-infinities and many other less obvious dualities.

Ibn al-Arabi was well aware that this paradoxical relation between the Creator and all manifestations is in clear apparent contradiction with the widely accepted philosophical maxim, a central assumption in the prevailing contemporary Neo-Platonist philosophical cosmology, that from the One only one can emerge (or proceed) . Logically, according to our normal simple intuition that is primarily based on physical embodiment, it is not possible to imagine a relation between the One and the many without affecting the unique Oneness of the One, because He must meet each individual one at the same time, so He must have many simultaneous aspects. Ibn al-Arabi solves this riddle by asserting that the interface between the One and all the many existent things doesn t happen all at once. Rather, at any single instance of time, there is in reality only one single relation or interface, a unique divine with-ness , as he calls it, following the Quran [57:4], between the One and only one of the many multitudes of entities in the world. But what happens at this particular instance with the other entities, since their existence is preserved only through this unique creative relation between them and their Creator? The answer is: they do cease to exist, but their existence is maintained by (immediately) re-creating them again, perpetually. As we have repeated explained in the previous volumes, this principle of re-creation, or the ever-renewed creation , is based on some central verses from Quran, including: (Are We tiered of the first creation? Nay, but they are unaware of the creation anew.) [50:15], and: (each Day He is upon one task) [55:29].

Therefore, in order to understand the relation between the unique Oneness of the Real and the apparent multiplicity of creations, Ibn al-Arabi adds time to the previous philosophical statement, which can be then restated as:

from the One only one can proceed at a time.

Ibn al-Arabi, however, affirms that this particular mode of creation was chosen by Allah to be like that, although in fact He might have created the world in any other way, so it is not any (external) restriction imposed over Him, the Exalted. In other words, this principle is not necessarily implied by the Existence of the Real, that only one can proceed from Him at a time, and that it is impossible otherwise. But He willed that, and if He had wished that the world should exist all at once, and that nothing were ever dependent on anything else, it wouldn t be difficult for Allah to create it like that. In such a case we would be living in a completely different logic. Yet, even within this primordial source of our current logic, causality is a macroscopic statistical phenomena and not any designated principle that cannot be broken. Therefore, because it explains the dynamic emergence of space-time geometry, the Duality of Time Theory explains the very cause of causality and how it can be broken in certain circumstances, such as the non-local behavior of quantum tunneling and entanglement.

The genuine complex-time explains how the geometry itself is being created dynamically, so the Universe becomes self-contained without any other predefined background geometry or topology. The dynamically created time-time geometry is essentially granular, but this depends on the relative position of the observer. In a simple statement, since observation is an instance of time, the observer exists in a fractal dimension between two consecutive complete integer spatial dimensions, as we are currently living, or evolving in the outward fractal dimension of time, between two and three spatial dimensions. Therefore, we will always see the two-dimensional space continuous, because we only see it after its creation, while the three-dimensional space will be discrete because we see it only one two-dimensional image at a time, but we can then imagine it to be continuous because we integrate these images with their super-symmetrical psychological folds to imagine the third dimension. In reality, however, this third dimension is only achieved as we progress with time and does not itself evolve in time, from our current position in this Lower World, though this might be the case in the Hereafter as we described in Chapter VII of Volume I.

In the Duality of Time Theory, complex numbers are genuinely natural, while the reals are one of their extreme approximations that are realized only when moving at the speed of light. Real numbers are the property of vacuum that is an absolute space without time, while the physical reality is evolving in space-time, thus covered by the hyperbolic granular geometry on , rather than the abstract Euclidean geometry which describes absolute space continuum, such as  or , or  in general. Therefore, we should incorporate the inner and outer components of time properly into geometry, in order to be able to get rid of various persisting problems of infinities and singularities. In order to achieve this goal, applied mathematics must obey the normal level of symmetry, which is Lorentzian and granular, because it deals with practical situations that always involve time, so it is subject to the same laws of Relativity. After setting the rules correctly for relativistic mathematics, we can then apply the appropriate approximations depending on the particular systems under question, just like we normally differentiate between relativistic and classical physics though we mostly apply the latter. This is in contrast with abstract mathematics that should be primarily understood as timeless counting , or moving at the speed of light, in all directions, in which case we can assume real and normal complex numbers  and . Abstract mathematics is the language of the divine and spiritual realms, because they are based on continuous spaces, while the physical and psychological worlds are primarily based on the granular hyperbolic geometry. We could use this abstract language in hypothetical situations, where time is not an important factor, but that should be approximated properly to suit the particular problem we are trying to solve, otherwise we would be incurring some errors that could be negligible in most situations but also could become huge and completely faulty.