IV.2.2 The Mathematical One-to-Many Relation

Because of acquiring new degrees of freedom, with each level of higher symmetry, more and more divine attributes are granted to the creation to make them realize into their presence in the unlimited and eternal possibilities of Time, or the Age, as the divine Name of Allah. As we explained in Volume I, the Age is an endless eternal circle that does not have a beginning nor an end for itself, but it is all an eternally ongoing present, or the continuous existence [II.69.13, IV.362.32]. In terms of the Duality of Time Theory, the Age is the absolute space without time, so it is the absolute light, or the super-energy state . Conversely, with every breaking of symmetry, the creations descend down to the physical world, described by heaviness and inertia, which is eventually the absolute or super-mass state . Practically, however, the creations are alternating between these two extreme states, and this happens in terms of the sequential splitting and pairing between the two extreme states of super-fluid  and super-gas , according to the equation: , which is the same matter-antimatter creation and annihilation. These four primordial states are also the same classical four elements of Nature: water, air, earth and fire, as we shall describe further in Chapter I.

Whenever two opposite arrows of time are complemented, a new dimension of space is created with a higher level of symmetry, and inversely, when a spatial dimension is split into two arrows of time, symmetry is lowered down closer to the physical world, whose ground state is described by , but also it could have higher ground states such as , where  describes a homogeneous space of some dimension. The breaking of symmetry is the fundamental cause for the emergence of the outward time that we feel, which comes as a result of the desire of keeping or bringing more than one thing into existence at the same instance. This is what causes the inertia that is the main property of the physical world, which then causes the delay in keeping up with the normal timeless flow of creation. As we shall explain further in Chapter II, this emergence of the outward time is concurrent with the creation of mass, or condensation of space into time, or energy  into mass , and also charge and other coupling parameters, depending on the number of spatial dimensions, or degrees of freedom. This process is exactly like the spontaneous symmetry breaking, for example when ice forms as a result of cooling liquid water. When heat is drained out of water it freezes into ice. Similarly, when air or the super-gas state  is drained out of fire that is the super-energy state , the super-fluid state  forms, which is the aether that then condensates into matter. This has been symbolically depicted in Quran when Allah says: (And a Sign for them is the Night: We withdraw therefrom the Day, and behold they are plunged in darkness) [Quran, 36:37]. In Chapter IV of Volume I, we explained how Ibn al-Arabi applies this key verse to reconstruct the real flow of time.

Nevertheless, each individual point of space has exactly the same ultimate symmetrical properties of the whole space, and that s why Ibn al-Arabi stresses that: in everything there is everything, even if you do not recognize that [13, CH. V], which means, amongst other things, that the internal structure of the Single Monad is as complicated as the world itself, and this is one of the key properties of fractals, such as Mandelbrot set, Julia set and Sierpinski triangle, where the structure keeps repeating itself on any larger or smaller scale.

Therefore, in the absolute sense, symmetry is a property of absolute space, and it is broken only with the flow of time, and that s why there must always be two orthogonal arrows of time, which are the same complementary states of super-fluid  and super-gas  described above. In each one of these two sides time is causing the illusory sense of real existence, while in reality, the creations are imaginary and the real existence is attributed only to God. In this Real Being, every point of space is itself the whole changeless and ultimately symmetrical space, without flowing time. This mysterious fact has been nicely expressed by Ibn al-Arabi in his Kitab al-Tajalliyat, the Book of Theophanies, from which we choose the Theophany of Perfection , which has been roughly translated by Henri Corbin into French, and then into English by Ralph Manheim, in Alone with the Alone [9, p. 174]. Based on this translation, we provide in the following a more accurate alternative, and the pronouns are capitalized here because Ibn al-Arabi is attributing this discourse to Allah, the Exalted:

Listen, O My beloved!

I am the conclusive entity of the World.

I am the center of the circle (of existence) and its circumference.

I am its simple point and its compound whole.

I am the Word descending between heaven and earth.

I have created perceptions for you only to perceive Me.

If you then perceive Me, you perceive yourself.

But don t ever crave to perceive Me through yourself!

It is through My Eyes that you see Me and see yourself.

But through your own eyes you can never see Me!

My dear beloved!

How often have I called you, and you have not heard Me!

How often I am revealing Myself to you, but you are not seeing Me!

I have made Myself into fragrances, but you do not smell Me!

And in delicious food, but you have not tasted!

Why can you not discover Me through the objects you are touching!

Or breathe Me through fragrant odors?

Why do you not see Me in the things you observe?

Why do you not hear Me in everything you hear?

Why? Why? Why?

For you, My delights surpass all other delights.

The pleasure I procure to you surpasses all other pleasures.

I am superior than all other honorable things to you.

I am Beauty, I am Grace.

My beloved, love Me, love Me alone!

My beloved, desire Me, attach yourself to Me.

Do not attach yourself to others!

Embrace Me, kiss Me, for you will never find anyone closer to you than I.

Others love you for their own sakes, and I love you for yourself.

And you, you flee from Me!

My dear beloved!

You cannot treat Me fairly.

For if you approach Me, I approach you multiple folds.

I am nearer to you than yourself, than your soul, than your breath.

Who among creatures would treat you as I do?

My dear beloved!

I am jealous over you of your own self.

I want you to belong to no other, not even to yourself.

Be Mine, and I will be for you as you are for Me, when you are not even aware of it.

My dear beloved!

Let us go toward Union.

And if we find the road that leads to separation.

We will destroy the separation.

Let us go hand in hand.

Let us enter the presence of Love.

Let it be our mediator.

And imprint its seal upon our union.

For ever...

This Theophany of Perfection summarizes the Ultimate Symmetry between the single point and the encompassing space. This also summarizes the instantaneous process of creation, or re-creation, which is breaking this symmetry into the two arrows of time, and then restoring it through each subsequent annihilation. This reunion is also the fundamental cause of motion, formulated in section i.4 as the Principle of Love which leads to the stationary action that is the initial assumption of most physics theories. We have introduced these concepts in Volume II, and the one-to-many relation is already depicted in Figure IV.1, but we want to reproduce it here in another manner, in Figure IV.2, to stress this ongoing alternation between the point of the Real and the circumference of the World.

Figure IV.2: Despite their multiplicity, the indivisible central point, denoting the Real, meets each point from the circumference of the circle of creation. This One-to-Many relation can only be conceived with the oneness of time; that the individual entities of the multiplicity of creation may exist only one at a time, while the Single Monad is alternating between them.

From our unrealistic view, since we are evolving in the imaginary time, we are deceptively perceiving the (physical and psychical multiplicity of the) World as real, because it appears to be continuously existing in our (creative) imagination. That is why we are faced with geometrical infinities and singularities, because we are observing from within this imaginary space, which appears continuous and infinite, while it forms only one discrete state in the encompassing arrow of time that is one side of the higher spatial symmetry. We cannot completely describe this super-space while we are evolving inside it, restricted to only one of its two complementary sides, just like we cannot fully see both the day and night that are encompassing the earth, when we are living on its surface. The flow of normal time is breaking the eternal harmony of space, and splitting it into two symmetrical realms, just as the (sphere of the) day is split into the two hemispherical daytime and nighttime. That is why they are continuously and relentlessly seeking each other [Quran, 36:40, 7:54], like male and female, and the creation is their progeny, demonstrated in Chapters III and IV of Volume I.

Consequently, Ibn al-Arabi stresses that love is the original cause of all kinds of physical as well as metaphysical motions in the Universe, and this required the two primary divine attributes of Living and Knowing , followed by the two secondary attributes of Willing and Ability , which are the source of the four elements of Nature: water , air , earth and fire , respectively. For this reason, the Universal Soul is equipped with the two active and intellectual forces, responsible for physical and metaphysical motion, or change, and also directly linked to the physical and psychological arrows of time, which complement each other to form the homogeneous dimensions of space, as it had been explained in Chapters IV and V of the Duality of Time , and we shall elucidate further on that in this book, especially when we discuss super-symmetry in Chapter II. We shall also see in section i.4 that the Principle of Love leads to the known least action, which is the starting assumption in formulating the mathematical models of all physics theories, including General Relativity and some fundamental calculations in Quantum Field theories.