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A Mathematical Analogy of God

It has been Man's eternal problem to define, if not prove the very existence of God using the tools of his intelligence and logical reasoning. Even though the very need to bring God within the confines of a logical proof may be debated, the fact remains that amongst us there remains a large number who find it impossible to accept any concept without proof or direct experience. It may be because the kind of learning system that we have been exposed to, gives much emphasis to analytical thinking instead of the development of our intuitive faculties. Our mindsets have become unconsciously molded through years of such training and thus for us a truth without proof is no truth at all! So within the context of such a state of affairs how can we possibly define God and prove His existence? What would be His functions and attributes? While it is agreed that one may never be able to conclusively prove the existence (or non-existence) of God -- since the very act of bringing God within the parameters of a mathematical proof is tantamount to placing the proof above God and hence contrary to the definition of God being the only Absolute -- it is strongly felt that it is indeed possible to draw close analogies that explain the nature of God. In the following sections an attempt is made to explain the nature of God using such analogies (in other words, it is not the intent of this essay to provide a mathematical proof of God but only an analogy).

God as the Cause of all Causes

Let us first examine the argument for the existence of God as the cause of all causes (the cosmological argument):

1. For anything to exist there has to be a cause.

2. God is the primordial cause or the cause of all causes.

A mere extension of the above argument would apparently give the impression of disproving the existence of God. That is, extending the argument we get the paradoxical statement -- In order for God to exist there has to be a cause, hence God cannot be the primordial cause. This argument against the existence of God, though seemingly logical, is faulty on closer examination. Its main fault lies in the fact that it presupposes the existence of Time before the existence of God.

If an event A is the cause of event B, event A should necessarily have happened BEFORE event B. Let us consider the case where event B is the birth of Time (or change, since Change and Time are synonymous here). So what would be the nature of event A as the cause of event B in this case? "Event" A would no longer be an event (since an event is a point in time at which a change has taken place)! Since Time and Change itself did not exist before event B, the cause of event B, that is A would lose its status as an event and would just be the primal cause A. For obvious reasons (since Time itself did not exist) there cannot be an event before A and hence there cannot be a cause for A.

The Nature of God

Let us go back to the question of the nature of A. What would this pre-Time scenario be like? Was there any matter existing then? If there were any matter existing, then all matter in existence would necessarily be at absolute zero temperature thereby freezing all particle motion (since motion would require the existence of Time). The existence of matter would necessitate the existence of space and gravity. Now the existence of gravity without time would create certain complications since our understanding of gravity today is still not perfect. If there is a particle/wave nature to gravity then time most certainly has to exist alongside matter-space-gravity (since there would be motion of gravitational particles/waves). On the other hand if gravity is the space-time curvature and not a force at all even then Time has to exist for the existence of matter-space-gravity (since gravity is a product of space-time). Therefore we can conclude that in the pre-Time scenario matter did not exist. In other words there was absolute Nothingness prior to the existence of Time. This attributeless Infinite (Infinitesimal would be equally true) and absolute nothingness which is the Cause of all causes is what we can term as God. This is pure abstract, unimaginable, intangible Consciousness. This realization has been wonderfully expounded in the Vedas.

Now, how can we understand this Supreme Consciousness? Why is this Consciousness unimaginable? What tools do we have to conceive this Ultimate Abstraction if at all it is possible to conceive? Even though of elemental simplicity this Infinite Nothingness is unimaginable since the imaginer's role as an outside observer automatically negates the concept of Nothingness. It is impossible to separate the observer from the Observed. So what is the way out? Complete mergence with this Consciousness seems to be the answer. Experiencing this Consciousness by becoming It. Though it seems to be a rather lofty target it is by no means unattainable. The path to mergence is beyond the scope of this article. It would be sufficient to say that many before us from different cultures and sections of humanity have attained this state of mergence.

Now to the question of the tools that are at our disposal with which we can attempt to study this Ultimate Abstraction. Which is the science which we are all familiar with yet as abstract as the great Abstraction under study? What would the properties of this science be? As mentioned above, in the pre-Time scenario, this Consciousness existed as pure Nothingness, of pristine and elemental simplicity. So the closest analogy we can draw is the number zero, and the abstract science is none other than elementary mathematics. So how can, from this womb of Nothingness, this infinite cosmos come to be? Let us go back to math and examine something called the number line which most of us might have learnt at school. The number line is a line stretching to infinity at both ends (to positive infinity and negative infinity) containing all the real numbers including zero. It is something like shown below:

Since for every positive number there is a negative number of equal magnitude, then the sum of all numbers would have to be zero. In other words Zero contains All. Nothingness contains everything.

The same holds true if we take the case of imaginary numbers (of the form a+ib, where i = square root of negative 1) and consider their number line:

It is interesting to note that the only common element among the real and imaginary numbers is zero. If we put this imaginary number line (imaginary axis) perpendicular to the real number line (real axis) such that both are intersecting at zero we get something called the Gaussian complex plane. Looking at this plane comprising of the real and imaginary axes it would seem to us that zero is the centre from which light rays emanate to all infinities.

Now let x be any number, real or imaginary. x can be expressed as:

x = x + 0

Thus despite the grandeur of Nothingness, any and every number contains this Nothingness in its completeness. Now let us think of the things, people, souls, etc. around us as parts of a grand Whole, little windows to a grand scene. Aren't all these little parts analogous to numbers in the complex plane? Of course, there would seem the "frightful" possibility of equating inanimate matter and living beings! But would there? The Gaussian plane, as mentioned earlier, comprises of the real axis (the axis of matter and all things tangible), and the imaginary axis (the axis of the soul, ideas, thoughts, and other intangibility) and they intersect only at Zero.

Why does this Consciousness have to be attributeless? For the same reason that the number zero is neither positive nor negative. Does that mean this Consciousness is neither good nor bad, neither male nor female, neither beautiful nor ugly etc.? Precisely! But, at the same time it is also true that this Consciousness will be contained in things good and bad, male and female, beautiful and ugly etc. So it would seem that this Consciousness permeates the entire universe from the microscopic to the macroscopic levels. It is as complete at the level of quarks and neutrinos as It is at the level of quasars and galaxies.

This Reality is beyond all dualities and the illusion is in the scales of our perception!

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