Metaphysics & Geometry

Metaphysics is the science of the universals; it is the science of essences, i.e. realities that are universal and unchanging,i.e. do not depend on time or any particular degree of manifestation. Metaphysics is not the same as speculative philosophy or theories of creation. Metaphysics is and is true whether or not Big Bang Theory of the Hypothesis of Evolution are true. The subject matter of metaphysics proper is the Truth as perceived by the so-called Divine Mind. Metaphysics is not a human knowledge but is the content of the Divine Intellect or Pure Intellect. Metaphysics is not invented or learned; it cannot really be taught; it is only discovered, i.e. remembered, by a Seeing that is altogether other-worldly and absolute. This science, contrary to all other human sciences, is not done by speculation or experimentation but through intellection which is a transcendental, and by no means mental, activity of the spirit.

Metaphysics is about Truth Itself and not what men and women, whether saints or philosophers, have thought or said about the truth. Metaphysics is about the architectonics of reality as a whole, i.e. totality, as opposed to empirical science which consider reality only insofar as it is sensible and measurable by minds and men. We cannot say, for example, that metaphysics is other than physics though it is also not identical with it. Metaphysics encompasses all other sciences and is their very ground, but the nature of its relation to human sciences is always misunderstood; this relation is best understood only within the framework of an analogy, of course until the attainment of metaphysical realization which is the same as the Liberation. So, we offer the following analogy that we hope clarifies the nature of the relationship between metaphysics and empirical reality or empirical sciences:

Consider a video game in which your avatar, i.e. your embodied character inside the game-world, is put in a world similar to ours and its mission is to explore this world and find its natural laws. Basically, in this game you are a scientist that has to use the tools of the game to find the most general regularities of that world, things such as  gravity, electricity, etc. Now, if we want to transpose the idea of metaphysical knowledge into the context of this game, what element of the game should we choose? Let us begin by saying that metaphysics is not anything of the nature of a fact or a piece of knowledge within the game-world and can be sought and found in the same manner that one seeks and finds the facts of a world. It is not something that our scientist can find by means of exploring inside the world game.

Within the context of our game, metaphysical knowledge can be compared not to any natural law or any fact of the game-world but to the programming code that is behind the very phenomenon called the game-world and has made that world possible. Our scientist cannot find this underlying code by exploring inside the game-world and experimenting on its phenomena; he himself and all his explorations, etc. are nothing but the manifestations of the programming code underlying the game. To access metaphysical knowledge, i.e. the code in this analogy, the avatar does not even have to look outside himself or to move around, for this knowledge is, as it were, inside him, i.e. known by realizing that “there is a game” and then trying to transcend it. Now, how a game can be programmed so to make such our scenario possible, and whether it is possible or not, is entirely irrelevant here. The point of analogy was only to show the radical nature of this science of metaphysics and its relation to all other empirical sciences which can know only what is inside the game and not what is behind it. Even the methods of inquiry are radically different: In empirical science we explore and experiment, but metaphysical truths, i.e. that programming code, is not susceptible to such methods of investigations; the only way of accessing such knowledge is to somehow exit or transcend the game, or more precisely, to wake up rather than to look out and explore.

It is natural that the methods of inquiry inside the game, methods designed to find empirical facts and natural laws, can in no way help one even become aware of the possibility of a programming code behind the game, let alone finding that code. All such methods, all empirical sciences, are sciences of phenomena, but metaphysics, being the science of essences, i.e. the science noumena as opposed to phenomena, has nothing to do with phenomena but the meaning behind them. In other words, metaphysics studies the metaphysical roots of phenomena. Therefore, the failure of empirical methods in becoming conscious of the possibility of metaphysical knowledge, let alone discovering it, is only a failure and a shortcoming and doesn’t mean that there is no metaphysical foundation, or code, behind the game, a code that is different from the facts and natural laws inside the game simply because these laws are themselves manifestations, or projections, of that very code. One cannot use these methods to prove or deny the existence of a program behind the game, and this indicates the futility of all attempts at denying that there is a metaphysical foundation behind all things. The ultimate proof of metaphysical truths and realities is metaphysical realization, and this realization has been known and done and is not something up for discussion or refutation. As we have said many times, those trying to deny metaphysical knowledge, which by the way has nothing to do with god or religion but encompasses them, are like blind men trying to dispute the reality of a rainbow. A true metaphysician, i.e. a Jivan Mukta, never bothers trying to prove to anyone the possibility and reality of metaphysical truth; he can at best show the way for the seeker of truth to see and realize for himself that which is never a matter of opinion or speculation of any kind: The only proof of the Face is the face Itself.  

Now, what does all this have to do with geometry? Well, as we said metaphysics is the science of universal and immutable truths, realities that are unchanging, and hence do not depend on time or any becoming whatsoever. Thus, all theories of creation, modern or traditional, religious or secular, are only human theories and speculations and at best have symbolic value, for they all presuppose a becoming of some sort. In metaphysics, there is no becoming. Creation is a human fact; from a metaphysical, i.e. transcendental, point of view, creation and becoming are absurd and unreal concepts. But since we find ourselves as humans in the midst of a world of becoming, our thinking is conditioned by it and can understand things mostly in terms of being and becoming. At the same time, because of the transcendental nature of metaphysics it can only be understood through analogies until the point of metaphysical realization in and through which all metaphysical truths are grasped immediately and intuitively and with absolute certainty.

A proper and successful analogy is that which is based on a fundamental but common feature present in both sides of the analogy. Since immutability and the absence of time and becoming is the most fundamental and definite characteristic of metaphysics, the most appropriate analogical means for its expression should be another science that is devoid of the concepts of time and becoming. We know that all empirical sciences such as physics, biology, etc. are in fact about change and becoming, so they cannot possibly provide enough ground for a successful analogical method of communicating metaphysical truths. Of all the sciences accessible to man, the only one that is devoid of the concept of change and time is geometry, and in general pure mathematics. There is a direct correspondence between most propositions of geometry and abstract algebra, and this to the extent that we can even say geometry and abstract algebra are only two different ways of expressing same mathematical truths: In abstract algebra we are dealing with abstract symbols and their relationships but in geometry we are dealing with spatial relationships, so it is like abstract algebra only with the advantage of visualization. For this reason, geometry is a little more suitable for communicating metaphysical truths because it allows some space for visualization which is a great tool in all learning.

Thus, we believe and we can show that metaphysical truths, which are entirely independent of the concepts of god, creation, divine, etc. but are at the same time the very source and ground of all these concepts and realities, is best conveyed through geometry. And it is no surprise that geometry has always been considered a sacred science and present almost in all esoteric schools such as Pythagoreanism, Platonism, Neoplatonism, Eastern and Western religious esoterisms, and also in Freemasonry. For example, the letter G at the center of the symbol for Freemasonry consisting of square and a compass, traditional tools of architecture, stands both for God and Geometry, in which God is viewed as the Great Architect of the Universe who creates by means of immutable and intelligible relationships, i.e. geometrical forms. We only add that geometry is not to be seen as identical with metaphysics, and we should not think that in reality there are points and circles; but geometry and its concepts are used as the best symbolic means of expressing intelligible realities that are beyond any spatial relationships. In other words, geometry is the reflection of intelligible truths in the plane of human mind which can understand things only in terms of the conditions of time and space. The reflection of the sun in the pond is not the sun but can tell much about the sun, at least about its form. Metaphysics too exposes the universal forms by which truth can manifest Itself, the Truth Itself and in Itself remaining always unmanifest and only known by being it, a mode of knowledge accessed upon metaphysical realization, i.e. Supreme Identity.

It is outside the scope of this article to delve into geometry and show the metaphysical truths that are reflected in it. Our goal was only to show, firstly, the radical nature of the science of metaphysics and its relationship to all other spheres of human knowledge, and secondly, to suggest the best way of approaching this science, which is done through geometry. We hope that in the future we can devote a few articles to some aspects of metaphysics using geometrical truths. The main problem that makes metaphysics difficult to understand for the average mind is that metaphysics is not a science for everyone and requires a very refined and objective intelligence not deformed by the assaults made against the mind by the universal compulsory education. One needs to know some abstract algebra and be very well familiar with geometry, particularly the theory of functions, power series, Taylor Expansions, etc. in order to perceive the subtle metaphysical truth reflected in these forms. However, metaphysical truths, which is a way toward liberation and Supreme Identity, is not the only way. Religion and spiritual disciplines have the same end in view. While metaphysics is the way to Truth for the born philosopher, religion is a way for everyone, even the last man. The spiritual man if he succeeds may come to see the Face of Truth, but the metaphysician if he succeeds comes to see the Whole of Truth.

We end this piece by mentioning the simplest of all metaphysical truths whose reflection is found in the geometry of a circle:

Where there is a circle there is also a center, as no circle can exist without having and belonging to a center. A center, a singular point, however, can be without belonging to a circle. But what is a circle really? A circle is nothing but the expression of its center in terms of spatial relations. All the points on the periphery are the outward projections of the central point. In other words, a circle is nothing but a dimensionless point in expansive mode: Circle is the expression of a point. Or, when a point utters itself, the circle is that utterance.

Note that in expressing itself the center has not become, or turned into, a circle; the center doesn’t become the circle or cease to be the center; the center just is, and it is all that there is, for the circle is nothing but the center in its expansive mode: Circle is only a point’s dream. In reality, there is no expansion or contraction; there is only expression, the sound, The Word.

As every circle has a center and is nothing but a homogeneous expression of that center, every world, i.e. degree of manifestation, has an origin and is nothing but the homogeneous expression of that origin. This origin is exactly what is known as God in all spiritual traditions of the world.

In more abstract terms, a circle is the Taylor Expansion of a dimensionless point. Here, there are no two realities but only one reality with different names. To see and understand the exact logical and ontological relationship between the center and the points on the periphery of the circle consider this analogy: In life you are one person but with different roles or relationships. Say you are a man; to your wife you are a husband; to your son you are a father; to your father you are a son; to your employer you are the worker, and to your employee you are the boss; you can also be an uncle, a grandfather, a nephew, etc. As a father your relationship to your son is different from your relationship to your wife as a husband, etc. All these names, i.e. son, father, boss, husband, cousin, etc. which are different roles and relationships pertain to you, one and the same person. All these names designate different relationships that can be potentially established, or activated, within one and the same person; some of them may be only potential, for example you are only potentially a father when you have no kids, but once you have a child you have activated that potentiality which was within you all along and was nothing apart from you. Now, the logical and ontological relationship between you and all these names, i.e. relationships, is the same as the logical and ontological relationship between a central point and all the other points on the periphery of a circle spanned by that central point. Therefore, there are no many points; there is no becoming. There is one reality and multiple expressions, the expressions being only potentialities within one and the same point which is the basis of all Reality.   




4 thoughts on “Metaphysics & Geometry

  1. This post is such a rich, palatable food for thought for all the Truth hungry intellectuals out there..
    I wish more people read this, and I wish you continue doling out discoveries of your research with such helpful examples for the small minds like me here grappling with the ‘understandings’ of metaphysics..
    Just one question, on the potentiality, what do you attribute potentiality to in the real metaphysical context.Individual Perception?

    Liked by 1 person

    1. RamG I apologize for very late reply.
      About potentiality it is said that it is in the nature of the Absolute, godhead, Brahman, etc. Since Brahman is infinite it must contain everything within it but only in potential form because Brahman Himself is the only actuality, and the actuality of everything is borrowed from It. Individual perception is one such potentiality but in reality all perception is God’s perception; so there individual is really non-existent in itself and it is illusory because it is existence is borrowed from Brahman which is the ground of Being.
      The best analogy for seeing the relation between individual (particular) and the universal is our dreams. Our dreams are the reflections of the impressions of the waking state; or in the language of psychology, dreams are the animated subconscious. Now, in your dream you appear as an individual among many other individuals with whom you interact and talk, etc. In the dream all these individuals, including yourself, have perceptions (as we experience them in the dream); but their reality and perceptions are really the reality and perception of one single mind, the dreamer’s mind; those dream characters are real only in the level of the dream; but from the point of view of a higher state of consciousness they are all the many aspects of one single mind; those individuals are projections of that one mind. Now bring this comparison to the level of our waking state and see that comparing to the universal mind, this world is like a dream or subconscious. So all these individual beings your see, and their perceptions, are really only ideas or projections in the mind of God. All beings are Him and all perceptions are His.


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