Going Back To Some Basics part 5
What is Coordinate Space? we find a simple inner image of the Mind & also of the Universe’s vast Outer Space. Both images are of an essentially empty, formless Void, without boundary or inherent location, veritably infinite ∞.
To get to ∞–D we started at 0-D Space, the perfectly Infinitesimal Point, followed “up” by Extension for a virtual Quantum Fluctuation within a Planck quantum of Time, barely nudging into the 1-D Space of a infinite Line, which upon bending extends onto the infinite 2-D Plane. Not perfectly flat, the 2-D Plane warps & buckles into 3-D Space, & then with Time, a 4-D Space–Time, & then higher String Theory dimensions to Infinity as each bend, warp, or wrinkle invades a next higher-D Space. Beginning to end, the series is bracketed by interplay of 0 – ∞, Zero–Infinity Duality.
Indian Philosophy considers the Ego–self as the infinitesimal bindu 0-D Point. By analog duals, this bindu is the inverse of akash, the vastu the vast (actually translated as Reality), infinite-dimensional Ananta, the Infinite, like the Greek Apeiron, the All. The All in turn is the obverse of the zero point binding bindu. The interplay of these 2 extremes, in Cartesian Coordinate Space terms, dictates that the Container has no measurable size or locations without the reference Origin.
Consider oneself as if an invisible 0-D dimensionless & infinitesimal Point of View called Me, suspended as it were, in vast boundless Space. Are you near, or are you far? “From what?” you might well ask. How can you tell with no other point for comparison? Given some Other, another point in the Space, you are still at a loss to respond to the implicit how near/how far in any near–far query.
Coordinate Space references position & motion by establishing relative distance along x & y dimensions. Keeping track of positive & negative direction further completes relative distance to a relative displacement. In this way we get an answer to how near, how far.
The Reference Origin Point establishes the absolute numerical value or Coordinate Position of any Point in the Coordinate Space. Furthermore, with the absolute numerical value for our starting point, that is with respect to this Reference Origin, we address the preceding relative displacement question of “near / far” to where?
In the first case, we see that any Point & Location within a Cartesian Coordinate Space Container has that Location specified, firstly with reference Origin, a 0-D dimensionless & infinitesimal Point by which all other points are defined. Since the mathematical structures Coordinate Space & Reference Origin are so Objective, even if they could vaguely reflect Brahman & Atman, by their Objectivity, they do better at standing in for Mind & Ego, or Universe & Individual.
Limitless Coordinate Space has all points defined with respect to an infinitesimal Reference Origin Point, (0, 0) if we consider a 2-D example.
A limitless Universe is a container for Objects that all have meaning with respect to a specific Individual that I objectively call Me.
Limitless Mind is a container for Thoughts that all have meaning with respect to a specific Ego Reference Origin called “I” .
In each version, the Origin is contained within, but also defines the vast Space. Analogously, the Self is non-different from the vast Absolute Brahman. Thus the purest analogy, that Cartesian Space can claim, is that of an objective shadow of Self or Atman & the vast Brahman, in terms of Origin & Container. Murkier or more Dense is the equivalence of Mind & the Ego-Thought, & likewise Time & Now, Space & Here. The World & Body are the crudest Dual Analog in this series.
In the poetic comparison of vast infinite Space akash with its dual counter-part, the bindu or “bind” Point of 0-D, what is seen is the “forbidden” Arithmetic of reciprocal for Zero and Infinity, as duals of each other.
0 = 1/∞ ∞ = 1/0
The Ego-Thought is itself a more hardened, crystallized development of a pre-Thought Ego-notion imagined within Consciousness. In the Ego–Thought, the Me is a tiny thing, while Mind as a Space is considered boundless & vast. In Cartesian Space the Universe or the Mind is relative to that juxta-posed, Me or Ego Origin within Mind, & any 0-D point within infinite Space. The vast Mind is anchored & first delineated by the Ego or Me Origin. The Coordinate Space & the Origin then, the Mind & the Ego mutually Bootstrap each other into illusory existence by Dependent Origination. Vast Mind & infinitesimal Ego are like inverses or reciprocals of each other, much like Zero is the “reciprocal” of Infinity, & Infinity is the “reciprocal” of Zero.
Zero or 0-D is the infinitesimal point of no Extension, dimensionless, formless, indiscernible. This stands better as a symbol for the Non-Dual Absolute Reality, Brahman, or better yet for the identical Atman, the universal Self. Contrariwise, ∞ stands in better as an Objective symbol for Brahman, perhaps, but more truly for the Creator God, Isvara who is Brahman imagined with attributes, such as infinite Extension.
Without the Origin, the Coordinate Space of Mind is neither vast nor small, there would be no scale. Without placement within the Coordinate Space, the Ego would be neither minute nor huge, without some scale of reference. And so they both complete each other. Another illustrative phrasing could be that Mind is not actually differentiated from Consciousness without the Ego Origin, & Ego is not differentiated except as taken to be the reference Origin of Mind. Mind stripped of Ego is Consciousness. Ego stripped of Mind is the Self within this analogy.
Newton conceived Space as Aristotle did, as an unlimited Void. Einstein acknowledged relative distances between Objects but no intervening Space, at least not one of fixed & determined properties. The Eleatic philosophers lead by Parmenides denied the possibility of an empty Void. “Nothing” by definition is not something. Void Space it is not a cosmic swimming pool through which we can fly space-ships. Nor is it the Vacuum a Quantum piggy-bank out of which God or some inanimate Big-Bang can fashion Matter-Energy and Space-Time.
In more relative human terms, the same 0-D bindu reflects the supposedly fixed point of Me or Ego. Vast empty Space by the same token reflects the inner concept of Mind, the empty Container of Thoughts.
Rene Descartes represented the variation of simple functions by constructing graphs within the Mathematical device of his Coordinate Space. While physically represented as a piece of graph paper, the concept of Coordinate Space is that of a vast, boundary-less, formless, & empty Container which remains steady & constant like Newton’s absolute Physical Space. Each Location in the Coordinate Space is a potential Coordinate Point, defined in every case with reference to the central Origin Point where the Coordinate Axes cross.
In this next installment on the basic Duality of “Self” & “Other”, modeled in terms of Descartes’ Coordinate Space, we go past zero-dimensional, 0-D Point , & also 1-D & 2-D Surface to finish 3-D Volume Container & 4-D. But at the same time we introduce an additional key concept for 1-D through 4-D, that of the Mini-Container / Macro-Origin.
Now is the infinitesimal 0-D Reference Origin Point for 1-D Time. But on a larger timescale, such as human history, or the evolution of the Universe, then “my Lifetime” could be a relatively small Reference Origin without strictly being an infinitesimal 0-D Point such as Now. This practical 1-D Macro-Origin is also a Mini-Container to Me, since my Lifetime is an especially significant span of Time, as far as my interest goes. So a Lifetime can be a Mini-Container / Macro-Origin. For a Coordinate Space model of Mind, or whatever dimension, 1-D through 4-D, something like the collected ideas of my Personality could be a Mini-Container / Macro-Origin. A “world” in itself to Me, the Personality can also be a practical, though larger, Reference Origin. In 3-D Physical Space, my Vicinity could be a Mini-Container / Macro-Origin. In these examples, other Mini-Container / Macro-Origins could also be considered to fit a given application of the Coordinate Space model.
One important use of the Mini-Container / Macro-Origin lies in extending 3-D Physical Space or 4-D Space-Time to the grosser Coordinate Space of the “World” or Universe. When Coordinate Points become physical Objects in a World, there is no single infinitesimal 0-D Reference Origin Point available like Here which serves for the mathematical abstraction of 3-D Physical Space. One very useful Mini-Container / Macro-Origin for the World is the Body, & this is just where the Body comes into the Coordinate Space Model. The further significance of Mini-Container / Macro-Origins & the Coordinate Space Model is presented in the next & final installment along these lines. For now, suffice it to note that the Brain might be a smaller Mini-Container / Macro-Origin within the Mini-Container aspect of the Body. For again, physiologically speaking, the Body is a “world” in itself. The Body as a Mini-Container also clearly demonstrates how key Mini-Container / Macro-Origins always serve to define the Inside/Outside Duality, be that for the Body, my Vicinity, my Lifetime, my Personality, or whatever might be the Mini-Container / Macro-Origin considered.
Just as this concludes the basic outline of our Coordinate Space model of imagined Reality, so to does the following conclude Master Nome’s discussion of Inquiry & the Body & how the Self is subjective, while the Body & World are objective. In the installment will lay out the most fundamental mediations next time. The subsequent Master Nomes discussion commences the topic of Inquiry & the World.
meditations based on the Coordinate Space model. Subsequently we begin Master Nome’s discussion of Inquiry & the World.
The Self is not located in a Body. lt is not in Space. It is not located in relation to a Body. That is, it is not located in relation to a Body. lt is simply undefined by the Body. The Self being Space-like but not in Space, has no location. Being is neither a particular part of the Body nor confined inside it. If it were a spot or in a spot, the spot could be pointed out, & that very form would be the Self or would contain the Self, but, then, the Self would neither be Existence nor Real, neither Infinite nor Eternal, & there would be no Liberation from bondage. Then, the very declarations of the Wise would become false. This result & its causes are absurd. If the Self would be located throughout the Body or in a bodily spot, such location would be objective. The Self, though, is non–objective. The non–objective cannot have an objective location or other objective attributes. lf the Self were located in the Body, when that part of the Body underwent change or decay, so would Existence itself. If that part of the Body would be lost, the Self would be lost; if forgotten. then forgotten. The Self which is which is Real Being is never modified, is always present & is never forgotten. If the Self would be located throughout the Body, Existence would diminish & change as cells of the Body change. If one part were lost, even a single hair or cell, Existence would diminish accordingly. This, though, is not so, for the Self is changeless & ever undiminished. The Self is not located in the Body. The entire assumption of being located in a Body, as if the Body were a Container for the Self, is not true.
The perception. or idea of a Body & the notion of location appear in Mind, which is, & illumined by,
Consciousness, which is beyond all that. The known occurs within the knowledge of the knower, which is of the nature of Consciousness, & not one bit otherwise. Therefore, the Self is not the Body & is not in the Body. There is no Birth or Death for the Self, & the Self does not enter into or exit out of the Body. It is not in relation to a Body. It is not in the Body now, nor is it out of the Body at some other time. It is locationless.
The Self ever is ever as it is, with no modification. What it is, it is always. The Body, with its transience & mutability, is not an attribute of the Self. The Self does not possess a Body, for, otherwise, it would always have it, which is not so. Possession of a body is not in the nature of the Self & the Self, being Reality, never changes its nature. The Self does not have a Body, as possession implies division, or the duality of the possessor & the possessed & posits their relation. Being is Non-Dual & indivisible. Existence is Absolute. It is not in relation to anything. There is not anything to which it could have a relation, as a finite object might. The Self does not have a Body, as an attribute can only be for a “thing” & pure Existence is not a thing. The Self does not have a body. In this lies its great freedom.
The Body does not possess, or have as an attribute, the Self. The attributes of the Body are not the attributes of the Self. The Body is a form. The Self is formless. The Formless does not have a Form in any manner. The Self is Infinite & Space-like, ever the same, & bodiless. The Infinite does not wear a Body, & the Space-like has no Form. The Body does not possess the Self, & the Self does not possess a Body.
The Self is not the Body, the Self is not in a Body, & the Self does not have a Body. Know the Self to be bodiless. Thereby, abide as the Self, the bodiless Absolute.
[The above themes & 1600 pages more are freely available as perused or downloaded PDF’s, the sole occupants of a Public Microsoft Skydrive “Public Folder” accessible through www.jpstiga.com ]