Tractate 1 : The Error of Zeno (continued)

Zeno’s Paradoxes of Motion Revisited
Zeno initiated the concept of incrementalization, which in essence was the recognition of individuality. This individuality is not individuality only in terms of a living entity. Rather this individuality extends far beyond our universe and into the realm of unique individual universes themselves, universes infinite in terms of the dimensions length, width, depth, and time. Strangely enough, this ‘infiniteness’ of space is confined within a boundary bounding what we commonly call the universe or universes.

However, a boundary implies a ‘region’, which in turn takes up ‘space’, takes up ‘distance’, and as we shall see, takes up ‘time’, takes in time, and incorporates time. This ‘bounded’ ‘region’ ‘contains’ an infinite ‘quantity’ of time. But infinity is not always what it seems to be, as we shall see.

There is another alternative to concrete distance. There is a concept of abstract distance, which in effect takes up no ‘space’ for it is abstraction. Zeno showed us distance has two aspects to it. Distance has the aspect of physicalness and the aspect of abstraction. Both are real.

One is reality when one is immersed within it. From this viewpoint, from the viewpoint one perceives when one is immersed within the physical, the other, abstract distance, becomes a real illusion. One must not loose track of the fact, however, that abstractional distance does not ‘go away’ just because one is immersed ‘within’ the concrete functionality of distance, just because one is immersed within physical reality. Abstraction does not become unimportant, does not become ‘just’ an illusion when one is immersed ‘within’ the physical, the concrete, multiplicity.

One can erase the picture of a flower but the flower remains and the concept of the flower remains as well. Both the flower and the concept of the flower are real and both remain even after one erases the picture of the flower. Whether the flower itself or the concept of the flower itself, is ‘real’ is not the question for they are both ‘real’. When one is ‘real’, the other appears to be a ‘real illusion’. They oscillate back and forth from being ‘real’ to being a ‘real illusion’ depending upon where it is one ‘stands’ as one examines the flower, experiences the flower, finds oneself immersed ‘with’ the flower be it in an abstract sense or a physical/concrete sense.

Once ‘within’ the concrete, it is the reality of abstraction which takes on the appearance of being an illusion but which in fact is a ‘real illusion’, a ‘functional’ illusion. Once ‘within’ the abstract, it is the reality of the concrete, which takes on the appearance of being an illusion but which in fact is a ‘real illusion’, a ‘functional’ illusion. Neither the ‘real’ nor the ‘real illusion’ become unimportant to the whole for the whole cannot exist without the two for the two are integrated as one, and are in fact the ‘whole’. Each is dependent upon the other. The one, the Cartesian, the physical/concrete, is the engine of the other, the non-Cartesian, the abstract. And the other, the non-Cartesian, the abstract is the ‘creator’ of the other, the physical/concrete, of its own engine, of its means to ‘grow’ as opposed to stagnating or decaying away.

So which is the innate characteristic of which? Is the abstract – seamlessness the innate characteristic of the physical – multiplicity or is the physical - multiplicity the innate characteristic of the abstract – seamlessness. The complex answer is: It all depends upon where one is standing when one asks the question. Since we perceive ourselves to be ‘within’ the physical when we ask the question, the answer surprisingly becomes: the physical is the innate characteristic of the abstract. The physical is simply a ‘real illusion’. The physical has something inherently related to it. The physical is connected with time and time, by its very property of having infinity and zero attached to it, is limited.

And how can this be so? It is so because zero and infinity are one in the same, meet in the same place.

To better understand this concept one only need examine a simple number line:






Now it would appear the next step is:

But this is not so. It is only the case if one ignores the concept of individuality. If one retains the concept of individuality, then the graph becomes:



And what then is zero? Why zero is the beginning of the development of the unique individual point. But if that is so then the graph is once again incomplete and should in actuality become:



Or more simply put:



As we can see, individual units of mathematics, in fact individual points themselves, albeit they are incrementally so small they do not exist in terms of dimensions, begin with zero and expand to the point of infiniteness itself. Now this may be the case with mathematical points but what of individuality?

The individuality of each unique ‘piece’ of awareness also begins with zero, zero awareness, and expands into being itself, unique, through Zeno’s concept of infinite ‘multiplicity’ or as is the case of individuals, infinite numbers of events an individual experiences. Regardless of the number of years, months, days, hours, minutes, seconds… the individual, once put into action of being, having ‘become’, experiences infinitely.

Who is to deny, once having gone from point A to point B the individual has experienced infinitely. After all, one experiences while having gone half the distance and one experiences while going half the remaining half, etc. On the other hand one has experienced differently if one views the summation of one’s experience in terms of the summation of experience incurred when having gone two thirds the distance as opposed to the summation of experience incurred having gone one half the distance. The two summations of experiences provide the individual with an entirely different and unique perception of its existence. The very establishment of the zero point of becoming, what may better be referred to as virgin consciousness, one’s very existence, is in a sense an establishment of infinite existence for the individual in terms of multiplicity of being.

For example, lets us say the life existed for a nanosecond, Zeno’s paradox shows that in fact the life lived for half of a nanosecond and half of the remaining half, and half of the remaining half. But that deals with time, what about motion? In that nanosecond the form moved however little it moved and as such it moved half the distance from it original position its final position, and then half that half then half that half etc.

The individual’s perception of its total summation of half experiences is different from that same individual’s perception of its total summation of two thirds of its whole experience plus two thirds of the remainder plus two thirds of the remainder of the remainder etc.

Perceptions differ by increments of fourths, fifths, sixths,

Now mathematicians would step in at this point and say: No, it was just one continual flow from point ‘A’ to point ‘B’. But they are wrong. Calculus may allow us to understand, see, a continual flow of motion but Zeno is still correct, during each step of the way, at each point existing between point ‘A’ and point ‘B’, the life, awareness, was aware of, experienced, and as such an infinite series of experiences occurred, multiplicity occurred and Calculus cannot negate this fact.

Now it is true Calculus can provide us with a means of moving on and leaving this point of confusion behind but it cannot eradicate the fact that incrementalization does in fact occur.

‘So what?’, one may ask. So it is up to us, philosophers, to answer Zeno’s paradox, bring forth a rational resolution to this paradox. It is up to us, philosophers, to bring forth a rational resolution regarding Zeno’s paradox. Such a resolution takes a detailed understanding of this paradox. Understanding Zeno’s paradox assists us in understanding ourselves, understanding where we are, understanding what we are, and most interestingly of all, understanding why we exist, understanding what our function for existing is.

With this in mind lets once again look at the number line and think of it in terms of the abstract concept of awareness rather than the impersonal cold concept of points on a line.

The end of each unit on the number line can be thought of as the end of one increment of individuality and the beginning of another increment of individuality, a form of individualistic seamlessness. But seamlessness of distance can only be seamlessness when viewed in the abstract. The same applies to individuality. In the abstract then the diagram would look more like:



Now if we break this diagram up into its unique pieces of individuality we obtain:



Now where is time in all this? Time is a part of experience and so we obtain:



Therefore, it is the individual who moves through time. It is the individual who gains experience beginning with no experience, beginning with virgin consciousness and ends with the end of consciousness, the end of the individual traveling through time. So it is the individual leaves the concrete, the physical, multiplicity and moves into the abstract, seamlessness.

We can examine the concept regarding the meaning of Zeno’s implied concept of abstractional existence – seamlessness existing within the physical – multiplicity but first we need to examine the concept regarding Greek ‘incrementals’ a little further.

Or

One could say: Before we can go there, before we examine the concept of the meaning of Zeno’s implied concept of an existence, of the physical – multiplicity within which abstraction – seamlessness can be found, we need to examine the concept of Greek ‘incrementals’ a little further.

Now what is the difference between these two statements? The difference can be more clearly understood through diagrams rather than words.


The appearance of the ‘real’ and the ‘real illusion’:






Look familiar?

Now what does one view from the point of view of being ‘within’ death? One views experiences that are. One views all experiences that ‘are’ but none that ‘are yet to be’. One would think this concept of ‘to be’ implies the existence of time and that is true but not in the traditional sense for time is not a part of what the incremental pieces of awareness, find themselves located ‘within’ abstraction. Rather time is a part of the experiences individuality has created for itself, created for the whole while being a part of, ‘within’ the physical.

Thus time is not something ‘within’ which the whole, the abstract – seamlessness, finds itself immersed but rather time is something immersed within the pieces of individuality, tied to the physical, concrete multiplicity of the individual’s awareness. Time is but a process by which the chaos of the Brownian motion of time itself becomes orderly.

The implications of this will be fully addressed within Chapter 9: ‘Einstein and i’. At this stage of the examination of a new philosophical perception, we have all we can do to remain focused upon the concept of the individual in terms of abstraction – seamlessness and the physical – multiplicity.

So what of life and death? We view life as existing and death as the state of non-existence. As such we view life as not only being sacred but we view life as something to be protected at all costs. Some would say we should allow one individual to take the life of another rather than perform the ultimate act of finality ourselves, the act of taking the life of a third party threatening to take the life of an innocent second party.

From the point of view of ‘death’, or might we better say, from the point of view of purely abstract existence, it is the journey itself which must be protected. It is the journey, through the process of living life that has significance.

It must be noted here, that to perform capital punishment is not protecting life, protecting a journey. Once incarceration of the guilty party has occurred, the journey of others has already been protected. To electrocute the incarcerated life form, to electrocute the guilty party, is nothing short of needlessly terminating a journey, which has already been restrained from harming other journeys. In short, capital punishment is nothing less than ‘murder’.

The Greek concept of ‘the incremental’
So where does this bring us in terms of the Greek concept of incrementals? It brings us to the concept that it is the individual which must be protected, for the individual is ‘the’ increment of awareness.

We naturally fall into the argument that it is life, which we must protect but that in fact is only one perception that can be derived from this line of thought. Perhaps a more rational argument is that it is not life which must be raised to the level of the ultimate significance but rather the journey of life itself, the ‘right’ to travel in one’s own unique manner, uninhibited by the desire of others to dominate, subjugate, dictate how others are to journey, which must be raised to the level of the ultimate significance.

The validity of each argument, whether it is life or the journey of life that is to be protected, is dependent upon the location from which one views the argument - that the second point, the point that it is the journey, which must be protected, and not life as such, becomes a potentially viable alternative.

So lets look at the concept of life, the beginning of an individual, the initiation of the individual, the beginning of existence in the physical/concrete - multiplicity, and lets look at the concept of death, the end of the individual, the end of existence in the physical/concrete – multiplicity.

Just what does this have to do with ‘incremental’ concepts? The individual is in essence ‘an’ incremental piece of ‘the whole’. The individual is in essence a piece of the ‘whole’ of awareness.

Zeno's Perspective



Zeno’s perception generates a paradox for there is no ‘whole’ of perception. The perception becomes even more muddled when we move awareness from consciousness of its own awareness into what we perceive to be nonawareness of its own awareness:



So it is the ‘real’ and the ‘real illusion’ become the ‘real illusion’ and the ‘real’. The ‘real’ and the’real illusion’ alternate back and forth as one moves from one to the other. We do not, however, view it as such. Instead, we view it as life being the state of existing and death being the state of not existing, death being the end of it all….

In the case of life and death, the perceptual ‘size’ of the universe did not grow to accommodate, make room for the abstract. Zeno’s perception of an abstractual existence did not interpret into an understanding of death being simply a movement into a form of abstractual existence. Instead, we discard death because we view it as the end. As such, death did not expand upon our perception of what is but rather death simply became a non-existence taking up no space in reality and thus reality remained what it was: small, limited, a permanent location for temporary existence.

In spite of our faith in life after death, we have not been able to rationalize such a concept. Science has been unable to observe such an existence and philosophy has been unable to rationalize such an existence. As such, existence after death remains only a matter of faith.

We are an entity capable of forming perceptions using three basic means of action: believing, observing, and reasoning. As of yesterday, only one means of forming perceptions existed. This perceptual process for reinforcing the concept of eternity existing for the individual was a matter of faith, believing.

Zeno, with his paradox of motion, put into play the philosophical and scientific debate regarding an understanding of timelessness, of eternal existence. It was only a matter of time as to which, science or philosophy, was to reach an understanding of timelessness second.

That point has now been reached by philosophy. It could be argued philosophy has not reached a point of rationally understanding the existence of seamlessness, rationally understanding an existence without time being the ether within which existence is immersed.

It could be argued that philosophy has not reached an understanding regarding an eternal existence independent of time resting upon the understanding of mathematics and science, resting upon the understanding regarding the primitive concept of nothingness being the spark for the explosion separating the symmetrical concepts of matter, anti-matter, energy, and anti-energy.

Such arguments however, are not the point. The point is philosophy, as of the end of the twentieth century and the beginning of the third millennium, has reached this point and science has not. No, actually the point is the vote for an existence of a timeless awareness is now two to one in favor of the concept rather than two to one against the concept of timeless awareness. The tide has turned. The significance in this turning of the tide lies in the fact that an overwhelming majority, two to one, the two, religion and philosophy, verses the one, science, means we now have the votes necessary to move toward the acceptance of the individual as ‘the’ increment of timeless awareness. Thus the necessary votes to treat the individual treat all individuals, as ‘the’ significant entity because it is eternal.

This in turn brings us back to the question that had been previously asked: This seems so inconsequential when one views a small child starving in Uganda, but is it?

We can now return to the concept regarding the significance of such a child. No longer is the child simply a child, dies, and is no more. Two out of three means we have for developing perceptions, religion and philosophy, now both agree the child is not simply a child, dies, and is no more. Two out of three means we have for developing perceptions, religion and philosophy, now both agree the child is a child, leaves the temporariness of the physical, and enters the timelessness of the abstract.

(The function of this piece of awareness, of this child, to the Whole is intuitively obvious. Despite this fact, however, the concept will be dealt with in detail in many of the following chapters and in particular in Chapter 10: Heidegger and Chapter 14: Metaphysical Systems.)

Repeatedly we come back to Zeno. Zeno leads us from what was before he began thinking…

Physical Distance



…to what was after he began thinking…

Physical Distance - 'Multiplicity

&

Abstract Distance - 'Seamlessness"



…which in turn became a new but elusive concept of the physical – ‘multiplicity’ ‘containing’ abstraction – ‘seamlessness’. Zeno initiated the debate within which religion, philosophy, and science became embroiled. Zeno in essence defined the debate.

Zeno initiated the perceptual growth of what we understood to be true. Zeno forced us into debating the concept of multiplicity existing separate from the concept of seamlessness verses multiplicity existing simultaneously with seamlessness. This in turn forced us into examining multiplicity and seamlessness, examining where such concepts were ‘located’ with respect to each other, examining how such concepts interacted, and examining what our role was in such an interaction

Zeno began this long-term (twenty five hundred years) speculation through the process of expanding upon what we perceived to be with the simple introduction of his paradoxes of space/distance and space/time. Zeno lead to the growth of what it was we perceived to be. Zeno expanded upon our perception of the universe. Zeno added the concept of seamlessness to our perceptual understanding as to what was to be ‘found’ within the universe.

But the increase in perception did not resolve Zeno’s paradox for it did not explain why the paradox was a paradox when viewed from Zeno’s perception as seen from his ‘location’ ‘within’ the physical/concrete. The resolution of Zeno’s paradox would take a greater expansion than that proposed by Zeno – the inclusion of seamlessness/abstraction, within the concrete/multiplicity.

In essence, Zeno was standing on the departure platform he built and waving goodbye to us, humanity, as we boarded the train for the long trip which would lead us to our present destination, an understanding of a ‘location’, a definition, and a significance of what is.

After twenty-five hundred years we would find ourselves expanding Zeno’s perception of what is. After twenty-five hundred years, we would find ourselves looking at a simple diagram of a new perception of what is.



Or what one might call:

Philosophically speaking: ‘being’ being ‘Being’

Religiously speaking: symbiotic panentheism

Scientifically speaking: ? (symbiotic panentheism)