Tractate 8 : The Error of Einstein (continued)

To advance our understanding regarding our present perception of the ‘real’ illusion of physical reality we next need to deal with the concept of negativity. We need to examine the negative in relationship to the positive.

This leads us to the concept of Rational numbers as opposed to positive Rational numbers. First however there is one more correction, which needs to take place. As the diagram presently exists, each unique number blends with another. Each number can only be diagramed as a number because of the circle we have drawn ‘between’ them. For example we can see the number one is separate from the number two because it has a boundary, the circle.

However, a physical boundary takes up ‘space’, takes up ‘distance’, and as we shall see, takes up ‘time’, takes in time, and incorporates time.

The tractate regarding Zeno showed us 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 physical ness and the aspect of abstraction. Both are real. One is reality when one is immersed within it. From this viewpoint the other becomes a real illusion, but does not ‘go away’, does not become unimportant, does not become ‘just’ an illusion. One can erase the picture of a flower but the flower remains and the concept of the flower remains as well. Both are real and both remain. Which, the flower itself or the concept of the flower itself, is ‘real’ is not the question for they are both ‘real’. One is ‘real’ when the other is a ‘real illusion’ and the ‘real illusion’ becomes what is ‘real’ when the ‘real’ becomes the ‘real illusion’. The ‘real’ and the ‘real illusion’ go back and forth depending upon where it is one is located when one examines one or the other, as one experiences one or the other, as one finds oneself immersed ‘within’ one or the other.

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. The real and the ‘real illusion’ do not become unimportant to the whole for the whole cannot exist without the two for the two are integrated as one. Each is dependent upon the other. The one, the Cartesian, the 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, is the ‘creator’ of its own engine, is the ‘creator’ of its means to ‘grow’ as opposed to stagnating or decaying away.

What do the boundaries of zero dimensions, the means of separation, have to do with the concepts of abstraction and the physical? The boundaries are what they are. What are these black circles? The black circles are just what they were said to be. The black circles are, in essence, nothingness. The black circles are ‘something’, they are nothing and as something have functionality as nothingness. The black circles, nothingnesses, are the means by which unique individuality expresses itself. The circles are a means of individuality retaining its individuality through the existence of the somethingness of nothingness itself.

With the black circles of ‘nothingness’ one obtains an understanding of individuality, one obtains an understanding of unique and distinct individuality:

Positive Rational Numbers = {#’s > 0 which can be expressed as a/b where a and b are whole numbers and where b &Mac185; 0}

Tunnel of Positive Rational Numbers:

Without the separation of individuality created by the boundaries of ‘nothingness’, one loses order, distinctiveness, individuality and the diagram becomes:

So? So chaos reigns and becomes seemingly meaningless but as we shall see as we proceed, what seems to appear ‘to be’ need not ‘be’ what is. This paradox of chaos and lack of order evolving out of order is simply what all paradoxes are. This paradox is simply a lack of perceptual understanding and as such the paradox disappears with the infusion of perceptual understanding, abstract understanding.

Ok, ok, once again, now what?

Now we return to our task of understanding abstractual functionality through expanding upon our understanding of numbers, which is but one of many infinities to the infinite power forms of abstractual potentiality.

Positive Rational Numbers = {# > 0 which can be expressed as a/b where a and b are Whole numbers and where b &Mac185; 0}

Tunnel of Positive Rational numbers:

Now becomes:

Rational Numbers = {#’s which can be expressed as a/b where b &Mac185; 0 and where a and b are integers (as opposed to being Whole numbers)}

Tunnel of Rational Numbers:

The tunnel is gaining greater depth as we look down the tunnel from our position within the tunnel. It appears to be gaining the dimension of depth through the process of ‘moving’ in one ‘direction’ so let’s gain a better understanding of this ‘expanding dimension’ by turning around and looking in the other ‘direction’.

Now several characteristics emerge:

  1. The tunnel retains its division of individuality through the use of ‘nothingness’.
  2. Another aspect emerges which demonstrates the need for our previous apparent digression regarding the concept of Zeno and nothingness, which is that nothingness:

    a. takes up no space
    b. does not exist within the reality of the concrete
    c. does exist ‘within’ the realm of the abstract
    d. is the only ‘thing’, which retains its same characteristics ‘within’ both realities, ‘within’ the reality of the concrete, and ‘within’ the reality of the abstract.
    e. is, within both the reality of the concrete/physical and the reality of the abstract, ‘nothing’.

  3. It, ‘nothingness’ is not negation for as we see in the above diagrams negation is as real as the positive. ‘Nothingness’ is not just a concept of a lack of a concept, it ‘is’ and as such it has a function just as significant to the realm of abstraction as the significance of the lack of ‘nothingness’ has to the realm of the concrete/the physical.
  4. ‘Nothingness’ finds NO location for itself as its own unique individuality. Individuality can be seen as beginning at the black circle of zero and as individuality expands, takes on the characteristics of _ its experience, _ its experience, 7/8 its experience etc. until it finally emerges as ‘one’, emerges as individuality, emerges as an individual.

Now you will notice the individual does not begin at one and move to two. Rather the individual begins at zero, what is called a ‘virgin’ consciousness and moves on to become ‘one’. The whole of a unit of multiplicity of individuality never becomes ‘one’ however until the entity’s journey has ended, until the entity’s experiencing has ended. The second individual, two, does not necessarily begin after one has ended its journey, rather the second ‘one’ begins at zero, at its virgin consciousness, just as the first ‘one’ began at zero.

In terms of individuality, our graphic now becomes:

In this diagram the totality of the number, the totality of the individual number, the totality of individuality is composed of all its experiencing. Thus _ becomes a part of what makes up one and 1 _ becomes a part of what makes up the second individual.

Zero, ‘Nothingness’ remains just that nothingness. The characteristic of nothingness exists as itself whether nothingness exists in the realm of the negative numbers, the positive numbers, abstraction, or the concrete.

To move forward with understanding we need to expand our concepts of numbers to include the Irrational numbers. The Irrational numbers combined with the Rational numbers would give us the set of Real numbers.

Ironically, it was mathematicians not metaphysicians or philosophers who named real numbers: Real numbers. The significance of the name Real numbers will become apparent when we examine Imaginary numbers in the next section of this tractate. Real numbers are, in essence, all forms of numbers, both positive and negative, which fit between the circles of nothingness, which in turn separate our units of individual numbers. We have seen this set from the inside.

Now let’s step outside the set and get a look at what we have:

Tunnel of Real Numbers – outside view:

Keep in mind; the circles divide individual number from each other. These partitions are actually zero, nothing, yet they allow the uniqueness of each number to exist independent one from the other. Each number in turn is simply one unique number beyond the next and each number emanates from the point of its virgin origination and proceeds to its point of termination of experience which for numbers moves from the point zero to the point of being a whole unit. For numbers, what falls between these two points, zero and wholeness, are the concepts of Rational and Irrational.

It is interesting that mathematicians have named these sets independent of metaphysical thought. Surely, one has to wonder about the concept of ‘pure coincidence’, serendipity. Not only do the names, Rational, Irrational, Real, Imaginary, etc have huge implications for metaphysical thought but so to do the concepts the names metaphysically imply in terms of the new metaphysical system of ‘being’ being ‘Being’. The simultaneous correlations seem to be too ‘purely coincidental’ to be ignored. Perhaps this in itself is a testimony regarding the application of Ockham’s Razor ‘across’ subject matter boundaries.

If we expand the ‘length of the tunnel of numbers we obtain what appears to be an endless division-less tunnel. We ‘know’ however that the tunnel is composed of unique elements of individuality of numbers. As such the ‘endless’ division-less tunnel is not what exists, rather what exists is an endless tunnel comprised of unique units of individuality.

Imaginary Numbers
We have reached the outer limits of the Real numbers. Mathematicians at this point discovered they have a problem. There are mathematical operations we cannot perform with the existence of this set alone.

The square root of the number one can be found within the tunnel. The square root of one is plus or minus one since: +1 x +1 = 1 and –1 x –1 = 1. One cannot, however, find the square root of a –1within the tunnel. In order to establish a solution to the square root of a –1, one must create a new set of numbers. Having established such a set, one must then name the new set. Appropriately enough, mathematicians, after having established the new set, named the new set of numbers: Imaginary numbers.

The solution to the problem, the square root of a –1, now becomes +/- i. ‘i’ represents what we call the imaginary number of… It is the task of mathematicians to determine if this set has a one to one correspondence to the set of Real Numbers. The task of metaphysics is to determine how the concept of imaginary numbers relates to metaphysical systems and in particular to the new metaphysical system of ‘being’ being ‘Being’. The question for metaphysicians regarding ‘being’ being ‘Being’ becomes: How does the concept of imaginary numbers, imaginary things, fit into a system of non-Cartesianism powered by Cartesianism, ’being’ being ‘Being’?

It is graphics and in particular the graphics we have already established that will help us understand the answer to the stated question.