“One is the Onliest Number”
In conventional mathematics, an infinitesimal is defined as a number that is greater than zero, but whose value is too small to be measured. Such a concept seems as refractory to understanding as the concept that Infinity is a value so large that it cannot be measured. Both Infinity and infinitesimals have the quality of being unmeasurable, so for purposes of space/time Experience, the infinitesimal and Infinity are disregarded in favor of the fixed, tangible measurement.
However, measurements in general are of very limited value without a reference measurement. For example, to know what a “meter” is, you must have a reference meter that you can use in order to verify that, in fact, you have measured a true meter. Otherwise, a meter might be different for everyone who measures it. The surprise is that, even with a “reference” meter, no two meters are measured to precisely the same length because accuracy is dependent both upon the limit of resolution of the measuring device and upon the one doing the measuring.
So, is there a reference that we can use no matter what the measurement in question is? Truth is that the only reference we have that never changes is Infinity, and Infinity cannot be measured. Infinity is the Reference because Infinity is the essence of Reality. All other “references” are arbitrary dimensionals along whatever whole dimension the measurement is made.
Recognizing the need for a reference, scientists have sought reliable standards to be used as reference measurements. The ideal, or most reliable, standard would be a finite absolute measurement that never changes; no such measurement exists, so scientists have settled for standards that rarely change rather than one that never changes. However, choosing any measurement greater than zero, yet less than Infinity is, in truth, an arbitrary choice. Infinity, while Absolute, is not a measurable quantity so is not recognized as a standard for finite measurements.
But Infinity is the only true (absolute) Reference, so what does this mean in terms of standards and measurements? What this means is that any measurable quantity, when compared to Infinity, is so small that a true (absolute) measure cannot be assigned to it, only a symbolic or relative one. Furthermore, any measure which, by definition, is a limit, cannot have any meaning unless compared to another limit. Thus, the true meaning of measurements is relative, not absolute.
This also means that everything that has a measure assigned to it meets the definition of infinitesimal when compared to the true Reference, Infinity. Thus, the quality of the infinitesimal, rather than being of mere esoteric interest to mathematicians, is of vital importance in understanding Reality.
But what of numbers, such as 2, 11, or 1028? While the conventional understanding of numbers is that they can be arranged in a series such that at one end you have the smallest and at the other end you have the largest, this concept can be true only in a relative sense, as in the comparison of one finite quantity to another finite quantity. In terms of Reality, all finite numbers are divisive. What this means is that 2 symbolizes the 1 divided into two parts, each of which is smaller than the 1, and 11 symbolizes the 1 divided into 11 parts. Contrast this with the conventional understanding that 2 is “twice as many” as 1, and 11 is “eleven times as many” as 1. The observation that 2 is “twice as many” as 1, for example, is a comparison between two fractions of the One, and that is what yields the illusion of “greater” and “lesser”. This is easier to grasp if you consider that “2″ and “1″ are actually 2 ⁄ and 1 ⁄ . So, 2 ⁄ is “twice as much” than 1 ⁄ , but this is a relative comparison only because so long as Infinity () remains a part of each fraction, the actual values are infinitesimal. Leaving Infinity in each fraction references the Reference (i.e. ⁄ , the One), so in order to make space/time sense of these numbers, 1 ⁄ and 2 ⁄ must each be multiplied by in order to remove it from the equation. You are then left with 1 and 2 as relative quantities.
Look at an example using a group of apples. To evaluate this quantity of apples, the “universe” of apples must be referenced by default in order to establish a relative measure and thereby give meaning to it. This universe of apples is a finite quantity, so it can be used as a relative reference so as not to yield infinitesimals. Within the universe of apples, a portion of it, such as 11 apples, is a fraction of, not more than, the universe. Eleven apples do not exist apart from the universe of apples, so to measure 11 apples you must divide that universe such that you have a quantity you can call “11″.
Furthermore, you cannot reference the universe of apples without referencing the universe of fruits in order to establish what an apple is, relative to all other fruits! This referencing must go on until you, at long last, reference the Reference, Infinity. However, since a measured quantity becomes infinitesimal when compared to Infinity, those working with finite quantities will avoid any referencing that involves Infinity.
Finally, regarding things as separate items able to be counted is a concept that is part and parcel of the paradigm that separation is reality. Separation cannot be Reality, given that the concept of “all is One” is Reality. Therefore, the infinitesimal is an artifact of the illusion of separation, and is dependent upon the concept of limits, which is also illusory.
The primary reason why I am proposing that numbers greater than 1 are divisive is the basic mystical Truth that “all is One”. Thus, anything that is “not all” is less than, or “smaller” than One. One, then, is the center, and all numbers “below” One as well as all numbers “above” One are divisive in nature, and represent iteration of the One. With this in mind, we find that numbers as a series can be represented on a polaric axis, with the “infinitesimal” (a number just slightly more than zero) at one pole and the opposite of the infinitesimal (a number just slightly less than Infinity) at the other pole. In fact, all numbers are slightly more than zero because the definition of Infinity means that no matter what the “size” of a number, the number still meets the requirements of an infinitesimal when compared to the Reference, Infinity! So that observation shows that the two “poles” of this numeric spectrum are equivalent because the value of both of them is infinitesimal! Here’s another example: using this understanding, what is the difference between two points labeled 0.5 and 2 on this axis? The answer is that they are equivalent in value, because 0.5 is 1/2 of the One and 2 is the One divided into two equal parts. The symbols simply distinguish which “side” of the axis the measurement is being made along.
The “size” of this axis, as defined by the two polaric limits, is arbitrary, and in fact this variable and arbitrary nature is part of the reason why the space/time universe, or panfractalic, manifests as it does.
Next, what of negative numbers, and “imaginary” numbers, such as the square root of -1? These numbers are found along a second and third axis, respectively, defining coordinates in a space existing along three dimensions when taken together with the first axis. The first dimensional coordinate axis is the axis I described with “1″ at the center, the numbers “less” than 1 on one side and the numbers “more” than 1 on the opposite side. The second axis has -1 at the center, but the two sides are the numbers “larger” than -1 (like -0.5) and the numbers “smaller” than -1 (like -2, etc.).
The third axis has the root of -1 at the center, and the parts of the axis on each “side” of the center are like the parts on the first axis I described, with the exception that each of the values are multiplied by the square root of -1, or the symbol “i”, as designated by mathematicians. For example, the number on the third axis corresponding to the number “2″ on the first axis is the number 2i, or 2 multiplied by the square root of -1. The opposite side example would be a number such as 0.5i, or 0.5 multiplied by the square root of -1.
Using this model, a point may be located anywhere in this complex space by using three coordinates, one from each axis given. The center coordinates are (1, -1, 1i); contrast this observation with the conventional model, in which the coordinates of the center are (0, 0, 0). The idea that 0 is the center is congruent with the concept that such a thing as true “nothingness” exists. This would also include the idea that from nothing came all that we know of as the physical universe. Likewise, the possibility of having “nothing” (0) is an artifact of the concept of limitation and separation which, as I have previously explained, is not Reality. To “have nothing”, in Truth, would mean that you had no dimensional connection whatsoever to whatever you feel you don’t have, and the only way that would be possible is if Infinity could be separated from Infinity. I will cover the idea of zero in greater detail in the next chapter.
The apparent difficulty here is how 1, -1, and 1i can be equivalent, or identical in value. This difficulty is due to our use of symbols to represent dimensionality, and is not an insoluble mathematical problem. You see, while we are using different symbols to represent coordinates in a space along three dimensions; the center of one axis is the same as the center of the other two axes, but with each axis itself oriented differently (i.e. at right angles) to the others. In order to describe coordinates for points on the different axes and distinguish the axes one from another, we use a different symbol (the minus sign, “-”, or the letter “i”) but the “three centers” are all, in fact, the one center, or One.
Another way of describing the equivalency of 1, -1 and 1i is to state that all three have an absolute value that is the same. This absolute value is actually Infinity ( ⁄ , the One). This also shows the center to be the Infinite Point.
Having established that 1, -1, and 1i are equal in value, let us go further and point out that the nature of Infinity is that no matter where you are in Infinity, you are at the center. Infinity, by definition, is the Center. So if you select any point, that point is the center because the ultimate distance from “it” in every direction equals Infinity. With this in mind, the ancients were correct in asserting that the Earth was the center of all, but they would have been just as correct to state that the Sun was the center, or the Moon, your heart, or any other point in space (or out of space)!
Mathematical functions using negative numbers and/or imaginary numbers are necessary when working with multidimensional constructs because without them you’d have a difficult, if not impossible, time specifying values in more than one dimension. With this in mind, imagine the fun of working with all 11 space/time dimensions in a mathematical way!
The apparent complexity increases once you recognize that in this space we have defined with the three axes, there are infinite possible alternate sets of axes with set orientations differing by degrees (or fractions thereof) relative to the set of axes defining our space! This model provides the basis for the existence of alternate universes; these are not the same as the different realities resulting from the dimensional threshold maxima and minima that I described in Fractalic Awakening – A Seeker’s Guide. The alternate universes I am describing here would have the same applicable threshold maxima and minima defining what we know of as space/time, but the three fundamental spatial dimensions would be shifted axially relative to our universe. This shift would be along a dimension at right angles to the three axes I illustrated above (corresponding to the 4th dimension, time), and this shift could be represented by coordinates measured in degrees around a sphere relative to the “location” of our universe. For example, a one degree shift would mean that the net shift of all three axes in the alternate universe would equal a one degree temporal difference relative to the three axes that describe our universe. This alternate would be one degree separated from our space/time universe no matter how much time passes.
This shift along a dimension equivalent to time in nature makes these alternate universes physically invisible to us, but they can be perceived in our imagination because consciousness/Awareness can transcend our space/time dimensional limitations. This “imagination” can be developed so keenly that the perceiver actually “sees” the alternate in minute detail. In fact, it is the perception of these alternates (in varying degrees) that is the source of ideas for our “fiction” literature and movies.
Incidentally, conventional mathematics is actually a mathematics of infinitesimals. This is the logical deduction resulting from the recognition that all values that are finite, or less than Infinity, are infinitesimal. As I have demonstrated in this chapter, practical use of conventional numbers is possible only when Infinity is removed from the equation. However, removing Infinity from a mathematical formula does not eliminate it in Reality, but rather merely gives the illusion that Infinity does not exist. This observation also reveals that conventional mathematics is the mathematics of illusion.
The ability to interact with both infinitesimals and Infinity is one of the reasons why fractals, as generated on a computer screen and manipulated with programs that allow exploration and magnification of the constructs, are so useful on Path and in understanding of Reality.
About the Author
LariAnn Garner has sought knowledge of the meaning of life since her teenage years, and continues on that quest today. This quest has led her through exploration of different versions of Christianity as well as studies as wide-ranging as the Edgar Cayce material, Lobsang Rampa, the work of Robert A. Monroe and the Monroe Institute, the Bartholomew material, Ramana Maharshi, and much more. Her first published work is Fractalic Awakening – A Seeker’s Guide (http://fractalicawakening.com). She lives with her family in south Florida, U.S.A.
