Infinity and Infinitesimals - Part III

By: LariAnn Garner
Submitted: 2007-01-17 16:26:59
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Next, what of negative numbers, and so-called 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.

Number is the opposite of a positive one. In this new model, a negative number is simply a number on a coordinate axis at right angles to the so-called positive axis. The problem arose when positive numbers and negative numbers were placed on opposite sides of zero on the same axis. Consider that negativity should be understood as a dimensional, or directional, attribute, not a value attribute.

The truth, then, is that adding positive and negative numbers is like adding west and south; it can only be done in the sense of fixing the location of a point using west and south coordinates relative to a reference point, or center. The relative distance from the point described by the coordinates to the center would, in essence, be the sum of the two directional attributes, or vectors. However, this is not the same as a sum defined as the result of adding two numbers. Using this new coordinate axis 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, and encompasses 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 could have no consciousness of the fact, by definition.

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 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.

This apparent difficulty can be eliminated entirely by designing a completely new coordinate system requiring no negative or imaginary numbers. This can be done simply by starting with the center, which is Infinity, and constructing the three dimensional axes as before. However, the values for the first axis would be as follows: all numbers "left" of the center would be given the suffix "w", while all numbers "right" of the center would have the suffix "e". The second coordinate axis would have all numbers "above" center to have the suffix "n", and all numbers "below" center, the suffix "s". Coordinate axis number three would have all numbers "behind" the center given the suffix "d" and all numbers "in front" of the center given the suffix, "u". All numbers on each axis are positive because the location of the number relative to center is given by the suffix rather than by a "-" or a "+" sign. The first whole number in any direction from the center would be 2 plus the relevant suffix. Two examples are 2e and 2u. Locating a point in three dimensions is done easily with coordinates such as (5e, 15u, 21n). Using this new model, one can easily understand why all three axes have the same center, and why the center has the same value for all axes.

Having established that the centers of all axes 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 assert that the Sun was the center, or the Moon, your heart, or any other point in space (or out of space)!

Mathematical functions using numbers with suffixes or prefixes 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 dimensional 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 out of phase with our space/time universe no matter how much time passes.

While we are on the subject of so-called imaginary numbers, I must point out that there are no imaginary numbers. This illusion has arisen in part because of the unfortunate selection of the negative symbol to distinguish some numbers from others, plus the erroneous idea that a negativeThis 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.

Alternate universes are not to be confused with alternate realities. Alternate realities owe their existence to dimensional variances that are not universal, or equivalent for all dimensions in a universe. For example, while an alternate universe may have what I call a universal circumferential shift of 1 degree relative to our universe, an alternate reality may have a local circumferential shift of a fraction of a degree along only one dimension. This enables each of us to create our own alternate realities without these alternates differing enough to separate us individually into alternate universes. This means that all of our alternate realities intersect together in our universe, enabling us to share lives with each other, yet still have distinctively different experiences. Alternate realities are created whenever we make individual choices as we live our lives. This is because each choice made that differs from the choices of others is equivalent to a fractional phase shift, making the chooser's reality different from others by that fraction. By contrast, an alternate universe is created by incorporating one or more dimensional differences, relative to a reference state, at the moment of universal creation. The reference state can be either a previously created universe of a given type or a parametric set that defines universes of a specific type. In the case of our universe, the given type would be "space/time", or the specific parametric set that defines a space/time universe. Variances in dimensional values relative to the reference state set the new parameters for the alternate universe.

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.

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