Infinity and Infinitesimals – Part III

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 form, 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, basically, be the sum of the two directional attributes, or vectors. However, this is not the same as a sum defined as the consequence of adding two numbers.

Using this new coordinate axis form, a point may be located anywhere in this complicate space by using three coordinates, one from each axis given. The center coordinates are (1, -1, 1i); contrast this observation with the traditional form, 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 before explained, is not Reality. To “have nothing”, in Truth, would average that you could have no consciousness of the fact, by definition.

signs to represent dimensionality, and is not an insoluble mathematical problem. You see, while we are using different signs 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 discriminate 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 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 roles 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 size. 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

form 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 basic

spatial dimensions would be shifted axially relative to our

universe. This shift would be along a size at right

angles to the three axes I illustrated above (corresponding to

the 4th size, 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 average that the

net shift of all three axes in the alternate universe would equal

a one degree time related 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 discriminate some numbers from others, plus the erroneous idea that a negativeThis shift along a size equivalent to time in character

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 truly “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


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 size. This enables each of us to create our own alternate realities without these alternates differing enough to separate us individually into alternate universes. This method that all of our alternate realities intersect together in our universe, enabling us to proportion lives with each other, in addition nevertheless have distinctively different experiences. Alternate realities are produced 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 produced 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 before produced universe of a given kind or a parametric set that defines universes of a specific kind. In the case of our universe, the given kind 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, traditional mathematics is truly 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, functional use of traditional 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 discloses that traditional 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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