The Cosmology of Imaginary Space
by Tom Butler
Updated October 2014
A way of thinking about the organization of reality is proposed as an alternative to "vibration" as a description for relative "spiritual" maturity, "higher" or "lower" for a way to differentiate between the physical and the etheric and "planes of existence" seen as a "layer-cake" hierarchy of heavens. This article describes the imaginary space of the Mandelbrot Set as an analogous illustration of this alternative view.
A computer plot of the Mandelbrot Set contains a primary feature often called an "Apple Man." It is considered a fractal, referred to here as the "top fractal." the imaginary space also contains an infinite number of similar features which are seen in plots as fractals based on the Apple Man. The top fractal is seen as a attractor for the imaginary space.
From the perspective of the Implicit Cosmology, the Mandelbrot Set is analogous to the top life field and the top fractal is compared to Source. The many fractals are compared to life fields which are aspects of Source. The constant C used in the calculation to determine the characteristic of each point in the number set is analogous to understanding, so that movement toward Source is achieved by changing understanding (C). Further, each fractal is more or less distant based on C, and in a similar way, two life fields are said to only associate to the degree to which they agree in understanding.
The Mandelbrot Set
Im c = imaginary number coordinate for C; Re c = Real Number coordinate for C from Scholarpedia.com (Page has been removed)
Each system of belief has had a cosmology describing the relationship of what is considered "here" and where God and Heaven is thought to be. Most have shown reality as a series of layers, with the "here" on the bottom and "God on the top. The difference between the various layers is usually described as a difference in vibration or coarseness, and travel from one layer to the other is described in terms of "going there," or "being over there" or "the other side." Lacking a better set of terms, these words are useful for conversation so long as it is understood that they are just metaphors.
Based on lessons being learned from current study of transcommunication, it is becoming clear that reality basically a conceptual, subjective space and that the physical aspect of reality is a subset or aspect or reality that has been differentiated to provide a sense of a more concrete, objective venue for experience. Based on the Implicit Cosmology, a personality is only able to associate with aspects of reality with which it is in perceptual agreement (worldview). This agreement is thought to be a function of how well the individual personality has learned to understand the operation of local reality, which can be referred to as progression. Thus, the result of gaining understanding amounts to a change in personality's perception which is its ability to make sense of its environment. That is, personal reality (worldview) becomes aligned with the actuality of local reality.
The idea of moving about in reality by changing one's perception is consistent with many popularly held notions that how one experiences something is as much a function of how one thinks of the experience as how the experience actually effects the physical person. For instance, a city might be seen as a "hell-hole" to a person raised in the country but considered "home-sweet-home" to a person raised in that city. It is in this way that we make our reality. We do not create a separate physical aspect of reality because, as part of a collective, we inhabit a shared reality. We make a separate personal reality by how we perceive the physical reality.
In Math, a complex number is one that includes an ordinary number and an imaginary number such as: X + Yi. "Yi" is the imaginary number where "i" is written as i = (the square root of minus one), which is a disallowed state in ordinary math since a number times itself is always a positive number.
A plot of complex number space (imaginary space), is shown below. Below that, is a plot of the top fractal showing the coordinates on the imaginary and real number lines.
The Mandelbrot Set Equation
The Mandelbrot Set is the set of complex numbers C, where C = X + Yi, for which the sequence:
( C, C² + C, (C²+C)² + C, ((C²+C)²+C)² + C, (((C²+C)²+C)²+C)² + C, ...)
does not approach infinity.
The equation for the Mandelbrot Set is:
Z n+1 = Zn2 + C
where Z0 = C
Values of C that are in the Mandelbrot Set are those for which the value of Zn does not go to infinity. That is, the formula is calculated with an initial value of C, and then calculated again with that first result used for the new value of C. The equation is calculated in this way a predetermined number of times or until the result either goes to infinity or settles in a narrow range of numbers.
Each point in the Mandelbrot Set is used as C in a series of calculations to produce the plot of all points C in the set. When plotting this calculation, a color is assigned to each point, depending on if it goes to infinity very quickly (usually a light color), if it is still substantially changing after a predetermined number of calculations (usually a midrange color or intensity) or if it stabilizes within as narrow range (usually black).
Although the volume of this number set is a circle two units on in diameter, it is important to note that this imaginary space is infinitely small. That is, there is no limit to the number of zeros to the right of the decimal point for C. You can see this in some of the figures below where the coordinates and magnification factor (zoom) are shown.
How the set is seen is a function of the resolution of the display technology and colors used to display the plot. Because color values are assigned to number ranges, the color display tends to be stepped. The Top Fractal plot below shows a step-wise color assignment and the rest have been blended for maximum beauty.
An important feature of chaos theory is what mathematicians refer to as an attractor. This is a mathematical area or point on a plot that is the focus for a large percentage of the plotted points representing numbers that satisfy some mathematical test. You can think of the attractor as loci around which the results tend to gather. This may be a dynamic system, and certainly attractors can be analogous with social structures in which people tend to be attracted to certain behavior.
The top fractal in the Mandelbrot Set is an attractor for all of the subsequent fractals, which are more or less the same.
The "Apple Man" fractal in the Mandelbrot number set
Perhaps the most important point in this essay is that an idea can often produce very complex results. Conversely, a very complex system may be based on a simple idea. Any cosmology that describes a conceptual reality should be based on relatively fundamental principles that allow a large number of results. Those results may be unique depending on how the principles are applied, but they are always constrained by the principles.
As an example, in the Implicit Cosmology, individual personalities have self-determination, but that self-determination is constrained by the Principles of Agreement. In this way, a personality can "go" anywhere in reality that the nature of which is in agreement with the personality's understanding.
This Principle of Agreement can be an important factor determining social group dynamics, comprehension of ideas and difficulties in cross-culture. A commonly held view in religions is that people are access to certain parts of heaven based on their merit. The Principle of Agreement means that people self-limit, depending on their understanding (how they perceive their world).
The purpose of making the comparison between the Mandelbrot Set and the Implicit Cosmology is to give you a sense of how objects of reality might be related. From the earth-centric view we have learned since birth, we are conditioned to think that the rest of reality is "up there," just as is the rest of the physical universe. In the Implicit Cosmology, everything is here and now ... and conceptual.
You are probably accustomed to thinking of yourself as a person peering at the world through your body's eyes from somewhere inside your head. However, if it is true that mid is separate from brain, then are you your body or are you your mind? As it is explained in the essay on personality, you are seen as an etheric personality and your body is an avatar allowing you to experience the physical. This is shown in the "Life Field Complex"diagram.
The important point to consider is that, just as your conscious self and your unconscious mind are only perceptually removed and not physically removed, so are your conscious self and all other conscious selves only perceptually separate. In effect, your perception of your etheric personality, your collective and Source are just a change of perception away.
While the Mandelbrot Set does have a volume of two units in radius, it is infinitely small, and provides a pretty good model for a reality seen as everywhere and every when being here and now. In this analogy, the top fractal is related to Source the number set is related to the reality field of Source. Also in this comparison, fractals are attractors. As such, personality is attracted to its source fractal, and in turn its source fractal is attracted to the top fractal.
So, imagine that personality is created as an aspect of one of the fractals, somewhere in the number set as point C, probably close to a whole number. The objective of personality is to return to its source by gaining understanding; it is attracted to its source. So let the outcome of the calculation for the Mandelbrot Set for the point representing personality, Zn, be a measure of how much understanding it has gained. If the iteration goes to infinite very quickly, the personality has not gained much understanding and cannot approach its source.
Point C is still in the "orbit" of its nearest fractal, and in the same way, personality remains entangled with its source. As it gains in understanding, meaning Zn does not go to infinite as quickly, it is able to move closer to its source, eventually merging with it.
A cosmology is just part of a hypothesis, and as such, it is a working model that requires continued testing and reformulating based on current evidence. The "Imaginary Space" cosmology is proposed as a refinement of the layer cake models one sees in some of systems of belief. Terms such as "plane" and "vibration" remain useful metaphors, but they are too often taken literally. This cosmology suggests "Loci of reality" or "collective" are more correct terms than "plane," and "perceptual agreement" is more correct than "same vibration."
More images from the Mandelbrot Set
Magnification of the area located above and between the
Real Number: -1.255, Imaginary Number: 0.0405, Zoom: 64
Magnification of the bottom of the large circle of the Apple Man.
Real Number: -1.165, Imaginary Number: -0.288 Zoom: 64
This fractal is located right of the cardioid of the Apple Man.
Real Number: 0.37153125, Imaginary Number: 0.585390625, Zoom: 4069
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