Guidelines for Understanding Dimensionality
Focus | Summer 1999
As an analytical person by nature and an engineer by trade, I tend to be intrigued by conceptual questions involving mathematics and physics. One topic that I have considered at length is dimensionality--specifically the nature of higher dimensions. For the most part, my efforts at solutions have produced little more than a spatial headache. However, while attending the Guidelines program in April some very surprising insights concerning this issue were revealed. In order to present a meaningful account of those insights I must, like any well-trained engineer, give some attention to setting up the problem.
Part I - Spaceland: The Place of Physical Constraint
The following explanation of dimensionality is abstracted from the second edition of the book Flatland, written by Edwin Abbot in 1884. Abbot’s construct is as follows:
* Pointland: a point has no or zero dimensions. It has no measurable features of length, width, or height.
* Lineland: if a point is moved along a straight path, then a line is formed. The line has one dimension. It has length.
* Flatland: if a line is moved horizontally along a straight path such that no point in the line passes through a point previously occupied by any point in the line, then a rectangle or square is formed. The square has two dimensions. It has length and width.
* Spaceland: if a square is then moved vertically along a straight path such that no point in the square passes through a point previously occupied by any point in the square, then a cube is formed. The cube has three dimensions. It has length, width, and height.
We exist physically in three-dimensional reality, which results in a dilemma. If a cube is moved directionally along a straight path, such that no point in the cube passes through a point previously occupied by any point in the cube, then . . . what? The resulting object would most surely be four-dimensional. But what is this dimension? What is the resulting object? In what direction must the cube be moved in order to realize this object? Once these questions have been resolved, the process can be reiterated to obtain a resulting object of five dimensions, and so on. So what is a linear, serial-processing mind to conclude? Prior to attending Guidelines, I had begun to suspect that actually determining the mathematical, geometric solution might not be the most significant function being tested by this problem.
Part II - Lightland: The Space of Limitless Love
The following experience occurred during a Guidelines tape exercise which instructs the listener to meet with an Inner Self Helper at Focus 21 and sequentially explore his/her physical, emotional, and energy selves. My sole intent during this exercise was to take the knowledge offered about each aspect of myself and to be open to receiving and considering it as the most productive information for me to have at that time.
My Guide met me at Focus 21, and we proceeded through the exercise according to the instructions. During the portion of the tape for exploring the energy self, I became aware of a cube nestled in the three standard spatial axes. What’s going on? I asked. Go ahead, move it, she replied. I’ve tried and I can’t; I need another axis, I hinted. There was no response. So, once again I tried to move the cube without passing it through any previously occupied points. Once again, I was unsuccessful.
Don’t worry. . . . You can’t fully understand or comprehend this in your current form [while you are bound to being human], she explained. Keep looking at it. As I examined the cube further it appeared to expand. This expansion rushed through and around me in a rapid burst of light and energy that seemed to go everywhere instantaneously. I looked out, across the surrounding expanse, and could discern no edges. I looked in, to where the cube had been, and could see nothing but a brightly radiating point. The cube was everywhere yet nowhere.
It is love, she explained. It will be easier for you to think of this as limitless, unbounded, and unconstrained, but not as infinite. Why not infinite? I asked. Because infinity is too hard for you [humans]. . . . Try to think of it as NOT infinite, yet as still continuous. I took a moment to absorb this information. I took a longer moment to absorb the feelings of peace and vibrancy that were saturating me, almost overwhelming me. I wanted to remember it all.
It seems that the most revealing events are often the least expected. I am still not exactly sure what to make of this one. I realize that my Guide’s last statement is a mathematical paradox. Her advice on perspective seems to be related to the fact that continuous is a less intimidating word than infinite and that continuous in this context refers more to a homogeneous totality than to mathematics.
One of the messages here concerns not beating myself up over “solving” the problem-- it is simply beyond my current level of reasoning ability. Another message is that understanding dimensionality is primarily an energy problem rather than a physical problem and must be approached accordingly. Perhaps the most important message is that love (or love energy) is essential to the construct of any higher dimension--just as length, width, and height are fundamentals of the three dimensions in which we live. Thus, visualizing and comprehending the fourth dimension, as well as any beyond it, requires a full understanding of the expansive and unconditional nature of love.
In any case, I now realize where my attention should be focused.
Systems engineer Todd Phillips attended the Gateway Voyage in June 1997. Little did he imagine that the levels of consciousness he would encounter upon returning for Guidelines in April 1999 would illuminate a problem he had been wrestling with for years.
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