E8 Lattice, Spheres, and Dimensions

By Nobleman Nash Hollowhill - December 28, 2009 

 

The Joy of Living by Yongey Mingyur Rinpoche contains an explanation of a model of the universe as a great net of infinite connections, where at each point of intersection lies a gem with an infinite number of facets, and upon each facet is a reflection of the larger whole. This is a simple representation of a fractal, a hologram, and a unified field theory. The ideas that parallel this example are themselves, vastly interconnected and self-referential. For instance, Garrett Lisi’s E8 Lattice of an Exceptionally Simple Theory of Everything is an all-encompassing paradigm based on a near-spherical hyper-dimensional polygon. The sphere has 248 points, each representing a different element or particle, and it is described as having 248 dimensions. If every point on the sphere is a reflection of the whole, every point can also be described as spherical. Because a fractal is self-referential in all of its extensions, this may indicate that in dimensions beyond our traditional models, larger spheres may exist, and in each lower level of complexity beyond the quantum level this pattern repeats without limit. Such an idea holds true for a hologram, in which each part of the whole contains a smaller image of the whole. This explains various anomalies of particle physics that contradict Einstein’s and Newton’s models. In addition, the idea of a unified field of unlimited energy, a zero-point field, or the Akashic field of Eastern mysticism, seems not only to be plausible, but to permeate nearly every scientific paradigm.

The dimension 0 is a single point, or location. It has no length, width, height, or duration in time. The first dimension is an endless line extending in two directions on the x axis and is indicated with the word length. The second dimension is an infinitely flat plane in which the y axis, denoted as width, intersects the x axis at a perpendicular angle. The third dimension is Euclidean space and contains length, width, and height. The higher dimensions are invisible to us but a theoretical explanation for the fourth dimension is linear time, or duration, and dimensions 5-10 include various alternate branches from the single path we experience during our lifetime. To reach the fifth dimension, one would need to occupy two spatial locations for a single durational value. To traverse this boundary and enter the sixth, one would need to hold three spatial values tangent without changing the duration in time in which each exists. The seventh dimension treats all possible beginnings and endings of our universe (what we traditionally refer to as infinity) and treats them as a single point. The eighth draws a line from this point and connects it with another possible point, representing an alternate infinity. The ninth branches from that line and includes an alternate infinity. Finally dimension ten treats all possible timelines for all possible universes existing in all possible infinities as a single point. Currently several theories exist for the total amount of dimensions, including 11, 26, 248, and of course, for all we know, there may be an infinite number of dimensions.

An analogy I drew for the combination of the previously mentioned fractal nature of the physical universe with the opening of dimensions includes a reference to Marshall McLuhan. His explanation of the spherical nature of the spiritual experience provides a very logical and elegant method for extrapolating these patterns. If we keep in mind the ideas that every part of the whole is a smaller picture of the whole, and that physical reality consists of a series of multi-dimensional spheres intersecting at singular points in their manifolds, a method for describing the unfolding of dimensions may in fact use this model. To preface this I also should explain that the Hopis also described a spherical nature to the dimension(s) of time. In The Joy of Living, the phenomenon of “Spacetime Foam” is explained. From a distance, the curved nature of the interconnectedness between space and time appears continuous, like a uniform surface of foam, but upon closer observation, the parabola takes on miniscule curves which appear to be spherical, like bubbles. If we picture the dimension 0 to be a sphere with no observable or measurable attributes, or the capacity for them, we can imagine the first dimension as branching out from this center until it meets a boundary at an indeterminate length, which we may suppose to be the edge of a sphere. Because the edge of a sphere is at all points perfectly perpendicular to the straight line that can be drawn between the point on the edge and the center, the parabola that intersects with the straight line appears to be of the next-higher dimension because up close it appears perpendicular, but from a distance, it is a curve that is as close to perpendicular as can be measured. This means that the boundary of the sphere seems from the first dimension to be the dimension 2, but in fact, it is simply a boundary the likes of which lies at the center of the sphere in dimension 0.

To the 2nd dimension branching out from the 1st perpendicularly (or just nearly,) the boundary it reaches at an indeterminate width appears in direct opposition and thus can be named height, but like the parabolic boundary met by the 1st, this boundary is also simply a point such as the dimension 0. To us, in the third spatial dimension as we step through the fourth temporal dimension of duration, which appears perpendicular to our notion of height, all previous dimensions, 0, 1, 2, and 3, behave exactly like the dimension 0, while the dimension 4 behaves exactly like the dimension 1. Thus from any previous dimension branching out toward the next, the boundary that one arbitrarily draws to limit the unidirectional line can be seen as the boundary of a sphere in relation to its center.

This gives rise to the notion that there may in fact be fractional dimensions: 0.5, 0.25, 0.125, 1.5, 1.25, 1.125, 2.5, on to infinity, with this same ratio of boundaries drawn at near-perpendicular points relating to the dimension 0 and the intermediate dimension(s). What exists in the dimension 1 exists in the dimension 0.5 and 0.25, what exists in the dimension 2 exists not only in the dimension 1, but also in the dimensions 1.5 and 0.75 at the same ratios. What exists in the dimension 9 exists in the dimension 4.5, 2.25, 1.125. These concepts exist with respect to the notion of musical overtones. Because all motion is vibratory, this means each separate phenomenon can be assigned a pitch. These may not coincide perfectly with our 8 whole step octave or 12 half step chromatic scales, but each separate frequency has overlapping multiples which can be named as one note or another. 440 cycles per second is used in standard tuning as “A”, as is 880, an octave above, and 220, an octave below. By halving each frequency we lower it by 8 whole steps, by multiplying it by 2, we raise it 8 whole steps. Every fundamental note if played acoustically inherently contains subtler frequencies which are usually even multiples of the original frequency, with different instruments amplifying these in different ways, owing to the unique timbre of certain instruments. A single tone may contain nearly silent instances of twice the fundamental tone, three times the fundamental tone, four times the fundamental tone, and any number of higher multiples. So an individual frequency may be divided or multiplied by a single number in order to find its place on our scale, or a more complex scale such as one which contains quarter-tones. This means that our reality, whichever dimension, fractal dimension, or fractional dimension in which it exists, may be merely a subtle overtone of the much deeper nature of reality, which vibrates at a lower constant rate and contains a more complete representation of the whole picture.

To sum up, I will relate each of these concepts to the E8 Lattice or 248-pointed sphere: “The most beautiful shape in all of mathematics.” I believe upon inhaling DMT, the “Chrysanthemum” described by Terence McKenna, that one sees with the eyes closed, may be a phantom image of the fundamental structure of reality. In my experience, the Chrysanthemum is almost perfectly spherical, multifaceted, fractal, self-referential, kaleidoscopic, holographic, mandalic, and so on. It is the most complex and perfect hallucination one could ever anticipate to see, and in many people’s experiences, in which contact with entities was made, it was intimated that this “place” exists in the future. Right now, this structure cannot be seen as complete. We haven’t identified or named 22 of the elements or particles necessary to solve the puzzle, and the Large Hadron Collider is a candidate for the possibility of finding them. To assume that this 248-pointed object is spherical is an idea that exists outside of time, or in a hyper-dimensional viewpoint. Because we could never fully comprehend such a transcendental object, we must limit our experience in this dimension of time to brief instances of realization of the completeness of our own situation as compartmentalized autonomous structures reflecting the unity and balance of the larger picture. The unified substrate from which all existence once sprung, and to which it will return, governs our lives without judgment and we play an undeniably influential role in its completion through confidently seizing the moment we have been handed and emulating its intrinsic sacred wisdom with actions based on our intuition and the foresight to make ends meet.