Mankind uses straight lines to approximate curves. Nature uses curved lines to approximate straight lines.
The calculus is man's attempt to quantify curved surfaces, areas and volumes.
For example, in order to approximate the area under a curve, we use what are called Reimann sums:
As you can see, the areas of the rectangles are added up to approximate the area under the curve from the beginning at X0 to the end at X6. Each rectangle sticks out a little bit over the curve, but makes up for it by being a little deficient on the other side. If we make all the rectangles of equal width and then make that width infinitely small, we can get an almost exact approximation of this quantity.
However, nature does exactly the opposite. When nature needs something straight, she approximates straightness with a combination of curves. For example, to get the square wave shown below, we can combine a whole bunch of sine waves:
As we add more and more sine waves to the mix, the resulting graph becomes almost exactly the square wave. But not quite. For as we will soon see, anything that exists must be curved.
By combining sine waves we can make any curve we want. This idea is used in computer aided design and manufacturing. For example, if a car manufacturer wants to make a car body, he needs to know how it will be shaped. The entire surface of the car body can be designed with a computer first and the bugs worked out before the manufacturing process begins. In fact, the design of any form can be accomplished by the combination of sine waves of different frequencies and amplitudes.
Why does nature use curved lines instead of straight lines? A straight line seems much easier to understand and it sure is easier to generate! A curved line requires a constant change of direction so it is more complicated.
Nature uses curved lines because of the fundamental property of particles. It turns out that motion must be curved, not straight.
There are no perfectly straight lines in nature because perfectly straight lines allow for instantaneous travel between two points. A straight line means, absolutely no stops or change of direction along the way. Something which moves instantaneously can't exist, because there is no persistence. Something that exists, that has mass, must take some little bit of time to go from point A to point B. This applies internally to the atom as well, since it is a vibration. There is no such thing as an instantaneous vibration! Therefore, all matter and energy must be traveling along curved paths, at the microcosmic and macrocosmic scales.
Instantaneous movement is only possible to a pure potential. In nature we do not observe things moving from one place to the other with no time lag. Even light has a measurable speed.
A curved line means a continuous change of direction. There is a certain time-lag that is required to negotiate the new change of direction, which leads to persistence, and thus time. So we could say that time itself is curved, not straight! Everything in existence is curved, and is traveling in spirals. Persistence, existence itself, is curved.
To go from B to A in a perfectly straight line is a piece of cake. There are no stops anywhere along the path, no decisions to make. The end is always in sight, so in effect, one can 'be there' in no time at all! A perfectly straight line acts just like a wormhole or a portal, because the length of the line is irrelevant.
To go from B to A in a curved path, however, there has to be a conscious decision to 'turn left' at every single point along the way. At point B, the natural tendency is to keep going to H, at point F, it is easier to keep going in the same direction to L, and so on. To make the curved line there must be a slight hesitation at every point along it; in every moment, a new decision on which direction to go in. This hesitation is what causes the persistence of objects in nature, and time itself (Einstein showed us that space itself curves slightly around physical matter). We all know how easy it is to keep doing something once we are into it, even if it is a bad habit, and how hard it is to change.
Change takes time!
Vibrations are waves
All motion generates a vibration in the aether. We can think of these vibrations as waves.
What is a wave? A wave can be thought of as resulting from rotation of a point on a circle around the center of the circle:
This might seem silly, because all we have is a circle. But a wave is just a measure of the height of the pulse:
As point C goes around the circle to D, the height of the lines increase, then decrease:
From C to D is the first half of the wave pictured above. If D travels back to C again, completing the circle, the entire wave is generated.
So all waves can be modeled as a complete rotation, or orbit, of a particle around in a circle.
The continued orbiting or oscillation of a particle creates a vibration.
Consider the following curve:
Every point along this curve is on the circumference of some circle. We might need several hundred circles of differing radii in order to describe the figure above, but the principle holds.
A curve in 3 dimensions is no different. Here is a picture of an egg:
If you took an ellipse in 2 dimensions which was fatter at one end than the other and rotated it 180 degrees, you'd get an egg shape. If you take a circle and rotate it 180 degrees you get a sphere:
All curves result from rotation.
All motion is essentially rotational. Motion in space creates vibration.
All vibration is oscillatory. All vibration is wave-like. Therefore anything that exists is in rotational motion, and the path it describes is curved.
We suppose the aether to be composed of thought, the basic quanta of matter and energy. A thought, we will say, is something internally alive, for it proceeds directly from consciousness. A thought is conscious, and can be considered to be a vibration.
The aether, in this conception, is composed of the subtle energy of thought, and is vibratory as well. The aether transmits thought like the air transmits sound. Since each thought creates a little bit of space for itself (otherwise it could not exist), as consciousness continues to create, the universe expands.
(There is no scientific evidence for an aether, of course, whether subtle or not. A scientist would say that we are reversing the clock back over a century, before the Mickelson-Morely experiment supposedly disproved the existence of an aether. Until 1887, however, even serious scientists believed in its existence as a transmitter of light. James Clerk Maxwell, who extended and mathematically formulated Michael Faraday's theories of electricity and magnetic lines of force, envisioned electromagnetic radiation (electricity, magnetism) traveling within a medium. Then Einstein eliminated the need for an aether altogether in his Theory of Relativity. Neither Maxwell or Einstein or any serious scientist would agree on a so-called aether composed of subtle energy, however. Call me ignorant or brilliant, your choice, but I believe that the aether is a logical extension of a system of thought that is based on the non-physical nature of consciousness.)
A thought can also be considered as a particle which generates a vibration within the aether due to its internal motion. Therefore we can think of a thought as having both the characteristics of a wave and a particle. In other words, every time someone thinks a thought, it "bumps up" against all of the other thoughts in the aether and sends forth a vibration, just as sound travels via molecules of air. The quanta themselves vibrate, interacting with other quanta and creating a background vibration, or OM, which may represent the fundamental frequency(s) of the universe.
A thought is alive and conscious and sends out a vibration in the form of a wave.
We suppose that the aether is of such a high frequency that it cannot be measured. In the transmission of radio signals, for example, the carrier wave is of much higher frequency than the modulating signal (the signal that contains the information), because it is much easier to transmit a signal of higher frequency, and the signal will travel further. A carrier wave of infinitely high frequency would not only travel infinitely far, but would do so instantaneously and with perfect ease. Such an infinitely high frequency would potentially have tremendous power, yet be so subtle that it's presence would be undetectable.
In effect, it would be a quantity which, becoming more and more refined, approached a nebulous boundary between something which IS (a quantity) and something which IS NOT (a quality). This pure potential would have no mass and no physical existence. It would be infinitely sensitive, and capable of instantaneously transmitting even the most infinitesimal movement. The aether is the postulated medium through which the Law of Vibration and the Law of Attraction function.
In the vibrational model, the aether is the combined thoughts of every consciousness that has ever existed since the First Thought. It is a medium so refined and so subtle that the instruments of present day science cannot begin to measure it. For all intents and purposes the aether is invisible, yet it is so sensitive that it can infallibly transmit vibrational signals from one end of the universe to the other. These vibrational signals impinge upon our consciousness in every moment.
Consciousness is extremely sensitive to all subtle vibration in the aether. When a conscious personality is open to receive, it can instantaneously translate the vibrational input impinging upon it. This process is called intuition. Many great scientific and artistic breakthroughs have resulted from inspiration or intuition from which the intellect then devises a satisfactory explanation to fit in with current theory.
In order to increase one's intuitive powers, one must be open to receive. First one must ask a clearly defined question. Formulating the question orients one's vibration to the question. And we know that a consistent pattern of vibration sets up a vibrational envelope at the proper bandwidth from which to receive similar vibrations. That's what Jesus meant when He said, "Ask and ye shall receive. Knock, and it shall be opened to you." Computer programmers say, "Garbage in, garbage out." In other words, you only receive the answer at your level of consciousness, which is to say, at your level of vibration!
"Channeling" is the process of directly receiving information from the aether, or from non-corporeal personalities. In the spirit/mind/body framework, the spiritual component (consciousness) of individual human beings interface directly with the aether. By calming the mind, relaxing the body, becoming receptive and having a clearly defined question at the forefront of your mind, you may consciously receive information from the non-physical realm. This information comes in the form of what I call 'thought packets' that contain images, feelings, and data which then must be translated by the receiver into language.
I have found that the stronger is your eagerness to get an answer, the stronger will be the response. The clarity of the is a combination of three things:
The strength of your signal, the clarity of your question, and your ability to open and receive the answer. It's the latter that most of us have trouble with. Working on the answer is how I personally block my intuitive powers. I have always felt the need to control my creative process, but in doing so, I set up energy blockages which prevent the vibration of the answer from impinging upon my conscious awareness. It's a rather amusing situation: I am trying so hard to receive the answer, the vibrations of which are being blocked by my trying to receive the answer!
Nothing I am saying here can be proven scientifically. Nothing I have said in any of the essays can be scientifically proven either. The entire subject of spirituality can easily be dismissed simply by saying that it is subjective. And that is perfectly true. In order for free will to exist, and for individual decisions and preferences to have any meaning, the universe must be designed to respond to, and support those preferences. The only way to validly prove anything is to personally test it. Whether or not someone else gets results with your methodology is utterly irrelevant. If something works for you, then it's true for you!
Consciously developing your intuition is fun! And informative too.