Sunday, August 21, 2005


Substance, Form, Structure, Dynamics, Being and Function; which is more fundamental? It is an age old question. In this work, this is the determined order: Being, Dynamics, Form and finally, Structure. Function, to be studied later, can arise from different levels, and is not viewed as being fundamental. Being is the most fundamental, where without, nothing else can exist. Being and substance are the same. After Being, there is the capacity to be dynamic, though Being itself is inert. Both Being and Dynamics are invisible to the observer. Dynamics includes what many refer to as energy, energy being a higher level manifestation of Dynamics. Next there is Form, inclusive of four fundamental forms: the Infinite Volume, the Surface, the Line and the Point. Structure, which was included by early thinkers, is the manifestation of form and pertains to chemical and atomic structures; thus, rather than being fundamental, structure is phenomenal. This seems all very well and good, but how have we arrived at these conclusions?
Which I ask you is simpler and more fundamental, a house made of bricks, or the bricks themselves? The answer is of course the bricks; the house being precluded by them. Destroy all the bricks, and there is no house. Destroy the house, and you might have some bricks remaining. Thus we have Nature's rule of simplicity; which every schoolchild can decipher.
When the early atomists first envisioned what these fundamental "bricks" might be, they became somewhat sidetracked; for besides being simpler than the house, the bricks were also smaller. Thus when men like Leucippus and Democritus began the quest for Ultimate Substance, they had already made up their minds to seek that which is small. Let us not do the same. Instead, imagine the simplest thing you can imagine, even if it is very abstract, or even whimsical, and even large. How about a soap bubble?
Now a soap bubble is considered to be one of Nature's most fundamental and elegant structures, along with the spherical carbon molecule recently discovered by researchers and astronomers; the former taking advantage in the opposition between two natural forces: the surface tension of liquids and gas pressure. Of course air currenBut three is still more than zero, so what can we do to reduce the soap bubble's complexity?
For one thing, we can get rid of its molecular structure by converting it from hydrolyzed detergent to an homogeneous, white, milky fluid, not consisting of ordinary matter. By homogeneous (HOmoGEN-ee-us), I mean that whatever its substance, it has no components or parts, such substance being uniformly the same throughout. I know this kind of stuff is hard to come by, so just imagine it. By doing this, we have reduced the soap bubble's complexity to only two: one each for its inner and outer surfaces.
Next, let's get rid of its inner surface by filling it up with this homogeneous substance, which is not necessarily white or even a fluid, leaving the soap bubble with one outer surface for a total measure of complexity of one. Not bad.
Anyone have a suggestion what to do next? Albert Einstein would know; go for that infinite radius, shoving the circumference of this sphere outward so far, that for one, the observer ends up being deep inside of it, so deep, that its outer surface, though technically still remaining an infinite distance away, has no meaning. In other words, not only would its outer surface be meaningless, it would be flat! In every sense of the word, the bubble and its homogeneous substance would be isocentric to the observer. Can we agree that its simplicity is now zero?
This is a very important milestone in thinking; to conceive of something that is utterly simple, which up and until now, has always been "empty space", which was always considered as nothing. Such a view is presently being circulated on Internet newsgroups; suggesting the space is stuff. I guess it's all part of the new TOEs emerging. Though just a wee twist in thinking, it will make a big difference in outcome. Such a form is called an Infinite Volume. It is defined as substance extending infinitely in three dimensions and denoted as (&,&,&), where & = infinity.
In and by itself, this leads nowhere, other than elucidating potential for other possible forms. For example, what if the form was designated as (&,&) or (&,&,&,&), or simply (0,0,0)? Well, the first two, I can't imagine what they might be, but the three zeros is obviously a point, since points are infinitesimally small.
This is really the value of mathematics, albeit very simple mathematics. Mathematics should be applied mathematics; seeking solution to conditional sets outside itself, rather than confining external sets to mathematical principle; the difference being quite subtle.
Besides (&,&,&) and (0,0,0), we could have these other combinations: (&,&,0), (&,0,&), (0,&,&) or (&,0,0), (0,&,0), (0,0,&); the first group consisting of two infinities being a surface and the second group with two zeros, a line.
Contrary to normal coordinates in geometry relating to a point location relative to the origin of a three-dimensional rectangular coordinate frame of reference, these coordinates relate only to the form in three-dimensional space without regard to its position or orientation to a frame of reference. Thus, in the case of a line or surface, it makes no difference the order of these coordinates, (&,0,&) being equivalent to either (0,&,&) or (&,&,0).
A quick summary:
(0,0,0) = a point (0,0,&) = a line (0,&,&) = a surface (&,&,&) = an Infinite Volume.
How simple are each of these forms? It has been established that the degree of complexity of an Infinite Volume is zero. Since a point has neither surface or volume, and of course no structure, it too has a degree of complexity of zero. It seems also, that a line, being infinitely thin has no surfaces nor volume nor structure, its degree of complexity being zero. Lastly and perhaps most important is the surface, where without, nothing will work; it having infinite area. Or is it two areas on either side of itself? This is quite confusing, because with the Infinite Volume of infinite radius, we were able to discount its area as being meaningless. Can we say the same for the surface?
There are no rules governing this, so any decision is uncertain. Because the surface is infinitely thin, is not one area the other area? The surface really can't have two sides to it. This being the case, how does one assign any value to area; for if we were to perceive one of its areas as one, we must as well perceive it to be two, in which case, direct logic breaks down. Don't you love it? Who said that logic can unearth the secrets of Reality in the first place anyway? Especially a Reality such as ours: embracing everything from cold logic to emotion?
Besides this conflict, there is the consideration that since a surface belongs to the set of four forms, it should be in parity to the other forms. Since the degree of complexity of the other three forms is in each case zero, the degree of complexity of the surface should also be zero.
Perhaps then, in perceiving area to be of import, this area must be associated with a volumetric substance; representing the skin of this volumetric substance, such as with our homogeneous soap bubble of finite dimensions.
In any case, if we do not accept the utter simplicity of the surface, since in this study the surface will be shown to be the principle and fundamental entity of Reality, we cannot go on.
Along with the four fundamental forms, are the prospects and possibilities of other forms consisting of one or more finite dimensions, such as a finite disc, a ribbon, a spheroid, etc. Since these finite forms are not essential to this work and are a bit whimsical, and if really found in Nature would produce a universe filled with all sorts of odd sizes: from large protons to small stars; something we do not observe, they must be discounted from further consideration. Also, there is the problem of similitude, which questions both the variable origin and homogeny of these finite forms.
At this point, we have arrived at ground zero. Nothing in our imagination can be simpler than these four forms, but can they be real?
Unlike anything else we might know of in Nature, with maybe a few exceptions, because these four forms have no structure, they obviously cannot be destroyed. Accordingly, if they were to exist, they would exist forever.
Also, since they have no constituent building blocks, they cannot be precluded by anything else. Lastly, since they have no structure, they cannot be created nor fabricated. This makes good sense, after all, how does one create form anyway?
This leaves us with this nagging question. If they are, how come they are?
One solution is chance. Oh I know, everyone hates chance; it's so impersonal and meaningless. To the panlogist, chance makes no sense. To the pantheist, how could god be left to chance? Well, already we're beginning to see how logic can falter at these exceedingly fundamental levels of discussion, and why should it not? And god, how could god be simpler than something so simple, that even chance may be inadequate in its cause? If god were that simple, then god couldn't even think, let alone know what's going on all over the universe, or be involved with its creation!
Let me ask you these questions? Do you think that god created empty space? Do you think that empty space is real?
It's quite mind-boggling. How could anything create nothing? Yet if empty space is real, it must be equivalent to an Infinite Volume, which is so pure in substance and Being that it cannot be created. Here's a comparison between the two:
Empty Space Infinite Volume
transparent transparent
black black
cold cold
lifeless lifeless
soft soft
extends everywhere extends everywhere
isotropic isotropic
isocentric* isocentric*
*to the observer
Our discovery is this. What men call oblivion and what men call real, are one-in-the-same, because we can view empty space as being equivalent to substance, simply because the Infinite Volume is homogeneous substance extending everywhere.
We have now come to a critical milestone in elementary philosophical thinking. But it does not stop here. If one of our four forms is indeed substance of the highest order, what we might refer to as non-clinical Being, then are not the other three forms substance as well?
In this were the case, the remaining three forms would be imbedded within or superimposed within the Infinite Volume, but what might be their difference? Are they all different types of substance which might allow differentiation? The answer is no; no more than we can demonstrate the existence of two substances, say A and B.
Why is this not possible? Homogeneous substance is without character and it is inert. It doesn't come with two labels. After all, if at the extreme range existence and non-existence are one-in-the-same, how could anything between them be at all different?
This leaves the question, if an Infinite Volume is both form and substance, why are not the other three forms, the point, the line and the surface, the same?
One solution, is flawed logic, by simple logical comparison we assumed a family of four, where in fact we have only a family of three: three forms.
In 1965, the embryonic beginnings of this study took root. Thirty years later, this understanding that,the Infinite Volume is singular Being of the highest order, and that the point, the line and the surface are pure form sans substance, was realized.
In dynamic geometry, we learned that motion was more absolute than form and thus this order of hierarchy was established:
BEING - Has the highest order of existence because of its simplicity and cannot not exist. It is homogeneous substance extending everywhere. It has been mistaken for nothing, non-existence, empty space, oblivion and zero space. It is cold, lifeless, soft, inert, black and transparent. It is invisible and undetectable. It is the backdrop for all existence and precludes all existence. Without it, nothing can exist, yet, this is not to say, that because of it, anything can.
DYNAMICS - Not form or substance or Being. The capacity for things to move. The Virtue of Motion. Without this Virtue, the cosmos would be inert and lifeless and but static form.
FORM - Points, lines and surfaces all of which are not inflexible. They have no volume are thus are not substance. All are capable of interaction if their conditions of state are identical. In the case of the point, it has only one condition of state: position. In the case of lines, they have the conditions of state of position, orientation and curvature. In the case of surfaces, they have the conditions of state of position, orientation and curvature. Two or more lines having the same orientation and position are collinear. Two or more surfaces which have the same orientation and position are coplanar.
Knowing these things, consider everything you think and imagine to be real from books to their contents, from people, wind and stars, dreams, numbers, spirits, gods smells and tastes, fears and trepidation, acts to become and acts which have occurred, courage, foolishness, forgetfulness, science and scientific principles; virtually everything and anything. Are they all real? Are they real within the context of this great cosmos? Whatever they are, they can be no more real than Being itself, and the Dynamics and Form which arises from such Being; for these things are precluded by nothing else. ts and gravity fit in, making our bigger soap bubbles sag out-of-round.
If one were to quantify the degree of complexity or the degree of simplicity (both being inversely proportional to the other), the soap bubble's outer surface could be assigned the value one, its inner surface one, and its molecular structure (hydrolyzed detergent) one, for a grand total of three; three units of complexity. Not bad for a start; a cube having at least seven degrees of complexity (six sides plus its structure).


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