Defense of the Polyhedral Atom
Welcome to Aquarius, Volume 12 (11/16/2007):
Is There a Square-the-circle Conspiracy? and Defense of the Polyhedral Atom
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Part 1) Is There a Square-the-circle Conspiracy?
The institutional authorities of mathematics say that we cannot square the circle. This means that we cannot construct a square with exactly the same area as a circle, using only the compass and straightedge. This is promoted as though it amounts to a proven fact and some kind of "disability" of geometry. This idea, that "we cannot square the circle," is known throughout the world, to children and adults. It is a concept that is more widely "known" than any Hollywood celebrity or culture hero. Why is this?
When you look for the explanation as to why it is so widely believed that "we cannot square the circle," the first evidence you find is the statement that a German mathematician, Ferdinand Lindemann, proved that we cannot square the circle in 1882 by proving that Pi is a transcendental number. This was before we had electronic scientific calculators and desktop computers. If you look a little further, you find that the "proof" written by Lindemann is nowhere to be found. There is no book and no mathematician who can show the proof to you or provide you with a brief, convincing explanation as to why we cannot "square the circle." If you look a little further, you may find, as I did, the statement that Lindemann did not produce a proof that we cannot square the circle. What he did is submit some mathematical evidence illustrating the mathematical obstacles to squaring the circle and he argued that "attempting to square the circle is not a good use of a mathematicians time."
So, which is it? Is there really a mathematical proof that we cannot square the circle? If there is, where is it? What does it say? Any response suggesting that the proof cannot be understood by ordinary people is unacceptable. Why is it accepted that we cannot construct a transcendental number? What about a product of a transcendental number and another number, such as Pi*MQ, or Pi*MQ*(5/6)? Pi*MQ is a constructible value. Is MQ as defined a transcendental number? MQ meaning M squared (M not = 1)(M^2 + 1/M^2) = 2 exactly. If MQ is not transcendental, then it is constructible and that would make Pi constructible.
Part 2) Defense of the Polyhedral Atom
What is the shape of an atom? We are accustomed to thinking of the atom as a sphere. In fact, the common image of an atom is the "planetary" or "orbital" image of the atom, with electrons traveling, like planets, in circular or elliptical paths around a central nucleus. Our knowledge of and theories about the "nucleus" of the atom gives us the name of "nuclear" physics. I believe the "planetary" and spherical image of the atom is wrong. My three main reasons are presented here.
1) The orbital model was originally an imagined imitation of planets revolving around a sun, held in their orbits by the force of gravity. But we do not have certainty that any "variation" of gravity is the same force that holds electrons in fixed orbits around a central nucleus. We have reason to believe that the electrons associate with the nucleus in "energy levels" and "sub-shells." The first "energy level" has one or two electrons; second level has up to eight; third level has up to sixteen, or eighteen; fourth level has up to thirty two, and so on, until a maximum number of electrons are present. In the naturally occurring elements, Hydrogen has one electron and Uranium has ninety-two electrons. The accepted configuration of the atom changes with the ongoing results of more or less continuous research and experience. A chemistry textbook published in the 1980s shows the "orbits" of electrons as shaped like "equal-arm dumbbells" and each "orbital" is a region in which "there is a high probability of finding an electron." It is also stated that the atomic orbitals in each atom "can be represented as a diffuse cloud of electrons."
This can be taken as exciting knowledge from the field of physics, or you could take it as I do: this is the physicist's oblique way of saying "We do not really know where the electrons are or exactly what they are doing." It looks like they are racing around the nucleus, at a very great distance in terms of their size and the size of the nucleus and the tremendous empty space between the nucleus and the electrons. It looks like they are traveling in paths that are not specifically circular or elliptical, but more complex, and even "diffuse," which suggests that their paths create a kind of three-dimensional rounded shape, like two raindrops connected at their narrow, pointed ends. All of the electrons as a whole appear to create a different form of rounded, three-dimensional shape by means of the dynamic paths they travel in a fixed pattern outside of the nucleus. Although much of what is said about the atom suggests its shape eludes us -- electrons are said to be found in accordance with "probability waves" -- this same textbook states that atoms are spherical, like a basketball or a golf ball. (General Chemistry, 3rd edition, by Kenneth Whitten, Kenneth Gailey and Raymond Davis. Saunders College Publishing, 1988. Previous editions 1981 and 1984). I would use the analogy of a steel ball bearing. The reason I would use the analogy of the steel sphere is because atoms are extremely "hard." The difficulty of "splitting" the atom gives us both the scientific and popular notion of enormous energy being released if atoms are "split" or broken apart. The great forces that hold the atom together are actually an unsolved mystery. Physicists make up names for these forces from time to time, sometimes rather lame names, such as "the strong force" or "the weak force." And sometimes they offer theories that make the creators of comic books seem conservative, such as "string theory" or "wormhole in space" or tearing the "fabric of time." I could go on. I know that I am ignorant of some of the research and explanations offered by physicists, but I still claim my right to disagree and argue that the reason for all of this theory about the atom instead of confirmed fact is that our idea of the atom is based on a questionable trust in electronic instrumentation, and upon complex mathematics which can always be laid over a simple reality. For example: square root of 36, times 10^(0.477121254) = cube root of 5,832 is the same thing as 6 times 3 equals 18, also the same thing as 10 plus 8.
2) Instrumental illusion (similar to optical illusion). The atom is too small for us to see accurately, even with an electron microscope. If an atom were the size of a human being, then the eyeball of a scientist studying the atom would be nearly twice the diameter of planet Earth, about 14,000 miles. The instruments used to study atoms are the electron microscope and particle accelerator. Each produces data, and physicists interpret the data. The data from a particle accelerator might be a streak of light on a dark plate. With what certainty do we know what these instruments are really detecting? If anything detected and indicated by a point or a line of light, or by a "cloud" or energy level is misinterpreted, then any and all theories based on that data are wrong. Such a misinterpretation could be deeming a point of light to be a particle when it might in fact be the result of a different and momentary radiation of energy. For me, electronic instruments detect something, but we could be wrong about what they are detecting. There could be a phenomenon of "instrumental illusion." Although this may sound outrageous to learned and hard-working physicists, let me point out what has occurred in the field of photography. There was a time when it was said that "the camera doesn't lie." But today we know that a camera, including a cinematic camera or a digital camera, can lie very well. Any one of us could watch ourselves on a movie screen shaking hands with Abraham Lincoln. An expert in the art of photography can compose a photograph of a tattoo on your chest that does not exist. I believe it is possible to place my fingerprint on an object I have never touched. This tells us that technical instruments are double-edged. Although they may be developed to detect the truth, just as the camera has been deemed to be an instrument that reveals the truth, such as a surveillance camera, they can also be used to lie with equal art. If an instrumental detection can deceive us, how do we distinguish between those occurrences when they reveal reality and when we are deceived? I do not trust the instruments that are trusted by the physicists.
3) The forces necessary to have spheres bound to one another, in position, by means of directional force, are not supported by a convincing, reasonable explanation. Such directional forces would have to be suspiciously enormous, and are not likely to be Nature's way. Imagine an atom that is a sphere "attached" to, or bound to another atom. Physics and chemistry textbooks illustrate and describe atoms being bound at a particular location on the surface of each of the two atoms. A carbon atom is not bound to a nitrogen atom or any other atom as though the two atoms were two soap bubbles, remaining connected even though they may slide over the surfaces of each other. Two or more atoms bound together are a molecule. Both inorganic and organic matter includes some extremely complex molecules made up of many atoms of several different elements. Whether such matter is simple or complex, atoms are deemed to bond to one another at specific locations on their surfaces. This means that the atom cannot be like a ball bearing. Ball bearings are hard spheres that are known for their low friction upon contact. They slip and slide over one another, which is obviously the exact opposite of providing a surface that enables bonding at a particular location on the atom's surface. Another concept is that the bonding is not enabled either by or at the surface of the atom, but the electrons of each atom interact or even entwine in a way that "ties" the two atoms together. This concept would involve the atoms binding by a means that involves interpenetration of each atom by the other.
To me, any model of the atom that deems the atom to possess the shape of a sphere presents the same problem. How can one sphere attach to another sphere with each sphere maintaining the attachment only at a particular location on its spherical surface? Here again, let me observe that the directional force to attach two spheres at a fixed point on each sphere's surface would have to be enormous. The force required would be far less if the atoms were polyhedral in shape. If atoms are polyhedrons, then their surface polygons could play a role, by virtue of matching shapes, in the bonds of one atom to another, or of one atom to two or three others. Elements are not deemed to exist in Nature as free separate atoms but as molecules. And the molecules of pure metals and of minerals are crystalline or polyhedral in shape. This means that so long as we maintain the concept of the spherical atom, we have to acknowledge an important gap in our understanding of the physical universe, which is simply that we do not understand how spherical atoms combine to construct polyhedral molecules. Organic molecular structures are also polyhedral, as is confirmed by "chaos theory" and fractal geometry. The question is: Why does Nature make a change from the method used to attach spheres to the method of constructing polyhedrons? For me, the answer is that Nature does not make such a change. The atom is a polyhedron and it follows logically that combinations of atoms possess the shapes of polyhedrons or conglomerations of polyhedrons.
I also believe that the shapes of atoms play the primary role in producing the electromagnetic qualities of the atom. This viewpoint of mine, which may be deemed "crazy" by practicing physicists, is consistent with the concept that "Proportion is Everything." I will offer a simple analogy. If I give you a cube of iron, and a chunk of copper, and a ball of rubber, you have what? A cube of iron, a chunk of copper, and a ball of rubber. But, if I shape the iron into an armature, and shape the copper into wire, and process the rubber so that I can shape it into tape and wrap it around the copper wire, and if I shape the copper wire by winding it in a specific pattern around the iron armature, I then have either an electric motor or an electrical generator, or an electro-magnet, depending on how I make the windings and connect the wire to the armature. This is only elementary electricity, I know, but it is a valid example of the most fundamental reality of the physical universe: the shape of an object determines its electrical or electromagnetic properties. Therefore, the cosmic question is whether shape, or proportion, is the sufficient cause of the electromagnetic properties of atoms and molecules. I believe it is, and although I am not in a position to prove it is true, I do believe it is of the greatest importance to humanity to learn as quickly as possible whether the polyhedral atom is absolutely ruled out. We need experiments designed to either rule out the polyhedral atom or the spherical atom, because a universe of polyhedral atoms is significantly different from a universe of spherical atoms. We desperately need to know which is correct. Without certainty around this issue, we are dangerously ignorant of how Nature really works.
I naturally take issue with the statement made by physicists that the Laws of Nature are different at the sub-atomic level from the Laws of Nature that govern our familiar world of tree, house and family. I cannot grasp how any scientist can subscribe to such an obtuse way of describing reality, by suggesting that there are more than one set of laws governing the real physical universe. Actors want to be singers, and physicists want to be wizards or priests or magicians. For me, to say that the Laws of Nature change depending on what floor you are on in Nature's proportional size elevator is just as much magical thinking as saying that you can teach a dog to fly by wishing. There is one universe. That's what the word means. I say there is one set of laws governing all matter, of every size, in every location. All physicist's and chemists need to do, to be ethical and responsible, is acknowledge that:
We do not yet understand the single set of physical laws that govern the behavior of all matter of all sizes in the one universe that we observe.
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