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Thoughts upon Reading Marko Rodin's on his unusual coil design

by Alastair Couper

abstract

The curious writings of Marko Rodin are examined for some lines of continuity with established theory. The ancient science of numerology is the basis on which this work is founded, but there is little in modern thought with which to link these old mathematical techniques. It is speculated that research into fractals will lead to some new connections with Rodin's theories. It is shown in detail that the Fibonacci sequence, archetype of growth, form, and the golden mean spiral, contains an explicit periodicity of 24 when analyzed with numerological techniques. This result duplicates essential features of Rodin's assertions. The intent is to point to the possibilities of tapping the apparently random zero point fluctuations that are theorized in modern physics, by showing the potential for structure in chaos.

Visionaries

Marko's original vision was essentially a perception of a four dimensional sphere, which becomes a complicated toroidal structure when projected into three dimensions. He also perceived a mapping of an energy flow on the surface of this projected toroid. The Rodin coil is the best guess at this stage as to how this original insight could be made in physical form. He conceives of a coil of very specific geometry which may or may not be a conventional copper conductor, he has no clear indication of how the winding is to be energized. The details of the flow of energy are encoded in his Sunflower Map, which is an elaborate numerological scheme rendered on the surface of the toroidal form. He expects strong gravitational effects from a properly executed and powered winding. Throughout his book he freely uses conventional terms in unusual ways: fractal, hologram, monopole, phased array, synchronized electricity, polarity, etc.; the effect being more like poetry than anything else. Rather than reject the work as being unschooled, I felt that these terms merit further scrutiny in the spirit of his writing.

Numerology

The foundation for the whole book lies in the numerological tradition, which is ancient, probably

something handed down from the Sumerians. As a modern, the whole of numerology seems trivial at most; and with various cultural overlays, downright superstitious. The science of the Ancients made much use of numerology along with astrology and sacred geometry, and one would guess these were branches of a central tradition. The assertion is made in this tradition that the base ten system is the most natural number scheme, as it mirrors some potent aspect of exisence. As an example, DNA molecules have ten rungs per complete turn of the helix. The key numerological operation is cross addition, wherein a given number's digits are added to each other horizontally and reduced to a single digit 1-9. Thus, 5682 becomes 21 becomes 3. This tradition would be trying to teach that in forming a physical quantity, single units carry as much weight as units of ten or units of a thousand. Elaborating on the DNA model, it is as if each power of ten denotes an additional dimension of spiraling. Thus the horizontal sum denotes a totalizing of positions on the spirals, the meaning being strictly geometrical in nature, as when a higher dimensional object is projected onto a lower dimensional surface.

Thus Marko begins with the sequence of powers of two: 1, 2, 4, 8, 16, 32, 64... .and turns this into a repeating pattern: 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5. The claim is that this doubling sequence is seen in all life processes and throughout nature. (Refer to figure 1.). It is this sequence, joined by its reverse, which form the bifilar doubling circuits layered around the torus. The quandary is, what energy conditions could these numbers refer to ? The remaining numbers form a gap space pattern: 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3... which separates the previous circuits. It is presumed that this sequence is associated with a vorticity of the vacuum or electromagnetic field between the conductors. It is shown that when these sequences are laid out in a grid, and various groupings are made using the horizontal addition, a fractal effect occurs where the same sequence of numbers appears at higher and higher levels of groupings. One is immediately reminded of the various examples of period doubling leading to chaos that are seen in all sciences these days. These bifurcation maps, such as that produced by the much studied logistics equation, show a repeating pattern at all levels of magnification, much as does the Sunflower map.

 A very curious correspodance to the Sunflower Map is provided by a technique pioneered by physicist Roger Penrose called quasitiling. This is a technique for covering a surface with so called tiles of non-equal shapes. An on-line application, called Quasitiler, uses a technique to achieve this tiling similar to that mentioned earlier, whereby a higher dimensional object is projected down to two dimensions. A typical output from the program show distinct similarity to Marko's work, especially as the initial dimensionality is increased to 13, its maximum capabilitry.

Many physical systems display fractal properties, and it is not known to what level the bifurcations of a nonlinear dynamical system extend to. They may extend all the way to the quantum level, and that fractals provide a means for the ever troublesome "collapse" of the wave function. All that is required to generate fractal behavior is two things: nonlinearity and iteration; which is to say take a nonlinear process and feed back some form of its output to its input. The numerological binary doubling sequence as used by Marko is indeed nonlinear and iterative, so it should be no surprise when he shows us the repeating fractal patterns of the Sunflower Map. And yet it is compelling at the same time. The question I ask at this point is: What can the study of fractals say about the possible extension of our theories of electromagnetism and gravity?

 Conventional engineering uses Maxwell's equations as its guide to field effects. These equations were developed through the use of experiments measuring the physical forces exerted by extended bodies, in effect glossing over the finer details which may be present in the fields. In the use of calculus and surface integrals, there is always a blur caused by allowing one component to become infinitesimal while another becomes infinite. The flavor of this blurring occurs in the following infinite series expansion:

1/x-1 = 1/(x-1) - 1/x + 1/x**2 + 1/x**3 +.... 1/x**n

 For any finite number of elements on the right hand side, the series is undefined at x-O. But if the series is allowed to go to infinity, then the left hand side results, which is undefined at x= + 1. Problems with infinities pop up like mushrooms in the lawn order of physics. (Peat, 1988, p. 260-1). Not withstanding the various extensions to EM theory which have been proposed, one needs to ask if linear continuous math be trusted for all purposes. Another case in point is shown in figure 2. Everyone has seen what happens when iron filings are used to show the shape of the field around a magnet. This is misleading in that each iron filing becomes a magnet itself, and what is shown is actually the force interaction between the two magnets. When the field is scanned by electrons, the picture is radically altered, and a complicated, apparently fractal pattern emerges. (Bearden, 1988, p. 44). My guess is that with a new technique, a similar, fractal result could be obtained for the static electric case as well, since we presently use electrons to sense the field created by electrons. As with the magnetic case, this only gives a force interaction, and doesn't indicate finer details. I feel that the "internal structure" which Bearden uses in his writings to describe the vacuum state is not random in any sense, but perfectly chaotic or infinitely structured. Marko has said "there is no chaos", which I take to be in the sense of no disorder. (The Koran states: Not an atom moves, which He does not know.) So white noise is the signature of infinite information, rather than zero information. And the fractal road of bifurcations is a map (perhaps one of many) of the territory. It is the virtue of the fractal approach to ungainly systems that high orders of complexity can often be collapsed to a very simple model which mimics the overall characteristics, not in the sense of a linearized approximation, but in the manner in which noise and order (or information) are transmitted by the system. Richard Feynman has remar ked, in relation to the "butterfly effect" or "sensitivity to initial conditions", which renders nonlinear systems like the atmosphere fundamentally unpredictable, that "there seems to be an infinity of calculation going on in a very small cube of air". Marko's mathematics purports to be a sort of Rosetta stone for modeling the ultimate order on the level of the quantum. He uses the term 'number crunching' to denote the leveling of the computational problem to a simple form.

 Dan Winter's writings have many points of contact here, particularly in the use of fractals, of toroids of specific geometry, and the notion that form and ratio are primary. With great poetry, he shows how spin and shape of a Unified Field conspire to effect the cascade of wavelengths from long into short, and vice versa, by sacred stone architecture and biological systems; and thereby allowing the translation of energy from one frequency to another. Note what a slippery concept "energy" is. We all seem to want it, and yet we don"t really know what it is. Here is Dan's version of the story of the One

Substance:

"When you have only one kind of flowing material to work with, it is like the universe is one giant flowing ocean. Then the only shape you can make is the vortex.., which makes donuts. Hydrogen as the basic building block of all the atoms, is really a wave shaped into a donut or torus." (Winter, 1994a, p. 130)

"The fractal nature of the waveform creates gravity. The relationship of the electron shell to the nucleus is fractal, as both have Platonic symmetry, and this permits the cascade for the wave to fall into shorter and shorter wavelengths. We call that one way wind gravity. Hydrodynamically it is a flow between frequencies, lower to higher, into a center, induced because the symmetry is fractal. It is the nature of recursion itself that creates gravity. It is that recursion or self-imbeddedness that creates the attractiveness in waveforms that draws them back to center, recursively making them nest in more and more self-imbedded patterns." (Winter, 1 994b)

It is this vortex mechanics which Marko is endeavoring to construct at the center "nozzle" of his torus form, or the "Primal Point of Unity". The swirling and spiraling of the Sunflower Map as it topologically distorts in the center gives the impression, artistically anyway, of the cascade between frequencies. It is as if Marko is attempting to construct a macroscopic electron. Is it possible that the flow of electrons in wire could be used to orchestrate this vortex flow of energy? We need to conceive of the energy as distinct from the moving electrons, as Bearden points out. (Bearden, 1993, p.6) After all, the drift of electrons in a conventional wire is only millimeters per second, whereas the energy involved in that flow, or ON that flow, travels at close to the speed of light. The work of David Bohm provides an additional insight here.

 Bohm has developed an alternative form of quantum theory which provides for a very different interpretation of what happens at the subatomic level, although it gives the same numeric results as the standard theory. (Bohm, 1980, p. 67-9). This is proper, as quantum physics to its credit can boast very precise levels of agreement between theory and experiment, although that is possibly a case of finding what is looked for. I will quote here from the book Turbulent Mirror, by Briggs and

Peat:

"Bohm's 'causal interpretation' is a proposal that introduces nonlinearity into the quantum theory. He realized that it's possible to write down Schrodinger's equation in a new way, essentially by splitting it into two parts. The first part describes a sort of 'classical electron'. The second equation describes a bizarre 'potential' in which the electron moves, a kind of infinite sensitivity possessed by the electron (or other particle) to its surroundings. Bohm calls this sensitivity the 'quantum potential'....

The quantum potential that dictates the way an electron moves is nonlinear and is determined, in an unimaginable way, by all the . . .particles that surround the electron in question. The quantum potential controls the movement of an electron inside an atom, or as it travels inside a piece of experimental apparatus.

Because of the extreme sensitivity of the quantum potential, an electron is constantly pushed into bifurcation points along its path, regions where it may be flung in one direction or the other. So complex is this nesting of bifurcations and wildly fluctuating regions that the result is the indeterminism and unpredictability that characterize the movement of an individual quantum such as an electron, 'quantum chaos' as it's sometimes called. But as far as Bohm is concerned, the quantum electron's movement is not one of chance and uncertainty; rather, it is totally determined- but by a potential of such endless complexity and subtlety that any attempt at prediction is out of the question.

For Bohm the quantum potential- which every particle possesses-is an infinitely sensitive feedback with the whole. Picture the electron as an airplane controlled, by an automatic pilot. The quantum potential associated with the particle is analogous to a radar signal informing the automatic pilot about everything in the plane's environment. The signal doesn't actually power the plane but can influence its course profoundly " (Briggs and Peat, 1989, p. 183)

 This idea of an information signal telling a particle where to go is also found in Bearden's writings, where he describes a scalar electric potential as being like a patterning of the chaotic vacuum, and that a spinning particle (spinning IS charge) "hooks" into the potential, somewhat like gears meshing. The particle is not pushed by the ESP, but moves from its own energy source. (Bearden, 1983, part IV, p, 17) The ESP only provides the pattern or information of where to move. I begin to get the image of the electric field as having a quality of complexity and baroque curliness as does the Mandelbrot set. Our notions of requiring work to move charge in a wire comes from the fact that our circuits discharge the electron potential in 'random' (a better word would be unsynchronized) collisions, delivering the depotentized electron back to the source where it must be pumped back up. Thus the original source potential is discharged. (Bearden, 1993, p. 11).

 Moray King has made a similar point in noting that electrons are not useful for polarizing the vacuum, due to the ease with which they are buffeted about by the quantum chaos. This is part of why electrons are conceived of as a "smear". He states that one must coherently move masses of nuclei to achieve a stable vacuum polarization, and the heavier the nuclei, the better. However, he further states that energy effects are also reported from the use of coils which cancel their magnetic fields, such as caduceus or bifilar wound coils. All the instances cited require a sudden, abrupt change of current, such as occurred in Tesla's apparatus when ball lightning was produced. This would be a case of electron flow alone generating some sort of self-organization in the fields around the coil. (King, 1989, p.77-88). The annals of energy research contain a bewildering array of reports and folk lore regarding the effects associated with these flux canceling coils. Dr. Hooper, who coined the term motional E field to describe his research on flux cancellation, has stated that increase of the speed of the charge flow would vastly increase the effects he measured. (Hooper, 1971, p. 4). Now increasing the speed of conduction sounds like superconductivity, in that it would require the orchestrated movement of all the charge carriers in synchronism to minimize jostling. This story is seen in Marko's writings as well, where he says that his geometry ensures the longest possible collision free path, allowing the flow of synchronized electricity, which he also refers to as accelerated electricity. (Could cooperating electrons be referred to as a smear campaign?) He claims that superconductivity is a result of form and proportion, and not of material content. Bill Ramsay has measured the flux characteristics of an initial prototype of Marko's coil, finding that it lies in between the open radiation of a solenoid and the enclosed flux of a usual toroid, with partial flux cancellation due to the bifilar configuration. (Ramsay, 1995, p. 10). Perhaps his toroid geometry could create a synergy of the separate quantum potentials, each telling all to move in such a way as to eliminate resistance. The use of 'gear teeth, mesh, number crunching, entrainment and transmission' throughout Marko's glossary seems to me to point to this idea. A very strong intuition that I have at this point is that if indeed this synergistic flow of energy is to be orchestrated in a wire coil, the driving or inducing signal will not be a simple sine wave or square wave, but must itself partake of the fractal and vortexian natures. It will have to reference in some way a transcendental condition, as does the transcendental number PHI which can not be contained in a number system, but can be invoked by simple geometry.

 Only a small "leg up" on the natural quantum chaos would be required for large results to be obtained. At present, chaos theory and Fibonacci sequences are making a big stir in investment methods on the stock exchange. There is presently an artificial intelligence program using these concepts to learn and adapt to the fluctuations of the stock market index, and to then make predictions. The program shows results which consistently give an advantage of a fraction of a percent over the usual odds. This is not impressive at first sight, but when one moves around large sums daily with an assured gain, the advantage quickly accumulates. This is similar to the presumed immensity of the background jitterbug' energy. A special geometry would give a return based on how well it accorded with a preferred path of least resistance.

 The I Ching

Further impetus in this direction comes from the work of Terence McKenna and his Time Wave theory. While this theory is as intuitive and elaborate as Marko's, it is also implemented in software which allows for some sort of testing. The theory states that the nature of time is not one of simple linear flow, but has a fractal quality with the usual attribute of repetition of self similar pattern at various levels of duration. The quality which is charted by his software is referred to as novelty (in the sense of A. N. Whitehead), and which he interprets in the historical perspective as the flow of new ideas and epoch making events into the life of earth. While it is arguable as to what Terence has actually accomplished, the process he used is potentially relevant to energy research.

 He began with the King Wen sequence of the 64 I Ching hexagrams, which he calls a "profoundly artificial arrangement", as a model for the way in which time's changes could be mapped. He then took the first order difference. between each hexagram, a sort of first derivative of the changing number of lines in the sequence. This generated a random appearing series having values of 1,2,3,4, and 6 (no changes of 5). It was then noticed that if this "waveform" were turned around in time and inverted, it would overlay the original at each end. This impressed Terence at the time as there were several interesting numerical relations that came out of this. What I thought of when reading this for the first time was that he was constructing something like a forward moving particle/ backward moving anti-particle pair. (Figure 3.) (Note the similarity to Marko's use of the forward and reverse binary doubling sequence.) He took this pair of wave forms through a series of mappings, all intuitively guided, to finally produce a sequence of 384 numbers which are the "seed" of his time wave.

This seed is then used as the basis in what is called a fractal transformation. If the 384 numbers are considered as elements of a discreet function v(n), then the function f(n) is the fractal transform given by:

f(n) = sum( v(n*(a**i)) / a**i ) for i = -infinity to + infinity

This function is constructed of an infinite number of versions of the original function which are stretched or compressed, and added together. In practice the number of additions need only go as far as required for numeric accuracy. The Time Wave Zero program uses this function as a way to calculate backwards in time from a given date. When Terence chose Dec.21, 2012 as the end date, he found that there was a very compelling coincidence between the sudden changes in the time wave and historically significant events on Earth, be it the appearance of mammals eons ago, or the sudden change of consciousness in the mid 60s. The function can be interpolated to any length of time. What is of interest to me in this is some notion as to how one could proceed in creating other nonperiodic wave forms of a fractal nature. See Terence's pages for more details on this fascinating creation. (And this one. And also this one.).

A complementary analysis of relevance is given by Lama Govinda, shown in figure 4. (Govinda, 1981, p. 152). Here we see the result of taking the same King Wen sequence used by McKenna, a temporal arrangement, through various transformations to give an abstract arrangement which is able to be shown most succinctly by this geometric mandala. While I do not want to push any analogies too hard, what McKenna's time wave and this form represent to me is a particle and wave duality; one an unfolding in time, the other a sort of Platonic solid existing in some timeless dimension, much like the vibrating plate patterns produced by Chladni and Hans Jenny which show a geometry resulting from a waveform in time. Or perhaps like a flowing liquid solution and a crystallized solid. (As Whitehead says, the sole appeal is to intuition.) This seems to define the essence of sacred geometry, which is to construct a shape or form, be it toroid or pyramid or whatever, that is the crystallization of a temporal wave form. The toroid which Marko and others favor is clearly a primary form. What can be said about the doubling sequence?

As pointed out by Lawlor in Sacred Geometry, (1982, p.28- 31), the division of the primordial unity into two is symbolized by the square, and the diagonal. It is the essence of cellular growth and

expansion. Doubling is a motion which makes no reference to anything but itself, and when out of control it causes cancer or explosion. So doubling requires a form in order to be useful. Marko maintains that the doubling sequence is fundamental to all energy processes. On the other hand, the Golden Mean spiral would appear to denote the rather different process of cascading between frequencies, as mentioned earlier. However, Marko shows that there is a relation in his math between these two energy archetypes which is a numerological transform not having any parallels in conventional math that I am aware of. But it does seem to me to be significant.

 It is clear that the Binary doubling sequence and the Fibonacci sequence are related by the following construction called the Pascal triangle, of Chinese origins:

1

11

121

1331

14641

1510105

Each number is obtained by adding together the numbers diagonally above. If one adds the rows across, the binary sequence is obtained. If the numbers are added on a diagonal path, the Fibonacci sequence is obtained. (As: 1=1, 1=1, 1+1=2, 1+2=3, 1+3+1=5, 1+4+3=8, 1+5+6+1=13, etc.'

The mood of numerology is to view numbers as geometric forms or process rather than simple quantity, so it is very difficult to see how these ideas could link with our normal scientific notions. Marko contends that the digits 1-9 represent an essential, perfect, and complete system. In reference to the Kabbalah, it is said that the Hebrews thought in terms of twelve, even though they counted in the decimal system. The Chinese thought in powers of two, especially 8 and 64. In figure 5,

we see these systems combined in a mandala of Tibetan origin. (The magic square at the center is one which is also used by John Searl, of levitating disc fame,in his design process.) (Govinda, 1981, p. 54). The transcendental numbers like PHI and root two do not have a simple numeric representation; they seem to point to another dimension than Earth bound integers. But again there is a mysterious connection between these various numbers that caught my attention.

I became intrigued with the idea of attempting to create a wave form which would invoke in some way the golden mean spiral vortex. Moray King has suggested using a "chirp" or logarithmic swept sine wave as an excitation for energy devices, in order to stimulate the cascade of energy between frequencies. But is there a signal which would partake of the fractal nature in a direct way? I began by examining the elements of the Fibonacci sequence, which gives an arbitrarily close approximatior to PHI by taking the ratio of adjacent values. If one takes the horizontal sum of each value of the series, the result will be as shown in figure 7. It is seen that, regardless of the numbers used to start, the sequence of numbers will always have a period of 24, with a significant symmetry between the first 12 entries and the second. There is also symmetry in the first order difference. My immediate question was, "Why 24, or twice 12 ?" We have 12 months, 12 inches, 24 hours, etc. In figure 8 I show further the symmetries which come from this sequence of numbers. In fact, one can start with any two ascending numbers, and following this Fibonacci process, end up with a very similar pattern There are only four different patterns which are possib le using this process, and these groupings again showing a natural symmetry. Finally, in figure 9, the sequence of figure 7 is detailed to show the magical appearance of Marko's two opposing binary doubling sequences along with the gap space sequence from this process, which points to some deep image of Universality. This was an unexpected result and lends weight Marko's assertion that the doubling sequence is indeed a fundamental construct. But the quandary remains as to what entities are performing this 'number crunching'. To a neo-Platonist, these glimpses of an unchanging form which lies behind the ever swirling transience of energy in motion are very appealing and encouraging. They have the same feeling as a conserved quantity in normal physics which is unaffected by transformations.

I can't say any further at this stage. How does numerology relate to energy states in electrical circuit?

Hopefully experiment will follow from all this. I must leave these speculations for now, and do something toward the next step. I hope that, if nothing else, I have stimulated thought and expanded a few minds.

References:

Bearden, T.E., 1983. Toward A New Electromagnetics. Tesla Book Co., Chula Vista, Ca.

Bearden, T.E., 1988. Excalibur Briefing. Strawberry Hill Press, San Francisco, Ca.

Bearden, T.E., 1993. The Final Secret Of Free Energy. Self published.

Bohm, David, 1980. Wholeness and the Implicate Order. ARK, London Briggs,. J. and Peat, F. D.,

1989. Turbulent Mirror. Harper & Row, New York.

Govinda, Lama, 1981. The Inner Structure of the I Ching. Wheelwright Press, San Francisco.

Hooper, W.J.,Oct. 5, 1971, "All Electric Motional Electric Field Generator", U.S. Patent 3,610,971.

King, M.B., 1989. Tapping The Zero Point Energy. Paraclete Publishing, Provo, UT.

Lawlor, R., 1982. Sacred Geometry. Thames and Hudson, London.

Peat, F.D., 1988. Superstrings, Contemporary Books, Chicago.

Ramsay, Bill, 1995. "Rodin Coil Design"; New Energy News, Dec., p.10-12.

Rodin, Marko. 1994. Aerodynamics, P.O. Box 950, Waimanalo, HI. 96795. ($30 postpaid).

Winter, Dan, 1994. Alphabet Of The Heart. Crystal Hill Farm, Eden, NY.

Jean Naudin website Location

A possible Curl Free-A Transceiver

The Time Energy Pump project

The following is from the Jean Louis Naudin website I suggest ou have a look at the vast array of information and experiements he has constructed and of the information provided at his website

created on 09/28/97 - JLN Labs - last update on 09/28/97

 Notes from Jean-Louis Naudin This device uses the "possible" emission of a curl-free-A potential which radiates from the Rodin coil both to its inside or center space and outside and beyond into space. The device is being under tests and I can't confirm this fact today. Also I give you this electronic diagram for your information and I take no responsiblity concerning the supposed characteristics (Faster Than Light (FTL) transmissions, E.T. communications

Obviously if you hold all the B-Field inside the coils of the torus, and then put something else in the center region outside the coils, you can get some additional potential and field energy there in the center of works. You can also get similar propagation outside the coil, with effects on distant objects.

 Rodin is apparently going by elementary electricity concepts but augmented by excellent native intuition. What he really is doing is attempting to separate the A-potential (i.e., the magnetic vector potential A) from the B-Field, and utilize the curl-free A-potential as an independent field of nature in the central "crossover" region. It is know that it is possible, the well known Aharonov-Bohm effect depends upon precisely this separation...¯

 In the Rodin's document about the coil design:

 A winding pattern for a torus which creates Synchronized Electricity. By winding in this manner, you orient the electrons moving through the windings and thereby minimize random collision of electrons, as well as heat, friction and reluctance. The right and left doubling circuits (beginning and ending at position 1; and, beginning and ending at position 2) conduct the flow of electrons in opposite, parallel diagonal directions. The dotted lines (beginning and ending on numbers which are multiples of 3) represent the gap spaces, the equal potential major grooves, which separate the winding.

 Today, according to my first series of test, I can say that this coil have some interesting spec:

 Obviously the center crossover region is active ,.. .A long ferrite rod placed through the center of the Rodin style coil change the value of the inductance.... So, the center region in Rodin style coil is quite active...¯

 I can confirm experimentaly this fact now, also more tests are planned soon.

 Rodin Coil Experiment

 You may see also some patents about EM transmission using the curl free A field