"All the World's a Stage We Pass Through" R. Ayana

Showing posts with label golden ratio. Show all posts
Showing posts with label golden ratio. Show all posts

Monday, 6 May 2013

Free Energy and the Cosmic Flux


Free Energy and the Cosmic Flux
Functional Thinking: an Interview with Eric Dollard by Tom Brown

 http://www.sinequanonthebook.com/images/crystal_1_.jpg

Eric P. Dollard, Wireless Engineer, is a scientist who bases his work on observation of phenomenon and practical experimentation. He is the Vice-President of BSRF and the author of five published papers on electrical phenomena: CONDENSED INTRO TO TESLA TRANSFORMERS, DIELECTRIC AND MAGNETIC DISCHARGES IN ELECTRICAL WINDINGS, SYMBOLIC REPRESENTATION OF ALTERNATING WAVES, SYMBOLIC REPRESENTATION OF THE GENERALIZED ELECTRIC WAVE (IN TIME), and THE THEORY OF WIRELESS POWER.

 In the course of Eric’s research he has investigated the works of Nikola Tesla, Charles Proteus Steinmetz, Philo Taylor Farnsworth II, Johann Sebastian Bach, Wilhelm Reich and other true Scientists of our era. I have personally witnessed the propagation of electricity without wires, the phenomenon of drawing several inch sparks off insulators and mysterious living forms in plasma gas bulbs connected to Eric’s Tesla apparatus. Eric speaks a knowledge gained by hands on experience. This interview will certainly change your point of view about the Borderlands of Science and will certainly shatter any preconceived notions you once had about Tesla, Free Energy, ELF, The American Dream, etc…..

Tom: What first interested you in the works of Nikola Tesla and electrical engineering in general?

Eric: I’ve always been interested in the subject. Years ago someone gave me a copy of Co-Evolution Quarterly that had an article on Tesla, Philo Farnsworth and Edwin Armstrong. That got me thinking about what was going on as I had basically reinvented the Tesla coil as a teenager using equipment given to me by RCA. Things started to connect at that point. Then I read PRODIGAL GENIUS (by John O’Neill) and it was like I was hit with a bolt of lightning. That book shocked me into action.

T: What do you think that Tesla was trying to attempt in his work?

E: It’s hard to sum that all up in one phrase.

T: Would the culmination be the transmission of electrical energy without wires?

E: That was part of his projects, using what could be called true single phase electricity, or mono-polar electricity. That’s the key to his transmission of electrical and mechanical energy – to convert it to a single phase form.

T: Would you say that monopolar electricity is electromagnetic?

E: No, its anti-electromagnetic.

T: You mentioned Philo Farnsworth, what type of work was he doing?

E: Farnsworth built the Multipactor tube, a secondary emission, negative resistance tube. It tends to take off when connected to apparatus such as a Tesla coil and exhibit electrical oscillations.

T: So, to use a catch-word of the day, it was a free energy device?

E: Yes, probably the only real free energy device that anyone ever demonstrated which can be reproduced.

T: Was there any relationship between the work of Tesla and that of Farnsworth?

E: They are really in totally opposite directions. Farnsworth was the high master of electronics… he was electronics. No one knew more about the electron than Farnsworth. Tesla was dealing with ether type forces that don’t involve material or atomic particles, they involve something a little finer than that.

T: You have worked extensively with Tesla coils and we have published your books on the subject. What do you feel is the actual use of these apparatus?

E: As a transmitter-receiver device, for transmitting energy without transmission towers or large arrays of dipoles, or equivalent.

T: What is the medium for the transmission of energy if wires are not used?

E: Whatever the general media is around us, call it the ether,or air or you can transmit it through the ground. Basically it just flows. The Tesla system is designed to transmit through the ground. There’s a lot of talk about propagating through the earth-ionosphere wave guide, which Tesla, In no way, shape or form envisioned. Most of his apparatus are for transmission through a common conducting medium and the earth is the best conducting medium available. The devices are one conductor electrical generators – just connect one terminal to the common conducting medium and all the other or terminal devices will receive the energy. There’s no pairs of wires or wave guides to bound the energy. These are what are called unbounded waves. The Tesla Magnifying Transmitter is a converter which converts electromagnetic energy into what is called magneto-dielectric energy.

T: What exactly is the dielectric side of electricity?

E: The side of electricity that represents the faster than light phenomenon.

T: How does the dielectric relate to Reich’s orgone energy?

E: Reich found that the orgone and the dielectric field are basically one and the same. If a dielectric field has the proper pulsations then you could almost call it the orgone energy. An example of this is the orgone accumulator, which is alternating layers of dielectric and reflecting material, like a capacitor. The reflecting is usually called the conducting in electrical engineering work but this is based on misconceptions from the 18th and 19th century with regards to how electricity flows. It’s well known that electricity doesn’t flow through wires, but that’s the conception that most people carry around in their heads. Of course people used to think the earth was flat, too. Reich s dogma assumed that the insulating or dielectric material had to be organic, but of course he was using glass wool and its stretching the term organic by applying it to glass wool. You could say the glass wool is organic because the silicone dioxide has two atoms of oxygen, but that’s not really true.

T: Have you found any evidence in your research relating the dielectric field to orgone energy?

E: Yes, the cosmic superimposition effect. If you take a low pressure gas (in a bulb) and place it in two superimposed dielectric fields, then you get spiral formations such as Reich wrote about in his book COSMIC SUPERIMPOSITION. These formations appear as spheres, galaxies and other cosmic forms.

T: So the high voltage terminal of a properly built Tesla transmitter puts out a dielectric field?

E: Right – a dielectric current – a current of many amperes flowing through free space without any electrons. This is a true electrical current.

T: Is this as you’ve demonstrated to me where you can draw a several inch spark off the insulator, which of course isn’t supposed to happen?

E: Right, an insulator isn’t supposed to conduct electricity so how can you draw a spark off of it? (laughter)

T: One thing I’ve noticed in these discharges is that they look like plants, like something organic, unlike regular discharges which look erratic and sparky. What explanation do you have for this?

Golden Ratio Discharge into Wood
Golden Ratio discharge burnt into wood with a Tesla Magnifying Transmitter built by Eric Dollard


E: Their shape is basically the Golden Ratio spiral. The log periodic spiral projecting out into space with all angles determined by the Golden Ratio. Now this is also the same shape that living objects form and you find that all discharges, in general, of potential energy will try to form this shape. You can see it in water patterns in sand and patterns in clouds in the sky. The patterns appear over and over and over again, just like the organic patterns burned into wood by the discharge of my Tesla coil. This is connected with the orgone right there. This type of monopolar electricity is in such a form that it will grow into organic patterns, a pre-life pattern from the ether itself. Any type of energy like this such as a stream flowing down the side of a mountain, a crack in a piece of window glass, or fresh water percolating up through the sand on a beach all make these organic patterns based on the Golden Ratio. Any time you have energy discharging you find this type of pattern. Of course this ties in directly with what Viktor Schauberger was saying. His work is actual proof of it. You can say there is a shape in space which is the log periodic spiral. It doesn’t exist in a tangible form because it is something that grows and decays. Its size fits the wavelength and frequency of the amount of energy to be discharged. Its not like you can map space to see this particular spiral, but if you release energy into space then the spiral will appear.

T: I’ve heard that Tesla made references in his work to using a TMT for bringing in storms. Do you feel that there is any relationship between what Tesla was doing and what Reich was doing with his cloudbuster?

E: I haven’t read too much information which indicates that Tesla was trying to control the weather. He makes scant references here and there about how weather-like phenomena appear, such as fog appearing in his laboratory, but that wasn’t Tesla’s particular aim, where Reich’s particular aim was in dealing directly with the actual forces. We have to remember that Tesla was a mechanistic, Victorian personality and he was trying to build machines that related to horsepower hours and BTUs and things everybody was concerned with at the time, and turn the globe into a giant amusement park.

T: Such as his plan to light up the atmosphere at night?

E: Right, you would never be able to see the stars, you’d just have the sound of electrical apparatus roaring everywhere. People weren’t ready for Nikola Tesla.

T: I get the feeling that you don’t approve of Tesla’s final vision for the earth.

E: Not the way he represented the ideas, but what’s interesting about the technology he made available, when used in perspective, is actually quite healthy for the planet. Then you’re dealing with energies that take on organic shapes and you’re one step closer to the type of energy that Reich theorized and made some actual physical discoveries of.

T: There’s some popular literature on the market today claiming that the strange weather patterns the earth has been experiencing over the last ten years or so are being caused by Soviet use of Tesla apparatus. Have you done any research which would confirm or deny such claims?

E: The claims are basically groundless. I did a four year research project at Sonoma State University (California) involving the relationship between the planets in general: the sun and the weather on this planet, and the effects of solar flares on the weather, the effects of planetary alignments on solar flares, the effects of these things on radio propagation, earthquake activity, and tried to tie the geometries of all these energy patterns together. I found the weather patterns were very tightly coupled to the solar flare cycles, the Russians really don’t have anything to do with this. Any effect the Russian Woodpecker signal would seem to have on it would be purely incidental because during these periods of intense solar flares signals like the woodpecker would be sounding louder and propagating better.

Maybe it’s an advantageous point for the Russians to utilize the signal. This seems to be the case. But to think that the woodpecker is making solar flares on the sun and controlling the times at which the planets align is absolutely absurd! As far as all these geometric patterns being seen in the sky, the Indians and other ancients knew about these patterns and they look like the patterns generated by mundane forces such as water and dielectricity.

T: What do you feel the woodpecker is and what is its use?

E: Its a non-Hertzian, shortwave signal which could be used for one of two things. Either it’s used for sounding and exploring the electrical system of the planet or more likely it’s a cryptographic signal utilizing the spread spectrum technology of frequency hopping and direct sequencing modulation. It is not an ELF signal!

T: Then the cloud patterns are the indicators of cosmic flux?

E: Exactly. A well trained observer can look at the sky and it serves as a metering of the intensity of the cosmic energy which exists at a particular point in space and time. I’ve utilized this during periods of heavy solar flares to get an idea of the flare’s more subtle characteristics by watching the geometries they produce in space, particularly at the intervals when the solar flares have stopped and all the earth is receiving the discharge from the flares. These discharges produce very profound cloud patterns and of course heavy rain. So the heavy rain cycles were produced by the enormous flares of solar cycle 21, which were cranked out between 1978 and 1982. The flares were most intense around 1978 and as the flares died down we got an upward cycle of precipitation. Now we’re at the point where the energy has mostly fizzled out and the weather is fairly indeterminate from the solar-terrestrial physics standpoint.

T: In January we’ve received reports that the coldest temperatures on record have hit England and on the same day we got a report of an abnormally high 46° temperature in Antarctica. Dog sleds have to be run at night because of the heat. My research shows that some of the major contributing factors to the erratic weather patterns have been the mass deforestation of rainforests to produce toilet paper and newsprint, and also nuclear testing which is directly related to earthquake and volcanic activity.

E: You have to keep in mind that mass deforestation and large amounts of thermodynamic and nuclear energy are going to have a much stronger effect than the subtle energies coming from the planets and the sun. Deforestation and nuclear energy are definitely going to be dominant influences. Being that the size of the earth and the scope of the phenomena are so large, and the frequency of events is slow, it’s going to take a while to see exactly what effect all these destructive actions are going have. It seems as though everyone intuitively knows that life is going to thoroughly disrupt and things are going to get pretty bad. You just can’t keep whacking on the earth and expect things not to start changing.

T: There has been a lot of varying literature on the polar shift appearing over the last 30-40 years. One aspect which I’ve pursued is the magnetic reversal of the poles. In some of the Native American prophecies they say that the earth will get very hot and then very cold, and then things will balance out again. Does this relate to any electrical phenomena as you understand it?

E: At the point at which the earth’s magnetic field equals zero which happens between maximum positive and maximum negative the planet will cease to be a magnetic energy type of situation and become a dielectric energy type of situation. In most spatial geometry systems which contain electric energy the point of zero magnetic energy is the point of maximum dielectric energy. Interestingly enough, for navigational purposes you wouldn’t be able to use iron, or magnetic, permeability type materials anymore. You’d have to start using dielectric permeability materials like ceramic for compasses.

T: Would this be a short lived situation?

E: It would be in balanced proportion to the magnetic and it is probably going on right now, but it is not generally acknowledged due to the lack of measuring instruments. Physicists have focused their attention strictly on magnetism. In a newspaper article I was looking through the other day I saw that the physicists now have an even bigger magnet so they can smash atoms ever harder and find more little tiny fragments to catalog and confuse themselves. What could be quirkier than a quark? (laughter)

T: If this is happening right now and there is a dielectric propagation during the changeover of the magnetic poles could this in some way account for the shifting of orgone streams and be a part of the phenomena of the strange weather we’ve been having?

E: Yes, it could definitely tie in. You’re talking about a whole different spatial geometry emerging as far as how electrical energy is distributed so you’re going to have all kinds of effects. The weather is filling in patterns that already exist in space determined by all these fields of force, most or which we don’t even know about yet. Tesla was able to open up a door into all these things, but he really didn’t explain how to do it. There are other flux fields that can be measured with his apparatus that get more into this dielectric type of situation. Tesla was successful in measuring the amount of charge on the planet, but no one really knows how he did that. That would be an experiment to try. The velocity of light continually changes which changes the capacity of all capacitors and changes the effect of orgone. A fundamental property of an orgone accumulator is that the dielectric material, which Reich called the organic material, serves the purpose of slowing down the velocity of light trying to draw in the orgone energy. Then the metallic layers reflect the electromagnetic part but the dielectric part penetrates through it without even seeing what’s going on. The accumulator serves as a magneto-dielectric separator. I don’t know if Reich would go along with this. He had his own way of looking at it.

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T: In science one has to look at different ways of viewing things if progress is to take place.

E: The important thing about Wilhelm Reich is not so much his apparatus or his theories but his concept of functional thinking. If you know the basic patterns of nature then you have no problem seeing all these phenomena. You have no problem looking up in the sky, knowing what all the cloud patterns mean. You have no problem developing apparatus to work with these energies because you just basically know. The great minds such as Johann Sebastian Bach and Nikola Tesla worked with these types of situations. You could say that all their work is based on archetypal forms. That’s what makes their inventions or music so powerful. They were discoverers and not just inventors or composers or whatever kinds of names are put on these types of people. They go beyond that, they have tapped in and can see these fundamental shapes and geometries that everyone else is numb to. Viktor Schauberger is post important for bringing these things down to a practical level. If you make the right shapes then organic energy or water flow becomes easily manageable, that is, engineerable. He only intuitively knew a lot of this so it still wasn’t worked in engineering science. If you bring in Tesla, Reich and, interestingly enough, Johann Sebastian Bach (who plays an important part in this) then you begin to find the nature of this basic form. If we take Tesla’s three phase electricity, or rotating magnetic field, we find that it is based on the archetypal form known as the solar cross or by various other names.

T: Mandalas, medicine wheels?

E: Right, these are four quadrant types of forms, a balanced cross as opposed to an unbalanced cross.

T: This is where you get the Four Quadrant Theory of Electricity?

E: Right, electricity has to be viewed from a four quadrant type of situation. The right angle plays an extremely fundamental role in electricity. It is generally a right angle phenomenon.

T: This goes back to what we were discussing earlier about the positions of the planets in relation to solar flares and the weather. How do the quadrature relationships tie in with that?

E: When you take the planets like Mercury and Jupiter, which are the real activity generators, in right angle relationships involving the earth and the sun then you find that radio reception and electrical conditions on the earth tend to be disrupted. RCA used this for a number of years, its called radio astrology. Astronomers refuse to even talk about it, but you have a big company like Radio Corporation of America basing all their circuit predictions on it. They were big time, too. They had the big time circuits. They had the patents on radio and they’re using astrology. Many old time RCA employees would talk about how the planets affect people’s behavior, it’s just common knowledge to them because they have meters right there where they see these cosmic disturbances, and of course when they go out on the street or drive home they find that people are also modified by these various waves that were affecting shortwave transmission.

T: Since we’re talking about behavioral modification, there is a lot of talk currently claiming that the Soviets are modifying behavior using extremely low frequencies (ELF). This is being attributed to Tesla apparatus. What exactly did Tesla do with ELF7

E: Tesla never did any work in ELF. His work was with the high frequencies, the opposing end of the spectrum. Tesla was the first to break away from the low frequency phenomena and that is what makes his work so important.

T: What about literature claiming that the Russians are using Tesla’s ELF transmitters? E: As far as I can tell, its basically a paranoid fantasy.

T: No direct relationship to any scientific work you’ve done or any mention by Tesla?

E: No, I’ve never seen evidence of such things, but I don’t want to discredit people’s work in that area.

T: Right, I feel that Dr. Robert Beck has done some tremendous and ground-breaking research into how ELF fields affect people’s behavior. My question was to find out if any of this research is related to Tesla’s work in any way.

E: There’s no connection at all to Nikola Tesla. Its my personal opinion that the communists are not attempting anything of the sort.

T: So Tesla’s name is being used as a technique to enhance various people’s theories?

E: Basically, what’s interesting is that these behavioral modification techniques are found on television commercials here in this country. American TV commercials that involve a lot of money use certain images, frequencies, wavelengths and such. This is along the lines of what has been proposed that the Russians are doing, but it all comes through the TV screen. It Is not being transmitted through the ground or the ether or the earth-ionosphere wave guide.

T: So you’re saying chat high tech TV commercials are a form of psychotronic programming?

E: Yes, they’re totally psychotronic. People in a sensitized state will react to that stuff pretty heavily, whereas the average person sees it as just something else on the TV.

https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiH9edUBjL6jcfsAvjqiiogxhiWN_8nseY_Yx3i29Ml6SAUM_ey9DTgoXZtQJonQI7ZVCgm2C68ZqhVxGAPmgtqi_0qwNssAtziru1yUll_ZYVXVHlqET033YCrduXSnDlqwcanRxQaV3BM/s400/tom+banwell+aether.jpgT: Do you see these psychotronic images, not just on TV, but actually in the products being sold to consumers?

E: Its everywhere. Architecture represents the thought patterns of each era, so now we have an architecture which is sort of the logical conclusion of modernism, or what I refer to at this point as techno-fascism. The covers of Omni Magazine serve as a perfect example of techno-fascistic art. There is sterility and everything is in rectangular x, y, z, coordinates. The images are usually faceless and abstract. Of course architecture and art have a direct influence on people. It gets right down to the inside without having to go through any thinking process or educational process. If we take for example any piece of great music which has been around for a while, for a few hundred years, and people still want to listen to it for some reason. It doesn’t matter if they’re English or French or Russian, everybody likes it. The same thing with mathematics – it doesn’t matter if you’re German or Yugoslavian, any equation is still the same, the numbers and letters are still the same. There’s no instructions needed, you just go right to work. So the art and architecture now is kind of an engineered thing designed to maximize the efficiency of consumption in the things that are desired in this particular type of techno-fascistic society.

T: How does this relate to automobile styling?

E? Well of course that’s architecture again. There’s generally three or four architectural patterns produced by all automobile manufacturers and interestingly enough, once you start looking for these things, you notice each automobile manufacturer actually uses the same letters and numbers for the same form of car that all the other companies do. It seems almost as if there is some sort of program, but it seems that now, rather than being a characteristic style of the era, there is a plan behind all of it. Of course its easy to cook up all these conspiracy theories about this, it could be accidental. It is interesting to study to see what representations exist in the modern era.

T: Its not accidental that the psychotronic programming has filtered into television programming, is it?

E; No. There’s strong evidence indicating that its not accidental. The best case of that which I’ve seen is that of a picket fence I saw in the surf on a TV commercial to give a flash of vertical lines, which is a fundamental geometry used in all high tech TV commercials. It’s either an x, y, coordinate grid, or horizontal lines, which are very popular, but very often vertical lines. Its hard to distinguish exactly what determines which one Is used. Now I saw a commercial where people were playing on the beach and out in the surf was a small picket fence. Now how many times does a person see a small section of picket fence in the surf? It won’t stay there too long anyway. So apparently it was necessary to use it to place the vertical lines. Whether this is an architectural style or whether It has an archetypal meaning still has to be determined.

T: That would be a whole area of research in itself, the deciphering of TV commercials to see what is being put into people’s heads.

E: It’s the same thing with the food. You go to the store and grab’ two loaves of bread. You look at one loaf and its ingredients read like a chemical rubber company’s handbook on organic chemistry. It tastes like garbage and it doesn’t do anything good for you. It’s just worthless stuff. If you get a loaf of bread that has none of that stuff in it then it tastes good and makes you feel good. These chemicals don’t really prolong the life of the bread, they don’t make the food taste any better, yet they’re in there. Why are they in there? They don’t do anything... why are they in there?

T: It can’t be an accident.

E: No, they certainly didn’t slip in. They’re all precisely measured and metered.

T: There’s also a lot of stuff that’s not required to be on the label. Take for example the new soft cookies in the stores. They contain plastic, but since plastic is not a food it doesn’t appear on the list of ingredients.

E: That reminds me that in the 1930s PCBs were going to be used to extend the life of chewing gum. Shortly afterwards came the phrase “Better Living Through Chemistry.” From an ecological standpoint the chemical destruction of the planet has to be feared more than the nuclear or anything else. We have all these PCBs and everything just floating on the surface of the oceans. What’s going to happen when it all soaks in?

T: Well we have the phenomenon of whales beaching themselves, and of course the scientists can’t figure it out because they see everything as being disconnected.

E: That one’s not too hard to figure out. Take a large naval aircraft carrier. This thing is going to have some heavy duty sonar on it with a peak output power of about 750,000 watts. This is 750,000 watts of sound, which is precisely in the wavelength that the whales communicate on. They can hear their own sounds halfway across the ocean and now the ocean is filled with these incredible shrieking noises that sound like spark gaps, ringing sounds and rapid explosions. It probably sounds like being in a battle zone. It’s no wonder why they would want to hop out of the water. Their environment has been turned into a raucous.

T: I’ve heard that the sound that whales make is a direct transmission of a three dimensional picture. Before the advent of propeller driven boats and sonar and whatever the whales could communicate around the world in 3D.

E: Sure, we’ve screwed ourselves. Nikola Tesla worked in a clean electrical environment to make his various measurements. Now the space is just alive with 60 cycles and its harmonics. You can walk out into the deep desert, and after meditating and calming down for a while, you can feel the air itself hum like a giant induction motor. This pulsating 60 cycles is just roaring In the air. You have to keep in mind that the entire electrical system of the country is operating in phase conjunction. Everything has to move together. Every motor, every transformer, every piece of machinery that produces electromagnetic vibrations is all locked in phase. Everything is moving in unison and whacking on the planet simultaneously and the planet actually hums at 60 cycles.

T: What do you feel are the prospects for a beneficial technology and who do you think are the sources for actually producing it?

E: It seems to me that the best place to start is with Viktor Schauberger and Wilhelm Reich. There’s not really too many people doing anything real these days. There’s a lot of people making claims.

T: The only other person I’m in touch with besides yourself who is actually producing something that works is Trevor James Constable. He’s really figured something out about how these subtle etheric flows operate on the planet and he can demonstrate it over and over again.

E: Yeah, there aren’t too many around like Trevor. The same thing is with the “free energy” thing. Now that I’ve completely gone through all the various works I’ve really run across only one person who is really doing anything, and I know he doesn’t want his name mentioned in public. This person is not known by anybody. All the people out there making all these claims and hoop-de-doo are frauds. Every single one of them is a fraud! And that leaves out none.

T: So basically the free energy thing is like the ELF stuff, its just a technique for getting people promoted in the public eye? E: Right, also everyone is trying to accomplish it with bigger and bigger magnets, the favorite toys of the physicists. Free energy will never come out of magnetism unless the magnetism is tricked with hysteresis, and of course very little is understood about that. Free energy will come from the dielectric field where energy grows rather than decays, perhaps orgone energy will be the way.

T: I’ve been checking into the concepts of the four ethers as presented by Rudolf Steiner and the Anthroposophical schools, and Trevor Constable has shown that the Chemical or Tone ether is related to the water system of the planet and is functionally equivalent to orgone. I’ve found through looking into your work that this ether is also related to the dielectric field. Electromagnetism doesn’t fit in and was considered a corrupted ether along with the nuclear force. These weren’t natural forces.

E: In alternating current engineering the magnetic wave is the one that is consumptive and retarded, whereas the dielectric wave is productive and advanced. You could say that electromagnetism is the fundamental geometry of consumptive retardation.

T: That makes a good analogy of our present society. E: Exactly, because everything always fits together. All of our machines and apparatus and theories are extensions of our own thought patterns. Its all basically an architectural type of situation.

T: It seems as though the true promise for beneficial technology lies in the etheric, organic side, the side of life. It seems as though when one presents this information on living energy to scientists, rather than looking at it objectively, they react in a rage. Reich called this the emotional plague and his work has suffered from it. What do you think is with these scientists who refuse to face scientific verification of energies such as orgone.

E: The problem Is that they are not scientists, they’re not following the precepts of science. They’re mystics worshipping a nuclear type of destructive energy. My contention about nuclear power plants is that they’re not there to generate energy, they serve as temples to worship this energy of decay and destruction and disease. The high laws are the laws of thermodynamics where everything must diffuse, decay and dissipate. It’s quite obvious that they’re pretty much worthless for generating electricity because, for one reason, they cost too much. They have to pump billions and billions of dollars into them and they hardly produce enough electricity to justify their existence, let alone break even. So they serve no practical purpose even though they were purported in the late 1950s to be so-called free energy devices. You look at the way things were in the 50s and you find it’s basically death worship. That’s one thing that surprises me now is that people want to get back to the 50s and relive those images.

T: So you’re saying that the American Dream has turned out to be a nightmare?

E: The American Dream is to destroy the earth. We’ve succeeded in training everybody else how to do it too, so in case we fail they can take over where we left off.

T: I know what you mean. New Zealand’s native forests are being stripped to make disposable chopsticks for the Japanese. Eric, in closing do you have any final message?

E: Tell everyone to quit their jobs and smash their televisions.



From the March-April 1987 Journal of Borderland Research
Via Borderland Research @ http://borderlandresearch.com/functional-thinking-an-interview-with-eric-dollard-by-tom-brown


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Friday, 23 March 2012

Sacred Geometry: How to Create a Multiverse

Sacred Geometry
How to Create a Multiverse

Sacred Geometry graphic by Craig Nicholson.

 
Mathematics is a wonderfully clean subject. It is not subject to opinion, nor does it rely on heated debates as to what the correct answer is. And geometry specifically is pure beauty! It is a great synthesizer, merging the linear, rational aspect of math through the left-side of the brain with the graphical, artistic aspect of pattern and beauty through the right brain.


It unites the mind and the heart (called the "intelligence of the heart" by the ancient Egyptians), spirit and matter, science and spirituality. These are all apparently separate halves of the Whole.

Plato said in the Republic (VII, 527 d, e) that it is through geometry that one purifies the eye of the soul, "since it is by it alone that we contemplate the truth." Mother nature uses geometry everywhere you look, from the spirals of the nautilus shell, sunflower centre and spiral galaxies to the hexagon symmetry of snowflakes, flower petals and honeycomb.

         Geometry in nature arranges the shapes of the molecules and crystals that make up our bodies and the physical cosmos. It is the key to the creation of the universe. A good primer on this subject is Michael Schneiders interesting book A Beginner's Guide to Constructing the Universe. In his introduction, he says: "It's a shame that children are exposed to numbers merely as quantities instead of qualities and characters with distinct personalities relating to each other in various patterns. If only they could see numbers and shapes as the ancients did, as symbols of principles available to teach us about the natural structure and process of the universe and to give us perspective on human nature."



         Studying and meditating on geometry helps us to better understand the laws, patterns and blueprints within nature. As we are part of nature, it can help us key in to and become more of our true selves, the magnificent spiritual beings who we really are. But if you are not into that, just studying the wonders and beauty of geometry is a healthy and thoroughly enjoyable past time anyway!




         
Sacred geometry has many diverse and extremely interesting aspects. We start with Pythagoras of Samos, who helped put sacred geometry "on the map", and then go logically through the process of creation into more specific areas of sacred geometry.

Pythagoras.

         People have understood the spiritual significance of geometry for ages, from the ancient Egyptians to the Vedas in early India. These were studied by Pythagoras, who helped immensely in putting sacred geometry "on the map" i.e. making it more generally known. Born around 580 BC in Samos, this amazing Greek philosopher, mathematician, and spiritual leader formulated principles that influenced the thought of Plato and Aristotle and contributed to the development of mathematics and Western rational philosophy. He founded the Pythagorean brotherhood in Cortona, a mystical school developed as the archetype of a golden-age educational community.

        They uncovered many of nature's secrets, and held that at its deepest level, reality is mathematical in nature. (Pythagoras once declared: "All is number." This theme has been repeated many times since, including by Bruce L. Cathie in his many books on harmonics, like The Bridge to Infinity.) They studied the mathematical laws behind the rhythm and harmony of music. They also pondered the intangible, not only by the logic of the mind but by the intuitive faculties of the heart. Pythagoras believed in life after death and reincarnation, and taught that the soul can transcend the cycles of rebirth and rise to union with the divine. Their community followed an ethical and moral code, and strove to put their spiritual knowledge into practical everyday use.

         John Strohmeier and Peter Westbrook say the following on page 66 of their book Divine Harmony: The Life and Teachings of Pythagoras (Berkley Hills Books, 1999): "For Pythagoras, mathematics was a bridge between the visible and invisible worlds. He pursued the study of mathematics not only as a way of understanding and manipulating nature, but also as a means of turning the mind away from the physical world, which he held to be transitory and unreal, and leading it to the contemplation of eternal and truly existing things that never vary. He taught his students that by focusing on the elements of mathematics, they could calm and purify the mind, and ultimately, through disciplined effort, experience true happiness."

         Unfortunately for Pythagoras (and for all of us since) there was much jealousy directed towards him and his community, plus resistance to his enlightened ideas. He and many of his followers were eventually killed, and his teachings largely destroyed. So much of what we know about him is from third-hand accounts, some of it being aimed at discrediting him. But his legacy and genius live on, and many after him have been inspired to study and elaborate on this wonderful subject.



Geometry and creation.

 

         The role of geometry in the process of creation is covered well by Robert Lawlor, in his fascinating book Sacred Geometry: Philosophy and Practice (Thames and Hudson, London, 1982). In it he says the following: "The perspective of volume offers yet another metaphor for the original and ever-continuing creative act of the materialization of Spirit and the creation of form. The very ancient creation myth coming from Heliopolis in Egypt gives an example of this mode of envisioning. Nun, the Cosmic Ocean, represents pure, undifferentiated spirit-space, without limit or form. It is prior to any extensive, any specificity, any god. It is pure potentiality. By the seed or will of the Creator, who is implicit within this Nun, the undifferentiated space is impelled to contract or coagulate itself into volume. Thus Atum, the creator, first creates himself or distinguishes himself from the undefinable Nun by volumizing, in order that creation might begin."





The Five Platonic Solids.


"What form, then, might this first volume have? What indeed are the most essential volumetric forms? There are five volumes which are thought to be the most essential because they are the only volumes which have all edges and all interior angles equal. They are the tetrahedron, octahedron, cube, dodecahedron and the icosahedron, and are the expressions in volume of the triangle, the square and the Pentagon: 3, 4, 5. All other regular volumes are only truncations of these five. These five solids are given the name 'Platonic' because it is assumed that Plato has these forms in mind in the Timaeus, the dialogue in which he outlines a cosmology through the metaphor of planar and solid geometry."





In this dialogue, which is one of the most thoroughly 'Pythagorean' of Platos works, he establishes that the five elements of the world are earth, air, fire, water and aether (prana). Lawlor continues: "Plato's fabricator of the universe created order from the primordial chaos of these elements by means of the essential forms and numbers. The ordering according to number and form on a higher plane resulted in the intended disposition of the five elements in the physical universe. The essential forms and numbers then act as the interface between the higher and lower realms. They have in themselves, and through their analogues with the elements, the power to shape the material world.

         "As Gordon Plummer notes in his book The Mathematics of the Cosmic Mind, the Hindu tradition associates the icosahedron with the Purusha. Purusha is the seed image of Brahma, the supreme creator himself, and as such this image is the map or plan of the universe. The Purusha is analogous to the Cosmic Man, the Anthropocosm of the western esoteric tradition. The icosahedron is the obvious choice for this first form, since all the other volumes arise naturally out of it."

     
  Icosahedron:
The Hindu tradition associates the icosahedron with Purusha, the seed image of Brahma, the supreme creator himself.
     
  Dodecahedron:
The icosahedron generates the dodecahedron, representing Prakriti, the feminine power of creation of the matter (mother) universe. The star born within it's pentagon (below) produces the Golden Ratio, the energy of resurrection and symbol of the Christ.

The star born within the pentagon:




Patterns created from the moving 3-D Icosahedron lattice above:






The Golden Ratio



The golden ratio is the mathematical proportion 1:1.618034...ad infinitum. Often called by its Greek name phi, it is also known as the Divine Proportion, the Golden Ratio, the Golden Section and the Golden Mean. It is indelibly inscribed in the heart of nature and man. Trace the thread of this "golden mean" from daisy to pyramid, from pine cone to Parthenon. Or from seashell to spiral nebulae as described above. The cosmos weaves its garments with perfect integrity, laced by the golden ratio. It is so omnipresent that many philosophers, artists, mathematicians, and scientists have considered it an essential component of beauty, perhaps integral to life itself. Plato considered it the key to the physics of cosmos. The Egyptians thought it more than a number and believed it symbolized the creative process and the fire of life.


        This magical proportion is found by dividing a line (AC) at a particular point to yield two unequal sections, where the smaller one (AB) is proportionate to the larger one (BC) as the larger one (BC) is to the entire line (AC). The ratio is expressed as AB/BC = BC/AC. There is only one such point (B) on any line. It is easy to produce this ratio geometrically. One of many ways is the five-pointed star, as drawn within a pentagon above. Every outside line on the pentagon is in a phi ratio to any line of the star. Also, every line on the star has 3 segments. One side segment is in a ratio of 1:1.618 to the rest of that line. This ratio is what was used in the architecture of the great pyramids of Egypt, and results in the focusing of universal energy (a.k.a. prana) at a particular point, which helps in rejuvenation of life (or the preservation of dead bodies). This resurrection energy and ratio is the mark of the Christ, the victor over death and rejuvenating principle in nature.



Phi and the Great Pyramid.

 

        
In the diagram above, the big triangle is the same proportion and angle of the Great Pyramid, with its base angles at 51 degrees 51 minutes. If you bisect this triangle and assign a value of 1 to each base, then the hypotenuse (the side opposite the right angle) equals phi (1.618..) and the perpendicular side equals the square root of phi. And that’s not all. A circle is drawn with it’s centre and diameter the same as the base of the large triangle. This represents the circumference of the earth. A square is then drawn to touch the outside of the earth circle. A second circle is then drawn around the first one, with its circumference equal to the perimeter of the square. (The squaring of the circle.) This new circle will actually pass exactly through the apex of the pyramid. And now the “wow”:

A circle drawn with its centre at the apex of the pyramid and its radius just long enough to touch the earth circle, will have the circumference of the moon! Neat, huh! And the small triangle formed by the moon and the earth square will be a perfect 345 triangle (related to the Pythagorean Theorem). Using the 345 triangle is also the easiest way to draw a squared circle.



Visualizing crystal structures for higher consciousness.


If you really want to get into the spirituality and personal growth aspect of sacred geometry, it is recommended to meditate on the geometric structure of crystals. David Tame, in his fascinating book The Secret Power of Music, (Destiny Books, 1984) says the following: "On the subject of crystals, modern esotericists have often recommended crystals, pictures of crystals, and models of the molecular structure of crystals as a subject for meditation. Contemplation upon their geometry is said to provide a route by which the consciousness of man can attune itself to the various qualities of the Consciousness of the Supreme."

         Here is a related and rather challenging exercise. It is a message from the Ascended Lady Master Leto through the messenger Elizabeth Clare Prophet, April 15, 1976, found on an audio tape (#B7629). "You have been told .... to meditate upon the crystal and its structure. Now I ask you ... to select images of crystals and then to diagram the molecular structure of crystals and to begin to memorize these structures and to endow them with flame, and to realize that your altar is a place of change .... And therefore consider that the crystal, especially of rare gems and their molecular structure - and I meditate now with you upon the structure of the emerald - is a means of contacting the plane of Spirit. For these emanations of the mind of God manifest in matter are parallel to the energies manifest in Spirit. They are time-space coordinates of the coalescing of energy in infinity.

         "If you can therefore meditate upon, and endow your meditation with the flaming fire, this is what will take place: You will trace from effect to cause, to first cause, the very components of creation. And if you will study the treatise on alchemy by beloved Saint Germain, you will find that your visualizations will bring into manifestation elements of the Christ consciousness, abundance, the ability to expand a mandala for the community of the Holy Spirit."
(Quoted with permission. Copyright © Summit University Press. All rights reserved. Website: www.tsl.org)

         It is not that easy to find the molecular structure of crystals. To help you on your way, here is a link to an excellent website by the Institut Laue-Langevin (ILL) in France on The atomic structure of materials. This site allows you to obtain a 3D VRML model of structures by clicking on flagged links. If you do not have a 3D viewer on your computer, click the Help link at the top of their page. Once you have one, click on the “Gems and Minerals” link. Clicking on flagged links will allow you to navigate WITHIN and around these 3 dimensional crystal structures. Very cool! PS: If you have any ideas on how to “endow these structures with Flame”, please share them with us. Thanks.




Cymatics and Creation by Sound.


Now we come to one of nature's greatest mysteries, the creation of matter by sound. "And God SAID, let there be light." "In the beginning was the WORD, ... and the Word was God." Jesus and his followers obviously studied the ancient Hindu Vedas, written long before his time. They state: "In the beginning was Brahman with whom was the Word. And the Word was Brahman." The sacred texts of India teach that sound holds the key to the mysteries of the universe, to the creation and constant changing of our world. They put much emphasis on mantras, spoken prayers and sacred music. We in the West, constantly being bombarded by discordant sounds and music, are largely unaware of its tremendous power.

         The book Cymatics: A Study of Wave Phenomena & Vibration by Hans Jenny sums up the phenomena of the effect that sound has on matter. He developed techniques to show that every frequency and musical note has a particular geometric pattern that it forms, like this colour image on the book's cover. 
Cymatics book coverHe built on the work of Chladni, who created sand patterns on a metal disc through sound. You can find more on Cymatics at this AlphaOmega website. More insight into this subject is given by David Tame in his fascinating book The Secret Power of Music mentioned above. In his chapter The Physics of the Om, he says: "Complex and meaningful patterns are even more apparent in Jenny's sound-affected substances when viewed at the microscopic level. Then are revealed beautiful and mathematically-precise mandala-structures looking like groupings of microscopically-viewed snowflakes. The stress-interactions created in substances by their exposure to sound frequencies always result in formations replete with meaningful numerological, proportional and symmetrical qualities."

         He goes on to discuss the works of several researchers who prove that the whole-number ratios of musical harmonics correspond to an underlying numerical and geometric framework existing in nature and matter. This sheds light on Goethe's statement "Geometry is frozen music." The book also covers research on the effects of sound and music on the human body and psyche. In general, the findings show that classical type music promotes physical and mental health, whereas rock music has the opposite effect…



From Wholesome Balance  @ http://geometry.wholesomebalance.com/index.html & http://geometry.wholesomebalance.com/Sacred_Geometry_2.html




Sacred Geometry

 

Sacred Geometry Introductory Tutorial

 

by Bruce Rawles

 

In nature, we find patterns, designs and structures from the most minuscule particles, to expressions of life discernible by human eyes, to the greater cosmos. These inevitably follow geometrical archetypes, which reveal to us the nature of each form and its vibrational resonances. They are also symbolic of the underlying metaphysical principle of the inseparable relationship of the part to the whole.

It is this principle of oneness underlying all geometry that permeates the architecture of all form in its myriad diversity. This principle of interconnectedness, inseparability and union provides us with a continuous reminder of our relationship to the whole, a blueprint for the mind to the sacred foundation of all things created.

 

The Sphere

 


(charcoal sketch of a sphere by Nancy Bolton-Rawles)

Starting with what may be the simplest and most perfect of forms, the sphere is an ultimate expression of unity, completeness, and integrity. There is no point of view given greater or lesser importance, and all points on the surface are equally accessible and regarded by the center from which all originate. Atoms, cells, seeds, planets, and globular star systems all echo the spherical paradigm of total inclusion, acceptance, simultaneous potential and fruition, the macrocosm and microcosm.

 

The Circle

 


The circle is a two-dimensional shadow of the sphere which is regarded throughout cultural history as an icon of the ineffable oneness; the indivisible fulfillment of the Universe. All other symbols and geometries reflect various aspects of the profound and consummate perfection of the circle, sphere and other higher dimensional forms of these we might imagine.

The ratio of the circumference of a circle to its diameter, Pi, is the original transcendental and irrational number. (Pi equals about 3.14159265358979323846264338327950288419716939937511…) It cannot be expressed in terms of the ratio of two whole numbers, or in the language of sacred symbolism, the essence of the circle exists in a dimension that transcends the linear rationality that it contains. Our holistic perspectives, feelings and intuitions encompass the finite elements of the ideas that are within them, yet have a greater wisdom than can be expressed by those ideas alone.

 

The Point

 .

At the center of a circle or a sphere is always an infinitesimal point. The point needs no dimension, yet embraces all dimension. Transcendence of the illusions of time and space result in the point of here and now, our most primal light of consciousness. The proverbial “light at the end of the tunnel” is being validated by the ever-increasing literature on so-called “near-death experiences”. If our essence is truly spiritual omnipresence, then perhaps the “point” of our being “here” is to recognize the oneness we share, validating all “individuals” as equally precious and sacred aspects of that one.

Life itself as we know it is inextricably interwoven with geometric forms, from the angles of atomic bonds in the molecules of the amino acids, to the helical spirals of DNA, to the spherical prototype of the cell, to the first few cells of an organism which assume vesical, tetrahedral, and star (double) tetrahedral forms prior to the diversification of tissues for different physiological functions. Our human bodies on this planet all developed with a common geometric progression from one to two to four to eight primal cells and beyond.

Almost everywhere we look, the mineral intelligence embodied within crystalline structures follows a geometry unfaltering in its exactitude. The lattice patterns of crystals all express the principles of mathematical perfection and repetition of a fundamental essence, each with a characteristic spectrum of resonances defined by the angles, lengths and relational orientations of its atomic components.

 

The Square Root of Two

 


The square root of 2 embodies a profound principle of the whole being more than the sum of its parts. (The square root of two equals about 1.414213562…) The orthogonal dimensions (axes at right angles) form the conjugal union of the horizontal and vertical which give birth to the greater offspring of the hypotenuse. The new generation possesses the capacity for synthesis, growth, integration and reconciliation of polarities by spanning both perspectives equally. The root of two originating from the square leads to a greater unity, a higher expression of its essential truth, faithful to its lineage.

The fact that the root is irrational expresses the concept that our higher dimensional faculties can’t always necessarily be expressed in lower order dimensional terms – e.g. “And the light shineth in darkness; and the darkness comprehended it not.” (from the Gospel of St. John, Chapter 1, verse 5). By the same token, we have the capacity to surpass the genetically programmed limitations of our ancestors, if we can shift into a new frame of reference (i.e. neutral with respect to prior axes, yet formed from that matrix-seed conjugation. Our dictionary refers to the word matrix both as a womb and an array (or grid lattice). Our language has some wonderful built-in metaphors if we look for them!

 

The Golden Ratio

 


The golden ratio (a.k.a. phi ratio a.k.a. sacred cut a.k.a. golden mean a.k.a. divine proportion) is another fundamental measure that seems to crop up almost everywhere, including crops. (The golden ratio is about 1.618033988749894848204586834365638117720309180…) The golden ratio is the unique ratio such that the ratio of the whole to the larger portion is the same as the ratio of the larger portion to the smaller portion. As such, it symbolically links each new generation to its ancestors, preserving the continuity of relationship as the means for retracing its lineage.




The golden ratio (phi) has some unique properties and makes some interesting appearances:

  • phi = phi^2 – 1; therefore 1 + phi = phi^2; phi + phi^2 = phi^3; phi^2 + phi^3= phi^4; ad infinitum.

  • phi = (1 + square root(5)) / 2 from quadratic formula, 1 + phi = phi^2.

  • phi = 1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/…)))))

  • phi = 1 + square root(1 + square root(1 + square root(1 + square root(1 + square root(1 + …)))))

  • phi = (sec 72)/2 =(csc 18)/2 = 1/(2 cos 72) = 1/(2 sin 18) = 2 sin 54 = 2 cos 36 = 2/(csc 54) = 2/ (sec 36) for all you trigonometry enthusiasts.

  • phi = the ratio of segments in a 5-pointed star (pentagram) considered sacred to Plato and Pythagoras in their mystery schools. Note that each larger (or smaller) section is related by the phi ratio, so that a power series of the golden ratio raised to successively higher (or lower) powers is automatically generated: phi, phi^2, phi^3, phi^4, phi^5, etc.



  • phi = ratio of adjacent terms of the famous Fibonacci Series evaluated at infinity; the Fibonacci Series is a rather ubiquitous set of numbers that begins with one and one and each term thereafter is the sum of the prior two terms, thus: 1,1,2,3,5,8,13,21,34,55,89,144… (interesting that the 12th term is 12 “raised to a higher power”, which appears prominently in a vast collection of metaphysical literature)



The mathematician credited with the discovery of this series is Leonardo Pisano Fibonacci and there is a publication devoted to disseminating information about its unique mathematical properties, The Fibonacci Quarterly

Fibonacci ratios appear in the ratio of the number of spiral arms in daisies, in the chronology of rabbit populations, in the sequence of leaf patterns as they twist around a branch, and a myriad of places in nature where self-generating patterns are in effect. The sequence is the rational progression towards the irrational number embodied in the quintessential golden ratio.

This most aesthetically pleasing proportion, phi, has been utilized by numerous artists since (and probably before!) the construction of the Great Pyramid. As scholars and artists of eras gone by discovered (such as Leonardo da Vinci, Plato, and Pythagoras), the intentional use of these natural proportions in art of various forms expands our sense of beauty, balance and harmony to optimal effect. Leonardo da Vinci used the Golden Ratio in his painting of The Last Supper in both the overall composition (three vertical Golden Rectangles, and a decagon (which contains the golden ratio) for alignment of the central figure of Jesus.

The outline of the Parthenon at the Acropolis near Athens, Greece is enclosed by a Golden Rectangle by design.

 

The Square Root of 3 and the Vesica Piscis

 


The Vesica Piscis is formed by the intersection of two circles or spheres whose centers exactly touch. This symbolic intersection represents the “common ground”, “shared vision” or “mutual understanding” between equal individuals. The shape of the human eye itself is a Vesica Piscis. The spiritual significance of “seeing eye to eye” to the “mirror of the soul” was highly regarded by numerous Renaissance artists who used this form extensively in art and architecture. The ratio of the axes of the form is the square root of 3, which alludes to the deepest nature of the triune which cannot be adequately expressed by rational language alone.

 

Spirals

 



This spiral generated by a recursive nest of Golden Triangles (triangles with relative side lengths of 1, phi and phi) is the classic shape of the Chambered Nautilus shell. The creature building this shell uses the same proportions for each expanded chamber that is added; growth follows a law which is everywhere the same. The outer triangle is the same as one of the five “arms” of the pentagonal graphic above.

 

Toroids

 



Rotating a circle about a line tangent to it creates a torus, which is similar to a donut shape where the center exactly touches all the “rotated circles.” The surface of the torus can be covered with 7 distinct areas, all of which touch each other; an example of the classic “map problem” where one tries to find a map where the least number of unique colors are needed. In this 3-dimensional case, 7 colors are needed, meaning that the torus has a high degree of “communication” across its surface. The image shown is a “birds-eye” view.

 

Dimensionality

 

The progression from point (0-dimensional) to line (1-dimensional) to plane (2-dimensional) to space (3-dimensional) and beyond leads us to the question – if mapping from higher order dimensions to lower ones loses vital information (as we can readily observe with optical illusions resulting from third to second dimensional mapping), does our “fixation” with a 3-dimensional space introduce crucial distortions in our view of reality that a higher-dimensional perspective would not lead us to?

 

Fractals and Recursive Geometries

 



There is a wealth of good literature on this subject; it’s always fascinating how nature propagates the same essence regardless of the magnitude of its expression…our spirit is spaceless yet can manifest aspects of its individuality at any scale.

 

Perfect Right Triangles

 



The 3/4/5, 5/12/13 and 7/24/25 triangles are examples of right triangles whose sides are whole numbers. The graphic above contains several of each of these triangles. The 3/4/5 triangle is contained within the so-called “King’s Chamber” of the Great Pyramid, along with the 2/3/root5 and 5/root5/2root5 triangles, utilizing the various diagonals and sides.

 

The Platonic Solids

 


 



The 5 Platonic solids (Tetrahedron, Cube or (Hexahedron), Octahedron, Dodecahedron and Icosahedron) are ideal, primal models of crystal patterns that occur throughout the world of minerals in countless variations. These are the only five regular polyhedra, that is, the only five solids made from the same equilateral, equiangular polygons. To the Greeks, these solids symbolized fire, earth, air, spirit (or ether) and water respectively. The cube and octahedron are duals, meaning that one can be created by connecting the midpoints of the faces of the other. The icosahedron and dodecahedron are also duals of each other, and three mutually perpendicular, mutually bisecting golden rectangles can be drawn connecting their vertices and midpoints, respectively. The tetrahedron is a dual to itself.

From April, 2000 through (at least) December, 2003, we conducted a poll on which Platonic Solid folks liked best; here’s the results from that period. If there’s interest, I’ll start another poll to see if the preferences has shifted!
:-)





Here are some animations of counter-rotating polyhedra and images of the Platonic solids showing their relationships as duals.

Here are fold-up patterns for the Platonic Solids.


The Archimedean Solids

 



There are 13 Archimedean solids, each of which are composed of two or more different regular polygons. Interestingly, 5 (Platonic) and 13 (Archimedean) are both Fibonacci numbers, and 5, 12 and 13 form a perfect right triangle.


 

Stellations of The Platonic Solids and The Archimedean Solids

 



This is a stellation of a dodecahedron where each pentagonal face is capped with a pentagonal pyramid composed of 5 golden triangles, a sort of 3-dimensional 5-pointed star.

Here are more images of polyhedra (Platonic and Archimedean Solids.)

 

Metatron’s Cube

 



Metatron’s Cube contains 2-dimensional images of the Platonic Solids (as shown above) and many other primal forms.

 

The Flower of Life

 




Indelibly etched on the walls of temple of the Osirion at Abydos, Egypt, the Flower of Life contains a vast Akashic system of information, including templates for the five Platonic Solids. The background graphic for this page is a repetitive hexagonal grid based on the Flower of Life.



SacredGaiametry


From The Geometry Code @ http://www.geometrycode.com/sacred-geometry/




The Fibonacci Sequence

edieval mathematician and businessman Fibonacci (Leonardo Pisano) posed the following problem in his treatise Liber Abaci (pub. 1202):

How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on?

It is easy to see that 1 pair will be produced the first month, and 1 pair also in the second month (since the new pair produced in the first month is not yet mature), and in the third month 2 pairs will be produced, one by the original pair and one by the pair which was produced in the first month. In the fourth month 3 pairs will be produced, and in the fifth month 5 pairs. After this things expand rapidly, and we get the following sequence of numbers:


1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ...

This is an example of a recursive sequence, obeying the simple rule that to calculate the next term one simply sums the preceding two:


F(1) = 1
F(2) = 1
F(n) = F(n – 1) + F(n – 2)


Thus 1 and 1 are 2, 1 and 2 are 3, 2 and 3 are 5, and so on.

This simple, seemingly unremarkable recursive sequence has fascinated mathematicians for centuries. Its properties illuminate an array of surprising topics, from the aesthetic doctrines of the ancient Greeks to the growth patterns of plants (not to mention populations of rabbits!). Consider, for example, the following diagram:






Here we have taken squares with sides whose lengths correspond to the terms of the Fibonacci sequence, and arranged them in an “outwardly spiraling” pattern. Notice that the rectangles which result at each stage are all roughly the same shape, that is, that the ratio of length to width seems to “settle down” as we build the pattern outward. Notice also that the ratio of length to width is at every step the ratio of two successive terms of the Fibonacci sequence, that is, the ratio of the greater one to the lesser. These ratios may be thought of as forming a new sequence, the sequence of ratios of consecutive Fibonacci numbers:





This sequence converges, that is, there is a single real number which the terms of this sequence approach more and more closely, eventually arbitrarily closely. We may discover this number by exploiting the recursive definition of the Fibonacci sequence in the following way. Let us denote the nth term of the sequence of ratios by xn, that is,





Then using the recursive definition of F(n) given above, we have:





Now supposing for the moment that the sequence converges to a real number x (a fact which requires proof, but we'll leave that aside), we may observe that both xn and xn - 1 have the same limit, that is,





Consequently, the real number x to which the sequence of ratios converges must satisfy the following equation:





This is a simple equation to solve for x: it is really a quadratic equation, and its positive root is the value we are looking for:






This number was known to the ancient Greeks and was called by them the Golden Mean. It is usually denoted by the Greek letter f (phi), and sometimes by m (mu). They believed that the proportion f:1 was the most most pleasing, indeed the aesthetically perfect proportion, and all of their artwork, sculpture, and especially architecture made use of this proportion. A rectangle whose sides had this proportion was called the Golden Rectangle. (And that is the shape being more and more closely approximated by our “spiralling rectangles” above.)

Whether or not you agree with the Greeks’ aesthetic judgment, it's a safe bet that Nature herself does:






The growth of this nautilus shell, like the growth of populations and many other kinds of natural “growing,” are somehow governed by mathematical properties exhibited in the Fibonacci sequence. And not just the rate of growth, but the pattern of growth. Examine the crisscrossing spiral seed pattern in the head of a sunflower, for instance, and you will discover that the number of spirals in each direction are invariably two consecutive Fibonacci numbers.

The Fibonacci sequence makes its appearance in other ways within mathematics as well. For example, it appears as sums of oblique diagonals in Pascal’s triangle:







From Math Academy @ http://www.mathacademy.com/pr/prime/articles/fibonac/index.asp






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