Squaring the Circle

Squaring the circle has been a mathematical problem that has been discussed for thousands of years. It is a problem that has never been solved and in the 19th century, it was proven to be impossible to do. This site, http://en.wikipedia.org/wiki/Squaring_the_circle explains the problem and its history in a lot of detail.


The squared circle has been a popular theme in the occult and in Alchemy for centuries and it still an important symbol within it. The square represents the physical world, because it represents the four elements, the four cardinal directions, the four seasons etc. The circle represents the spirit because it is infinite and it goes out in all directions. The triangle represents the union of body, mind and spirit. The circle in the center represent the individual's spirit, whereas the outer circle represents the greater spirit of the Creator, which encompasses all things. It starts off with a spirit and ends with a spirit.


As explained on the page The Axis of the Universe in many occult and witchcraft rituals a circle is cast but is also then squared, "Magic rituals are performed in a circle with the practitioner visualizing a circle, or a sphere, of energy emerging out of the center and creating a magic space of power. The altar itself is in the center where the tools to perform the magical operations are and the higher realms are accessed through the center of the magic circle. There is a paradoxical thing in magic where the circle is squared when the magician calls forth the spirits from the four corners, each one representing one of the four elements, of the Earth to participate in the ritual.

The four elements come together in the center of the squared circle to become the fifth element that is the totality. This is the doorway to higher realms. It is created by creating a singularity of the physical world."


This is a statement from Marian Green in the book A Witch Alone, "Like other paradoxical matters in magic, ritual circles are square!"


This is further explained by Marian Green, "find items to use for the marking out of the square circle. The simplest set of symbols of the Elements of Earth, Water, Fire and Air are earth from the garden, water from the tap, a lighted candle and something scented. You can use a rock, pebble or slab of wood, which grows in the ground, for Earth."  


The impossibility of squaring the circle is a good metaphor for the relationship between the spirit and the physical. They are both there, but they can't be joined together. The Hermetica saids it pretty well in 1:[15] "Because of this, unlike any other living thing on earth, mankind is twofold - in the body mortal but immortal in the essential man. Even though he is immortal and has authority over all things, mankind is affected by mortality because he is subject to fate; thus, although man is above the cosmic framework, he became a slave within it. He is androgyne because he comes from an androgyne father, and he never sleeps because he comes from one who is sleepless. <Yet love and sleep are his> masters."

This is another quote from The Hermetica on living with two natures IV:[6] "it is impossible to be engaged in both realms, the mortal and the divine. Since there are two kinds of entities, corporeal and incorporeal, corresponding to mortal and divine, one is left to choose one or the other, if choice is desired. One cannot {have both together when one is left to choose}, but lessening the one reveals the activity of the other."



[7] "Choosing the stronger, then [ ], not only has splendid consequences for the one who chooses - in that it makes the human into a god - but it also shows reverence toward god. On the other hand, choosing the lesser has been mankind's destruction, though it was no offence to god, with this single reservation: just as processions passing by in public cannot achiever anything of themselves, though they can be a hindrance to others, in the same way these people are only parading through the cosmos, led astray by pleasures of the body."


The Bible has this famous quote about trying to serve two masters, Matthew 24, “No one can serve two masters. Either you will hate the one and love the other, or you will be devoted to the one and despise the other. You cannot serve both God and money."

The Cherokee Indians put it in a very good way with this story, "One evening an old Cherokee Indian told his grandson about a battle that goes on inside people. He said, ‘My son, the battle is between two ‘wolves’ inside us all.One is Evil. It is anger, envy, jealousy, sorrow, regret, greed, arrogance, self-pity, guilt, resentment, inferiority, lies, false pride, superiority, and ego. The other is good. It is joy, peace, love, hope, serenity, humility, kindness, benevolence, empathy, generosity, truth, compassion and faith.’ The grandson thought about it for a minute and then asked his grandfather: ‘Which wolf wins?’ The old Cherokee simply replied, ‘The one you feed.'" This is a universal teaching across so many different cultures because spirit is above the human and it will give these ideas to anyone who is enlightened. 


The book called Alchemy Unveiled, by Johannes Helmont, makes it clear that the Magnum Opus, or Great Work, of the Alchemist is to overcome the lower nature and become the higher nature, "Everything a Human Being does with diligence and perseverance, comes alive in him and takes on a shape and form which strives to attain dominion over him; that means, to become the controlling "I". Good and evil forces can be awakened in the Soul in such a way and be brought to a sort of rebirth. In earlier days, these forces were called spirits and demons. The Good brings a heavenly force, brings within himself a good Spirit or Guardian Angel to a rebirth. Evil brings a hellish force, an evil spirit or devil. The hellish spirits or demons are spawns of the Devil of the wrong life's passionate desires of Human Beings; the heavenly Spirits or Angels, by comparison, are the personification of high virtues. Such a force will not always immediately turn into a ruling "I" within the Human Being, but instead, generally into a "Part-I". In such instances, there seem to be two or more "I" complexes present within a Human Being at the same time. These often contradict each other and quarrel amongst each other about the supremacy. Should the Human Being be successful in strengthening the pure original human nature and elevate it to its true dignity, then little by little, "the devils" will flee from him. At this point the Human Being, who has been previously plagued by demons, emerges as a "Born Again Human Being" from this inner quarrel, and paradise opens itself up to such a person with its divine wonders. This is actually the true Process of the Magnum Opus of the true Alchemists, which for centuries, was completely wrapped up in a mysterious darkness."

The very symbol of Freemasonry means combining the square and circle, because the compares draws the circle and the square draws the square. In Freemasonry, the the compass and square have a very spiritual significance.


There's and important scene in the 1967 show called The Prisoner, which is explained on this page. In these scene, Number 6 is put in a chair and he has a circle and square entering into his third eye and merging together. This represents the merging of his spirit and the physical world, when this happens he loses consciousness, representing his true self losing consciousness.   



The artist called El Greco had a strange habit of painting square halos, instead of the usual circle halos, around Jesus Christ's head. In this painting, Jesus has a Sun in his right eye and a crescent Moon in his left eye. These represent the polar opposites of the physical world he lives in and the square halo represents that his physical body is holy.

The most famous representation of man is The Vitruvian Man by Leonardo Da Vinci, which is based on the correlations of ideal human proportions with geometry described by the ancient Roman architect Vitruvius in Book III of his treatise De Architectura. This ideal man is both within a square and a circle. The ideal man has a unity of spirit and matter.

The purpose of so many spiritual exercises is to rise above the animal, or the flesh and to ascend to higher realms. That is the true goal of any Alchemist and seeker. This is an excellent quote by Johannes Helmont in Alchemy Unveiled, "Whosoever knows how to separate the Immortal from the Mortal, the blessing from the curse, to bring the indestructible back into the original Being (as it was in the beginning) and into its original dignity, is the one, who imitates GOD'S Work of Creation in a small way, and he is a true Alchemist."

Both the square and the circle have a center in them and even though they are incompatible, they have that feature in common and that is the paradox that can actually unify them and make them work in harmony with each other, which is explain in a lot of detail on the page The Axis of the Universe on this website. That page explains that the circle is really the empty point and the center is really the only thing that exists. The square likewise is also an empty point. The centers of the square and the circle are one and the same. That is how the circle can be squared, by becoming the origin of both.


The center of the square is the fifth element, which is the totality of all the elements of the Universe and the center of the circle is the totality of everything in the Universe, therefore they are one and the same thing.  

In physics quantum mechanics deals with the micro universe and the theory of relativity deals with the macro universe. The problem with both of them is that they don't agree with each other and the attempt at unifying them is called the Unified Field Theory. They were unified in the Big Bang, as in at the beginning or the center. Like with the polar opposites of the square and the circle, the micro and the macro are unified at the center. They become one when they go to their earliest origins.

The Fibonacci spiral shows squares with a spiral emerging from the smaller ones to the larger ones. Each square is an image of the smaller squares that preceded it. Imagine the squares are everything from an atom, to a star system, to a galaxy all the way up to the Great Attractor and all of the objects that make up nature. A spiral is caused by objects that orbit a center that is moving which means that nothing orbits in a circle, but in a spiral as this videos shows. All the textbooks are wrong.


The smaller the squares are the faster the spiral becomes like in a cyclone and the squares become smaller and smaller until they reach the Planck Length which is the smallest possible length. This unifies the spiral and squares into a singularity that is what a Black Hole is. It becomes nothingness and that is how a circle can be squared, in the nothing. The most dangerous part of a Black Hole is not the center of it, but the surrounding area called the Event Horizon, much like the surrounding area of the eye of a cyclone. The center of a Black Hole is not dangerous because there is nothing there. Time, speed and distance collapse to zero which is what a singularity is.

When the square and its spiral becomes a zero they become one and the same in the singularity.










Nikola Tesla once said that "If you want to find the secrets of the universe, think in terms of energy, frequency and vibration." Everything in the Universe is a vibration as this video mentions and as explained on the section called The Infinite Spirals of Nature and the One Center They All Orbit section of this page. Everything from the atom up to the galaxy and whatever the Great Attractor is to time and space itself is a vibration. A vibration, cycle, or more properly oscillation, is a spiral that has been flattened out so there are up and down movements revolving around an invisible center, which is the Singularity that is the cancellation of space and time. An oscillation is really just a flat line that has been warped and the flat line itself is a point or center that is moving. Think of the oscillation as being the cycles of time and the flat line as been the movement of space. The constant is the combination, or balance, between time and space. The whole oscillation, from the atom all the way up to the entirety of the Universe, is really just a point that is moving through space and warping to create the cycles of time. Gravity is a by product of the warped line wanting to become flat and the flat line wanting to become a point again. When thought of this way the point is really the only thing that exists and that is how the center of anything is the center of everything and this is how God is the infinite sphere whose center is everywhere and whose circumference is nowhere. The center that is the Pleroma, meaning the totality, is the point and the Universe is the empty point.

If the Universe is really just one point expressing itself in infinite ways then imagine a frequency that is made up of smaller frequencies which are made up of smaller frequencies still until the smallest levels are reached. Imagine the frequency of the galaxies, the frequencies of their star systems, the frequencies of their planet's orbits, the frequencies of their satellites, the day and night frequencies, the frequencies that are in the Human body, the frequencies of the atoms etc. The biggest frequency of them all is the thing that is called the Big Bang, but these frequencies are all just one frequency and this is why it is called the Universe or one verse. 

As this video mentions all matter and energy are excitations in quantum fields, with the quantum field being zero, or nothingness, which is where speed, distance and time come to rest. Physicists imagine these quantum fields as being boxed grids, but is the One Electron Universe theory is true, then the quantum field could really just being some God Particle being omnipresent, meaning everywhere, at once and expressing itself in many different vibrations producing the particles of the Universe. When looked at closely these particles do look like waves, because they are vibrations. It's only when looked at from afar that they look like particles and when particles are looked at from afar they look like the Universe and everything that makes it up. But all those infinite vibrations are really just that one zero that becomes all the vibrational numbers.   

In Alchemy the Prima Materia, or the First Matter, is central to the whole process of transmutation. It may seem like superstition but Physicists themselves say that the entire Universe emerged out of nothing Ex Nihilo. What else would the Prima Materia be except the Singularity of everything that is really nothing. To transmute matter, or anything else such as the soul, it first has to be broken down into its primordial nature, purified and rebuilt. These are some definitions of the Prima Materia from Wikipedia, "the ubiquitous starting material required for the alchemical magnum opus and the creation of the philosopher's stone. It is the primitive formless base of all matter similar to chaos, the quintessence or aether." Mary Anne Atwood had this to say about it, "That there abides in nature a certain pure matter, which, being discovered and brought by art to perfection, converts to itself proportionally all imperfect bodies that it touches." Lastly this quote from Theatrum Chemicum describes its properties really well, "They have compared the "prima materia" to everything, to male and female, to the hermaphroditic monster, to heaven and earth, to body and spirit, chaos, microcosm, and the confused mass; it contains in itself all colors and potentially all metals; there is nothing more wonderful in the world, for it begets itself, conceives itself, and gives birth to itself." The Big Bang itself, whatever it was and whatever its purpose was, can be seen as the ultimate Prima Materia, but that Prima Materia still lies underneath the entire Universe because the potential for emptiness that the Singularity that a Black Hole is is underneath all space and time, like how the low pressure of a cyclone lies underneath the Earth's atmosphere. 

There's a really bizarre theory called The One Electron Universe and it means just what the name suggests. It may seem like the most implausible idea ever to suggest that the Universe is only made up of one electron, but it does explain some useful things. The first one is that it explains why all electrons are the same, but it also may explain the problem caused by Quantum Entanglement, where entangled particles can somehow communicate many thousands of times the speed of light. If there's just one particle, then of course there would be entanglement no matter the distance, because it's all the same particle. Even more incredible is that it explains how the entire Universe, or an entire Universe, could emerge from the Singularity that caused the Big Bang. Perhaps it's not matter being compressed but the time and space that the single electron occupies and expresses itself in that is compressed. This same thing would apply to the super density of a Black Hole. This theory, if it were true, would support the idea that the center of anything is the center of everything, that God is an infinite sphere whose center is every and whose circumference is nowhere and that there is only one frequency to go with the one wave of the one electron. This would certainly be that First matter that makes up everything.   


This video mentions that time and space are connected to each other so that if movement goes up, time goes down and if time goes up, movement goes down. The maximum speed of the physical Universe is the speed of light and at that speed time goes to zero. On the other hand if movement is zero then time is at maximum. Logic would suggest if an object goes faster than the speed of light then time would go into reverse, but that's assuming that time as space are connected in a line which isn't the case. Rather, they are connected in a circle. This means that there is always going to be a balance between the two so they are the same distance from the center. This is the constant that Albert Einstein talked about. The occultists say that reality is contained within the circle and the Physicists say that time and space and all the energy and matter contained within it is contained in a circle. But for this system to work the bottom part of the circle of reality, or time and space, has to be negative, so there isn't backward time but backward matter. It is better to think of the container as not being a circle as such but a twisted circle so that the backward matter is locked away on the other side of the singularity that is the balance that is the constant of time and space. The interesting part is at the end when the video mentions that in a Black Hole the circle that contains time and space collapses into the point in the middle of it so that effectively the nothing become the everything. An object going into a Black Hole will have its movement reduced to zero in effect going into that state of rest that the Gnostics, the Hermeticist and the Tao Teh Ching talked about.














The square in the occult can represent the four elements, the four seasons, the four cardinal directions etc. But as that video showed it can also represent the four constants of time and space with positive time, negative time, forward movement and backward movement. These four constants of time and space are bound in a circle which is the balance of the two so that they are always at the same distance from the center. For this system to work the top part of this circle of reality has to be matter and the bottom part has to be antimatter. In Physics there is a theory called Baryon Asymmetry which states there should be an equal amount of antimatter in the Universe but if that were the case then this Universe would cancel itself out. This is what Wikipedia says about this problem, "In physical cosmology, the baryon asymmetry problem, also known as the matter asymmetry problem or the matter–antimatter asymmetry problem, is the observed imbalance in baryonic matter (the type of matter experienced in everyday life) and antibaryonic matter in the observable universe. Neither the standard model of particle physics, nor the theory of general relativity provides a known explanation for why this should be so, and it is a natural assumption that the universe is neutral with all conserved charges. The Big Bang should have produced equal amounts of matter and antimatter. Since this does not seem to have been the case, it is likely some physical laws must have acted differently or did not exist for matter and antimatter. Several competing hypotheses exist to explain the imbalance of matter and antimatter that resulted in baryogenesis. However, there is as of yet no consensus theory to explain the phenomenon. As remarked in a 2012 research paper, "The origin of matter remains one of the great mysteries in physics."" Maybe the solution to the problem is by twisting the circle of reality so that the nothing of the circle becomes the everything that infinity is. 

The balance is elsewhere in the nowhere that is the center, or the gateway, to the other side of the infinity loop. Perhaps in the Black Hole both matter and antimatter come together and time and space cancel out. The Singularity is where the circle gets squared so that the center that lies underneath becomes the only thing that exists in non existence. 

This video points out that the circle, which is a representation of zero, creates vibrations. All energy and matter are excitations or vibrations in the quantum field which is zero. This is how all the Universe is created Ex Nihilo, or out of nothing.

This same Circle of Reality can create other vibrations as well to create all the particles of the Universe. Everything is moved in something at rest as The Hermetica states. The center of the Circle of Reality is The Axis of the Universe and if there is a Prima Materia this would be it.

But the hands of the Circle of Reality don't move in a circle as such, but in a spiral as mentioned before. So imagine a clock whose hands move in a spiral instead of a circle. This would happen because the axis is itself moving. Imagine the Circle of Reality moving around in an infinity loop and its hands of space and time grow as it reaches the extremities of either side of the loop, but shrink as they move towards the center. The hands of space and time don't grow forever but start inverting as they shift to be in keeping with the law of equilibrium. As the Circle of Reality heads towards the center space and time shrink and accelerate. This phenomenon has been erroneously called Dark Energy and the problem with it is that Physicists assume that the Universe will keep accelerating until there is what they call the Big Rip in space and time, which goes against the law of equilibrium. 

The Squared Circle is really the Cubed Spiral.

Going back to the One Electron Universe theory, perhaps there's and anti matter version of this called the One Positron Universe on the other side. In the matter Universe the electron is on the outside of the atom being time and the proton is on the inside being space. In an anti matter Universe the positron is on the outside being time and the electron is on the inside being space. They each get a turn being on the outside and inside. If a spiraling clock has an AM and PM then everything that has a vibration, which is everything, does the same thing. In the center of everything, called a Singularity, the First Matter and the Squared Circle, the electron and proton change places and invert in order to abide by the law of equilibrium. This would be the true God Particle that makes the everything of the Universe.  

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