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.