Mathematics and Geometry

Interestingly enough, geometry and numbers can help as well. Each level of the cave represents a number. One is the number of the shadows, Two is the number of the Fire, and Three is the number of the outside world, and Four is the number of the Sun. Using these numbers in geometric terms, each stage is related to the number of points of a geometric figure. The first stage, the shadows, is merely just a point. It has no connections, it has no direction, and it has no understanding of anything beyond it. It is just a point in space. As a person is released to see the Fire, they gain another point. They now have two, opposite points: the Fire and the shadows, the light and the dark, the good and the evil. These two points have a single connection, a single line between them. It is essentially a string for tug-of-war. This is the source of duality, the source of conflict. Compromise at this level lies in the various shades of grays that the fire makes, not merely the vast black and bright white of the flame. One could argue that there are more colors in the flame than just white; however, until a person exits the cave and sees the true colors of the outside world, the fire will be too bright for them to make any distinctions between white and any other color (besides black). Everything will be light or dark; we know not what color is at this level. In the world outside the cave, there are 3 points, a triangle. The triangle is the simplest and yet, the strongest 2-D geometric figure. It has the least amount points (a line is not a 2-D figure because it has only length or width, not both) necessary to make a 2-D geometric figure, and it is the only 2-D geometric figure in which all the points touch. If you try to touch all the points in a square, the resulting criss-cross would give you four triangles. Thus the triangle is the perfect symbol of compromise because all points are connected and held in balance by the other points. It is here, in the outside world, that we understand and can see color. We move beyond duality and into compromise and understanding. The final stage has 4 points. This can be seen as triangular pyramid, the simplest 3-D geometric figure. Like the 2-D triangle, all points of the triangular pyramid are connected to the rest of the points. It also gives a good illustration of the relationship between the sun and the outside world. The base triangle of the pyramid represents the outside world, and the point at the top represents the sun or the source shining down on the triangle that is the outside world.

Geometry is not the only place where these number combinations show up. Joseph Campbell discovered the number 432 to be found in many cultures throughout the world. The Hindus have a measurement of mythological time in which there are 10 periods. As humanity progresses through each Yuga, the morality of the world decreases until it is at its worse in the 10th period (Kali). Each Yuga is 432,000 years long. In Norse mythology, there are 540 doors in the great warrior hall of the Odin. At the end of days, 800 warriors will go through each door to fight the anti-gods in an Apocalyptic battle (Ragnarok). 800 times 540 equals 432,000. According to ancient Sumerian history, there were 10 kings who ruled for 432,000 years before the deluge or the flood. In the Bible, there are 10 patriarchs, starting with Adam, who ruled for 1656 years. In 1656 years, there are 86,400 weeks (7 may have been their base number, based on the Biblical creation week, and I will explain more about the base 7 later), and if you divide that by two, you get 43,200. There are approximately 25,920 years in a complete cycle of the zodiac. If you divide 25,920 by 60, which was the number base (we use a base 10 system) of Mesopotamia in 3200 BC, you get 432. Campbell also notices that, according to an exercise physician, the target resting heart rate is 60 beats per minute. If your resting heart rate is at 60 beats per minute, you are considered to be perfectly healthy. 60 beats per minute spread out over an entire hour is 3600 beats. In the span of 12 hours, that would be exactly 43,200 beats. (Campbell 208-210) In 24 hours, you would have two sets of 43,200 beats, thus belying the sense of duality: 43,200 beats for the day and 43,200 beats for the night. Likewise, if your heart-rate is one beat per second, then there are approximately 86,400 seconds in a day, split by the duality of night and day into 43,200. Taking this even further, the holy number of God in Christianity, as described in the Apostles Creed, is 777. The mark of the beast, or Satan, in Revelation is 666. If you divide 777 by 18 (which is just 6+6+6), you get 43.2, thus the relationship between Christianity’s dualistic deities, God and Satan, Light and Dark, is equivalent to the numerical concept of 432. As Campbell said, “this is the hidden, the occult, secret of the universe, society, ourselves, and all things, and its number is 432, the number and prime sign of the occult.” (210)

Lastly, 432 can be said to be a metaphor for the relationship between God or perhaps the Tao or the Force, Humanity, and the state of Duality. If four represents God, three represents Humanity, and two represents Duality, then the relationship between them is the intricate number, 432. Also, if seven is considered to be perfection and seven is just three plus four, then seven is equivalent to the God of Humanity. Equally, if six is considered to be evil and six can be represented by two plus four, then six is equivalent to the God of Duality. One could also say that six is just three plus three, in which case humanity is its own worst enemy. This however does not stand with the concept of seven because humanity could not be the root of duality and the root of perfection simultaneously, or could it?


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