My most recent late night discussion with my wife began on the topic of how people push us to follow certain paths in life simply to draw benefit for themselves. I have always loved music and wanted to pursue music as my life path for many years; however, over time I was pulled away from following this dream by a series of unfortunate life circumstances, and settled into an average work-a-day life just to get by. Some people in my life have repeatedly tried to push me to pursue that dream, even though doing so would now be detrimental to the life and security I have built over the years; and to all external appearance, these people only want to see me succeed and be happy, but I have come to understand that one person in particular has an ulterior motive for their 'encouragement', for through me pursuing and mastering a working understanding of musical theory, I would then be in a position to fill in gaps in that person's knowledge of the divine mathematics of all musical systems, which the individual has struggled with for many years.
The primary example of this musical mathematics presented itself in the circle of fifths, a diagrammatic representation of the formation of chords in both major and minor scales. the circle is depicted with twelve notes around its circumference representing all of the sharp and flat notes constituting the major scale, and another twelve notes on the inside circumference of the circle representing those sharps and flats in the minor scale. The major scale typically begins with the key note of 'C' at the top of the circle, followed by 'G' in the 1 o'clock position, then 'D', and so on. the structure of chords can be determined by tracing a line across the area of the circle, joining each of the notes which make up the chord, and in doing so, geometric shapes are created. Also, the fact that there are twenty-four notes in the circle in total, but two of them are the key note 'B natural' which does not factor into the formation of any major key chord structures, means that only twenty-two notes are regarded as 'active'. This coupled with the fact that there are seven notes in an octave (the eighth being the same as the first not in the scale), gives us the enigmatic ratio of 22/7. Michael Hayes writes in his groundbreaking book The Infinite Harmony, that 22/7 is the first whole number ratio arising from Pi, since 22÷7=3.142857, and is 0.001% accurate to the true value of Pi (3.141592).
This led us on to discussing the relationship between Pi and Phi (1.61803), and their presence in all natural organic and inorganic structures. We found it interesting that whilst Pi has its whole number representation in the circle of fifths and the ratio of 22/7, Phi has its whole number equivalent in the Fibonacci sequence, in which each number is the sum of the two preceding numbers (i.e. 1,1,2,3,5,8,13,21 etc). Pi holds the root to forming geometric shapes whilst Phi holds the root of the Golden Spiral, which is present in everything from microscopic sea life, to the proportions of the human body, to weather systems and spiral-arm galaxies. The even more intriguing aspect to these mathematical works of art is that they are fractal in nature, meaning that they are self replicating in accordance with their own mathematical law, reproducing the same shapes of patterns within and from themselves to infinity. My other observation was that, at least in the case of 22/7, the sequence of decimals appears to decrease in value as it progresses (3.142857142856142855 etc). This got us thinking about how when one tries to draw a circle around a square, then repeat this on a larger scale whilst adhering to the Phi ratio, the corners of the square will not touch the inner circumference of the circle as it did the first time. Only on the fourth repetition do the two shapes reunite perfectly before falling out of alignment again until the seventh repetition, though not as far out of alignment as they were before. This is another visual demonstration of the fundamental laws of natural formations, that absolute perfection is non-existent despite the initial appearance of it. However, just as the shapes grow further apart before realigning, all things in nature correct themselves in order to realign with a pre-existing principle of natural order, all things adjust and adapt their imperfections to achieve a state closer to perfection than what they had before. In the same way, the decimal numbers in 22/7 decrease to come ever closer to a more rational number, a more complete or whole number. It is mathematics' way of striving to achieve perfection, oneness with itself, trying to return to a single point of unity with everything. Just as numbers refine themselves, and geometric shapes fall in and out of alignment to finer and finer degrees, all natural structures, be they people, animals, plants, minerals, weather patterns, sub-atomic formations etc., they will always strive for unity with all other things in existence, all strive for perfection in accordance with the laws of Phi and Pi, the thumb print of the Gods, the tell-tale signs of intelligent design in the universe.
And with that soul-stirring realisation, my wife paused with a satisfied look on her face and concluded the discussion with, "...and that's why we need to poo!" I could not control my laughter, nor could I understand how this was relevant; but she laid my confusion and hysterics to rest by explaining that all things need to take in pat of something else to sustain themselves, an exchange of energy, and in recompense, all things excrete waste which then serves in sustaining something else. Nature takes our imperfections and uses them to the advantage of other living things in the constant pursuit of universal unity and perfection. So folks, if you're ever wondering why everybody poops, you know it's all because of mathematics! Thank you for reading this article. I hope it was helpful and/or interesting. To all of you, have a good day or night, wherever you are in the world, and may the Gods be with you!
Enki Endymion. O(
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