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A Non-Mathematical Digression

The idea that philosophy is primarily and inherently linked with mathematics may be a stumbling block for some readers.  Geometry, itself, may not seem too daunting to such individuals -- after all, significant portions of this particular branch of mathematics are quite graphic and may even be considered as aesthetically pleasing.  On the other hand, the mere mention of long division or the appearance on the page of an equation involving strange symbols, may cause consternation and/or heart palpitations in anyone who has ever become self-convinced or been diagnosed as suffering from math anxiety. -- a disease now running rampant in classrooms being taught by reality-challenged mathematicians.             

Calvin and Hobbes by Bill Watterson might have put this into the best perspective when Calvin informed Hobbes:  “You know, I don’t think math is a science.  It think it’s a religion.”  “A religion,” Hobbes replied, scratching his ear.  “Yeah” Calvin quickly replies.  “All these equations are like miracles.  You take two numbers and when you add them, they magically become one new number!  No one can say how it happens.  You either believe it or you don’t.  This whole book is full of things that have to be accepted on faith!  It’s a religion!”  In his typical style, Hobbes notes, “And in the public schools no less.  Call a lawyer.”  Calvin then puts it all in perspective.  “As a math atheist, I should be excused from this.”           

Despite Calvin and Hobbes’ profound understanding and at the same time, twisted justification for being “excused from this”, basic arithmetic skills are in fact necessary in life -- if only to receive the correct amount of change (and like other puns occasionally appearing herein, this one was intentional).  Accordingly, and with full apologies to Calvin and others of his opinion, arithmetic will be considered herein to be essential in studying philosophy.  This view, one might hasten to add, is not just an advocacy based on this treatise which happens to include numbers, but rather an opinion which is steeped in ancient spiritual traditions, myths and esoteric philosophies.  

For example, the secrets of ancient mysteries, spiritual initiations, and other lofty ideals have traditionally required of the initiate the possession of three primary skills:  Magic, Alchemy, and Astrology.  In this light, we can think of Magic as the art of manifesting desired responses from other intelligences, Alchemy being the transmutation of physical reality, and Astrology encompassing an understanding of external influences upon human beings.  In the past, practitioners have tended to specialize in one area or another (which may be unfortunate inasmuch as all three are required).  In modern times, however -- even when we have greater access to resources -- none of these disciplines are particularly in vogue with mainstream science and technology (at least, not overtly).  This is in spite of the fact that these three disciplines are often demonstrated in everything from staring at someone’s back until they sense your staring and turn to face you (Magic), to the reality of artificially induced low temperature and/or naturally occurring biological transmutation of elements or isotopes (Alchemy), to accomplished practitioners of Astrology becoming ever more credible based on the results of open-minded scientific research.   

The reason we mention these traditions at this juncture in the narrative is that within the three primary disciplines of Magic, Alchemy, and Astrology, there are also included what is termed “The Seven Liberal Arts”.  These arts are considered to be the spiritual warrior’s essential tools in their quest for self-development.  The “Big Seven” Liberal Arts include:  Grammar, Rhetoric, Logic, Arithmetic, Geometry, Music, and Astronomy.             

Grammar, in this case refers to a true initiate being deliberate in speech such that Right Thought, converted into Right Speech, leads to Right Action.  Meanwhile, Rhetoric is a far cry from the political bastardization of the word, and relates more to expressing the good, the truth, and the beautiful.  This may include utilizing the vehicles of prose, illustrations (graphic and otherwise), and eloquence designed to inspire -- and all hopefully with no binding attachment to a particular point of view (as we said: it has nothing to do with politics).  Rhetoric may also include debate or “interactive communications” which promote the expression of the good, the truth, and the beautiful.  The third tier, Logic, involves a chain of reasoning, proof, thinking, or conclusions; as well as scientifically investigating the principles governing correct or reliable inferences.  Importantly, logic is only valid when it is based on true Assumptions -- i.e. faulty (and typically unstated) assumptions should not be used to derive an untruth or flawed conclusion.  

When Logic is combined with Rhetoric and Grammar, it can provide a powerful tool for studying philosophy.  In fact, all of the seven arts may be considered to be the core of any viable spiritual training, and the lack of one or more of these tools in the initiate would, theoretically, constitute a serious difficulty in any quest for spiritual understanding and development.  The klunker, of course, is that this view of philosophical study includes the next two tiers of Arithmetic and Geometry.  But not to panic!  This is not necessarily mathematics in the sense of differential equations, vector and tensor analysis, Fourier Series, Cristofel Symbols, Hilbert Spaces, multidimensional algebras, and other advanced mathematical disciplines.  Instead we’re talking about Arithmetic and Geometry in their most basic, relatively uncomplicated form.              

Keep in mind that Arithmetic is more than just the foundation of mathematics. Arithmetic alone -- without the aid of “higher” mathematics -- may very well reveal to the observant student, the entire creative process of the cosmos!  In effect, along with Geometry, Arithmetic has the unique capability of demonstrating the Good, the Truth, and the Beauty of the universe (and perhaps whatever lays beyond).  This is particularly true when Arithmetic and Geometry are applied to examples of the seventh tier of the Seven Liberal Arts, Astronomy, where the beauty and sheer magnificence of the planets, stars and galaxies are made manifest in such dazzling glory.  [e.g. The Hand of God, M. Reagan, Templeton Foundation Press, London, 1999]  

This then is the content of this treatise: a brief attempt at demonstrating the complexity and oneness of all that is, and at the same time, hopefully, utilizing six of the Seven Liberal Arts.  (Music may be incorporated by the readers humming as they read, or simply listening to classical music -- the preference, incidentally, would be Baroque, largo music, with a tempo at approximately sixty beats per minute.  No kidding.)  

And, of course, music is fundamentally mathematical -- geometry and numbers/ratios -- and thus all seven of the Liberal Arts are gently included in the mixed bag of tools for growth and transformation.  

It might also be relevant at this juncture to recall the story of an ancient kingdom which had as its national pastime, the playing of the game, Backgammon.  This board game, complete with checker like objects moved about according to throws of the dice, was avidly practiced by everyone in this ancient kingdom from the King himself to the lowliest peasant.  One day, however, an ancient entrepreneur attempted to introduce into this same kingdom the game of Chess.  The King very carefully considered this proposed game as an alternative to Backgammon in being the prime diversion of his people.  But then the King decided instead to outlaw Chess.  When the stunned entrepreneur inquired why, the King explained that Backgammon allowed for luck and thus taught the importance of the vagaries of life.  Chess, on the other hand, was mathematical in the extreme and perhaps more importantly, did not allow for the lesser intellects to occasionally pull out a win, even in competition with the foremost game practitioner.  Chess, effectively, did not reflect life due to its complete adherence to a set of rules and minimal attention to blind luck.  

Obviously, the King’s decision was a win for the non-mathematicians in our ranks.  Or so it would appear.  However, as an understanding of Chaos Theory, fractals and ESP).  This is not necessarily wonderful news for Las Vegas, but experiments at Princeton University and elsewhere have made it clear that the luck of the dice can be influenced by mental powers, and in the process one can reduce or eliminate many (if not all) of the “vagaries of life” by mental processes.  Think of it as our thoughts being prayers -- and where the prayers are regularly answered.  

In any case, a degree of mathematical familiarity is essential in Sacred Mathematics, F lo Sophia, Sacred Geometry, astronomical gems (such as in the Harmony of the Spheres or A Book of Coincidence), Connective Physics, The Fifth Element, Numerology, Astrology, Cydonia, Time Wave, and so forth and so on.   

Just keep in mind that the sign over the doorway leading into Hell reads:  “Lighten up.”  


Communications, Education, Health         Sacred Mathematics         Fear of Flying

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