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.
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:
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.
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
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
In any case, a degree of mathematical familiarity is
F lo Sophia, Sacred Geometry, astronomical gems (such as in the Harmony of the
or A Book of
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
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