Divine Unity of All
This enigmatic problem has fascinated some of
the greatest minds throughout the history of mankind. People such as Pythagoras
(a person one of its formulas bears the name of to this day), Plato, Aristotle,
and the list goes on and on. What is so fascinating about this seemingly simple
equation? That’s exactly why this was written, to give a brief understanding of
what the implications of this problem are.
Oftentimes
when looking at ancient spiritual concepts and applications, rarely is the
issue of mathematics a center of focus, or some may think. Using the
Pythagorean Theorem as an example, it can be seen that there was always a
strong inclination towards mathematics in ancient philosophical and esoteric
circles, albeit not in the way it is normally thought of. Its origins are often
shrouded in myth and legend since there is mainly well researched theories
regarding the historical roots of this particular theorem, also referred to as
the 47th Problem of Euclid in some other circles such as the
Freemasons in our current date.
According
to some ancient sources and speculation, Pythagoras obtained this information
through his travels to Egypt where he was initiated into the rites of the
temples of Isis, Osiris, and even Serapis.[1]
Upon his return to Greece, he began his own philosophical schools where the
mysteries of the universe were philosophized among some of the brightest minds
of the time. He believed that the mysteries of the universe were understandable
through the use of mathematics and the relations of numbers upon each other.[2] He
believed in the importance of understanding mathematics (especially geometry)
so much that it was required of all of his pupils to have a great understanding
of it before they would be admitted into his school.[3]
One of his contemporaries would be Plato who would take his version of
deductive reasoning and apply it to many of the mathematical concepts taught by
Pythagoras, but that is something else entirely.
The
theorem that still bears his name was exoterically (average public
understanding) taught for the purpose of architecture, which can be seen with
many of the buildings in Greece. Esoterically it was taught that it described
the relation between the Primordial Spirit, Primordial Matter, and, most
importantly, the Logos.[4]
One of the legs of the triangle (the shorter leg) represented Primordial Matter
while the other (the longer leg) represented Primordial Spirit.[5]
When these two forces intersected, they produced a cosmic vibration and created
the creative force in the cosmos known as the Logos in many circles. Logos
simply translates to “word” but that is only surface level understanding of
what it meant to those who were in the school. For example, what is a word? Put
simply, it is the vibrational expression of a thought which formed into an
expressed idea, hence Logos. It essentially explains the trinity (or even
Trimurti) in mathematical terms.
After
the death of Pythagoras, the theorem was still taught in the same way as
previously mentioned in the Eleusinian Mysteries up until around 170 BCE. This
where things get interesting. With the spreading of Christianity, many of the
secrets that were taught in these schools began to take on a Christian garment
of sorts, since their religion was considered monotheistic and all other
deities were considered devils. This can be seen when Theodosius destroys
Alexandria and deprives the world of 2/3 of its knowledge. Fortunately, it was
saved through people who were initiates in some of the ancient schools of
thought that escaped and learned how to hide in plain sight amongst the
despotic rule which early Christianity consistently displayed.
Approaching
our present era, the esoteric teachings are still held in the hands of some of
the contemporary schools of thought, the Freemasons being one of them. In
Freemasonry, it is still described as it was during the times of the Eleusinian
Mysteries, although not in the initial three degrees of the Blue Lodge. It is
discussed in great depth in the teaching of the Scottish Rite of Freemasonry.
To give some context as to why this is significant, many of the world’s
greatest minds and greatest influencers were (and still are for that matter)
Scottish Rite Freemasons, where the undoubtedly went through some of the
teaching the author of this work has as well, the author being a member of said
fraternity.[6]
It’s
interesting to speculate on the repercussions of what may have happened if
Pythagoras never went to those Temples in Egypt. Nonetheless, we are fortunate
that he did and that he passed this knowledge to the people who would pass it
down to us.
The
mathematics of the 47th Problem of Euclid can become very complex in
its understandings, and it should be noted that it did not originate for the
practical purpose we think of today. Initially it was intended to share what
the philosopher Pythagoras taught about the Universe, in a spiritual and divine
sense. For Pythagoras, mathematics was a way of understanding the divine and
was essential for all other understandings with regards to the operations and
understandings of it as well.
The
initial mathematics are thus: a² + b² = c². For its practical purpose in the material sense,
it allows for the proof of the existence of a 90 degree angle, great for
showing a building is structurally sound and perpendicular to the surface. With
this simple formula, man could begin to build higher and stronger structures.
Oddly enough, Pythagoras received this information from the Egyptians who
taught their mathematical secrets in their Rites.[7]
This formula is also effective in
showing the lengths of any of the sides of those types of triangles. Simply by
substituting the variable with its appropriate number and solving the equation
with algebra, you can discover the length. This is also very effective for the
use of architecture and can also be seen in some works of art to this day.
Now the intended esoteric purpose of
this formula shines its true colors with the metaphysical mathematical
explanation, which should allow for a deeper understanding of their views of
matter and spirit. “The Pythagorean and other schools of philosophy conceived
the one divine nature of God to manifest itself in the threefold aspect of
Father, Mother, Child.”[8]
In mathematical terms this simply means that the hypotenuse is directly
contingent upon the other two legs or sides, they giving life/birth to the
hypotenuse. Now, there is debate in some philosophical circles as to which of
the legs represents the spirit and which is matter, those two expressions being
their intended meaning. If one takes into account that the majority of esoteric
explanations show a superior spiritual existence as opposed to a material one
would assign the longer side to the spiritual source of existence, the smaller
being matter, and of course it would be opposite for those that believe
otherwise. Speculation is capable for as long as there is no discovery of some
MS explain which correlates to which.
The metaphysical mathematics are
explained as thus: “These three [the three sides of the triangle] constitute
the Divine Family, whose dwelling place is creation and whose natural peculiar
symbol is the 47th Problem of Euclid. God the Father is spirit, God
the Mother is matter, and God the Child—the product of the two—represents the
sum of living things born out of and constituting nature. The seed of spirit is
sown in the womb of matter, and by an immaculate (pure) conception the progeny
is brought into being.”[9]
As is shown, the physical numbers
that most associate with its mathematics were not its only mathematical
representation, nor was it its initial purpose. The ancients were more
concerned with expanding consciousness and advancing in their spiritual nature,
but they understood that existence was a reflection of the divine (as above so
below) and these formulas served a purpose in their everyday lives. This can be
seen as top how they viewed mathematical understanding as an expression of
divine thought.
The
real-world applications of the 47th Problem of Euclid are many and
all of them bring some better understanding of the world around us. Whether it
be in the physical understanding or the metaphysical understanding; this
problem has fascinated and helped some of the greatest minds that have ever
walked this Earth.
Another
more metaphysical use of it, especially when conducting philosophical thought
experiments, is to use the two legs to represent time and space. This allows
the mind to somewhat grasp the concept of potentiality being proportionate to a
time and space ratio. By adjusting the lengths of either leg, the change in
direction of its potential and how it correlates to existence as a whole can be
seen to alter. What gets really interesting is when the application of
nonlinear time and space being malleable are added to the thought experiment.
This creates different perspectives and understandings (or lack thereof) of the
effects this has on the universe. This, of course, is purely theoretical and is
some of the thought experiments the author of this work does while conducting
meditative thought experiments.
These
sorts of thought experiments that can be explained with the use of mathematics
are the foundation of some of our greatest discoveries as human beings.
Einstein was notorious for the sue of thought experiments and credits them for
his discoveries.[10] They
change the structure of thought from concrete to abstract and allow the mind to
formulate a different perspective of the universe. The world is no longer
viewed in the dead letter formulas, rather it becomes alive in a completely
different manner.
Finally,
it can be used to identify with one’s self on a deeper level of understanding.[11]
This is in philosophical and theosophical level. When the application of the
Divine Expression that was previously explained, the inner Self can be seen for
what it really is. It shows an interconnectedness of not only all humans, but
of all life in the cosmos. If the current scientific narrative of the universe
originating from a solitary point is still accepted, this formula shows the
proportions and existence of what we call life being one in form, polar in
expression, much like a magnet.[12]
This
allows for one to see that the Divine is not “out there” but rather is and
always has been part of the very essence of your being. It also shows that
matter is dead without an animating force to move it (occultists call this
simply spirit but is also named Fohat).[13]
The interesting implications this adds to everything in existence can leave the
mind spinning. Needless to say, it gives a metaphysical explanation of the
existence of an intelligent animating force that not only exists but is
essential for the existence of everything else. This isn’t to be confused with the
notion of a personal deity like that of many religions. Philosophy has many
names for this force ranging from Plato’s Intelligencers, Leibniz’s Monadology,
and Aristotle’s Unmoved Mover. The change in understanding at a fundamental
level of humans that this can bring is by far one of the greatest real-world
applications.
As
should be clear, the 47th Problem of Euclid is not just some simple
formula and easily explained with just mathematical terms. It carries with it a
great and deep philosophical understanding of man and his relation to the
cosmos. It shows how matter itself is animated and caused to be the way it is.
It is even in line with many scientific and mathematical understandings of the
universe, and to think of how ancient its understanding is puts so much more
into perspective. Its history dates back to the pyramids of Egypt and its
application can be seen in all ancient monuments. It is still used in the
construction of our homes and buildings, and it is still used with
philosophizing on the nature of existence. The 47th Problem of
Euclid is one of the most enigmatic, beautiful, and practical mathematical
understandings of our human history.
Bibliography
§ Edward
Abdill, Masters of Wisdom, (New York, New York, 2015)
§ HP
Blavatsky, The Secret Doctrine, (New York, New York, 2016)
§ Manly
P. Hall, The Secret Teachings of All Ages, (New York, New York, 2003)
§ Albert
Pike, Morals and Dogma, (Washington DC, DC, 1906)
[1] Manly P. Hall, The
Secret Teachings of All Ages, (New York, New York, 2003), 191-221
[2] Ibid
[3] HP Blavatsky, The
Secret Doctrine, (New York, New York, 2016), 480
[4] Albert Pike, Morals and
Dogma, (Washington DC, DC, 1906), *
[5] Ibid
[6] Some of the information
given is the author’s personal work which is unpublished as of this current
moment in time. Also, some page numbers of these books change with different
publishers which can cause confusion for some who are unfamiliar as to why this
happens with some of these particular works such as Morals and Dogma.
[7] Manly P. Hall, The
Secret Teachings of All Ages, (New York, New York, 2003), 191-221, p. 191
[8] Ibid
[9] Manly P. Hall, The
Secret Teachings of All Ages, (New York, New York, 2003), 191-221, p. 291
[10] Edward Abdill, Masters
of Wisdom, (New York, New York, 2015)
[11] Manly P. Hall, The
Secret Teachings of All Ages, (New York, New York, 2003), 191-221
[12] HP Blavatsky, The
Secret Doctrine, (New York, New York, 2016)
[13] Ibid
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