LOGOIC PERSONALITYJudi Laws © 2003
Only in recent years has sacred geometry engaged the attention of an ever-widening esoteric audience. This comes as something of a surprise, given HPB’s statement about: “Geometry,
the “
…the evolution and correlation of the mysteries of Kosmos, of its growth
and development—spiritual and physical, abstract and concrete—were first
recorded in geometrical changes of shape.” ( “Perhaps the time has come…to the fifth
Root Race entering the Age of Aquarius which sign is the transmitter of
only one ray, the fifth. Of no small significance is the Tibetan’s emphasis
on the importance of mystical geometry.” ( For ease of entry into the geometry, it may help to frame the
discussion along lines familiar to all esotericists, i.e., the fourth
kingdom in nature, and the seven rays. “All these Rays of Cosmic Mind,
Primordial Activity, and Divine Love-Wisdom are but essential quality
demonstrating through the agency of some one factor.” ( “ Ray four on which the soul of humanity is manifesting provides the closest alliance with the Divine Ray, the former being the optimal vehicle for moving the Second Logos toward his goal. Hence, the three cosmic rays mentioned above correspond to
our third, fourth and fifth rays, the numbers indicating the second phase
of logoic development in our threefold solar system (for examples of this
3-4-5 process, see Operating in these ways takes us far beyond arithmetic’s simple numerals and quantitative values. It demands a quantum leap into geometry, variously preceded or qualified by an adjective such as sacred, mystical, contemplative or philosophical. Rooted, literally and figuratively, in the forms and force familiar to us all, this discipline is a cross between the spiritual and the mathematical. At the most basic level, numbers themselves reveal this hybrid characteristic. Two examples will make this point. First, the historical veneration of the number 4: “It
is said that it expressed a living being, I, bearer of the Triangle…the
emblem of God, i.e., man bearing within himself a Divine Principle.”( Second, “The Moving to a higher level of abstraction to witness the connect between the sacred and the geometric, the measurable and the incommensurable, we come up against irrational numbers such as pi (3.14159…). Most of us can recall its relationship to a circle, symbol of ONE or Unity. If the diameter of a circle has a value of one, the circumference will always be of the incommensurable type: 3.14159…x one (or any other number). This ratio of known to unknown inheres in virtually all three-dimensional or volumetric forms in nature. As we will soon see, the incommensurable ratios, e.g., the relationship of one to p (pi), “… are unique in their ability to consistently
replicate through endless divisions in space, even as the identical ratio
remains present in the relationship of one level of subdivision to the
next.” ( “The relationship between the fixed and
the volatile (between proportion and progression) is a key to Sacred Geometry:
everything which is manifest, be it in the physical world or in the world
of mental images and conceptions, belongs to the ever-flowing progressions
of constant change; it is only the non-manifest realm of Principles which
is immutable.” ( ## The Logoic PersonalityThe Ancient Wisdom presented to the Western world by HPB and the Tibetan was written in a manner that is fequently more like an encryption than an elucidation. Toward the end of her life, HPB was queried by Colonel Bowen on how to study Theosophy: “She says: If one imagines that one is going
to get a satisfactory picture of the constitution of the Universe from
the S.D. one will get only confusion from its study. It is not meant to
give any such final verdict on existence, but to LEAD TOWARDS THE TRUTH.”
( It is in pursuit of TRUTH that I found what
I consider to be a viable hypothesis in the application of sacred geometry
to one sentence in Bailey’s “From
these three cosmic planes (embracing the sacred personality of the Logoi,
solar and planetary) come the united energies of three constellations
which control and energise our solar system: the Great Bear, the Pleiades,
and Sirius; these work through the medium of the seven rays and these
in turn express themselves through the twelve constellations which form
the great zodiacal wheel.” ( The first round of brooding on this passage raised the question
of what the sacred personality is. By the Law of Correspondences, and
assuming a fivefold manifestation (physical to atmic planes inclusive),
cosmically, I saw that one of the Brothers of Fohat—AGNI—“ This
Lord of the mental plane, cosmically and systemically, funnels and unifies
the energies coming from the three major constellations, situated on the
third, fourth, and fifth cosmic planes. Two of these placements are made
explicit in the Tibetan’s writings: the Great Bear on the cosmic buddhic
( Consequently, inference from other information on this constellation
is all we have to guide us. Perhaps the most persuasive argument rests
on the statement that the Great Bear and the Pleiades “are a higher correspondence
to atma-buddhi.” ( “…the central point around which our Universe of fixed stars revolves.” “…the central group of the system of sidereal symbology.” “…the sidereal In this vein, a fourth indicator of prominence
appears in Complications arise exponentially as we endeavor to wrap our minds around the lower three cosmic planes, having little or no direct experience thereof. Nevertheless, reassurance and encouragement are provided repeatedly in the Tibetan’s writings, mainly in the form of incentives available through the Law of Correspondences or Analogy. Two instances will suffice to highlight His strong suggestion that we expand our reach upward, periscopically: “Until our students extend their concept
to include in their calculations the logoic astral and mental bodies as
the Logos seeks to express emotion and mind on the physical plane (through
His physical body, a solar system)they will not progress far towardstheheart
of the solar system.” ( “[the student] should endeavour to ascertain
the relationship between the universal mind (or the systemic mind) and
cosmic mind…” ( Returning
to the logoic Personality, when viewed from the cosmic mental plane, it
is constituted of the three Logoi (Brahma, Vishnu, Shiva) who “are seen
functioning as one.” ( Greater detail is given on ways the three constellations work
within our planetary scheme ( • Great Bear … Spiritual energy … three higher planes … the Monads •--- Pleiades … Buddhic force … fourth plane … the solar Angels • Sirius … Manasic force … two lower planes … the four kingdoms of nature Whether this particular planar allocation of forces and energies obtains for all planetary schemes is, for me, an open question. One last point about the ## TrianglesThroughout the writings of HPB and the Tibetan, triangles abound:
the Science of Triangles; Upper and lower Triads; the Trinity, triple
Logos or Hindu Trimurti; Three Crosses, etc. And always the Law of 1-3-7
confronts us, from Unity to Triplicity to Septenary…to multiplicity. “First
came three, or the triangle”, says HPB ( No wonder that the faces of all five Platonic solids (regular
polyhedra) are divisible into some arrangement of triangles! Three (the
tetrahedron, octahedron, and icosahedron) have triangular faces, each
of which contains six right-scalene triangles; each face of a cube is
comprised of four right-isosceles triangles; and each pentagonal face
of a dodecahedron is made up of ten right-scalene triangles. ( To get a sense of what’s so special about
the number three and its geometric representation, we must understand
the viewpoint of the ancient mathematical philosophers whose distance
from present-day humanity is much greater than the millenium which separates
us from them. For Plato, the concept of Number was not primarily enumerative,
but “Form”-al and relational—a quantitative and exoteric aspect plus a
qualitative and esoteric aspect. The former is characterized by a definite,
finite, particularizing power, and the latter, a universal synthesizing
power. ( Reality
seen by Plato as pure essences or archetypal “Ideas”, “cannot be perceived
by the senses, but by pure reason alone. Geometry was the language recommended…as
the clearest model by which to describe this metaphysical realm.” ( From
the ancients’ perspective, One, Unity, Monad, and two, Duality, Dyad,
were Paradoxically, this Law of Attraction and
Repulsion cuts both ways: it divides and unites. “It might strictly be
called the Law of Adjustment or of Balance.” ( It
takes three points to bring forth a two-dimensional geometric figure,
the first to appear being the triangle, as noted previously. Simply visualize
or draw a circle with a point at partially the center, being partially
overlapped by a second circle of the same size and radius; the center
of each circle lies on the circumference of the other circle. Therein
are three points to be connected: one line between the two center points,
and one line drawn from each center point to the apex formed by the intersection
of the two circumferences. The shared, almond-shaped area that gives birth
to the triangle is called the No better symbol than the triangle can be found to typify the
endless process of two oppositional points (terminii of the line that
joins the two circles’ centers), such as spirit and matter, being resolved
or mediated through the third point ( ## Philosophic GeometrySince we’re travelling through lofty regions of the Logoi’s personality, our map and compass must be of universal magnitude, yet be calibrated so as to facilitate verification from the occult classics. My survey of this area has afforded the following decoding for one corner of the cosmoscape: The sacred personality of the Logoi (solar and planetary) can be explained by the Pythagorean triangle, also called the Diaphantine or sacred triangle—the 3-4-5 right-triangle. Bearing in mind the classic proportion, 3-4-5, that defines
the Pythagorean triangle, several passages outline these number-concepts,
and suggest their application to the logoic personality. First, the Pentad,
since “ “…the figure of the universe is bounded
by pentagons… a Dodecahedron, the geometrical model imitated by the Demiurgos
in constructing the material universe.” ( “[Five] is the second and third Logos united
in evolution.” ( “… the 5 is the universal quintessence which
spreads in every direction and forms all matter.” ( Because we live “inside the box”, literally, i.e., fourth globe, chain, scheme, Round, Hierarchy, etc., It’s hard to get outside it. But with a little help from the fourth plane, we “budding buddhis” may see a glimmer in the following statements, mentioned earlier. “…the Quaternary, the perfect number, was
the noumenal, ideal root of all numbers and things on the physical plane….
[It] was with the ancients only “[To the Pythagoreans, the Tetrad was] the
most perfect number, because it emanated from the Getting to the four of form via the triangle becomes evident if we subdivide the triangle into four smaller triangles. If you cut out the larger triangle, score the three partitioning lines, and fold the three points upward, you will have your very own 3-D tetrahedron. Moving up from the fourth to the third level puts us in a very
different atmosphere—that of Tri-Unity. At the beginning of creation,
Brahma (masculine; the initial circle with central point) projects outward
a perfect reflection of himself (second circle with central point; the
female aspect, Vach) which latter produces the Son, Viraj—a recreation
of Brahma himself from within the The commencement of manifestation, marked by the emanation of Father-Mother-Son, takes a new twist, described by HPB: “By mystic transmutation they became the
Quaternary—the triangle became the TETRAKTIS.” ( On this point, the Tibetan adds: “The Sacred Four are…[Father, Mother, Son]
and their united manifestation making. The active evolving solar system,
the logoic ring-pass-not. This is the Macrocosm.” ( So the Threeness, the triangle, becomes the Fourness, the Quaternary. Then there’s one more conversion to note: “The triangle becomes a Pentagon (fivefold)
on Earth.” ( Lest readers think we’ve been flying too high for too long,
let’s get grounded with a pencil and paper exercise to show how “the triple
triangle, a figure of five lines uniting five points” (
One glance at any pentagon inscribed within a pentagram indicates to the eye and mind that these figures are self-replicating and self-accumulating: five triangles projecting outward from the sides of the pentagon…which is divisible into five smaller triangles. Connect the five points of the pentagram, and you haves pentagon that’s larger than the one within the original pentagram. The open secret of this unending progression is the relationship of the side of the pentagon to its diagonal, the ratio of one to F (phi)—another of those pesky incommensurables involving the square root of 5, an irrational, supra-rational or transcendent number. According to one author, the “Pentad draws us into the most
widespread shape in nature—the spiral.” ( “Availing Himself of the rotary motion of
all atoms, He adds to that His own form of motion or of spiralling periodical
movement, and by circulation along an orbit or spheroidal path which circles
around a central focal point in an ever ascending spiral….”( Many are the Teaching’s references to the hand-in-glove relationship
between Three and Five. Whether it’s about triangles and pentagons producing
each other, or the inversion of the third and fifth planes ( I am persuaded that we might benefit from following His lead. My inclination to move in this direction occasionally finds me on a new thought-train. One example emerged as I was pondering the three vis-a-vis the five. The
ciphers themselves, their morphology engaged my attention, and posed questions.
Did the number three acquire its shape by dividing a circle (symbol of
the ONE) into two hemispheres, opening like a hinged bracelet (3)? Was
a similar process responsible for the five? Were the two Greek accents( As students of esotericism, we are continually stretching our minds to grasp the significance of numbers’ enumerative values via numerology. However, as denizens of the higher manasic realms, we extend our reach even further by attempting to engulf, digest and assimilate the principles and conceptual values of numbers. Adopting this approach permits us to move past arithmetical values to enigmas aplenty. The Sacred Triangle confronts us with its 4-line at crosspurposes to the 3-line. Four, the perfect number in manifestation, wars against the first perfect number, Three, at spiritual levels. Contained within the numeral 4 is a triangle, two sides (3-line and 4-line) of which are shared by two right-angle arms of a cross. Paradoxically, it is the challenges of the three Crosses that lead the successful to the promised land of At-ONE-ment on the fourth plane. While there’s much to be gained from geometrizing, from drawing geometric figures on two-dimensional sheets of paper, each such drawing is but a frozen nano-second of cosmic reality. The mind scoops up these figures, puts them on the dumbwaiter, and sends them Upstairs for restoration to their roles in an ever changing, dynamic world. Motion continuously swallows sand castles, shifts our degree of well-being, turns night into day, changes our seasons, and brings solar flares to glitch our electronics. And we must ride these waves to understand what they’re about, and how we are rivulets running and rippling into the Greater Flow-through. Some readers will have been disappointed by this piece, as they were looking for a tit-for-tat correspondence of the major constellations, three cosmic planes, and side-lengths of the Sacred Triangle. My inner compass pointed in quite another dirction: fanning the embers of faint orange to flame in minds eager to board a new mode of conveyance to the Heart of things.
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