OVERCOMING DECAY, INCREASING VITALITY ;
David
Cochrane, Excerpts ;
resonating angles are extraordinarily powerful according to wave
theory, as the
striking of a tuning fork at
one end of a room and the other tuning fork echoing
back the same note
testifies.
"......This is similar to a crystal-forming function
in nature, and is entropy-defying
and life-enhancing......from the viewpoint of wave
theory, then, there is as a
double-resonance, which in turn creates a huge
astrological resonance. ....
Thus, we have a curious consonance formed between John
Addey's harmonic
theory and the ancient system of Arabic Parts. The
consonance is extraordinary
because resonating angles are extraordinarily powerful
according to wave theory,
as the strking of a tuning fork at one end of a room and
the other tuning fork
echoing back the same note testifies. That we can use
harmonic theory
retrospectively to identify Arabic Parts as the most
important derived points
in the chart produces perfect alignment of ancient
astrological methods and
harmonic astrology.
That we can use harmonic
theory retrospectively to identify Arabic Parts as the
most important derived
points in the chart produces perfect alignment of ancient
astrological methods and
harmonic astrology.
..
..
Al Kindi & the Stellar
Rays : ancient developer of frequency analysis.
"If it were given to anyone to comprehend the whole
condition of the celestial harmony,
he would know fully the world of the elements, with all that
is contained therein at any place
and any time, as knowing the caused from the cause... and
whoever has acquired the knowledge
of the whole condition of the celestial harmony, willknow the past, the present and the future.[1] "
RELEVANT LINKS FOR AL-KINDI :
http://
http://
https://
http://
http://
https://
DAVID COCHRANE ON THE ARABIC PARTS : Symmetry is always created when there is
planetary resonance, so Witte is correct; whether one prefers to focus on the
symmetry or the resonance, one is actually identifying the same phenomenon.
Planetary resonance is based on wave theory, which allows an even wider number
of astrological influences to be integrated into a single conceptual framework.
"......This is similar to a crystal-forming function in nature, and is
entropy-defying and life-enhancing......from the viewpoint of wave theory,
then, there is as a double-resonance, which in turn creates a huge astrological
resonance. ....Thus, we have a curious consonance formed between John Addey's
harmonic theory and the ancient system of Arabic Parts. The consonance is
extraordinary because resonating angles are extraordinarily powerful according
to wave theory, as the strking of a tuning fork at one end of a room and the
other tuning fork echoing back the same note testifies. That we can use
harmonic theory retrospectively to identify Arabic Parts as the most important
derived points in the chart produces perfect alignment of ancient astrological
methods and harmonic astrology.
Zoller correctly points out that Arabic Parts were discarded in modern times
because of their apparent non-rational basis, but, amazingly, they are now
found to be completely rational and harmonic astrological theory (i.e. wave
theory) confirms that Arabic Parts should be given the very high priority and
importance that they are given in classical astrology.
ARABIC PARTS
THE MATHEMATICAL BASIS OF ARABIC PARTS
AND A PARADIGM SHIFT IN ASTROLOGY
By David Cochrane
Copyright © 2005 All Rights Reserved INTRODUCTION:
SEE HIS LINK ONLINE AT ;
http://www.astrosoftware.com/ArabicParts.htm
An Arabic Part forms an isosceles trapezoid with the 3 points used in the
Arabic Part formula. This fact has enormous implications regarding why Arabic
Parts are important, how they work, and even the fundamental assumptions of
astrology! However, the underlying geometry of Arabic Parts has been almost
completely overlooked throughout the entire history of astrology.
ISOSCELES TRAPEZOID:
An isosceles trapezoid is a four-sided figure which has two opposite sides of
the same length, and the shape is vertically symmetrical. Note that an
isosceles trapezoid is similar to a parllelogram, but has very different
properties from a parallelogram. A parallelogram has 4 parallel sides and does
not have symmetry, except in the case of a rectangle. A rectangle is
simultaneously a parallelogram and an isosceles trapezoid.
A remarkable property of an isosceles trapezoid is that it has two pairs of
equal angles. For example, if you measure the angles between the PF (Part of
Fortune), Sun, Moon, and Asc, you will find two pairs of parallel angles.. In
the author's birth chart (May 1, 1949, 4:26 AM, East Meadow, NY, USA), for
example, rounded to the nearest degree the Asc is 3 Aries, the Sun is 11
Taurus, the Moon is 15 Gemini, and the PF is 7 Taurus. Therefore, the Asc-PF
angle is 34 degrees and Sun-Moon angle is 34 degees. Also, the Asc-Sun angle is
38 degrees and the Moon-PF angle is 38 degrees. There are always two pairs of
angles that are identical in an isosceles trapezoid, and because the Asc, Sun,
Moon, and PF form an isosceles trapezoid this is also true among the 3 points
and the Arabic Part used.
FORMULA:
In the previous paragraph I used the PF formula of Asc+Moon-Sun. The reader may
know that the PS (Part of Spirit), whose formula is Asc+Sun-Moon, is regarded
by many authorities as being the PF if the Sun is in the first six houses. Very
interestingly, the PS also forms an isosceles trapezoid with the Sun and Moon.
In the author's chart, the PS is 29 Aquarius. The PS-Asc angle is 34 degrees
and the Sun-Moon angle is 34 degrees. Also the PS-Sun angle is 72 degrees and
the Asc-Moon angle is 72 degrees.
Given three points, there are three other points that form an isosceles
trapezoid with these three points. In the case of what is widely regarded as
the three most important points in the chart (the Sun, Moon, and Asc), two of
the points are the PF and PS. Both ancient and modern astrologers very rarely
use the third point. The formula for the third Arabic Part that can be
constructed with the Sun, Moon, and Asc is Sun+Moon-Asc. When I first began
experimenting with this Arabic Part, I called it the Part of Integration but
then I noticed that it was already listed in my software and has the name Part
of Redemption, and this Arabic Part is attributed to al Biruni. I have not yet
researched al Biruni's work to see if he used this Arabic Part because it is
the third isosceles trapezoid that can be formed with the Sun, Moon, and Asc,
or perhaps someone simply wanted to experiment with the third formula that is
possible in adding two of the three points and
subtracting the third. I will use al Biruni's term, the Part of Redemption
(PR). There is an elegant relationship between PF, PS, and PR; the formula
involves adding two of the three points and subtracting the third. This elegant and
simple formula calculates the three points which form isosceles trapezoids with
any three points. In the author's chart, PR is 23 Cancer. The two pairs of
identical angles are: Asc-Sun and Moon-PR are 38 degrees, and Asc-Moon and
Sun-PR are 72 degrees.
Because most ancient astrologers appear to have not noticed, or were not
concerned, with the fact that PF and PS form isosceles trapezoids, it is not
surprising that the PR was largely overlooked. Most Arabic Parts formulae begin
with the Ascendant, so subtracting the Asc instead of adding it may not have
been an intuitively obvious thing to do. From the standpoint of the geometry
involved, however, the PR would appear to be a natural corollary of the PF and
PS.
As the reader no doubt noticed, particular angles are repeated in a given
chart; in the author's charts, these angles are 34 degrees, 38 degrees, and the
sum of these two angles which is 72 degrees. This repetition of particular
angles can be viewed as a consequence of the three isosceles trapezoids having
overlapping sides. Even more important is this vitally important fact: whenver
two angles are the same in chart, there are two pairs of identical angles. As
soon as two angles are the same, then an isosceles trapezoid is formed and
there are two pairs of identical angles. This is similar to a crystal-forming
function in nature, and is entropy-defying and life-enhancing.
The reason that I propose viewing the formation of two pairs of angles as
entropy-defying whenever one pair of angles forms is this: one can view the
double pairs of angles in an isosceles trapezoid as a huge resonance; from the
viewpoint of wave theory, then, there is as a double-resonance, which in turn
creates a huge astrological resonance. One can argue that this double
resonance, from the standpoint of wave theory (or harmonic astrology, which is
founded on the concept of waves), is far more powerful than the usual
application of wave theory to support the concept of minor aspects. In fact,
from the point of view of wave theory, the PF, PS, and PR are arguably the most
important derived points in the chart! Thus, we have a curious consonance
formed between John Addey's harmonic theory and the ancient system of Arabic
Parts. The consonance is extraordinary because resonating angles are
extraordinarily powerful according to wave theory, as the striking of a tuning
fork at one end of a room and the other tuning fork echoing back the same note
testifies. That we can use harmonic theory retrospectively to identify Arabic
Parts as the most important derived points in the chart produces perfect
alignment of ancient astrological methods and harmonic astrology.
This perfect alignment, however, contrasts with the growing
philosophical chasm that has developed between some adherents to ancient
methods and those that espouse modern "scientific" methods. For
example, in the book The Arabic Parts: Lost Keys to Prediction Robert Zoller
refers to Kepler's astrology as "distorted" and John Frawley has
similar scathing remarks about Kepler's introduction of minor aspects to
astrology. Kepler's explicit description of minor aspects is the first known
clear articulation of the concept, and minor aspects are a fundamental concept
in the harmonic astrology further developed by John Addey in the 20th century.
In the article The Newtonian Merry-go-round Bernadette Brady has identified
major shifts in astrological through in the 20th century. Brady bases her
thesis on a study of articles in major British articles. My less formal,
personal anecdotal observations since the early 1970's in the United States
confirms Brady's historical trends. According to Brady we are now in a cycle
where disillusionment with simple Newtonian proofs of astrology is inspiring us
to develop greater interest in qualitative, rather than quantitative models,
and many astrologers now have forsaken the view that astrology just needs more
research to be validated in simple experiments. I agree with Brady's
observations. This movement away from astrology as a simple science is huge,
and there is a growing wave of interest in pursuing more subtle views of
astrology, incorporating concepts such as divination, chaos theory, etc. Works
by Patrick Curry, Geoffrey Cornelius, Garry Phillipson,
and many others are creating a new framework for understanding astrology in the
21st century.
BASIS OF ARABIC PARTS IN EUCLIDEAN
GEOMETRY AND WAVE THEORY:
The identification of a basis for Arabic Parts in Euclidean geometry and wave
theory, therefore, may be greeted by some skeptically, as an anachronistic
throwback to the old days of Newtonian thinking. However, the magic performed
by these simple Euclidean methods does not end with the above observations, and
there is much more insight to be gleaned by a close study of the mathematics
that lies behind our astrological methods.
For example, many astrologesr are familiar with the fact that PF and PS are equidistant from the Asc axis
and are therefore mirror points of each other.
PR has a similar symmetry around a point as follows:
PR and PS are equidistant from the Sun and therefore are mirror points of each
other.
PR and PF are equidistant from the Moon and therefore are mirror points of each
other.
Consequently, PS is closely tied to the Sun, as it has a mirror point around
the Sun, and PF is closely tied to the Moon, as it has a mirror point around
the Moon.
Therefore PS is solar and PF is lunar, which is another way of saying that the
ancient doctrine of sect is critically important to an understanding of PS and
PF, and PR serves as the balancing point around the Sun and Moon.
Thus, our analysis of the geometry of Arabic Parts has identified that sect is
involved in understanding PF and PS. This is a most extraordinary discovery
because we now have a mathematical basis for understanding why the ancients
used one formula for day charts and a different formula for night charts!!!
SUMMARY:
To summarize: Not only are Arabic Parts indicated by harmonic astrological
theory, but even the doctrine of sect applied to the Part of Fortune and Part
of Spirt is indicated by harmonic astrological theory.
This finding completely destroys what we had previously assumed: that Arabic
Parts are a mystical formula not amenable to Newtonian analysis, and even goes
beyond this to demonstrate complete agreement between an ancient technique and
harmonic astrology.
Zoller correctly
points out that Arabic Parts were discarded in modern times because of their
apparent non-rational basis, but, amazingly, they are now found to be
completely rational and harmonic astrological theory (i.e. wave theory)
confirms that Arabic Parts should be given the very high priority and
importance that they are given in classical astrology.
Understanding the geometry of Arabic Parts illuminates our understanding of
Arabic Parts, while also opening up new insights, such as the introduction of
PR, along with PF and PS. Note that the geometrical foundation of Arabic Parts
is a mathematical truth regardless of whether one believes in astrology or not,
and regardless of whether one thinks that this geometry is relevant to a
greater astrological understanding of the Arabic Parts.
The isosceles trapezoid is an elegant concept that integrates many seemingly
disparate astrological concepts, such as midpoints, antiscia and solstice
points, Jonas birth control, Vedic tithi returns, the traditional aspect
patterns of grand trines, grand crosses, mystic rectangles, and yods, and even
the very popular composite chart that was introduced in the 20th century.. The
isosceles trapezoid was identified by the founder of the Hamburg school of
astrology Alfred Witte. Witte referred to isosceles trapezoids as planetary
pictures. Rather than find the fourth point that makes an isosceles trapezoid
(an Arabic Part), Witte interpreted isosceles trapezoids that occur in the
chart. He did not, to my knowledge, emphasize the geometric shape or the fact
that planetary pictures and Arabic Parts are mathematically identical; he was
more intrigued by the symmetry that planetary pictures have.. Symmetry is always created when there is
planetary resonance, so
Witte is correct; whether one prefers to focus on the symmetry or the
resonance, one is actually identifying the same phenomenon. Planetary resonance
is based on wave theory, which allows an even wider number of astrological
influences to be integrated into a single conceptual framework.
A large number of astrological techniques are either comprised of isosceles
trapezoids, or can be viewed as derivatives of isosceles trapezoids. A full
discussion of the relationships of these astrological techniques to isosceles
trapezoids and to each other requires hundreds of pages, but hopefully this
very terse introduction to some new vistas in astrological thought has been
informative, interesting and inspiring to the reader.
The re-introduction of simple mathematical and scientific models into astrology
at this time may create some consternation, but it may well be that the current
paradigm shift in astrology towards divination and qualitative research will
give way to a higher synthesis that incorporates the astrology of Kepler and
Addey with ancient methods to create a framework that is not distorted, as
Zoller refers to Kepler's astrology, but rather stronger, durable, and more
useful and practical than our current edifice. My own sense is that we are on
the verge of yet another paradigm shift even before we have settled comfortably
into our current movement away from the quantitative and Newtonian approach and
towards divination and qualitative research. No doubt this is an unpopular view
but we can all agree that interesting times lie ahead of us!
A final note: After reading this article, several people have asked how they can
access this information in their software. There are many techniques that
employ these concepts, such as composite charts, etc., but most often people
want to find PR in their charts and know what isosceles trapezoids occur in
their charts.
An isosceles trapezoid mathematically is simply a midpoint conjunct or
opposition a midpoint, and a list of midpoints conjunct and opposition
midpoints is a good way to view them. My observations indicate that an orb of
only about 1/2 degree is used for aspects to Arabic Parts and for midpoints
conjunct midpoints, so I look at them up to about a 1 degree orb but pay close
attention to only those configurations that are within about 30 minutes orb..
Evidently the planetary resonance occurs only when the angular distances are
nearly identical. Kepler 7 users can see PR in the list of Arabic Parts using
the default list of Arabic Parts. Select Listings and then Arabic Parts; sort
by Arabic Part name to quickly find "Redemption" listed, or you can
view this Arabic Part in the Arabic Parts wheel. You can select Listings, and
then select Harmonic Patterns Listings, and then select the first option of
"Harmonic triangles and Midpt conj Midpt" and scroll to the
bottom of the listing. For my own use I change the orbs from 3 degrees to 1
degree; to change the orbs, click on the "Orbs of Aspects" buttons on
the screen where you select the report, and then click the Next button until
you get to the end of the list of aspects, and change the applying and
separating orbs of the midpoint conjunct midpoint and midpoint opposition
midpoint to 1 degree. Note that oppositions are regarded as equivalent to
conjunctions because the midpoints in both cases lie on the same midpoint axis.
Users of other major astrological software can probably select these features
in a similar manner in their programs.
References:
Brady, Bernadette, The Newtonian Merry-go-round, article at website
www.geocosmic.org, 2005
Cornelius, Geoffrey. The Moment of Astrology, The Wessex Astrologer Ltd,
Bournemouth, England, 2003
Frawley, John. The Real Astrology, Apprentice Books, London, England, 2000
Kepler, Johannis. The Harmony of the World, American Philosophical Society,
Philadelphia, PA, 1997
Phillipson, Garry. Astrology in the Year Zero, Flare Publications, London,
England, 2000
Zoller, Robert. The Arabic Parts: A Lost Key to Prediction, Inner Traditions
International, Rochester, VT, 1980
=============
The Astrology
You Don't Know - And How It Affects You
http://www.astro.com/astrology/in_unknownastro_e.htm
"...persons connected via projects, purposes, or
destiny tended to cross paths often at improbable times and places. I coined
the phenomena Shell Route Collision; and when these crossings occurred, my
friends would yell out, "Shell route collision!" to humor me. The
metaphor was drawn from the orbital trajectory that electrons follow. While
circling the same atom's nucleus their trajectories invariably overlap. With
this knowledge, I could stand back and watch a shell route collision moment
form. Later, in what I take for an omen of agreement, I came upon a Kurt
Vonnegut novel where the noted author related largely the same observation. He
termed it the Karass Theory."
When people take the time to decode Astrology's cosmic
alphabet, they gain immense insight into the nature (and timing) of
inter-personal, unfolding dramas. Generally, the more precise the overlap, the
greater the intensity. And that takes us to the Zodiac's 360 degrees. Powerful
esoteric books have been written on this subject; and since my favorite one
opens with the warning: This book is not for profane hands, I will not give its
author away. Suffice it to say that the info contained suggests that the 360
degrees, like chords streaming out from our solar system's center, form a
living mandala. It's encoded with recognizable qualities. Some of the degrees
speak quite definitively about occupations. I once made this point to a lecture
group using as Exhibit A an individual known to the community for his
true-to-history costume designs. He happened to have his Venus situated on a
degree of costuming! My own chart degrees speak of prophecy. Astrology, in my
view, allots the most accurate means for expressing that art.
While psychology, for the most part, focuses on nature
(inherited traits) and nurture (how children are raised), neither can account
for the fact that in any community, people fall into the same basic roles.
These archetypes are real and enduring. In fact, how
often has an individual encountered someone who looks just like someone they
know even though there is no genetic link between these persons? All that human
flesh is heir to flows direct to us from the filaments of time. The basic
Zodiac archetypes are refined further through the 360-degree Mandala of time.
Its projections operate like celestial DNA. This wheel of time marks human
destiny. It also ensures that in every land, the same human types will exist.
That way, the lesson plan articulated by the planetary clockworks will assert
regardless of one's place of birth.
Location is an underrated tool of astrological
analysis. Often it explains what transits and progressions do not. In my own
rather Mercurial life, I've noticed that synchronicity comes into play. For
example, during that sojourn in San Diego, I was undergoing my first Saturn
return with transit Pluto also conjunct natal Saturn. In other words, themes
associated with transiting planets suited the locations I gravitated towards.
Scientific skeptics have sought to disprove astrology
by utilizing linear tests that fail (although the scientists will argue
otherwise) since it is impossible to square the circle. These
"scientists" typically focus on sun signs alone and leave out the
holistic character of natal charts. Naturally, when only a single factor is
drawn from the full gestalt, that factor cannot produce data that substantiates
the full scope of astrology. For instance, since Aries is governed by Mars, the
archetype tied to war, it might be assumed that Aries natives will invariably
gravitate towards the armed forces. Students of astrology understand that the
sun placement in Aries might be offset by Mercury and Venus positioned in
peace-loving Taurus, and Mars placed in the diplomatic sign of Libra. In such
instances Aries can lead in the arts rather than on the battlefield.
http://www.astro.com/astrology/in_unknownastro_e.htm
SEE ALSO ASTROLOGY &
CONSCIOUSNESS :
OUR USERS AND MEMBERS HAVE
UNIQUE EXOTIC EXPERIENCES, SEE ;
YOU MIGHT EXPERIENCE THIS TOO! CLICK THE BELOW GRAPHIC ;
SEE ALSO : Astro
Biology And The Science Of Astrology
SEE ALSO ASTROLOGY & CHAOS THEORY
..
Al Kindi Stellar Rays
"If it were
given to anyone to comprehend the whole condition of the
celestial harmony, he would know fully the world of the elements,
with all that is contained therein at any place and any time,
as knowing the caused from the cause... and whoever has acquired
the knowledge of the whole condition of the celestial harmony,
will know the past, the present and the future.[1] "
Al Kindi, ancient developer of frequency analysis
http://www.skyscript.co.uk/alkindi.html
( CLICK THIS LINK )
