Cubic Prison – Projective Geometery
http://soundofstars.org/vastcube.JPG
CUBIC
PRISON IN SPACE SURROUNDING OUR SOLAR SYSTEM ET AL.
EXCERPTS ; "A giant, vast, synthetic cube had been carved out of space
itself and within it was a vast void dark space, containing only a very small
number of stars and within this apparent prison was deposited our own solar
system, sun and earth"
http://www.nct.anth.org.uk/sunpos.htm
Weirdly, on the other side of the cubic walls of this prison, space took on a
very very different characteristic and that was
this....
Stars, (outside of our prison), are so densely packed and so close together that
the there is no night sky or darkness really, anywhere - at least for an
incredibly vast expanse
If you lived on a planet in this region and looked up at the 'night' sky all
you'd see would be blinding light, everywhere.... for seemingly forever.... ( is this where the legends of 'Heaven' come from ? )
Funny, that - eh ? It almost smacks of the C.S.
Lewis science fiction novels such as ;
http://en.wikipedia.org/wiki/Out_of_the_Silent_Planet
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
ARABIC PARTS
THE MATHEMATICAL BASIS OF ARABIC PARTS
AND A PARADIGM SHIFT IN ASTROLOGY
By David Cochrane
Copyright © 2005 All Rights Reserved INTRODUCTION:
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
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.
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
( CLICK THIS LINK )
