Tuesday, December 8, 2009

Miscalculations of Post-Vedic Astrologers & Resetting the Balance & Measures of the World

The following 4-part series by Patrizia Norelli-Bachelet is a recent response to Shri S. K. Kattacharjya of the World Association of Vedic Studies Yahoo Forum (WAVES-Vedic Forum). The issue at hand is the proper measurement of the Vedic Year or Zodiac. Ms. Norelli-Bachelet gives convincing evidence as to why the Tropical Zodiac is the true measure of the Vedic Year, not the Sidereal Zodiac as is followed by 'Post-Vedic' Astrologers who call themselves Vedic. One need not read Shri Kattacharjya's original post to appreciate the message bellow; but it can be read (along with other comments on this issue) on WAVES by joining the forum. His belief is that the Makar Sankranti, or entrance into the cardinal astrological sign of Capricorn is rightfully celebrated on 17 January in accordance with the Sidereal Zodiac, not on the December Solstice.


Friends, In my comments to Shri S. K. Battacharjya, much was left unsaid. His sober reply merits a more thorough answer. The issue is far too important and has been neglected for far too long.


Before all else, one point needs to be made, since without it no real sense can be made of the Vedic way. A true Vedic Astrologer – not the Post-Vedic kind that calls itself ‘Vedic’ – and all the astrology of the ancient world into the present, is geocentric. This undeniable fact has been allowing scientists to debunk astrology by claiming that the entire premise is wrong and proof of the under-developed concept the ancients had of the cosmos, and particularly of our solar system. They assumed that this geocentricity was due to ignorance of the fact that the Sun is central in our system and all the planets, including the Earth, travel around the luminary. Actually this argument reveals more ignorance on the part of science rather than astrology; but what is confounding is that there was not even one astrologer around to counter these ignorant attacks. A HOROSCOPE IS PERFORCE GEOCENTRIC, be this in a natal, a horary or a mundane chart, because the requirement is to place the individual or the event CENTRAL, or the object for which a horoscope is cast: that becomes the point of convergence and the resultant map of the heavens is then read.

The question of the Sun’s centrality was never the issue. To compound matters we have the proof that no one among the community of astrologers was able to counter this simple falsehood; the result is that all have been intimidated by Science to the point that a Post-Vedic system has been devised in the effort to fall in line with ‘scientific thinking’. This is the true basis of the Post-Vedic astrology, which seeks to pass itself off as ‘Vedic’. Today when the campaign gains force to displace that latter-day system in favour of the original Vedic method, we hear aggressive voices from the Post-Vedics claiming that their astrology is actually ‘scientific’. But science, as we know it today, plays absolutely no role in this matter. We cannot expect scientists to be yogis or philosophers; but we do expect, and demand, that astrologers – especially those who call themselves ‘Vedic’ – follow a specific sadhana to grasp the deepest implications of the Art.

SKB lucidly provides an example of the loss of Earth-centredness in Post-Vedic astrology (though to call what they do ‘astrology’ is equally misleading). When he describes the so-called ‘fixed’ stars as the givers of light, we have a further confirmation that the true Vedic Astrology has been lost because it is only in the ecliptic Tropical Zodiac that we find the path to the home of the Immortals, the goal of the Vedic ‘journey’ which the Rig Veda itself makes clear.

Since the constellations are always shifting according to the (mis)calculations of the Post-Vedics, Capricorn/Makar is no longer conjoined to the shortest day of the year – i.e., the December Solstice. Again, by the contrived separation of the inseparable, it is discovered that Post-Vedics know nothing about the Art, much less about the Vedic Journey. Knowledge, as the word implies, must be the foundation of astrology, of zodiacal wisdom. The path of Knowledge can never be understood via, for example, Nakshatras projected onto the sidereal circle. The harmony must be Earth-centred. And it must therefore find its balance on the Cardinal Poles of the Equinoxes and the Solstices. The fourth and highest is the victory rasi of the Veda, the tenth-month Capricorn.

The method to bury the Veda was to separate Solstice from zodiacal Capricorn/Makar, as SKB has sought to do, leaving merely a ‘seasonal’ function to those famous all-important Cardinal Poles. In view of the loss, the Knowledge went underground to survive. Now, to resuscitate that buried treasure we must wade through the accumulated mire Post-Vedics have engulfed the Art in, recalling the task of Matsyavatar’s retrieval yuge-yuge.


SKB has brought up the fact that Capricorn was not called Makar in the Mahabharat, and for this we thank him; rather it was the significantly meaningful BRAHMA instead. This is not different from either Capricorn or Makar, as I can easily demonstrate.

The Trinity of Brahma, Vishnu and Siva is repeated four times through the ecliptic ‘one circle’ of the Veda. Here we have another proof that the Epic, as in so many other places, was NOT referring to the sidereal circle but the Tropical Zodiac because the triune Godheads are also balanced on the Cardinal Poles in this manner, via the ancient and current categorisation of the signs: Cardinal = BRAHMA, Fixed = VISHNU, Mutable = SIVA; or Creation, Preservation, Destruction. Of course this is another aspect of the Art – very important if one seeks Knowledge – that has been buried for centuries. No astrologer today, east or west, refers to Cardinal, Fixed, and Mutable, as the triune Godheads. I resuscitated this knowledge decades ago in my very first books on astrology, even before coming to India where this Knowledge, I soon realised, had been completely buried in mire. Now, SKB has provided the proof by citing the Mahabharat that my seeing is correct, if proof is needed.

As the fourth and highest Cardinal Pole, the sign SKB indicates as Brahma, we have confirmation not only of the zodiacal wisdom but, and this is the most important aspect, that it was and remains the Earth-centred tropical zodiac which holds that wisdom because the Cardinal Poles provide stability for that ‘one circle’ whose ‘360 spokes shake not in the least’. Stability is not found in the constellations with their constantly shifting Ayanamsha of the Post-Vedics. There is no Equinox/Solstice stability in the sidereal circle, which is crucial to the Veda.


I will proceed to the most important point of all: there is no path of higher knowledge leading to the goal of Immortality in the Nakshatras. The names given to them are proof enough. Whereas, the names, hieroglyphs, rhythms and measures of the Tropical Zodiac rasis provide true seekers of Vedic Wisdom with the most colossal store of wisdom of all times.

I challenge all Post-Vedics to prove the contrary. On my part, I will present the Vedic content of the tropical zodiac; let any one or all of them put forth whatever wisdom of the same standard that they have come upon in the study of this ancient and contemporary Art.

To end with one important aspect of the Vedic wisdom, I will refer to the apex of the Rishi’s quest once again, Capricorn/Makar/Brahma – providing proof based on higher knowledge of the Vedic order to support the statement that Capricorn cannot be separated from the Solstice as is currently being done, a method SKB upholds. Again, I must ask, on what basis?

Here is the reason why not only was it held as the rasi/month of Victory and the summit of the Journey, but also exactly why IT CANNOT BE SEPARATED FROM THE TENTH MONTH SOLSTICE. Again, we turn to the Earth for the answer, and this will reveal not only the Earth-centred focus of the true Vedic Astrology but also the practical application of the Art in that the physical reality of our planet’s own journey around the Sun, touching quarterly as it does these Cardinal Poles of Equinoxes and Solstices, very accurately describes exactly what that culmination meant and why it had to be in consonance with the actual structure of our very own solar system and its harmonies. What I will describe will also help us realise why Bhisma chose to leave this plane on no other date but the December Solstice, the shortest day of the year. For the fact is only at that precise time is a ‘portal’ opened to the land of the Immortals. The physical reality is our best indication of exactly what the Rishis experienced when they attained Immortality, remaining forever after to preside over the fortunes of Bharat from that eternal plane.

The light of the Sun is compressed at that precise moment of the solstice; the shortest day reveals this compression to a point. This is what the Rishis and Bhisma achieved after much diligent and difficult tapasya. Indeed, after they had successfully completed the Journey as explained in detail in the Vedic Myth and the Hymns. Compression of the consciousness-being to a point was and remains the key. And only those who have experienced this compaction can understand (hence, the Rishi asks ‘Who can comprehend this?). Bhisma then, in full consciousness, crossed the threshold through that Point to the land of the Immortals and remained ever connected to this Earth plane, just as the Rishis of old had done.

I repeat that this, my friends, is the reason why it is inadmissible that we continue to extol the scientific imposition of a separation between zodiacal signs and the Earth-centred harmonies of our system in favour of the constellations.


If this Earth-centred Vedic experience is understood, it will also explain how so fundamental a focus on the Tropical Zodiac for the Journey was lost. It was when astronomy became separated from the sacred and a ‘science’ unto itself that the idea arose of an ‘unscientific’ astrology which required rectification by Science. Since there were no Vedic Astrologers in Bharat at the time, only pundits (not Yogis, bear in mind), the latter were easily cowered down into accepting the lead of science in a field well beyond its scope. It was then that the focus shifted to the constellations in lieu of the Tropical Zodiac of the ecliptic, disregarding the irrefutable evidence in all the sacred texts that this was and remains an aberration. At the same time yogas, philosophies, cosmologies arose which followed the same logic: to seek ‘light’ in the Beyond – in the case of astrology it would be translated into eschewing the Earth-measure and adopting the sidereal system with its floating Ayanamsha.

Truth is ever present, nonetheless. Thus, the two branches developed into ‘proof’ for one another. But in both cases, ‘scientific’ cosmology and spirituality, no such solid proof can be provided for the accuracy science claimed it alone could furnish; just as no religion can furnish proof of ‘heaven’ in an afterlife, or else in a sequence of rebirths. These demand faith, belief – not science, not the factuality we find in the Vedic Way.

Briefly, this means that from that point onward Swar became ‘otherworldly’; Earth-orientation was lost and all Measure was from that beyond, as exemplified in the sidereal circle, not FROM THE EARTH outward. Measure of the sidereal brand was thus IMPOSED upon the Earth from beyond – contrary to the most fundamental precept of the Veda, that all stems from WITHIN. Ironically, and here lies the rub, no accuracy and factuality was forthcoming, as imagined, since that sidereal circle does not actually have an Ayanamsha, a Zero Point. Its existence is entirely ‘relative’, as our science is today; while the Vedic Way was as ‘absolute’ as the unchanging Cardinal Equinoxes and Solstices. For the latter we do not require any ‘rectification’. Their measures are what they are and have been across the Ages. All we need to do, as the ancient texts indicate, is to calculate Mahavishuva (March Equinox) and Capricorn Sankranti (December Solstice): no guess work, no reliance on this pundit or that. Above all, no speculation in matters that stand beyond relativism.

Patrizia Norelli-Bachelet
Aeon Centre of Cosmology

1 December 2009

Additional Notes: The below images from Glenn R. Smith's 'Sidereal Zodiac' show the difference between the Tropical and Sidereal Zodiacs. In the Tropical Zodiac the Vernal Equinox is always the Zero Point or beginning of the Tropical Year, beginning with 0 degrees Aries. In the Sidereal Zodiac the 0 Point of Aries (the Zero Point of the Sidereal Year) slips backwards 1 degree approximately every 72 years. Currently the Sidereal Zodiac has shifted some 23 degrees/days backwards from the Tropical Year and hence entrance into the signs of the Sidereal Zodiac is calculated 23 days later than the Tropical Zodiac.

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Tuesday, December 1, 2009

Fractals and the Divine Matrix

'A fractal is "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity.' [1]

In 2008 PBS aired a program on Fractals produced by NOVA - Hunting the Hidden Dimension, which will give the reader a broader appreciation for the significance of the rise of fractal geometry and mathematics:

The Phi Ratio or Golden Mean is known as a rudimentary fractal which is expressed in the Fibonacci sequence and in geometry. The following 'Fibonacci spiral' and Pentagram fractal show a progression of 'self-similar' and inter-nesting Phi proportions:

Modern man’s interest in and understanding of Fractal mathematics and geometry has come a long way since 1872 when Karl Weierstrass found a mathematical function that is ‘continuous everywhere but never differentiable’.

This continuity of form was dubbed a ‘fractal’ 103 years later by Benoit Mandelbrot in Les objets fractals (1975). Notable examples of such continuity or ‘self-similarity’ from the early 1900’s were the Koch snowflake and the Levy-C curve. In 1938 Paul Levy published his book Plane or Space Curves and Surfaces Consisting of Parts Similar to the Whole. In the 1960’s computers were used to produce self-similar or recursive designs and these designs became expressive of the revolutionary spirit and creativity of that decade. They were, and still are, symbolic of a dramatic shift in perceptions and fit well within the category of Psychedelic Art. Mandelbrot and the IBM computer helped to put fractal geometry on the map so to speak (i.e. in our field of vision/consciousness). It was in many ways the birth of a new geometry for a new age.

‘From the point of view of mathematics … nested shapes tended to be viewed as rare and pathological examples, of no general significance. But the crucial idea that was developed by Benoit Mandelbrot in the late 1960s and early 1970s was that in fact nested shapes can be identified in a great many natural systems and in several branches of mathematics.' [link]

Yet, long before Mandelbrot, computers and the coining of the word ‘fractal’, knowledge of ‘self-similarity’ existed. The Fibonacci sequence, which actually hails from ancient India, is one such example. Apparently Leonardo Fibonacci (1170-1250 C.E.) introduced both the Hindu-Arabic numeral system which is still in use today throughout the world and the Fibonnacci sequence to Europe in his 1202 C.E. publication Liber Abaci (Book of Calculations). Considering the Vedic civilization’s deep understanding of the self-similarity between macro and microcosm and its gnosis of mathematics and measurement, it is not too surprising to find that the Fibonacci sequence is one of the many enduring gifts ancient India has given the world. Knowledge the Golden Ratio is traced back to the Artha-Veda (thought to be written at least 5000 years old) and somewhat more recently to the work of Pingala (450 – 200 BCE), a Sanskrit grammarian who referred to the Fibonacci sequence as matrameru, translated as ‘mountain of cadence.’ Meru means mountain. And matra, mean not simply cadence (measure of movement or rhythmical flow) in poetic or spoken verse, but also a measure of any kind (time, space, number, distance), a particle, an atom, a degree of a circle, or a minute portion. It also means ‘the full measure of anything, the whole or totality’ and ‘mother’.

It is entirely possible that the multi-dimensional, multi-scale meaning of the word matra is expressive of the Vedic knowledge and conception of what we now call fractals or self-similarity, nested structures or recursive design in nature and cosmos. The infinite repetition of the whole (the Material Cosmos) in individual form and throughout time was certainly basic and fundamental Vedic gnosis. On this basis they measured, acknowledged and recorded the inherent harmonies of time and space, and attuned themselves to these inherent harmonies.

Hence in Vedic cosmology, the Earth’s Day is equivalent or ‘self-similar’ to the Earth’s Year which is equivalent to the Precession of the Equinoxes which is, in turn, equivalent to even larger cycles of time. The tradition of dividing the Precession of the Equinoxes into 12 ages, the Year into 12 months, the Day into 24 (2 x 12) hours is another testimony of the ‘fractal’ nature or ‘fractal’ geometry of Time. The same 360 degree structure and the same stages and flow of development apply equally to the micro-cycle of time as to the macro-cycle. Out of this holistic thought or consciousness, come many fascinating equivalences and correspondences such as the Precession of the Equinoxes being measured in terms of the Vedic Yuga which is equivalent to the radius of the Sun in miles (432,000), and the 86,400 seconds of the Earth’s day being ‘self-similar’ to the 864,000 mile diameter of the Sun.

What is interesting to me is that in the Vedic civilization the infinite replication of the macrocosm in microcosmic forms was understood as a whole, divinely orchestrated, harmonic perfection. The minute portion of the whole was understood as an individual expression of the whole and inseparable from the whole … in a sense, unbreakable. Yet the word modern man has adopted word for these minute portions or repetitions of the whole – ‘fractal’ – is derived from fractus, meaning broken, fractured, shattered, vanquished or defeated.

To name a repetition of the whole after a word that means broken, shattered and defeated seems to me to be quite an oxymoron … a reflection of a isolated consciousness that feels irrevocably broken off from the Universal Mother and hence shattered. It is sad really, to contemplate the loss of knowledge of and harmony with the Divine Matrix that we have endured over how ever many millennia – the fall from the Divine Matra (the Universal Mother or Matriarch and all her measured parts and expressions) that leaves us with such a shattered identity. But, according to Sri Aurobindo and the Rig Veda, even our apparent set backs are useful stages in the evolutionary journey towards recovering our true identity, recovering our self-similarity and harmony with the Earth, the Cosmos, and all of creation.

A new-found appreciation of self-similar or recursive forms or designs of the Divine Matrix emerged in the art, architecture and science of European Renaissance, in part due to the 1509 publication of Luca Pacioli's Divina Proportione whose subject was the Golden Mean or Golden Ratio. Leonardo da Vinci (1452 – 1519) abundantly used the Golden Mean in his creations. Johannes Kepler (1571-1630) is another man whose appreciation of the Golden Mean and self-similar or nested structures has lived on through his work to illuminate our modern understanding of our Earth and Cosmos. His idea that the structure of the solar system was a macrocosm of nesting platonic solids was apparently incorrect, but out of his appreciation for a soulful Earth and Cosmos and the repetitive geometries of nature came his discovery of the Kepler solids and three laws of planetary motion. [Pictured on the right is Kepler's Platonic solid model of the solar system from Mysterium Cosmographicum (1596).]

In our modern world fractal geometry and mathematics (symmetrical and asymmetrical) are applied towards computer technology, communication, data storage and the transmission of data, graphic arts, animation, wireless technology (via smaller and smaller antennae), nano-tecnology, energy technology and diagnostic medicine. Fractals are also the building blocks of modern Physic’s Chaos Theory which strives to explain the unpredictable nature of whole systems.
‘Fractal geometry and chaos theory are providing us with a new perspective to view the world. For centuries we've used the line as a basic building block to understand the objects around us. Chaos science uses a different geometry called fractal geometry. Fractal geometry is a new language used to describe, model and analyze complex forms found in nature.’
I have recently read that the essence of Chaos Theory is really about finding the underlying order underneath the apparent chaos. It seems then that like the name ‘fractal’, “Chaos Theory’ is something of a misnomer. The human mind is faced with the task of fathoming the pervasive and integral order and multi-layered dynamism of the whole and of self-similar sub-systems of the whole. We labor (even if unconsciously) to find the perspective from which all dynamism and form are known, seen and experienced as a harmonious expression of, and re-creation of the One Universal Being. This was the perspective achieved by the Vedic seers and needs to be restored in our new age.

At some point our modern understanding of fractals and Chaos Theory must come full circle and reunite with the Vedic gnosis of macro and microcosm and gnosis of a divinely or supramentally orchestrated Order. For this to happen there must be some recognition that a point-less or soul-less system is not capable of order. There also must be some recognition that ‘fractal’ geometry applies to the structure of Time as well as to the structure of material creation (the Matrix). The ancient calendar systems of the Vedic and Mayan civilizations and their various epochs, ages and cycles of time, including the 12 month Vedic Year – which is one and the same as our modern Tropical Zodiac, will begin to make much more sense to us as our modern understanding of self-similar or nested micro and macrocosmic structures in both time and space begins to expand. The world-wide and world-unifying cultural renaissance or rebirth that will result from this expansion in understanding and consciousness is something that sages and prophets have been predicting for ages.
The immortal’s thoughts displaced our bounded view, …
All things now bore a deeper heavenlier sense;
A clear harmony marked their truth’s outline,
Reset the balance and measures of the world.
Each shape showed its occult design, unveiled
God’s meaning in it for which it was made
And the vivid splendour of his artist thought.

– Sri Aurobindo, Savitri Book VII, Canto V

Additional Notes:
Readers interested in the Geometry of Time should read The Gnostic Circle by Patrizia Norelli-Bachelet in which the 9 year cycle of time and larger cycles of 9 such as the 25,920 year Precession of the Equinoxes are seen as an expansion of the 12 month year. The larger cycles of time are seen as ‘self-similar’ to the 12 month year in that one journeys through the same 12 stages/month of development (i.e. signs of the zodiac) in larger scales of time and space.

Related Links:
* Number and the Supramental Matrix by Lori Tompkins
* The Simultaneity of Time, Spirit and Matter by Lori Tompkins
* Macrocosm, Microcosm & the Laws of Time and Space (Quote from PNB's The Gnostic Circle
* A Higher Vision of Time Is Needed... (Quotes from PNB's Time & Imperishability and some commentary)
* The ALL-pervading Energy of Time - the New Time (Quote from PNB's The New Way, a study in the rise and establishment of a gnostic society).

* The Geometry and Superstructure of Time 
* 'Time as a Power (not an Enemy) of Self' by Lori Tompkins
Learning the One Song, Learning the Universe by Lori Tompkins
In Harmony's Way by Lori Tompkins
* God Forever Geometrizes  by Lori Tompkins

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