SAUNDARYA LAHARI
NEW SECTION
VERSE 11
KEY VERSE
THE SRI CHAKRA - CROSS AND LONG-SECTIONAL VIEWS
A CONIC SECTION
TOGETHERNESS - ANGLES AS 43 ELEMENTS
A CONIC SECTION
TOGETHERNESS - ANGLES AS 43 ELEMENTS
चतुर्भिः श्रीकण्ठैः शिवयुवतिभिः पञ्चभिपि
प्रभिन्नाभिः शम्भोर्नवभिरपि मूलप्रकृतिभिः ।
चतुश्चत्वारिंशद्-वसुदल-कलाश्च्-त्रिवलय-
त्रिरेखभिः सार्धं तव शरणकोणाः परिणताः
प्रभिन्नाभिः शम्भोर्नवभिरपि मूलप्रकृतिभिः ।
चतुश्चत्वारिंशद्-वसुदल-कलाश्च्-त्रिवलय-
त्रिरेखभिः सार्धं तव शरणकोणाः परिणताः
caturbhih srikanthais sivayuvatibhih pancabhir api
prabhinnabhih sambhor navabhir api mulaprakrtibhih
catus catvarimsad vasudalakalasra trivalaya
trirekhabhis sardham tava caranakonah parinatah
prabhinnabhih sambhor navabhir api mulaprakrtibhih
catus catvarimsad vasudalakalasra trivalaya
trirekhabhis sardham tava caranakonah parinatah
With the four of Shiva and of Shiva maids five,
And severally the nine of prime nature, with eight and sixteen petals,
Three circles and three lines are thus complete
The forty-three elements that make up your finalized angular refuge.
And severally the nine of prime nature, with eight and sixteen petals,
Three circles and three lines are thus complete
The forty-three elements that make up your finalized angular refuge.
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This verse refers to the well-known Sri Chakra. The term "Chakra" suggests a global unit of consciousness. It is represented as a circle for two-dimensional convenience, but it is meant to be more than a circle. It consists of triangles with their bases placed conversely trying to interpenetrate each other from opposite sides. On the plus side, the numerator set of inverted triangles represents the masculine principle of Shiva. The lower set of upright triangles, on the denominator side, evidently represents the feminine counterpart of the numerator set.
A rectangle can be imagined by us to join the apexes of the base angles of the two reciprocal sets of triangles. A circle can be considered as the limit of a polygon of infinite sides; similarly, at the opposite limit, a triangle would be the most elementary polygon. A series of alternating odd and even numbers could be so arranged with the four first digits on the first line, one less - three - on the next, and so on, until we form with these numbers a triangle; thus, polygons and numbers have between them a relationship. If we should consider a polygon with an infinite number of sides as a fully matured form of consciousness, all the other elements, starting from a triangle, could be united as inclusively contained within the two limits of a triangle and a circle. In the fourth line of this verse, the "finalized angular refuge" suggests the same maturity of finalization described in Verse 7 as the "autumnal full moon face". The lower and upper limits, respectively, could be recognized between the triangle and the circle and thereafter the three circles could be treated as three grades of further maturation and abstraction.
The Pythagoreans worshipped the tetraktys, which is a triangle, numerologically understood. The polygon of infinite sides becomes a circle by maturation of the triangle. The triangles are seen to have their apexes on a vertical parameter or axis, some of them in ascending, and some in descending order. We can count four such apexes from the top as we descend along the vertical axis; similarly, we can count five apexes in an ascending order. When translated into three-dimensional or four-dimensional space, as in conics and solid geometry, we can see somehow the forty-three elements under reference here. Hilbertian mathematics speaks in terms of choses mathématiques - mathematical things - which are treated as elements or units, by which the structure of mathematics as a whole is revealed. Within the scope of an endless series of numbers, it is possible to arrange them so as to obtain all the polygons possible in geometric figures. Adding together the four of Shiva and the five of the Shiva maids gives us nine points or apexes which touch the vertical axis. These nine are referred to as of the order of "Prime Nature". Nature (Prakrti) is the negative counterpart of the Spirit (Purusha) of Samkhya philosophy. Although Advaita Vedanta is against the dualistic treatment of Nature and Spirit as rival absolutes; here, in order to distinguish the function of Shakti from that of Shiva, for the sake of argument at least, the notion of a Prime Nature (Mulaprakriti) is retained. This is to be treated not as a doctrinal, but as an epistemological and methodological necessity. Thus we have found some raison d'être for the apexes and the triangles in this verse.
The base angles, in turn touched by the circumscribing circle, are to be treated as the petals of a flower or the radiating lines of the points of a compass. This circle could be divided into eight divisions of forty-five degrees each. We could further subdivide it into sixteen, because space could be four-dimensional or multidimensional, according to the fraction of a right angle that we treat as a unit. If the circle is treated as a cross- section of space, and if we treat the inner circle and the outermost circle as the limits of what is conceptual and what is perceptual within consciousness; and if we put in an intermediate circle which participates on both sides, we can roughly see the significance of the three concentric circles. The outermost circle represents the limit of the horizontal maturation of this geometrical figure, which combines a horizontal as well as a vertical gradation of elements. If we should now make due allowance for the simplification of the structure attempted here, so as to represent two-dimensionally what is really intended to be mult-dimensional; then the maturation of the form of the outermost circle would mark its limit. Since the two orthogonal axes within the circle are equalized, it would mean that there is a harmony between the two tendencies of horizontalization and verticalization, within which Absolute Consciousness with a negative perspective can be said to operate. Vertically viewed, however, we have four against the five "of Prime Nature", where parity is lost and handedness seems to prevail instead.
Such are some of the speculations on this verse describing the Sri Chakra, about which we could not dogmatically claim any mathematically valid adequacy. Like time and space articulated with each other, we have to imagine something similar to what Henri Bergson has described in the following passage:
"Across time and space, which we had always known to be separate and, for that very reason, structureless, we shall perceive, as through a transparency, an articulated space-time structure. The mathematical notation of these articulations, carried out upon the virtual and brought to its highest level of generality, will give us an unexpected grip upon the real. We shall have a powerful means of investigation at hand, a principle of research which, we can predict, will not henceforth be renounced by the mind of man, even if experiment should impose a new form upon the theory of relativity."
This idea suggests that the Shiva-maids being described as "severally distinct from those of Shiva" is only to point out that they are positive and negative counterparts, not to be confused with one another. Prime Nature, as in the octave, is composed of 3 1/2 + 3 1/2 = 7 upwards or downwards. Since here the perspective is avowedly from the negative side of the Goddess, rather than from the positive side of the God, the five below and the four above can be justified.
The finalization is both horizontal and vertical. A circle represents the harmonious integration of vitalistic and pure tendencies in the Beauty of the Absolute Goddess.
The eight and sixteen petals refer to points of the compass, as we have said. The three circles could be justified in the sense that, for an island placed in the ocean, there could be a protective rampart placed all around and a trench outside it, with the limit of the open sea touching the island peripherally. Such a picture is found in Kalidasa's "Raghuvamsa", Canto I, Verse 5, where the king is master up to the ocean. Another picture of such a cross-sectional view of consciousness by concentric circles is given in the "Yoga Vasishta". In this analogy, we are looking down a well at an ascending bucket from which water is simultaneously descending through a hole in the bottom of the bucket.
The word "refuge" suggests that, when the contemplative creates a direct bipolar relationship with this Sri Chakra, it will make him think of all elements together at one and the same time. Such a complete meditation will be effective as a final refuge, both as a means as well as an end, in his spiritual progress.
It is a far cry from the kind of final good or salvation understood in the prophetic religions prevailing in the West to the way of salvation implied in this meditation on the Sri Chakra, representing the beauty of the Goddess. The gap between the two versions is a difficult one to bridge. While admitting this glaring incompatibility between the prophetic and the pagan ideas of salvation and liberation, it is possible, through a proper interpretation in the light of a mathematical structuralism and more modern scientific notions of reality, truth or beauty treated together, to arrive at some method by which the gap could still be bridged. Our comments on individual verses will at least help to reconcile these two standpoints and bring them closer together by abolishing the element of contradiction between them.
To the modern mind, familiar with radio and television by which families on our planet are in direct electromagnetic contact with the outermost frontiers of our expanding universe, the task of schematically understanding these waves or pulsations, whether related to light or sound, is not too hard to imagine, thus tending to make the whole world into an intimate village.
The latest satellite being sent out into outer space even contains a gold-plated plaque inscribed with a kind of universal proto-language intended to be deciphered by some intelligent being in this universal elsewhere or nowhere.
Maxwellian equations and Hertzian oscillations, which both belong to this electromagnetic universe, give us in terms of absolute equations and vectorially understood wave motion, two perspectives of the dynamism of what can be called the heartbeat of life itself which could be fitted together and unitively understood. Textbooks of physics already contain such figurative representations of electromagnetic pulsation based on the sinus function, on which all energy transmission must depend, independent of distance. The magnetic field is always at right angles to the electrical current. This orthogonality gives us the basis of a quaternion structure, which a unit of harmonic motion would represent by crest as well as trough, both electrically and magnetically understood. Equations verify the geometrical figure and vice-versa. It is the Pythagorean diagonal, based on logarithms, that is primarily involved here, as also notions of processes in differential calculus, involving both parameters and asymptotic curves which verify equations, understood also in the machine language of cybernetics, which could help us to bridge the gap that seems to divide the two rival positions we have referred to above.
A further study of the relational content of the remaining verses would help the reader to arrive at least at a greater degree of unitive understanding, which is the special contribution of the Advaita Vedanta of Sankara to world thought, whether physical or metaphysical or both. An integrated view of physics and metaphysics would further justify the Sri Chakra.
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(The Tetraktys: (greek τετρακτύς), or tetrad, is a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the fourth triangular number. As a mystical symbol, it was very important to the secret worship of the Pythagoreans. ED.)
(David Hilbert: German Mathematician, is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis. ED)
(Handedness or chirality: a chiral phenomenon is one that is not identical to its mirror image. The spin of a particle may be used to define a handedness for that particle which (in the case of massless particle) is the same as chirality. A symmetry transformation between the two is called parity. Invariance under parity by a Dirac fermion is called chiral symmetry. ED)
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(Raghuvamsa: a Sanskrit mahakavya (epic poem) by the most celebrated Sanskrit poet Kalidasa. It narrates, in 19 sargas (cantos), the stories related to the Raghu dynasty, namely the family of Dilipa and his descendants up to Agnivarna, who include Raghu, Dasharatha and Rama. The earliest surviving commentary written on the work is that of the 10th-century Kashmirian scholar Vallabhadeva. The most popular and widely available commentary, however, is the Sanjivani, written by Mallinatha (ca.1350-1450). ED)
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ADDITIONAL COMMENTS WITH STRUCTURAL DIAGRAMS RELATED TO THIS VERSE FROM SAUNDARYA LAHARI/NOTES
WORD FOR WORD
caturbhih srikanthais - with four of Shiva
siva yuvatibhih pancabhir api - of Shiva-maids five
prabhinna bhihi sambhoho - and severally distinct from those of Shiva
navabhir api mula prakrtir bhih - and those nine too of prime nature
trayes (in text catus) catvarimsad - making 43 in all (in text 44)
vasudala kalasra trivalaya trirekhabhis - with 3 circles and 3 lines with 8 and 16 petals are thus complete
sardham - taken together
tava carana konaha parinatah - make up Your finalized angular refuge
caturbhih srikanthais - with four of Shiva
siva yuvatibhih pancabhir api - of Shiva-maids five
prabhinna bhihi sambhoho - and severally distinct from those of Shiva
navabhir api mula prakrtir bhih - and those nine too of prime nature
trayes (in text catus) catvarimsad - making 43 in all (in text 44)
vasudala kalasra trivalaya trirekhabhis - with 3 circles and 3 lines with 8 and 16 petals are thus complete
sardham - taken together
tava carana konaha parinatah - make up Your finalized angular refuge
There are 44 manifestations or elements in the Sri Chakra, which is the "angular refuge" referred to here.
At the centre there are 4 triangles pointing downwards and 5 upwards, because ontology on the negative side is more important than teleology on the positive side.
The 44 elements are later given monomarks and categorized.
The 44 elements are later given monomarks and categorized.
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With this verse, the treatment becomes completely schematic.
This is meant to clarify some other secret mystical schematismus. (See Kant)
There are no analogies here. only schemasor structures.
This is meant to clarify some other secret mystical schematismus. (See Kant)
There are no analogies here. only schemasor structures.
Look out now for 44 verses of schemas.
There are five triangles with the apex upwards, four down, circles etc.
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DISCUSSION OF THE DEVI, AND OF VERSES 10 AND 11
(These two verses, 10 and 11, are easier to understand if looked at together, so many of the structures and comments below apply to Verse 10, but help us to understand Verse 11. ED)
The Devi has to be understood as itis central, not only to the Saundarya Lahari, but to the Advaita Vedanta tradition of erotic mysticism.
Only in this way can Vedanta be presented in a useful manner. Vedanta must be able to solve problems, especially marital.
(Marital problems involve men and women; Vedanta deals with the positive or masculine principle and the negative or feminine principle (Shiva and the Devi) interacting as they do in the structure of the Sri Chakra in this verse. ED)
The whole of the universe is composed of two forces - represented in this work by Shiva and the Devi - originating at opposite poles, and meeting in a neutral, central zone, called by Descartes the zone of occasionalism. Descartes discovered the secrets of the Upanishads in his meditations.
So the Goddess must become the centre of meditation - thus the meditation becomes normalised. Only that version of philosophy which makes real values of the conceptual and the perceptual is worthwhile.
In order to have a pure conceptual understanding of Brahman, the Absolute, the Devi must be given positive status. She is not only a female, She gets a real dimension, which finally becomes the Absolute. (See Sankara's other writings) Sankara was fully conversant with the most precious aspects of Hindu Philosophy. He made no mistakes because his intuition was right. But you can go still further into the mystical experience and be completely overwhelmed.
"I do not have mystical trances. I have trances of a mild nature, and I have certain mild occult or psychic powers. I always get the book I want." (Nataraja Guru)
The Devi is a normalised god - all the other gods are hypostatic.
She is a neutral Goddess.
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VERSES 10 AND 11
In these verses there is a kind of emanation (eternal value factor) from between the legs of the Devi, being sprinkled on the Nadis (psychic nerves).
In these verses there is a kind of emanation (eternal value factor) from between the legs of the Devi, being sprinkled on the Nadis (psychic nerves).
The vertical reference of that is as noble as any joy which can be had through meditation.
By her intentionality, she is blessing (sanctifying) everything in the universe. (Eidetic intentionality).
There is a transient (horizontal) as well as an immortal (vertical) dimension in everything.
Whenever there is a ritual, there is a Mantra which goes together with it. There is participation from both sides.
The two legs represent the virtual and the actual.
There is the thinnest of parameters between them (the vertical axis) - like when one eye is seen as the sun, the other as the moon.
There is a jingling of bells on the waist of Shiva which sufficiently represents him in this verse.(See below).
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Here there are three functions to the Goddess:
Benediction (sprinkling),
Beauty of face,
Breasts both heavy and proud.
She is bent at the waist by the heaviness of the breasts.
The bend suggests a thin logarithmic spiral at the waist, and the heavy breasts indicate the denominator aspect.
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When you get into the third dimension, you need logarithms.
Shiva destroys the three cities and shows the Absolute is more important.
(Shiva as Tripurantaka is accredited with destroying three mythical cities of the Asuras. ED)
(Asuras: The opposite of Suras or Devas (the fair or bright entities inhabiting the Vedic heaven). Demons. These might have come into being with reference to anyone who opposed the Aryan penetration ideologically or in historical actuality Bhu-Sura, the earthly god, is a term which would seem to lend support to this view, as it connotes a Brahmin complete with sacrifices and his twice-born quality, on wearing the sacred thread, which is a kind of baptism in Brahminhood. The conflict between the Devas and Asuras permeates the whole of the spiritual literature of the Vedic Indians and has to be understood historically or in pure dialectics, according to the requirements of the context. Max Mueller thinks there is an affinity between Ahura (Ahura Mazda) of the Zoroastrians and Asura. ED)
When Shiva descends on the vertical axis, how do you know he is there, functioning?
By the jingling of the bells on the waistband.
This also indicates that his waist is at the horizontal level.
Thus, in this verse, Shiva is adequately represented as present.
Thus, in this verse, Shiva is adequately represented as present.
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The Devi is only a protolinguistic representation of the Absolute on the perceptual side. It lends itself to description.
Brahman, the Absolute, is a bright light, incapable of being described.
The Devi is only a protolinguistic representation of the Absolute on the perceptual side. It lends itself to description.
Brahman, the Absolute, is a bright light, incapable of being described.
In this verse we have a structure at the negative or normal limit.
Also, normalised schemas or structuralism.
Another translation:
With five Shiva - maids
Of Shambo the distinct ones
The nine (basic) of prime nature
Of 43 elements
With 8 and 16 petals, 3 circles and 3 lines
Complete (making up a total)
Is thy refuge in angular matured form
Of Shambo the distinct ones
The nine (basic) of prime nature
Of 43 elements
With 8 and 16 petals, 3 circles and 3 lines
Complete (making up a total)
Is thy refuge in angular matured form
This is a Sri Chakra with all of its component parts normalized.
Triangles are relational and represent a certain order.
Triangles are relational and represent a certain order.
Space can be represented by a line. All this is to show the relations within the Absolute.
How can we explain the putting of the Absolute into a structure, with a certain number of components?
Who asked you to put the Absolute into a structure?
How can the Absolute have any geometric structure hiding in it?
Who asked you to put the Absolute into a structure?
How can the Absolute have any geometric structure hiding in it?
The human mind is most at home when it can think of a solid - that is, on the perceptual, immanent or negative side - according to Bergson.
The mind can also think of a concept: this is why we have Para- and Apara-Brahman. (The immanent and transcendent Absolutes).
How do we justify the houses or angles?
You cannot predicate anything about Brahman, so why draw diagrams?
You cannot predicate anything about Brahman, so why draw diagrams?
It is a defect of our minds, which either need a geometric solid or a category on which to fix.
There are two kinds of philosophies, algebraic or geometrical.
We have also the algebra of geometry and vice-versa.
This question of making drawings is an epistemological one: we make schemas to show the relations within Brahman.
There are two fundamental distinctions - Para and Apara, immanent and transcendant.
When geometry and algebra both confirm a point, that is final.
(Post - Hilbertian mathematics has to be studied, a mathematical reality is as valid a "thing" as any philosophical point. (A Universal Concrete.)
Abstractions of thought must meet the form of logic.
The relation between forms of thought and forms of logic: for example, there are two proofs to Pythagoras' theorem: one is visual, the other is intellectual - and it is the same thing with Brahman and Absolute Beauty.
Brahman is an abstraction of the mind, how can we relate it to Beauty?
There is Para Vidya and Apara Vidya (immanent and transcendent knowledge) - one is geometric, one is abstract, like algebra.
There is Para Vidya and Apara Vidya (immanent and transcendent knowledge) - one is geometric, one is abstract, like algebra.
We use schemas or structures because the mind needs something to hold onto.
Just to speak of the Absolute is elusive: we want "a gooseberry to hold in the hand" (A Vedantic simile for knowing something with certainty - it is like holding a prickly gooseberry tightly in one's hand. ED), something definite.
The Gita says that if you know Samkhya properly, you will also know Yoga - and vice-versa. "He who sees Samkhya and Yoga as the same, he alone sees the truth".
(Samkhya and Yoga are twin schools of Philosophy - Samkhya is concerned with knowledge; Yoga is more concrete - the Guru is comparing them to Para and Apara Vidya or algebra and geometry - see two paragraphs above. ED)
In the Colloquy of the Gods in Kena Upanishad, the same Akasha (Space or Ether) gives up the figure of the Devi. This is the greatest secret of the Upanishads. (See Kena Upanishad q.v.)
(An editorial note: we must remember that the Sri Chakra is not only to be thought of two-dimensionally, but also three-dimensionally as made up of interpenetrating cones rather than triangles.
Below is an illustration that may give some idea of this, though it is made up of pyramids, rather than cones. ED)
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TO MAKE A FILM:
In the film, the Vidyarthi (wisdom-seeker) is outside the picture of concentric ritual circles, he winds up with a mystical experience, while the others partake of the ceremony.
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Then all fades out into the Vidyarthi or wisdom-seeker.
This can be given 10 minutes:
A) Architectonic
B) Geometric forms, logarithmic spirals, conic sections etc..
CINEMA SCRIPT - SERIALIZATION.
Each structure and verse must be individually viewed,
then dynamically viewed,
then serially viewed.
then dynamically viewed,
then serially viewed.
Structural stills with dynamic animation and explanation,
Then swinging into the text.
Then swinging into the text.
1) Still picture.
2) Explanation of still.
3) Animation and dynamism.
2) Explanation of still.
3) Animation and dynamism.
For dynamism: show Kali, the negative spirit of the Absolute, from Kali Natakam, by Narayana Guru. (See Contents: "Shorter Poems of Narayana Guru" on this site. ED)
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The stills will be few in number and will be referred to several times throughout the film to explain things.
Ten minutes explanation at the beginning of the film.
Ten minutes explanation at the beginning of the film.
Kali Natakam: you cannot have more eroticism than in this dance, but it is vertical eroticism; it will not hurt anyone.
Then, a Yogi in meditation, with Chakras - a bird flying in the Numerator and Kundalini in the Denominator.
This is a fully geometric structure, he is now describing the Devi in pure mathematical terms.
There are four triangles with their bases above for Shiva and five with base below for the Devi.
Taken all together, there are 44 elements - 9 triangles, 3 circles, 3 lines, the 8 petal lotus, the 16 petal lotus.
There seems to be dispute about the proper number here.
The English translation by a Malayali Pundit has innumerable theories.
14+8+16+3+3=44 - Structural factors are to be used:
14 OUTSIDE ANGLES
8 LOTUS PETALS
16 LOTUS PETALS
3 OUTSIDE LINES
3 CIRCLES, INCLUDING CENTRE
All these factors are to be seen as mathematically conceived elements or structural loci.
This verse describes a full Chakras, the most concrete yet.
The Sanskrit-Malayalam rendering indicates either 43 or 44 structural loci.
This must refer to conics; when they say "triangles from opposite directions" they must mean conics.
CONICS IN VERSES 11 AND 12
The ancient Hindus, who founded Tantra, were not conscious of conics.
The ancient Hindus, who founded Tantra, were not conscious of conics.
(EDITORIAL NOTE - THE "TRIANGLES" FORMING THE SRI CHAKRA ARE TO BE VIEWED 3-DIMENSIONALLY AS CONES NOT TRIANGLES)
How to count these angles?
When they say three circles, letters and magenta; it is plane geometry.
But when they say Kali....
The three concentric circles framing the Sri Chakra are peripheral and central only - this is plane geometry.
The Greeks developed conics to a high degree, calculating ellipses, parabolas, charting the paths of stars, etc..
An ellipse must be fitted into a conic section to be defined.
It is a flame or a lotus or lightning.
It is a flame or a lotus or lightning.
The face, or Bindu, is put into place with Shiva.
Then speaks the descending pride of Shiva and the ascending pride of Parvati.
The bells on Shiva's waist are peripheral and at the outer limit (upper?).
Then the heavy breasts of the Devi are to be put into a conic section.
The inside cones do not count (Shiva Kanyas - "Shiva maids") since there can be an infinite number of cones in a cone.
The Chakra is something about which you can make a predication = prabhinna (? illegible)
This is the house of the Devi with its 14 exterior angles, etc.
The interior angles are merely Kanyas (maid-servants of the Devi).
After counting the 5 and 4 triangles, think of them as one, joined in the totality.
This is "the house where You reside" (your refuge, which you occupy).
"The centre is where You reside, the exterior angles represent Your physical house."
"The centre is where You reside, the exterior angles represent Your physical house."
Parvati has the function of manifesting the world, while Shiva represents the pure vertical axis.
Thus she cannot represent the final Absolute, but is absorbed into it.
These three circles are the girdle of the structure, with lotus petals and magenta and chromatic colours, coming from the waist of the Devi.
The Indian mind wanted to represent something, but had an incomplete knowledge of solid geometry.
A woman is already on the negative vertical axis - there is no religion or meditation required.
Poets worship gods, make poems; women do not need to do this.
A woman's body is existential beauty itself
A spot of light represents the unknown Self on the Numerator side.
Cancel all the Chakras which condition you.
The Sri Chakra is a lotus floating in a well.
Cancel all the Chakras which condition you.
The Sri Chakra is a lotus floating in a well.
Riemannian space is geodesic.
Lobachevskian space - many parallels are possible - two trumpet shapes.
Imagine marbles in a bucketof water - the marbles are Riemannian space
- the water is Lobachevskian space
In the Sri Chakra, inside becomes out, and right, left - as in the Kandukavati (See Saundarya Lahari Notes ED)
There are nine points of intersection - five below, four above.
There are nine points of intersection - five below, four above.
Mulaprakriti, Prime Nature, is the negative starting point.
Eight petals is the four of the quaternion structure divided - subdivided again makes sixteen.
Eight petals is the four of the quaternion structure divided - subdivided again makes sixteen.
The three circles and three lines represent sattva, rajas and tamas (the three gunas or nature modalities) - these are also three degrees of abstraction - see the "Raghuvamsa" of Kalidasa: there are references to a sea, a trench and a rampart as the frontiers of the absolute kingdom.
Further quotations from the Raghuvamsa:
"Rule till result comes" this is vertical absolutism.
"Take taxes like a cloud taking up moisture to produce rain".
A bucket full of water with a hole in it is rising from a well - drops fall down - forming the Sri Chakra.
(EDITORIAL NOTE - THE "TRIANGLES" FORMING THE SRI CHAKRA ARE TO BE VIEWED 3-DIMENSIONALLY AS CONES NOT TRIANGLES)
An angle is a refuge - trigonometry and sinus curves are all based on triangles.
Higher mathematics, trigonometry, logarithms etc., are all based on triangles.
The dynamism is all related to triangles.
The Devi is an hourglass shape structurally reduced to its limit:
Her waist is almost non-existent: "mitya kalpita madhye" .
Chirality, ambivalence, polarity - there are structural elements here, as well as in modern mathematics.
Equations and graphs verify each other - geometry and algebra meet.
