Yantra literally means Loom, 'Instrument or Machine'. In actual practice a Yantra is a symbolic representation of aspects of divinity, usually the Mother Goddess. It is an interlocking matrix of geometric figures, circles, triangles and floral patterns that form fractal patterns of elegance and beauty. Though drawn in two dimensions, a Yantra is supposed to represent a three dimensional sacred object. Three-dimensional Yantras are now becoming increasingly common. Although the Yantra is primarily a meditation tool both for serious spiritual seekers as well as sculptors in the classical tradition, its Shakti is also available to new seekers with sincere devotion and good intention.
Since time immemorial, it is believed that mystical Yantras reveal inner basis of forms and shapes abounding in the universe. Yantras function as revelatory symbols of cosmic truths.
Bolton and Macleod discuss Sri Yantra
The term yantra, which literally means an instrument for holding or restraining, may be used to denote a variety of linear diagrams which play a significant role in the meditative practices of Tantric Hinduism. Yantras may be simple designs such as the cross, triangle, square, circle or lotus pattern, symbolizing basic concepts, or may be more complex combinations of such elements in figures representing in abstract form the particular creative forces in the cosmos which are called divinities. they are closely related to the mandalas used by both Hindu and Buddhist Tantrism, in which geometric design is supplemented by elaborate symbolic images of the deities which by their various forms and attributes indicate different aspects of the hidden order of reality. As Mircea Eliade says (1), the yantra is 'the linear paradigm of the mandala', expressing the same principles in geometric form. Like mandalas, yantras are used in the context of meditation and worship as visual-aids to concentration of the mind leading to realization of abstract principle which is the inner meaning of the visible representation.
The best known and geometrically the most complex yantra is the Sri-yantra, also known as the Sri-yantra, employed by the Sakta school of Tantrism which visualizes the divine primarily in female form. The structure of this yantra is enigmatically described in the Saundarya-lahari (The Wave of Beauty) (2), a lengthy poem praising the great goddess
whose dwelling place the Sri-yantra is said to be:
By reason of the four Srikanthas (srikantha is an epithet of Siva) and the five damsels of Siva (which have the nature of Sakti), which are penetrated by Sambhu (i.e. bindu- the dot in the centre) and constitute the nine fundamental natures, the 43 (or 44) angles of your dwelling place are evolved, along with the 8-petalled and 16-petalled lotuses, the circles and the three lines. (stanza 11)
Plate 65, Rawson, Sri Yantra, a diagram of the continuous process of Creative Generation, with indwelling Mahavidya Devatas in all the triangles and stupa and lingam motifs combining Buddhist and Hindu symbolism. Nepal, c. 1700. Gouache on cloth 20 x 24 inch
The diagram may be more accurately described as a bilaterally symmetrical figure composed of nine interwoven isosceles triangles, usually depicted with five triangles pointing downwards and four pointing upwards. The former are said to correspond to the yoni representing the dynamic female principle of energy (Sakti), while the latter correspond to the linga representing the static male principle of wisdom (Siva). (The Buddhist Tantrics, incidentally, regard the male principle as dynamic and the female as static.) The central dot called bindu represents the original unity of the male and female principles prior to creation and the paradoxical point female principles prior to creation and the paradoxical point from which the manifestation of the cosmos emerges. The interpenetration of the nine basic triangles gives rise to a number of subsidiary triangles (43 including the central triangle enclosing the bindu) which form the abodes of the deities, representing the particularization of the original creative forces into more concrete manifestations. Sometimes the names of deities and Sanskrit syllables are written into these triangles, or images of the deities are placed in them.
In most versions of the yantra this central design is enclosed by two circular lotus-patterns with eight and sixteen petals, a girdle of three concentric circles, and finally a square arrangement of straight line ('the three lines') with four openings or 'doors' at the cardinal points called 'World House' (bhugra). This square outline, which is common also to mandalas, symbolizes the royal palace in which the deities reside - an area of sacred space protected from the disintegrating forces of chaos. In general, the Sri-yantra is a 'cosmogram' - a graphic representation of the universal processes of emanation and reabsorption reduced to their essential outline. As Eliade puts it, the yantra: 'An expression in terms of linear symbolism of the cosmic manifestations, beginning with the primordial unity.'
Patrick Flanagan's Construction of the Sri Yantra from embedded or nested GoldenRatio Triangles
calls the Sri Yantra the 'king of power diagrams' and describes its energetic effect as seventy times greater than that of a pyramid construction. This means that a three centimetre Sri Yantra possesses a greater energetic effect than a two metre pyramid. The Sri Yantra's extraordinary energetic power depends upon its exact geometry. This complex geometry is the key to its effect and has interesting mathematical implications. In this yantra you find not only the 'Golden Section' but also parallels to the geometrical structure of the hydrogen atom and to the ratios of its emission lines.
Flanagan had a dream in which he was told by Sai Baba how to construct the Sri Yantra from embedded or nested GoldenRatio
Construction of the Sri Yantra explained
The base angle of the largest trinalges of most representations of Sri Yantra are about 52 degrees, close to the base angle of the Great Pyrmaid of Cheops, which is 51deg50'. With such a base angle, the ratio of the hypotenuse to half the base is phi, the GoldenRatio
The design was investigated with the largest two triangles having this base angle. The construction continues similar to the 7x7 grid method. The result is striking, for apart from the fact that the error (at Z and W) is not noticeable, the overall shape is very simlar to examples from the literature. The error is only .3616% of length of the diameter. A small change in base angle results in large error - a 53 degree angle has an error of 9.125%!
The Oregon Desert Sri Yantra
Air National Guard pilot Bill Miller was the first to report it during a fly over on August 10th, 1990. Out of no where appeared a giant pictograph a quarter of a mile wide in a dry lake bed east of Steens Mountain, about 70 miles southeast of Burns in a place called Mickey Basin. It hit the news services on Sept. 14th and was soon identified as an ancient Hindu meditation symbol called a SRI YANTRA. Ufologists Don Newman and Alan Decker went out the morning of September 15th and reported the symbol as being furrowed into the dry lake bed about 3" deep and that the area was noticeably missing any signs of tire tracks or foot prints, even though their own tire tracks left 1/4" deep marks on the crusty surface of the dry lake bed. After further investigation, their colleague, Jim Deardorff, wrote up the story for UFO Magazine from which the below summary and photos were taken.
By this time the Bend Bulletin, The Associated Press and The Oregonian had all picked up on the story. In one article, a mention by some architechs had the cost of just carrying out the survey for such a project at around $75,000 to $100,000. The overall lengths of the lines within it totaled 13.3 miles, and the uniformity of the depth of the furrows, along with the uniformity of the way the clods of soil had been displaced out side of the furrows equally on both sides was very impressive. It was also noted by investigators that although the long straight lines that formed the outer edge deviated from being true straight lines by as much as 8 inches, that deviation disappeared and the lines appeared straight when the pattern was viewed from the air. ....
Bill Witherspoon latest publication in MIT's Leonardo
Although there seems to be information on the internet suggesting that Bill Witherspoon is not the artist responsible for the Sri Yantra found in the Oregon Desert over a decade ago the renown MIT press just published an excerpt of his article "Art as Technology" in their Leonardo Journal.
Currently Bill is selling fake skies at http://www.theskyfactory.com/
More online resources
- Artistic and Historical Background
- Art of Sri Yantra
- Historical Methods of Duplication
- The computational complexity of Sri Yantra
- A curiosity: The mathematics of sriyantra
- The spiritual meaning of Sri Yantra
- Dan Winter on the self-awareness and the Life forces within geometries