Adam Blatner

December 12, 2008

Yoga is the practice of seeking mystical connectedness; there are many of these and they arise out of both Hindu and Buddhist traditions. More recently, yoga has become more popular in Western cultures, especially in the form of the health-promoting body exercises called hatha yoga.) In addition to body postures, though, as noted, there are many other ways of spiritual development in yoga, ranging from chanting specific simple or more complex melodies to contemplating and drawing certain diagrams to a variety of types of meditation.

One of the more traditional diagrams for contemplation consists of a pattern of five downward pointing triangles overlapping with four upward-pointing triangles, this variably being placed in a circle surrounded by the lotus-petal diagram so common in South Asian art. A yantra is a visual equivalent of a mantra, a yogic device for contemplation.

I draw and enjoy geometric constructions and drawings based on these, especially in the form of mandals (about which I write on another webpage, and examples also found on other webpages).

Sri (pronounced Shree) is an honorific, meaning especially sacred, and this yantra has been fun and fascinating for me: Learning to draw it so that the lines work has been a challenge. If the lines are too far apart or close together, it doesn’t come off, or it’s too squinched. I’m getting better at it, but I cannot say I’ve perfected my technique.

While this yantra has been given a variety of traditional interpretations, my tendency is to re-think everything, to consider what an interpretation might be in light of the discoveries of modern science, and expressive of my current drift in philosophy.

To me, then, the Sri Yantra expresses the peculiar resonances generated by a variety of multi-dimensional interpenetrations, which invites us to contemplate both dimensionality and inter-penetration.


It began with a mathematical way to describe physical space by assigning the parameters of length, height, and depth to objects. Zero dimensions is a point, which in fact doesn’t exist. As far as we know, even the tiniest point has some microscopic length and height, and in actual life, also depth—even an atom or a sub-atomic particle. (Actually, neither does one or two dimensions exist in our universe, but are theoretical constructs, mainly expressed in the two-dimensional space of a piece of paper.) One dimension is length—expressed as a straight line. And two dimensions includes also width, which allows the line to curve, close, form shapes, letters, etc. In fact, these forms do have width, but of a thinness that is insignificant in our thinking for most purposes. (Art restoration and some forms of detection that deal with layers of paint or what might be written in invisible ink might deal with the matter of thickness of the writing medium on a surface, but most situations just deal with what is represented on the surface rather than the physical nature of the representation—the signified rather than the sign. I have some interest also in the nature and evolution of signs, letters, alphabets, etc.)

Much of mathematics and scholarship treated the world as if it followed certain rules according, first, to the geometry described by Euclid—the geometry of flat (two-dimensional) surfaces. As we became more aware that this geometry didn’t apply to curved surfaces, geometry became correspondingly more complex. Einstein found it useful to assign to time also the concept of dimensionality, as time is involved in the movement of forms through space, their change, transformation, growth, development, decline, etc. However, in so doing, Einstein shifted the meaning of the term “dimension” a bit—and that shift is significant! It invites us to re-think dimension not simply as an aspect of physical space, but as a category that interacts with all other categories.

In my thinking, that re-definition offers a solution to a traditional conundrum: How can mind, which seems different in basic quality from matter, yet coexist with matter? My answer is that mind is simply another dimension, one that interpenetrates with all matter. A corollary is that there is no matter without some degree of mind, feeling, experience. (There is an extensive argument for this that has been developed by Alfred North Whitehead and before him, also other “process” philosophers—and since Whitehead, also. I am sympathetic with this approach, which shifts our perspective from looking at the world in terms of things moving to events happening— the latter then being analyzed by Whitehead as having their own unfolding dynamics, undercutting the illusion that there ever was or can be mere “thing-ness.” It’s sort of analogous to recognizing that neither can there be mere space without time.)

All this lays the foundation for another mystery: What is spirit, enlivenment, or the apparent gradient of consciousness ranging from sleep to awakeness, and from ignorance to insight? Can humanity and wisdom evolve and become more conscious? I am biased towards this being likely, and am interested in promoting the process, however modestly, in our own time.


This brings us back to the Sri Yantra. It is a symbol or a crude map of what I think is going on:

First, let us consider the four upward-pointing triangles, which express  what science admits is basic to our existence, the ground of our being. And yet this is true also of stars and rocks.
 – matter, the sheer density, inertia, stability,
    as well as its aggregate power (in the form of gravity) or force (when matter moves through time)
 – space, the matrix of existence
 – time, another dimension of that matrix
 – energy, the sheer interplay of these components

 Now, what makes this foundation alive, in a sense, and even interesting, is the way the spiritual principles descend, inter-penetrate, and enliven these basic dimensions. So the five downward-pointing triangles represent (at first hunch, and from the largest to the smallest):
– complexification, the draw toward new properties emerging at each new level of complexity (with an emphasis on mind itself becoming more complex, collective, and multileveled or organismic)
– differentiation, the formation of subtypes, permutations, species, along with the way the archetypes or potentials converge as a nexus to form an individual
– vibration, the dynamic pulse within time
– mind, the essence of subjectivity
– spirit, the essence of impulse of becoming

These interact, enliven existence, rippling outward, all operating at once. They generate stars, complex and larger stars, somewhat analogous to the many chakras or centers of consciousness that are expressed within the psyche and also along the spine in another type of yoga—kundalini yoga.

Now, I’m not fixed on this scheme: it is provisional, but evocative in my imagination. How do the various principles play off each other? For one thing, each interpenetration generates ripples, more widespread dimensions and closer-in dimensions.

For example, we have the individual’s body as an inner core, the ego or accumulation of roles and learning around it; the person’s interpersonal relations as another layer, and broader group affiliations as a wider layer, reaching out and being influenced by and in turn contributing to and co-creating the yet wider culture.
            - - - -

   Below is  a drawing that suggests the way the parts could fit inside each other.

And to the right is a drawing that suggests that put together, this more 3-D figure would be a kind of step pyramid or castle.

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This may seem to be a weird way to think, but it is closer to the way mathematicians ponder geometrical forms or scientists think about unusual findings registered in a test instrument — whether it be an oscilloscope, telescope, microscope, spectroscope, etc.  The game is to imagine that a finding means something. It’s not just a random blip. Especially when it shows up repeatedly under certain circumstances. So what does it mean? Enter theory-building.  

The Sri Yantra works in my mind at several levels. When I draw it, it serves as a centering mandala, it expresses a kind of order within the welter of ambiguities of this world, as if to suggest that, yes, there is a kind of map: It is a map inward, through layers of your own mind, past the particulars, to attend to the more essential dynamics.

Here's some more play with this:
    This pattern was featured as a metaphysical force-field generated by toys sent from a future civilization in the 2006 motion picture, "The Last Mimzy" from New Line Cinema  (now available on DVD). (The children's capacity to understand these forces allows them to save the world.) This Sri Yantra mandala is used in the movie as a portal for time travel. (This information from Discovery magazine, December 2007 issue, pg. 70.)
   Here are some questions:

    1. What is the smallest number of overlapping triangles you must draw to make the Sri Yantra? 

     2. The red sybmolizes the feminine, and the white symbolizes the masculine. How many red shapes are there? How many white shapes? How many triangles of any size are there altogether? Include triangles that are composed of both red and white shapes.
   (Answers at end)

More to be added in time.
For more about the Sri Yantra, see comments in middle of lecture on mandalas as an aid to understanding "deep maturity."

Answers:   1. To draw the Sri Yantra you must draw nine triangles, 4 pointing up and 5 pointing down.
2. There are 43 red shapes and 31 white shapes.

3. There are 120 triangles of all sizes altogether, 50 pointing up and 61 pointing down.