Sacred Geometry

[Sefiru]

I'm sure that most of us have number symbolism as part of our practices, and there is loads of information about the symbolism of numbers. It's often about groups of things, though: two candles, reciting a spell three times, and so on. Shapes of things don't get as much attention. There's the Pentacle, and ...?

Do you own anything that is spiritually significant because of its geometry, and what is its significance? (If your answer is 'a pentacle', please elaborate: I'm sure there's plenty of variation.)

Does geometry play any other role in your practice?

I don't actually have much in this category, though I am oddly fascinated by septagrams; as per usual for me, I have no idea what this means yet.

[Altair]

Do you own anything that is spiritually significant because of its geometry, and what is its significance? (If your answer is 'a pentacle', please elaborate: I'm sure there's plenty of variation.)

See the metamythos mandala in my signature below: a circle circumscribed around an equilateral triangle. When I was trekking the Himalayan mountains, I had it rendered in the Tibetan tanka style commonly used for mandalas, and it hangs framed on the entrance wall to my bedroom:



SIGNIFICANCE: The circle represents the ultimate, all-encompassing divine, which if personified is female; the triangle represents the divine manifest as space, time, and thought, which if personified are male aspects (thus an up-pointing triangle) of the female. Each side of the triangle is also the long axis of a vesica piscis, symbolizing the union of each male aspect with the all-encompassing female to give birth to the universe as we know it.

But beyond those specifics, a circle circumscribed around an equilateral triangle has always struck a deep chord in me (and I suspect in others as well). The circle contains the greatest area that can be encompassed by a regular geometric shape of a given radius; the equilateral triangle within it comprises the smallest area given that same radius. So together they suggest the alpha and omega, the meeting of polarities. I think that deep chord is at least in part why that combo was chosen as the symbol for Alcoholics Anonymous.

Does geometry play any other role in your practice?

A HUGE role. I've only scratched the surface of how I try to integrate it. The potential for symbolism that is both hidden yet powerfully resonant on a subconscious level is off the charts.

I've even taken tentative steps beyond just geometry to incorporate symbolic use of non-geometric mathematical concepts in my practice. It's buried in my book in such a way that for most folks it will go completely unnoticed (because even a hint of math tends to put people off). 

For example, the god Night is a god of thought and the unknown, of mystery and otherness and anything conjured from imagination. (He's one of three sides of the equilateral triangle, alluded to above). In the book, whenever he speaks in the first person, the "i" is always lower case (never "I"). This is more than affectation; it references his unending quest to understand his own identity...but it's also a math reference. In math, a lowercase "i" represents a very important and well-known concept called the imaginary unit (the square root of -1, a number that because of the follies of multiplication can only exist in our imaginations). It's the perfect metaphor for a god whose entire essence is rooted in imagination.

So yeah. In my practice I'm big on sacred geometry and the math behind it and beyond it.

[Hariti]

Do you own anything that is spiritually significant because of its geometry, and what is its significance? (If your answer is 'a pentacle', please elaborate: I'm sure there's plenty of variation.)

Does geometry play any other role in your practice?

I have a Kali Yantra, which I made myself, sitting on my altar right now. Yantras are generally considered to be a form of sacred geometry. I don't have a picture to share of it, unfortunately.

[Hariti]

I have a Kali Yantra, which I made myself, sitting on my altar right now. Yantras are generally considered to be a form of sacred geometry. I don't have a picture to share of it, unfortunately.

I guess I should elaborate a little bit! A Yantra is a device used in Hinduism, and sometimes in Esoteric Buddhism, as the focus for meditation and in certain Tantric rituals. https://en.wikipedia.org/wiki/Yantra

Mine looks somewhat like this, but with different coloration (the color has symbolic meaning as well):



The central point represents both *creation* and the *creator* in the ultimate sense of the world. God, Brahaman, Shakti, the "Big Bang." It is the instant the universe was born, and the state to which it will eventually return.

Triangles represent sexuality. Upward triangles represent male sexuality, downward triangles represent female sexuality.

Hexagrams represent either sexual union, or dual sexuality. It's the combination of male and female sexuality. It can be used for hermaphroditic beings, or in Yantras representing sexual union.

The Lotus represents purity, perfection, and symbolizes the flawless nature of the God/Goddess.

The circle represents the *physical* manifestation of the divine in the material world.

The outer square represents the planet earth and the four cardinal directions.

Those are the common elements seen in many Yantras. The primary Kali Yantra has all of them except the hexagram, because Kali is an exclusively feminine force.

[Sefiru]

For example, the god Night is a god of thought and the unknown, of mystery and otherness and anything conjured from imagination. (He's one of three sides of the equilateral triangle, alluded to above). In the book, whenever he speaks in the first person, the "i" is always lower case (never "I"). This is more than affectation; it references his unending quest to understand his own identity...but it's also a math reference. In math, a lowercase "i" represents a very important and well-known concept called the imaginary unit (the square root of -1, a number that because of the follies of multiplication can only exist in our imaginations). It's the perfect metaphor for a god whose entire essence is rooted in imagination.

I've hardly ever seen any mathematical symbolism that goes beyond integers. This is cool! (I am now thinking about the significance of irrational numbers such as pi.)

Actually, one of the things I find interesting about the pentagram is its connection with the Fibonacci Sequence: if the inside pentagon has sides of length 3, the points will have sides of length 5, and a pentagon drawn around the points will have sides of length 8. And so on.

[Sefiru]

I guess I should elaborate a little bit! A Yantra is a device used in Hinduism, and sometimes in Esoteric Buddhism, as the focus for meditation and in certain Tantric rituals. https://en.wikipedia.org/wiki/Yantra

Do Yantras have any connection to mandalas?

[Altair]

Do Yantras have any connection to mandalas?

I second this question. I want to know more!

[Altair]

I've hardly ever seen any mathematical symbolism that goes beyond integers. This is cool! (I am now thinking about the significance of irrational numbers such as pi.)

Pi isn't just irrational; it's a transcendental number, a subset of irrationals that's even more rare and exotic. (I don't pretend to understand what they are; I just appreciate that something in their nature--aptly termed transcendent--makes them awesome.) If irrational numbers are the gold of sacred geometry, transcendental numbers should be platinum.

For me, since the circle is the symbol of the ultimate divine, pi is the mathematical representation of that divine essence: the Great Goddess's true name, "elusive to its last syllable even in the incontrovertible language of the gods"--my attempt at poetic allusion to the fact that pi famously continues in decimal form endlessly without repeating, as all irrational numbers do.

(With pi for the Great Goddess and i for Night, that's two of the three key components of a mathematical equation that lies at the heart of my mythos. This simple, elegant equation is considered the most beautiful in all mathematics, and when I "found" it underlying my myth cycle, unveiling itself in the story's climax, it was a eureka moment.)

One doesn't have to understand all the math. I certainly don't! But if one examines geometry and more broadly math in general, even just a little bit, the potential symbolic uses are staggeringly effective.

[Sefiru]

Pi isn't just irrational; it's a transcendental number

I am now sad that Transcendental Meditation is not, in fact, meditation on the digits of pi. (But it should be!)

(With pi for the Great Goddess and i for Night, that's two of the three key components of a mathematical equation that lies at the heart of my mythos. This simple, elegant equation is considered the most beautiful in all mathematics, and when I "found" it underlying my myth cycle, unveiling itself in the story's climax, it was a eureka moment.)

This one, right? It's ... astounding, is the only word I can think of.

I'm also quite impressed by infinite series for calculating pi. As in, it's wondrous that they look so simple and actually work.

[Hariti]

I second this question. I want to know more!

Are they related? Yes, they very much are! However, the exact nature of that relation is muddy. It seems that some sources consider Yantras to be a *form* of Mandala, while other sources consider Mandala to be another name for Yantras. They are both used in multiple traditions, and have been used for centuries.

[Hariti]

Are they related? Yes, they very much are! However, the exact nature of that relation is muddy. It seems that some sources consider Yantras to be a *form* of Mandala, while other sources consider Mandala to be another name for Yantras. They are both used in multiple traditions, and have been used for centuries.

Generally, the distinction, in modern practice, is done on a case-by-case basis. A particular symbol is categorized as a Yantra or Mandala based upon A) What is was traditionally considered & B) What it actually look like. In general:

Yantras are smaller than Mandalas,
Yantras use less colors than Mandalas,
Yantras have more straight lines geometry than Mandalas,
and also, most (but not all) Yantras are associated with a specific deity, (usually a Goddess).

That said, these aren't hard rules, and there are some patters which meet all of these and are still called Mandalas.

[Altair]

This one, right? It's ... astounding, is the only word I can think of.

Yes, that's the one: beautiful since it brings together the most important constants, the most basic numbers (1 and 0), and the basic operations (adding, multiplying, and raising to the power of, each operation performed only once) in so simple a way that it's, as you put it, astounding.

(And I find it astounding without really understanding the math.)

It's an equation that seems to say something fundamental about the way things operate, sitting at the heart of the universe. So I found a way to sit it there.

The logarithmic constant--e--was the missing piece. It's a transcendental number nearly as important as pi, and it emerges from all sorts of natural growth patterns. e seems to be at the root of accumulating transformations...but I confess, once more I barely begin to understand the math.

Still, e seemed an apt symbol for the Song of Diversity the Great Goddess sings in the mythos; that music of Hers is the recurrent metaphor of the whole myth cycle, an expression of the ordered systems that organize in our universe despite its tendency towards entropy. The song turns Her unity into a dynamic, changing multiplicity--an accumulation of transformations. e fit.

So I assigned e to the song (hidden in the text; virtually every adjective used to describe the song, from "eternal" to "exquisite", starts with the letter e). That's when the equation fell into place: In the pivotal conclusion of the mythos, Night embraces his true identity and ascends to become the next Great Goddess, resetting the universe to a new beginning where the myth cycle starts all over again.... or put another way: The song, raised by the power of Night (who will sing it) compounded with the Goddess (who sings it), upon completing 1 cycle, returns to a new point of origin--



I used math in a final flourish; Night's last words are the spell he casts for his ascension: "Eadem mutata resurgo" ("I rise again, changed but the same"). It fits the moment perfectly, but they also happen to be the words the mathematician Jakob Bernoulli had carved on his tomb in tribute to the logarithmic spiral.

Of course, this may all be hogwash--me shoehorning in stuff that isn't inherently there. But it gives me a sense of peeking at the inner workings of existence. I feel in touch with something fundamental. And that's what religion is for, right?

Sorry to blather on. I get off on this stuff.

[Altair]

Do you own anything that is spiritually significant because of its geometry, and what is its significance? (If your answer is 'a pentacle', please elaborate: I'm sure there's plenty of variation.)

Does geometry play any other role in your practice?

First off, apologies, Sefiru, for dragging your thread off course. I took it upon myself to talk sacred mathematics in general, when you asked specifically to talk not about numbers, but about shapes (which of course are connected to numbers, but still).

These three shapes also play a role in my practice:





I don't own anything with these geometries except my aforementioned mandala, into which these shapes are prominently incorporated. Nearly 35 years ago, when I unwittingly began devising what would become my practice, they were the first things I drew as I put pen to paper.

SIGNIFICANCE: These shapes are meant as symbols of the three aspects (male) of the ultimate divine (female). This relationship is reflected in the shapes themselves; if the ultimate divine is a circle, the aspects derive from taking the 2 halves of that circle and recombining them in different ways.

Reducing them to their absolutes, they represent space (Cosmos), time (Chronos), and thought/the unknown (Logos, a.k.a. Night), respectively.

[Altair]

Generally, the distinction, in modern practice, is done on a case-by-case basis. A particular symbol is categorized as a Yantra or Mandala based upon A) What is was traditionally considered & B) What it actually look like. In general:

Yantras are smaller than Mandalas,
Yantras use less colors than Mandalas,
Yantras have more straight lines geometry than Mandalas,
and also, most (but not all) Yantras are associated with a specific deity, (usually a Goddess).

That said, these aren't hard rules, and there are some patters which meet all of these and are still called Mandalas.

Is there a difference in how mandalas and yantras are used?

(You said in your earlier post that "a Yantra is a device used in Hinduism, and sometimes in Esoteric Buddhism, as the focus for meditation and in certain Tantric rituals." Does that hold true for mandalas too?)

[Hariti]

Is there a difference in how mandalas and yantras are used?

(You said in your earlier post that "a Yantra is a device used in Hinduism, and sometimes in Esoteric Buddhism, as the focus for meditation and in certain Tantric rituals." Does that hold true for mandalas too?)

Hmm. Yes and no. They are used for meditation and ritual, but not the same rituals. Mandalas are often used by Hindu Brahmin in traditional Vedic rituals, as well as in Tantra, while Yantras are much more frequent in Tantra. In Buddhism, both Mandalas and Yantras are used in Tantric rituals, but Mandalas normally represent abstract ideas  or sacred places, while Yantas are used to focus on deities.

In Hinduism, many Yantras are believed to actually, literally call the presence of the deity they represent. They also rarely (almost never) contain representational images of people or deities.