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Archive for the ‘sacred geometry’ Category

Don’t we love symmetry? The way we hang things on our walls, arrange furniture, and landscape our yards is a testament to our deep-rooted need for it. We are ourselves physical exemplars of symmetry: two eyes, two cerebral hemispheres, two kidneys, two lungs, two ears, two arms and legs, two chambers of the heart ( right and left atriums and ventricles), two nostrils, five fingers on each hand, on and on. In music, we tend to prefer balanced harmony over discordant sound (though 20th century music introduced the unusually effective and evocative discordant sound of twelve-tone music).

We also see symmetry throughout the natural world. Nature seeks out equilibrium. Symmetry and the aesthetics of beauty are intimately intertwined. Mathematics is no exception and the study of mathematical symmetry has been a passion of esoteric mathematics for a long time. These mathematical investigations have also gone well beyond delving into the world of three dimensions. In fact, in the 1800’s, mathematicians studying symmetry introduced a 128-dimensional structure considered perhaps the most complex example, called E8.

I have written before about the extraordinary capacity of the human mind to imagine abstract maths that are then later embodied in empirically verified phenomena. E8 is apparently no exception. The most recent issue of New Scientist (January 16-22, 2010, page 12) reports that physicists of the University of Oxford have identified the E8 signature in super-chilled crystals. It appears that the electrons in the crystals organize themselves in accordance with the relationships defined by the structure of E8.

Once again, human imagination precedes natural discovery. To have dreamt it in the 19th century, in the disciplined language of mathematics, only to find it in the 21st, attests to the extent to which mind is fed by universal archetypes that move toward final expression in consciousness. We make conscious what is already there at the heart of matter awaiting revelation.

The source of such revelations is intimate and infinite: an inexhaustible fountain of revelation.

© Brother Anthony Thomas and The Harried Mystic, 2009. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited.

References:

Exotic Form of Symmetry Makes Real-world Debut

Mathematicians Solve E8 Structure

Mathematicians Map E8

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1st Major Snowfall of 2009 in the Northeast

Our first snowstorm of the season has been a blizzard with a great deal of snow. G-d’s powdered sugar adorns all the trees. The Beloved inspires randomness in this spray of trillions of tiny crystals on the ground, buildings, and trees. Only the whimsy of the wind combined with the structure of frozen crystals can produce such exquisite images.

Any one crystal seemingly doesn’t matter much. It’s fall would very likely go unnoticed. But, when joined with a universe of others, it forms a pure and weighty blanket; a frozen community made up of miniscule fragile structures. When taken all together, it takes heavy plows, and intense shoveling labor to move the mountains of white.

All small things, unique, fragile, beautiful, and intelligently crafted in themselves, find their purpose in relationship to one another. Every flake matters as does every weave of fabric in a fine carpet.

Like a pointillist, the Beloved’s artistry on the scale of the large is best understood among the worlds of the very small.

“Blessed are the meek for they shall inherit the Earth. ”

© Brother Anthony Thomas and The Harried Mystic, 2009. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited.

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As we go ahead on our course in life’s spiritual voyage, we come to explore the multifaceted and multidimensional character of Spirit. We look at all of its diverse manifestations and forms, symbolic expressions, signs, and personal experiences. As we progress, as typified by our education, we dive into literatures that themselves present increasing degrees of complexity and nuance. We stretch as we go from our earliest studies of simple geometries to the more complex ones and then on to even more abstract mathematical imagining.

Often ignored in all this diversity and language and intellectual sophistication, is the lowly point. We hardly give the small dot on a page much attention ( unless, of course, it separates dollars from cents, pounds from pennies). So, what’s a point anyway?

In geometry, the “point” is an object in space  lacking in extent ( volume, area, length, etc.). In the Cartesian plot, it is  a unique position in space defined by paired values x and y. In any event, we spend most of our time thinking about trends, three points or more, and the geometric shapes. What, then, of the forgotten, lonely point?

In astrophysics, there is a vibrant dialogue that has been underway for some time on “gravitational singularity.” This also refers to a “point” where the “gravity well” runs so deep that objects, including light, enter but do not re-emerge.  Singularities are points of infinite density at the center of “black holes.” It is thought that our universe began as a singularity just prior to the “big bang.” In fact, you and I began life, in a sense, as biological singularities: single points that then became ever more complex through specialization of cells.

In turning to the matter of Sacred mysteries, there are striking parallels.  Out of the very simple comes complexity. From the still point at the center, humankind has evolved complex systems of expression to capture the naked singularity that cannot be so clearly seen, but that exerts such great power on our consciousness.

Alpha & Omega are points, not trends, not triangles, not cones, nor circles. Ultimately, we will all get to the point, and it will be a return.

Practically speaking, this meditation awakens a sense of the reason we meditate at all. To get to the point, the singularity, the origin and the destination.

I include here a relevant prayer and meditation from the Liturgy of the Order of the Christos [ A Celebration of the Cosmic Heart] incorporating poetry from a number of the Nag Hammadi texts.

Ω

Glory be to you, O Father.

Glory be to you, O Word.

Glory be to you, O Grace.

Glory be to you, O Mother.

Glory be to you , O Most Holy.

We give thanks to you, O Light.

In whom darkness does not dwell.

Gloria in Excelsis Deo.

Who are you O Holy One that comes out of Light?

What mouth can speak your name, or mind conceive your nature?

You hold the whole of creation within the circle of your care.

You are the Center,

The Circumference,

The Origination.

The Destination.

Maranantha, AMEN!

© Brother Anthony Thomas and The Harried Mystic, 2009. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited.

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Doughnuts!

At the center you’re on the edge.

Yes, that’s right. Whether you fancy Dunkin Donuts or Krispy Cremes, the true doughnut ( the one with a hole in the middle), is a fitting metaphor for the spiritual life. Forrest Gump’s good and ever wise mother notwithstanding, chocolates are not the most fitting symbol. What I am talking about is the geometry of the Spirit. When you travel along an edge of the doughnut, you are also moving around the center.

Mathematicians refer to the doughnut shape as a torus, and its shape is “liminocentric”. So, what’s the meaning of this obscenely multi-syllabic word? In the case of liminocentricity, traveling along an edge, or, an outside part of the shape, is paradoxically also traveling inside of it. Many who talk about this kind of shape refer to the “chinese boxes” by way of analogy, wherein a series of smaller boxes fit inside larger ones. To be liminocentric ( limen, denoting thresholds, and centric, for center) small and large details of the shape are also the same.

The term was first used by Psychologist John Fudjack in his 1995 paper, Liminocentric Forms of Social Organization. The word has caught on in circles as diverse as physics, art, and consciousness studies. So, what’s all the fuss about?

In living spiritually, thresholds matter a lot. The moments of insight are most often threshold moments: we feel on the verge of some discovery. Perhaps we see something with fresh eyes, as if for the first time, or we are challenged in a way that seems to pull us into a new, unfamiliar space. But in opening ourselves to it, we are somehow closer to the center of reality, nearer a compelling truth.

Moses’ metaphorical encounter with the “burning bush” was liminocentric. He was at an unprecedented threshold, having stepped on holy ground where nothing was as we generally experience it. A bush burns without being consumed, and his relationship with the One embodied in the heat of the flame is at once personal, transpersonal, and Other. According to the Jewish Study Bible, the voice of Yahweh signs himself by uttering the words,” I will be what I will be.” The  burning bush was wholly and fully present, and also alive to all possible futures at the same time.

Moses stood on a mountain facing an awesome and, no doubt, terrifying visage, face to face with the ineffable, and they spoke: A Divine Q&A. He stood on a precipice, an edge, a verge of unknowing, and, at the same time, entered into the Bridal chamber, was at the center, at-onement with the Intimate Mystery.

Mathematicians and astrophysicists have gone far in exploring the geometry of liminocentricity. In fractal geometric terms, it is an apt model for the topology of the universe. The torus shape is ubiquitous: storm systems, galaxies, and black holes. There is no finer meditation than to open one’s eyes to the shapes of nature all around.

As we perceive the varieties of beautiful forms, we come to fully experience the outward topologies in deeply personal ways. Consciousness, it seems, is shaped as nature is shaped. Gazing inward, we experience our own threshold moments in which we are traveling an edge, and yet are closer to the center. We are involved in something seemingly small in finite time and space, but mindful, as a result, of the incomprehensibly vast.

  • Being present at the birth of one’s child;
  • The moment of awe standing on the perimeter of a volcanic caldera;
  • Holding the hands of a loved one as they pass away;
  • Hearing a lover’s heartbeat while feeling one’s own;
  • Being really awake in that fleeting split second in between two thoughts and listening to true silence;

As I move through this last day of the holiday weekend here, I will be taking special notice of things liminocentric, and of those moments that are both edges and centers, and where the structure of small details mirrors the large.

In any event, my next doughnut promises to be a very special treat indeed.

© Brother Anthony Thomas and The Harried Mystic, 2009. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited.

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Arch-de-Triumph-spiral-staircase

If a GPS device could be metaphorically strapped to the “waist” of our soul’s travels in the noosphere, what would the course of the overall journey look like on a moving map?

Would it be, as is generally presumed in Western thought, a more or less straight line of progression with frequent stops, side trips, obstacles to maneuver around, and an ample mix of retrograde motion?

Or, would we instead find that the geometry of sacred wandering was more like a circle, as it is often depicted, or an ellipse perhaps? Would it be better characterized as a series of parabolic cycles with ramping up time in practice followed by a peak experience, and then a falling back toward the “ordinary-verse” of our usual routine, and the daily hum-drum?

How about a series of S-curves with a rapid stepping up of spiritual energy, then a peaking followed by a refractory plateau phase with an accompanying pursuit of the next S- curve!? So far, the S-curve image feels right as I hold the metaphor up against my own experience.

Thinking about this today a fair bit, I have actually settled, for the moment, on the image of a helical spiral. As we progress along our chosen yellow-brick road, energy generally feels like it’s mostly gently spooling up with occasional spikes up and down.

Assuming a commitment to daily practice, that energy should on average continue to move in spiraling cycles. Carrying the metaphor forward, the helical spiral doubles back toward earlier points but at a different energy level and with a different spiritual signature. We may in the spiraling process stumble upon “old” relics of meditations and ruminations past, yet see them suddenly with new eyes and as if for the first time.

Marcel Proust once wrote: ” The journey of discovery consists not of finding new lands, but having fresh eyes.”

Practically, this means that we need to keep a journal of our daily contemplative experiences, recording what happened, what we saw, what we felt physically, what was familiar, what was new, and what was familiar yet somehow new. This gives us a chance to anchor different vistas that we see from many vantage points as we spiral forward on our winding path.

Those anchor points are profoundly reassuring and remind us, in the dry periods of sameness and boredom, that every movement along the helical spiral is relevant. A seeming back-slide is just a cycle around the back side.

What’s the trajectory and geometry of your journey? How would you diagram your experience?

© Brother Anthony Thomas and The Harried Mystic, 2009. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited.

spiral

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