Posts Tagged ‘neo-pythagoreanism’

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 Anton 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.


Exotic Form of Symmetry Makes Real-world Debut

Mathematicians Solve E8 Structure

Mathematicians Map E8

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Quantum superposition is the bizarre physical principle that, if the world can exist in any configuration, than it can also exist in one that is a combination of any number of them at the same time. The mind similarly demonstrates this property in ways that substantiate the fact that we are not separate. We exist in many potential simultaneous configurations of consciousness, span time and space, and the world of dreams manifests these configurations.

Last night, I dreamt that my son was in trouble with the law. He was in jail with pending charges. At the same time, I was in jail awaiting arraignment on pending charges. It seems that I was both my son and myself.

This is not especially remarkable as we have all experienced elaborate and confusing dreamscapes where space and time simply do not behave themselves as they seem to in waking time and where we can live many lives in diverse places and as many people. Here’s the more interesting twist.

In realtime, the 21-year-old son of a family friend is awaiting the court’s disposition on charges that were recently brought against him during the holidays. A police officer responded to reports of a domestic argument in which this 21-year-old was caught up in a moment of rage in his home.

Shocked to then see a police officer at his bedroom door, he continued his angry tone and did so with the officer as the target. In response, the officer chose to forcibly restrain him, push him to the floor while hurling profanities at him, and handcuff him. Once subdued, this officer is then alleged to have started beating the young man with his bare fists.

Now, his dad, expressing understandable concern for his son, asked the officer to please stop hitting him. In response, the policeman handcuffed and arrested him also. His wife, a very sweet woman, who wouldn’t hurt a fly, then became very upset and tugged on the police officer’s jacket asking him to stop hurting her husband.

At this point, the officer handcuffed and arrested her. The entire family spent the night in jail and no one actually did anything wrong. The police were originally called out of concern for their son’s rage in hopes of calming him down. Last I heard, the court is talking about 30 days of community service for both parents, which their lawyers are contesting, and the multiple charges against their son are being legally reviewed.

So, in view of these circumstances, a Kafkaesque dream about my being jailed with my son in jail for no clear reason is not especially surprising. One could argue that the dreams were simply a reflection of my concern for this good family that lived through a night of hell and who face an ongoing and, by all indications, undeserved legal battle in the months ahead. I would agree with that, were it not for one further development.

When I awoke, I heard from my son in Korea who was just back from the hospital there after a night of violent and unrelenting gastrointestinal symptoms. It turns out the dream was prophetic. While having nothing to do with the law, it was symbolic of my son’s distress and his need to get in touch with me. The surreal plot surrounding the arrest of this family and their pending charges served as a frame for my sense that my son was having trouble. This scenario involving prescient dreams has happened many times over the years. In addition, many people, who share their dreams with me, report similar experiences all the time.

Consciousness laces the universe together. We walk around each day wrapped in the delusion that we travel independent pathways. In fact, our pathways mystically intersect in complex ways. There is no such thing as meaningless coincidences. This is not an example of magical thinking but of synchronistic event horizons. Denying this ubiquitous human experience is poor science. It rejects phenomenological data about archetypal fields in favor of simpler and more easily analyzed effects.

We are beckoned every day to embrace our legacy as children of the stars and mature physical science is leading the way in revealing the entangled and infinite reach of consciousness.

© Brother Anton 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.

Shakespearean Costumes for Midsummer Night's Dream ( Public Domain)

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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.


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 Anton 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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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 Anton 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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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 Anton 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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A line, a triangle, a circle, and a square,
These are on paper some forms to compare.

Pyramid, cube, cylinder, sphere,
This is how things really do appear.

Then to 4-folds, past sight to idea,
Imagining worlds of magic, quite near.

Polytropes dancing, tesseracts slide,
Hyperspheres gyrate with angels inside.

5-folds, 6- folds, then seven and more,
The Beloved invites us to come and explore.

The rooms of His temple are many, some hidden,
” Come join me, come rest,” we are lovingly bidden.

We struggle to do it, we tremble in fear,
No need to resist, our Great Lover is near.

In taking the leap and accepting the Call,
We leave well behind us the Flood and the Fall.

Then Home once again, at ease, and contented,
Our hesitant nature at last now relented.

A New dawn breaks,  a nova- luminous face,
Singing of infinity and hyperspace.

Consider form, shapes, those irregular and those bizarre. Imagine dimensions more than 3. Go back and play with compass and protractor, and know that you are in contemplation of infinite mystery.

We are made to do these things by our curious and creative nature, and that’s the surest sign of an open invitation and warm welcome.

Shall we then RSVP?

© 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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In the title of one of his books, Stephen Hawking declares: “God made the integers.” While we discovered numbers, mathematics is a remarkable lens on  the properties of the Universe.

Number is archetypal, an essential objective pattern underlying and organizing the cosmos. Numbers are to mathematics what words are to poetry and literature and all conversational forms of communication.  

The archetype of number is, as Jung expressed it, part of our collective unconscious. It is a revelatory medium, albeit an abstract one, that sheds light  on the structure and inter-relationships among objects and forces in the physical world.

Since consciousness arises out of matter, it is easy to fall into the trap of dualism: mind vs body. In fact, they are the same thing. Mind is a property of the Universe and, so, when we engage in mathematical explorations, we act as the vehicle for matter’s reflection on itself. 

Mathematicians engaged in complex investigations into the properties of numbers ( number theorists) and those employed in all the other branches of the field, invest in a unique form of contemplation  (if very stylized and formal).

We do not have to go to the farthest extremes of mathematical preparation and sophistication to take a spiritual journey through numbers. A few moments of thought in quiet active imagination can yield a small taste of the  exquisite character of the deep structure of our world.

Numbers are magical, mysterious, and can unlock our innate mysticism. Numbers are everywhere. They are  richly presented in sacred scripture.

Just consider a few of the powerful, evocative, and profoundly meaningful numbers repeated so often in western Biblical sources:

  • The number three and the trinity,
  • The 12 (the Ogdoad), and the twelve tribes of Israel, the twelve Apostles, and the twelve signs of the zodiac;
  • The number “8” and its use as a signifier of the Christ in ancient texts ( the “888”);
  • The number “9” and the  nine planets, the nine personalities described by the Enneagram, the nine major planets, etc.

Consider also the archetypal character of number in the fractal geometries of nature: the number of petals on flowers, the shapes of leaves, the manner in which trees grow. Mathematics  is the language of nature, and  I agree with Mario Livio when he says ( in his book of the same title) that  “God is a Mathematician”.

Number is everywhere, in us and all around us. They can be potent vehicles for lifting our sights in contemplative prayer as much as does poetry. This morning, I am taking a few moments to meditate on a four-number sequence: 0, 1, 2, 3 & 4.

If you would allow my free associations without self-editing or analysis in the sequence 0 to 4:

  • zero – the state of latent being, not yet here, absent but not meaningless, pregnant with portent, the moment just before the big bang, the moment just before the joining of sperm and ovum, the state of potential energy, the place of nothingness out of which I came, the place to which I will one day return, the alpha and the omega, the prima materia, the moment before the first breath, the moment after the last.
  • one – I am, you are, a person’s sense of aloneness, a solitude yearning for companionship, a sense of being special, uniquely named, uniquely destined, a purpose incarnate, a thought, a word, a prime, that moment just before going from rest to motion, the singularity.
  • two – right-left cerebral hemispheres, Gemini, the couple, the Janus head , holding hands, stereoscopic vision, the line, two dimensionality, two ones in an embrace, the basic dance, the simple molecule, a tending toward attraction, bonds, forces in convergence, forces in interference, conflict and exchange, shifting perspective, a chance to be so much more.
  • three– the family, the two setting common sight on the third, the complete musical chord, two on the road to Emmaus met by the third, their master/ teacher and friend, friendship, the platonic solids, the dimensionality of space as we see it and experience it, the cube, the middle way, the trend, the birth of interpretation, movement from items to groups, possibilities, a tending toward fullness ( the “pleroma”), faith-hope-charity, the triune G-d, past-present-future, the narrator in a fictional work, the Easter Triduum,the synoptic Gospels (Matthew, Mark, & Luke).
  • four –  adding the Gospel of John, time, the fourth dimension, seeing through mind into Mind, the abstract, fantasy, the author behind the narrator in the story, sibling play & rivalry, structure of the heart, playing the 7th with the 1st, 3rd and 5th of the musical chord, the number of seasons, the compass rose, variations, the observer, in-laws and the eternal cycle, 4! (factorial) =24, a leap to higher dimensions, the G-d within.

We need not shy away from number (or math in general) when we think of matters spiritual. Like  the evolution of the World’s languages, the symbolic language and the natural quality of numeracy in nature is a reminder that Spirit is everywhere. It calls us to the next level, and then the next, with each thought, act, discovery, and product of mind.

A deep structure, a pattern of givens tending toward consciousness, and reaching back to before our universe came into being, is at the Heart of all that we are and all that we are becoming.

Perhaps you too will find some value in trying out this approach to meditation: one quite different from the usual that can illuminate and add great depth to a short time set aside in quiet repose and contemplation.

Counting Petals

© 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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