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Posts Tagged ‘sacred mathematics’

It’s been about two months since I last posted. The time has been one of frequent travel, fashioning new material to spark fresh dialogues among clients, and a time, otherwise, for  fewer words.

Authentic writing needs fresh perspectives. It  is good for the soul to invite incubation. So, my last 60 days have been about emptying.

It’s been said that nature abhors a vacuum and moves quickly to fill it. Yet, there’s a lot of vacuum in the Cosmos. Maybe this simply isn’t so.

Nature does not abhor a vacuum so much as it finds its shape according to unseen patterns that make it up. Vacuum conjures up  a great and infinite emptiness. On the contrary, the Cosmic vacuum is a plenitude.

Overwhelmed by unimaginable distances, could it be that we mistake the vastness of the seemingly empty expanse of space for the fearsome darkness of “non-being”?

Space-time is an n-dimensional funky quilt that we can only marvel at as we gaze on it abstractly through the lens of mathematics. Nonetheless, the very fact that we imagine it  suggests our intuitive and playful sense of its underlying fullness.

When we silence the mind’s manufacture of crafted sentences and paragraphs, and even briefly hit the pause button, it may just be that we then unleash the deeper depths, wider views, richer hues, and that fertile vastness that buoys all our hopeful imaginings and heartfelt expressions.

I sing a song in praise of true away time, a brief silencing of  our own voice so the poet inside the silence is the voice more clearly heard.

© Brother Anthony Thomas and The Harried Mystic, 2010. 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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Great (Holy) Saturday – April 3, 2010

This is the solemn day on which the Church recollects the time during which Jesus is entombed. It is the time before the bulb re-emerges after a dark winter’s incubation. It is the dark cloud obscuring the Sun that surely will burn brightly and warm the planet once again when its cover moves by. It is the potential within the kinetic, the pause before your next breath, the time of sleep just before re-awakening, and that ever so brief silent pause between two waves arriving at the beach.

The Orthodox reference to the “harrowing of hell” captures the theological import of Christ’s passing into the netherworld to redeem and carry into paradise the souls of the deceased, most significantly, the archetypal Adam and Eve. The presumed stain of Original Sin is cleansed at His incursion into Hell, bringing Light to the darkest of places. Altars world-wide remain stripped of linens and vestments shift to pure white. Mass is not performed until midnight ( or the symbolic start of Easter ( Resurrection Sunday) at another late Saturday night appointed time). The world waits.

The entire Triduum is about preparation and expectation. Waiting is a core theme across all spiritual teachings. On this day before the most Holy of days in Christendom, what is it that we await? How does the mythology of the church relate to our lives and the realities that we construct around us? Where is the relevancy of such mystical events for a post-modern scientific society?

Firstly, that I use the word “mythology” is not meant to suggest that the events we celebrate are any less real. Quite the contrary, it only attests to my intent to apply anagogical reasoning to these events as we must when it comes to mysteries that we know tacitly or in poetic and non-experimental ways. That I love my wife, daughter, and son requires no proof though, were you to ask me to do so, I would resort to the lexicon of the Heart. It is a thoughtful phenomenological detailing that presents the clearest and most robust path to understanding the “mysteries.”

The “Free Online Dictionary” ( thefreedictionary.com) defines anagogy as: “A mystical interpretation of a word, passage, or text, especially scriptural exegesis that detects allusions to heaven or the afterlife.” It defines “mystical” as:

1. Of or having a spiritual reality or import not apparent to the intelligence or senses.
2. Of, relating to, or stemming from direct communion with ultimate reality or God: a mystical religion.

Heaven and the afterlife are metaphors for infinite consciousness, non-mortal being, the Platonic realm of forms ( or the inherent matrix of foundational archetypes that prefigures and predisposes the created to coalesce in its diverse forms), the well of souls ( or the unknowable place from which our individual consciousness came and to which one day it returns), and the ground that informs our deepest dreaming, our prayerful intentions, our moments of insight, epiphany and enlightenment. With this framework in mind, then, I ask: What is it that we await on this “Great Saturday”?

It is summed in three words: the inexhaustible Light! Light plays a major role in all of scripture, Western and Eastern. Light is a powerful and intrinsic need of all living things and it plays a very central role in the story of the life of every human being. We experience the light in very similar ways. After a long winter, few can resist the allure of a surprisingly bright day. People move out of their homes and take to the streets and the open markets and cafes. In the United States, college students from the North, Midwest and Northwest move in a great exodus toward the more direct sunlight on Spring break. In Europe, many head south. In the East, the same applies as people move toward the equator and further south of it to enjoy the beneficient sunlight, the warmth, and the penetrating rays that are so deeply restorative.

The light plays a key role in consciousness and experience from very early in life. We open our eyes after birth for the first time and light streams in. After a period of adjustment, so much of our learning and the development of language and thought is based on vision. As young children, who among hasn’t had a bad night with fears of things emerging from the darkness; those compelling fears that take archetypal monstrous forms. The cure for such moments is pretty much always the same: turn on the light.

Some years ago, while traveling on business, I was awakened around 2 AM experiencing a frightening shortness of breath. I was momentarily terrified. My first thought was to turn on the light after which I dressed and went to the lobby of the hotel where other people were present. On doing so, everything settled down. On long-distance car trips, there are stretches of road across farmland in the U.S or mountain roads where there is very little light. Such driving late at night is especially unnerving and I always find myself less tense when I see lights in the distance: the sign of civilization and the presence of other people.

As I write this, my daughter is on the road somewhere in Illinois on her way back to college after her Summer break. I spoke with her last night and she was stopping in a small town for the night. Her comment was simply: ” It is so dark here. I can’t see a thing. It’s time to stop, get something to eat and turn in. I’ll continue in the morning.” I’ve said before that we are made of the same stuff as stars. Indeed, all that exists ultimately came from the stars. We are light-centric creatures and this need is expressed in many ways in all the corners of our lives. Our language is replete with light references: enlightenment, to light on a flower, alight, delight, daylight, earthlight, light headed, light-hearted, limelight, highlight, etc. We are capable of contemplating the Infinite and so we routinely do in our visions, including the perfect and infinite Light: a light that knows no evening, the Christic Light. That is what we await on this Great Saturday.

How does the mythology of the Church ( and this phototrophic disposition) relate to our spiritual lives and the realities that we construct around us in this post-modern, scientific age? Maths are axiomatic, based on faith in certain logical propositions, and maths can and do arrive at conflicting conclusions. It appears that in this most regal of the logical endeavors of humanity there is more than one right answer. Non-euclidean geometries deviate in key ways from the axioms of Euclid and arrive at justifiable and verifiable conclusions that simply do not square with Euclidean propositions.

So, are there multiple realities and diverse possible worlds? Absolutely. And what about scientific certainties? There are few of them actually. In fact, the uncertainty principle and the two as yet irreconcilable forms of lawfulness (Newtonian and Quantum mechanical) cause us to continue to search for new unifying theories. New maths arise all the time, and have especially done so over the course of the last century. This raises the bar on what it means “to know.” There is a mystical character to number theory. Science applies rarified and esoteric methods and a language of its own ( filled with poetry, by the way) to study the mystery of being. So, in fact, science and mysticism intersect all the time. It is dogma that gets us hung up.

The big objection from many is that scientific truth is “verifiable” and the tenets of religious belief are not. That is so. However, the foundations of “religion” are rooted  in verifiable experiences. We experience the dearth of light and rejoice at its return and that motivation is observable and verifiable. Reductionism to the absurd is illogical and fruitless. One should always avoid the tyranny of one method to study the phenomena around us. Experimentation has its proper place, but historical and phenomenological methods do also.

In focusing less on belief and more on experience, such days as this Holy Saturday present us with archetypal mystery. In our services and prayers, we use poetry and anagogy to know from the inside out, to use intuition and to share something that arises from the collective unconscious. The divine flows through us and the mystery of the Crucified God is emblazoned in the consciousness of Christendom. In Buddhism, similarly, the tension between clear sight and real suffering is the pivot around which engaged Buddhism revolves.

Anagogical reason must and will never take a back seat to logical analysis and experimentation. To even attempt doing so is to do violence to what it means to be who we are. We must ever strive to tell the story of insight, intuition and experience remembering the difference between our models and the real thing. We dress up G-d in many ways, but that the human condition is always searching for the Supreme Ultimate is undeniable. The diverse manners in which we adorn the Mystery are beautiful, but we need to remind ourselves that it is an adornment.

Beneath all the dressings, the liturgies, and the scaffolding of beliefs erected along-side, what matters is at the heart. It is the raw experience of the Presence of the Light that splits the darkness of death. It is the Light of the resurrected Christ that we await. It is the annihilation of the dual nature of thought and the redemption of the world of creaturely selfishness and the sense of being alone. It is all about remembering who we really are and from whence we really come.

Let us await the Light giving ourselves the time today to also study our own inner darkness.

© Brother Anthony Thomas and The Harried Mystic, 2010. 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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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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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 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.

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

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When studying in the mid-80’s for my doctorate in psychology, we considered it a fact that brain cells are the only ones in the body that do not regenerate. At the time, I thought it an odd feature of physiology given the centrality of the brain over the course of human evolution. It seemed absurd that brain cells would be so fragile and irreplaceable given their adaptive significance.

Two years ago, then 20 years after the doctorate, I took a post-graduate course in biological psychology as a refresher, and everything had changed: a change that is continuing and accelerating. Now, thanks to improved technology such as fMRI (fluorescent magnetic resonance imaging) it is the overwhelming weight of the evidence that neuroplasticity is fundamental to brain physiology. In other words, neural networks and pathways are freshly laid down and altered as we learn and grow and as we are challenged muscularly, emotionally, and cognitively each day.

“Positive neuroplasticity” is the capacity of the brain to regenerate functioning that has been impaired by stroke, dementia and the aging process, severe head trauma, or as a consequence of other CNS ( Central Nervous System)  diseases. There are now cognitive training exercises that neuropsychologists present to patients that can significantly improve diverse functioning, including balance in the elderly, memory functioning, and even offer support in the self-regulation of chronic pain.

All this being said, I am thinking about the alchemical treatise attributed to Hermes Trismegistus, The Emerald Tablet, also known as the Smaragdine Table, Tabula Smaragdina, or The Secret of Hermes. Sources of this document are traceable to 650 AD. It was regarded as the central document of the Hermetic tradition.

In it, one passage has especially captured my imagination as I consider the revelations of brain science.

It reads:

That which is below is as that which is above, and that which is above is as that which is below, to perform the miracles of the one thing.

This ancient alchemical principle adds further framing to a better understanding of the mirroring in human nature of the core nature of the Cosmos. If the “above is as that which is below,” then neuroplasticity is an epiphenomenon of  Cosmic Mind. In other words, what we are learning about the temporal mind tells us something about the infinitely extensive and timeless “neuroverse”.

(more…)

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Russian Orthodox icon of the Transfiguration (Theophanes the Greek, ca. 1408).

Can we replace faith in G-d with direct knowledge? The Perennial Philosophy, or religioperennis, invites us to do just that.

Rene Jean Marie Guenon, Abd al-Wâhid Yahyâ, an important proponent and student of metaphysics, focused his prayerful attention on the esoteric and universal aspects of world religious traditions. He himself, a European, chose to focus on Hinduism, and was later received as an initiate in the Sufi tradition.

Guenon talked about the “mystical infinite” and “mystical zero.” The Infinite embraces all possibilities. Mystical zero is non-being and, so, has in it no possibilities.

We see the sacred infinite in humanity’s use of symbols that serve as windows into mystery. The icons of Orthodox Christianity are a case in point. The venerated images represent portals into divine space & time.

Our acts of bowing before the Buddha or before icons, the power of prostrations to change one’s state of mind, the fingering of the rosary beads, and so many other similar practices, make the Infinite fully present for us. We can imagine infinity, though we are ourselves finite.

The Infinite and the transcendent become concrete in our experience. We feel it. We sing about it. We write about it, and our dreams are limitless tapestries.

We can look out to the cosmos and, through the invention of mathematics, look more deeply into the idea of time, and contemplate the large-scale structure of the universe. We infer physical attributes based on known laws and theory that lead us to reflect on the condition of the universe in its first microseconds.

This is all heady stuff. It does suggest that the Infinite is undeniably within us, wrapped around us, and that it is personal. The mystical infinite is not an abstract idea, just like my love for my family is not abstract. It is self-evident. The Mystical Infinite is deeply personal.

The products of imagination, coupled with our rich observations and imaginative hypotheses and insight, are concrete evidence of the pulse of the Infinite resident in the human spirit.

To see a world in a grain of sand,

And a heaven in a wild flower,

Hold infinity in the palm of your hand,

And eternity in an hour.  – William Blake

The Mystical Infinite emerges continuously in our thoughts and interactions.

  • our capacity to transcend natural self-interest and altruism;
  • our poetry opening phenomena to reveal the Spirit;
  • our works of fiction creating alternate worlds, populated with colorful characters, and through whom we live multiple lives in diverse times and places;
  • our science opening up our minds to ever deeper mystery;
  • our finite and limited senses opening up our consciousness to the infinite gradations and finer nuances;
  • Cantor’s set theory and mathematical work on infinity proving that there are even different kinds of infinity (e.g., the infinity between two real numbers, and the entire set of all integers, etc.) also suggests perception that goes beyond the usual.

The universe is alive, emerged from mystical zero, to complexify, and express itself in many diverse forms of Being. How, then, can there be any doubt whatsoever of the Presence of the Mystical Heart of Infinity.

Love, true agape, is itself sufficient demonstration of a transcendent function. Add to it the powerful emergence of the collective archetypes in every facet of our lives, and we experience the Beloved as lovers. It is not an object of study, but a dance of eternal intimacy.

How beautiful to be conscious and to know without doubt that infinity is within us, among us, and is our true home: our origin and our destination. QED

© 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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Russian Orthodoxy was a nursery for remarkable and controversial mystical practices. One sect, later declared heretical by the Russian Orthodox Church, is known as the “Name Worshippers”.

Their adherents, with early prominent members also making significant contributions to the mathematics of infinity and set theory, held to a discipline of continuously repeating aloud, or inwardly, the name of Jesus. This has connections to the Hesychast tradition and the “Prayer of the Heart” of the Philokalia: ” Lord Jesus Christ, Son of God, have mercy on me a sinner.”

The Western manifestation of such a practice is the Rosary, albeit the prayers recited are greater in number and the process more involved. Hesychasm was bound to run afoul of the Orthodox Church.

Many mystical movements and the mystics themselves have historically been punished or censored in one fashion or another. Meister Eckhart, and extraordinary mystical preacher, was misunderstood and found himself in trouble with the Church. The list is fairly lengthy and includes teachers and adepts among us today.

The rejection is, however, understandable, as the mystic speaks a transcendent language that goes underneath and beyond canonical interpretations, formalisms, and dogma. They speak from a direct lived experience of the scared. Their language is consequentially more often richly metaphorical and visual, sensual, and appears to cut through the many distinctions and debates of exotericism.

There is great value in Hesychasm fro us today in the practice of continuous repetition of simple mantra. It is also a matter of spiritual taste whether this approach will bear fruit for you, but I, for one, find it remarkable in its effects.

Having practiced the “Prayer of the Heart” for many years, I find myself reciting it automatically as a centering prayer, and especially in times of great trouble or stress. In undergoing medical procedures, I catch myself reciting it, or, more correctly, I find it being recited within me.

Some object to the prayer as it appears to place emphasis on one’s identity as a sinner. It’s important to discriminate between the Eastern Orthodox and western meanings of “sin.” In the west, sin is all about mistakes for which one needs to seek forgiveness and attached to which there is a piper to pay. The attributions of sin are more judgmental, and punitive in character.

Here, again the East excels in seeing farther and in more nuanced ways. Sin, for Orthodoxy, is illness. It is recognition that one is in need of re-balancing, healing, and the restoration of a wholesome spirit by the Grace of the Beloved.

How wonderful is that?

It doesn’t surprise me that the Russian mystics of the Name Worshippers would also be tied to the mathematics of the Infinite. The two speak to each other in intimate ways. In these instances, their math was an outer sign of an inner spiritual grace.

© 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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