Archive for the ‘mathematical imagination’ Category

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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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.


Exotic Form of Symmetry Makes Real-world Debut

Mathematicians Solve E8 Structure

Mathematicians Map E8

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