I see life as an adventure of the mind and imagination. Whatever we do, wherever we go, however we thrive, it is our minds that define us as uniquely human, some weird and wonderful thing in this vast and varied universe of ours. The desire to help others discover that is a big part of why I’m a teacher.

We should all be students, all of our lives, because our world grows the more we learn about it, our lives expand and grow richer, our own identities deepen and ripen, who and what we are becomes something more than what it was. It’s easier to believe that about great literature, great music, great art, but I’m going to make the case for something not everyone realizes is so incredibly beautiful.

Mathematics is one of the great products of human genius. It is not the only one, maybe not superior to others that occupy its heights, but neither inferior to them. It occupies a pantheon of human consciousness that includes great literature that can take you on journeys of the imagination into ever deeper and subtler spheres of reality; brilliant music that provides not merely a beat to move to but an intricate language of tightly woven sounds that speaks to our very soul; philosophies and sciences and fine arts of various kinds.

But math is not least among them, and perhaps is most remarkable of all, music that has not been played, science unyoked from the constraints of observable reality or at least stretching an ever-more elastic tether to them. It distills some essence of the universe, of the macrocosms and microcosms, of ubiquitous and eternal forms, speaking a language that crosses cultural and linguistic barriers and historical epochs with a completeness that not even music and the fine arts can attain.

Math is the purified mind, the celestial symphony, a strange and beautiful sphere of human thought, god’s own soliloquy echoing within us. And when applied to the practical questions that assail us, either directly or through its verbal twin of logical analysis, it enables us to do better, to discipline our passions and channel our thoughts, to arrive at wiser rather than more foolish conclusions. It is a vehicle of both beauty and purpose, a tool and an instrument, delicately plucked to play truths too subtle to otherwise hear.

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Due to the appreciation of the fractal images I use here and on the Colorado Confluence Facebook page (, and the interest in fractals and the Mandelbrot Set that that appreciation has generated, as well as the relevance of fractals to my overarching evolutionary ecology of natural, human, and technological systems paradigm (see the essays linked to in the first box at Catalogue of Selected Posts, and particularly The Fractal Geometry of Social Change, for an explanation and description of the connection), I’ve decided to post here a few different video “zooms” of the set.

These are not just visually interesting and beautiful displays: They are the exploration of the underlying patterns of complexity found in nature. The Mandelbrot Set is an extremely intricate fractal generated by iterations of a simple (though mathematically sophisticated) mathematical algorithm. Zooming in on any part of the swirling pattern reveals a degree of complexity equal to that on the larger scale, across limitless levels. I selected such images to represent Colorado Confluence because I believe (as many of my essays on Colorado Confluence explicitly expound upon) that life in general is of an essentially similar nature, swirling patterns of complexity within complexity, and that our challenge, in this human endeavor of ours, is to continue to ever-better align our consciousness and our efforts with these subtle and intricate systems of which we are a part. Enjoy!

Notice the coral-like formations in this one!

There are many, many more Mandelbrot Set zooms out there! Look for the most beautiful ones, and comment here or on the Colorado Confluence FB page with the URL.

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