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The Mandelbrot Set may offer us a true and terrifying glimpse of “divine intelligence”. It may be a Rosetta of Creation. There is a place just beyond philosophy and outside of mathematics, where only the poet can go. His capacity for awe and sensitivity to beauty cast a light where others find only darkness. Emerson had those eyes. Perhaps you have them too. Can you conceive of the mind for which infinity itself is not a difficult abstraction but a territory of touristic familiarity? The Mandelbrot Set places in our hands a view of the universe which our own science can neither refute nor confirm, for we cannot see the edges of its truth. It suggests that all of the recurring patterns in nature we have so far discerned (the tree, the spiral, radial symmetry, the orbit, etc.) are the consciously duplicated themes of an intelligent and systematic Creation. God’s own fingerprints, if you will. Are these recurring themes merely signs of the Maker’s creative style, or are they the perfect designs which only a perfect designer could have achieved? Faith can accommodate both interpretations. The Mandelbrot Set is quite simply a “little universe”, which humans can inspect from the transcendent perspective of an omniscient god. As we can perceive and marvel over Mandelbrot, so must God see all he has made. And in the same way that there are no insignificant replicas among Mandelbrot’s infinite replications, we are as sovereign in all of existence as we have so often dared to believe.

The Mandelbrot Set also gives us a most salutary social model to follow. Charity, empathy and selfless benevolence would surely be natural to all human relations if only we managed to see ourselves not as individuals, but as incidences of the same divine design, inseparably bound brother to brother by a common beauty. I may suffer, but never alone. For in this system, I am sustained by others and there are also those whom I sustain. All suffer and exalt, all give and draw courage, if not when I do, then just as I do. I can no longer see myself as an individual in any prior sense. I have broken free of the myopia of selfishness, which had limited my vision only to the matters of my own longing and disappointment. I am one member in a Community of Survival, with both a stake in and a duty to the wellness of all the persons I shall ever meet.

Below, I have linked to a Web site where it is possible to experience and navigate through the Mandelbrot Set yourselves. Nothing less should satisfy you. Infinity is a difficult thing to serve descriptively, especially in words. What does it mean to “go on forever”, as we are told time has and will, as we are told numbers do? That’s just swapping out one intractable abstraction for another of a different name. There is still no way to touch it. Man’s experience with time is laughably brief, even as a species. And very large numbers, when unconnected to tangible things, are only digits on a page, flat, uninspiring and evocative of nothing. Even the concretization of huge numbers at the hands of cosmologists scarcely raises their value as windows to infinity. Knowing that galaxies are as numerous as the grains of sand on a beach fires the imagination, but doesn’t really steer you in the right direction. The problem may be the linearity of our thinking. We like to count things; and counting is both the definition of the finite and the antithesis of the infinite. To free your mind from this trap, think of infinity not as a destination, but as a process — without end. Consider a number, and then strip it of all its self-referential meaning. Six is not one more than five, nor one less than seven, but a “thing” whose only observable attributes are that it is exactly like every number in just one essential way, and connected to all numbers by a process. It is the immutability of this process which accounts for the essential sameness. In prior example, the process is simple integer counting (+1, +1, etc.). In the Mandelbrot Set, the process is the perpetual iteration of a deceptively concise equation (Z=Z2+C).

As you will soon see, even this limited tour of the Mandelbrot Set begins to cavort with extremely large numbers very quickly. You will be staring at objects which are billions, even trillions of times smaller then the original image. Or, said another way, you will increase the size of the original image from about 2 inches to more than the size of the sun. As you play, remember that (but for the limitations of the server where these images reside) you could spend the rest of your life zooming ever-closer, and still not meaningfully approach infinity — not in the mathematical sense. But you will surely taste it. Enjoy. Tour the Mandelbrot Set

This entry was posted on Tuesday, October 31st, 2006 at 1:58 pm and is filed under 2001, Religion, Philosophy, Advanced Mathematics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.