Nature, Science, & Mathematics: August 2002 Archives

The Fractal Feast

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I mentioned in the very first of my blog impressions that I was interested in fractals. More than interested, much of my dissertation centered about fractals and non-linear dynamics. So, while I'm no expert, I do like them and so I thought I'd tell you about the most perfect (and my favorite) fractal--the Eucharist.

This is not meant as sacrilege, nor even as metaphor. God thought and imagined the fractal before we could ever name it, and little wonder that He should use it. What precisely is a fractal? Well, there are lot's and lot's of possible definitions--"a geometric figure with a non-integral dimension," for example. There are more technical definitions, and there are more informal definitions. For my purposes, I've settled on the midground definition of "an object or figure that exhibits self-similarity." Now admittedly, this is loosely true of all fractals and only completely true of perfect fractals. A perfect fractal would be exactly the same at whatever magnification you viewed it. Let me see if I can explain. Take an equilateral triangle. Now, from each of the three side, draw another equilateral triangle with base exactly one-third the length of the original base (however, in your drawing, you will exclude or erase the portion of the original base that is now "covered" by the new triangle. (You now have figure that looks a bit like a six-pointed star.) Now from each of the sides of the new figure, draw a new equilateral triangle with base one-third the length of the second, one-ninth the length of the first. I think you get the idea.

Consider now the Eucharist. It is the complete body and blood, soul and divinity of Jesus Christ, our Lord and Savior. You cannot get a "part of the body" or "some of the blood" or a "portion of the divinity" or a "fragment of the soul." In consuming the Eucharist we receive the complete Savior. Now, on some occasions, the priest may have to break a host in order to assure that there is enough for everyone. Does this broken host represent a part of the body of Christ. When he breaks it, do we only receive the body and not the blood, or the soul and not the divinity? Or do we receive half of each? No. We all know that no matter how small the fragment of the host, so long as it has been properly consecrated, it contains the fullness of the body and blood, soul and divinity of Jesus Christ. In fact, this is true down to the smallest possible fragment that could still be recognizable as bread (probably not true on an atomic level, although I'll leave that speculation to quantum physicists and others better qualified than me). But certainly, so long as the material is still recognizable as bread, it is the Body and Blood of Jesus Christ. (This is why some of the cleansing techniques I have seen in some churches approach blasphemy. It is also why the plumbing used in the sacristy to wash the vessels of Mass was (at least in the past) grounded--that is, not channeled into a sewer system. If we are at all serious about our faith, this should still be mandatory, but I don't know if it is.)

Everything written above about the consecrated host is also true of the consecrated wine. The smallest sip contains the exact image of the entire cup. There is no fragment of God that we receive. Indeed, the Eucharist is the perfect fractal, retaining to the smallest detail the exact image of Jesus Christ to all who consume it. It is awe-inspiring to contemplate this essential mystery of the Eucharist. It is the perfection of God's plan and in it one could read a message of Divine Love. No matter how little you receive, you receive all there is to receive. In this sense, the Eucharist is a perfect fractal feast. The person of God is complete in every part of every element, down to the smallest recognizable fraction of that element. This mystery deepens as you think about it and it leads you into an understanding of the pervasiveness of God. He is all in all in all. In everyone who consumes the Eucharist, every portion of that person (the entire person) is divinized by contact and intermingling with the Divine. And there is no end to this. As once said, in saecula saeculorum.

Of course, all of this is speculation and metaphor, and if incorrect in any way, I gladly accept all correction. Thanks.

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This page is a archive of entries in the Nature, Science, & Mathematics category from August 2002.

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