by John Hazard
I saw the movie “Signs,” and it reminded me of what is so interesting about crop circles. The film uses the mysterious appearance of these patterns in the cornfields to concoct a Hitchcockian horror thriller, and it suggests that alien beings of evil intent are their creators. I think the crop circles could be alien, but I doubt they were generated by “greys” in the cornfield.
There is a book called Flatland, written by a mathematician named Abbott in the late 19th century. It is the story of beings who live in the second dimension of a mathematical plane, in space defined simply by X and Y co-ordinates. The beings learn that there is another dimension, with an unimaginable (to the XY creatures) Z axis. Abbott describes the way a three dimensional object would appear to a being from the second dimension.
Imagine a sphere that sits in space, and hovers just above a plane. The beings who inhabit the plane can have no awareness of the sphere as long as the sphere does not touch the plane. When the sphere touches the plane (intersects it) the sphere appears to the XY creatures, as if by magic, as a point that becomes a circle. As the sphere moves through the plane, the experience in the second dimension is that of a circle that expands in time, until the equatorial apex is reached, when it recedes in size and passes all the way through, then disappears again, as if by magic.
Abbott’s description shows us a way to think about our own multiple dimensional existence. He implies that human beings might also be surrounded by events which seem to be one sort of phenomena, which might, strangely, but in fact be some other type of event, which could seem magical, or implausible, to ordinary rational consciousness.
The idea that there are more dimensions beyond our comfortable “three space” is not new. String Theory, part of physics, is an effort to craft a “theory of everything.” Mathematics is the language used to describe the ten or so dimensions in this model. We can model string theory using mathematics, but we can’t really imagine an actual physical experience that might reflect (reveal?) the existence of these higher dimensions.
There is another branch of mathematics, also relatively new on the scene, called fractal geometry. Through images of its computations that are drawn by computer, this form of math offers a way to visualize the forms found in nature.
A key element of fractal geometry is something called “self-similarity”. You can easily see how self-similarity manifests itself. Just look at a stalk of broccoli. Notice that the smaller parts look like the larger whole. You can see this self-similarity everywhere: trees, clouds, rocks, even the performance charts of stocks in the market show this principle.
Now stay with me here. Since all things in Nature seem to be fractal, what about consciousness? What might fractal consciousness be? How would it manifest? Is consciousness scalable?
Human beings show creativity. Is creativity an exclusively human phenomenon, or something more universal? Could creativity have a fractal dimension?
Might string theory, with its description of multiple dimensions, have consciousness as a component of these “higher” dimensions?
Which brings me back to crop circles. The hard core rationalists among us (most folks, seemingly) are having a hard time explaining these things. They believe it is all done by hoaxers with rakes who create these images in the cornfield overnight, in the dark, without leaving any footprints. I guess it’s plausible, but only up to a point.
Crop circles have assumed all kinds of shapes, but for the most part, they have appeared as elegant, harmonious, mathematically derived forms. Over time, the crop circle imagery has complexified. There have been astonishingly beautiful patterns that are pure fractal (yes, fractal) mathematics, made from dozens of interwoven circles and executed with computer-like graphical and mathematical precision.
Perhaps there have been hoaxers, playful Englishmen with rakes and time on their hands, who have made some of these crop circle patterns. But realizing these truly complex and precise fractal shapes overnight would seem a near impossibility. It would take days, and daylight, plus the assistance of a mathematician and a computer graphics artist to execute something as perfect as these forms.
It seems to me that these beautiful images created in a cornfield are more like Tibetan sand paintings than anything else. Sand paintings are mandala patterns. They are meant to foster a meditative state of mind. The monks who make them are very careful and meticulous.
So, if hoaxers are creating these crop circles, they must be Tibetan monks.
Or maybe not. Recalling Flatland, recalling string theory, recalling the idea of fractal consciousness, perhaps the crop circles are just what they appear to be: magical impressions in the cornfield that appear suddenly, as the higher dimensional intelligence behind them uses our own graphical mathematics to send us a message.
NASA’s own Voyager project has sent probes into space in the hope that an alien intelligence might find the probe. As a form of communication, the scientists, led by Carl Sagan, have sent a message encoded in universal mathematical language.
Our space scientists could not send a more universal message of consciousness than a graphically rendered image of the Julia set, one of the most familiar forms from fractal geometry, and manifested in crop circles.
If crop circles really are manifestations of intelligence, the message has yet to be deciphered.
That will come. But I doubt they are evil and out to get us, as in “Signs.”
Instead, I imagine the progenitors of these mysterious forms to be more like the monks who make the sand paintings. Such pure manifestations of beauty do not reflect an evil intent. They have meaning as beautiful mathematical objects, because they represent a description of Nature’s integral order. They provoke contemplation and wonder, not fear.