Sunday, June 10, 2007

In The Eye Of The Encoder

I stumbled on two separate stories this week that struck me as too coincidental to ignore.

The first was an article in Discover about a California plastic surgeon's realization that beauty seems to be related to mathematics. In this case Doctor Stephen Marquardt, seeking to perfect the results of his surgical facial reconstructions, went about trying to uncover what it is that “beautiful” people hold in common. What Marquardt discovered was the "eerie proportional coincidences" that kept recurring in the ratio of the width of beautiful people's mouths to the width of their noses (1.618), of the width of their noses to the tips of their noses (1.618), or that the triangle formed by their noses and mouths was a strangely recurrent perfect acute golden triangle.

If you are a mathematician you might recognize those ratio and terms as being significant in the natural world. In fact, that ratio (which has been more accurately calculated as 1.61803398874989484820458683436 ... but I digress) is defined as a “unique ratio such that the ratio of the whole to the larger portion is the same as the ratio of the larger portion to the smaller portion. As such, it symbolically links each new generation to its ancestors, preserving the continuity of relationship as the means for retracing its lineage.”

This ratio, and the aesthetically pleasing Golden Triangle derived from it, shows up in human-designed objects like the pleasant-to-the-eye, commonly accepted shapes of rectangles used to frame pictures, or the triangle-faced sides of the Great Pyramids – placed there by intentionally by their human designers. But what is more notable is that humans design such things with this ratio in mind in the deliberate attempt to mimic its appearance in the natural world in such disparate locations as the infamous mathematical Fibonacci Sequence, the spirally expanding geometry of the Chambered Nautilus shell, the similarly appealing geometry of flower petals, or in the famously “perfect” proportions of DaVinci’s Vitruvian Man.

It seems, in other words, that this mathematical concept not only keeps showing up in our natural world but that, when it does, it invokes in us a sense of pleasure that we have come to know as beauty. Notice however that the real seat of what we call beauty is not, as we have been told ad nauseam, in the subjective “eye of the beholder.” It is really an objective trait built into the object which we, as observers, are only wired to recognize – even if we can’t say why.

I wish I could claim this as some kind of powerful observation that I have just uncovered but this is not a new idea. I can’t find the source of the following for the life of me but it has been noted that …

Plato believed in the existence of absolute truth, goodness, and beauty. Beyond our fuzzy and confused view of things is the reality of eternal standards and structures. There are many (more or less) good things; there is one absolute good. There are many (more or less) beautiful things; there is one absolute beauty ... The highest idea or form -- the form of all forms -- is the idea of the Good itself. According to Plato, this idea is not an inert structure, but has power. Plato compares the power of the Good to the power of the sun. The sun illuminates things and makes them visible to the eye. The absolute good illuminates the things of the mind (forms) and makes them intelligible. The good sheds light on ideas. What exactly is the idea of the good? Plato is reluctant to say. The vision of the idea of the Good is, according to Plato, too much for human minds. It is possible that the idea of the Good is the idea of absolute order. Order is what makes beautiful things beautiful, just persons or cities just, true speeches true. (truth is the order or correct arrangement of words, putting words together that belong together).

There are areas of his philosophy where Plato diverges into wildly anti-theistic (and therefore anti-Christian) concepts – but this is not one of them. Plato lived a few hundred years before Christ so he cannot be blamed for denying Him specifically. He may well have been aware of, and influenced by, Jewish thought. But what Plato did make an effort to do was seek the truth. And, at least in this category of thinking, he seems to have found it.

Substitute God for Good in the quotation above and you find an undeniably Christian definition of Truth, Goodness, Beauty and Order as having their source in the mind of God.

If, as Galileo Galilei is reported to have said, "Mathematics is the language with which God wrote the universe," it becomes easy to see why a California plastic surgeon so easily uncovered the connection between mathematics and beauty. He is not the first to do so.

The idea that mathematics has divine origins was quantified by Leonhard Euler who, upon discovering the following “identity” labeled it as “proof that God exists.”

Though I would never be tempted to use this as some kind of practical apologetic argument, one does have to wonder why three seemingly unrelated numbers (pi, the ratio of a circle’s circumference to its diameter; i, the imaginary number and the square root of -1, and; e, the natural logarithm so prevalent in calculus, probability and limit theory) would have any such relationship to one another. These are irrational numbers, not invented by mathematicians, but discovered by them as constantly popping up in every mathematical and scientific nook and cranny they explore. Indeed, physicist Richard Feynman called Euler’s identity equation "the most remarkable formula in mathematics."

Even the renowned atheist Bertrand Russell expressed his sense of mathematical beauty in his Study of Mathematics, in Mysticism and Logic, and Other Essays with these words:

Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry

How is it that mathematical concepts like these serve to describe the world so well? Only if beauty is really in the mind of the Encoder – an objective reality inherently built into the makeup of the universe itself.

(This is a topic for which a powerful argument has already been written. If you want to delve into it more, check out “A Meaningful World: How The Arts and Sciences Reveal the Genius of Nature.”)

This, like many other qualities of the universe, is so transparently obvious we have come to take it for granted. And this brings me to the second story that caught my eye -- a correspondence by James Emery White in which he addresses the idea that the trappings of the distracted life in which we are all so caught up is causing us to lose our ability to appreciate the inherent beauty that surrounds us in the creation.

White tells the story of a social experiment staged by essayist Gene Weingarten and The Washington Post at 7:51 a.m. on Friday, January 12, 2007 in the middle of the morning rush hour at the Washington, D.C. Metro at the L’Enfant Plaza station. There, 39-year old Joshua Bell, one of the finest classical musicians in the world, donned blue jeans, a tee-shirt and Washington Nationals baseball cap, put his $3.5 million Stradivarius violin on his shoulder and began to play some of the most elegant music ever written. You can see a short video of his performance here.

Over 1,000 people passed by Bell that morning -- key words, "passed by." Only six or seven of those who entered the Metro station where Bell was playing even offered him a passing glance. In his comments on this, White references British author John Lane, whose 2003 book, Timeless Beauty, speaks to "the loss of the appreciation of beauty in the modern world. People still have the capacity to understand beauty, he said, but beauty has become irrelevant to them."

While we have good reason to address the lack of respect for Truth and Goodness in our culture, it seems that we are less adept at understanding, or even noticing, that same culture's lack of respect for Beauty. Everything we value in this life has its basis in one of these three or their combination. Even the technological gadgetry that so easily distracts us owes its design to the mathematical order, trustworthiness and beauty of the Grand Designer's mind. We would do well to stop, look, and listen to the art, music, literature and poetry that derive from the same fundamental Source as our iPod. And we would do well to honor the beauty of this creation with all the respect, reverence, awe and honor it deserves.

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