I recently had the chance to catch the BBC-produced The Human Face, a documentary series narrated by John Cleese with exemplary sidekick Elizabeth Hurley.
Among the ideas that stuck with me was the theory that the brain memorizes each face based on an exaggeration of the unique qualities it possesses. Which is to say, the "familiar" memory is more of a caricature than a photograph. People may indeed recognize caricatures of familiar faces more readily than they do accurate sketches, or even photographs. The theory goes that the uniqueness of each human face is based on very subtle differences, so the brain helpfully exaggerates those differences when storing facial memories. Logical enough.
The program went on to talk about the mathematical Golden Ratio, or Phi. Humans have employed it for a host of pursuits, from heavenly architectural design to precise painting composition to, it's been said, structural form in Mozart sonatas. Even the measurements of wallet-sized things (credit cards, drivers licenses, and so on) seem to approximate Phi. We take it with us wherever we go. Why? Mostly because mom nature has apparently employed the ratio in everything from the spiral patterns on flowers and pine cones (13 spirals diverge from the center of the pattern in one direction while 21 diverge in the other), to the relative lengths of bee body parts and human finger bones. This is old news to Fibonacci fans, but I was new to most of it, and I learned some things from the documentary and a little research on the web. The ratio has a curious mathematical property I tripped over on a calculator:
1 / 1.618 = .618
...so to calculate the golden ratio based on one, you get the same decimal part whether 1 is the lower or the higher number in the ratio. More generally:
1 / 1 + Phi = Phi
That's a recursive definition and .618 is a rounded-off version of the decimal part, to which there is no end and toward which a basic mathematical series trends: The Fibonacci series (where each number derives from the sum of the two preceeding numbers) tends toward this ratio along its entire length: 8/5, 13/8, 21/13, and so on. Turns out there is even more mystery to the ratio since it can be defined in multiple ways.
So how does this apply to the human face? Well, one section of the documentary explores the idea that to whatever degree there is universal human beauty, it corresponds to a template based on Phi. The relative width of the nose and mouth of a beautiful person is Phi, their eyes are located a Phi's length along the entire length of the head. And so on. A doctor in the series extended the ratio (which serves as the basis for "ideal" rectangles, triangles, hexagons, decahegrons...) into a template to which you can underlay the face of yourself or your favorite hottie-or-nottie. Creepy.
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