Natural Math & Beauty

By Tim Sunderman

July 2009

Mathematics is a topic that is almost exclusively understood and taught in terms of numbers. But our living experience of math is much more oriented to our perceptual acuity to proportion. In other words, the understanding of one half can be represented in both of these ways:

1/2

It is because of the dual ways that the brain employs to process and store information. The left brain hemisphere understands math as numbers and concepts as words. Conversely, the right brain hemisphere understands math as visual proportion and concepts as images. It is very holistic and non-linear in its processing of knowledge.

To that extent, there is a ubiquitous proportion that we all understand in that right brain fashion, but is so categorically omitted from math education as to be essentially unheard of. The proportion is called the golden section or phi ratio (the Greek letter Phi). This proportion is found throughout nature. It’s numeric proportion is about 62 percent (specifically .61803... continuing as an infinite non-repeating decimal). But more precisely, there is only one way to divide a line where the shorter segment (about 38%) has the same proportion to the larger (about 62%) as the larger has to the whole line (100%).

Well, that is a very wordy definition that is required to translate into left brain concepts, but the right brain can see it clearly in this diagram:

If we take the two sections of the line and use them as the height and width of a rectangle and overlay them onto images of nature, we see the recursive embedding of this math into almost every living thing as well as weather patterns, solar systems, galaxies, and even in the atomic range.

phi ratio in teeth

Albrecht Durer self portrait 1493

Cnidus Aphrodite 4th c. copy

Not only is this proportion found throughout nature, but it is the mathematics of our very sense of beauty itself. A study was conducted where infants were shown a slide screen upon which were projected two faces. One face was considered beautiful (by common standards), and one was more ordinary. The babies were fitted with glasses that could detect which image they spent most of their time looking at, and almost without exception, the babies spent about eighty percent of their time looking at the so-called beautiful faces (regardless of the race of the viewed face or the race of the baby). This experiment was first conducted in the 1970s, and was repeated many times since then by different researchers. The experiment was set up to investigate whether our sense of beauty is inculcated through socialization or if it is a pre-existing manner in which the brain is organized. Because the infants chosen for the experiment were about three months old, it is acknowledged that that is too young to learn the complexities of beauty. And so, the experimenters were left with the incontrovertible evidence that our sense of preference for facial features appears to be preset into our biology at birth.

But the elusive subjectivity of beauty was too unscientific to leave open-ended. The phi ratio proportions of the human body were long known to art in nearly every culture, and it provided a natural first point of conjecture for a mathematical assessment of beauty. A matrix of phi ratio lines were laid as a grid over photos of faces, and not surprisingly, those faces that are generally agreed-upon as being beautiful had the least deviation from the major points of the grid, whereas ordinary-looking people had greater deviation.

The prevailing theory to explain the observations is almost self-evident ― the greater the deviation from phi ratio proportions, the greater the likelihood of birth anomalies, the less desirable the individual may be for partnering for healthy offspring in the biological, evolutionary sense. And yet, we do not rely on this contrived system of measurements as we make our way through the world and turn our heads to the object of beauty walking by.

It is our internal sense of mathematics as an assessment of conformity to built-in standards of proportions. Just as we do not need to be taught when musical tones are in or out of harmony, likewise our ability to sense proportion is supported by deeply embedded directives (like pleasure chemicals in the brain) to analyze our perceptions. But, like the professional musician who has spent time to hone his or her sense of pitch to maintain perfect tuning, we can reinforce our natural sense of math by consciously comparing proportions, symmetry, horizontals, verticals, and balance. Certainly, this is part of the training of artists, but should also be part of our everyday experience to deepen the creativity of our own lives. Eyes are to be used for more than to keep from bumping into things and sending text messages.