April is the fourth month, and Bumbastories feels obliged, nay compelled, to acknowledge the number four. You’ll excuse me for all this fourplay, but let’s talk about the four.
Let’s talk about the symmetry of the four. We see it, we use it all the time. Check out these 4-based tesselations from the Alhambra palace in Gbrenada.
An aside about tesselations: A tesselation is a repeating geometric pattern. Somehow they appeal to our sense of beauty. Indeed they are beautiful. A hundred years ago the early Gestalt psychologists first pointed out some of these organizational principles that are rooted or hard-wired in our perception. For instance, the tendency of the mind to automatically group objects together, to distinguish automatically between “figure and ground”. Also to search for the “whole”. More abstractly, I suppose we search for the “main idea”. The mind’s proclivity toward symmetry is another of these universal features of our perception- and what a lovely one it is.
The aesthetic pleasure we receive from a beautiful pattern is perhaps a serendipitous benefit, nay a bounty, of our perceptual wiring. We enjoy order. We love it.
It’s a human thing. We enjoy order and the order of beautiful patterns.
What good fortune (for us) that the sultans and Nasrid potentates who built the Alhambra palace in Granada, Spain were forbidden by Biblical edict to worship graven images. As a result they decorated their palaces with extraordinary geometric tile work, these tesselated decorations – which Bumba had the great privilege to visit and photograph a couple of years ago.
Presented here are some of the four-based tilings. The artisans of the Alhambra also used the three and the six, the eight, and even used five-fold symmetry to construct their opulent decorations. We’ll just stick to the four today.
The four, as a square, represents stability. Clearly it tesselates easily. The cross, the four seasons, the four questions, the four letters of God’s name are not total coincidences the mystics tell us. Personally I think that coincidence is largely underrated. However, the four cardinal directions seems to call to something deep within us. The American Indians have shown the power and beauty of the four directions and the importance of proper orientation in life. So stay on the Red Road, brothers.
And don’t be no square!
MORE ON THE FOUR
The Quatro: the tesselations of the square, the grid. Everything laid out on graph paper, a world made of little boxes.
The usefulness (to humans, not so great for all the other species) of patterns based on the four has been astounding. Pyramids, temples, and skyscrapers arise square and straight from their cornerstones. Roads and cities laid out on grids. Brick by brick, square by square. Maps of distant lands. Maps reaching to the heavens.
Analytic geometry, the great bridge between algebra and geometry – so kindly revealed to us four hundred years ago by the Frenchman Descartes – allows us to visualize patterns and mathematical functions. Equations are made manifest in two or three dimensional space. Functions come to life. Newton’s calculus arises. Motion is finally described via a set of laws. The scientific age, the Industrial Revolution follow. All thanks to poor Rene Descartes, who, while lying sick, poor fellow, on his back in bed and lazily watching a fly walk across the ceiling, suddenly conceived of the grid: which materializes two abstract variables onto the two dimensions we now call the x and y axes. What a guy that Rene Descartes. Here’s to Rene Descartes and the symmetry of the four.