Hey, it’s April! Spring is here! The robins are singing, and the bells are ringing for me and my gal. It’s time to “spring in the air and jump in the lake”, as Groucho would say. But Grouchoisms aside, and, now that I think of it, T.S. Elliottisms and his “April is the cruelest month” stuff aside too…….All these things aside, and all things considered, Spring is undoubtably the most beloved of the four seasons. If they took an opinion poll, like a Gallop Poll, I’m sure Spring would win hands down – at least in the Northern Hemisphere. In the Southern Hemisphere, tho, their hands would be up. No matter. In whatever your hemisphere, Spring is a time of rebirth. Hurray. We get another go-round. Another chance to get things right. And we sure need it. Happy New Year!
April being the fourth month, Bumbastories feels obliged, nay compelled, to acknowledge the number four. Yes, I know, we’ve talked about the four before on Bumbastories in our March Through the Numbers section, (see it in the Numbers Games is Here Category in the Header). But anywaze, here it is again: the FOUR. That’s right. Here comes a re-post. that you could click on. What for? you ask. Couldn’t we Fast Forward? Yikes! When is this four play going to stop?
The symmetry of the four. We see it, we use it all the time. Bumbastories continues with the count down, the walk through the numbers. Today we feature the four, the quatro.
When we look at a tesselation, a repeating geometric pattern, we see, we organize it, in quite predictable ways. A hundred years ago the early Gestalt psychologists first pointed out some of these organizational principles, these intrinsic patterns of perception: the tendency of the mind to automatically group objects, to distinguish automatically between “figure and ground”, and to search for the “whole” (which is more than the sum of its parts, they remind us). More abstractly, I suppose we search for the “main idea”. The mind’s proclivity toward symmetry is another of these universal phenomena of 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. As living creatures we already defy the law of entropy: we actually decrease entropy, we organize atoms and molecules while we’re alive – into some amazingly complicated and awesome patterns, I may add. That lovely spiral to the right is a model of a DNA molecule, based on the five-fold symmetry by the way.
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 (they used the eight a lot but that’s just two fours) 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, lying on his back in bed watching a fly walk across the ceiling, suddenly conceived of the grid: defined by 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.
BUMBASTORIES APRIL SINGALONG
Two songs to sing along with. Don’t worry, only one song need be picked.
First, Dylan’s I Shall Be Released
And/or Hudie Ledbetter’s Irene Goodnight
ANOTHER SCIENCE BOOK
Atom: Journey Across the Subatomic Cosmos is another gem by the late, great, and amazingly prolific Isaac Asimov. It will teach you a lot of science. It’s good for you. Although written back in 1991, the book is up-to-date enough for most readers. The history of physics, starting with the early Greeks up through the quantum revolution is presented with Asimov’s characteristic ease of style. The sub-atomic particles are described at length – which is very important for those of us who don’t know quark from shinola! As for nuclear fission, fusion, and then the quantum world, Asimov, as always, explains things simply and with almost no math. He likes to provide a lot of historical context, as he traces the development of the major concepts in physics. It’s a history lesson as well as a physics one. The clarity of his language and the sincerity of his desire to teach and convey his knowlege to others is Asimov’s hallmark. Atom: Journey Across the Subatomic Cosmos is an excellent book. If it’s not in your public library, ask for it. And meantime pick up another Asimov book. It’s a near certainty that the library has at least a couple of other Asimov science books. What a writer. What a gift.