I don’t know why it surprised me so much that the snowflakes in my digital night photos were hexagonal. But they were, and it did, and the six-sided shape has since taken over a corner of my mind. It is everywhere in nature, in honeycombs and on turtle shells, crystals and snowflakes. The cooling and cracking of lava over centuries has created towering six-sided basalt columns in Northern Ireland, Washington state, and other places around the world. The more you look for polygons in nature, the more they pop out at you in the cracks in the land or the veins of leaves.
Bubbles are spherical until they meet up with other bubbles and economy of space turns them into hexagons. Plant cells have a strong honeycomb-like structure. We borrow this marvel of engineering for our sundry purposes: chicken wire and soccer balls, hex nuts and space telescopes. Geodesic domes. Beautiful in its efficiency, there is an aura of universality to what bees design naturally, without conscious thought.
In the mid-19th century questions traveled back and forth between Charles Darwin and his friends: Does the honeybee comprehend the geometry of the hexagon? Does it have some sort of instinctive genius? Is the honeycomb just a matter of cylinders being squished into submission? Darwin ultimately explained the process as one of repetitive motions—simple actions and feedback from simple sensations. There was a lot riding on this. Explaining how a bee was able to create a structure that was “absolutely perfect in economising labour and wax” was pivotal to his theory. The swarm that made “the best cells with least labour” would transmit their “newly-acquired economical instincts to new swarms, which in their turn will have had the best chance of succeeding in the struggle for existence.”
The honeycomb is so elegant that we just can’t resist trying to apply the design to our own species. The “Central Place Theory”, a theoretical model of the distribution of our population, is the result of this deductive reasoning. It goes something like this: Assuming that the honeycomb is a natural and universal pattern of constructed growth, our towns and cities must then exhibit it. See exhibit A – proof positive!
Working in the other direction, that is, using the efficient hexagonal pattern to design a community, Tessellation (or tiling pattern) theories of housing abound.
Several living arrangements that employ the honeycomb are the “honeycomb cul-de-sac” design, complete with central gardens; the tessellation plan for efficiency in slum housing; a luxury stacked honeycomb-façade apartment complex with a pool on every balcony. The perfect honeycomb speaks to our yearning for order, our need for control.
My initial explorations into the puzzle of the hexagon began with water. With its elegant covalent bonding, it is surely implicated in this human/hexagon attraction. Ice is a honeycomb-like lattice of hydrogen and oxygen, a direct outcome of shared bonds. Each O atom is surrounded by four H atoms, and weak bonds form between adjacent molecules. The result: a crystal formation that is less compact than liquid water and, yes, hexagonal in structure.
We look to the patterns of nature for comfort. We look to them for order. We borrow from them to create designs on the land, and on paper. We try to understand them in our terms, not the honeybee’s. Well before Darwin, in 36 BC, the Roman scholar Marcus Terentius Varro came up with the “Honeycomb Conjecture,” the idea that a hexagonal grid is the most efficient way to divide a surface into equal cells with the smallest total perimeter. It wasn’t until 1999 that University professor Thomas Hales came up with mathematical proof of what the bees knew all along. The same mathematician spent years of his life proving another vexing assumption, “The Kepler Conjecture,” which came about 400+ years ago when Sir Walter Raleigh wanted to know the most efficient way to pack cannonballs in the hold of a ship, and astronomer Johannes Kepler was called on for expert help. The “Kepler Conjecture” led directly to an early version of atomic theory.
And so one thing leads to another. Our ability to see conch shells in the heads of sunflowers, mare’s tails in the sky, branching in trees and streams and rivers, leads us into computer calculations that unlock the language of nature, each new answer leading to a fireworks display of new questions.
We look to nature for inspiration, and engineer our cannonballs into ships, our voices into cables, our bodies into space. It’s a numbers game of enormous proportions.
Here’s hoping we win.
“Philosophy is written in that great book which is constantly open in front of our eyes–I mean the universe–, but we cannot understand it if we do not learn first the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometric figures, without whose help it is impossible to understand a single word of it; without which one wanders in vain through a dark labyrinth.” Galileo, 1623