The Flatiron Building, New York City
hat crosses our minds when we hear the word Structure
? I imagine beams and girders, trestles and Tinkertoys
. Then I dig deeper and all its other meanings tumble forth. Structure means so many things.
But they all reflect the way pieces make up some whole entity: Molecules are made of atoms, symphonies of notes, skyscrapers of girders ... You and I are made of cells. Structure might mean the thing itself, or the way we put parts together, or relationships among parts.
And we soon realize that all whole things are structures. The Greeks did have a word for the one thing that was not
a structure. The word was stoicheion
. A stoicheion was the imagined least building block of any thing. Physicists struggle to know what the stoicheia of matter really are. Itís now clear that theyíre far less than the atom -- maybe tiny strings -- we donít yet know.
But let us stay in this world thatís palpable to us. Every object we can see, even with the most powerful microscope, is built of pieces. Everything
we know is a structure in our wholly built world. Built by humans -- built by chance or built by God -- built by poets, composers, biochemists, artists -- by beavers and by birds -- by evolution, by gravity, by heating and cooling.
And, like a Russian nesting doll, structures lie within structures within structures ... A society is built of families, and they of individuals. Individuals are made of organs made of cells made of molecules made of atoms, made of ... what?
Yet, while structure is universal, it is neither trivial nor simple. Perhaps by looking at structures of many kinds and forms, we might gain a better sense of our own structure. For its form is elusive. We are physical structures, but we are also mental structures. And the two are interwoven.
Thereís more: We may think that insects and crustaceans are the only creatures with exoskeletons. But you and I also have a very real exoskeleton. A lobster cannot live without a structure of shell holding it together. We too would quickly die without our exoskeletal structures of clothing, shelter, food supply ... Strand a human in the wilderness, and that poor soulís first order of business will be to reconstruct some minimal technological exoskeleton. When such situations have arisen, thatís always been a daunting task. For yours and my exoskeletons are vast -- cities, farms, sewage systems, factories. They also include art, books, music, and our many tools of play.
So with that in mind, we shall look at the structures that serve us. As we do, weíll try to keep a question in mind: What do a machine and a motet have in common? How are crystal, biological, organic, and mathematical structures kin to one another? Let us try to extract the essence of this built world
that we all share.