The Geometry of Thinking
The Greek word, “geo”, like the Germanic word, “earth”, probably meant the hard, flat surface, the dirt and rocks beneath the dome of the heavens. The Greek “cosmos”, the German “world,” and the Latin word from which “ecumenical” originates, were words for the inhabited earth, the ordered and rational which we'd managed to wrestle from the unconscious void, the chaos beyond our borders. Geometry is a Roman word, not a Greek one, and they used it to mean the measure of the civilized world, the boundaries and boxes, the walls behind which order was maintained and preserved. Pythagoras didn't have a word for geometry. Instead, he used the words for number from which “arithmetic” originates, and learning, which was the original meaning of “mathematics”.
Ancient Greece had no use for geometry in the Roman sense. Their domain was a cosmos of water surrounding islands which each functioned as independent worlds. “Cosmos” comes from the Greek, and the Romans seemed to have little use for the word. Greece had a notion of independent worlds coexisting within a larger cosmos. Rome understood and acknowledged only the one world, which grew more expansive as its empire grew. The Greeks discovered while the Romans conquered. The seafaring peoples of Greece had “pilots,” which the continental peoples of Rome replaced with “commanders,” and commanders were the same whether at sea or on land. The cosmological world view of the Greeks was corrupted by Roman geometry.
Richard Buckminster Fuller labeled his geometrical discoveries “synergetics,” or, “energetic-synergistic geometry.” It's an awkward term with religious overtones, and is, I think, in large part responsible for the marginalization of its readership. Fuller thought he was rewriting Euclid for the space age, replacing primitive concepts like “up” and “down” with “outward” and “inward”, and the earth-bound concept of “foundation” with the concept of “structure” which didn't rely on a flat earth, perpendicular angles, parallel lines, and a single direction for gravity. He could have called it “Fuller's Elements,” but that would have been presumptuous. He might rather have retreated to Pythagoras and dispensed with all the specialized terms, forgoing the title for the subtitle: Explorations in the Geometry of Thinking.
Ancient Greece had no use for geometry in the Roman sense. Their domain was a cosmos of water surrounding islands which each functioned as independent worlds. “Cosmos” comes from the Greek, and the Romans seemed to have little use for the word. Greece had a notion of independent worlds coexisting within a larger cosmos. Rome understood and acknowledged only the one world, which grew more expansive as its empire grew. The Greeks discovered while the Romans conquered. The seafaring peoples of Greece had “pilots,” which the continental peoples of Rome replaced with “commanders,” and commanders were the same whether at sea or on land. The cosmological world view of the Greeks was corrupted by Roman geometry.
Richard Buckminster Fuller labeled his geometrical discoveries “synergetics,” or, “energetic-synergistic geometry.” It's an awkward term with religious overtones, and is, I think, in large part responsible for the marginalization of its readership. Fuller thought he was rewriting Euclid for the space age, replacing primitive concepts like “up” and “down” with “outward” and “inward”, and the earth-bound concept of “foundation” with the concept of “structure” which didn't rely on a flat earth, perpendicular angles, parallel lines, and a single direction for gravity. He could have called it “Fuller's Elements,” but that would have been presumptuous. He might rather have retreated to Pythagoras and dispensed with all the specialized terms, forgoing the title for the subtitle: Explorations in the Geometry of Thinking.
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