A lot of what the Greeks said about the history of geometry is probably mythical, but let's take their story seriously enough to begin our inquiry in Egypt. What would geometry have meant to the Egyptians? One clue comes from the word itself. Geo-metry literally means “earth measurement” in Greek. In other words: surveying. It makes sense that the Egyptians would have been master surveyors. We know they were master builders. Also, their agriculture depended on the annual flooding of the Nile, and floods have a nasty way of knocking boundary markers aside. A person who could redraw the boundaries after a flood would be a very valuable and important person.
How would the Egyptians have looked at him and his art? To understand this you need to appreciate one fundamental way in which the ancient world was different from ours: science, religion, and magic had not yet separated. Science/religion/magic in the ancient world was a way of thought teaching that underneath the superficial aspects of the world there is an invisible order. The visible world, the world that our senses perceive, is constantly in flux. But the underlying invisible order is eternal. Someone who has been initiated into the secrets of the invisible order can work wonders that common sense would say are impossible.
Science, magick, and religion still teach the existence of an invisible order. But now they each teach it in their own way, and we usually don’t even notice the commonality. Science teaches us that all these apparently solid objects are actually clouds of tiny particles whose motions are controlled by invisible forces. Magick teaches the existence of invisible correspondences between objects and their symbols, and of spirits who can be invoked to manipulate events. And what about religion? William James wrote: “Were one asked to characterize the life of religion in the broadest and most general terms possible, one might say that it consists of the belief that there is an unseen order, and that our supreme good lies in harmoniously adjusting ourselves thereto.”
To us these all sound very different, and it matters greatly to us whether the invisible entity we are dealing with is an abstract physical law like gravity, a capricious spirit like the loa of voodoo, or a universal moral force like justice or the Tao. The ancient mind did not often make such distinctions. Evidence for the existence and usefulness of one part of the invisible order was evidence for the existence and usefulness of all of it.
The Greek mathematician Proclus wrote: “This, therefore, is mathematics: she reminds you of the invisible form of the soul; she gives life to her own discoveries; she awakens the mind and purifies the intellect; she brings light to our intrinsic ideas; she abolishes the oblivion and ignorance which are ours by birth.”
And so, the surveyor who could redraw the boundary lines when all visible markings had been washed away was a miracle worker, just like the healer who cast out demons, or the priest who prepared your body for the afterlife. Knowledge of geometry would most likely have been the guarded secret of a priesthood.
Go up a level in the outline of The Unreasonable Influence of Geometry