The Invention of Geometry

Herodotus, in his Histories, documents the strange and remarkable events of an ancient world that is completely foreign to us.  In some ways, however, he describes a world very similar to our own.

A Faithful Wife

Here is an example of the strange:  In Book II, Herodotus tells the story of an Egyptian king who was blinded by the gods for throwing his spear into the raging Nile, to try to tame it.  The only cure for his blindness was to wash his eyes with the urine of a woman who had always been faithful to her husband.  The king tried the urine of his wife–and it did not work.  Yikes!

He obtained samples from all the women of the royal court; still nothing.  Finally, he went door to door throughout the countryside of Egypt and at long last, after thousands of wives, found urine that worked.  The king rounded up all the women who had given samples into a huge walled city, except the last woman, and burned the city to the ground.  The king married the positive sample giver.

Herodotus does not say how any of the husbands reacted to any of this.

Inventing Geometry

The urine/eye king was Pheros.  Pheros’ father, Sesotris, invented geometry.

In Ancient Egypt, the Nile River basin was a floodplain.  Each year, the waters would slowly rise all the way to the hills, then recede and leave rich fertile soil in the wake.  Farmers would grow their vegetables and grains in these floodplains before the next annual flood.

The water rose and receded to different levels each year, so the surface area under cultivation changed from one year to the next.  When the Egyptian tax assessors went out to calculate property values, they had no consistent guide, because the math to measure surface area did not exist yet.  Each year the fields were different sizes.  Farmers became very adept at arguing down their tax bills by claiming they had less land under production than the previous year.

To solve the problem of taxing the Nile floodplain, King Sesotris invented geometry.  Geometry, a new technology, was a powerful tool for the government in collecting revenue.  It was very accurate.

My Property Tax Bill Just Arrived

I remembered this history about the Egyptians when I got my latest property tax assessment in the mail.  I opened the tax bill and was outraged as usual at the amount, and noticed where it said you could go down and appeal your taxes.

The tax man sat behind his desk in his neat, spare office.  There was a huge map of the county on the wall, with the property lots sub-divided by name, and my small farm was barely a dot on the map.  Facing him on his desk were pictures of his family and a large computer monitor.

I have met the tax man around town several times and I hate to admit it, but he is a pretty good guy.  If you have to have a tax guy, this is the one you want.  Of course, I didn’t tell him that.  I yelled and hollered at him just like everybody else.

When I offered a protest to my tax bill, the gentleman entered my name and address into his computer.  Then he began to list highly specific details about the structures on my property.  He described the dimensions of my barn down to the inch.

“Okay,” he said, “right here, for example, we assessed taxes for the awning on your barn, which is 10 feet, 6 inches, running 30 feet down the length of the barn”.

“That’s impossible!” I said.  “I only used 10 foot boards on that section!”  A barn, even though it is an agricultural structure, is liable to property tax, about the same as a modest house.

“I’m just telling you what the dimensions are,” he said.

I built my barn from scratch.  I know the length and breadth of every board, not just from my handwritten designs on yellow legal pads, but from physical memory, from lifting up each board, fitting it into place, nailing it down, and grabbing the next board.

Sitting in the tax man’s office, I did some mental math on the 2X6 braces on both ends of the awning, and remembered that I left some lip on the overhang.  Yeah, that might account for 6 inches.

“How can you possibly know this information?” I said.

We Have New Technology

The tax man turned the monitor toward me.  On the screen was a stunningly clear picture of my barn from above.  The details were so vivid that we could see the barely perceptible change in color of the awning from the barn roof.  The tax man slowly focused down, and we could see the bottom edge of some feed bags under the awning.  He continued to dial in the focus and I could see the “Lysse” of Lysse and Eckel across one bag, a section of green water hose, and the broken handle on a feed bucket.

The software program provided a digital overlay of the exact dimensions, length and width, in white script, across every surface of the barn.

“We have new technology,” the tax man said, “that allows us to survey properties from a helicopter, and then this software program provides the dimensions, and that calculates square footage of the structures.”  He showed me the calculations on a spreadsheet on the next screen.  “We rate the structure according to type, and this program calculates your tax bill.  It is very accurate.”

I looked at the screen in something between disbelief and shock.

“So,” he said, “did you want to dispute anything about your barn?”

The Ancient Egyptians, with their eye urine and their new-fangled geometry, would be very interested in this technology.

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