Monster Flatland Lines Sense Something In Their Path

I was surveying the goings on of Flatland below, and encountered these lines. It could have been one line folded in on itself or, more likely, two lines cooperating with each other. Whatever it was, it must have been hungry. I knew it could sense my presence, through gravitation or other invisible forces. It seemed […]

Rectilinear Beginnings

Looking from left to right, one sees parallel lines and right-angle corners. As we get into the white field, the black horizontal line turns into a blue/white interface and starts to sag. In the blue field, there is a white dot and a larger black one. One could say that the right hand side of […]

Lines Part 2

I added sfumato to yesterday’s skeleton of lines, theoretically combining Leonardo DaVinci and Michelangelo’s choices in painting: soft, gradual changes in tone, with no outlines of Leonardo, and definite outlines of Michelangelo. There is an inside-out character to this part of the study compared with the initial stage:

Lines Part 1

I never realized that Leonardo DaVinci (L) and Michelangelo di Lodovico Buonarroti Simoni (aka Michelangelo (M)) knew each other. They didn’t get along too well, apparently. From what I’ve read, I would rather have known Leonardo. He was so curious about everything. Michelangelo was more competitive and a bit of a snarky fellow.* L and […]


The biography of Leonardo DaVinci that I am reading, has a passage that tells about his revelation that there are no lines in nature. Leonardo explained that there is an “infinite gradation of shades and blending of them, which does not allow precise borders.”*  Apparently, Leonardo studied and wrote quite a bit about shadows and […]