For Leap Day 2020 I booked an afternoon at a tattoo shop in Minneapolis for myself, Emily, and two friends. It was the first tattoo for Emily and for me. A friend who had worked with me for about a decade named the artist when I asked for the best. We all wanted simple line drawings, no color. Emily had a design in mind. I told the artist I was “trying to figure out some sort of mathematical thing related to circles and waves or something.”
What I sent him was the Fano plane: seven points and seven lines, drawn as a triangle with a circle through the midpoints of its sides. I called it a snowflake, described it as a twisted sphere whose tips were knobs to torque the center, and suggested it might look good drawn like an electronic trace. The picture came off a paper about the E8 lattice that I had printed out and did not understand. It had a Fano plane on one page, and that was the part I wanted, without the arrows and with smaller points.
I wanted the smallest, simplest thing that stood for universality and for the number systems themselves. Seven points and seven lines with nothing left over, tied to the octonions through their multiplication diagram. To me it stood for the many sides of one. I wanted something that said timeless math-love, and this was it.
He wrote back that the other designs were fine, but he did not do tattoos like that. Geometric work was not his thing. Was there something more image-based I had in mind?
I asked for the absolute simplest version instead, and tried to say what I was actually attached to:
The only part that matters to me is the general shape of a circle surrounded by a triangle (ideally, with the full 6 “line-ish” things and one “circle-ish” thing) – it wouldn’t need to be straight lines that make up the shape
The lines could be scraggly. They could be built from smaller images, or filled in. What had to survive was which lines met which points. He asked what subject matter I wanted fitted into the geometry; he needed a push in a direction.
So I offered a fallback that might have been the same problem in disguise: the letters RCHO, in blackboard bold, the doubled-stroke letters mathematics uses for the reals, the complex numbers, the quaternions, and the octonions. Lettering he could do all day long. I sent a sketch, asked for the letters to stay open and unfilled if that was workable, and left the rest to him.
The night before the appointment he sent drawings for everyone. Mine was a Fano plane after all, in his hand: the triangle, the circle, three lines through the middle, and seven small open circles where the points sit.
Pretty sweet fano plane you got there :-D
That is where my mail stops and the photographs pick up: wrapped in plastic the same afternoon, then healed, on the inside of my forearm. The triangle, the circle, three lines through the middle, and seven small open circles where the points sit. It healed into exactly what he sent.