“Hello, sailor! What’s that?”
Marilyn Frack creaked as she leaned forward in her black leather outfit to peer at my wrist, or rather at what was on it.
“It’s a nautilus,” I said. In fact, it wasn’t: it was a watch with a ceramic nautilus-shell pattern as its face. But pragmatics allows for brevity.
“It’s naughty lust?” she said. “Fie! We’ll have none of that!” Her coquettish smile and tone made it clear she really meant “nothing other than that.”
“Indeed,” I said, trying to be as dry as I could, “we will have none of ‘fie.’ Although the spiral of the nautilus shell is often thought to be a golden spiral, expressing the ‘golden mean’ ratio, phi, it is in fact a logarithmic spiral.”
She straightened up a little. “Which means?”
“Which means that each chamber is geometrically similar to each other chamber – the same proportions but different size. An infinite logarithmic spiral will look identical at any magnification.”
Edgar Frick wandered up; I hoped his presence would detach his paramour from me slightly. Marilyn may not have a grip quite like that of the nautilus’s tentacles, which cling so tightly to prey that they will sooner rip from the nautilus’s body than from the prey, but she is indefatigably flirtatious.
“Do I hear something about a Mandelbrot set?” Edgar said.
“Another fractal geometry,” I replied.
Marilyn creaked up against Edgar’s matching leather kit. “He’s trying to nottle us.”
“Would I be so shellfish?” I protested.
“Look, darling,” Marilyn said, showing Edgar my watch, “it’s an endless succession of similar chambers.”
“Like our last vacation,” Edgar said.
“That did spiral out of control.” Marilyn paused. Then smiled.
“The nautilus,” I said, returning to my watch if possible. “A free-swimming cephalopod. It can adjust its buoyancy and propel itself by intaking and expelling water.”
“How did they come to name a weight machine after it?” Edgar mused.
“The machine controls resistance with the aid of a spiral cam,” I replied.
“So it’s not because you really have to shell out for one,” Marilyn said. She turned to Edgar. “Luscious, how much did ours cost, with the after-market leather add-ons?”
“About as much as a nuclear submarine,” Edgar replied. He knew that I knew that he knew that the first nuclear submarine was the USS Nautilus, just one in a series of many vessels named the Nautilus, including not only the submarine in Jules Verne’s 1870 novel Twenty Thousand Leagues Under the Sea but its namesake, the first actual practical submarine, launched in 1800.
I could see the wheels spinning inside Marilyn’s head. I almost broke into a cold sweat as I considered she might be about to launch into a line of discourse relating to rigid cylinders and seamen.
But instead of a cute observation, she made a rather acute one. “Nautilus comes from the Greek for ‘sailor,’ yes?” Edgar and I both nodded agreement. “So these various submarines called Nautilus are sailors containing sailors, recursive, the smaller inside the bigger, but similar and repeating. Vaguely reminiscent of a nautilus shell.”
“Yes,” I said, relieved and impressed. “That’s a rather entertaining line of thought. And submarines probably have Nautilus machines on them for exercise. And of course they have other features like nautiluses: buoyancy and propulsion, and perhaps the inner structure…”
“A long succession of chambers with seamen in them,” Marilyn said, leering at Edgar and sweeping her hands over him.
…”Look at the time,” I declared, glancing perfunctorily at the hands sweeping over the nautilus on my wrist. And escaped.