Great fleas have little fleas
Upon their backs to bite ’em,
And little fleas have lesser fleas,
And so ad infinitum
And the great fleas themselves, in turn, have greater fleas to go on;
While these again have greater still, and greater still, and so on.
Augustus De Morgan, British mathematician and logician (1806 – 1871), from A Budget of Paradoxes (1872)
The concept of infinity is hard to get your head around. Trying to come up with a visual representation, I think of the kaleidoscopic “event horizon” scene in the film 2001. Or more recently thinking of Rey, in The Last Jedi, confronting multiple images of herself in the dark pit. Since her movements cycled consecutively like the Rockettes chorus line doing a kick, it’s pretty apparent a finite number of Rey’s were involved.
I think of a classic New Yorker cartoon by the masterful Charles Addams depicting an “infinite” regression of mirror images in a barbershop with a monster hidden in one of the dwindling reflections.
When I was an undergraduate in college a built a little box where I tried to create a miniature mirror regression. The box had the proportions of a dollhouse hallway. On one end was a regular mirror. On the other was a small two-way mirror -the kind that people can look into but an imaginary tiny man within the hall would only see another mirror.
I had cut a peephole on the outside of the box to look into the two-way mirror, expecting to see a perfect little regression of images. I foolishly failed to realize that the peephole would be reflected too, so although there was a mirror regression, a round hole with my staring eye looked back at me, sort of like that peculiar glowing Masonic eye symbol above the pyramid on the dollar bill.
Mathematicians, philosophers, and astronomers are entranced by infinity. Remember Zeno of Elea’s “Achilles and the Tortoise” paradox? Some astronomers actually believe the universe might be infinite.
For physicists, infinity can be vexing. When physicists tried to link quantum mechanics with Einstein’s general theory of relativity to understand black holes, the probability of particle location becomes infinite. What the heck does infinite probability mean? Evidently nothing too helpful because the effort was considered a bust.
Infinity came up in a previous post regarding Hugh Everett, the physicist who theorized that every quantum condition gave rise to a new universe. If there are an infinite number of universes are there worlds where Norse mythology is actually true? This was one of the premises of a beloved fantasy of my distant youth called The Incomplete Enchanter, by L. Sprague de Camp and Fletcher Pratt.
A psychologist travels not only to the world of Norse myth, but also to world of fiction –Edmund Spenser’s Fairy Queen. After all if the multiverse is truly infinite, why not? Perhaps there’s a world where my cartoon character, Edzl the Nebboid, actually exists! Edzl is the main protagonist of my new comic-in-progress, Pause & Reflect Comics.
The Buddha taught that the “Brahmaviharas” are boundless. These are the 4 qualities: loving kindness, compassion, sympathetic joy, and equanimity. Many teachers and practitioners are convinced that these are truly limitless. You don’t need to take anyone’s word for it, however. Go see for yourself.
Next time (maybe): a follow-up on Abbott’s “Flatland” and a look at the 10 or more spatial dimensions in string theory.