When I was in my twenties, I read Roger Penrose’s The Emperor’s New Mind and was blown away by it. That is, in the 5% or so that I could understand, I was blown away. Never have I read a science book that, paradoxically, filled me with hope and optimism. And awe.
The book is probably more timely today than ever. With all the hype about AI and machine learning, people are starting to freak out about humanity’s place in the future.
Penrose’s main thesis, after all, is that human consciousness is not machine-like. Citing the work of brilliant people such as Kurt Gödel, Alan Turing, and himself, Penrose lays out an extremely compelling argument as to why computers—no, not even quantum computers—will ever really think, no less achieve actual consciousness. This conclusion enraged an army of science fiction fanboys and others who believe that the “the brain is a machine made of meat”.
In building his argument, Penrose refers to examples of discoveries scientists and mathematicians have made that could not (in his opinion) have been discovered by any algorithmic process. One of these examples is his own rather brilliant work in the area of aperiodic tilings.
Aperiodic tilings are something that even a STEM idiot like myself can understand. Anyone who has ever looked down at an intricately tiled parquet floor and wondered about the pattern can relate to this. Most floor patterns—even very complicated ones—will reveal themselves as repetitive if viewed from a sufficient height. But some patterns never repeat, even if you view them from the second floor or the fifteenth or Alpha Centauri. This aperiodicity can only be demonstrated, of course, via mathematical proof, which is often maddeningly complex in and of itself. Mathematicians are constantly seeking out new collections of tile shapes (which, paradoxically, are usually simple enough to cut out of a piece of construction paper with kiddie scissors) that yield these aperiodic tiles.
In the 1970s, Penrose himself discovered an aperiodic tiling that used only two shapes—a “kite” and a “dart”. This was a record at the time since other aperiodic tilings had been discovered but they made use of more shapes.
Knowing this, I read with some amusement that a new aperiodic tiling had recently been revealed that uses only one shape. A funky shape, surely, but still just one, thus making it an aperiodic monotile. The only wrinkle was that the shape had to be “flipped” at certain points for the tiling to work.
Then, a few months later, lo and behold, another aperiodic monotile was discovered, and this one required no flipping. The dudes who found it were David Smith, Joseph Samuel Myers, Craig Kaplan and Chaim Goodman-Strauss of the University of Yorkshire.
Truly, this discovery has no impact whatsoever on my daily life, or yours I would bet. And yet it’s still really cool. This mathematical artifact has been hidden there for all eternity, and just now, in 2023, some nerds discover it.
That’s why I still have faith in humanity. The nerds. They will save us.
Author’s Note: hat-tip to the good people at openculture.com for bringing this news to my attention, and for posting the video that I have linked above.
Ash Clifton, Writer 