Category: Math

The Coolest Discovery You’ve Never Heard Of

I recently learned that this year’s Nobel Prize in Physics went to a team of scientists who conducted experiments on quantum tunneling. Their experiments were conducted in the 1980s, which is typical of how the Nobel committees work—it takes around thirty years for a scientific consensus to build that a body of work was truly worthy of a Nobel Prize. 

I was interested in this news because, like most sci-fi nerds, I have an unflagging fascination with quantum mechanics. Heck, I even have a passing understanding of the fundamentals. (No, not just from Star Trek; I’ve read a few actual books! With facts, and stuff!)  A few years ago, I even tried to write a non-fiction book about Bell’s Theorem, which is a famous consent in Quantum Mechanics, albeit one that  you’ve probably never heard of (unless you’re a physicist or a science teacher or a sci-fi nerd). 

John Stewart Bell (copyright CERN)

To be frank, I had never heard of it either, until I read about it in a science book and then ventured to the Wikipedia page, where I learned that the theorem was written by an Anglo-Irish physicist named John Stewart Bell in the 1960s, and it hit the scientific community like a hurricane. Later, in 1975, another physicist Henry Stapp called it “the most profound discovery of science.”

When I read this quote, I thought, “Whoa, dude! If it’s really the most ‘profound discovery of science’,” I should probably learn something about it.” 

And I did. Sort of.

Obviously, I will never really understand the underlying math, or even the root concepts that the math represents (which is one reason I abandoned the aforementioned book project). But the theorem itself is pretty easy to understand….

Continue reading “The Coolest Discovery You’ve Never Heard Of”

Nerds in the News

An Aperiodic Monotile has been discovered. Hooray!

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.