Nerds in the News

Nerds in the News: Alex Cohen

Alex Cohen (Photo Courtesy of Clay Mathematics Institute)

If there are two words dear to every sci-fi nerd’s heart, they are quantum and fractal. How many sci-fi tropes have been created over the past thirty years just by adding one of these words to the front of some other, more pedestrian word? “Quantum drive.” “Quantum torpedo.” “Fractal encryption.” “Fractal-verse.”

So, when I stumbled up this article, “Graduate Student Proves a Quantum Uncertainty Principle for Fractals,” whose title has both “quantum” and “fractal” in it, I clicked immediately. And, after reading the first few paragraphs, I realized two things. First, this must be a truly momentous discovery. Second, it’s really, really cutting-edge, so much so that it doesn’t have many YouTube videos devoted to it, nor even a Wikipedia page.

The article describes how a young physicist, Alex Cohen, who was a grad student at the time, published a paper last year which proves “the fractal uncertainty principle to all higher dimensions.” To break that down a bit, the fractal uncertainty principle is an application of Werner Heisenberg’s famous Quantum Uncertainty Principle—which states that certain combinations of quantum properties such as momentum and position cannot be accurately measured at the same time—to fractals, those mesmerizing, infinitely-repeating mathematical structures that look the same no matter how far you zoom in or out on them.

Of course, at first glance, the two concepts seem completely opposite to each other. The uncertainty principle illuminates the limitations of measurement and predictability, while fractals describe completely pre-determined, unchanging patterns that continue into infinity. What gives?

Article in Quanta Magazine Describing Cohen’s Discovery

It seems that ten years ago, another young nerd named Semyon Dyatlov studied how chaotically moving particles (like the molecules in a gas) can sometimes—if they are occupying a one-dimensional fractal geometric plane—get trapped in a fractal-shaped rabbit-hole, following a fractal path forever. Dyatlov wondered if quantum-based particles (such as electrons or photons) could also become trapped in such a rabbit-hole. As it turns out, they cannot. He proved this mathematically while, at the same time, creating a brand-new concept in physics: the Fractal Quantum Uncertainty Principle, orFUP. (A rare, math-heavy video on the subject is pasted at the end of this post. Watch it if you dare.)

Dyatlov’s brilliant work put paid to the question of quantum particles in a one-dimensional plane. But what about worlds with, you know, more than one dimension? Like ours, for instance?

Turns out, the math to handle this question is extremely friggin hard—even for guys and girls who understand one-dimensional fractal manifolds. As a practical matter, the problem might even be impossible.

Well, you know the old saying about what happens whenever a person (usually a very learned, respected old man) says something is impossible; some young whippersnapper comes along and does it. That’s what occurred last year when an MIT doctoral student wrote a paper proving the FUP in all dimensions. Pretty cool, huh?

Of course, I have no idea how Mr. Cohen actually proved this. I doubt he could explain it to me, even if I gave him a year or two of my full attention and an infinite supply of crayons. But I suspect that his proof will turn out to be a huge, consequential discovery, one that will eventually have real-world, practical applications. After all, I don’t believe there is such a thing as pure science. Every time a branch of intellectual study is labelled as “useless,” someone finds a way to use it—and often with world-altering consequences.

Even if Mr. Dyatlov’s and Mr. Cohen’s discoveries fail to bear practical fruit in my lifetime, I’m sure that all the new science and mathematics that springs from it will be beautiful to behold. If you’re smart enough to understand them.

Which, alas, I am not.

A lot of movies have been made about a so-called eco-apocalyse, in which catastrophic climate change, or pollution, or crop-failure, or overpopulation, or some mixture of all-of-the-above wipes out big swathes of humanity. And some of those scenarios might yet play-out if we keep sleepwalking (make that speed-walking) into the future.

Right now, however, environmental issues are manifesting in unexpected and almost mundane ways. Take house insurance. Here in Florida, frequent and more-powerful hurricanes are driving up premiums to insane levels. It’s the same along the gulf coast of Mississippi and Alabama. And a friend of mine from Texas told me the same thing is happening there (flooding is the disaster-de-jour, in his neck-of-the-woods). And then we have electric bills. Each year, increased demand for electricity (for air-conditioning and, now, frickin data centers) is driving up the cost of utilities. And what about clean drinking water? Near-constant drought (punctuated by hurricanes) makes it difficult to provide clean drinking water to growing populations in some parts of the country. This leads more people to buy bottled water. In parts of Mississippi, you will see everyone buying huge flats of the stuff from Wal-Mart, leading me to believe that bottled water is the primary of hydration for many rural Southerners.

So, whenever I run across a news story like this one about a small, ingenious invention of the sort that might—just might—help get us out of this mess, it warms my heart. And even more so when the inventors are young people. In this case, seventeen-year-old Virginian Mia Heller came up with a new, cheap, reliable way to filter microplastics from water. Her system is based on a type of nanoparticle-infused oil called a ferrofluid, which basically pulls the microplastics out of the water like a magnet. The oil is reusable and easy to make.

Will this invention take off? Will it scale? I don’t know, but it gives me hope. I often think of how the great Nazi Wehrmacht was defeated, in part, by clever G.I.s from America, some of whom came up with the clever idea of mounting a phone on the back of their tanks. With this phone, a ground-trooper could speak directly with the guys inside the tank and tell them where to shoot and move. It was the kind of simple, “no-brainer” innovation that the Germans, with their rigid class system and demoralized population, never came up with. And it helped win the war.

Climate change and pollution are Ms. Heller’s generation’s World War II. And I’m really hoping that smart people like her can figure out a way to save my generation’s collective butt.

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).

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….

What I’m Reading: Would You Baptize an Extraterrestrial?

I learned many things from reading the excellent nonfiction book Would You Baptize an Extraterrestrial? For instance, I learned that the Vatican has its own astronomical observatory, which is run, in part, by the authors, Guy Consolmagno and Paul Mueller. Both men are also Jesuits. (The current Pope, Francis, is also a Jesuit—that’s another thing I learned).

Now, I was raised Catholic, and I thought a knew a thing or two about the religion. But not only did I learn from this book that the Vatican has its own observatory, but that it has had one for hundreds of years. In fact, I was so taken by this discovery that I Googled “Vatican observatory” and, to my amazement, found that the Vatican also runs an observatory in Tucson, Arizona.

Talk about synchronicity! When I was twenty-two years old, I went off to attend grad school at the University of Arizona, in Tucson, and I distinctly remember the first night I spent there. I impressed by the size of the city—much larger than my little hometown of Gainesville, Florida—but also by how beautiful the desert sky was. Even in the downtown area, the stars were clearly visible. This was no accident; the city, I was told, purposely kept the streets relatively dark, in deference to the many astronomical observatories that surround the valley, which could not function if too much light pollution bled from the metro area.

Apparently, the Vatican’s observatory is one of them.

Nerds in the News: Calcea Johnson and Ne’Kiya Jackson

The latest entry in my continuing series celebrating Nerds in the News (STEM nerds, mostly, as opposed to book nerds, of which I am one) goes to these two young, awesome math nerds. Back in 2022, using nothing but trigonometry (which, as it happens, was the only class I failed in high school), they came up with an entire new proof of the Pythagorean Theorem. Even more incredible, these two mathematicians were both teenagers at the time. And they still are!

Now, they have updated their original proof with five new variations.

I am, of course, terrible at math, but I am endlessly fascinated by it. One of my favorite non-fiction books of all time is Simon Singh’s excellent Fermat’s Enigma, which recounts master-mathematician Andrew Wiles’ quest to solve Fermat’s Last Theorem, which eluded math nerds for hundreds of years. (Wiles solved it in 1993.) Coincidentally, that problem also directly concerned the Pythagorean Theorem, and Singh recounts the story like a centuries-old mystery. One interesting point about the tale is that many advances in the hunt for the solution were made by amateur mathematicians, which is exactly what Ms. Johnson and Ms. Jackson are. (This is due to their youth; I have a feeling they will go on to have great careers after…you know, they graduate college).

Congratulations, Ms. Calcea Johnson and Ms. Ne’Kiya Jackson!

Nerds in the News: Janna Levin

How often do you see a mainstream, broadcast news interview that covers so many nerd-worthy topics? This one has astronomy professor Janna Levin discussing Dyson Spheres, alien civilizations, sci-fi writer Olaf Stapledon, and Freeman Dyson himself.

Very few writers in history have had as big an influence on my imagination as Freeman Dyson. Not only did he come up with the idea (mostly) of a Dyson Sphere (which, in slightly modified form, became the inspiration for Larry Niven’s Ringworld novels), he always wrote visionary articles on space exploration, climate change, genetic engineering, the future of energy, and even E.S.P.

Enjoy!

Related:

A Book Nerd’s Reaction Oppenheimer

Freeman Dyson Interview

Classic Sci-Fi Book Cover: Ringworld

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.