In science, says Princeton University physicist Paul J. Steinhardt, there are two kinds of impossible. The first kind of impossible claim is when a proposal would violate the basic laws of physics. But the second kind is simply based on assumptions that might contain a loophole. Steinhardt has spent his career chasing these “might actually be possible” claims.

Steinhardt’s new book, The Second Kind of Impossible: The Extraordinary Quest for a New Form of Matter (Simon & Schuster) chronicles his 30-year obsession with a structure called the quasi-crystal, from proving that it could theoretically exist to traveling to remote parts of Russia to discover whether it might be found in nature.

The Verge spoke to Steinhardt about the uses of quasi-crystals, why nobody believed it was possible, and how a physicist ended up digging for meteorites.

This interview has been lightly edited for clarity.

Let’s start with the basics. Your book is all about how you proved the existence of quasi-crystals. What exactly is a quasi-crystal?

They are a new form of matter and a new kind of material. They have an arrangement of atoms and molecules that were deemed impossible, and yet they exist.

In crystals, the atoms are arranged in a very simple, regular way, a single cluster that just repeats. It was believed that that was the only way. Everything we observed regularly repeated, so people thought other arrangements were impossible.

That was a law of mathematics, but apparently not a law of nature. Nature had another possibility. My student at the time, Dov Levine, asked if there might be a loophole. What if you had two clusters repeating at different rates? Cluster A of atoms repeats at one frequency and Cluster B at another frequency. Those are quasi-crystals, and their existence means there’s a whole new world of forms of matter.

Aside from being interesting just because they exist, what are quasi-crystals useful for?

They have novel physical properties. They’re harder than regular crystals made of similar elements. For example, there’s an airplane alloy that’s light and hard, and it was made without anyone realizing why it was so hard. Later, they discovered that it wasn’t pure crystal. Unbeknownst to them, it had some grains of quasi-crystal.

Quasi-crystals can also be used when you need something that’s especially hard, like hypodermic needles or industrial parts. And it turns out that they’re not just hard but they’re slippery like Teflon. So imagine you can take your pot and pan and coat it with this, and it doesn’t scratch. That’s just the tip of the iceberg. We’re still learning about other physical properties that it can have and what we can potentially do with electronics and photonics.

One moment I liked from the book was when you and Dov were trying to prove that quasi-crystals could theoretically exist, and you learned that another lab had unintentionally proven that they actually existed. What was that like?

This other lab, with Dan Shechtman, was doing a project of classifying all the aluminum alloys you could make, and he accidentally found a quasi-crystal. It looked like a crystal, but it had one of the “forbidden” or impossible symmetries that basically looked like the symmetry of a soccer ball. He didn’t know what to make of it. This was happening at the same time we’d been working on a theoretical paper saying this soccer ball-like crystal was possible.

“We ended up putting an expedition to go to the Kamchatka Peninsula to this obscure stream across the tundra in the middle of nowhere.”

The crucial moment came when a collaborator visited me at an IBM lab outside of New York City. He had that paper and started to read the title and the first few words. I was concerned that we had been completely scooped, but as I read it, I realized they didn’t really know what they had. Then I flipped to the page that had the crucial figure of the pattern, and that was the “wow moment” when I knew what they had discovered was exactly what we had worked on predicting.

I didn’t say a word. All I had to do was stand there, walk over to my desk and pick up one of the images we had suggested theoretically. Sure enough, it was a pattern just like the one on the paper. It was that golden moment that happens in science when you know something that no one else in the world knows. For me, that’s always been the thrill of doing science.

After that, you became really interested in the question of whether it could be found in nature, right?

Once I knew it could be made in a lab, I thought maybe it could be found in nature. Why not? But how do you search for them? You can’t just look around in the ground.

I went to several museums like the American Museum of Natural History in New York and The Smithsonian in Washington, DC. I looked in display cases, hoping someone had identified something close to a quasi-crystal. That failed, so I worked on other things for about the next 15 years, though I kept coming back to it.

In 1998, I started working with a geologist at Princeton to find quasi-crystals in some obscure places using crystal databases. We wrote a paper explaining our method and explaining that so far, we hadn’t succeeded but inviting anyone to join us. After six years, I got an email from an Italian geologist named Luca Bindi. He said, “I’d like to join your search.”

“Quasi-crystals are actually space visitors.”

That was one of the luckiest moments in the whole story because almost immediately Luca became as fanatical about this search as I was. We became very fast collaborators and very fast friends. He brought up the possibility of a mineral in an obscure collection in a storage room and brought a sample, and, sure enough, inside this complicated mess of a rock, there were little grains of quasi-crystals. We thought that was the end of the story, but a colleague at Princeton said this couldn’t possibly be a natural material. He said it had to be a byproduct of human activity because the combination of elements had never before been seen in any material in nature. So that sent us back to the drawing board.

But you decided to pursue the possibility of natural quasi-crystals, right?

We decided to pursue it, and, well, the next two years were a detective story to trace the origin of that little rock with various twists and turns. We eventually traced it back to young Russian prospectors in a completely uninhabited region of Far Eastern Russia. We ended up putting an expedition to go to the Kamchatka Peninsula to this obscure stream across the tundra in the middle of nowhere to see if, by luck and digging and digging, we were lucky enough to find even one grain of the material.

Despite all those improbable events, we were lucky. We found nine or 10 grains of similar material, which were quasi-crystals. We figured it out correctly, and, more importantly, what we learned by collecting all those materials is that this material had formed in space. Quasi-crystals are actually space visitors and furthermore, these grains were older and had formed before any of the rocks you know of on Earth. They’d formed from the primal material that makes up the Solar System.

We not only learned that nature can make a quasi-crystal, but it can make it in a way we still don’t completely understand. We found three different types in the same meteorite, including one that had never been made in a laboratory. So nature helped show us something we didn’t know existed, and it connects to a story about the origin of the Earth. Of course, there are still more questions to answer.

It took 30 years for all this to happen. What made you keep persevering?

I go to many talks and seminars, and I’m always interested when someone says something is impossible. My senses became sharp, and I’m always trying to think about what they’re assuming and is there some way I can work my way around it. The questions are always bashing around in my head, and I’ll want to go wherever it takes me.