Geometry and Permafrost

Quick Study
Photo by Tony RinaldoPhoto by Tony Rinaldo

The theoretical physicist Paul Steinhardt RI ’13 is certainly busy at the Radcliffe Institute, where he is the 2012–2013 Lillian Gollay Knafel Fellow. In addition to pursuing a radical alternative to the big bang theory and studying a new class of synthetically designed materials, he is drafting a popular book that details the search for a new form of matter known as a quasicrystal—appropriate pursuits for someone who holds the title of Albert Einstein Professor in Science at Princeton University.

Who are your heroes?
I enjoy having heroes, so I have many, ranging from personal to scientific. If I have to limit myself to one, it would be Richard Feynman, who was a profound influence since I first met him as an undergraduate at Caltech.

What inspires you?
Being told something is impossible.

What is your fantasy career?
I feel fortunate to be living it.

What is the most challenging aspect of being a Radcliffe fellow?
Time management—so many interesting people, so many activities, and too few hours in a day.

You liken crystal geometry to tiling. If you could retile your shower in any pattern, what would it look like?
I might choose a quasicrystal pattern that no one has ever seen before. (An infinite variety of patterns are possible for any symmetry, and there are an infinite number of symmetries. I have a program that makes a design based upon a random choice among this infinitude and, hence, can provide a tiling that no one has ever seen before.)

These quasicrystals have a geometry that was previously thought impossible. Can you briefly explain this?
For thousands of years, all known minerals and pure materials were crystals, in which the atoms stack together like building blocks or bricks in a regularly repeating pattern in three dimensions. Regular patterns only allow certain symmetries; for example, you can put squares, rectangles, hexagons, triangles, and parallelograms together to make regular tessellation of your shower floor, but try doing it with pentagons, heptagons, or any shapes with higher symmetry—it is hopeless.

Similarly, in three dimensions, crystals cannot have any fivefold, sevenfold, or higher-fold symmetry axes, as was first proved in the 19th century. Since then, scientists have thought these symmetries were impossible for solids. However, in the 1980s, my student and I showed this is incorrect, with new structures we called “quasicrystals.” One of my projects as a Radcliffe fellow is exploring the first naturally formed quasicrystal that we discovered, in a remote region of far-eastern Russia.

You collected that quasicrystal by traveling with an international team to a restricted area of Russia, Chukotka, where you panned for meteorite fragments for 10 days. How would you describe that region?
In a word, otherworldly. There is virtually no one to be seen once you leave the one major town. Nature is in control. Almost everywhere is permafrost. Winter is never far away. The sky never gets truly dark at night. Beautiful strange clouds and unusual rainbows appear almost daily. Russian bears and billions of mosquitoes are constants. In short: peaceful, beautiful, strange, and dangerous.

We noticed a cat in the expedition photos. How did a cat end up on the scientific team?
Bucks the cat was brought by our driver, Victor Komelkov, and his wife, Olga Komelkova, who was both camp cook and lawyer for the team. Bucks was a fearless traveler who sat atop Olga in the truck most of the way to and fro.

What’s the best way to kill time on the permafrost?
Sitting alongside Victor, I was transfixed by watching every twist, turn, and dive he made with the vehicle. There were no roads, so he had to make moment-by-moment decisions on which way to turn. I tried to see if I could get to the point where I could guess which turn to make, but I never succeeded, even after more than seven days in the field. There were other things to watch—the wildlife and flowers, for example—and in one area there were giant porcini mushrooms that we collected and later consumed.

Where to next?
Wherever the science leads us. It’s too early to say.

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