Scientific discovery is the successful extension of human knowledge into the unknown. Particularly satisfying are those discoveries that appear impossible at first glance but upon closer inspection reveal a long-overlooked loophole in our most basic assumptions. The Second Kind of Impossible: The Extraordinary Quest for a New Form of Matter by Paul Steinhardt is the story of several such gaps in the fields of crystallography and mineralogy. It is a thrilling mix of scientific memoir and true detective story. Most importantly, it is a tale of the excitement that drove the author to extraordinary insights far outside his original area of expertise.

Aperiodic Penrose tiling at Oxford University.

Aperiodic Penrose tiling at Oxford University.

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Quasicrystals, the main subject of the book, are complex ordered phases of matter first found in metallic alloys. Their study has a rich history filled with unique protagonists and unexpected developments. Thus they are a perfect topic for a scientifically themed book aimed at a general audience.

The first part of The Second Kind of Impossible introduces the foundations of quasicrystal research. It covers the origins of crystallography in the 18th century through the end of the 20th century, when quasicrystals became established as a real and fascinating form of matter. In the 1970s mathematician and physicist Roger Penrose introduced Penrose tilings, intricate and aesthetically beautiful patterns with long-range order but without periodicity. The tilings were thought to be a mathematical gimmick until two independent advancements brought them to the attention of a wider community. At Princeton University in the early 1980s, Steinhardt and his graduate student Dov Levine envisioned an icosahedral generalization of Penrose tilings. They dubbed that hypothetical new form of matter quasicrystals. Unbeknownst to Steinhardt, materials scientist Daniel Shechtman, using electron microscopy, had already identified an aluminum-manganese alloy with icosahedral diffraction symmetry.

Steinhardt describes both the mathematics that went into his theory and his construction of geometric models from styrofoam balls, pipe cleaners, and paper. The astonishingly fruitful interplay between theory and model building soon explained all aspects of Shechtman’s discovery and subsequent developments. After that success, Steinhardt needed a new challenge to continue his research. As of 1999 all known quasicrystals were synthetic in origin, so Steinhardt began wondering if perfect quasicrystals might develop without human intervention.

The book next dives into Steinhardt’s 20-year hunt to answer that question. He reasoned that if a natural quasicrystal existed, it could be found in some known but incompletely characterized mineral sample. But as a theoretical physicist and cosmologist, he had no formal training in mineralogy. He contacted experts in materials characterization around the world to ask for their assistance and collaboration.

The reader follows Steinhardt as he recounts scouting crystal diffraction databases and exploring the intricacies of microscopic crystalline grains. Convincing colleagues of his unexpected findings was not always easy. Against the odds and after many drawbacks, including dealing with smugglers and deciphering clues in secret diaries, Steinhardt and his closest collaborator, Italian geologist Luca Bindi, traced the origins of a natural quasicrystal candidate to one of the most remote places on Earth: the Koryak Mountains in Siberia.

In the final part of the book, Steinhardt and a team of 12 scientists, prospectors, and support personnel make an adventurous field expedition to the Koryak Mountains. There they hope to find needles in a haystack—tiny rocks only millimeters in size, surrounded by thick clay in the banks of a pristine river bed. The samples they eventually uncover are of extraterrestrial origin and date back to the beginning of the solar system. I refrain from recounting the many astonishing turns of events the team encountered. But suffice to say that a fiction writer could hardly have thought of better plot twists. This section was the highlight of The Second Kind of Impossible. The hunt captured and held my attention; I could not put the book down.

One of the book’s strengths is its accessibility. Despite the specialized topic, Steinhardt conveys with engaging passion his motivation and how it changed over the course of his quest. He describes his struggles with unreliable sources, competitors, and skeptics. His approach—assembling a “red team” of critics and a “blue team” of advocates that engaged in friendly competition until the scientific truth was revealed—is a formidable demonstration of how to avoid confirmation bias. Finally, and this I find a particularly important moral, Steinhardt uses his personal perspective to demonstrate that scientific discovery is often not a solitary effort. Instead, true progress comes from openness to the world and the acceptance of potential failure. The events described in the book are an extraordinary display of tenacity and serendipity, and the writing is captivating, entertaining, and full of fascinating scientific content. I strongly recommend The Second Kind of Impossible to experts and lay audiences alike.

Michael Engel is an assistant professor of chemical and biochemical engineering at Friedrich-Alexander University in Erlangen-Nuremberg, Germany. He has been working on crystallization processes for 15 years and reported the first icosahedral quasicrystal discovered in computer simulation.