Impossible!

The word resonated throughout the large lecture hall. I had just finished describing a revolutionary concept for a new type of matter that my graduate student, Dov Levine, and I had invented.

The Caltech lecture room was packed with scientists from every discipline across campus. The discussion had gone remarkably well. But just as the last of the crowd was filing out, there arose a familiar, booming voice and that word: “Impossible!”

I could have recognized that distinctive, gravelly voice with the unmistakable New York accent with my eyes closed. Standing before me was my scientific idol, the legendary physicist Richard Feynman, with his shock of graying, shoulder-length hair, wearing his characteristic white shirt, along with a disarming, devilish smile.

Richard Feynman

Feynman had won a Nobel Prize for his groundbreaking work developing the first quantum theory of electromagnetism. Within the scientific community, he was already considered one of the greatest theoretical physicists of the 20th century. He would eventually achieve iconic status with the general public, as well, because of his pivotal role identifying the cause of the Challenger space shuttle disaster and his two bestselling books, Surely You’re Joking, Mr. Feynman! and What Do You Care What Other People Think?



He had a wonderfully playful sense of humor, and was notorious for his elaborate practical jokes. But when it came to science, Feynman was always uncompromisingly honest and brutally critical, which made him an especially terrifying presence during scientific seminars. One could anticipate that he would interrupt and publicly challenge a speaker the moment he heard something that was, in his mind, imprecise or inaccurate.

So I had been keenly aware of Feynman’s presence when he entered the lecture hall just before my presentation began and took his usual seat in the front row. I kept a careful watch on him out of the corner of my eye throughout the presentation, awaiting any potential outburst. But Feynman never interrupted and never raised an objection.





The fact that Feynman came forward to confront me after the talk was something that probably would have petrified many scientists. But this was not our first encounter. I had been lucky enough to work closely with Feynman when I was an undergraduate at Caltech about a decade earlier and had nothing but admiration and affection for him. Feynman changed my life through his writings, lectures, and personal mentoring.

When I first arrived on campus as a freshman in 1970, my intention was to major in biology or mathematics. I had never been particularly interested in physics in high school. But I knew that every Caltech undergraduate was required to take two years of the subject.

I quickly discovered that freshman physics was wickedly hard, thanks in large part to the textbook, The Feynman Lectures on Physics, Volume 1. The book was less of a traditional textbook than a collection of brilliant essays based on a famous series of freshman physics lectures that Feynman delivered in the 1960s.

Feynman showed me that it is acceptable to explore a diversity of fields if that is where your curiosity leads.

Unlike any other physics textbook that I have ever encountered, The Feynman Lectures on Physics never bothers to explain how to solve any problems, which made trying to complete the daunting homework assignments challenging and time-consuming. What the essays did provide, however, was something much more valuable—deep insights into Feynman’s original way of thinking about science. Generations have benefited from the Feynman Lectures. For me, the experience was an absolute revelation.



After a few weeks, I felt like my skull had been pried open and my brain rewired. I began to think like a physicist, and loved it. Like many other scientists of my generation, I was proud to adopt Feynman as my hero. I scuttled my original academic plans about biology and mathematics and decided to pursue physics with a vengeance.

I can remember a few times during my freshman year when I screwed up enough courage to say hello to Feynman before a seminar. Anything more would have been unimaginable at the time. But in my junior year, my roommate and I somehow summoned the nerve to knock on his office door to ask if he might consider teaching an unofficial course in which he would meet once a week with undergraduates like us to answer questions about anything we might ask. The whole thing would be informal, we told him. No homework, no tests, no grades, and no course credit. We knew he was an iconoclast with no patience for bureaucracy, and were hoping the lack of structure would appeal to him.

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A decade or so earlier, Feynman had given a similar class, but solely for freshmen and only for one quarter per year. Now we were asking him to do the same thing for a full year and to make it available for all undergraduates, especially third- and fourth-year students like ourselves who were likely to ask more advanced questions. We suggested the new course be called “Physics X,” the same as his earlier one, to make it clear to everyone that it was completely off the books.

Feynman thought a moment and, much to our surprise, replied “Yes!” So every week for the next two years, my roommate and I joined dozens of other lucky students for a riveting and unforgettable afternoon with Dick Feynman.

Physics X always began with him entering the lecture hall and asking if anyone had any questions. Occasionally, someone wanted to ask about a topic on which Feynman was expert. Naturally, his answers to those questions were masterful. In other cases, though, it was clear that Feynman had never thought about the question before. I always found those moments especially fascinating because I had the chance to watch how he engaged and struggled with a topic for the first time.

I vividly recall asking him something I considered intriguing, even though I was afraid he might think it trivial. “What color is a shadow?” I wanted to know.

After walking back and forth in front of the lecture room for a minute, Feynman grabbed on to the question with gusto. He launched into a discussion of the subtle gradations and variations in a shadow, then the nature of light, then the perception of color, then shadows on the moon, then earthshine on the moon, then the formation of the moon, and so on, and so on, and so on. I was spellbound.

During my senior year, Dick agreed to be my mentor on a series of research projects. Now I was able to witness his method of attacking problems even more closely. I also experienced his sharp, critical tongue whenever his high expectations were not met. He called out my mistakes using words like “crazy,” “nuts,” “ridiculous,” and “stupid.”

The harsh words stung at first, and caused me to question whether I belonged in theoretical physics. But I couldn’t help noticing that Dick did not seem to take the critical comments as seriously as I did. In the next breath, he would always be encouraging me to try a different approach and inviting me to return when I made progress.

One of the most important things Feynman ever taught me was that some of the most exciting scientific surprises can be discovered in everyday phenomena. All you need do is take the time to observe things carefully and ask yourself good questions. He also influenced my belief that there is no reason to succumb to external pressures that try to force you to specialize in a single area of science, as many scientists do. Feynman showed me by example that it is acceptable to explore a diversity of fields if that is where your curiosity leads.





One of our exchanges during my final term at Caltech was particularly memorable. I was explaining a mathematical scheme that I had developed to predict the behavior of a Super Ball, the rubbery, super-elastic ball that was especially popular at the time.

It was a challenging problem because a Super Ball changes direction with every bounce. I wanted to add another layer of complexity by trying to predict how the Super Ball would bounce along a sequence of surfaces set at different angles. For example, I calculated the trajectory as it bounced from the floor to the underside of a table to a slanted plane and then off the wall. The seemingly random movements were entirely predictable, according to the laws of physics.

Here I was, standing in front of Richard Feynman explaining that these long-standing rules were wrong.

I showed Feynman one of my calculations. It predicted that I could throw the Super Ball and that, after a complicated set of bounces, it would return right back to my hand. I handed him the paper and he took a glance at my equations.



“That’s impossible!” he said.

Impossible? I was taken aback by the word. It was something new from him. Not the “crazy” or “stupid” that I had come to occasionally expect.

“Why do you think it’s impossible?” I asked nervously.

Feynman pointed out his concern. According to my formula, if someone were to release the Super Ball from a height with a certain spin, the ball would bounce and careen off nearly sideways at a low angle to the floor.

“And that’s clearly impossible, Paul,” he said.

I glanced down to my equations and saw that, indeed, my prediction did imply that the ball would bounce and take off at a low angle. But I wasn’t so sure that was impossible, even if it seemed counterintuitive.

I was now experienced enough to push back. “Okay, then,” I said. “I have never tried this experiment before, but let’s give it a shot right here in your office.”

I pulled a Super Ball out of my pocket and Feynman watched me drop it with the prescribed spin. Sure enough, the ball took off in precisely the direction that my equations predicted, scooting sideways at a low angle off the floor, exactly the way Feynman had thought was impossible.

In a flash, he deduced his mistake. He had not accounted for the extreme stickiness of the Super Ball surface, which affected how the spin influenced the ball’s trajectory.

“How stupid!” Feynman said out loud, using the same exact tone of voice he sometimes used to criticize me.

After two years of working together, I finally knew for sure what I had long suspected: “Stupid” was just an expression Feynman applied to everyone, including himself, as a way to focus attention on an error so it was never made again.

I also learned that “impossible,” when used by Feynman, did not necessarily mean “unachievable” or “ridiculous.” Sometimes it meant, “Wow! Here is something amazing that contradicts what we would normally expect to be true. This is worth understanding!”

So 11 years later, when Feynman approached me after my lecture with a playful smile and jokingly pronounced my theory “Impossible!” I was pretty sure I knew what he meant. The subject of my talk, a radically new form of matter known as “quasicrystals,” conflicted with principles he thought were true. It was therefore interesting and worth understanding.





Feynman walked up to the table where I had set up an experiment to demonstrate the idea. He pointed to it and demanded, “Show me again!”

I flipped the switch to start the demonstration and Feynman stood motionless. With his own eyes, he was witnessing a clear violation of one of the most well-known principles in science. It was something so basic that he had described it in the Feynman Lectures. In fact, the principles had been taught to every young scientist for nearly 200 years.

But now, here I was, standing in front of Richard Feynman explaining that these long-standing rules were wrong.

Crystals were not the only possible forms of matter with orderly arrangements of atoms and pinpoint diffraction patterns. There was now a vast new world of possibilities with its own set of rules, which we named quasicrystals.

We chose the name to make clear how the new materials differ from ordinary crystals. Both materials consist of groups of atoms that repeat throughout the entire structure.

The groups of atoms in crystals repeat at regular intervals, just like the five known patterns. In quasicrystals, however, different groups repeat at distinct intervals. Our inspiration was a two-dimensional pattern known as a Penrose tiling, which is an unusual pattern that contains two different types of tiles that repeat at two incommensurate intervals. Mathematicians call such a pattern quasiperiodic. Hence, we dubbed our theoretical discovery “quasiperiodic crystals” or “quasicrystals,” for short.

My little demonstration for Feynman was designed to prove my case using a laser and a slide with a photograph of a quasiperiodic pattern. I flipped on the laser, as Feynman had directed, and aimed the beam so that it passed through the slide onto the distant wall. The laser light produced the same effect as X-rays passing through the channels between atoms: It created a diffraction pattern, like the one pictured in the photo below.

I turned off the overhead lights so that Feynman could get a good look at the signature snowflake pattern of pinpoints on the wall. It was unlike any other diffraction pattern that Feynman had ever seen.



I pointed out to him, as I had done during the lecture, that the brightest spots formed rings of ten that were concentric. That was unheard of. One could also see groups of pinpoints that formed pentagons, revealing a symmetry that was thought to be absolutely forbidden in the natural world. A closer look revealed yet more spots between the pinpoints. And spots between those spots. And yet more spots still.



Feynman asked to look more closely at the slide. I switched the lights back on and removed it from the holder and gave it to him. The image on the slide was so reduced that it was hard to appreciate the detail, so I also handed him an enlargement of the tiling pattern, which he put down on the table in front of the laser.



The next few moments passed in silence. I began to feel like a student again, waiting for Feynman to react to the latest cockamamie idea I had come up with. He stared at the enlargement on the table, reinserted the slide in the holder, and switched on the laser himself. His eyes went back and forth between the printed enlargement on the table, up to the laser pattern on the wall, then back down again to the enlargement.

“Impossible!” Feynman finally said. I nodded in agreement and smiled, because I knew that to be one of his greatest compliments.

He looked back up at the wall, shaking his head. “Absolutely impossible! That is one of the most amazing things I have ever seen.”

And then, without saying another word, Dick Feynman looked at me with delight and gave me a huge, devilish smile.





Paul J. Steinhardt is the Albert Einstein Professor in Science at Princeton University, where he is on the faculty of both the departments of physics and astrophysical sciences. He cofounded and directs the Princeton Center for Theoretical Science. He has received the Dirac Medal and other prestigious awards for his work on the early universe and novel forms of matter.

From The Second Kind of Impossible: The Extraordinary Quest for a New Form of Matter by Paul J. Steinhardt. Copyright © 2019 by Paul J. Steinhardt. Reprinted by permission of Simon & Schuster, Inc.