Deliberate Rest

A blog about getting more done by working less

Category: Walking (page 1 of 3)

Happy Hamilton Day, and walking insights

Mathematical Bridge
Mathematical Bridge, Cambridge

It may not be on your calendar, but Sunday October 16 is Hamilton Day, the anniversary of the day Irish mathematician William Rowan Hamilton carved his most famous insight, on the algebra of quaternions, on a bridge while walking with his wife. This is one of the more famous examples of an “a-ha” moment in the history of science; because it is well-documented, it illustrates several features of such events that sometimes get overlooked.

Today quaternions are used in 3D game engines and graphics (among many places), because they provide a very efficient way of describing how objects should move. (Slate has a more detailed explanation of them.) Hamilton had long been interested in complex numbers, numbers that include the “imaginary” number i (the number whose square equals -1). Real numbers can be represented on a number line– for example, 1, 2, 3, and 64 can all be placed on the same line– and complex numbers can be mapped onto a plane. What about numbers that can be described using three dimensions, and have more than one imaginary number? How would you perform basic algebraic functions on these “triplets,” as Hamilton called them– e.g., adding them together, or subtracting them, or multiplying and dividing them? Addition and subtraction were not so hard, but multiplication was a challenge.

Punting on the Cam
Hung up on the problem

On October 16, 1843, while walking with his wife along the Royal Canal, “an under-current of thought was going on in my mind, which gave at last a result, whereof it is not too much to say that I felt at once the importance,” he later wrote to one of his sons. “An electric circuit seemed to close; and a spark flashed forth.” He took out a knife and wrote the equation on a stone on the Broome Bridge, to guarantee the insight wouldn’t be lost. The way to solve the problem, he realized, was not to work with triplets, but to work with quaternions, numbers whose value could be represented in four dimensions, but which could be multiplied more easily.

But there’s more to the story. We often focus on these moments of insight because they’re dramatic, and are good stories; but this can obscure the fact that they’re part of a much bigger process. Graham Wallas argued that there are four stages in the creative process, or the “art of thought” as he called it (interestingly, he never uses the word “creativity” in his study): preparation, incubation, illumination, and verification.

Moments of illumination, he noted, don’t actually happen without periods of work (the preparation) and rest (the incubation): the flash of insight isn’t a shortcut, but the culmination, of a long process. Your mind needs to have a lot of facts stored, a history of working on the problem, a sense of which approaches to the problem are promising and which are dead ends.

Punting on the Cam
One more view of the Mathematical Bridge

Hamilton’s moment on the bridge on October 16, 1843 felt like a bolt of lightning, but the insight arrived after years of effort: “I felt a problem to have been at that moment solved– an intellectual want received– which had haunted me for at least fifteen years,” he said. In fact, he had been working on it for so long that even his children had developed a ritual: “on my coming down to breakfast,” Hamilton later recalled to one son, “your (then) little brother William Edwin, and yourself, used to ask me, ‘Well, Papa, can you multiply triplets’? Whereto I was always obliged to reply, with a sad shake of the head: ‘No, I can only add and subtract them.’”

Another characteristic piece of the story is that he was walking when he had the insight. Many stories of illumination take place while the thinker is in motion. Erno Rubik, inventor of the Rubik’s Cube, had an epiphany about how to design a connector that holds the blocks in his cube together while allowing them to rotate while walking along the banks of the Danube.

Budapest, Hungary

In his account of the discovery of Fuschian functions, the great French mathematician Henri Poincaré describes a series of a-ha moments that came while boarding a bus, on a walk on a seaside bluff near Caen, and walking down the street in Paris.


And we now have experimental evidence that walking and creativity work together: Stanford psychologists Daniel Schwartz and Marily Oppezzo found that even walking on a treadmill that faces a cinder block wall stimulates creativity.

The Main Quad, Stanford University

Another easy-to-overlook element in the story is that such moments of illumination tend to come to people who have spent time cultivating the ability to move through the preparation and incubation phases. Geneticist and Nobel laureate Barbara McClintock recalled a walk at Stanford when she was working on an especially tricky problem as a turning point in her creative life. She had long gone on walks to help shake loose ideas, but after her Stanford walk she felt a new level of confidence in and control over the process: from then on, she could “summon it when needed, and to use it in the service of scientific discovery,” she told her biographer.

As a teenager, Hamilton had discovered that “A long walk is a fine opportunity for wooing the Muse,” and for much of his life he walked as a way of helping solve challenging problems. His moment on the bridge wasn’t a one-time event, in other words; he had spent years learning how to use walks to shake loose ideas.

The examples of Hamilton and others show, I argue in my book, that we should treat deliberate rest as a skill. Whether he was conscious of it or not at first, Hamilton discovered in his teens that walking was a way to stimulate his creative thinking, and he appears to have used that knowledge to help him solve problems. Likewise McClintock definitely used walks to get her creative mind going. Even if he didn’t plan for them in quite the same way (it’s not clear to me), Poincaré wasn’t surprised that insights came while he was walking. We can learn from their examples, and from more recent work on walking and insight, to help ourselves become more reliably creative.

John Littlewood’s advice to mathematicians: 4-hour days, acquire the art of “thinking vaguely,” and “work all out or rest completely”

Views of Cambridge from Great St. Mary's
Cambridge from the bell tower at St Mary’s Church

I’ve quoted from this before, but I love John Littlewood’s essay “The mathematician’s art of work,” In this extract, the Cambridge offers “some practical advice about research and the strategy it calls for.”

In the first place research work is of a different order from the “learning” process of pre-research education (essential as that is). The latter can easily be rote-memory, with little associative power: on the other hand, after a month’s immersion in research the mind knows its problem much as one’s tongue knows the inside of one’s mouth. You must also acquire the art of “thinking vaguely,” an elusive idea I can’t elaborate in short form. After what I have said earlier, it is inevitable that I should stress the importance of giving the subconscious every chance. There should be relaxed periods during the working day, profitably, I say, spent in walking.

HOURS A DAY AND DAYS A WEEK On days free from research, and apart from regular holidays, I recommend four hours a day or at most five, with breaks about every hour (for walks perhaps). If you don’t have breaks you unconsciously acquire the habit of slowing down. Preparation of lectures counts more or less as research work for this purpose. On days with teaching duties, I can only say, be careful not to overdo the research. The strain of lecturing, by the way, can be lightened if you apply the golfing maxim: “don’t press.” It is, of course, hard not to. Don’t spend tired periods on proof correction, or work that needs alertness; you make several shots at an emendation that you would do in one when fresh. Even in making a fair copy one is on the qui vive for possible changes.

Either work all out or rest completely. It is too easy, when rather tired, to fritter a whole day away with the intention of working but never getting / [116-117] properly down to it. This is pure waste, nothing is done, and you have had no rest or relaxation. I said “work all out”: speed of associative thought is, I believe, important in creative work; another elusive idea, with which my psychological doctor agrees.

For a week without teaching duties- and here I think I am preaching to the converted – I believe in one afternoon and the following day off. The day off need not necessarily be Sunday, but that has a restful atmosphere of general relaxation, church bells in the distance, other people going to church, and so on. The day, however, should stay the same one of the week; this establishes a rhythm, and you begin relaxing at lunch time the day before.

At one time I used to work 7 days a week (apart, of course, from 3-week chunks of holidays). I experimented during a Long Vacation with a Sunday off, and presently began to notice that ideas had a way of coming on Mondays. I also planned to celebrate the arrival of a decent idea by taking the rest of that day off. And then ideas began coming also on Tuesday.

In these paragraphs, Littlewood beautifully and informally summarizes some of the key practices of deliberate rest: the conscious use of rest to nurture and sustain subconscious creative thinking, the mixing of focused and unfocused periods, the advocacy of exercise, and the practice of keeping an eye out for insights after breaks. It’s all in here, which is why I’m so enthusiastic about it.

Source: John Littlewood, “The mathematician’s art of work,The Mathematical Intelligencer 1:2 (June 1978), 112-119.

Walks and world events

Given the many benefits of walks in nature, the suggestion by Jason Mark, the editor of Sierra Magazine, that “The Paris climate negotiators should go take a hike” isn’t half bad:

The Vexin Français Regional Nature Park is a scant 30 miles from the conference center, and the negotiators could get there and back in a day. The park, northwest of the city, is a 175,000-acre preserve of fields, forests, meadows and marshlands. The place served as an inspiration for painters such as Van Gogh and Cézanne, and perhaps the landscape would inspire the climate diplomats, as well.

Mark points out that during the talks that established the United Nations, participants spent a day in Muir Woods at a service honoring the late Franklin Delano Roosevelt. It was about three weeks into the conference (on May 19th, after an April 25 start), and was a day that had been suggested (while FDR was still alive) by Interior Secretary Harold Ickes. As Ickes had explained to FDR in February 1945:

Not only would this focus attention upon this nation’s interest in preserving these mighty trees for posterity, but here in such a ‘temple of peace’ the delegates would gain a perspective and sense of time that could be obtained nowhere in America better than in a forest. Muir Woods is a cathedral, the pillars of which have stood through much of recorded human history. Many of these trees were standing when Magna Carta was written. The outermost of their growth rings are contemporary with World War II and the Atlantic Charter.

Likewise, Mark argues, time on a hike would help the Paris negotiators get some perspective on their work:

Political scientists and environmental activists often point out that the problem with global climate change is that it’s too big. We’re hard-wired to respond to immediate threats, and since global warming is so large — and most of its worst effects are in the future — we have a hard time wrapping our minds around it. All of the science can seem abstract. And even as the weather gets increasingly weird and unsettling, it can be difficult to separate the signal from the noise and to understand exactly which wild weather phenomena are connected to our reckless emissions.

What better way to ground — really, ground — the negotiators [at the Paris talks] than for them to take a hike?

In my book, I have a chapter about the benefits of walks for clearing one’s head and stimulating new ideas, and why many Nobel laureates, great composers, writers, CEOs, and famous doctors were avid hikers and mountain-climbers. A single walk might not spark a breakthrough, but it can’t but help the Paris talks.

Nature and creative problem solving: how days in the wood boost creativity

This morning via Michael Hyatt, I came across a 2012 study on  “Creativity in the Wild: Improving Creative Reasoning through Immersion in Natural Settings:”

Adults and children are spending more time interacting with media and technology and less time participating in activities in nature. This life-style change clearly has ramifications for our physical well-being, but what impact does this change have on cognition? Higher order cognitive functions including selective attention, problem solving, inhibition, and multi-tasking are all heavily utilized in our modern technology-rich society. Attention Restoration Theory (ART) suggests that exposure to nature can restore prefrontal cortex-mediated executive processes such as these. Consistent with ART, research indicates that exposure to natural settings seems to replenish some, lower-level modules of the executive attentional system. However, the impact of nature on higher-level tasks such as creative problem solving has not been explored. Here we show that four days of immersion in nature, and the corresponding disconnection from multi-media and technology, increases performance on a creativity, problem-solving task by a full 50% in a group of naive hikers. Our results demonstrate that there is a cognitive advantage to be realized if we spend time immersed in a natural setting. We anticipate that this advantage comes from an increase in exposure to natural stimuli that are both emotionally positive and low-arousing and a corresponding decrease in exposure to attention demanding technology, which regularly requires that we attend to sudden events, switch amongst tasks, maintain task goals, and inhibit irrelevant actions or cognitions. A limitation of the current research is the inability to determine if the effects are due to an increased exposure to nature, a decreased exposure to technology, or to other factors associated with spending three days immersed in nature.

The findings are very much in line with everything I’ve been reading about scientists’ vacations, and help flesh out our understanding of why these breaks weren’t a distraction from their work, but helped them be more creative.

And while we think of technology-driven distraction as a new thing, it’s not really: I have people complaining in the late 19th and early 20th century about the constant distractions of letters, telegrams that need a reply, people coming to call, etc.. Of course if’s more persistent now, and our devices are designed to do a better job of grabbing our attention, but what this means is that old solutions are more adaptable to modern conditions than we might at first realize.

Alain Connes: “when fighting with a very complicated problem… go for a long walk”

Advice from Alain Connes (from the Princeton Companion to Mathematics) on being creative:

Walks. One very sane exercise, when fighting with a very complicated problem (often involving computations), is to go for a long walk (no paper or pencil) / and do the computation in one’s head, irrespective of whether one initially feels that “it is too complicated to be done like that.” Even if one does not succeed, it trains the live memory and sharpens one’s skills.

Lying down. Mathematicians usually have a hard time explaining to their partner that the times when they work with most intensity are when they are lying down in the dark on a sofa. Unfortunately, with e-mail and the invasion of computer screens in all mathematical institutions, the opportunity to isolate oneself and concentrate is becoming rarer, and all the more valuable.

Erno Rubik, Graham Wallas, and the invention of the Rubik’s Cube

Just over forty years ago, Erno Rubik invented what is now one of the most famous puzzles ever: the Rubik’s Cube. Recently I saw an interview with Rubik conducted by one of my former bosses, Paul Hoffman.

Paul Hoffman and Erno Rubik, inventor of the Rubik’s Cube (EG8) from EG Conference on Vimeo.

The interview got me interested in Rubik and how he came to create the Cube. It turns out that Rubik was in his late twenties, teaching at the Academy of Applied Arts in Budapest, and sharing an apartment with his mother. He had studied sculpture in college, and was teaching his students about three-dimensional structures. He had a long interest in geometry and puzzles; the bedroom in his apartment (he still lived with his mother at the time) was stuffed with models and puzzles.

Pac Man confusion

That much is clear, and other parts of the story are told consistently, but there are two slightly different accounts of why he was working on the cube. One is represented by this article in Mental Floss, and the story is recounted as one of a pure intellectual challenge:

In 1974, a particular project had him stumped. For months, he’d been working on a block made of smaller cubes that could move without causing the whole structure to fall apart. So far, each attempt had failed. The evidence was strewn all over the two-bedroom apartment he shared with his mother.

One spring day, a frustrated Rubik left the apartment and wandered the streets of Budapest. He followed a gentle bend in the Danube River, a path he had walked countless times before. At one point, he stopped to listen to the water lapping ashore and looked down at the polished round pebbles that lined the riverbank. Suddenly, his heart started racing.

The solution was right at his feet: If individual blocks hinged on a rounded core, they could move freely while maintaining the shape of a cube. Rubik raced home and created a prototype held together with paper clips and rubber bands—a structure consisting of 21 smaller cubelets, adhered to a rounded interlocking mechanism.

In other tellings, the project is sparked by his teaching. For example, Rubik told The Guardian in 2012,

I was searching for a way to demonstrate 3D movement to my students and one day found myself staring into the River Danube, looking at how the water moved around the pebbles. This became the inspiration for the cube’s twisting mechanism. The fact that it can do this without falling apart is part of its magic.

I experimented in my mother’s flat, using wood, rubber bands and paper clips to make a prototype. I needed some sort of coding to bring sense to the rotations of the cube, so I used the simplest and strongest solution: primary colours. Putting the stickers on the finished cube felt very emotional.

Brightly-colored cubes on my desk

As he told CNN in 2012, “Usually structures are pieces that are connected in some way or another,”

and usually these connections are stable things. So all the time “A” is connected to “B.” But with the structure of the Rubik’s Cube, you realize these elements are moving very freely, but you don’t understand what keeps the whole thing together, so that was a very interesting part of it.

A 1986 Discover Magazine article explicitly favors the first account over the second:

Many of the early stories about the Cube related that it was built to teach Rubik’s students how to “deal with three-dimensional objects.” I never understood what this meant, much less how the Cube could teach it. The mystery was cleared up after I arrived in Budapest. At the Academy they chuckled at the thought of using the Cube in class, and Rubik dismissed the idea. Yes, he had shown the Cube to his students, but he hadn’t built it for them. He built it because he was a designer who likes playing with geometric shapes. 

But no matter how it starts, Rubik’s story is almost a perfect example of the four-stage model of thinking and discovery that Graham Wallas outlined in his classic 1926 book The Art of Thought. (Wallas never uses the word “creativity,” by the way.)

When working on difficult problems, Wallas argued, people generally go through four stages.

The first stage is Preparation: they organize a line of attack, consciously work through alternatives, and eliminate possibilities. Sometimes this is enough to solve a problem, if it’s not too hard; but most interesting problems don’t give up so easily.

With the harder ones, there follows a second phase: Incubation, a period of “voluntary abstention from conscious thought on any particular problem.”

Mental relaxation during the incubation stage may of course include, and sometimes requires, a certain amount of physical exercise…. When I once discussed this fact with an athletic Cambridge friend, he expressed his gratitude for any evidence which would provide that it was the duty of all intellectual workers to spend their vacations in alpine climbing.

There are also countless stories of people going on walks in this phase. I don’t know where Rubik was living, but the walk along the Danube detail makes perfect sense to me, since the river runs right through Budapest.


In fact, for a long time the city was two cities on opposite sides of the river, Buda and Pest. Only in the late 1800s, with the building of permanent bridges across the Danube, were they formally united.


After some period, this period ends with a sudden third phrase, Illumination, in which the answer suddenly dawns (or is suddenly present in the conscious mind). This is the moment of insight, the a-ha moment, the epiphany, whatever you choose to call it.


The fourth and final stage, when the new idea is tested, and a proof worked up or prototype finished, is Verification.

My daughter soldering

Whatever the inspiration, there are elements of the Rubik’s Cube story that are pretty consistent: his working on the problem for a long time (Preparation); being stumped with the problem of how to hold a three-dimensional structure of multiple cubes together (Incubation); taking a walk along the Danube, and seeing in the movement of the water around the pebbles the solution to the twisting mechanism problem (Illumination); and a few days’ work to build the first prototype (Verification).

But the discovery of the Rubik’s cube structure is only the first moment of inspiration in the story. There’s a second. As he wrote in an unpublished autobiography, Rubik put colored stickers on the cubes as a way of keeping track of them. But at one point he noticed something cool:

It was wonderful to see how, after only a few turns, the colors became mixed, apparently in random fashion. It was tremendously satisfying to watch this color parade. Like after a nice walk when you have seen many lovely sights you decide to go home, after a while I decided it was time to go home, let us put the cubes back in order. And it was at that moment that I came face to face with the Big Challenge: What is the way home?

Two things are striking about this. First, there’s the metaphor of the walk again. You’ve been out made some nice discoveries, seen “lovely sights,” and now it’s time to go home. Solving the puzzle is a kind of homecoming.

Budapest street in the evening

The second is that this makes clear that Rubik didn’t set out to design a puzzle. He set out to create a cool three-dimensional structure. It was only after he had built it that he discovered it was also a puzzle.

It took him a month to solve puzzle. At first, he wasn’t even sure it was possible: after all, the cube has some 43 quintillion possible combinations. As he told Discover, working on it was like “staring at a piece of writing written in a secret code. But for me, it was a code I myself had invented! Yet I could not read it. This was such an extraordinary situation that I simply could not accept it.” 

Budapest street in the evening

The first time he solved it, he said in his CNN interview, “it was a very emotional feeling.” His mother was happy, too, he told Discover: “I remember how proudly I demonstrated to her when I found the solution of the problem, and how happy she was in the hope that from then on I would not work so hard on it.”

But the cool thing about the cube is that, because it’s so much of a challenge, it’s not like a game where once you know the solution, you’re done. As he explained in the CNN interview:

But then it’s not something like a jigsaw puzzle where you start to work on it, spend some time on it, and in the end it’s solved, it’s finished. If you find a solution with the cube, it doesn’t mean you find everything. It’s only a starting point. You can work on and find something else, you can improve your solution, you can make it shorter, you can go deeper and deeper and collect knowledge and many other things.

Or, as he put it in the Discover article, “with the Cube there are many flashes [of insight], there are many a-ha’s.” The Cube is a generator of a-ha moments that is itself the product of an a-ha moment. 

Game over!

“I’ve got it down to a fine art: walk, scroll, glance up, stop, tap, walk”

In the Guardian, Viv Groskop confesses that “I’m a bit of a wexter:”

We all have bad habits, and now there’s an appropriately nasty word for mine: wexting (using your phone as you walk). I’ve got it down to a fine art: walk, scroll, glance up, stop, tap, walk. A lot of the time, rather like a teenage boy, I have been wexting without realising I’m doing it. I don’t think this awful expression is going to catch on, by the way, so I’m just making the most of it while it’s new.

Habitual wexting is not going to send me blind. But I do think it is making me behave antisocially. The tipping point? This week I noticed a photograph of women priests celebrating the first female bishop, holding their phone screens aloft, like fans at a One Direction concert, as they paraded outside York Minster. They were at the consecration of the new suffragan bishop and they were merrily wexting away.

Here’s the scene:

Which, perhaps inevitably, reminds me of this:

Bored and Brilliant: Day 1

WNYC’s Bored and Brilliant challenge starts today.

What’s on the agenda?

As you move from place to place, keep your phone in your pocket, out of your direct line of sight. Better yet, keep it in your bag.

I would think if there was one place in the world you could wander around with our looking at your cellphone, it would be New York, but as host Manoush Zomorodi recently found, a third of people on the streets are looking down at their phones while walking. (In my experience the number is astronomical on subways.)

Times Square at night

The podcast features an interview with me, which we conducted a few weeks ago.


You can listen to it below. Manoush and her team did an excellent job editing it.

It concludes with several suggestions for how to better manage your phone, using whitelists, special ringtones, and so on. It was fun.

I really like the Bored and Brilliant challenge because, unlike many “put down your phone and get back to the real world” sorts of challenges, Manoush and her team seem intent on providing listeners with advice about what to do instead of checking their mail a dozen times an hour. Too often these campaigns treat digital distraction as a moral failing that simply requires Being A Better Person; the Bored and Brilliant approach is more constructive.

It’s also perfectly balanced between my last book and my next one. As I said in another recent interview, while The Distraction Addiction is about the benefits of mindfulness, the next book is about the benefits of mind-wandering— and how digital technologies do a brilliant job of intruding on both, by offering diversions that seep into our time as effectively as water into a basement.

Mindfulness and mind-wandering don’t just share a mutual enemy. They’re linked to each other. (By mind-wandering I mean not distraction— having your attention drawing to B when it should be on A— but rather allowing your mind to be focused on nothing at all, and leaving it free to attend to what it wants, without conscious effort.) The evidence I’m seeing is that people who are capable of concentrating really hard on a subject are also very good at intentionally disengaging their minds; that, in effect, improving your ability to do the one improves your ability to do the other.

So to be brilliant, it seems, you must be bored.

“A walk of twenty or thirty miles a day is one of his favorite amusements”

One of the things that constantly amazes me about our ancestors is how much more exercise they got in the course of a day, and especially how much exercise writers and scientists would get. Consider, for example, this account of early 19th-century social reformer Francis Place, from Graham Wallas’ biography The Life of Francis Place:

A very good description of Place and his daily life about this time, was given in the Northern Liberator. “Francis Place… is in the sixty-fifth year of his age. He is about five feet seven inches high, with a head which would delight the phrenological taste… and is of a stout, stalwart frame. A walk of twenty or thirty miles a day is one of / his favorite amusements; but his time, from six in the morning to eleven at night, is generally spent in his library, where he is surrounded with books, pamphlets, journals, and memoranda of every kind.” [177-178]

Place also spent some time at Ford Abbey, Jeremy Bentham’s home between 1814 and 1818.

Ford Abbey, from a collection at University College London

He left this account:

“I rise at six and go to work; at nine breakfast in the parlor…. From breakfast time to one o’clock I am occupied in learning Latin; this is also done aloud in the walks…. At one we all three walk in the lanes and fields for an hour. At two we all go to work again till dinner at six…. After dinner, Mill and I take a sharp walk for two hours, say, till a quarter past eight, then one of us alternately walks with Mr. Bentham for an hour; then comes tea, at which we read the periodical publications; and level o’clock comes but too soon, and we all go to bed.” [76]

These multi-hour walks were not at all unusual, even for people who spent a lot of time walking to, you know, just get from Point A to Point B. Just one more example, from the biography of one of Place’s intellectual descendants, the late 19th-century Utilitarian philosopher Henry Sidgwick, describing his habits as a student at Cambridge in the 1850s:

For active exercise he was restricted to the daily walk between two and four, which was then the common practice of the reading man who did not boat and could not afford to ride. It must be remembered that in the fifties at Cambridge boating was the only organised sport within the reach of everybody. There was no regular football ; cricket was confined to the May Term, and few colleges had their own grounds; racquets and fives were only just beginning; croquet (if that can be called exercise), lawn-tennis, the bicycle, and polo were none of them yet invented. Sidgwick had no aptitude or liking for boating ; and even if he had tried it, the exertion would have been too great to be permitted after he fell ill. In one way the attack was a blessing in disguise, since it forced him to realise the importance of regularity in open-air exercise, which otherwise, with his insatiable intellectual curiosity and his ever-growing range and variety of interests, he might have been tempted somewhat to neglect. [19]

“How can one look happy when he is thinking about the anomalous Zeeman effect?”

Yet another anecdote on walking and mind-wandering, this time from Chemistry World:

In late 1922, Wolfgang Pauli took an aimless stroll through Copenhagen’s beautiful streets, deep in thought. Presently, the Austrian physicist met a colleague who remarked in a friendly manner, ‘You look very unhappy.’ Pauli answered fiercely: ‘How can one look happy when he is thinking about the anomalous Zeeman effect?’ How indeed?

Pauli recalled the episode shortly after winning the Nobel prize in physics in 1945 for his formulation of the exclusion principle: each electron in an atom must occupy a unique quantum state. Although he didn’t know it as he wandered around Copenhagen, struggling to explain how magnetic fields split atomic spectra, Pauli was unwittingly laying the foundations for his greatest insight.


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