What’s in it for me? Meet the great minds that shaped our understanding of the physical world.
Whether it’s quantum mechanics, the theory of relativity, or the logic of primes – important ideas in math and physics can appear so abstract they’re dizzying to think about.
But these big ideas have real and dramatic consequences for our understanding of the world. And the people who came up with them led real and dramatic lives. Did you know, for example, that Alan Turing died from eating an apple laced with cyanide?
These blinks won’t just help you understand the most important scientific ideas of the last century – they’ll also introduce you to the zany characters who conceived them. From the hidden dimensions of string theory to Kurt Gödel’s eating habits, you’ll get a glimpse into the lives of the people behind some of the biggest scientific discoveries in modern history.
In these blinks, you’ll learn
what Einstein and Gödel thought about quantum mechanics;
about a very difficult way to earn a million dollars; and
why Alan Turing’s death remains a mystery to this day.
Toward the end of his life, Albert Einstein struck up an unlikely friendship with the young logician Kurt Gödel.
Of all the unique characters in the history of science, perhaps no one is as iconic as the German-born physicist Albert Einstein. Nearly anyone would recognize an image of the eccentric genius with the wild hair.
In 1905, while still holding down a day job at a patent office in Switzerland, Einstein published four short papers that forever changed how we understand the world. In the first one, he showed that light comes in discrete particles, later dubbed photons. In the second, he finally proved that atoms were real and showed how to calculate the seemingly random way they move around in gas or liquids. In the third paper, he introduced his theory of relativity, completely upending our notions about space and time. And in the last one, he coined his famous formula E=mc2, illuminating the relationship between mass and energy.
These papers were undoubtedly extraordinary achievements, and they shot Einstein to world fame. But few people know that Einstein spent the last years of his life in isolation, sneered at by the rest of the scientific community.
Here’s the key message: Toward the end of his life, Albert Einstein struck up an unlikely friendship with the young logician Kurt Gödel.
In 1933, with his greatest discoveries behind him, Einstein fled from Germany to the US and settled in Princeton, New Jersey. At the time, his star in the scientific community had already begun to fade. This was partially due to his opposition to quantum mechanics, a hot new theory that sought to explain the movement of subatomic particles. Einstein regarded the implications of quantum theory as too “spooky” to be true, alienating himself from much of the scientific community at the time.
And so he spent his days going on long, solitary walks around the Princeton campus. After a while though, he found an unlikely walking companion: the much younger Kurt Gödel. The genius logician Gödel was highly regarded for his incompleteness theorems, with which he had shown that no logical system is 100 percent airtight. With his ideas, Gödel challenged the notion that humans could ever achieve something like absolute knowledge.
While Einstein’s star was fading, Gödel’s star was shining brighter than ever. In terms of personality, too, the two men were polar opposites. Einstein was cheerful and gregarious, whereas Gödel was serious and pessimistic. Even by the standards of quirky old Einstein, Gödel was a strange fellow. It was rumored that he lived off a diet of baby food, butter, and laxatives.
Despite their differences, Einstein and Gödel shared a deep intellectual connection. They both believed that mathematics was not just some abstract game of symbols, but a discipline deeply rooted in physical reality. This wasn’t a very popular opinion at the time. Gödel also shared Einstein's skepticism of quantum mechanics. And on the matter of time, Gödel took Einstein’s famous relativity theory even further than its originator. We’ll see how in the next blink.
Gödel drew on Einstein’s relativity theory to show that time is impossible.
In the early twentieth century, physicists were sure of two things: One, the laws of physics are absolute – meaning they’re valid for everyone, everywhere. Two, the speed of light is absolute – meaning the speed of light is the same for everyone, everywhere.
But with his theory of relativity, Einstein proved that if these things are true, then space and time have to be relative. He first drafted this theory in a short paper published in 1905, and later expanded it into the general theory of relativity.
To many scientists, however, Einstein’s theory was so upsetting that they initially refused to accept it. Indeed, when Einstein received the Nobel Prize for his work on the photoelectric effect in 1921, the academy forbade Einstein from mentioning relativity theory in his acceptance speech.
The key message here is: Gödel drew on Einstein’s relativity theory to show that time is impossible.
Here’s a thought experiment to illustrate the main idea behind the theory of relativity. Imagine you were observing a light beam fly past you at some distance. For this example, let’s suppose the speed of light was only 100 miles per hour. Now, imagine that you see your friend chasing after the light beam in a car traveling at 60 miles per hour. From your vantage point it would look like the light beam was moving at a speed of 100 miles per hour and outpacing your friend by 40 miles per hour. For your friend, it would look like the light beam was only moving away from him at 40 miles per hour. Right?
This is where things get strange. Just like you, your friend would measure the speed of light to be 100 miles per hour regardless of how fast he was moving towards the light beam. How can this be? What Einstein theorized was that, if the speed of light is the same for all observers, the distances and the times they measure must be different. In other words, as your friend is chasing the light beam, the distance he would measure to the light beam would be longer than yours and, if he had a clock with him in his car, it would tick slower than yours.
As strange as it sounds, a wealth of experiments has borne this out since Eintein first posited it more than a hundred years ago. With this, Einstein completely upended the laws of physics.
Gödel took Einstein’s idea even further. Trying to solve Einstein’s equations, he came to the conclusion that the universe wasn’t expanding, but rotating. In such a rotating universe, it’s theoretically imaginable that someone could travel back in time. If time travel is mathematically possible, Gödel concluded, then time itself doesn’t exist at all.
Illusion or not, Gödel’s own time on Earth met a tragic end. After Einstein’s death in 1955, the brilliant mathematician grew more and more secluded. He also became increasingly paranoid; convinced that someone was trying to poison him, he finally stopped eating altogether. In January of 1978, he died of self-starvation at Princeton Hospital.
Numbers have their own music – and we’ve developed a special ear for it.
For many people, math is pretty hard. Most people would probably deny that they have any kind of mathematical intuition. But they do – in fact, we all do.
In the 1980s, the neuroscientist Stanislas Dehaene was studying a French man who’d suffered an injury to the back left half of his brain. As a result, the man had extreme difficulties processing numbers. Asked to add two and two, for example, he would sometimes answer “three,” sometimes “five.” However, Dehaene noticed, he never gave an answer as outlandish as “nine” or “20.”
The key message here is: Numbers have their own music – and we’ve developed a special ear for it.
Dehaene concluded that our brain must have a special “number sense” that allows us to roughly estimate and add together objects in our environment. Later, he even located the precise brain cells that enable us to do this. There seems to be a special number 4 neuron, for example, which gets particularly excited when we’re looking at four objects. By now, researchers believe that a dysfunctional “number sense” may express itself as dyscalculia, a difficulty in processing numbers that is similar to dyslexia.
Higher mathematics, of course, relies on much more than our rudimentary number sense. It also involves areas of our brain dedicated to processing visual and linguistic information, in order to process written digits and words for numbers. But in higher mathematics, too, scientists often rely on their intuition.
Here’s an example. One of the great mysteries of higher mathematics is the distribution of prime numbers. A prime number is any number that is divisible only by 1 and itself, such as the numbers 3, 17, and 2179. Throughout the number sequence, prime numbers are spread further and further apart. But sometimes, even very large prime numbers are lumped closely together – 1,000,000,009,649 and 1,000,000,009,651, for instance.
In the nineteenth century, German mathematician Bernhard Riemann discovered a mathematical function that may hold the key to understanding the “music of the primes.” The Riemann zeta conjecture holds that the zeros of the Riemann zeta function can help us predict the distribution of all prime numbers. But so far, no one has been able to conclusively prove its verity. Indeed, the Riemann zeta conjecture is one of the greatest unsolved problems in mathematics today. There’s even a million-dollar reward for anyone who can prove it!
Despite still being unproven, the Riemann zeta conjecture is so beloved by mathematicians that they often assume its truth in calculations. They make this judgement based on criteria that might strike some of us as quite un-mathematic – we’ll learn more about them in the next blink.
Pure mathematics is more about beauty than usefulness.
What is math, anyway?
The answer is, as answers so often are, inconclusive: it depends. Applied mathematics, for instance, uses numbers, functions, and calculations to solve real-world problems. A lot of people who study mathematics end up applying their skills in other research fields like physics or biology, or in commercial areas like business and finance.
But a handful of mathematicians get caught up in another, loftier, and more abstract branch of the science: pure mathematics. This kind of mathematics is not really about finding practical solutions to real world problems. It’s more about manipulating numbers, functions, and calculations on their own to find interesting connections between them.
Some people, like the famous philosopher Ludwig Wittgenstein, have thought that pure math is basically just a logic game played with numbers. But others, including “Platonists” like Einstein and Gödel, have held that even abstract mathematics has a basis in the real nature of our world.
The key message here is: Pure mathematics is more about beauty than usefulness.
Pure mathematicians are interested in finding proofs for a mathematical statement or problem – often posed decades earlier. The Riemann zeta conjecture we got to know in the last blink, for example, is one of seven “Millennium Prize Problems,” a collection of the greatest unsolved problems in mathematics to date.
When they’re hunting for proofs, mathematicians are not just looking for any kind of proof though – they’re looking for beautiful ones. Some mathematicians go so far as to consider beauty the ultimate measure of a theory. For them, beauty usually means a mix of simplicity, strangeness, and inevitability.
Beauty may seem like a strange criterion for a science so considered with rigor and logic. But throughout history, beauty has often been equated with truth. In his famous 1940 book A Mathematician’s Apology, British mathematician G. H. Hardy argued that pure mathematics is more like art than science – it’s not about solving problems, it’s about painting a compelling picture using the language of mathematics.
One area of mathematics that makes almost anyone stop and appreciate the beauty of math is Benoit Mandelbrot’s fractal geometry. In the late 1970s, the Polish-French-American mathematician introduced the idea that certain rough physical structures are “self-similar,” or “fractal.” If you break apart a cauliflower, for example, you’ll notice that each little floret looks like a tiny head of cauliflower. This holds for many structures in our universe, such as clouds, networks of blood vessels, and clusters of galaxies. Later, when he worked for IBM in New York, Mandelbrot used some of the very first computers to show how complex fractal patterns can arise from very simple formulas – often producing stunning, geometric digital drawings.
Infinity doesn’t come in just one size.
Since the beginning of history, scientists have been fascinated by infinity – whether it be the idea of endless space, endless time, or endless numbers. Actually, it’s not just scientists who’ve been fascinated by the subject. For many of us, the notion of infinity holds an intriguing, almost magical power.
What many people consider infinity comes in two versions. Of course, there’s infinitely big. When scientists explore this type of infinity, their work often approaches mysticism. Some Russian mathematicians of the 1920s, for instance, conflated their mathematical explorations of infinity with theological explorations of God.
But there’s also the idea of the infinitesimally small, or infinitesimal – and it’s no less puzzling than the infinitely big. In mathematics, for example, each number is divisible into infinitely many fractions.
The key message here is: Infinity doesn’t come in just one size.
Since the time of the ancient Greeks, mathematicians have used infinitely small fractions to calculate certain geometric forms and volumes. But for a long time, scientists regarded the idea of the infinitesimal with suspicion. That’s because most of them didn’t believe that infinitely small fractions actually existed in the real world. They were convinced that the smallest unit of the physical world was an atom, which couldn’t be split up any further.
In the seventeenth century, French mathematician Blaise Pascal shortly revived the idea of the infinitesimal, using it to calculate the areas under curvilinear forms – that is, forms characterized by curved lines and shapes. Isaac Newton, too, made use of the infinitesimal when he calculated the exact orbit of a planet around the sun. But Newton agreed with his contemporary Gottfried Wilhelm Leibniz that infinitely small quantities were nothing but “well-founded fictions” in mathematics – useful, but not really real.
Over the next two centuries, the infinitesimal fell out of fashion. Most mathematicians didn’t see the point of basing calculations on quantities that didn’t really exist. They feared that somewhere down the line, this approach would turn up huge contradictions.
It was only in the 1960s that mathematician Abraham Robinson was able to rehabilitate the image of the infinitesimal. Robinson was able to draw on Gödel’s completeness theorem – the counterpart to his incompleteness theorems – to show that even if we can’t be sure of the reality of the infinitesimal, we can still be sure of the logical consistency of the calculations that involve it. That, Robinson argued, should be enough to satisfy the standards of modern mathematics.
But perhaps the infinitely small isn’t just a useful fiction. Today, we know that atoms can indeed be divided – specifically, into electrons, protons, and neutrons. The latter two can be divided into even smaller particles called quarks. And there’s some evidence that even quarks can be divided up further. So maybe the universe is not just infinitely big – maybe it’s also infinitely small.
After he pioneered modern computing, Alan Turing died under mysterious circumstances.
The history of science is littered with strange and untimely deaths. But perhaps none is as mysterious as that of Alan Turing, the father of modern computer science. Turing died in June 1954, apparently from eating an apple laced with cyanide. The death was ruled a suicide, but many people are not convinced.
During World War II, Turing was responsible for cracking the code of the Enigma machine, a device the Germans used to encrypt their communication. This proved a huge help to the British forces in winning the war. Shortly before his death, Turing was also prosecuted because he was gay. Did he kill himself because of the stigma? Or was he killed because he knew too much?
Here’s the key message: After he pioneered modern computing, Alan Turing died under mysterious circumstances.
Turing got his PhD in mathematics at Princeton in 1937. During his time at Princeton, he conceived the blueprint for the modern computer. Turing’s abstract computing devices were dubbed “Turing machines.” You can think of a Turing machine as a little scanner that travels over an infinite tape composed of squares. On each square, the scanner can write or erase a 0 or a 1. The scanner’s next action depends on the state it's in, as well as the symbol of the square it’s on. By moving back and forth on the tape, the scanner can implement any logical algorithm, no matter how complex.
When he cracked the Nazi code, Turing put his theoretical ideas about computation to the test. The German Enigma machine used a complex system of rotating wheels to encrypt each letter in such a way that only a specially programmed receiving machine could decipher it. But Turing found that by analyzing certain repeat phrases the Germans used, such as “weather,” he could detect logical consistencies in the way the Enigma coded letters. To help with his work, he built a counter-coding machine called the Bombe, which is now considered a milestone in the history of computing.
Turing’s wartime achievements were only revealed in the 1980s, decades after his death. After the war, he settled down in Manchester, where he began an affair with a young man. When the man’s acquaintances robbed him, Turing went to the police. But instead of receiving justice, it was he who ended up being prosecuted for his homosexuality – and sentenced to chemical castration.
This incident occurred two years before he died. Was this unfair treatment by the same government he’d helped win a war what made Turing commit suicide? Or was someone trying to silence him? In 2013, Turing was pardoned by the British Queen, but to this day, no one can explain his mysterious death.
String theory could explain everything – or nothing at all.
If there’s a holy grail of physics, then it’s certainly the theory of everything – a theory so powerful that it explains everything from the smallest subatomic movements to the eternal laws of nature.
Einstein’s general theory of relativity went a long way in explaining the fundamental interactions of gravity, mass, space, and time. And a little later, quantum theory helped explain how subatomic particles behave at the micro-level – apparently in a much more random and uncertain fashion than huge physical forces. Both general relativity theory and quantum mechanics seem to be true. But for a while, no one was able to bring them together. Until string theory came along.
Its main idea is this: the smallest elements that make up our world aren’t discrete particles, but tiny, vibrating “strings of energy.” Different vibrations produce different natural phenomena.
Here’s the key message: String theory could explain everything – or nothing at all.
By introducing the idea of vibrating energy strands, string theory is able to explain both the macro-forces outlined by relativity theory and the micro-uncertainties described by quantum mechanics. But not all scientists think this explanation is very useful.
On the surface level, it’s what many scientists would call a “beautiful” theory: it’s simple, elegant, and able to explain a lot. But as soon as one dives a bit deeper, string theory reveals its ugly complications.
For example, in order for the math behind string theory to add up, physicists have to assume that the world has at least nine spatial dimensions. But where are those extra six dimensions we never get to see? Well, they’re folded up so that they’re imperceptibly small, says the string theorist.
Unsurprisingly, this complicated dimension-math created a lot of complicated problems. In the 1980s, theoretical physicist Edward Witten worked out some of the flaws of string theory by adding vibrating membranes and blobs on top of the vibrating strings. He called his proposal “M-theory.”
For some scientists, this was all a bit too much. In 2006, theoretical physicist Peter Woit published a book exposing the all-too-powerful doctrine in contemporary physics. According to Woit, the voices of scientists who don’t support string theory are downright suppressed in the scientific community.
The problem, as Woit points out, is that to date, there’s no empirical way to prove that string theory is correct. It now comes in so many variations that it can be used to predict everything and nothing. Indeed, in 2006, French brothers Igor and Grichka Bogdanov were able to publish a series of papers on string theory in highly regarded scientific journals – papers which, it later turned out, were completely made-up nonsense.
The main reason the nonsense remains so popular, it seems, is that so far, no one has thought of anything better.
Physics gives us a clue about how it will all end.
Scientists today pretty much agree on how the universe started – with the big bang, 13.82 billion years ago. They also agree that the universe has been expanding. What they don’t agree on is how it will all end.
So far, they’ve come up with three competing theories on how the universe will end. The first one assumes that the expansion will go on forever, until all particles of the universe are spread so far apart that life as we know it becomes practically impossible.
Physicists call this scenario the big chill – and it comes with a surprising twist. Since this ever-expanding universe is infinitely big, it’s theoretically possible that once every billion years or so, a few of the remaining particles in the universe will come together in such an unlikely constellation that they produce a form of consciousness.
The key message here is: Physics gives us a clue about how it will all end.
Physicists call the temporary conscious entities that will float around in the chilled universe Boltzmann brains. But this isn’t the only weird, distant-future sci-fi scenario that modern physics has to offer.
The second theory of how it all ends proposes that the expansion of the universe will eventually stop. The universe will then begin to collapse back onto itself. This scenario is dubbed the big crunch. But here, too, there might be an upside. Physicist Frank Tipler, for example, has argued that the universe will produce such massive amounts of energy during its collapse that it will be able to drive an infinite amount of computation – and mere seconds of conscious life will spread out to near infinity.
If that’s not enough for you, scientists have recently proposed another theory: the big crack-up. This theory is based on the notion that the universe isn’t just expanding, but expanding faster and faster. In ten to twenty billion years, protons will eventually decay, and matter will dissolve entirely. Sounds fun, right?
But at least we can rest assured that humanity will probably be around for a while longer. We can determine this by applying the Copernican principle. If you’re seeing a theater play, for instance, there’s a 95 percent chance you won’t be among either the first or last 2.5 percent of its viewers. The same principle holds for everything. This means that we can be 95 percent sure that we’re not among the last 2.5 percent of humans ever to live.
That’s a pretty confident margin! And since humans have already been around for 200,000 years, this means we get at least another 5,100 – and maybe as many as 7.8 million – years before our eventual extinction. So whether the universe dies by ice or fire, we probably won’t be around to witness it.
Final summary
The key message in these blinks:
They might seem daunting to the layman, but math and physics hold the key to understanding our world. Over the past few centuries, our concepts of time, space, and our own existence have changed radically through the discoveries of genius scientists like Albert Einstein, Kurt Gödel, and Alan Turing. Nonetheless, genius scientists are also just people – and often, their lives have met tragic ends.
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What to read next: The Order of Time, by Carlo Rovelli
One of the questions explored in these blinks was whether time really exists. Einstein thought time was simply a matter of perception. Gödel thought time didn’t exist at all. But they weren’t the only physicists fascinated by the subject.
In The Order of Time, contemporary physicist Carlo Rovelli delves deep into the latest scientific research on the phenomenon of time, unsettling many of our commonplace ideas about it in the process. So, if you have the time, check out our blinks to The Order of Time to learn more!