When Einstein Walked with Gödel summary

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.

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.” 

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. 

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. 

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?

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. 

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.