The Mystery
in Action
“When we start to look closely at all this complexity, surprising patterns begin to emerge. It is these patterns that I believe point to an underlying code at the very heart of existence, and that controls not only our world and everything in it, but even us.” - Marcus du Sautoy (Professor of Mathematics, University of Oxford)
THE FINAL MYSTERY
DISCOVERING THE UNIMAGINABLE
The Mystery Beyond the Multiverse
“A mystery lurks beneath the magic carpet of science, something that scientists have not been telling, something too shocking to mention.” - John D. Barrow. (Professor of Mathematical Sciences, University of Cambridge.) The Magic of Infinities
“There are no more moments in all of eternity than there are in, say, one minute. In both cases there is an infinite number.” - Paul Davies, Director of the Centre for Fundamental Concepts in Science, Arizona State University. Atoms and the Multiverse
“This idea that the universe has multiple histories may sound like science fiction, but it is now accepted as science fact.” - Stephen Hawking, former Lucasian Professor of Mathematics, University of Cambridge. The Final Mystery
“It is a matter of contention whether anything resembling a ‘theory of everything’ will ever be found.” - Sir Roger Penrose, Emeritus Rouse Ball Professor of Mathematics, University of Oxford.
“A mystery lurks beneath the magic carpet of science, something that scientists have not been telling, something too shocking to mention.” - John D. Barrow. (Professor of Mathematical Sciences, University of Cambridge.) The Magic of Infinities
“There are no more moments in all of eternity than there are in, say, one minute. In both cases there is an infinite number.” - Paul Davies, Director of the Centre for Fundamental Concepts in Science, Arizona State University. Atoms and the Multiverse
“This idea that the universe has multiple histories may sound like science fiction, but it is now accepted as science fact.” - Stephen Hawking, former Lucasian Professor of Mathematics, University of Cambridge. The Final Mystery
“It is a matter of contention whether anything resembling a ‘theory of everything’ will ever be found.” - Sir Roger Penrose, Emeritus Rouse Ball Professor of Mathematics, University of Oxford.
Figure 1. Isaac Newton
Isaac Newton and Gravity
It still shocks me to think that Newton managed to discover how gravity works and apply this to how the planets orbit the sun, and things so utterly different and unconnected as falling apples and the moon creating the ocean tides … using nothing more sophisticated than a feather quill and ink made from soot and water! No experiments, no laboratory - it’s quite preposterous when you think about it. So powerful is this mathematics that three hundred years later it is still the main tool used to plan all space missions. No wonder Wigner thought it a miracle.
Discovery of Neptune
Another example that illustrates the astounding power of equations took place in 1846 when a Cornishman and a Frenchman, who had never heard of each other, and using different methods, both discovered the planet Neptune - just by manipulating symbols on a piece of paper, and probably by candlelight! At the stroke of a pen (literally), they discovered that our Solar system is far bigger than any human had thought possible. Only later did telescopes find it. From studying the movement of the then known planets, they figured there must be another one, and by using mathematics they were able to pinpoint where it should be. When telescopes were trained in the suggested direction, they found it, exactly where it had been predicted!
Figure 2. James Clark Maxwell
James Clark Maxwell and Electromagnetism
A landmark in the mystery of mathematics occurred when Maxwell discovered the equations that showed electricity and magnetism to be the same thing. I mean, lightning and fridge magnets? You could hardly think of two more different things. And then how he was totally shocked when he first realized that they were the same thing as light! Nor did it stop there, the equations also revealed the existence of radio waves and the rest of the electromagnetic spectrum which were only discovered later. From… squiggles on paper? Our whole Information Age has been made possible by this mathematics, and Maxwell is considered to be in the same company as Newton and Einstein.
Einstein and Relativity
The mystery of mathematics gets even more astonishing when we come to Einstein. With his Theory of Special Relativity (1905) he discovered that all matter is just locked up energy, and even more surprising, that space and time are the same thing, now called space-time. Our senses tell us that this is just bizarre, yet the equations have been proven to be true countless times. To come up with his masterpiece, the General Theory of Relativity (1915) he had to learn a new kind of geometry discovered by Riemann a hundred years earlier as a purely mathematical exercise. But it turned out to prove that gravity is not a mysterious force that attracts things like apples falling to the ground, it’s the result of objects bending space. So, contrary to all our senses, space is actually a ‘thing’! A big enough miracle in itself, but also that it could describe not just our solar system ‘out there’, no - it could describe the whole universe! If you think about it too long, the enormous power of mathematics to describe our reality can become a bit frightening. How can patterns that merely follow an internal logic by means of arbitrary figures possibly describe something as gigantic as the observable universe?
Figure 3. Albert Einstein
Einstein and the Cosmological Constant
When he tried the equations out, they kept telling him that the universe had to be either expanding or contracting. It could not be static and stationary. Yet everyone who had ever looked at the night sky and thought about the universe, from the Sumerians onwards, had never dreamed that it could possibly be moving. Einstein was no different. He thought the equations had to be wrong. So he cheated. He told everyone he was doing it of course, and he added a bit to the equations to keep the universe still, and called it the Cosmological Constant.
Just over ten years later Hubble was able to measure that the universe was indeed expanding! This is surely one of the greatest discoveries in all of science. If Einstein had only believed in the equations, how much bigger would his legacy have been? He later admitted that it was the greatest blunder of his life. I want to add an anecdote here, just briefly, because it neatly illustrates the mysterious power of equations. In 1931 Einstein visited the U.S.A. When he was in California, Hubble invited him and his wife Elsa to have a look at the telescope on Mount Wilson where he had discovered that the universe was expanding. When it was explained to Elsa that all the mass of the equipment was used to determine the size and shape of the universe, she is said to have replied, “that’s nothing. My husband does it on the back of an envelope!”
Paul Dirac and the Discovery of Antimatter
Figure 4. Paul Dirac
One of the most spectacular examples of the power of equations to describe our world comes from Paul Dirac (Nobel Prize in Physics, 1933). When he was trying to combine Special Relativity with Quantum Theory, the equations kept telling him that there was a particle never seen before which was exactly the same as an electron but with a positive charge. Try as he might he couldn’t get rid of it. He became really frustrated with it, and in the end accepted it just to make the equations work.
He had discovered antimatter. Something that a human mind could hardly conceive of, not even in dreams. Yet a few years later Carl Anderson, doing experiments with high altitude balloons, detected the same particles that became known as positrons. Since then it has been shown that every known particle has an antimatter partner, and antimatter is regularly produced now in accelerator experiments. Even more important, it is accepted that, microseconds after the Big Bang, a contest between matter and antimatter decided the actual structure of our universe and hence the emergence of our consciousness. Discovered, yes… just by manipulating squiggles on a piece of paper! This is the mysterious and awesome power of mathematics.
More Evidence
There are many other examples like the prediction by Louis de Broglie (Nobel Prize in Physics, 1929), that particles are also waves, or the discovery of the ‘pion’ by Hideki Yukawa (Nobel Prize in Physics, 1949). Then there is the prediction known as the Eightfold Way discovered by Murray Gell-Mann (Nobel Prize in Physics, 1969) which led to the discovery of quarks when everyone, including Gell-Mann, thought that they were just a mathematical convenience. The most recent example is the Higgs particle discovered mathematically by Peter Higgs and others in 1964 and which was only confirmed 48 years later in 2012. And finally there is the staggering triumph of John Bell’s Theorem which appears to prove that the whole universe is connected! More about this in the book.