Chapter -1:
Before the Beginning
Numbers flow past us like a blizzard, wherever we are on the planet. We drive in rivers of numbers. We listen to numbers on headphones. We wear changing numbers on our wrists. We live in numbers, talk in numbers and watch numbers for entertainment. Numbers rule our lives, they wake us up, tell us where to go, how to get there and when to leave. Numbers are judges of all, they assess and compare with complete authority and impartiality. But numbers also lie; they may mean anything except the truth. Numbers can save our lives, and a love of the wrong kind of numbers can ruin us. Numbers can be our friends, our lifelines and our lucky charms. Numbers can also kill us. You are made of numbers. So am I.
Thousands of years ago, when there was no difference between science and religion, numbers seemed to hold the key to understanding the universe. They might not have trickled down in front of our eyes like a scene from The Matrix, but lurking inside many forms were important numbers that seemed too common to be coincidental. The same ratios kept reappearing in nature, perhaps between the diameter of a circle and its circumference, or in the curvature of seashells. The same geometric shapes and the numbers embedded within them kept being discovered in unlikely places, such as the spacing of the planets of our solar system. Even something as unlikely as a speed -- for example the speed of light -- seemed to be at the heart of the construction of our universe. In those days it was widely believed that such numbers pointed to the mysterious underlying design of God. An understanding of those numbers would be like reading divine messages written into the fabric of existence. Those pioneers and adventurers who dared to explore the uncharted territories of numbers were exploring the very substance of their world. They were unpicking the details of life, the universe and everything. Their solutions were not a single number, but a whole collection of important numbers, as well as tools to manipulate those numbers.
Today, science has taken over from religion. We still believe that our universe has hugely important numbers associated with it. We now know that they are the patterns visible in the woven tapestry from which everything is made. Some patterns in the tapestry are made from such thick threads that they catch the eye immediately: numbers such as π, e and θ. Some form the bulk of the material: numbers like 0, 1, 2, 3 and √2. Some stand out like accidental spills on the fabric, such as 10 and 13. Other numbers and concepts, like c and ∞, point to the size and shape of the tapestry. Some, such as i, are only visible as tenuous ripples of complexity that flow through the cloth.
Those who explore the fundamental truths of nature are now known by names such as mathematicians, astronomers and physicists. But however we label them, these people were (and still are) explorers. They did not weave the tapestry they examined. They did not invent their numbers or mathematical ideas as a novelist might invent a story. They searched for the truth, and tried to explain it, inventing new languages of numbers simply to be able to write down their discoveries. Some pursued this goal for science, some for religion and some for fame
The explorers we will follow in this book were very clever and many have been called geniuses -- but they were people too. They had complicated lives, had arguments, failings and successes. Galileo was a medical school dropout, Newton threatened to burn down his parents' house, Bernoulli stole his son's work, Pascal was a bully and Einstein had a child out of wedlock. Some were murdered because of numbers. Others lost their sanity. Put them all. in a room together and you'd probably be deafened by the shouting. But they all had an appreciation of numbers that made them exceptional. They came from all over the world, yet their language was universal. As their explanations improved, so did the language of numbers.
Through our quirky pioneers we learned how numbers make shapes, angles and connections, enabling us to measure our land, to design and build complicated machines. We discovered the numbers of interacting waves, allowing us to understand music, the swing of pendulums and the bizarre properties of light We learned how numbers describe position, speed and accelerations, enabling us to understand the motion of the planets and comprehend the planet we live on. We learned how numbers define time, space and the different sizes of infinity, enabling us to understand how the flow of time changes and how our universe began. Today we continue to learn the numbers that affect subatomic particles, and those behind complex systems such as economies, societies and consciousness. These remarkable achievements have created our modern world of telephones, cars, music, computers and airplanes. They have enabled almost every modern device you use, the food you eat and the lob you do. Your entire lifestyle is shaped by our understanding of numbers
This book is about the explorers of numbers and the inventors of mathematics. The motivations and beliefs of these eccentric characters are often surprising However, more surprising than their discoverers, are the numbers themselves.
Albert Einstein once said, "There are two ways to live your life. One is as though nothing is a miracle. The other is as though everything is a miracle." Numbers don't remove your ability to marvel at the world, they increase it.
Numbers are miraculous, as you're about to find out.
