Not one of those worlds will be identical to Earth. A few will be hospitable; most will appear hostile. Many will be achingly beautiful. In some worlds there will be many suns in the daytime sky, many moons in the heavens at night, or great particle ring systems soaring from horizon to horizon. Some moons will be so close that their planet will loom high in the heavens, covering half the sky. And some worlds will look out onto a vast gaseous nebula, the remains of an ordinary star that once was and is no longer. In all those skies, rich in distant and exotic constellations, there will be a faint yellow star – perhaps barely seen by the naked eye, perhaps visible only through the telescope – the home star of the fleet of interstellar transports exploring this tiny region of the great Milky Way Galaxy.
The themes of space and time are, as we have seen, intertwined. Worlds and stars, like people, are born, live and die. The lifetime of a human being is measured in decades; the lifetime of the Sun is a hundred million times longer. Compared to a star, we are like mayflies, fleeting ephemeral creatures who live out their whole lives in the course of a single day. From the point of view of a mayfly, human beings are stolid, boring, almost entirely immovable, offering hardly a hint that they ever do anything. From the point of view of a star, a human being is a tiny flash, one of billions of brief lives flickering tenuously on the surface of a strangely cold, anomalously solid, exotically remote sphere of silicate and iron.
In all those other worlds in space there are events in progress, occurrences that will determine their futures. And on our small planet, this moment in history is a historical branch point as profound as the confrontation of the Ionian scientists with the mystics 2,500 years ago. What we do with our world in this time will propagate down through the centuries and powerfully determine the destiny of our descendants and their fate, if any, among the stars.
CHAPTER IX
The Lives of the Stars
Opening his two eyes, [Ra, the Sun god] cast light on Egypt, he separated night from day. The gods came forth from his mouth and mankind from his eyes. All things took their birth from him, the child who shines in the lotus and whose rays cause all beings to live.
– An incantation from Ptolemaic Egypt
God is able to create particles of matter of several sizes and figures . . . and perhaps of different densities and forces, and thereby to vary the laws of Nature, and make worlds of several sorts in several parts of the Universe. At least, I see nothing of contradiction in all this.
– Isaac Newton, Optics
We had the sky, up there, all speckled with stars, and we used to lay on our backs and look up at them, and discuss about whether they was made, or only just happened.
– Mark Twain, Huckleberry Finn
I have . . . a terrible need . . . shall I say the word? . . . of religion. Then I go out at night and paint the stars.
– Vincent van Gogh
To make an apple pie, you need wheat, apples, a pinch of this and that, and the heat of the oven. The ingredients are made of molecules – sugar, say, or water. The molecules, in turn, are made of atoms – carbon, oxygen, hydrogen and a few others. Where do these atoms come from? Except for hydrogen, they are all made in stars. A star is a kind of cosmic kitchen inside which atoms of hydrogen are cooked into heavier atoms. Stars condense from interstellar gas and dust, which are composed mostly of hydrogen. But the hydrogen was made in the Big Bang, the explosion that began the Cosmos. If you wish to make an apple pie from scratch, you must first invent the universe.
Suppose you take an apple pie and cut it in half; take one of the two pieces, cut it in half; and, in the spirit of Democritus, continue. How many cuts before you are down to a single atom? The answer is about ninety successive cuts. Of course, no knife could be sharp enough, the pie is too crumbly, and the atom would in any case be too small to see unaided. But there is a way to do it.
At Cambridge University in England, in the forty-five years centered on 1910, the nature of the atom was first understood – partly by shooting pieces of atoms at atoms and watching how they bounce off. A typical atom has a kind of cloud of electrons on the outside. Electrons are electrically charged, as their name suggests. The charge is arbitrarily called negative. Electrons determine the chemical properties of the atom – the glitter of gold, the cold feel of iron, the crystal structure of the carbon diamond. Deep inside the atom, hidden far beneath the electron cloud, is the nucleus, generally composed of positively charged protons and electrically neutral neutrons. Atoms are very small – one hundred million of them end to end would be as large as the tip of your little finger. But the nucleus is a hundred thousand times smaller still, which is part of the reason it took so long to be discovered.* Nevertheless, most of the mass of an atom is in its nucleus; the electrons are by comparison just clouds of moving fluff. Atoms are mainly empty space. Matter is composed chiefly of nothing.
* It had previously been thought that the protons were uniformly distributed throughout the electron cloud, rather than being concentrated in a nucleus of positive charge at the center. The nucleus was discovered by Ernest Rutherford at Cambridge when some of the bombarding particles were bounced back in the direction from which they had come. Rutherford commented: ‘It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch [cannon] shell at a piece of tissue paper and it came back and hit you.’
I am made of atoms. My elbow, which is resting on the table before me, is made of atoms. The table is made of atoms. But if atoms are so small and empty and the nuclei smaller still, why does the table hold me up? Why, as Arthur Eddington liked to ask, do the nuclei that comprise my elbow not slide effortlessly through the nuclei that comprise the table? Why don’t I wind up on the floor? Or fall straight through the Earth?
The answer is the electron cloud. The outside of an atom in my elbow has a negative electrical charge. So does every atom in the table. But negative charges repel each other. My elbow does not slither through the table because atoms have electrons around their nuclei and because electrical forces are strong. Everyday life depends on the structure of the atom. Turn off the electrical charges and everything crumbles to an invisible fine dust. Without electrical forces, there would no longer be things in the universe – merely diffuse clouds of electrons, protons and neutrons, and gravitating spheres of elementary particles, the featureless remnants of worlds.
When we consider cutting an apple pie, continuing down beyond a single atom, we confront an infinity of the very small. And when we look up at the night sky, we confront an infinity of the very large. These infinities represent an unending regress that goes on not just very far, but forever. If you stand between two mirrors – in a barber shop, say – you see a large number of images of yourself, each the reflection of another. You cannot see an infinity of images because the mirrors are not perfectly flat and aligned, because light does not travel infinitely fast, and because you are in the way. When we talk about infinity we are talking about a quantity greater than any number, no matter how large.
The American mathematician Edward Kasner once asked his nine-year-old nephew to invent a name for an extremely large number – ten to the power one hundred (10100), a one followed by a hundred zeroes. The boy called it a googol. Here it is: 10, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000. You, too, can make up your own very large numbers and give them strange names. Try it. It has a certain charm, especially if you happen to be nine.
If a googol seems large, consider a googolplex. It is ten to the power of a googol – that is, a one followed by a googol zeros. By comparison, the total number of atoms in your body is about 1028, and the total number of elementary particles – protons and neutrons and electrons – in the observable universe is about 1080. If the universe were packed solid* with neutrons, say, so there was no empty space anywhere, there would still be only about 10128 particles in it, quite a bit more than a googol but trivially small compared to a googolplex. And yet these numbers, the googol and the googolplex, do not approach, they come nowhere near, the idea of infinity. A googolplex is precisely as far from infinity as is the number one. We could try to write out a googolplex, but it is a forlorn ambition. A piece of paper large enough to have all the zeroes in a googolplex written out explicitly could not be stuffed into the known universe. Happily, there is a simpler and very concise way of writing a googolplex: 101010; and even infinity: µ (pronounced ‘infinity’).