Cosmos - Carl Sagan [117]
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: 1010l00; and even infinity: ∞ (pronounced “infinity”).
In a burnt apple pie, the char is mostly carbon. Ninety cuts and you come to a carbon atom, with six protons and six neutrons in its nucleus and six electrons in the exterior cloud. If we were to pull a chunk out of the nucleus—say, one with two protons and two neutrons—it would be not the nucleus of a carbon atom, but the nucleus of a helium atom. Such a cutting or fission of atomic nuclei occurs in nuclear weapons and conventional nuclear power plants, although it is not carbon that is split. If you make the ninety-first cut of the apple pie, if you slice a carbon nucleus, you make not a smaller piece of carbon, but something else—an atom with completely different chemical properties. If you cut an atom, you transmute the elements.
But suppose we go farther. Atoms are made of protons, neutrons and electrons. Can we cut a proton? If we bombard protons at high energies with other elementary particles—other protons, say—we begin to glimpse more fundamental units hiding inside the proton. Physicists now propose that so-called elementary particles such as protons and neutrons are in fact made of still more elementary particles called quarks, which come in a variety of “colors” and “flavors,” as their properties have been termed in a poignant attempt to make the subnuclear world a little more like home. Are quarks the ultimate constituents of matter, or are they too composed of still smaller and more elementary particles? Will we ever come to an end in our understanding of the nature of matter, or is there an infinite regression into more and more fundamental particles? This is one of the great unsolved problems in science.
The transmutation of the elements was pursued in medieval laboratories in a quest called alchemy. Many alchemists believed that all matter was a mixture of four elementary substances: water, air, earth and fire, an ancient Ionian speculation. By altering the relative proportions of earth and fire, say, you would be able, they thought, to change copper into gold. The field swarmed with charming frauds and con men, such as Cagliostro