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In a branch of physical chemistry known as exploratory synthesis, chemists try mixing selected elements together at different temperatures and pressures to see what comes out. About a decade ago, one of the hundreds of compounds discovered this way—a mixture of copper, yttrium, barium, and oxygen—was found to be a superconductor at temperatures far higher than anyone had previously thought possible. This discovery may ultimately have far-reaching implications for the storage and transmission of electrical energy.
To get some sense of how much scope there is for more such discoveries, we can calculate as follows. The periodic table contains about a hundred different types of atoms, which means that the number of combinations made up of four different elements is about 100 × 99 × 98 × 97 = 94,000,000. A list of numbers like 6, 2, 1, 7 can represent the proportions for using the four elements in a recipe. To keep things simple, assume that the numbers in the list must lie between 1 and 10, that no fractions are allowed, and that the smallest number must always be 1. Then there are about 3,500 different sets of proportions for each choice of four elements, and 3,500 × 94,000,000 (or 330,000,000,000) different recipes in total. If laboratories around the world evaluated one thousand recipes each day, it would take nearly a million years to go through them all. (If you like these combinatorial calculations, try to figure out how many different coffee drinks it is possible to order at your local shop. Instead of moving around stacks of cup lids, baristas now spend their time tailoring drinks to individual palates.)
