Why Beauty is Truth Read Free Page A

matter. They’re important for themselves.”
    Gamesh was about to say something highly improper when he noticed the teacher walking into the classroom, so he covered his embarrassment with a sudden attack of coughing.
    â€œGood morning, boys,” said the teacher brightly.
    â€œGood morning, master.”
    â€œLet me see your homework.”
    Gamesh sighed. Humbaba looked worried. Nabu kept his face expressionless. It was better that way.

    Perhaps the most astonishing thing about the conversation upon which we have just eavesdropped—leaving aside that it is complete fiction—is that it took place around 1100 BCE, in the fabled city of Babylon.
    Might have taken place, I mean. There is no evidence of three boys named Nabu, Gamesh, and Humbaba, let alone a record of their conversation. But human nature has been the same for millennia, and the factual background to my tale of three schoolboys is based on rock-hard evidence.
    We know a surprising amount about Babylonian culture because their records were written on wet clay in a curious wedge-shaped script called cuneiform. When the clay baked hard in the Babylonian sunshine, these inscriptions became virtually indestructible. And if the building where the clay tablets were stored happened to catch fire, as sometimes happened—well, the heat turned the clay into pottery, which would last even longer.
    A final covering of desert sand would preserve the records indefinitely. Which is how Babylon became the place where written history begins. The story of humanity’s understanding of symmetry—and its embodiment in a systematic and quantitative theory, a “calculus” of symmetry every bit as powerful as the calculus of Isaac Newton and Gottfried Wilhelm Leibniz—begins here too. No doubt it might be traced back further, if we had a time machine or even just some older clay tablets. But as far as recorded history can tell us, it was Babylonian mathematics that set humanity on the path to symmetry, with profound implications for how we view the physical world.

    Mathematics rests on numbers but is not limited to them. The Babylonians possessed an effective notation that, unlike our “decimal” system (based on powers of ten), was “sexagesimal” (based on powers of sixty). They knew about right-angled triangles and had something akin to what we now call the Pythagorean theorem—though unlike their Greek successors, the mathematicians of Babylon seem not to have supported their empirical findings with logical proofs. They used mathematics for the higher purpose of astronomy, presumably for agricultural and religious reasons, and also for the prosaic tasks of commerce and taxation. This dual role of mathematical thought—revealing order in the natural world and assisting in human affairs—runs like a single golden thread throughout the history of mathematics.
    What is most important about the Babylonian mathematicians is that they began to understand how to solve equations.
    Equations are the mathematician’s way of working out the value of some unknown quantity from circumstantial evidence. “Here are some known facts about an unknown number: deduce the number.” An equation, then, is a kind of puzzle, centered upon a number. We are not told what this number is, but we are told something useful about it. Our task is to solve the puzzle by finding the unknown number. This game may seemsomewhat divorced from the geometrical concept of symmetry, but in mathematics, ideas discovered in one context habitually turn out to illuminate very different contexts. It is this interconnectedness that gives mathematics such intellectual power. And it is why a number system invented for commercial reasons could also inform the ancients about the movements of the planets and even of the so-called fixed stars.
    The puzzle may be easy. “Two times a number is sixty: what is the number we seek?” You do not