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number-philosophy, the cult would kill. Yet as deadly as the secret that Hippasus revealed was, it was small compared to the dangers of zero.
    The leader of the cult was Pythagoras, an ancient radical. According to most accounts, he was born in the sixth century BC on Samos, a Greek island off the coast of Turkey famed for a temple to Hera and for really good wine. Even by the standards of the superstitious ancient Greeks, Pythagoras’s beliefs were eccentric. He was firmly convinced that he was the reincarnated soul of Euphorbus, a Trojan hero. This helped convince Pythagoras that all souls—including those of animals—transmigrated to other bodies after death. Because of this, he was a strict vegetarian. Beans, however, were taboo, as they generate flatulence and are like the genitalia.
    Pythagoras may have been an ancient New Age thinker, but he was a powerful orator, a renowned scholar, and a charismatic teacher. He was said to have written the constitution for Greeks living in Italy. Students flocked to him, and he soon acquired a retinue of followers who wanted to learn from the master.
    The Pythagoreans lived according to the dicta of their leader. Among other things they believed that it is best to make love to women in the winter, but not in the summer; that all disease is caused by indigestion; that one should eat raw food and drink only water; and that one must avoid wearing wool. But at the center of their philosophy was the most important tenet of the Pythagoreans: all is number.
    The Greeks had inherited their numbers from the geometric Egyptians. As a result, in Greek mathematics there was no significant distinction between shapes and numbers. To the Greek philosopher-mathematicians they were pretty much the same thing. (Even today, we have square numbers and triangular numbers thanks to their influence [Figure 5].) In those days, proving a mathematical theorem was often as simple as drawing an elegant picture; the tools of ancient Greek mathematics weren’t pencil and paper—they were a straightedge and compasses. And to Pythagoras the connection between shapes and numbers was deep and mystical. Every number-shape had a hidden meaning, and the most beautiful number-shapes were sacred.
    The mystical symbol of the Pythagorean cult was, naturally, a number-shape: the pentagram, a five-pointed star. This simple figure is a glimpse at the infinite. Nestled within the lines of the star is a pentagon. Connecting the corners of that pentagon with lines generates a small, upside-down, five-pointed star, which is exactly the same as the original star in its proportions. This star, in turn, contains an even smaller pentagon, which contains a tinier star with its tiny pentagon, and so forth (Figure 6). As interesting as this was, to the Pythagoreans the most important property of the pentagram was not in this self-replication but was hidden within the lines of the star. They contained a number-shape that was the ultimate symbol of the Pythagorean view of the universe: the golden ratio.

    Figure 5: Square and triangular numbers

    Figure 6: The pentagram
    The importance of the golden ratio comes from a Pythagorean discovery that is now barely remembered. In modern schools, children learn of Pythagoras for his famed theorem: the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. However, this was in fact ancient news. It was known more than 1,000 years before Pythagoras’s time. In ancient Greece, Pythagoras was remembered for a different invention: the musical scale.
    One day, according to legend, Pythagoras was toying with a monochord, a box with a string on it (Figure 7). By moving a sliding bridge up and down the monochord, Pythagoras changed the notes that the device played. He quickly discovered that strings have a peculiar, yet predictable, behavior. When you pluck the string without the bridge, you get a clear note, the tone known as the