Finding Zero Read Free Page A

Fibonacci sequence, and he showed me how it is obtained, each number being the sum of the two previous ones: 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. If you divide a number by its predecessor, you get something approximating the golden ratio of 1.618. (For example, the sequence continues with 55 and 89. The ratio of 89 to 55 is 1.61818 . . .) I found this idea enthralling.
    We went into the Parthenon and saw some statues, beautiful likenesses of the goddess Athena still with traces of ancient red and gold paint on her face. Laci bent down and pointed to the pedestal of one of the statues and showed me letters carved in the marble. “Look,” he said. “This is what I wanted you to see.” I saw a letter I did not recognize—it was Greek. “Greek letters were not only used for writing, but also for numbers,” Laci said. The letter he was pointing to, he explained, was the Greek delta. It stood for the number four. “This was the fourth statue out of the assemblage that once stood here,” he said.
    After spending an hour admiring this monument of ancient Greek civilization, we left the temple and began to descend slowly. We stopped to sit down on a flat marble slab that was once part of this columned edifice. From here we could admire the Parthenon. It was hot, and we drank water from plastic bottles Laci had bought. After a few moments, he took out a notebook and showed me how the Greeks used letters as their numerals, and how their arithmetic, using only letters and no zero, worked. Here is what he wrote:

    The Greek letters used as numbers (including the archaic letters digamma, koppa, and sampi).
    The Greek alphabet of that time, the fifth century BCE—the height of classical Greece—included letters that had been extinct since antiquity: digamma () for 6; koppa () for 90; and sampi () for 900. So by the fifth century BCE the Greeks had revived letters in an alphabet they no longer used for writing, just so they would have enough symbols for numbers.
    Laci pointed out that the custom of using letters for numbers was rooted in Phoenicia, from which the Hebrew alphabet hails as well. Some Orthodox Jews to this day, he explained, have watches with faces displaying Hebrew letters for the numbers from 1 to 12.
    We then went to the museum of Athens, one of the greatest archaeological museums in the world. Among beautiful statues of gods and goddesses I saw several stone inscriptions with numbers represented as letters.
    On the way back to the ship, Laci asked the driver to stop in an alley in Piraeus and had me wait in the cab while he went into what looked like a store selling discount electronics. When he came back, he had a small package in his hand. “It’s just a small transistor radio,” he said to me. These were the new popular products of the time, the early 1960s, and people were going crazy overthem. You would see a person walking down the street listening to a transistor radio as often as today you might see someone talking on a cellular phone. “Just a present for someone,” he said. I thought nothing more about it at the time.
    After leaving Piraeus that evening, the Theodor Herzl sailed to Naples, and the passengers spent the day visiting nearby Pompeii. Next, there was a stop at Civitavecchia, the modern-day port of Rome (in antiquity Rome’s port was Ostia). The passengers had a tour of the city, with an in-depth study of Rome and the history of its empire. For a boy interested in the history of numbers, this was a cruise to remember.
    In Pompeii, Laci and I traced the Roman numerals—all Latin letters—that were used for house numbers in this ancient town. Its ruins were in a remarkable state of preservation as they had been covered by volcanic ash for almost two millennia after the catastrophic eruption of Vesuvius in 79 CE. At its museum we saw more numbers written using letters, and it was fun to read them and even try basic