Finding Zero Read Free Page B

arithmetic.
    Rome was a feast for a budding number-hunter. Roman numerals were everywhere. Most interesting were the milestones the Romans had placed along their straight-as-a-ruler roads, and I slowly became adept at reading the distances on these ancient markers, which I saw in museums and on the most famous of Roman roads, the Via Appia Antica.
    Laci explained to me how the Romans devised their number system. He drew for me all the Roman numerals: I is one, V is five, X is ten, L is 50, C is 100, D is 500, and M is 1,000. Heexplained that this method made it necessary for the written numbers to grow, and grow, and grow . . . He showed me how a Roman might have had to multiply XVIII by LXXXII, and ultimately get the answer MCDLXXVI. For us today, this operation is simply 18 × 82 = 1,476, and we can do it quickly and efficiently. Laci challenged me to perform such a calculation in the Greco-Roman system and made me construct its multiplication table; it was so huge and complicated that it took me a week to do. Amazingly, he said, this inefficient numerical system remained in wide use in the West until the thirteenth century, when it was replaced by the numbers we know today. 1
    I learned more about numbers from this lover of mathematics than I ever did at school, and I was grateful to him. But the mystery of where the ten numerals we use today originally came from continued to haunt me. At the same time, as I matured through school and pursued adventures to discover numerals while traveling the Mediterranean aboard my father’s ship, I began to understand the abstract—and even more mysterious—concept of a number. I realized that 3, for example, stood for the idea of “threeness”—something that was shared by all things in the universe that were three. All of them were to be described, in their quality of threeness, by the unique symbol 3. Equally, 5 stood for the quality of “fiveness” shared by everything that was five in number. This fascinating discovery made me even more eager to find where the numerals came from since they actually stood for something even deeper and more alluring than I could have ever imagined as a young child. I wanted to dedicate my life to traveling the world in search of an answer to the origin of numbers. Whoinvented these wondrous ten numerals? I asked myself this question all the time, and also, Who ever came up with the amazing idea that a concept of “threeness” or “seventeenness” or “three-hundred-and-five-ness” could be captured simply by a combination of ten signs arranged in certain ways?

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    In 1972, after high school and the obligatory service in the Israeli army, I was accepted as an undergraduate in mathematics at the University of California at Berkeley. I now made one more voyage on my father’s ship. By then, all the passenger ships had been sold because Zim Lines had lost too much money due to poor management of the company’s cruise division, called Zim Passenger Lines, and my father was now the captain of a small, slow, old cargo ship, the M.V. Yaffo, which sailed between the Mediterranean and the Americas. So I hitched a ride aboard my father’s ship, embarking in Haifa in late July for the long trip that would ultimately bring me to Berkeley.
    A cargo ship is as different from a cruise ship as a truck is from a limousine. Like a working truck, a cargo ship can be dirty and dusty, but its cabins are roomy; with no passengers, there’s no need to cram many people into limited cabin space, and the crew is therefore more comfortable. But the flipside is that there is nothing to do: no cocktail parties or bars or ballrooms, and no exciting social gatherings. A voyage on a cargo ship can be lonely.But Laci was still my father’s steward, and I was very fond of him. We often talked about mathematics during this trip.
    As an adult, I now understood that the mystery that had held my attention since