Finding Zero Read Online Free

early childhood was really two mysteries. One was where the first numerals originated: In which part of the world, and when, did people first invent the nine numerals, and zero, that with time evolved into the numbers that rule our world? And the second was a deeper conundrum, which I was now sophisticated enough to discern: How did humans abstract the concept of number? How did the idea of a number originate, and how did it develop and mature through history, to bring us to the digitally dominated society in which we live today?
    Laci and I spent many hours together discussing this latter idea as the ship slowly made its way across the ocean. It was a far deeper discussion than I had ever had with him as a child, certainly, and he brought to it his full intellectual abilities as a one-time doctoral student of pure mathematics at the top Russian university, where mathematics has always been one of the most important fields of study. It was a pleasure to sit with Laci on deck chairs discussing mathematical concepts I was only beginning to understand and be fascinated by—building on the earlier ideas he had taught me as a child: numerals, numbers, prime numbers, and the mysterious Fibonacci sequence.
    Having finally crossed the Atlantic, we docked for a few days in Halifax, Nova Scotia, and then continued to New York City; Charleston, South Carolina; and finally Miami, where I disembarked before the ship continued on to the Caribbean andSouth America. Before I left ship to fly to San Francisco and start my studies, Laci said one last thing to me in parting: “Remember how when you were little we used to talk about where the numerals came from? Maybe you’ll find out. I once read in a science magazine that a French archaeologist may have found something about the numbers in Asia decades ago—something important relating to the zero. But I don’t remember any of the details.”
    Laci’s parting words intrigued me, but I had no opportunity to pursue this research further. At Berkeley, I had a full plate of math courses, challenging but often enjoyable, and I had to worry about grades and exams and learning to become a mathematician.
    However, through my courses—mostly mathematics, but also anthropology, sociology, and philosophy—I learned a fair amount also about numbers and their development.
    Numbers, as a concept, are much older than we might think. In 1960, a Belgian explorer named Jean de Heinzelin de Braucourt was surveying the region of Ishango, at the border of present-day Uganda and Congo (then the Belgian Congo), when he discovered a strange-looking bone: a baboon’s fibula bearing what looked like numerous tally marks. Analysis later concluded that these markings might evidence very early counting. The bone has three sets of identical notches, adding, respectively, to the totals 60, 48, and 60. The markings are grouped in several sets containing 5, 7, 9, 11, or 13 tally marks each. This bone was scientifically dated to about 20,000 years ago—the Paleolithic era—when humans lived in hunter-gatherer groups. The Ishango bone provides some of the earliest known evidence of a form ofcounting by humans who lived in Africa so long ago, and it is now displayed at the Royal Belgian Institute of Natural Sciences in Brussels.

    The Ishango bone: a baboon fibula, about 20,000 years old, bearing notches believed to represent early evidence of counting by our species.
    What does the Ishango bone represent? It seems that in prehistoric times, early humans roaming the bush in Africa used bones of dead animals as a way of drawing the first one-to-one correspondence between the number of animals they were able to hunt and notches they made on a piece of bone. This was not quite counting, but it was close. Anyone could see that a bone that had more such tally marks implied that its owner had hunted more animals—perhaps without really knowing what the actual number was. Of course all