[...]... times My approach to these adventures will in part be that of a naturalist, collecting the wonderful variety of forms zero takes on - not only as a number but as a metaphor of despair or delight; as a nothing that is an actual something; as the progenitor of 1 THE NOTHING THAT IS us all and as the riddle of riddles But we, who are more than magpies, feather our nests with bits of time I will therefore... is altogether of the " and more, exactly what number is that? Won't we have to invent a new symbol after all? Different cultures came up with different answers Perhaps from scoring across a stroke like these on a tally-stick, perhaps from handsignals wagged across the market-place, the Romans let X stand for a heap of ', V for , ('V, that is, as half - the upper half — of 'X' - a one-hand sign) and... device that the philosophers never described, but whose descendants you see to this day in the worry-beads of the Greeks and the backgammon games of their taverna: the counting board And even before this - though these boards go back at least to the seventh century 21 THE NOTHING THAT IS BC (the Babylonians may even have used them a thousand years earlier) - they had theirfingers,and clever ways offlyingthrough... It hasn't ended has hardly in fact begun, although the polish of its works might give them the look of monuments, and a history of zero mark it as complete But zero stands not for the closing of a ring: it is rather a gateway One of the most visionary mathematicians of our time, Alexander Grothendieck, whose results have changed our very way of looking at mathematics, worked for years on his magnum... he calculated in the Babylonian sexagesimal system, as we do) So stood for 41° 00' 18", and for 0° 33' 04" Doesn't the ornamented bar show that zero hadn't yet the status of a number but was used by the Alexandrian Greeks as we use punctuation marks? Further evidence of this comes from the sort of complication that keeps scholarship alive For the only manuscripts we have of the Almagest are Byzantine,... yet further away from what would have aided thought? You might argue that it all went back to their admiration of the Egyptians, who had neither a zero nor a positional way of writing numbers For the Greeks, however, admiration always turned into rivalry; their impatience with the inelegant (and the Egyptian number system lacked any elegance) led to that endless messing about we enshrine as the Scientific... claim that such flexibility was the greatest advantage of this notation Whoever it was, in the latter days of Babylon, that first gave to airy nothing a local habitation and a name, has left none himself Perhaps that double wedge fittingl ommemorates his place in history 13 TWO THE G R E E K S HAD NO W O R D FOR IT Why had it taken so long to signify nothing? Why was the use of zero after that still... impulse at play again? Or a code to exclude the uninitiated? Differences that grow from having your neighbors a mountainvalley away? Or just a Greek kind of cussedness of spirit? Whatever the reason, the continuing lack of positional notation meant that: they still had no symbol for zero It was probably the Greeks under Alexander who discovered the crucial role that zero played in counting, when they invaded... Rehman, Abdulhamid Sabra, Brian A Sullivan, Daniel Tenney III, Alf van der Poorten, Jared Wunsch, Michio Yano and Don Zagier Finally, I can't thank enough, for their unfailing support when it most mattered, the Kaplans of Scotland; Tomas Guillermo, the Gilligans and the Klubocks of Cambridge; the HarrisonX ACKNOWLEDGEMENTS Mahdavis of Paris; the Franklins of iltshire; the Nuzzos of Chestnut Hill; the Zelevinskys... Thomas Burke, Henry Cohn, Paul Dundas, Matthew Emerton, Harry Falk, Martin Gardner, Nina Goldmakher, Susan Goldstine, James Gunn, Raqeeb Haque, Takao Hayashi, Michele Jaffe, James Rex Knowlson, Takeshi Kukobo, Richard Landes, Boris Lietsky, Rhea MacDonald, Georg Moser, Charles Napier, Lena Nekludova, David Nelson, Katsumi Nomizu, Yori Oda, Larry Pfaff, Donald Ranee, Andrew Ranicki, Aamir Rehman, Abdulhamid . Press. Library of Congress Cataloging-in-Publication Data Kaplan, Robert, 193 3- The nothing that is: a natural history of zero /Robert Kaplan p. cm. Included index ISBN 0-1 9-5 1284 2-7 1. Zero . scoring across a stroke like these on a tally-stick, perhaps from hand- signals wagged across the market-place, the Romans let X stand for a heap of ', V for ,. ('V, that is,. rather a gateway. One of the most visionary mathematicians of our time, Alexander Grothendieck, whose results have changed our very way of looking at mathematics, worked for years