By Richard Webb Read more: “The nature of nothingness” I USED to have seven goats. I bartered three for corn; I gave one to each of my three daughters as dowry; one was stolen. How many goats do I have now? This is not a trick question. Oddly, though, for much of human history we have not had the mathematical wherewithal to supply an answer. There is evidence of counting that stretches back five millennia in Egypt, Mesopotamia and Persia. Yet even by the most generous definition, a mathematical conception of nothing – a zero – has existed for less than half that time. Even then, the civilisations that discovered it missed its point entirely. In Europe, indifference, myopia and fear stunted its development for centuries. What is it about zero that stopped it becoming a hero? This is a tangled story of two zeroes: zero as a symbol to represent nothing, and zero as a number that can be used in calculations and has its own mathematical properties. It is natural to think the two are the same. History teaches us something different. Zero the symbol was in fact the first of the two to pop up by a long chalk. This is the sort of character familiar from a number such as the next year in our calendar, 2012. Here it acts as a placeholder in our “positional” numerical notation, whose crucial feature is that a digit’s value depends on where it is in a number. Take 2012,