assumed not to have influenced Old World numeral systems. Quipu, a knotted cord device, used in the Inca Empire and its predecessor societies in the Andean region to record accounting and other digital data, is encoded in a base ten positional system. Zero is represented by the absence of a knot in the appropriate position. Classical antiquity The ancient Greeks had no symbol for zero (μηδέν, pronounced 'midén'), and did not use a digit placeholder for it. According to mathematician Charles Seife, the ancient Greeks did begin to adopt the Babylonian placeholder zero for their work in astronomy after 500 BC, representing it with the lowercase Greek letter ό (όμικρον) or omicron. However, after using the Babylonian placeholder zero for astronomical calculations they would typically convert the numbers back into Greek numerals. Greeks seemed to have a philosophical opposition to using zero as a number. Other scholars give the Greek partial adoption of the Babylonian zero a later date, with the scientist Andreas Nieder giving a date of after 400 BC and the mathematician Robert Kaplan dating it after the conquests of Alexander. Greeks seemed unsure about the status of zero as a number. Some of them asked themselves, "How can not being be?", leading to philosophical and, by the medieval period, religious arguments about the nature and existence of zero and the vacuum. The paradoxes of Zeno of Elea depend in large part on the uncertain interpretation of zero. By AD 150, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for zero () in his work on mathematical astronomy called the Syntaxis Mathematica, also known as the Almagest. This Hellenistic zero was perhaps the earliest documented use of a numeral representing zero in the Old World. Ptolemy used it many times in his Almagest (VI.8) for the magnitude of solar and lunar eclipses. It represented the value of both digits and minutes of immersion at first and last contact. Digits varied continuously from 0 to 12 to 0 as the Moon passed over the Sun (a triangular pulse), where twelve digits was the angular diameter of the Sun. Minutes of immersion was tabulated from 00 to 3120 to 00, where 00 used the symbol as a placeholder in two positions of his sexagesimal positional numeral system, while the combination meant a zero angle. Minutes of immersion was also a continuous function (a triangular pulse with convex