## That’s Maths: Many philosophers regard ‘nothing’ with anxiety, nausea or panic

This article is about nothing: nothing at all, as encapsulated in the number zero and the empty set. It took humanity millennia to move beyond the counting numbers. Zero emerged in several civilisations, first as a place-holder to denote a space or gap between digits, and later as a true number, which could be manipulated like any other. The numeral 0 is simple: it is a symbol representing the number zero. But the concept of zero is deeper and has long been of concern in metaphysics, the branch of philosophy that explores the nature of being, existence and reality.

In the Encyclopedia of Philosophy, PL Heath described "nothing" as an awe-inspiring concept, which many writers regard with anxiety, nausea or panic. Philosophers have never felt easy on the matter, which leads them into paradox. The Greek philosopher Parmenides said it is impossible to speak of what is not, thereby contradicting himself. Martin Gardner, the great populariser of maths, and a philosopher by training, wrote a fascinating article, Nothing. He described the Far Side cartoon about a mountaineer descending a deep hole in the ground. Asked why he was doing this, he replied "Because it's not there."

#### Emergence of zero

The Babylonians used a base-60 system. They had a symbol – two slanted wedges – that acted as a place-holder between digits, much as we use 0 to distinguish 307 from 37. But their symbol was never used in isolation: it was more like a punctuation mark than a number. Since the symbol never appeared at the end of a number, there was ambiguity between numbers such as 3 and 180 (3 x 60) that were resolved only by the context. Similar place-holders were found in China, Central America and elsewhere.

Surprisingly, the classical Greeks had no symbol for zero, even as a place-holder. Later (about 130 AD) Ptolemy used a zero symbol in the Almagest, his work on astronomy. The Indian scholar Pingala used the Sanskrit word sunya to mean zero, but the earliest unequivocal use of zero as an actual number was by Brahmagupta in the seventh century AD. He also discussed negative numbers and the rules for their arithmetic manipulation.