Zero: A philosophical history of an Indian idea – I

This post is the first of a trilogy, where I will be revisiting a somewhat hackneyed topic: the Indian roots of Zero. However, rather than make it a bland rehearsal of Zero’s history replete with references to familiar names like Aryabhatta and Bhaskaracharya, the aim is to give a snapshot of just how crucial India’s philosophical climate was in facilitating the discovery of Zero. Part I explores how Greek philosophy prevented Zero from taking off. 

The Greek Zero Phobia: Ex nihilo nihil fit (From Nothing comes Nothing) 

Looking back at the mathematics taught in school, one may well wonder that Zero has got to be the easiest bit. If I have three toffees and give away all my toffees, I will have zero toffees left. In retrospect, this seems simple enough, surely simpler than, say, the Pythagoras theorem or calculating square roots. Given zero’s intuitive simplicity we are prone to assume that zero must have been figured out way before the other complex stuff like the Pythagoras theorem. Yet, natural as zero seems to us today, for the ancient Greeks, Pythagoras included, it was a dreadful idea: an idea that threatened to bring down the edifice of their logic and philosophy. As a consequence they chose to live without the zero. As Charles Siefe notes the consequences of this were serious: ‘Zero’s absence would stunt the growth of mathematics, stifle innovation in science, and incidentally, make a mess of the calendar.’ 

Let’s first consider the least disastrous, even silly, consequence of the Greek Zero phobia. When the world celebrated the turn of the Millennium on 31^st December 1999, we celebrated a year too soon; the millennium was to actually turn on 31^st December 2000. The reason for the miscalculation: the Gregorian calendar (based on Dionysius’s 6^th Century calendar), did not have year Zero. The Gregorian calendar jumps from 1 BC to 1 AD with no year zero in between. This is akin to a digital watch starting the business of timekeeping at 1:00 hours rather 00:00 hours and showing 13:00 when it is noon. Remedying this defect the modern Astronomical calendar fixes 1BC as year Zero and 1AD as year 2. The ISO also follows a similar notation with 1 BC fixed as year 0000. 

The Roman numeral system was happy to do without a zero. Not only did they not have the number Zero, they didn’t even have a placeholder zero digit like the ones we find in 101 and 1001.As a result they settled for a convoluted system of numerals. For good reason the Roman numerals have become extinct and we don’t find them used other than on clock faces or for indicating chapter numbers in trilogies like this one.  Just imagine doing long multiplications with Roman Numerals. How tortuous would it be to manually figure out MMMDCCCLXXII multiplied by MCCIX. In the Indian system of counting- now in vogue the world over- this would read 3872 × 1209. With the positional system and the use of place holding zeros this multiplication could be done manually by a seven year old. As John Barrow notes, the Roman numerals lacked two crucial features ‘the zero sign and a positional significance… which are features that lie at the heart of the development of efficient human counting systems’. Curiously even the Romans never counted with their numerals. For counting they used the abacus and noted the results of calculations with their numerals. Later when the Indian place value system of counting was introduced in Europe, a person counting manually with the Indian position system could perform mathematical operations way quicker than the person calculating with an abacus. For an interesting depiction of this see this illustration from Gregorius Reisch’s Margarita Philosophica (1503). 

The philosophically less interesting reason for the absence of zero in Greece was that they were Geometers. For Greeks, mathematical calculations were computation of areas of geometrical figures and numbers were nothing but shapes and forms; hence the Greek obsession with square roots and ratios. But geometry has no place for Zero as it is impossible to imagine a geometrical figure without dimensions; for instance, how does one think of a square without dimensions? 

The more philosophically significant reason for the Greek Zero Phobia was their world view. The Greeks clung firmly to the dictum Ex nihilo nihil fit: out of nothing comes nothing. The Greek world of Plato, Aristotle and Ptolemy was a finite world with no place for either the concept of nothingness or that of infinity. Plato held the view that everything in the universe was a mere approximation of its ideal which existed in the world of forms. Thus there was a form of a horse, table, cup and the works which existed in the world of forms and the objects in the phenomenal universe were mere manifestations of those ideal forms. Thus everything comes out of this world of forms which is eternal and absolutely true. Before Plato, Parmenides held the view that there could be no such thing as ‘nothing’. Aristotle’s universe was finite and he strongly believed that there could be no void in it. As Brian Rotman remarked the idea of nothingness presented itself to Aristotle as ‘a dangerous sickness, a God denying madness that left him with an ineradicable horror vacui’. 

As Siefe says summing up the Greek Zero phobia, ‘it was not ignorance that led Greeks to reject Zero…nor was it the number-shape system, it was philosophy’. Platonic and Aristotelian ideas constituted the bedrock of Western Philosophy for a better part of two thousand years. Zero and its related concepts, void and infinity, threatened to unsettle this edifice. In this philosophical atmosphere Zero could never have and never did emerge. Zero needed a habitat where the void and infinity were not shunned but embraced openly. India was to be the place where that was to happen.

(To be continued…)