The zero, both as a concept and as a place-holding numeral in our number system, is critically important to the history of science. Conceptually, zero is nothingness, which permits efficient arithmetic calculations. As a place-holding numeral, zero allows the base-10 number system to work, such that the same 10 numerals (1, 2, 3, 4, 5, 6, 7, 8, 9, & 0) can be used at different positions in a number.
For example, a 3 alone means three, but when followed by two zeros, it now becomes 300 (3 hundreds, 0 tens, 0 units). This place-holding zero also gives meaning to numbers that do not contain zero. The number 423 could not be written this way if 420 did not exist, and 420 needs a zero as a place holder for empty units. Without the zero, these numbers and their manipulations would not be possible.
The use of the zero significantly improved previous numerical systems, including the Roman system, which was used until the late Middle Ages, as well as the Babylonian and Egyptian systems. These older systems were extremely cumbersome and did not allow simple arithmetic computations.
Almost everything we do depends upon mathematics and this zero (e.g., anything electronic or computer-based like a cell phone or GPS system is controlled by strings of zeros and ones), which leads to the question, where did the zero originate?
The book, Finding Zero: A Mathematician’s Odyssey to Uncover the Origins of Numbers, by Amir D. Aczel of Boston University provides a fascinating answer to this question.
Aczel hypothesized that the number system that we use today was developed in the East because of religious, spiritual, philosophical, and mystical reasons. Specifically, Aczel believed that the Buddhist concept of nothingness, or Shunyata, was crucial in the development of the conceptual zero and the Jainism notion of extremely large numbers lead to the development of infinity as a concept.
Western logic is a very unambiguous and restrictive kind of logic. For example, Aristotle’s logical deductive statements exemplify the Western way of thinking:
Eastern logic takes a different form, by embracing contradictions. Take the following example, from the writings of Nagarjuna, a prominent second-century CE Buddhist philosopher and teacher:
To someone trained to think via Western logic, this set of options seems like a bizarre way of thinking about reality. The key to understanding this logic lies in the word Shunya, which is the Hindi/Sanskrit word for zero.
Shunya is related to Shunyata, which is the Buddhist philosophical concept of the void. The number zero and the Buddhist emptiness, which is the goal of meditation and an ideal on the road to enlightenment (i.e., Nirvana), are the same. Buddhist emptiness is a philosophical concept, and the zero as a number stems from this idea.
The set of options provided above in the Nagarjuna text are referred to as the catuskoti (or tetralemma). The catuskoti stems from early Buddhist logic, in which it was standard to assume four possibilities for any state of affairs: that it held, that it did not, both (i.e., that it both held and did not hold), or neither (i.e., it neither held nor did not hold).
According to Eastern logic, the only way to solve this logical conundrum, that something can be true, not true, both, or neither, is to conclude that the last two options (both true and untrue and neither true not untrue) are empty. In other words, the catuskoti (or 4 sides of the tetralemma) collapses, and we are left with the empty set, the void, the Shunyata, or the ultimate zero.
Buddhist philosophy emphasizes the void, which is not prevalent in Western religions or Western thinking. So, the zero in the East may be 1,600 years old, or as old as the Buddha himself.
The concept of infinity also seems to be an Eastern invention. Hinduism contains many references to infinity, including infinite time and infinite space. Jainism, too, was interested in very large numbers, and some Jain texts (e.g., Anuyoga-vara sutra) indicate that the ancient Jains understood infinity at least 1,800 years before mathematicians in the West. Western religion, in contrast, contains vague notions of God being infinite, but does not explore this idea.
Until the 1930s, many European scholars believed that the zero in our number system originated as a European or Arab invention. The oldest known zero prior to that point, dated to the mid-ninth century, had been discovered in India in the city of Gwalior at the Chatur-bhuja temple. This era, however, coincided with the extensive Arab trading network, and thus it could not definitively place the origin of the zero in Europe, Arabia, or the East. A zero that predated the emergence of Arab trade would provide strong support for Aczel’s hypothesis that the zero was an Eastern invention.
In pursuing support for his hypothesis, that the zero originated from Buddhist philosophy and logic, Aczel traveled through Southeast Asia, eventually leading him to discover the following:
In 1891, an artifact that would later be labeled “K-127” was discovered at Sambor on Mekong in Cambodia. In 1931, George Cœdès, a French archeologist, translated the inscription, realized it contained the oldest inscription of zero, and published his findings (the reference is provided below). K-127 was then moved to Phnom Penh, where it was placed in a national museum. In 1969, K-127 was moved to Siem Reap, where it was placed in Angkor Conservation. In 1990, the Khmer Rouge, the instigators of the Cambodian genocide, destroyed thousands of archeological artifacts from Angkor Conservation.
In 2013, after searching for the first zero for over 4 years, Aczel found his way to the Angkor Conservation in the hopes that K-127 survived the Khmer Rouge destruction. Amazingly, he did manage to find K-127, among rows of seemingly discarded artifacts in a shed. This artifact, which bears the earliest known inscription of the zero of our system ever discovered, states:
Which is translated as:
The çaka era began in AD 78, so, according to the Christian calendar, this inscription dates to 605 + 78 = AD 683.
This archeological find in Cambodia provides evidence that the first known zero of our number system originated in the East, as it predates the emergence of Arab trading that connected the East with Arabia and Europe. Both the West and East, however, are responsible for the development of our numbers in a purely mathematical sense (e.g., European scholars in the fifteenth through nineteenth centuries explored rational, irrational, and complex numbers).
This artifact is now located in the Cambodia National Museum in Phnom Penh.
So, Eastern religious and philosophical ways of thinking gave our number system the all-important zero! I loved this book not only because these interconnections between religion, philosophy, and mathematics are so incredibly fascinating, but it also called me to question how Western and Eastern logic influences the way I think about my own discipline, communication.
Note: The zero was also independently used by the Maya in the West, but that zero was confined to Mesoamerica, and our zero and number system did not stem from the Mayan use.
Aczel, A. D. (2015). Finding zero: A mathematician’s odyssey to uncover the origins of numbers. New York, NY: Palgrave Macmillan.
Cœdès, G. (1931). A propos de l’origine des chiffres arabes. Bulletin of the School of Oriental Studies, University of London, 6(2), 323-328.