As the 108th Science Congress ends January 7, an excerpt from Amir D Azcel’s 2015 book, ‘Finding Zero: A Mathematician’s Odyssey to Uncover the Origins of Numbers’
The Naneghat inscriptions at Naneghat, a pass in the Western Ghats near Pune, may have the earliest numerals that ultimately evolved into the ones we use today. Photo: iStock In India, mathematics and logic—and the intermingling of mathematics and numbers with sex—are very ancient. The earliest known texts in an Indian language are the four collections of religious hymns and rituals, mentioned earlier, known as the Vedas. These were composed in an ancient form of Sanskrit called Vedic Sanskrit, also known as Old Indo-Aryan. The Rig Veda is the oldest of these ancient documents and is believed to have been composed as early as 1100 BC. This text already displays a tendency toward extensive use of numbers, especially powers of ten. Here are some of its verses:
No bad hymns am I offering by exerting my intellect
In praise of Bhavya ruling on the Indus
Who assigned to me a thousand sacrifices,
That incomparable king desirous of fame.
A hundred gold pieces from the fame-seeking king,
Together with a hundred horses as a present have I received,
I, Kakshivant, obtained also a hundred cows from my master
Who exalted thereby his fame immortal up to heaven.
The historian of India John Keay records in his book also the ending verse of this hymn, noting that “by substituting sexual terms for words like ‘bliss’ and ‘creation,’ it is just possible to grasp a meaning that made an expert, B. K. Ghosh of Calcutta University, describe this hymn as obscene. We may view it as erotic”:
O resplendent lord, with brilliant radiance may you be delighted. May your own bliss be consummated. Your delightful creation, The holder of your bliss, is as exhilarating as the bliss itself.
For you, the vigor, equally invigorating is the bliss,
O mighty, giver of a thousand pleasures.
Sexual imagery finely intertwined with the use of numbers. According to John McLeish: “From the time of their earliest civilizations, the inhabitants of the Indian subcontinent had a highly sophisticated awareness of numbers.” McLeish further says that the people of Mohenjo Daro—the first known city in India, the location of the first recorded civilization that flourished some 5,000 years ago in the Indus Valley—“used a simple decimal system and had methods of counting weighing and measuring that was far more advanced than those of their contemporaries in Egypt, Babylonia, and Mycenean Greece. Vedic altars had to be built to exacting mathematical prescriptions; the correct dimensions and the right geometry were crucial.”
It appears that numbers in ancient India were invented for religious purposes very early in human history. While numbers were of a practical concern in the West—a necessity of banking,—in the East numbers acquired a spiritual, religious meaning.
I read many sources on Indian mathematics. In the 1925 book on the history of mathematics by David Eugene Smith, I found the following:
The early numerals of India are of various kinds. The earliest known forms are found in inscriptions of King Ashoka, the great patron of Buddhism, who reigned over most of India in the third century BC. The characters are not uniform and vary to meet linguistic conditions in different parts of India. Karosthi numerals are simply vertical marks; the Brahmi characters are more interesting. The Nana Ghat inscriptions, from the Nana Ghat cave, 75 miles from Puna, are a century after Ashoka’s edicts.
These last numerals from the Nana Ghat inscriptions include a 7 that looks just like our 7, and the 10 looking like the Greek letter alpha. They are shown below.
These appear to be among the earliest numerals that ultimately evolved into the ones we use today. Buddhist monks inscribed them on the wall of a cave high on a mountain in the Western Ghats. They lived in the cave and used it as a place of worship during the second century BC. We also know that Buddhist travelers throughout Asia were the main conduit for the eventual spread of the base-10 number system across the continent. To visit the cave, one must make the arduous four-hour climb up the steep incline to the bluffs that hide the entrance to this underground Buddhist site. The Indian government has not done enough to preserve the site, and the inscriptions bearing numerals that are the progenitors of our number system are now degraded through vandalism and neglect.
But where did the numerals go from there? How did they develop further, after their formulation during the time of Ashoka? At the National Museum in New Delhi I found a large display explaining the evolution of the letters in Hindi and in other Asian languages. Not far from the display area I saw a working research center. I walked over and began a conversation with two researchers; I was surprised by what one of them said: “We don’t like to admit it, but our written language really originates from Aramaic.” This was unexpected.
“Well,” the middle-aged scholar wearing a jacket and bow tie continued, “India had long-standing trade relations with the Middle East and with Greece, and Aramaic—the lingua franca of the ancient Near East—influenced the development of our own script.”
But I assumed that the numerals could not have come from there, since numbers used in the Near East were either the base-60 Babylonian ones or the Greco-Roman letter-kind of numerals. I made this observation to the two researchers, and they nodded in agreement and said that perhaps the numerals were indeed a genuine Indian invention, even if the progenitors of the written script had arrived here from the Near East.
In fact, the earliest numerals ever used were in all likelihood Phoenician letters, from which the Hebrew, Aramaic, and other Semitic alphabets evolved. Phoenician is the oldest language in the Near East, and we know that Pythagoras traveled in this region and learned some of his early notions about mathematics from the Phoenicians and the Egyptians and their priests. Our letter A and the Hebrew letter aleph both derive from the Phoenician letter aluf, which means bull and was inspired by a stylized drawing of the head of a bull. This letter once stood for the number 1. As aleph it is still employed in that role by some religious Jews today. As alpha, it was used for 1 by the ancient Greeks. The Romans then chose to use I for 1, II for 2, and so on, while the Greeks continued in their own alphabet with beta and gamma for 2 and 3, and so on, and the ancient Hebrews with bet and gimmel, and onward.
So the Nana Ghat inscriptions are extremely important because they provide strong evidence that our numerals are a genuine Indian invention made during the distant past, and then perhaps developed further while spreading around the world. These numbers were preceded by earlier Indian numerals, the Brahmi script seen in monuments of King Ashoka (slightly different from the Nana Ghat numbers); these, in turn, are related to the Kharosthi script, another alphabet employed in writing Sanskrit and regional languages starting in the third century BC in north India and Pakistan.
Noting that all these scripts bearing early numbers are Indian has made experts conclude that our numerals originate in India. But what about the zero?
Excerpt reproduced with permission from Pan Macmillan India
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