2 and 3
Fig. 24.58. Evolution of Indian numerals 2 and 3
“[T]he superposition of two or three horizontal lines, first transformed into one complete sign by a ligature, gave birth to the same forms as the Indian numerals for 2 and 3, whose palaeographical styles vary considerably according to the era, the region and the habits of the scribe.”
—Georges Ifrah, The Universal History of Numbers, 2000.
The nine numerals
“The nine numerals (of Indian origin) that we use today . . . are drawn in just one stroke of a pen or pencil. This is one of the characteristics of our numeral system, whose remarkable simplicity we forget because we have been using it all our lives.”
—Georges Ifrah, The Universal History of Numbers, 2000.
zero and the place-value system
“[T]he discovery of zero and the place-value system were inventions unique to Indian civilisation. [Just as] the Brahmi notation of the first nine whole numbers . . . was autochthonous and free of any outside influence, there can be no doubt that our decimal place-value system was born in India and was the product of Indian civilisation alone.”
—Georges Ifrah, The Universal History of Numbers, 2000.
the little circle
“[T]he word-symbols that the Sanskrit language used to express the concept of zero conveyed concepts such as the sky, space, the atmosphere or the firmament.
In drawings and pictograms, the canopy of heaven in universally represented either by a semi-circle or by a circular diagram or by a whole circle. The circle has always been regarded as the representation of the sky and of the the Milky Way as it symbolizes both activity and cyclic movments.
Thus the little circle, through a simple transposition and association of ideas, came to symbolise the concept of zero for the Indians.
Another Sanskrit term which came to mean zero was the word bindu, which literally means ‘point’.
The point is the most insignificant geometrical figure, constituting as it does the circle reduced to its simplest expression, its centre.
For the Hindus, however, the bindu represents the universe in its non-manifest form, the universe before it was transformed into the world of appearances. According to Indian philosophy, this uncreated universe possessed a creative energy, capable of generating everything and anything: it was the causal point.”
—Georges Ifrah, The Universal History of Numbers, 2000.
the modern name of zero
“When the Arabs adopted Indian numerals and the zero, they called the latter sifr, meaning ‘empty’, a plain translation of the Sanskrit shunya. . . .
When the concept of zero arrived in Eurpoe, the Arabic word was assimilated to a hear-homophone in Latin, zephyrus, meaning ‘the west wind’ and, by rather convenient extension, a mere breath of wind, a light breeze, or–almost–nothing.In his Liber Abaci, Fibonacci (Leonard of Pisa) used the term zephirum, and the term remained in use in that form until the fifteenth century. . . .
[I]t was Fibonacci’s term . . . which gave rise to the modern name of zero, by way of the Italian zefiro (zero is just a contraction of zefiro, in Venetian dialect). . . . There is absolutely no doubt that zero owes its spread to French (zero) and Spanish (cero) (and later on to English and other languages) to the enormous prestige that Italian scholarship acquired in the sixteenth century.”
—Georges Ifrah, The Universal History of Numbers, 2000.
the ‘figure numbers’
“The fact that the Roman numerals were so deeply rooted in the customs and affections of the people at first made it exceedingly difficult for the new Indian numerals, the ‘figure numbers,’ to replace the old familiar Roman numerals. . . . [I]n northern Europe the Indian numerals first began to be used by ordinary people about 1500. This date, the change from the fifteenth to the sixteenth century, is the great intellectual watershed of modern history, the time when all the new movements generally came to the fore.”
—Karl Menninger, Number Words and Number Symbols; A Cultural History of Numbers, 1969.
Who could understand such a thing?
“Today we can no longer understand the stubborn reisitance to the new numerals during the early Middle Ages; to us they seem so much easier to work with than the cumbersome Roman numerals. . . . [T]he counting board served medieval Europe as a perhaps slow but essentially equivalent and above all highly visual means of computation. Computations with the new numberals, in contrast, were certainly not as easy to visualize. But most of important of all they embodied an intellectual obstacle that was scarcely overcome during the first few centuries of their presence in the west: the zero!
What kind of crazy symbol is this, which means nothing at all? Is it a digit, or isn’t it? 1, 2, 3, 4, 5, 6, 7, 8 and 9 all stand for numbers one can understand and grasp — but 0? If it is nothing, then it should be nothing. But sometimes it is nothing, and then at other times it is something: 3 + 0 = 3 and 3 – 0 = 3, so here the zero is nothing, it is not expressed, and when it is placed in front of a number it does not change it: 03 = 3, so the zero is still nothing, nulla figura! But write the zero after a number and it suddenly multiplies the number by ten; 30 = 3 x 10. So now it is something — something incomprehensible but powerful, if a few ‘nothings’ can raise a small number to an immeasurably vast magnitude. Who could understand such a thing?”
—Karl Menninger, Number Words and Number Symbols; A Cultural History of Numbers, 1969.
The End of the World
Jake Shimakuburu
Number signs
“Man differs from other animals most strikingly in his language, the development of which was essential to the rise of abstract mathematical thinking; yet words expressing numerical ideas were slow in arising. Number signs probably preceded number words, for it is easier to cut notches in a stick than it is to establish a well-modulated phrase to identify a number.”
—Carl B. Boyer, A History of Mathematics, 1968.