109. Zero
One of the milestones of civilization is the number symbol zero. This renders possible the unambiguous designation of numbers of any size with a small stock of figures. It is the zero that enables the symbol 1 to have the varying values of one, ten, hundred, or thousand. In our arithmetical notation, the symbol itself and its position both count: 1,234 and 4,321 have different values although they contain the identical symbols. Such a system is impossible without a sign for nothingness: 123 and 1,023 would be indistinguishable. Our zero, along with the other nine digits, appears to be an invention of the Hindus approximately twelve or fifteen hundred years ago. We call the notation “Arabic” because it was transmitted from India to Europe by the Arabs.
Fig. 28. Maya symbols for zero: a, monumental; b, c, cursive. (From Bowditch.)
Without a zero sign and position values, two methods are open for the representation of higher numerical values. More and more signs can be added for the high values. This was done by the Greeks and Romans. MV means 1,005, and only that. This is simple enough; but 1,888 requires so cumbersome a denotation as MDCCCLXXXVIII—thirteen figures of six different kinds. A simple system of multiplying numbers expressed like this one is impossible. The unwieldiness is due to the fact that the Romans, not having hit upon the device of representing nothingness, employed the separate signs I, X, C, M for the quantities which we represent by the single symbol 1 with from no to three zeroes added.
The other method is that followed by the Chinese. Besides signs corresponding to our digits from 1 to 9, they developed symbols corresponding to “ten times,” “hundred times,” and so on. This was much as if we should use the asterisk, *, to denote tens, the dagger, †, for hundreds, the paragraph, ¶, for thousands. We could then represent 1,888 by 1 ¶ 8 † 8 * 8, and 1,005 by 1 ¶ 5, without any risk of being misunderstood. But the writing of the numbers would in most cases require more figures, and mathematical operations would be more awkward.
The only nation besides the Hindus to invent a zero sign and the representation of number values by position of the basic symbols, were the Mayas of Yucatan. Some forms of their zero are shown in [Figure 28]. This Maya development constitutes an indubitable parallel with the Hindu one. So far as the involved logical principle is concerned, the two inventions are identical. But again the concrete expressions of the principle are dissimilar. The Maya zero does not in the least have the form of our or the Hindus’ zero. Also, the Maya notation was vigesimal where ours is decimal. They worked with twenty fundamental digits instead of ten. Their “100” therefore stood for 400, their “1,000” for 8,000.[17] Accordingly, when they wrote, in their corresponding digits, 1,234, the value was not 1,234 but 8,864. Obviously there can be no question of a common origin for such a system and ours. They share an idea or a method, nothing more. As a matter of fact, these two notational systems, like all others, were preceded by numeral word counts. Our decimal word count is based on operations with the fingers, that of the Maya on operations with the fingers and toes. Twenty became their first higher unit because twenty finished a person.
It is interesting that of the two inventions of zero, the Maya one was the earlier. The arithmetical and calendrical system of which it formed part was developed and in use by the time of the birth of Christ. It may be older; it certainly required time to develop. The Hindus may have possessed the prototypes of our numerals as early as the second century after Christ, but as yet without the zero, which was added during the sixth or according to some authorities not until the ninth century. This priority of the Maya must weaken the arguments sometimes advanced that the ancient Americans derived their religion, zodiac, art, or writing from Asia. If the zero was their own product, why not the remainder of their progress also? The only recourse left the naïve migrationist would be to turn the tables and explain Egyptian and Babylonian civilization as due to a Maya invasion from Yucatan.