Among all the extracurricular skills I learned as a child, abacus counting was by far the most meaningful. The “mental abacus arithmetic” we learned was not just operating an abacus; through long-term training, it was a way of “placing the abacus in the mind” and then doing mental calculation with it. After about two years of training between first and third grade in primary school, three times a day—morning, noon, and evening—even if one did not quite reach the level of a few speed-calculation prodigies, one could at least manage, say, to hear several dozen three- or four-digit numbers in succession, compute their sum, and keep up as fast as they were read out. The significance of this skill was not only that it increased calculation speed, but that it reshaped the very existence of numbers in our minds (even when I calculate 5+7 I do it through the abacus; the impression each number leaves in my mind is the arrangement of the beads), and, crucially, it greatly strengthened our confidence in mathematics, so that later math study proceeded without a hitch.
A few days ago, when I mentioned the abacus I had learned to butian shixiong, he joked that I could write a “Praise of the Abacus,” which would count as a topic in the history of science and technology.
When I got back, I actually went and looked up the “literature,” only to discover that it seems there has really been very little serious historical research in China on such an important contraption as the abacus. In fact, the abacus is absolutely crucial both to the development of mathematics in China and to Chinese culture. While looking through books, I only found one book by a Japanese author, The Analects and the Abacus; just from the title, you can tell to what extent he elevated the abacus’s status.
The introduction of Arabic numerals was of enormous significance in the history of science and technology in Europe. Arabic numerals greatly facilitated counting and calculation; especially in comparison with cumbersome Roman numerals, the introduction of Arabic numerals and their methods of operation not only promoted abstract mathematics, but probably also thoroughly transformed accounting and the entire commercial system at the institutional level. On the one hand mathematics, on the other commerce: it seems that the introduction of Arabic numerals was a key precondition both for Europe’s later Scientific Revolution and for the rise of capitalism!
But here one must ask: were Arabic numerals not originally from India? Why was it that ancient China, despite so much cultural exchange with India and learning so many things from India, did not “go to scripture” and import that wonderfully convenient system of notation? Why did it have to wait until the nineteenth century, alongside Western science, before it began to accept them? Arabic numerals started out from China’s neighborhood, passed through three hands, and took a roundabout route before finally coming in—why didn’t they come in earlier? If China had accepted Arabic numerals, along with the abstract ways of thinking they brought with them, a bit sooner, how would world history have developed then?
Why China did not introduce Arabic numerals from nearby, I suspect, was precisely because of this “abacus.” Thanks to the widespread use of the abacus in China, we did not need Arabic numerals in order to perform calculations more easily and more quickly than Western accountants who computed on paper with Arabic numerals! Compared with this primitive computer called the abacus, Arabic numerals are simply clumsy and backward! In short, the existence of the abacus gave ancient China no reason at all to introduce Arabic numerals.
Whoever writes a History of the Abacus—this being a topic at once in the history of science and technology, and also in economic history and cultural history—would probably produce something quite interesting. I don’t seem to have seen any similar book on the market yet~
Translated from the Chinese original with AI assistance. The original text is authoritative.
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