Slow-burn impact

The history of binary arithmetic shows that we should be concerned about pressure to demonstrate the immediate value of discoveries, says Lloyd Strickland

April 2, 2015

He added his writings on the subject to his pile of unpublished papers, which, at his death, totalled some 500,000 pages

Whether they like it or not, scholars these days are used to the idea that their work should demonstrate not just impact, but relatively swift impact. We should be grateful that it was not always like this. If it had been, some of the very best ideas that power modern life would very probably have been abandoned altogether because their significance was not immediately apparent.

A good example is binary arithmetic. This was, arguably, first conceived by Thomas Harriot (1560-1621), but he didn’t publish his findings and it was independently discovered in 1679 by the German polymath Gottfried Wilhelm Leibniz (who, a few years earlier, had discovered calculus and published it before Newton). Seeing no immediate significance in this new way of counting, Leibniz also made no attempt to publish it, and added his writings on the subject to his ever-expanding pile of unpublished papers, which, at his death, totalled some 500,000 pages.

But Leibniz revisited his discovery almost 20 years later, after coming to the view that binary arithmetic was of great importance to theology. He believed that the arithmetic, which was capable of generating all natural numbers using only zeros and ones, perfectly symbolised the creation of the universe from nothing by the one God. Indeed, he was so taken with the idea that he sketched a design for a memorial coin or medallion, the Latin inscription of which reads: “One produces all things from nothing, but the one is necessary”. To the sides are the words “image of creation”, alongside rays of light shining on what looks to be the watery deep, recalling the description of Creation from the book of Genesis.

Having identified a concrete use for his new method of counting – demonstrating to sceptics the truth of the core Christian belief in the creation of the universe from nothing – he began passing details of it to a number of his correspondents. One of those was Joachim Bouvet, a Jesuit who undertook missionary work in China. Bouvet was struck by the similarity between binary arithmetic and the mysterious hexagrams of the I Ching, developed by the Chinese thousands of years beforehand. Each of the 64 hexagrams consisted of a broken line (a yin) or a solid line (a yang). By equating the solid line with 1, and the broken line with 0, Bouvet suggested that the I Ching might actually be nothing more than Leibniz’s binary system in alternative notation.

Leibniz took little convincing that Bouvet’s theory was right. And what it meant, he realised, was that he had not so much discovered binary arithmetic as rediscovered it. Leibniz was so excited by the idea that he had unlocked a piece of ancient Chinese wisdom that he decided to make his (re)discovery public without further delay. Within a week he had written a short paper – “Explanation of binary arithmetic” – and sent it to an important scientific journal. The first half of the paper explained how binary arithmetic worked, while the second half outlined the theory that the Chinese had been aware of it thousands of years before. This led Leibniz to argue that there was merit in a two-way intellectual exchange with the Chinese, since they clearly had much to offer the Europeans. This stood in stark contrast to the attitude of many at the time, that the Chinese were merely there to be converted.

But Leibniz had less success in identifying practical uses for binary. He did note that using it “enables assayers to weigh all sorts of masses with few weights and could serve in coinage to give several values with few coins”, but none of his suggestions were followed up and, after his death, binary arithmetic became little more than a curiosity among mathematicians.

That was, of course, until it was put to use in the middle of the 20th century as the basis for the logic gates in modern digital circuitry, making the computer revolution possible. But the moral of the story, of course, is that if it had not been for Leibniz’s blue-sky thinking, and the lack of pressure on him to demonstrate the immediate practical value of his discovery, that revolution may not have happened when it did, or even at all.

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