Deciphering Zero

Source

Ah, numbers. We use them every day. We also know that there are different sets of numbers. We have Arabic numerals for everyday use, and we have Roman numerals for special events, like Superbowls and the year a movie came out.

Roman numerals were used exclusively in the Middle Ages for a long time. They were inconvenient for large sums, but Western Europe had no other option. Eventually, however, along came so-called Arabic numerals. They were introduced by Leonard of Pisa, better known today as Fibonacci. Fibonacci's Liber abaci ("Book of calculating"; it wasn't about the abacus) introduced Arabic numerals (which probably came originally from India) and a decimal system, with "places" for ones, tens, hundreds, and so forth. With these new numbers came something very new and strange to them: what we call "zero."

Of course they did not call it "zero" when it was first introduced. The Arabic word was ṣifr, or zephir, which when filtered through Old French became cifre and eventually the English cipher. John Sacrobosco (c.1195 - c.1256; mentioned here) in The Craft of Numbering explained:

A cipher tokens nought, but he makes the figure that comes after to betoken more than he should; thus 10. Here the figure of 1 betokens 10, and if the cipher were away, ..., he should betoken only 1, for then he should stand in the first place. [paraphrased]

The concept of the zero was so mysterious, the new number system so different and difficult to master (the British Exchequer clung to Roman numerals—at least partially—until the mid-17th century), that using them seemed like a secret code. The words encipher and decipher grew from the ability to make and read this code and understand the zero.

The Birth of Tick-Tock

A city without bells is like a blind man without a stick. —Rabelais

Rabelais (c.1494-1553) was a little late for this blog, but his statement in Chapter XIX of Gargantua indicates a reliance on time-keeping that the modern world can understand. It was not always thus, however, for the Middle Ages.

I discussed yesterday how early concepts of time by their nature might have made it difficult to think of time as something measurable. I mentioned a mid-1200s definition of time that came from Franco of Cologne, the mathematically-minded music theorist who created what is the basis for modern musical notation. Franco's most diligent biographer places him as chapelmaster at Notre Dame in Paris.

Johannes de Sacrobosco (c.1195-c.1256) taught at the University of Paris, probably contemporaneously with Franco. Johannes was an astronomer who, among other things, declared that there was a flaw in the Julian calendar: it was 10 days off. (That error wouldn't be corrected until long after.) He also wrote of an attempt he knew to construct a wheel that would make a complete rotation in one day. Robertus Anglicus wrote a commentary in 1270 on Sacrobosco's treatise, mentioning the device and further spreading the idea. In that same decade, a clock is described by someone writing in Spain that runs by the flow of mercury from chamber to chamber in a wheel.

It only took a generation for this idea to catch on. By 1300, clocks were becoming widely known (if not widely owned), but the early ones only measured hours—they rang bells, but had no faces with markings around a dial, no minutes or seconds were counted, that we know of.

The device described by Sacrobosco and Anglicus used a weight hanging from a line around a wheel or cylinder. The Middle Ages understood wheels, gears, levers and pulleys, but how could these be used to guarantee a steady revolution of the weighted wheel? Sometime around 1300, or not long after, some early mechanical "Eureka" moment took place. Someone designed what we call the "escapement," which rocked back and forth on a toothed gear, allowing the wheel to turn at a steady, measurable, predictable speed. It also had a side-effect: a steady sound that we have been listening to ever since.

The escapement.

Within a generation after 1300, Dante Alighieri (c.1265-1321) considers his audience familiar enough with clocks and their mechanism to use gears as a metaphor:

As the wheels within a clockwork synchronize
       So that the innermost, when looked at closely
       Seems to be standing, while the outermost flies. (Canto xxiv, Paradiso)

Humans could now mark time in sequences of ticks and tocks. Minutes and seconds could be distinguished. Hours could be regulated. Six hours before noon became the same, whether it were dark in winter or already light in summer. (That's right: the 12 hours from sunrise until sunset used to be extended or shortened depending upon the season.) This was a change from the canonical hours described by the Rule of St. Benedict, for whom prayers at Matins were supposed to end as the sun rose, and therefore had to be started at different times depending on the season. In 1370, Charles V of France installed a clock in his palace, and decreed that all clocks in Paris be set according to his. Punctuality, crucial feature of our modern world, was born.