Computational Sciences. How come an Italian invented the decimal point in the 15th century

Surprise: the decimal point was invented about 150 years earlier than previously thought. This was revealed by an analysis of the astronomical tables he compiled Italian merchant and mathematician Giovanni Bianchini in the 1440spublished on Historia Mathematica. Historians say the discovery rewrites the origins of one of the most important mathematical conventions and suggests that Bianchini, whose economic background contrasted sharply with that of his fellow astronomers, may have played a more significant role in the history of mathematics than previously thought.

“It’s a very beautiful discovery,” said Jose’ Chaba, a historian of astronomy at Pompeu Fabra University in Barcelona, ​​Spain. “The decimal point was a breakthrough for humanity, it enabled the ease and efficiency of calculations that are the basis of modern science and technology,” Chaba continued. It was previously believed that its first appearance was in an astronomical table written by the German mathematician Christopher Clavius ​​​​​​​​in 1593.. “But now it is clear that the inspiration was taken from Bianchini,” specified the historian of astronomy. Bianchini worked as a Venetian merchant before becoming the administrator of the estates of the powerful d’Este family, who at the time ruled the Duchy of Ferrara. In addition to managing property and managing investments, Bianchini was responsible for writing horoscopes, which meant he had to master astronomy. He has published several works on topics ranging from planetary motions to eclipse prediction. Glen Van Brummelen, a historian of mathematics at Trinity Western University in Langley, Canada, hoped that Bianchini’s work could help reveal how and when Islamic astronomical knowledge reached Europe. Instead, it was understood from what he wrote that the decimal point was not a legacy of that culture, but an actual invention of an Italian merchant.

“As a businessman – said Brummelen – Bianchini would have traveled everywhere; so it seems natural that he found something in Islamic science on his travels and used it as inspiration. Instead, it seems that many of the things he did were simply the result of his incredibly creative mind.” By Bianchini’s time, European astronomers were exclusively using the sextuple system, based on 60, inherited from the Babylonians. The hexadecimal system is still used today to record latitudes and longitudes, both celestial and terrestrial. It divides the entire circle into 360 degrees, each degree into 60 minutes and each minute into 60 seconds. However, it is difficult to perform operations such as multiplication with hexadecimal numbers.

For example, astronomers would have to convert the value to the smallest unit to do the calculation and then convert it back later. However, merchants and accountants learned to calculate using actual weights and measures, in which the units could be divided in different ways: for example, 12 inches to a foot and 3 feet to a yard. In order to make simpler calculations, Bianchini invented his own decimal scheme, describing a system of measuring distances in which a foot, 30 centimeters, was divided into ten equal parts, called “unties”, each of which was divided into ten minutes, and then in ten “seconds”. This system was unsuccessful, and it is believed that his bias towards base 10 did not affect his astronomy. But in examining a treatise written by Bianchini in 1440, entitled Tabulae primi mobilis BVan Brummelen realized that in some places he was using not only the decimal number system, but also the decimal point that we use today.

Van Brummelen suggests this Bianchini’s background in economics may have been the key to his invention, because he did not deal with six-fold numbers from the beginning of his career, as other astronomers did. But his approach was perhaps too revolutionary to be accepted at first. “You had to learn a whole new arithmetic system to understand what Bianchini was doing,” Van Brummelen concluded.


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