11/01/2021

Beyond 10 digits: the various ways of counting

Foto: Freepik

In the heat of the moment, who hasn't resorted to using their fingers to speed up a calculation? Common among adults and children, this gesture leads us to deduce the reasons that led humanity to adopt the decimal numbering system. The most common counting bases in history are 5, 10, and 20; and they are equivalent, respectively, to the number of fingers we have on one hand, on both hands, and the sum of the fingers on our hands and feet. Despite being widely used, the decimal system is not a consensus among mathematicians. In the United States, the Dozenal Society of America has advocated, since 1944, the adoption of a counting system consisting of 12 digits.

This would imply the creation of two more numbers, in addition to the 9 and 0 of the decimal system. One of the main arguments of the movement is that the change would make it easier for children to learn mathematics. This is because the number 12 can be divided by 2, 3, 4, and 6; while the number 10 is only divisible by 2 and 5. In other words, the number of multiplication tables that are easier to learn and memorize would be doubled, considerably simplifying the understanding of fractions.

Basic mathematics would benefit the most if society were to adopt the duodecimal system. "[…] it would be much simpler to use money, measure anything, calculate a third or a quarter of a quantity…", said physics professor and system advocate Stephen Wood to the BBC .

Since the modern world follows the decimal system, it's easy to imagine how complex and costly a migration to a new counting model would be. But remnants of different arithmetic bases show that this type of change has precedents in history. The sexagesimal system used by the Babylonians, for example, is present in the way we record time to this day: with 60 seconds in a minute and 60 minutes in an hour.

When we order a dozen eggs at the market, for example, we are using the duodecimal system. Ounces (16 equal one pound) and quarts (four represent one gallon) are other units of measurement that are not based on the decimal system. So, shall we try it?

Source: BBC