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Friday, 5 February 2016

Numbers - mathematics, space, time, weights & measurements

In our current day and age, we still use 2 different, basic, and ancient numeral systems which both predate our current knowledge: the base-10 (or decimal system) and the base-60 system.

The oldest number set is most likely the decimal or base-10 system as it probably dates back to prehistoric times when we used the 10 fingers of both our hands to calculate. "Egyptian hieroglyphs, in evidence since around 3000 BC, used a purely decimal system" (Wiki). The base-10 system has various graphic representations, such as the Roman numerals (eg, I II III) and the Hindu-Arabic numeral system. Today we still use the Arabic numerals on our calculators (eg, 1 2 3).

The base-60 system is nowadays still used—in a modified form—for measuring time (eg, 60 seconds / minutes, 360 days), angles (eg, 360 degrees), and geographic coordinates (Wiki). Like many others, I have wondered why humans did not also use the decimal system (eg, 100 seconds, 100 minutes, etc). The "answer" is that our current concept of time and space is derived from the Babylonian calendar which in itself is based on a moon-sun calendar.

Remarkably, "the civil calendar from the holy Sumerian city of Nippur (Ur III period) was adopted by Babylon as their civil calendar. The Sumerian calendar of Nippur dates to 3500 BCE and was itself based on older astronomical knowledge of an uncertain origin" (Wiki).

In ancient times, weights and measurements were based on a base-60 system (eg, Mesopotamia). I have not been able to find any reason why the base-60 system is no longer in use for weights and measurements. I can only speculate that the use of the Hindu-Arabic numeral system (= base-10) in mathematics may have caused a paradigm shift in thinking. Nevertheless, this shift resulted in chaos: "Traditional names such as pound, foot, and gallon were widely used, but its values varied with time, place, trade, product specifications, and dozens of other requirements" (source).

Only in 1586, the Dutch/Flemish mathematician Simon Stevin declared that using decimals was so important that the universal introduction of decimal weights, measures and coinage was only a matter of time. France officially adopted the metric system on 10 December 1799. Areas annexed by France during the Napoleonic era were the first to inherit the metric system (Wiki).

Given the historic animosities between France and the UK, it's no wonder that the UK and its former colonies (eg, USA) still have not fully adopted the metric system and continue using the traditional British Imperial System (1824) for weights and measurements. 

Besides the base-10 and base-60 systems, there are a few other important concepts:
1. The number 0 (null, zero) is of a much later date than the base-10 and base-60 systems. "It first came to be between 400 and 300 B.C. in Babylon, Seife says, before developing in India, wending its way through northern Africa and, in Fibonacci's hands, crossing into Europe via Italy" (source).
2. Prime numbers: a natural number > 1 that has no positive divisors other than 1 and itself.
3. Numerology is any belief in the divine, mystical relationship between a number and one or more coinciding events (eg, 11:11 on a clock). 

It's rather weird to find out today that we do not know the origin of our time and space measurement (base-60), let alone the origin of our decimal (base-10) mathematical measurement. We just take both for granted.
Coldplay - Clocks (2002) - artists, lyrics, Wiki-1, Wiki-2

Confusion never stops
Closing walls and ticking clocks

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