Based on what?

las-columnas-1_2883334The other day I was talking about the misunderstanding that arose between a culture that counted in thousands, and a culture that counted in tens of thousands.  Does it make it even more difficult when people use a different base system than we’re used to?

Most cultures these days count in a base 10 system, most likely because we have five digits on each hand to keep track of the world with.   This means we count up to ten, remember that we have one lot of ten, keep counting to twenty, remember we have two lots of ten, etc.  Do you think you’d have trouble with bases 2, 5, 8, 12, 20, or even 60?  You might surprise yourself.

Base 2 (binary) is used primarily in computer-related fields, and relates to switches that can only be in the on or off position (1 or 0).

Base 5 has been used in many cultures (probably because we have five digits on one hand), and can be used as a sub-base for base 10, 20, or 60.

Base 8 is a counting system based on the gaps between fingers, and is used by the Yuki tribe of northern California (who also use 4 as a sub-base).  There is a theory that the Proto-Indo Europeans in the Bronze age used a counting system based on eights.  The word for nine, ‘newm’, is thought to have derived from ‘new’, and suggests to some linguists that nine and ten were, at some point, new numbers.

Base 12 is thought to have been related to the number of knuckles on one hand (not counting the thumb).  We still have words for twelve (one dozen) and twelve twelves (one gross).  We have two lots of twelve hours in a day, and twelve months in a year.  Twelve is not quite as easy to multiply, but simpler to divide in than base 10.

Base 20 is possibly based on the number of human fingers and toes, and was used by the Mayan civilisation and others in South America, and in some parts of Africa.  In English we still have the word ‘score’ (twenty), and in French there is ‘vingt’.  Eighty in French is ‘quatre-vingt’ (four twenties).  There is also evidence of base 20 in Irish and Danish counting systems.

Base 60 is thought to have been a combination of bases 10 and 12, and was used by ancient Mesopotamian cultures, as well as the Chinese.  As a result of the Sumerian usage, we still use base 60 to measure time and angles, with 60 seconds in a minute and 60 minutes in an hour.  The Chinese calendar has 6 cycles of 60 days in one year, and the Chinese Zodiac has four cycles of 12 (lasting 60 years).

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