History of Science and Mathematics Asked by Favst on September 2, 2021
Wikipedia’s list of numeral systems lists only $10,20,60$ as having been used in history. There are about twenty-five sets of symbols there used by different groups of people, but only three different bases. I’m a little surprised that, even if some of these civilizations learned about positional notation from others and did not independently discover it, they changed up the symbols without exploring whether a different base could be used. I would have thought that base $30$ would be a decent candidate since it multiplies the first three primes (there are advantages with respect to the quantity of terminating rational numbers and convenient divisibility rules) while having only half the number of distinct symbols as $60,$ which has been used by Babylonians, and the number of days in a lunar month is 29-30 days (see Arabic calendar)
Question: Has there been a large group of people that worked with a base other than $10,20,60$ for day-to-day activities?
I have read this thread and it also mentions bases $10,20,60,$ but no other significant ones. There is a TED-Ed talk about on this subject as well, but it doesn’t mention any others. excluding the usage of bases that are powers of $2$ for purposes related to computers.
Wikipedia:
Languages using duodecimal number systems are uncommon. Languages in the Nigerian Middle Belt such as Janji, Gbiri-Niragu (Gure-Kahugu), Piti, and the Nimbia dialect of Gwandara and the Chepang language of Nepal are known to use duodecimal numerals.
Also:
It is thought that Nimbia, which is isolated from the rest of Gwandara, acquired its duodecimal system from neighboring East Kainji languages. It is duodecimal even to powers of base twelve.
It also appears that many ancient progenitors of Indo-European languages were based on 4 or 12, due to remnant number words that don't line up with a purely decimal system:
Germanic languages have special words for 11 and 12, such as eleven and twelve in English. However, they come from Proto-Germanic *ainlif and *twalif (meaning, respectively one left and two left), suggesting a decimal rather than duodecimal origin.
Wikipedia's primary source appears to be this article by Shuji Matsushita.
Correct answer by Spencer on September 2, 2021
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