g33kski11z said:
wait, so seriously, if we had 12 fingers, it would be different??
Perhaps. Humans have always had 10 fingers, but not all human numbering systems use 10 as a base. In fact, many human numbering systems use more than one base.
Sumerian and Babylonian used a dual base system - 10 and 60. And their numbering system is still reflected in the way we measure time and angles. If it wasn't such an awkwardly large number, 360 would have been a good base, since there's approximately 360
days in a year (yes, they probably knew there were actually 365
days in a year, but building a numbering system using 365 would have sucked). As is, the stars shift approximately 1 degree per night (.99 degress per night on average).
Five is a rather natural base for a numbering system based on a repeating symbol for more than 1. It's hard to instantly recognize how many marks there are when there are more than 4. If you put a diagonal slash across the marks to finish off the group with the 5th item (or some other special symbol), you can then step up to counting the number of groups instead of individual marks.
The Romans used a dual base system - 5 and 10. Using that combination for a dual base system was kind of rare.
Base 20 is a fairly common numbering base. Most base 20 systems are dual base systems - 5 and 20. Why wasn't it more common to go straight base 5, where the next order of magnitude would be 25 instead of 20? Perhaps because humans have 20 fingers and toes? I don't know, but most groups of 5 were grouped by 4's instead of 5's. In fact, in Western culture, 4 groups of 5 would be a 'score' of items, whether it be sheep, stones, or years (as in 4 score and 7 years ago).
If your low numerals are merely a series of marks (Roman numerals I, II, III, etc), base 5 and 20 wind up being very common as the numbering system is built up to accommodate higher numbers. (Roman numerals would be an exception to that generalization, however.)
If you use symbolic notation for your lower numerals (1, 2, 3, 4, etc), base 10 winds up being very common - kind of. Egyptians and Greeks kind of used a base 10 system, but they didn't use a system as simple as ours, where you only had 10 numeric symbols that would be reused with their location in the number specifying whether that '1' was a 1, 10, 100 etc. They had unique symbols for 10, 20, 30, 40, etc; unique symbols for 100, 200, etc., which made for a lot of memorization. Base 10 had some significant successes, but it wasn't very common due to having so many symbols to memorize.
The idea of using the type of base 10 system we use today required something that was very rare in numberings systems: a zero. The Hindus were probably the first to use 0 and invented the first true base 10 system using only 10 symbols, relying on the symbols location within the number to indicate whether the '1' was a 1, 10, 100, etc. The Arabs borrowed the idea from the Hindus and eventually lent the idea to Europe, as well.
Think about that.
