Possible To Get A Not Base 10 Numeric System Widely Used?

As MattII commented, the Babylonians used Base 60 - which we still use! Anyone look at a clock lately?

(I first read about this in an Isaac Asimov essay; no, I don't know the title or where you can find it, I read the essay ~30 years ago.)

I'm not convinced that Base 60 is all that useful, but the advantage it has is that so many other Base counting systems are multiples of it (Base 2, 5, 10, 12, 20, any others you want like 3, 4, 6, 15, 30 as well).

I suspect that the Babylonians hit upon 60 (by say stretching a base-20 system for instance) for calendrical reasons--six sixties is nearly the number of days in a year. Also 60 is nearly the same number as 64 which is 8x8, so if they knew or were descended from a people who routinely used base 8, they'd be impressed with the all-round power of a base-60 system to come very close to unifying everything.

But where they came up with the 7-day week, which throws everything off, I have no frakkin' clue. Except that the lunar month is closer to 29 than 30 days so rounding it down to 28 and dividing that by 4 might have been right up those wacky Mesopotamian astrologer-priests' alley...:confused:

Octal has the advantage that it would be very easy to convert computer binary output into human readable octal numbers.

And I gather that sometime between say 1930 and 1990 someone or other tried to implement a human-comfortable form of built-up binary for casual counting and arithmetic. It features in Fred Pohl's The Coming of the Quantum Cats which was published in the late 1980s. In the set of alternate universes which proved to be technically dominant by the end of the story (and thus shut down the recent experiments in a set of somewhat less advanced ones in cross-time transport, since jumping sideways in time apparently had undesirable repercussions) the people from those timelines, or at least one of them, had such a system, using simple (rather silly-sounding!) words for binary counting up to base 8 or 16 or so, then presumably compounding bigger numbers using digits of these ("oodle-poo, toodly-oo, oppie-pop" were the way I remember them sounding). It just struck me as the sort of thing from OTL a guy like Fred Pohl would learn about and be struck as an interesting and possibly useful way of teaching people arithmetic. Perhaps a superior system of basic arithmetic put some of these allied advanced timelines ahead causing them to invent the cross-time switcher earlier; perhaps an early timeline that was advanced for quite other reasons happened to discover a neighboring timeline that used it and it seemed to the primary high-tech line like a good idea to adopt generally.

But yeah, from the replies to this thread it seems like base-10 is actually a rather parochial number base to have adopted!
 
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All widely used human counting systems were probably not "invented", but rather grew out of evolving common practice in non-literate societies. I've always thought that systems based on human digits (5, 10, 20) would be most natural and most common, and historical evidence clearly shows that they are (particularly base 10 and base 20). As has been pointed out, there have been some based on the gaps between digits (8) and others based on 12. But for the most part these are evidenced only by vestigial elements today. Also, it is arguable that many systems based on 12 may have been "invented" for specific economic purposes and supplemented decimal systems. I suspect that in 100 alternate timelines, a digit-based system would become dominant in 95 of them. Systems based on 5s or multiples of 5s would be more common because one can much more easily "tick off" numbers by moving fingers than by imagining gaps - especially when you start. I suspect that base 10 would outnumber the other main options (5 and 20), because it is very natural to extend a count across both hands. A base 20 system would probably only evolve where the toes were routinely left uncovered.
 
Shevek23 said:

But where they came up with the 7-day week, which throws everything off, I have no frakkin' clue. Except that the lunar month is closer to 29 than 30 days so rounding it down to 28 and dividing that by 4 might have been right up those wacky Mesopotamian astrologer-priests' alley...:confused:

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From what I remember (again from an Asimov essay), the seven day week came from the classical seven planets (Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn, only in Babylonian: ie, Ishtar, Marduk,etc). This was passed on to the ancient Herbrews, and then into the West via Christianity. I'm not sure who else derived such a thing as the seven-day week; what helped was that 52 weeks almost fits into a year.
 
That's why I like the Maya calendar, makes much more sense. :p You just got your 18 20-day months plus the extra 5 unlucky days at the end, combined with a ritual calender so that the same day will only repeat once every 52 years. So 8 Cauac 7 Zip will occur 52 times less often than December 14th or whatever.
 
In some languages it's not vestigial. Welsh (not sure about the other Celtic languages) has a fully functioning base-20 system (although a simplified base 10 system is gaining in popularity these days). 95 for example is pymtheg ar bedwar hugain, which literally translates as fifteen on four twenties.
Gaelic works in the same way. Your example of 95 would be coig deug is caither fichead or fifteen and four twenties, much like the French Quatre Vingt.

But then there are the older counting systems (which are still used by upland shepherds - or so I'm told) of Yan, tan, tethera, methera, pimp....
http://www.readingdetectives.org/cumbria/2009/09/yan-tan-tethera.html
 
and how would you call the roman way of counting? considering how much of europe they dominated. so their non-decimal way of counting was widespread as what the OP requested.
 
Iirc Base 12 was used in Ancient Mesopotamia - hence the 60 minutes of the hour and 24 hours of the day. Maybe if BB
abylon wins out over Persia - -

Actually we have 60 minutes in an hour and 60 seconds in a minute because we measure time in base 60. The Summerians and Babylonians both used Base 60.
 
Shevek23 said:

But where they came up with the 7-day week, which throws everything off, I have no frakkin' clue. Except that the lunar month is closer to 29 than 30 days so rounding it down to 28 and dividing that by 4 might have been right up those wacky Mesopotamian astrologer-priests' alley...:confused:

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From what I remember (again from an Asimov essay), the seven day week came from the classical seven planets (Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn, only in Babylonian: ie, Ishtar, Marduk,etc). This was passed on to the ancient Herbrews, and then into the West via Christianity. I'm not sure who else derived such a thing as the seven-day week; what helped was that 52 weeks almost fits into a year.

It might simply be that six days of work was best balance between productivity and sustainability before a day off. I believe it developed in India and China independently from the West. Certainly the French Revolutionary 10-day week was highly unpopular, and the Russian 5-day week was also abandoned.
 
English still has vestigial traces of base twelve (two dozen etc...). I've heard this exists in some tribes from counting the knuckles on one hand. Twelve is probably the most intriguing one as it is the easiest system to work with, divisible by two, three, four and six.

English and German both have traces of base twelve, if only in the fact that they have special names for "10+1" and "10+2" (eleven and twelve, elf und zwolf). Other European languages, such as Polish and Latin, use words that literally mean "ten and one" and "ten and two" in those positions.
 
English and German both have traces of base twelve, if only in the fact that they have special names for "10+1" and "10+2" (eleven and twelve, elf und zwolf). Other European languages, such as Polish and Latin, use words that literally mean "ten and one" and "ten and two" in those positions.

Maybe, maybe not... unlike Latin and other languages, the Germanic words for 11 and 12 have simply been mangled by language change and the etymology isn't as obvious. "Eleven" probably comes from a Proto-Germanic compound word which translates as "One-left", implying "One left after ten". Twelve is "two-left" -- which I think is a bit more apparent.

English measurements certainly do seem to be base-twelve... except where they are base-sixteen, that is. But that may simply be because twelve is so much easier to divide when you don't want to use decimal points.
 
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