Why Base-10 (almost) Universal???

I wonder if other societies, once-isolated from the West, developed a number system using something aside from base-10. (I know, I know - the Babylonians used 'base-60'. But their system didn't have 60 different types of digits, and so was not a 'true' base-60 system.)

I mean, most human societies WERE made up of human-beings where most possessed 10 fingers. But, aren't there any other things to base a number system on?

For one, the musical scale. I heard somewhere that 5-note octives and 12-note octives are natural, for these integers are derived from the continued fraction of (ln(3)/ln(2)). So wouldn't a number system based on the notes of a musical scale be cool?

How about basing a number system on astronomical numbers? The base-13 or base-12 (again) system would make sense, in a sense, given the number of times the moon orbits the earth every year. Base-7 makes sense too because 7 days approximates the length of each phase of the moon. (Hence, the 7-day week, right?)

Anything else known about this? Or to just make this fun, what other 'natural' integers would make good number system bases for other societies?

Yeah, base-2, base-16, even base-8. But MAYBE only if the ancients had digital computers....

Thanks, Leroy Quet

I like the idea of ternary (or trinary), but it would be terribly clumsy, wouldn't it? For example, this year would be 2202011 (I think!) rather than 2002. Still, it might be interesting to hypothesise (or even simulate) a ternary computer, with troolean (I typed 'trollean'!) values of True, False, and Maybe.

Imperial weights, measures, and currency provide a rich field for different number bases used in Real Life. A few examples:

16 oz to the pound. *14 pounds to the stone. 8 stone to the hundredweight. 20 cwt to the ton. *12 inches to the foot. * 3 feet to the yard. 22 yards to the chain. 10 chains to the furlong. 8 furlongs to the mile. *60 seconds to the minute. *60 minutes to the hour. *24 hours to the day. * 7 days to the week. 12 pennies to the shilling. 20 shillings to the pound. 21 shillings to the guinea.

I have had cause to perform mental arithmetic using *all* the above number bases (except guineas!), for real practical reasons, at some point or other in my life. I have starred the ones I still use regularly nowadays.

Well, electronic binary-based digital computers, at any rate. I presume the ancients had the usual complement of digits on their palm-top computers.

Interestingly, Imperial capacity measures /are/ binary in nature. I don't remember the whole hierarchy, I'm afraid, but bushels, gallons, quarts, pints and gills (plus the ones I've inadvertently left out) all form part of a '*this* is two of *those*' sequence.

US measures are up to the quart and IIRC Scottish measures are not (the pint in both cases is 20 oz, and the gill differs between the two). Both have gaps at 2 oz and 64 oz.

Actually, why use 60 seconds and 60 minutes and 24 hours? What is the basis of that scheme? Hardly practicle...

Or 360 degrees for a circle?

Both Babylonian.

But I don't know why they chose sixty.

See http://mathforum.org/library/drmath/view/57550.html

I have read that the names 'eleven' and 'twelve' are remnants of a twelve-based counting system, but I don't know if it was a true positional system using powers of twelve.

'As the centuries passed, more or less all the other information was translated into more modern notations. But the work of changing the scale in the trig tables was just too much to be contemplated. So nobody ever did it! As a consequence, trigonometric tables are STILL most often written in the Babylonian scale, and even the most modern technological gadgetry is likely to use it!'

This is is really ringing my BS alarm...much like the tale about standard railroad gauge being the width of a Roman horse's ass.

I have a 1936 CRC with the tables of the trig functions to the second of arc. Is Dr. Math telling us that this list is the one calculated by the Babylonians because it was too much work to recalculate it?

'eleven' is from Old English 'endleofan', meaning 'one left (over)'. 'twelve' is from 'twelf', meaning 'two left (over). Both these words have origins in a base-10 system.

The Romans did provide specific words for fractional weights with a divisor of 12. http://members.aol.com/jeff570/fractions.html has a basic intro on this.

It's been suggested that sixty was common because it has lots of divisors.

The Mayans used base 20.