civilizations using a non decimal numbering system - ever exist?

[vandal]

Particularly, the octal system or any proprietary system. I know hexadecimal, octal, and binary all have applications when it comes to computers, but has there ever been a society to use these systems in their everyday lives?

[Manda JO]

Summarian, and I think Egyptian were base 60; Mayan math was base 20.

[davejg]

Wasn't there some society that wanted to have base 60? The Babylonians or some something? That's what there's 60 seconds, so minutes, 360 degrees in a circle.

[Timothy Campbell]

I think it was the Babylonians who used sexagesimal (base 60). Imagine learning the multiplication tables for that one!

[Chronos]

It's not quite accurate to say that the Mayan system was base 60, since the base is only well-defined for a place-value numbering system such as our own, and the Babylonians didn't use place value. The Mayans, however, did use a true place-value base 20, and their system is actually a bit more elegant than our own: All of their twenty digits are constructed from a total of three symbols, and the meaning of the three symbols is fairly intuitive.

[GuanoLad]

Originally posted by davejg
Wasn't there some society that wanted to have base 60? The Babylonians or some something? That's what there's 60 seconds, so minutes, 360 degrees in a circle.

I thought there were 360 degrees in a circle because of the 360 days in a year thing. They rounded it down because 360 is such a great number to work with, divisible by 60, 10, 12, 5, 6, 4, etc, which is where the 12 hour clock really developed.

Or at least... I thought that was the way it went.

[kanicbird]

before base 10, and before 0 (zero my hero, how wonderful you are...) early man used what i heard called base 1:
1 = .
2 = ..
3 = ...
4 = ....
9 = .........
246 = a lot of them dots
also roman numbers did have some base 10 pattern to them but it was not a strict base 10 system

[RM Mentock]

Originally posted by vandal
or any proprietary system

I just want to point out that "proprietary" means private, or owned by an individual or corporation.

[Beruang]

For more info on 60 and Babylonians, check out

http://www.straightdope.com/classics/a4_194a.html

[Lumpy]

Also, there appears to have been an early base-20 system in Europe. English still has the word "score" to mean 20, and the French word for 80 literally means "four twenties".

[Lemur866]

Lumpy: Early Europeans also likely counted by dozens, since we have the term "dozen" still in our language. A dozen dozens is a gross. Base twelve is certainly more convenient than base 10 unless you are counting on your fingers.

But I think the central problem is imagining that ancient people used any sort of "base" numbering system like ours. They didn't have a well worked out system of notation, with zeros and place values and such. Even a system with special symbols for 60, or 12 wouldn't really fit our idea of what a base 60 or base 12 numbering system would be.

Just to give some idea, think of roman numerals. All of our little tricks for simple addition, subraction, multiplication and division are impossible using roman numerals. There were no "multiplication tables" and even if there were you wouldn't be able to just list up to 10 x 10 like we do, you'd need to show every number. There is no simple algorithm for multiplying numbers using roman notation, just try it sometime. The only easy way to do it is to convert the roman numerals to decimal, multiply, and convert back.

The ancient egyptian, babylonian, sumerian, etc systems were no better. These systems work fine if all you want to do is record the amount of a transaction or keep track of dates, but they are very difficult to do any sort of manipulation with.

[RM Mentock]

Originally posted by Lemur866
Just to give some idea, think of roman numerals. All of our little tricks for simple addition, subraction, multiplication and division are impossible using roman numerals.

Well, whatever they used, they had their own bag of tricks. They weren't our tricks, but surely Archimedes had some sophisticated tricks that weren't just his. The Babylonians, too.

[Squid Vicious]

According to the professer in the egyptian archaeology class I took long ago; the egyptians used a base 9 system. He even showed us how to work the math (I forget now, but I could probably figure it out if pressed). It was suprisingly easy. He also told us that the egyptians had no words for anything over 2 in their everyday language. They had 1, 2, and many.

[vanilla]

Welcome back Squid!
I read somewhere that the Babylonians started the numerical system basing it on 6's (60 minutes in an hour etc.)

[C K Dexter Haven]

<< He also told us that the egyptians had no words for anything over 2 in their everyday language. They had 1, 2, and many. >>

With all due respect, I find this not very credible. The story has been oft told -- I first read it in George Gamow's book, back in the late 50s, I think, about some African tribe. But I have to doubt its credibility when applied to the Egyptians, who did things like astronomy and architecture.

This was actually said by a professor of egyptology? I'll bow to superior knowledge, of course, but my suspicions are high.

[Kyberneticist]

Originally posted by Chronos
It's not quite accurate to say that the Mayan system was base 60, since the base is only well-defined for a place-value numbering system such as our own, and the Babylonians didn't use place value.
Finally think I worked that out.
For Mayan read Babylonian?

[Chronos]

Nice catch, Kyberneticist. Of course, it really isn't accurate to say that the Mayans used base 60, but I meant to say Babylonians there.

[dtilque]

In History class, the prof once described a method of multiplying two numbers that was used by the Egyptians, I think. The method involved doubling one number and halving the other. If halving produced a remainder, the other number was added into the the final result. He didn't understand how this worked, but I immediately recognized it as an implicit use of base 2 (hey, I was a computer science major).

But even that method is tedious in non-positional numbering systems. Try it some time with Roman numerals. It will be easier if you don't use prefix-subtraction notation (use IIII instead of IV for 4), but it's still no fun.

What the Romans used for calculating was a counting board. This was a board or table marked out with columns for units, tens, hundreds, etc. Counters represented the actual numbers. Addition was simple, you just put counters representing one number on the board, then added counters represented the other number. Perform any carries and you have the result. Subtraction wasn't too much more difficult, but I don't know how they did multiplication on it.

On some counting boards there were groves for the counters to be slid in. From what I understand, the counting board was borrowed by the Chinese, where some genius had the inspiration to put the counters on wires. I could be wrong here, but I don't think the Romans ever put the counters on wires to make a real abacus.

[RM Mentock]

Originally posted by dtilque
From what I understand, the counting board was borrowed by the Chinese, where some genius had the inspiration to put the counters on wires.

Here's a real eye-opener. If you've ever wondered just how bad it could get when researching a subject on the internet, here are links that claim the invention of the abacus was in
5000BC (http://www.cse.buffalo.edu/~burhans/S99/honors/tsld003.htm)
5000BC (http://wings.buffalo.edu/fnsm/cs/courses/cs101c/history-2.html)
3000BC (http://star.nec.rit.ac.th/~call/reading12.htm)
2600BC (http://oz.plymouth.edu/~budhp/BU324/history.html)
1000BC (http://www.ualr.edu/~gblane/cpsc1370/handouts/history/history1.html)
500BC (http://www.accent.co.uk/chinabacus.html)
500BC (http://www.scils.rutgers.edu/special/kay/sample53.html)
500BC (http://www.isb.bj.edu.cn/projects/ms/gr7/la/ancient_civilizations/china/abacus/lukec_abacus.html)
450BC (http://loki.stockton.edu/~vax104/csis1180/Lecture1_History/tsld007.htm)
1300AD (http://www.umanitoba.ca/faculties/education/edlab/activities/Abacus/learnabacus.htm)
1300AD (http://warrensburg.k12.mo.us/math/abacus/jason.html)

[Squid Vicious]

Yeah Dext, I, too, was skeptical about the 1, 2, many thing when he said it. It's been a while since I had that class, and I took it to fill a humanities requirement; so I don't remember his explanation well enough to repeat it acurately. I do remember being satisfied by his explanation. However, since we're now colleagues, I guess I could walk over and ask him some inane egyptology question. I'll get back to ya.

[Chronos]

I heard from one of my Latin teachers that in ancient Rome, there were actual shops that would do multiplications for their customers, basically by just having a big ol' table of the results. One shop would have the thirteens column of the times table, for instance, and another might have the twenty-sevens.

At least I know how I'll make my living if I ever get stuck in ancient Rome.

[dtilque]

Originally posted by Chronos
At least I know how I'll make my living if I ever get stuck in ancient Rome.
L. Sprague deCamp already beat you to that idea. See his book Lest Darkness Fall.

[Daniel Shabasson]

According to the recent book "Zero" by Charles Seife, the Babylonian base 60 system resulted directly from the use of the abacus. Once 60 stones were pushed across on the lowest wire, they would all be pushed back and one stone would be pushed over on the next wire to represent the 60 that had already been counted. Then the counter would be free to continue counting on the lowest wire. When another 60 had been counted on the low wire, another stone would be pushed over on the next higher wire, the stones would be pushed back on the lowest wire would be free for counting again. And so on. Clearly, there could be many wires on the abacus used, depending on how hight the number counted. The Babylinians then began to write down the results of the count by writing down the number of stones on each wire. The first wire was written down, then the esult of the second wire to its left, the third wire results to the left of that, and so on. This was the origin of the place system, which was unused anywhere else (including Egypt, but I think the Mayans did have a place system). The zero was developed as simply a place holder to indicate that the string did not have any stones on it.

[Collounsbury]

Originally posted by CKDextHavn
<< He also told us that the egyptians had no words for anything over 2 in their everyday language. They had 1, 2, and many. >>

With all due respect, I find this not very credible. The story has been oft told -- I first read it in George Gamow's book, back in the late 50s, I think, about some African tribe. But I have to doubt its credibility when applied to the Egyptians, who did things like astronomy and architecture.

This was actually said by a professor of egyptology? I'll bow to superior knowledge, of course, but my suspicions are high.

I doubt the credibility with regards to "some African tribe" too -- I have been learning an African langauge or two from West Africa and found that they have their own number systems also (although in one, all numbers above five are compounds of five plus X, bit funny but once one gets used to it...)

Problem with a lot of sayings about "funny places" is that they're just half made up from misunderstandings.