# Numbers are fun!

March 9, 2006 6:36 PM Subscribe

Asking for a friend... He's interested in examples of number systems not based on western sets of 10. Anyone know of good info on non-standard number systems used in other cultures or for niche purposes, such as hexadecimal?

helios writes...

Sort of. It was actually developed in India, and the west heard about it through Arabia. That's how we ended up with "Arabic" numerals that aren't Arabic numerals.

A good argument can be made that the Roman numeral system is not base ten. What base it is is open to interpretation. I would say it was base 5.

posted by tkolar at 7:12 PM on March 9, 2006

*Well, the base-10 system we use is not western - i'm pretty sure it originates from Arabic numerals.*Sort of. It was actually developed in India, and the west heard about it through Arabia. That's how we ended up with "Arabic" numerals that aren't Arabic numerals.

A good argument can be made that the Roman numeral system is not base ten. What base it is is open to interpretation. I would say it was base 5.

posted by tkolar at 7:12 PM on March 9, 2006

tkolar, I think for a number system to be base-anything, it has to have a zero.

In a base-X system, each digit is a multiple of X. Without 0, you can't do that.

It can still be, obviously, a number system, as the Romans could do math. It's just not a base-anything system.

posted by Malor at 7:15 PM on March 9, 2006

In a base-X system, each digit is a multiple of X. Without 0, you can't do that.

It can still be, obviously, a number system, as the Romans could do math. It's just not a base-anything system.

posted by Malor at 7:15 PM on March 9, 2006

- The check digit in ISBN numbers is in base 11 (0-9 plus X for 10).
- Base 12 (or duodecimal) is used in some obscure languages - Wikipedia mentions "languages in the Nigerian Middle Belt such as Janji, Kahugu, the Nimbia dialect of Gwandara, Mahl language of Minicoy and the Chepang language of Nepal are known to use duodecimal numerals."
- I've seen base 24, base 26 (also called hexavigesimal), and base 36 used in some specialized applications, such as serial numbers.
- Base 32 and base 64 are frequently used when encoding binary data in ASCII (base 64 is particularly common).

posted by RichardP at 7:16 PM on March 9, 2006

Malor wrote...

I think you're probably right. "Base" just isn't defined for non digit-based numerical systems.

posted by tkolar at 7:35 PM on March 9, 2006

*It can still be, obviously, a number system, as the Romans could do math. It's just not a base-anything system.*I think you're probably right. "Base" just isn't defined for non digit-based numerical systems.

posted by tkolar at 7:35 PM on March 9, 2006

If you've ever counted something by making hash marks, you've used base 1.

Tom Lehrer's song New Math is now running through my head.

posted by cerebus19 at 7:45 PM on March 9, 2006

Tom Lehrer's song New Math is now running through my head.

posted by cerebus19 at 7:45 PM on March 9, 2006

Remember, folks, base 8 is just like base 10, if you're missing two fingers

posted by dagnyscott at 7:58 PM on March 9, 2006

posted by dagnyscott at 7:58 PM on March 9, 2006

Traditionally the Chinese have a quasi base 60 system for counting calendar years. It's really 5*12 (of the 12 animal signs), and is represented by a set of Chinese characters. 甲 is 1, 乙 is 2 and so on.

posted by of strange foe at 8:03 PM on March 9, 2006

posted by of strange foe at 8:03 PM on March 9, 2006

The Yup'ik Inuit have a base 20 system with a sub-base 5.

posted by luftmensch at 8:50 PM on March 9, 2006

posted by luftmensch at 8:50 PM on March 9, 2006

*I think for a number system to be base-anything, it has to have a zero*

Huh?

posted by rdr at 9:24 PM on March 9, 2006

I'll put a bit more meat on that question. You need a placeholder but you don't need zero.

posted by rdr at 9:27 PM on March 9, 2006

posted by rdr at 9:27 PM on March 9, 2006

Terry Pratchett, author of many Discworld books, had a footnote in one ("Men At Arms", p.127) that talks about Troll counting systems, which are in essence base-4.

"In fact, trolls traditionally count like this: one, two, three . . . many, and people assume this means they can have no grasp of higher numbers. They don't realize that many can be a number. As in: one, two, three, many, many-one, many-two, many-three, many many, many-many-one, many-many-two, many-many-three, many many many, many-many-many-one, many-many-many-two, many-many-many-three, LOTS."

Also, a friend of mine and I were discussing possible origins of base-10 counting, and the most obvious one we came up with is that we have 10 fingers, so to counting them yields sets of ten.

posted by toomanyplugs at 11:06 PM on March 9, 2006

"In fact, trolls traditionally count like this: one, two, three . . . many, and people assume this means they can have no grasp of higher numbers. They don't realize that many can be a number. As in: one, two, three, many, many-one, many-two, many-three, many many, many-many-one, many-many-two, many-many-three, many many many, many-many-many-one, many-many-many-two, many-many-many-three, LOTS."

Also, a friend of mine and I were discussing possible origins of base-10 counting, and the most obvious one we came up with is that we have 10 fingers, so to counting them yields sets of ten.

posted by toomanyplugs at 11:06 PM on March 9, 2006

I am

posted by sourwookie at 11:35 PM on March 9, 2006

*so*"blessed" that as a kindergartner I had to be untrained from a base 11 system.posted by sourwookie at 11:35 PM on March 9, 2006

**cerebus19**: damn you.

*You can't take three from two, Two is less than three, So you look at the four in the eights place...*

Gah! Voices in my head!

posted by krisjohn at 11:45 PM on March 9, 2006

Base-12 in fiction: "The Cross-Time Engineer" series by Leo Frankowski featured an engineer timetravelling back to medieval Poland and raising an army to fight the imminent Mongol invasion. He used the opportunity to introduce a base-12 system. Advantages included the fact that 12 can be divided by 2, 3, 4 and 6. Also, quite a few constants (i.e.

posted by Harald74 at 11:46 PM on March 9, 2006

*e*) were rounder numbers in base-12 than base-10. The books are quite entertaining, but not great literature...posted by Harald74 at 11:46 PM on March 9, 2006

i looked at fibonacci numbers once (look like binary, but not a fixed base - instead of 2^n you use the fioonacci series so there's more that one way to write down most numbers; self link).

posted by andrew cooke at 2:08 AM on March 10, 2006

posted by andrew cooke at 2:08 AM on March 10, 2006

Since childhood, I've played mental games with base 27 (3^3), using 0 plus the 26 letters of the alphabet (0abc...xyz0abc...etc.). This system is also a handy way to start thinking in base 9, since 27 is a multiple of 9 -- and we all know that 9 is a cool number, anyway.

posted by syzygy at 2:17 AM on March 10, 2006

posted by syzygy at 2:17 AM on March 10, 2006

What Counts: How Every Brain is Hardwired for Math might be a good starting point. It's been several years since I read it, but I do recall a discussion of Papua New Guinean counting systems with bases and/or counting limits extending well beyong the ten-unit base. He also discussed counting words and base systems among the Ainu and the Maya, and doubtless there is more I cannot recall.

Be warned that the first edition, at least, is poorly edited; the typos will drive you wild.

posted by Elsa at 2:42 AM on March 10, 2006

Be warned that the first edition, at least, is poorly edited; the typos will drive you wild.

posted by Elsa at 2:42 AM on March 10, 2006

Someone recently posted this account of a math teacher teaching binary arithmatic to elementary school students using the Socratic method. Interesting sidenote, perhaps.

posted by sixacross at 7:17 AM on March 10, 2006

posted by sixacross at 7:17 AM on March 10, 2006

This wikipedia page is a handy starting point.

Just because we say/said "fourscore" doesn't make our system base-20, even vestigially. In French, "80" is read "quatre-vingt" (four twenties) even today. Doesn't mean they're on a base-20 system.

You can't beat balanced base 3 for wacky fun.

posted by adamrice at 7:17 AM on March 10, 2006

Just because we say/said "fourscore" doesn't make our system base-20, even vestigially. In French, "80" is read "quatre-vingt" (four twenties) even today. Doesn't mean they're on a base-20 system.

You can't beat balanced base 3 for wacky fun.

posted by adamrice at 7:17 AM on March 10, 2006

Not sure if this answers the question, but these people used a base-26 system (the letters of the alphabet, with a=0) to write out Pi and then searched the string for the appearances of English words.

It's a huge, huge page.

posted by ducksauce at 7:23 AM on March 10, 2006

It's a huge, huge page.

posted by ducksauce at 7:23 AM on March 10, 2006

rdr, isn't a placeholder essentially a zero? It basically means "nothing here, move along."

posted by solotoro at 7:40 AM on March 10, 2006

posted by solotoro at 7:40 AM on March 10, 2006

**EVERYTHING**you could possibly want to know is in A History of Numbers. The guy was a little obsessive in researching it all. The tome is massive. And it is completely awesome.

posted by five fresh fish at 10:16 AM on March 10, 2006

Response by poster: Thanks for all the replies, my friend is quite happy.

posted by efalk at 3:04 PM on March 10, 2006

posted by efalk at 3:04 PM on March 10, 2006

Remember reading about a base 2 numbering system used by Ethiopians.

posted by the cydonian at 8:52 AM on March 16, 2006

posted by the cydonian at 8:52 AM on March 16, 2006

This thread is closed to new comments.

The "60 seconds to a minute, 60 minutes to an hour" is a base-60 system which originated from the Babylonians.

The Mayan number system is base-20 (see this).

And computer science often uses octal (base-8) and binary (base-2) in addition to hexidecimal.

posted by helios at 6:43 PM on March 9, 2006