How to Count to 1296 in Ngkolmpu

[ysabetwordsmith]

So much fun.  :D 

I am reminded of the Cheela invention of counting, which uses a very similar method but ends up in base 12 instead of base 6.

Comments

[capri0mni]

I love the different ways counting emerges... And it shows (at least, it shows me) that: a) mathematics and numbers are tools (rather than existing a priori in the universe), and b) We fashion our tools for the jobs that need doing.

(And I love how yams can be neatly arranged in sixes).

But you don't need to look to science fiction to find base 12 -- in this video (from 2012): Mathematician James Grime (the most cheerful mathematician I've seen on YouTube) talks about the virtues of a base 12 counting system, and reminds us that before the French Revolution, British money, weights and measures, were all base 12 -- and how you can count to twelve on the fingers of one hand:

Base 12 - Numberphile

...Matter of fact, when I saw "base 6," before having read the article, I thought it was because: "Base 12, but halved"

Yes ...

[ysabetwordsmith]

Sumerian is base 12 also, hence the 60 seconds - 60 minutes - 24 hours pattern.

Re: Yes ...

[peoriapeoriawhereart]

I've had that sold to me as base 60; 12 makes more sense, it's just a handful of dozen (duozhen).

A dozen has the advantage that splitting it into equal pieces can happen in several ways. (Can you recall the hamster 'division' story? No hamsters were harmed, there just was some transitive math so all hamsters were whole.)

Re: Yes ...

[conuly]

60 makes sense too - you've got the prime factors of 2, 3, and 5 plus the non-prime factors of 4, 6, 10, 12, 15, and 30. You can count to 60 on your fingers by moving your thumb along the phalanges of one hand (for base 12) and then keeping track of how many times you've done that using the fingers of the other hand - five cycles of twelve makes 60.

Of course, once you invent 0 then you've got to come up with a numerical system that juggles 60 different symbols and it gets a bit unwieldy. Not prohibitively so, but somewhat.

Re: Yes ...

[kengr]

The references I've encountered say that Babylonian (and maybe Sumerian) were base 60. And that's where we got 360 degrees in a circle from as well.

And, of course, the Mayans and Aztecs used base 20.

ps. I recall buttons saying "Cheela are degenerate" at cons way back when. :-)

Re: Yes ...

[capri0mni]

Yup.

I really like the method for counting to 12 on your fingers as shown at the end of the video, and use it often (using my thumb as my point/counting finger, on my right hand, and using the fingers on my left had to count each unit of 12. That makes counting to 60 easy-peasy.

The main problem I have with that "Dozenal Society's" proposal is that the two names for the 'new' numbers they've chosen are simply altered pronunciations of the base ten names we already use...

The linguist part of me (especially the linguist part of me that's fed up with Euro-centrism) would rather they took number names from a language/culture that already counts in Base Twelve.

*Remembers that Internet Search is a thing*

I think I'll go look up the old Sumerian names, and start using them myself, anyway.

Re: Yes ...

[ysabetwordsmith]

>>I think I'll go look up the old Sumerian names, and start using them myself, anyway.<<

Yay!

*cackle* Dear barbarians who have been dead for 6,000 years: I win again. \o/

Re: Yes ...

[capri0mni]

Bwa-ha!

Re: Yes ...

[conuly]

The main problem I have with that "Dozenal Society's" proposal is that the two names for the 'new' numbers they've chosen are simply altered pronunciations of the base ten names we already use...

But most people who don't study etymology have no idea that "eleven" and "twelve" are base ten terms, they think they're just oddballs.

Re: Yes ...

[capri0mni]

Yeah. I can see how they might not know that "eleven" comes from the Anglo-Saxon for "one left over," or that "Dozen" comes from "Two plus ten"

But they do know that they're criticizing a Decimal system... You'd think they'd notice the link between that and 'dek' (their new word for the number after 9), at least.

tsk. It's that old division between the "hard" studies (math and science), and the "Soft" ones (history and languages): words are not worth paying attention to.

Re: Yes ...

[ysabetwordsmith]

Oh, have I ever got a patch for that.

Now aren't you glad I got fed up with that and invented a real language? Every time I've been in that situation.

Re:an as aside:

[capri0mni]

Are you familiar with the YouTube channel Artifexian? (That link goes to his curated playlist page).

He (Edgar), does videos on sci-fi worldbuilding, going into detail about the physics of different sized planets, stars, climates, atmospheres, etc. ...And then he addresses how all those different elements can influence different alien cultures, and the evolution of languages. His single longest playlist is on conlangs, and he cites examples from a wide range of existing human languages, and not just the "big 5."

Even though my writing hasn't taken me into this kind of worldbuilding, yet, I still enjoy his work, 'cause it gives my mind something to chew on when thinking about this world I'm living in.

Re: Yes ...

[conuly]

Why would we even need new words? Ten, eleven, and twelve work fine. Eleven is a bit syllableriffic, I suppose, but not that much worse than "seven".

Re: Yes ...

[ysabetwordsmith]

Because otherwise they're too easy to confuse with base ten. Me, I'm happier using a different language for each base. That way, they can't be confused and all the names match.

Re: Yes ...

[capri0mni]

Well because of writing equations numerically, instead of verbally. If we were to use "Arabic" numerals to write base six equations, like the Ngkolmpu counting system that started this discussion, "10" would be the answer to "What's 3 times 2?"

And "10" is the number representing "3 x 4," in base twelve.

So if we're going to switch to a base twelve system, we'd need two additional symbols to put on our phone buttons and number pads.

And those new symbols need new names, to make it clear that we're not working in base 10.

Now, if our culture were already universally working in base 12, then you're right -- we could just go on calling the new symbols "ten" and "Eleven" (though I'd argue the words for them would, instead, be derived from "two less" and "one less," instead of "one more" and "two more"