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Traipahni numbers and money.

So, I got some help from Brooke in figuring out how to convert between bases 10 and 6, because Traipah's math system is base 6. I haven't rigorously tested it yet, but I think I have it understood.

While I'm on the topic of Traipah's math system, I might as well mention I also worked out their money. Which, their money also being base 6, is different from our own. Our US denominations make a fair bit of sense, in that 10 goes into 100 ten times, and 20 goes into 100 five times. We could easily have a $25 bill if we wanted to, for that would go evenly into 100 four times.

Now base 6 being different, those denominations don't make sense anymore. 100 in base 6 is 36 in base 10. So I wrote out the numbers in a line and worked out which denominations would work best for Traipah. These are what I came up with:
* One
* Two
* Three
* Ten
* Twenty
* Thirty
* One hundred
* Three hundred
* One thousand

This makes 9 kinds of coins (all Traipahni money are coins made of woods like ironwood, since counterfeiting them would be too much work to go to, and be worth it [ironwood, stonewood, and related woods are a major pain in the arse to cut, especially into small coin shapes]). Or, expressed in base 6, they have 136 coins.

Anyway, with 1006 being 3610, and other base 6 considerations, this means:
* $1 goes into $10 six times. (Because 10 in base 6 is six in base 10)
* $2 goes into $10 three times.
* $3 goes into $10 two times.
* $10 goes into $100 six times. (Because in base 10, six goes into 36 six times)
* $20 goes into $100 three times.
* $30 goes into $100 two times.
* $100 goes into $300 three times.
* $300 goes into $1000 two times.
(Keep in mind, these are all base 6 numbers. If you're confused, write the numbers out in a line and look for yourself. Remember base 6 counting goes 1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20, and so on til 50, 51, 52, 53, 54, 55, 100.)

With base 6 numbers being deceptively less than would seem to be, to those accustomed to base 10, this means that $100 in Traipahni money, even before the exchange rate is taken into consideration, is $36 in US money. Which is why I'm also pondering whether there should be a $10,000 coin.

Oh crap! I hadn't even thought about money less than $1. Maybe those will be something else, like paper. I've seen paper pennies. Hell, I have a paper Chinese penny. Yeah, I think the ones less than $1 will be paper.

Okay, using the same notions as before, here are the paper denominations:
* One cent
* Three cents
* Ten cents
* Twenty cents
* Thirty cents

I decided, though, that since pennies are basically worthless here, the same might be true on Traipah. Traipahni people being much more sensible, they don't make pennies anymore. (Though some are still in circulation.) The three cent bill is equivalent to a nickel, twenty cent bill is like a quarter, and the thirty cent bill is a half-dollar. Bear in mind, I don't have any names for any of these, aside from the names for the numbers.

I do wonder, though, if the paper money ought to be coated with something, to keep it from rotting. And I guess the same thing would be true of the wooden coins, because even though ironwood and stonewood are strong and a royal pain to cut, they can still rot. So they're probably varnished or something. (How strong are these woods? I think a laser cutting torch might have a hard time with them. Wouldn't be impossible, just difficult and time consuming.)

Only thing I need now, concerning the Traipahni money, is the names and designs on the coins. And color, I suppose. That should be fairly simple, though. I don't think the color will matter much on the coins, ironwood and stonewood being so hard to cut. And the color probably won't make much of a difference on the paper money.

Oh, another thought: obviously, the coins should be embossed, for blind persons. I think the same could be done with the "paper" money; coat the paper money in plastic (eco-friendly and biodegradable, if resistant to degredation), and the plastic can be used to emboss the paper.

~ ~ ~

One last thing concerning Traipahni numbers. Three powerful sacred numbers in Yahgahn have always been 3, 6, and 9. Of course now, with the base 6 math, those numbers would be represented as 3, 10, and 13 now. And another number sacred to me, 1310 is, now, 216. Unless 13 has been sacred to me because I've somehow known all along, subconsciously, that it's how to represent 9 in base 6?

On a Discordian slant, I figure 23 is still a good Discordian number even in base 6, since 5 still exists, and 2+3 still equals 5. However, some associations with 23 no longer work, since 236 is 1510. So for instance, humans only have 23 pairs of chromosomes if that 23 is in base 10.

This was cross-posted from http://fayanora.dreamwidth.org/1071728.html
You can comment either here or there.

Comments

( 7 comments — Leave a comment )
christinathena
Mar. 18th, 2012 05:50 am (UTC)
1, 2, and 3 would be odd, since that would have a coin (3) that's 1.5 times the value of the next-smaller coin (2). My preference would be (written in base-6) either 1, 2, 10, 20, 100, 200, etc. or 1, 3, 10, 30, etc. Thus, each coin is exactly 2 or 3 times the size of the next smaller denomination. Similar to how the predecimal British system, with 1 shilling = 12 pence, had 1d, 3d, 6d, and 1 shilling (or, in medieval times, 1d, 2d, and 4d, then 1 shilling).
fayanora
Mar. 18th, 2012 08:14 pm (UTC)
I dunno. I see what you mean, but I like both twos and threes. I'll give it some thought.
christinathena
Mar. 18th, 2012 05:59 am (UTC)
Also "Oh crap! I hadn't even thought about money less than $1. Maybe those will be something else, like paper. I've seen paper pennies. Hell, I have a paper Chinese penny. Yeah, I think the ones less than $1 will be paper." - there's a reason most currencies use coins for small values and paper for large. In fact, the only ones that use paper for small denominations are A) those that have undergone a lot of inflation and never adjusted (or are currently in high inflation) or B) those that have temporarily eliminated coins for reasons of metal shortages (for example, the use of 3 cent, 5 cent, 10 cent, 25 cent, and 50 cent bills in the US during the Civil War). Paper is, in the long term, more expensive than coins. It's cheaper in the short term to produce a paper bill than to produce a coin, but a coin lasts a LOT longer than a bill, so in the long run, you end up spending more money making paper bills than coins, making it rather counterproductive to make small denominations be paper.

"Which is why I'm also pondering whether there should be a $10,000 coin"

10,000 in base six is 1,296 in decimal. What's their currency worth in US dollars?

"Oh, another thought: obviously, the coins should be embossed, for blind persons. I think the same could be done with the "paper" money; coat the paper money in plastic (eco-friendly and biodegradable, if resistant to degredation), and the plastic can be used to emboss the paper."

That's not necessarily important if the coins are of different sizes. US coins, for example, are easy to distinguish by touch by the fact that the 1 cent and 5-cent coins have smooth edges while the larger coins have milled edges, and they're of different sizes (penny and dime are similar in size, but easily distinguished by the feel of the edge). Some currencies also use features such as holes in the center of the coins (for example, the Japanese 5- and 50-yen coins) and sometimes different shapes (a few currencies have coins that are 12-sided. I've got an old Israeli coin that's scalloped, a sort of wiggly shape; I've also seen square- or diamond-shaped coins, and Tokugawa-era Japan had rectangular coins)
fayanora
Mar. 18th, 2012 08:34 pm (UTC)
10,000 in base six is 1,296 in decimal. What's their currency worth in US dollars?

I have no idea. The future this takes place in is around the year 3100 AD, and Terran territories use "credits." And to be honest, I don't know how to determine the worth of their money outside their planet. The Traipahni economy has long been post-scarcity, and became even more so after first contact with humans and other races. They all know their economy is just a big game, a habit they maintain for no real significant reason, and they know their money has no more inherent worth than Monopoly money. This knowledge gives their economy more stability than the economies of people who take economics seriously, but since even the Traipahni people themselves know that, ultimately, their money has no real worth... true that no money has inherent value, I know, but I have no idea how people outside Traipah would view this laid-back approach to economics, or how it would affect their money's worth on other planets.

That's not necessarily important if the coins are of different sizes.

Oh duh. I hadn't thought of that.

Still, I suspect they carve the denomination marks into the coins, if nothing else. Probably other stuff as well, like official seals or whatnot. Though that raises the question of who can "print" money on Traipah... they have a government, but its only functions are A. Mediate disputes. B. Make sure the off-worlders behave, and deport the ones that make too much of a nuisance of themselves. I don't think I trust any government to be in charge of the money, and I don't think the Traipahni people would, either. Possibly there's a committee of Guilds that work together to mint coins and print small change, with other Guilds on the committee to balance out the power equation. (Wouldn't want the Woodworker's Guild and the Papermaker's Guild to have too much power over the money, even if everyone knows the money isn't really worth anything.) Maybe even The Unity Order (a religious/secular Order similar to Unitarian Universalists, that already works with the Order of Kusahnia to run the schools) is on that committee.
fayanora
Mar. 18th, 2012 08:38 pm (UTC)
PS
Come to think of it, square or diamond shaped coins might be easier to carve from ironwood and stonewood than round coins. And in some ways, square coins would stack more easily.
christinathena
Mar. 18th, 2012 06:02 am (UTC)
Also, why the inconsistent use of 2 in your denominations? You have $2 and $20 but no $200, and you have 20-cent but not 2-cent. Surely such a logical culture would use a consistent pattern. :-)

(For example, real-world examples, the Euro has coins of 1c, 2c, 5c, 10c, 20c, 50c, 1 euro, 2 euro and bills of 5, 10, 20, 50, 100, 200, 500, so a constant 1, 2, 5 pattern; the Yen has coins of 1, 5, 10, 50, 100, 500 and bills of 1000, 5000, and 10,000 for a consistent 1,5 pattern (there was a commemorative 2,000-yen bill issued in the year 2000 but it never took off))
fayanora
Mar. 18th, 2012 08:41 pm (UTC)
Also, why the inconsistent use of 2 in your denominations? You have $2 and $20 but no $200, and you have 20-cent but not 2-cent. Surely such a logical culture would use a consistent pattern. :-)

Damn, I didn't notice that. Hmm... I guess I'll have to either add $200 and 2c, or remove all 2's. But I like the twos. I'll have to look at that aspect of the patterning again.
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