Economics with different numerical base systems.

[erisiamk]

Hi all. For my WIP I have a race of aliens that use a base-8 number system, due to the whole 4 digits-on-a-hand trope. This has lots of implications, with one of them being the subdivision of cash. If the aliens had a A$100 note, it could subdivided into two A$40 notes, eight A$10 notes, or sixty-four A$1 coins, and so on.

My first questions is, how would this base-8 dollar be subdivided? If there were 64 "cents" to a dollar, and I had 32 cents, how would that be represented in A$?

The other question I have is, how will exchange rates work between currencies of different base systems? Will they work at all? If a human went into a bank and asked for $100 USD at a 1:1 rate of A$, would they give him a A$100 bill (worth 64 A$1 bills) or one A$100, four A$10, and four A$1 bills (worth 100 A$1 bills)? Would the aliens be able to swindle a ludicrous amount of money from unsuspecting human traders?

 

[thaddeus6th]

It'd be 0.4, I'd guess (as 4 is half of 8).

I think people would adapt fairly quickly.

 

[Wizraban]

I guess the conversion would be part of the normal translation process. So 100 A$ in alien speak would be translated as 64 A$ in human speak.

 

[JonH]

I think your first question divides into two. What is the subdivision, and how should it be depicted? If you're happy with the simple 64 cents to the dollar, then I agree showing it with an octal point is fine, or you can show it as two separate values. So eight and a half dollars would be A$10.40 or A$10 40c.

Of course if $1 = A$1, $64 = A$100 and $100 = A$144. And that's what I'd expect to see in the exchanges, although there might be a bit of head scratching to check the figures.

You just depict numbers differently in octal. They are still the same numbers. Coming from Earth you'd read A$100 as sixty-four dollars. So I don't think anyone would get confused for long. I'm sure experienced traders wouldn't get confused at all. If you can get to a bank on an alien planet, you can afford a calculator!

However, if you wanted to confuse the tourists, and you could get around the problem that they'd just use an app, you might want to take a leaf out of Britain's pre-decimal currency and really go to town. Have sixteen slivers in the dollar and eight dulls in the sliver, or one-hundred-and-twenty-eight dulls to the dollar, which in octal would be 200d. Then eight and a half dollars would be A$10/10/-. Eight dollars, eight slivers and two dulls, would be A$10/10/2, and pronounced "eight dollars, eight and two". Ten slivers and two dulls would be called "ten and two" and shown 12/2 (with no preceding symbols). When you added in the problems of subdivisons of a dull and the nicknames for various coins, I think tourists could be forgiven for making mistakes - they always did in Britain when I was a kid. But traders, not so much.

 

[Dozmonic]

Aliens with 8 digits would likely use base 8 maths, not base 10. Or they'd use base 12 because fractions are really great in base 12 and they only have to visualise one extra hand. At a push they'd use hex, because it's just visualising their fingers and toes.

We have different base systems in use all around us
12 inches = 1 foot
3 feet = 1 yard

60 seconds = 1 minute
60 minutes = 1 hour
24 hours = 1 day

 

[Dave]

If they divided a A$100 note in two, surely they would get two A$40 notes with no change.

That might be confusing to the humans, but as Dozmonic just pointed out, we can cope with imperial measurements and time in different bases. Manually working out wages from clockcards is hard work but it is still done.

 

[Dozmonic]

They wouldn't have a A$100 note, any more than we'd have a £120 note.

 

[Dave]

I'm not sure I understand that. They would have a A$100 note. A$77 + A$1 = A$100

 

[Dozmonic]

They'd only have a A$100 note if they used base 10
If using base 8 they'd have A$80, A$40, A$20, A$8 and then coins

Edit: I see where you're coming from actually. And my notes above are slightly wrong, but hey, who knows what they'd have in reality. All we know is we'd have to find some way to relate to it in terms we know, such as we do with time

Double Edit: I still think they'd go for base 12. Giving A$3. A$4, A$6, A$12, A$24, $A48, $A96 notes

 

[JonH]

They'd only have a A$100 note if they used base 10
If using base 8 they'd have A$80, A$40, A$20, A$8 and then coins

Edit: I see where you're coming from actually. And my notes above are slightly wrong, but hey, who knows what they'd have in reality. All we know is we'd have to find some way to relate to it in terms we know, such as we do with time

If their values are written in octal, they couldn't have an A$80 or an A$8, because the number eight is written 10, not 8.

I agree about the fact they could have any number basis for their currency. It's up to the OP.

 

[Ursa major]

I think people would soon get the hang of using bases other than 10 (or 60) being used. After all, if it was so hard, I and the other children in my class wouldn't have been taught about it in the first year of junior school. Besides, if these aliens are meeting us, one of us would soon have an app that would do the calculations for us.

But to take this a bit further, generally only one currency is legal tender in a given currency area. Another currency would only be met in real life when one was converted into the other (at, say, a bureau de change). Okay, the person using an unfamiliar currency might want to convert it back into their own to see what they're paying or getting, but that happens even where the same base is used. (Not that dealing with different bases (and I mean bases) is new: after all, non-Brits used to their own decimal currencies dealt with £.s.d. in the past, with 12 pence to the shilling and twenty shillings to the pound.)

And, finally, what backs an alien currency? Would it be convertible? If an Earth-born explorer landed on an inhabited planet, what are the odds that the aliens there would accept dollars, euros, yens, yuans, pounds, etc.? The same odds would apply to aliens visiting us. Unless the aliens took over completely.

 

[erisiamk]

Yeah, when I mentioned a A$100 bill, that would correspond to A$77 + A$1 as stated by Dave. I hadn't considered a base-12 system, but the extra sub-divisibility would obviously be useful and it wouldn't be too far of a stretch as some sort of revised number system.

The part of the story where the aliens would actually have economic trade with the humans is set some time after the main events of civilizations meeting and having some initial conflicts before learning to co-exist. Aliens would occasionally work and have fun on Earth, and vice versa for the humans on the alien planet. There are extended embassy-like mega-cities on both planets where both humans and aliens have equal citizenship and sway, so both currencies would be legal tender in these areas, presumably? Exchange wouldn't be important for everyone, but I'd like to analyze the mechanics more closely for when this sort of thing could crop up.

I'm not entirely sure whether /all/ human and alien currencies would feasibly be accepted in places like this, or whether standardized currencies would be used, however.

It does seem that personal computing, apps etc would make this a moot problem for anything other than spontaneous cash exchange, of course.

I'll definitely have to look at other foreign currencies more closely when considering these interactions; for some reason I completely forgot about the old British currency, having not been old enough to see it go around

 

[tinkerdan]

I can see that there might be some confusion here in trying to resolve a ten fingered system with an 8 fingered system so it's probably counter productive to mention that there might be some inflationary or deflationary characteristics that also need to factor in and just basic value across the board might be to simplistic and $100 in one system may never be statically comparable to the other system anyway so that 100 though corresponding to 77+1 in a simplistic way it would have no true correlation until we determined how 1 corresponds to 1 after all economic factors are applied.

Truthfully though it all seems like a lot of 'hand-waving' to me.

 

[Dave]

They could use a duodecimal system if they had 3 arms, but they would be even more hand-waving.

 

[Dave]

I saw this and had to repost here:

There are only 10 kinds of people in the world, those who understand binary and those who don't.

 

[psychotick]

Hi,

Best to remove nine and ten completely from your vocab. They don't exist in base eight. Likewise there is no hundred dollar bill - there is no hundred. So in base ten their notes would be one dollar, eight dollars, sixty four dollars etc. I'd tend to get rid of the word dollars as well since it sort of denotes metrics.

Better to go with something completely alien.
So you start with one credit(?)
Eight credits to an octet.
Eight octets to an octal.
So your character makes change for an octal by giving him two four octet notes.

Then your damned human comes along with a one hundred credit note which is actually one octel, four octets and four credits. It would be written as 144 base eight.

Humans - too many damned fingers!

Cheers, Greg.

Cheers, Greg.

 

[Ursa major]

As an aside, why is "credit" so often used as the name of a currency unit? If it's your money, it isn't a credit (a term that implies someone, or some institution (the state?), has lent you the money).

Now in some economic systems, this might be correct (although it would be nice to have this at least mentioned, as surely it would have implications for the whole society). But, frankly -- and this isn't a criticism of psychotick's use of the word, as he wasn't writing a story -- it simply looks like a failure of imagination, particularly when there's nothing special about the names of currencies: they can be just about anything.

 

[JonH]

As an aside, why is "credit" so often used as the name of a currency unit? If it's your money, it isn't a credit (a term that implies someone, or some institution (the state?), has lent you the money).

I think it's because it doesn't come from the economic meaning of the word credit. If you do something creditable you are given credit for it. Money is society's way of saying thank you for taking part as much as a system of rationing and a medium of exchange.

 

[Ursa major]

But whatever its source (and most people think they're entitled to their money, not that they're being allowed to use something that's akin to pocket money or, worse, something that might be revoked**), the meaning of credit in normal usage indicates something that is owed to someone or something else; hence credit cards (as opposed to debit cards).




** - Even the phrase "We've credited your account with..." sounds like you've been done a favour rather than being given something that was already rightly yours. It seems to encapsulate a power relationship that isn't necessarily there.

 

[Mr Orange]

but if your account is in credit, then that moneyed is owed to you by the bank.