Octal number system

[zompist]

An interesting question is how, if your conworld uses a different number base, you represent this in fiction. If you have base seven, for example, do you refer to "sixty-nine" or something like "one forty-nine, two sevens, and six"?

Interesting. It could be a nice bit of local flavor, but could also be overdone. I don't think readers want to do a lot of arithmetic to understand what's going on.

I'd be tempted to invent some calques, explain them in a footnote, and not rely on precise renderings. E.g. for base 7, maybe we use "sundred" to represent 49. Characters can explain that a city is a sundred leagues away, or that something costs three sundred pounds of gold. Pedantic readers can work out exactly what that means; everyone else can just take it as "kind of a hundred." As readers, we normally just need an idea of magnitude.

(You could use your conlang's terms, of course. But I think readers' patience is limited. E.g., in the Elder Scrolls games, I'm fine with the days of the week being Sundas, Morndas, Tirdas, etc.— it adds color but sounds familiar. The month names are less successful. "Morning Star, First Seed, Rain's Hand"... they're fine for citing a date, but don't expect me to remember their order or even what season they're supposed to be.)

[rotting bones]

In one of my novels that no one else has read (The Nothingness Engine), a character sees mathematical glyphs and without comment, reads a number that does not correspond to any decimal value. Strictly speaking, it's not just a difference in base. The glyphs correspond to an octonion-based model of physics used by aliens provisionally called Gsaid. The reader has been informed of this fact beforehand, but the text only describes the glyphs and the result, leaving out the procedure by which it's reached. My justification is that the reader mainly wants to know what happened, and analyze only those specifics that interest him. It's not the writer's job to dictate what those should be.

[xxx]

in fact, in fiction, real conlang is never necessary...
it's almost a lack of imagination or storytelling talent...

Except as a trap for geeks or to earn extra money with licensed products ...
but even in this case, a neo-conlang is better than a real language with full functionality ...

who would care except a group of conlangers ...

[Richard W]

For instance English is docenalism-ready, who use different names from 0 to 12...

Not really: 11 and 12 are 'one left over', 'two left over' in Germanic, worn down enough so that the derivation is forgotten.

So as eight seems to be a pair of fours, and nine is a *new* something, (start of the third four?), perhaps English isn't really ready for base ten. But as twelve is three fours, perhaps 'eight' and 'nine' are OK for base twelve.

More to the point, 'ten' and 'eleven' have been able to function in smaller numbers since Old English times, and that makes them read for use in base twelve.

[zompist]

For instance English is docenalism-ready, who use different names from 0 to 12...

Not really: 11 and 12 are 'one left over', 'two left over' in Germanic, worn down enough so that the derivation is forgotten.

So as eight seems to be a pair of fours, and nine is a *new* something, (start of the third four?), perhaps English isn't really ready for base ten. But as twelve is three fours, perhaps 'eight' and 'nine' are OK for base twelve.

More to the point, 'ten' and 'eleven' have been able to function in smaller numbers since Old English times, and that makes them read for use in base twelve.

What I was responding to was the "different names from 0 to 12" part.

As I said, I love base 12. But having unanalyzable roots for everything short of the radix is not a requirement to use that base.

[Richard W]

But having unanalyzable roots for everything short of the radix is not a requirement to use that base.

Agreed. An interesting question is how discordant the words can be. Time (24 hour clock) and dates (days in the month) are pretty discordant. A century from now, will 'twenty three hundred' be a natural way of saying 2,300 in English?

[zompist]

An interesting question is how discordant the words can be. Time (24 hour clock) and dates (days in the month) are pretty discordant. A century from now, will 'twenty three hundred' be a natural way of saying 2,300 in English?

A hundred years isn't long... we're talking about how your kids will talk.

But your point is quite right in the long term... these things can change. We used to say "three and twenty", after all.

Or maybe in a couple hundred years Indian English will be more influential, and English speakers will be talking about crores and lakhs.

[Richard W]

In a hundred years time it will be "twenty one nineteen", and there will have been the year "twenty one hundred". It actually took a while for the year number to get back to the normal pattern. In 2001, we barely heard of the year 'twenty oh one".

[bradrn]

A century from now, will 'twenty three hundred' be a natural way of saying 2,300 in English?

That’s already a pretty natural way for me to say it. In general, I find that for numbers around that range I have more than one way to say them. For instance, 1500 can be any of ‘one thousand five hundred’, ‘one five hundred’, ‘fifteen hundred’, ‘one and a half thousand’.

[Xwtek]

Obviously, this is not very feasible in the long run, since beyond a certain point you're dealing with increasingly large bases - the 10th place is base-23 - but since this is a mediaeval culture it's not really a practical issue. Also, I suspect that, like the Greeks, they use letters as numbers, so they can cope easily with large bases.

Medieval people already use a number like one million. Even earlier, ancient Egypt already uses it. And in your number system, one million is:

(1)(548)(53)(4)

Which is not really manageable.

[Salmoneus]

Actually it's (1)(10)(0)(2)(6)(3)(4) - that is, 1x720720 + 10x27720 + 0x2520 + 2x840 + 6x60 + 3x12 + 4x1.


The number of possible values for each digit is a rather erratic sequence: 11, 4, 13, 2, 10, 25, 16, 18, 22, 4, 2, 28, 61, 36, etc. (assuming we continue the idea of ignoring the lower of two bases where one is only twice the other).

I think if they use letters as numerals, it's reasonable to have up to 28 numerals. This would let them express numbers up to 2.3 trillion without difficulty.

[Richard W]

Actually it's (1)(10)(0)(2)(6)(3)(4) - that is, 1x720720 + 10x27720 + 0x2520 + 2x840 + 6x60 + 3x12 + 4x1.

So in answer to akangka, where we think in millions, they would use 1)(0)(0)(0)(0)(0)(0) ( = 720720₁₀, where as I was taught at school, and Ada continues, base 10 is privileged as the base in which to express bases). What wouldn't work is counting in this functional equivalent of a million.

The number of possible values for each digit is a rather erratic sequence: 11, 4, 13, 2, 10, 25, 16, 18, 22, 4, 2, 28, 61, 36, etc. (assuming we continue the idea of ignoring the lower of two bases where one is only twice the other).

I think if they use letters as numerals, it's reasonable to have up to 28 numerals. This would let them express numbers up to 2.3 trillion without difficulty.

Or they could use non-positional base 11 then 4 numbers, just as the Sumerian system used non-place notational decimal numbers up to 59 as its digits. Babylonian 'digits' from 0 to 9 can be read at a glance. That's 13 symbols up to 2.3 trillion, or 14 if they have one zero for positional digits and another to write 10₁₁ and 20₁₁ so that you don't accidentally merge two positional digits.

[Pabappa]

The last thirty or so posts are far over my head but they look very interesting. I worked with non-basal arithmetic a long time ago and I might revisit it. Even so, I need to retain at least one culture with a pure decimal system to explain the 10x10 syllabary grid that evolved early on..... unlikely that a culture not used to counting to 10 would come up with something like that.

[Xwtek]

The number of possible values for each digit is a rather erratic sequence: 11, 4, 13, 2, 10, 25, 16, 18, 22, 4, 2, 28, 61, 36, etc. (assuming we continue the idea of ignoring the lower of two bases where one is only twice the other).

Wait, I don't get it. According to the link to the OEIS, the sequence is monotonously increasing.

[Pabappa]

https://www.youtube.com/watch?v=H5EUjnEKzjQ

^^^^ topical

funnily enough, the glyphs he posts about halfway through are just like the ones i came up with for Andanese twenty years ago .... except mine were decimal. Theres just not a lot of possible shapes if you want glyphs you can stakc and still be square.

my old script evolved into this:

andan100btms-SMALL-bw-3.png (535 Bytes) Viewed 8593 times

yes i know that's ridiculously small.... i worked with it pixel by pixel and it was easier to do it at the smallest possible size so i didnt have try to aim the pencil spot on.