

smitchnz: How does math work for Irathient/Castithan (they seem to be similar...I suspect that the Castithan uplifted the Irathient math system whole...;) )? In English we get to ten and then it's eleven. In other base 10 systems it would be ten one, ten two etc. English does it similar once we get to twenty  Twenty one etc. Currently we have the words for 05 for Irathient (and symbols for 09), and words for 13 in Casithan, but I am curious about what happens once you hit "ten" (20) or higher.
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All right, now to the meat of this question. First, a bit of a history lesson. Castithan has been base20 since Castithans started bathing. Indogenes can use whatever system they want, and so they developed a base7 system when they developed their writing system (I imagine that project being something like an Apple product launch). Irathients, on the other hand, used a base18 system. And before y’all math historians get up on me, I found a way to count to 18 using just your hands. Start at the left with the thumb. Count the thumb tip. Then count the space between the thumb and index finger. Then count the index finger tip. Proceed in this fashion till you get to the end then jump to the other hand and repeat starting with the pinky tip. When you get to the tip of your other thumb, guess what number that is? EIGHT. TEEN. #micdrop
Anyway, since the Indogenes are flexible, they can deal with base20 (or basewhatever). Elsewhere, the Votanis Solar System came to an intergalactic accord and settled on base20. It’d be kind of like if we all converted to metric (we really should. Just keep feet/yards for height and sports). This meant that anyone without a base20 system would be pressured to move to a base20 system. This is precisely what Irathient did.
So, back to your query, smitchnz, Castithan didn’t uplift the Irathient system: Irathient adjusted to the Castithan system. Consequently, it makes most sense to begin this discussion with the Castithan system.
Below are the numbers 019 in the Castithan orthography:
The Castithan numeral words you see above are just for counting. If you want to modify something (e.g. to say “five stripes”), you have to use a different form of the word (i.e. jalya ajivano). In the case of the numeral “one”, ave, the form is totally different—thus, ave if you’re counting, but fila gialino, “one rug”.
The forms of the numbers are as you see above. 18 is my favorite. Looks like the graphic manifestation of the name of a piece of furniture from Ikea. Some of these are just stupid—like 15. I created them that way on purpose because the Castithan language itself was supposed be evocative of some of the worst absurdities in English (e.g. our crazy spelling system). In particular, I wanted the numbers to be funky so they would look particularly out of place when grafted onto the Irathient numeral system, which we’ll look at next.
As I said, Irathient is now base20, thanks to Castithan. The numbers 019 are shown below:
Those shapes should look rather familiar. Comparing the two sets is probably something like comparing Devanagari numerals to Gujarati numerals. The forms are unique, though, for the most part (Irathient borrowed the Castithan word for “zero”). The forms you see above are just for counting. To modify a noun, most of the time you strip off the final vowel and treat the word like an adjective. Thus, to say “three rivers”, you’d say ulik tukagnu.
To me, the forms look atrocious (so much cleaner in Castithan), but that, again, was the point. The style is nonIrathient. The original Irathient numbers would have been much more in keeping with the style of the writing system, but they were washed away by Castithan imperialism. This is what they’re left with.
Of the words used above, there are a few things to notice. First, the words for 9, 10 and 18 don’t inflect the way the others do. They wear their etymologies on their sleeve, though, so it’s obvious why they don’t: they’re nouns, not adjectives. The word theganu comes from the same root as eganu, which means “fist” (because when you get to nine, one full hand has been counted). Thetusu is related to the verb shetusu, “jump” (since at this point you jump to the other hand). Then the word thenu is the same word for “end” or “conclusion”. When modifying a number, they have to take on adjectival morphology, e.g. nurrise nǝthetusu “ten maps”.
So. Now that that’s out of the way, the next question is: What happens when you get to twenty and twenty one? You actually see a bit of a preview of that with the Irathient numerals for 18 and 19. Thenu was the old numeral that ended the chain—the 18 in the base18 system. 19, then, was the next one. That’s basically what’s done for 20 and 21 in both Castithan and Irathient. In Castithan, the word for twenty is suda. To form numbers beyond that, you just add the next numeral, so suda ave is 21, suda kama is 22, etc. What’s 30? 30 is basically the equivalent of 15 in a base20 system, so it’s not special at all; it’s just suda china, 2010. Once you get to 40, you start to see a system where you add the suffix sta to a numeral, so kamasta 40, dunista 60, surista 80, etc.
Irathient is a little crazy when it comes to this. You saw thenu ki zema for 19. The word ki is not an Irathient word. That’s actually the Castithan word for “and”. It was borrowed into Irathient specifically for the numbers, because Irathient doesn’t really build the way Castithan does. Thus, when you get to 20, where the word is suta, the numeral follows it attached by ki, thus suta ki zema 21, suta ki ekta 22, suta ki kagne 23, etc.
Since Irathient’s versions of 20, 30, 40, etc. were all done in multiples of 18, all the equivalent words were borrowed directly from Castithan. A list is given below (Castithan on the left, Irathient on the right):
 20 suda~suta
 40 kamasta~kámasta
 60 dunista~dúnista
 80 surista~súrista
 100 jalista~gyálista
 120 vyenggasta~víngasta
 140 wogasta~úgasta
Etc. Notice that the Irathient forms were borrowed at a time before a lot of the sound changes in Castithan happened, and their pronunciation reflects that.
Anyway, math works much the same way it does in English with a base20 system; it’s just that everything’s halved in how you express it. In English, 10 + 10 = 20, and the same is true in a base20 system, except that their 10 = our 20, and so their 20 = our 40. Also, their numerals 1119 are considered just as basic as our numerals 19. Where an English speaker would say “Count to 10”, a Castithan speaker would probably say “Count to 20”. Thus, their games of hideandgoseek will be inherently longer. (But will their parents have more patience? I doubt it. There’s seem to be something useful about giving a child till the count of three.) Of all the bases I could’ve picked, base20 is probably one of the least taxing. Now Indogene math… That I don’t even want to think about.
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