Designing a numeral system

[StrangerCoug]

So I'm finally trying to get serious again about making a conlang again. I've named it Ŧattuintčïkë /θatˈtwint͡ʃːɨkə/ (short for vlatlakë Ŧattuintčïkë /ˈvlatlakə θatˈtwint͡ʃːɨkə/, loosely "the speech of ours"). There's no online scratchpad for it yet, so I'll supply IPA throughout, but it shouldn't be hard to pick up the pattern between the spelling and the pronunciation except for the stress of derived words.

I'm working on its numeral system right now. I've got the following basic numbers (it's base 16, and I imagine four limbs with four fingers and toes on each). Unless otherwise marked, they're just basic roots as far as even I know right now, but I'm not so entrenched in the conlang design that I can't do back-derivations. For transparency of derivation, I describe what I call Old Ŧattuintčïkë in this thread, which I intend to use primarily for a conreligion for which it's the liturgical language. For the number system, it's not supposed to be that different from "classical" Ŧattuintčïkë (the language spoken in daily life in my conculture), which simplifies things a little pronunciation-wise, and none of the terms in the below list are spelled differently between the two.

• ŋrï /ŋrɨ/: one
• đas /ðas/: two
• voo /voː/: three
• šop /ʃop/: four
• tleu /tleu/: five
• zëï /zəɨ/: six
• buiri /ˈbwiɾi/: seven
• jaŋ /d͡ʒaŋ/: eight
• lot /lot/: nine
• sata /ˈsata/: ten
• iuu /juː/: eleven
• karaa /kaˈraː/: twelve
• kaze /ˈkaze/: thirteen
• gʼït /ɡʔɨt~ɠɨt/: fourteen
• floʼ /floʔ/: fifteen
• dladžei /dladˈʒei/: sixteen
• laumï /ˈlaumɨ/: 256 (and once meant "many"; that's now loomï /ˈloːmɨ/)

Other numbers are formed from the above. 17-20 are the only exceptional forms, being 1-4 suffixed with –lora /ˈloɾa/ meaning "left" (an idea from Germanic), giving ŋrïlora, đaslora, voolora, and šoplora. Pretty much everything else up to 255 literally means "X sixteens and Y", which you can derive with the dual marker –de /de/, the plural marker -ǥe /ɣe/, and the word for "and", dë /də/. Laumï declines for dual and plural too, and 16³ = 4,096 is just dladžei laumïǥe /dladˈʒei ˈlaumɨɣe/, so I can actually handle numbers up to 65,535 with this system. (I don't have 0, but no problem: think of what "none" should be and use that )

Here's where I get stuck: Did people before about ancient Roman times or so regularly need to go as high as 16⁴ = 65,536? Is it plausible for my conculture to get by with just laumï laumïǥe if they need to handle the high tens of thousands and above until more advanced mathematics come along? I'm not familiar with the scale of numbers used in ancient times.

[k1234567890y]

Ancient people didn't seem to use numbers larger than a ten thousans often, and larger units might be more something philosophical and astronomical but not for daily lives.

[StrangerCoug]

Fixed a couple mistakes: don't ask me how dladžei became dlažedi

[Salmoneus]

Base-16 seems rather unrealistic for humans. Does any language use that system?

[k1234567890y]

Base-16 seems rather unrealistic for humans. Does any language use that system?

there's a natural language using a system that is close enough to a base-16 system:

https://en.m.wikipedia.org/wiki/Ngiti_language

[Xwtek]

Base-16 seems rather unrealistic for humans. Does any language use that system?

Well, this is not human language.

there's a natural language using a system that is close enough to a base-16 system:

https://en.m.wikipedia.org/wiki/Ngiti_language

No, it is base-4. In human language, language with small base is commonly used by hunter-gatherer society, since they don't deal with large number. As human becomes advanced, larger bases, especially 10 and 20, gets popular. The reason why 10 is used is because how people count.

[StrangerCoug]

Base-16 seems rather unrealistic for humans. Does any language use that system?

Well, this is not human language.

It's also implicit in the OP that it's not meant to be:

I imagine four limbs with four fingers and toes on each

I may have caused that misunderstanding by asking about the scale of numbers the ancient Romans used—that was to give an idea of the technology level of my conculture at the point I want to work with.

there's a natural language using a system that is close enough to a base-16 system:

https://en.m.wikipedia.org/wiki/Ngiti_language

No, it is base-4. In human language, language with small base is commonly used by hunter-gatherer society, since they don't deal with large number. As human becomes advanced, larger bases, especially 10 and 20, gets popular. The reason why 10 is used is because how people count.

I'm trying to get away from bases 10 and 20 to break with Standard Average Me, but it reminds me of the conlangs I made that are base 20 with a subbase of 5 (also Standard Average Me to an extent).

[zompist]

The one thing that strikes me as odd is having basic roots for all numbers up to 16. Numbers usually have etymologies— even the IE ones do, though we don't remember them. Base 20 systems are usually named based on fives and tens.

Just to correct a couple statements about large numbers— some hunter-gatherers do have extensive number systems— e.g. the Inuit can get into the thousands, while the Ojibwe had a term for million.

The Romans didn't have roots beyond a thousand, but they could express higher numbers (awkwardly) by multiplication. But the Indians are the champions in this area— they had names for powers of 10 up to 10^145.

[mèþru]

what do you mean exactly by "pre-Roman"?
Also, some southern Ojibwe tribes had farming; they might have been the source of terminology for higher numbers.

[StrangerCoug]

The one thing that strikes me as odd is having basic roots for all numbers up to 16. Numbers usually have etymologies— even the IE ones do, though we don't remember them. Base 20 systems are usually named based on fives and tens.

Just to correct a couple statements about large numbers— some hunter-gatherers do have extensive number systems— e.g. the Inuit can get into the thousands, while the Ojibwe had a term for million.

The Romans didn't have roots beyond a thousand, but they could express higher numbers (awkwardly) by multiplication. But the Indians are the champions in this area— they had names for powers of 10 up to 10^145.

OK, I think I'll leave what I have and work on plausible back-derivations of where my numbers came from.

what do you mean exactly by "pre-Roman"?

Again, it's a reference point for the technology level of my conculture.

[mèþru]

It doesn't say much. Do you mean before 1 ab urbe condita? Before the Empire? Before a specific war under the Republic?

[StrangerCoug]

OK, so maybe not basic roots for anything above 3. I've got these so far:
šop (4) is clipped from šoppu which means hand, foot, or paw.
tleu (5) is the masculine for tleï, which means "left" (as in the direction, not "remaining" like lora)
floʼ (15) is clipped from floʼï which means "almost" (which I feel like itself shouldn't be a basic root, but one thing at a time).
dladžei (16) is short for dladi žei, which means "whole body".

An idea: To what extent can numbers be loanwords? Maybe I can create a naming language to explain why not all of the number names are transparent to these people.

Before the Empire?

Let's say that.

[mèþru]

There were definitely several European mathematicians by the conquest of Greece (still Republic) who had worked with millions in their equations. I don't think anyone did anything with billions yet, but IDK.

[zompist]

An idea: To what extent can numbers be loanwords?

Extremely. Numbers are readily borrowed from a more advanced culture. (Though 1 and 2 much less so.)

[Xwtek]

OK, so maybe not basic roots for anything above 3. I've got these so far:
šop (4) is clipped from šoppu which means hand, foot, or paw.
tleu (5) is the masculine for tleï, which means "left" (as in the direction, not "remaining" like lora)
floʼ (15) is clipped from floʼï which means "almost" (which I feel like itself shouldn't be a basic root, but one thing at a time).
dladžei (16) is short for dladi žei, which means "whole body".

An idea: To what extent can numbers be loanwords? Maybe I can create a naming language to explain why not all of the number names are transparent to these people.

Try to break these into base-4 number, and contract it.

[Xwtek]

The one thing that strikes me as odd is having basic roots for all numbers up to 16. Numbers usually have etymologies— even the IE ones do, though we don't remember them. Base 20 systems are usually named based on fives and tens.

Just to correct a couple statements about large numbers— some hunter-gatherers do have extensive number systems— e.g. the Inuit can get into the thousands, while the Ojibwe had a term for million.

The Romans didn't have roots beyond a thousand, but they could express higher numbers (awkwardly) by multiplication. But the Indians are the champions in this area— they had names for powers of 10 up to 10^145.

Thanks for the cool infomation.

[StrangerCoug]

OK, so maybe not basic roots for anything above 3. I've got these so far:
šop (4) is clipped from šoppu which means hand, foot, or paw.
tleu (5) is the masculine for tleï, which means "left" (as in the direction, not "remaining" like lora)
floʼ (15) is clipped from floʼï which means "almost" (which I feel like itself shouldn't be a basic root, but one thing at a time).
dladžei (16) is short for dladi žei, which means "whole body".

Now I've got explanations for one through three: If you take the words I have for them and add the suffix ḑï /d͡zɨ/ (and you voice the ⟨s⟩ at the end of đas to a ⟨z⟩ to fit my conlang's phonotactics—yes, the spelling changes too, here), you get the adjectives I just added for "this", "that" (near the addressee), and "that over there" (i.e. far from the speaker and addressee). I'm still trying to think of how exactly one gets the other as I type, but the spelling rule in my conlangs is that you usually don't reflect changes in voicing in the spelling across morpheme boundaries, which strongly suggests to me that the same thing happened to them as to šoppu to get the numbers: the latter are clipped forms.

I still like the idea of solving the issue with the other numbers with making up a naming language for a more mathematically advanced conculture (probably one that has the basics of arithmetic down) and borrowing from that. My first thought is a reasonably friendly trading partner, but then again, my conculture's an empire and I don't know what stops mathematical knowledge from being a tribute...