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This is a seximal (base 6) counting system that is inspired by toki pona.
Adding a bunch of words to the language is kind of orthogonal to the spirit of toki pona, and I suspect that something like this has already been done by someone out there, maybe jan Misali specifically, but I still wanted to work through it for myself, so here it is.
The toki pona language is a constructed language (conlang) designed by Sonja Lang sometime in the last couple decades. Among other features, it has a very small vocabulary of around 120 words, and it uses only 14 letters in its alphabet.
A seximal counting system has only six digits instead of the ten digits that we're used to. I think that the term "seximal" for base-6 counting was recently popularized by jan Misali, who is a maker of online videos, and also a fan of toki pona.
I'll write seximal numbers inside square brackets in this article, so [1] = 1, [5] = 5, [10] = 6, [20] = 12, and so on.
The toki pona language is deliberately small, and only supports a few number words:
ala - 0, none
wan - 1
tu - 2
mute - several, 3 or more
ale - many, countless
The toka pona book then goes on to suggest a constructed number system if you really want one, using these numbers as particles and building your word by adding them together:
ala - 0
wan - 1
tu - 2
luka - 5 (hand)
mute - 20
ale - 100
So, for example, "wan tu" is 3, "luka luka" is 10, and so on.
I found toki pona's approach kind of unsatisfying, so I tried my hand at working out something different. I'll call it the "tox" system for now.
Tox has six base particles. Some are borrowed or derived from toki pona, and others have been arbitrarily invented.
la - 0
wa - 1
tu - 2
so - 3
pe - 4
lu - 5
To count small numbers, join the base particles into words and add an "-n" suffix.
[1] 1 wan
[2] 2 tun
[3] 3 son
[4] 4 pen
[5] 5 lun
[10] 6 walan
[11] 7 wawan
[12] 8 watun
[20] 12 tulan
[31] 19 solan
[45] 29 pelun
[55] 35 lulun
In addition to base particles, there are "power" particles which are used for powers of [100] 36.
0 la
[100^1]=[1,00] 36 ka
[100^2]=[1,00,00] 1,296 ni
[100^3]=[1,00,00,00] 46,656 jo
[100^4]=[1,00,00,00,00] 1,679,616 me
[100^5]=[1,00,00,00,00,00] 60,466,176 ta
To construct numbers larger than 36, combine the base particles with the power particles in this way that feels intuitive to me, but for some reason is difficult to write an explanation for:
[1,00] 36 waka (wa=1 * ka=100^1)
[2,00] 72 tuka (tu=2 * ka=100^1)
[1,00,00] 1,296 wani (wa=1 * ni=100^2)
Combine large numbers with small numbers:
[1,01] 37 waka wan (wa=1 * ka=100^1 + wan=1)
[3,54] 142 soka lupen (so=3 * ka=100^1 + lupen=54)
[5,03,20] 6,600 luni soka tulan (lu=5 * ni=100^2 + so=3 * ka=100^1 + tulan=20)
To form higher powers, combing the power particles in the same way that base particles are combined to form larger base numbers.
[100^11] 78,364,164,096 wakaka (wa=1 * kaka=100^11)
[100^30] ~1x10^28 wajola (wa=1 * jola=100^30)
In this way, even extremely high day-to-day numbers (equivalent to trillions or quintillions) can be expressed without too much trouble.
By definition, numbers larger than [100] 36 are constructed using power particles. But it's clear that you could just extend the base particles to make larger numbers. This is a style choice, similar to how English can say both "one thousand four hundred" and also "fourteen hundred". They are the same number, just styled differently.
[1,11] 42 waka wawan. wawawan.
and so on.
To read a number written in base [14] 10, read each digit individually instead of trying to convert it.
1964. wan wason walan pen.
and so on.
Is that even useful? Does it mean anything at all? Hard to say, but at least it's something.
Zero has its own word, borrowed from toki pona. It feels important enough to depart from the pattern.
[0] 0 ala
Uh, there's some particle or adjective to indicate a negative number, but I haven't bothered to come up with one. Let's borrow (as best I can) from toki pona again and say that "sewi" can indicate a positive number and "pi sewi ala" indicates a negative number.
[21] 73 tuwan. tuwan sewi.
[-21] -73 tuwan pi sewi ala.
Uhh, I didn't get that far.
The idea was to provide a counting system that can construct arbitrarily large numbers using a relatively small inventory of particles. As currently written, it uses 13 particles.
-n ala la wa tu so pe lu ka ni jo me ta
Some of the inconsistencies are deliberate, but I'm sure that there are some that I didn't intend. I won't try to identify which is which here.
I don't really intend this counting system as something to be added to toki pona, even though I obviously used that as a starting point and borrowed a lot from it. I gave it the name "tox" partly to distance it from toki pona (the letter "x" isn't part of the toki pona alphabet).
In the beginning, I tried to organize it so that the constructed numbers wouldn't duplicate (many) toki pona words, but I stopped checking that before I got very far. I haven't actually studied toki pona as a language, just as a curiosity.
I haven't made any attempt to try to use this counting system. Like any base 6 counting system, I'm sure it would be quite difficult for base 10 users to get used to. Ah well.
emptyhallway
2023-10-03
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