o kama sona e sona nanpa kepeken toki pona

No, I’m not drunk.

(Although Justin Aion did ask if I was high on Facebook today after I asked why our ears don’t have “ear flaps” the same way our eyes have eye lids. Why do stoners have a monopoly on off-the-wall questions, I ask you!)

The assumption would be fair though, I’m posting to my blog (for once) and the title is gibberish.

Well, it isn’t!

Of course, it doesn’t really matter if I was drunk and it was gibberish, as I always write like a drunk talks anyway: rambling and long to get to the point. But you know this already if you are a reader of my blog. Hang with me, I’ll get there eventually. Anyway. It’s not gibbberish.

It’s toki pona!

It may be a poorly constructed phrase in toki pona, but it is toki pona nonetheless. The title, if I said it correctly, can be translated to

“Learn Math Using Toki Pona”

or more literally

“begin knowledge of number knowledge using simple language”.

What is toki pona? It is a conglang, or constructed language, created by a Canadian linguist Sonja Lang in 2001. The name of the language, toki pona, is literally the “language” (toki) of “good” (pona). Pona can also be translated as simple (and several other words, for reasons I’ll get to in a minute), so toki pona can also be translated as “the simple language”.

And simple it is. Which is what makes it so interesting to me (and the reason I learned it). Unlike more famous constructed languages made for science fiction or fantasy worlds (like Klingon or Dothraki), toki pona was constructed to simplify the thoughts of the speakers of toki pona: there are roughly 120 words in toki pona. Every other idea must be expressed using combinations of these base words. A speaker does not create new words by smashing these together in the pormanteau fashion of German, but by describing ideas with creative phrases. (Although it is reminiscient of a portmanteau in a way, and portmanteau is how I learned of toki pona through my friend Bryan. Thanks, Bryan!)

As an example of this building of phrases, consider the word car. There is no specific word for car in toki pona. To say car in toki pona you would have to say “tomo tawa” or “structure of moving”. Earlier today I asked some people who have been speaking toki pona for a while why the phrase is not “ilo tawa” or “machine of moving”. The answer, it seems, is because tomo means house, building, room, or generally any enclosed space that you could be in. Since you are in the car when you use it, it is tomo tawa, but you might call a motorcycle “ilo tawa”. (Or “ilo tawa pi sike tu”. Literally “moving machine of two circles”.) Even more interesting, what something is called depends on the speaker’s point of view. In an interview with The Atlantic, toki pona creator Sonja Lang says if you were in a car wreck, you might call the car “kiwen utala” or “hard hitting thing” instead of tomo tawa.

All of this seems like a lot of work! Why bother with a language that takes so much more effort to speak when we have exact words for things in other languages? Sonja was inspired by Taoist philosophies of simplicity, but as I am not a fan or follower of Taoist thought, that is not the reason I decided to learn toki pona. (And indeed you do not have to ascribe to Taoism to learn or enjoy speaking the language.)  I’ll get to my personal reasons in a minute, but this is related to the Sapir-Whorf Hypothesis, which posits that the language of a speaker affects their viewpoint and even how they think. Toki Pona is meant to force the speaker to slow down and think about what they want to say: to simplify.

For me, this idea of having basic building blocks from which an entire language is built is very appealing to me as a mathematician. It has flavors of David Hilbert’s program to completely axiomatize mathematics. The math community found out later that this was impossible thanks to Gödel, but we still use starting axioms to define a common environment or idea and work from there. Euclid’s Elements is still a great text thousands of years later. Toki Pona is more versatile than other languages in a way because of this structure. When you don’t know a word for something in English, you have to describe it to someone else (or to Google) until you find the word you were looking for. In toki pona you just describe the idea as it seems to you and chances are if you are talking to another tokiponaist they will know what you mean.

I managed to learn the basic word list between my graduate school work in a little over a week. There are, of course, some common phrases that the toki pona community uses that are practically words because of their ubiquity. Acquiring these and the grammar structure of toki pona will take me a longer, but the simplicity of the language and the utility of the basic words means it won’t be all that long. And in any case it will be a lot shorter than the time it would take me to pick up French or Russian or Japanese. Learning a new language has been a fun break for me and a nice change of pace from my graduate courses in mathematics. I’m also hoping to get my brother to learn so that we can enjoy the unique privacy of speaking a language other than English in public. (Ever since I learned “ob”, or as the PBS show Zoom called it, “ubbi dubbi”, from a library video when I was 6 or 7 I’ve enjoyed “secret languages” and codes.)

So, what’s the point of this post other than for me to tell you how cool toki pona is and repeat a few ideas from the articles I read about toki pona?

I was thinking about the relationship between mathematics and language. More specficially, I was first thinking about how you would talk about or learn mathematics in toki pona.

Really, you can’t.

In fact, you can’t really count properly in toki pona. Like an ancient culture that hasn’t really developed the idea of numbers very well yet, counting in toki pona goes like this:

one     wan

two     tu

many     mute

Yep. That’s all the “official” numbers we have for toki pona as set out by Sonja Lang. Now, toki pona speakers later decided the word for hand or arm, luka, would also mean five, but you still don’t have a lot to work with. The only other math related word in toki pona is one that you have seen already. I used it in the title: nanpa. Which is number. Or counting. Or as I used above, a modifier on the word “sona” (knowledge) to mean mathematics. (Remember, there aren’t a whole lot of words in toki pona so there isn’t a 1-to-1 correspondence between a toki pona word and an English word. A typical toki pona word has to do a whole lot more work than a typical English word.)

Imagine trying to translate even a basic algebra lesson on linear equations into toki pona. Take a look at the word list. Think of some of the words and phrases you would use or that you would want your students to use while talking about slope. Can you find those words in that list? Not really! Anything you want to say would have to be a long string of modifiers and ambiquities and generalities. The best I can do off the top of my head for “linear” would be “linja sama” or “same line”. Algebra I would be a nightmare in toki pona, let alone a real analysis class where you want to communicate the idea of the space of infinite sequences that are p-summable. It’s not happening. Toki Pona is an awful language to talk about math. It’s not what it is for. Toki Pona is for talking about how much you like telo pona pimeja (“good dark liquid” aka coffee).

But now we’ve arrived at the point of this blog post which actually started out as a tweet and quickly got out of hand, as you can see if you stayed with me thus far.

Is there a best language for talking about mathematics?

This question has more than one interpretation.

Of the languages spoken by humans on planet Earth, which one is best for communicating the ideas of mathematics?


Is there some Platonic ideal for a language that perfectly describes mathematics?

(Some people confusingly say that mathematics itself is the best language for communicating mathematics by saying that mathematics itself is a language, and while I might see why they take that view, I don’t believe it is an accurate assessment of the nature of mathematics, but that’s a tangent I’m not interested in following right now.)

The Platonic ideal angle is interesting because of Ithkuil, a conglang meant to be able to describe all possible human thoughts. I suppose mathematics is a subset of all possible human thoughts, but maybe it isn’t. (And even if it is, Ithkuil isn’t any more suited to communicating mathematics than toki pona; every syllable of every word must be carefully crafted to follow the strict rules of the language. You may have an exact word to talk about a linear equation, but it will take you longer than the class period to compose it.)

When I asked the question to myself I was thinking along the lines of the first interpretation. Which language spoken by humans is best for communicating ideas about mathematics? I don’t know what the answer is. English does an acceptable job, but is a better one out there? For example, in English we use the word love to mean a lot of different things. I love my wife and my son. But I also love pizza. And I will love the dog that I will eventually own. And so on and so on. In English we use love (and other words) to mean more than one thing. (Which apparently is more certain than whether Aleut languages have more than one word for snow.) Greek differentiates between types of love and has more than one word to express the different kinds of love.

And this reminds me of toki pona too! Which Greek word for love do you use? Well, it would depend on how you view that love! (I may be misunderstanding how rigid the Greek is here: perhaps it is not as flexible or subjective as I imagine it to be. I don’t speak Greek. Yet.) If you are familiar with Evangelical Christian subculture in America, the alleged “overuse” of the word love and the comparison to Greek is a common topic of discussion and one that rustles my jimmies because it ignores the contextual aspect of the English. But that is also an argument that I won’t get into right now. The reason I bring it up is that if English has words for ideas that toki pona does not, and Greek has words for ideas that English does not, and so on, is there a language that has better words for describing math?

The joke on the internet is that the Germans have a word for everything. (In fact, they probably have a word to describe how annoyed they get when English speakers make jokes about them having a word for everything.) And German, as a natural spoken language, isn’t so nearly as unwieldy as something artificial and experimental like Ithkuil. Some very good mathematicians spoke German, but that doesn’t really mean anything. Some very good mathematicians also spoke a bunch of other languages. So what is it?  This article describes how some Asian languages are better suited for helping small children learn to count, but since the body of knowledge of mathematics so far accumulated by human beings far surpasses basic arithmetic, this doesn’t really answer my question. It may be interesting to examine the native languages of mathematicians, or catalogue how many math papers are published in each language, but I don’t know if these measures would answer the question very well either.

What do you all think? Because I seriously have no idea. I don’t even know if there is an answer. In fact, even if the answer exists I don’t know if we could find it! But it sure is fun to think about.


P.S. If you want to learn toki pona (and I highly recommend you do, it’s a lot of fun and easy to pick up) you should check out the following links:

Official Toki Pona Site

Best Toki Pona Lessons I Have Found So Far

Easy Way To Memorize The Words Of Toki Pona