Can you count in a language without numbers?

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A couple weeks ago I was introduced to the fascinating case of the Piraha people.  This is a small tribe in the Brazilian Amazon, the sole surviving offshoot of a larger people called the Mura.  Neither group is all that big.  The Mura have just 12,000 and the Piraha just under 1,000.

The Piraha were brought to my attention because I have been thinking a great deal about numbers lately.  Specifically, I’m trying to figure out of mathematics is real in a sense, or if it is merely a formal convenience that happens to allow humans to analyze and manipulate reality with precision.

This is an old debate that goes back a long way and intersects not only with mathematics but science, philosophy, linguistics, economics, technology and, well, pretty much everything.  We use numeric language so instinctively that we don’t even notice it.  Pay attention today and tomorrow.  How often do you think and speak in terms of numeracy?  Too many to count, so to speak!

The Piraha are fascinating because they don’t have words for numbers.  They don’t speak of “one”, “two”, “three”, “four”, etc.  Seems strange doesn’t it?  This leads many linguistic theorists to speculate about how language shapes perception, which is known as linguistic relativity.  Today I gather that most linguists hold a softer stance, which is to say that there is a reciprocal relationship between language and cognition.  How flexible is language, and how moldable is cognition?

If I lived among the Inuit for a bit it seems certain that I would return with many more words for snow than I had entered and that I would become quite attuned to the different textures of precipitation to which they referred.

But, if I traveled to a new place and discovered many animals that had never been seen before, I would certainly begin to develop a vocabulary to describe them as I paid attention.  Another such example is when different people do the same psychotropic drugs and begin to develop a shared vocabulary for the different proprietary sensations that come with them.

So, it seems clear to me that language and cognition are mutually plastic.

I was interested in numeric cognition though.

The Piraha don’t refer to specific numbers.  So, can mathematical reasoning be a condition for experience?

Kant thought it was, and asserted it as one of his categories in the famous Critique of Pure Reason of 1781.  Granted, he was a white Westerner.  Is this really so universal as he claimed?

And do the Piraha disprove it?

I don’t think they do, even if they challenge it.

Here’s my sense of it.

Watch this (SHORT - promise!) video:

Two things stand out to me, and indicate that they do think mathematically, even if it doesn’t immediately seem that way.

1. They do refer to quantities, and they have 2 words for this.  One means “a few” and the other means “a lot”.  At a certain point it switches from a few to a lot.  The video doesn’t show us when exactly, nor does it refer to experiments that look for a consistent point; indeed, there may not be one.

This is essentially a version of the ancient “Sorites Paradox” which asks when a heap emerges as grains of sand are added to a pile. https://en.wikipedia.org/wiki/Sorites_paradox

So, they have a sense of quantity.  There is also a word for “big”, which I would argue is also related to quantity.

2. But here’s the second, and more significant.

At the end there is that moving quote: “They don’t know how many children they have, but they know all of their children’s names and they know all of their children’s faces.  They don’t need to know how many children they have to know who their children are and how they feel about them.”

While they many not number them, they know their children’s faces, which is to say that they are distinguished from all else, and they are named.

But, what is distinction, and what is naming?

When we distinguish any object, when we name anything, what are we doing?

I would assert we are numbering it in a very real sense.  Are we not?

Specifically, we are numbering it as “1”.  "Singling it out" as we so often say.

While the Piraha may not have a word for 1 as we do, I would argue that “1” is merely a mathematical (or computational) extension of entity.

If we perceive an entity, and draw a boundary around it, it becomes countable through what we call “natural numbers”, which are the counting numbers, starting with 1.  I think 1 must be the primary number, or else the world doesn’t “add up”.

I call this the “(Entity 🔄 Boundary 🔄 Unity) Transcendental Generative Trialectic” - or EBU TGT - by the way, and I believe it is not only the precondition for experience, but existence as well.  I don’t know how it could be otherwise.  That’s a debate we could have, but it is clear to me that even the Piraha, while they don’t manipulate quantity in the same sense that we do, abide by this.

To name anything is to acknowledge the EBU TGT.  What is within the boundary is the entity, and what is around the entity is the boundary, and this is a unity, which becomes a unit.  We can then accumulate units through the sequence of the natural numbers.  All other mathematics emerges from that I suspect.  It is merely a matter of precision.

The Piraha do work at a certain level of precision, and for their purposes few and a lot are sufficient.  It can’t build a car, launch a rocket, or program a computer.  But that’s not what they do.

And, I suspect that much of the Western neurosis actually longs for a mode of being more like the Piraha, liberated from the meta-drive of technological development and advancement, toward which our entire civilizational infrastructure is oriented in some way, and from which emerges greater and greater technological capability that simultaneously empowers and demoralizes.  Every new technology shows great promise and also great disadvantage.  And it never stops.  And it is our entire orientation.

The alternative is to freeze progress, as some social groups try to do.  Or to live like the Piraha, for whom a few and a lot is sufficiently precise for science and technology.

And this is not a judgment, merely a therapeutic diagnosis.  I call it the “Human Meta-Drive for the Expansion of Labor-Saving Technology”.  We are never really saved; our creativity and ingenuity is simply rerouted.

Is this compelling?  Cruel?

As I said, it’s just a diagnosis.

Remember, though, that I was thinking about mathematics, and whether all humans have a form of it.  And I think we do, and it’s because reality emerges through entity, and unity is the foundation of computation.

The meta-drive was a psychotherapeutic bonus, and I think many of us need that right now.

By the way, if you appreciated that, you might enjoy my 2023 book The Complete Science of Human Dynamics, which gives 5 other species-level psychotherapeutic diagnoses:

Oh, and I almost forgot!  Contemplating the Piraha language provokes deep questions about what it means to engage with reality, and exactly what language is doing.  Large Language Models, LLMs, help us with this process, illuminating the deep structure of language.  I created a custom GPT that allows you to translate English into Piraha ontology, while still in English.  They don’t have temporality (past/future/present) either.  I've been playing with it all afternoon.  Give it a try!  It’s fascinating, and seems to make the computer think pretty hard.  After all, it is performing a feat of not only linguistic, but metaphysical translation...

https://chatgpt.com/g/g-68af6386446c81918b4f2050e0b638e9-living-river-translator

And...did you hear?  I just started a Facebook group for visionaries, thinkers, and dreamers like you to connect, support one another, and discuss the big questions.  Check it out here!