How communicatively optimal are exact numeral systems? Once more on lexicon size and morphosyntactic complexity
Challenging the view that exact recursive numeral systems are communicatively optimal, this study analyzes 52 diverse languages with a refined complexity metric to demonstrate that many systems are significantly less efficient than previously thought due to unaccounted morphosyntactic variations.
Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
Imagine you are trying to design the ultimate menu for a restaurant that serves every possible number of dishes, from 1 to 99.
You have two main goals to make the menu "perfect" for your customers:
- Keep the vocabulary small: You don't want to memorize 99 unique words. You'd rather have a few base words (like "Ten," "One," "Two") and combine them.
- Keep the phrases short: You don't want customers saying "Ten-plus-ten-plus-ten-plus-one" for 31. You want them to say "Thirty-one."
For a long time, linguists believed that every language in the world had figured out the perfect balance between these two goals. They thought languages were like master chefs who had evolved the most efficient menu possible: a small list of ingredients that could be combined quickly to make any dish.
The New Study: "Wait, some menus are messy!"
This new paper by Cathcart and his team says, "Not so fast." They looked at 52 different languages and found that many of them are actually inefficient. They have messy menus that don't follow the perfect rules.
Here is how they discovered this, using a few simple analogies:
1. The "Hidden Cost" of Irregularity
Previous studies counted how many "base words" a language had. But they ignored the weird exceptions.
- The Analogy: Imagine a language where "One" is uno, "Two" is dos, and "Ten" is diez. But for "Eleven," instead of saying "Ten-one," they have a completely random word like once. And for "Twelve," they have doce.
- The Problem: Previous researchers treated once and doce as just "extra words" on the menu. But this paper argues that these aren't just extra words; they are unpredictable glitches.
- The Metaphor: Think of a language like a Lego set.
- Efficient Language: You have a few standard bricks (1, 2, 10). You can snap them together to build any number. It's easy to learn and fast to build.
- Inefficient Language: You have the standard bricks, but for numbers 11 through 19, you have to use special, weirdly shaped bricks that don't snap together with the others. You have to memorize each one individually. This makes the "Lego set" (the vocabulary) bigger and the "building process" (speaking) more complicated, even though the final tower looks the same.
2. The "Perfect Curve" vs. The "Messy Scatter"
The researchers used a computer to simulate millions of "perfect" menus. They drew a line (called a Pareto frontier) showing the absolute best balance between having a small vocabulary and short phrases.
- The Result: When they plotted real languages on this graph, they found two distinct groups:
- Group A (The Efficient Chefs): These languages (like Japanese or many others) sit right on the perfect line. They have a small vocabulary and short phrases. They are doing exactly what the theory predicted.
- Group B (The Messy Chefs): These languages (mostly from the Indo-Aryan family, like Hindi, Kashmiri, and Dhivehi) sit far away from the perfect line. They have huge vocabularies full of weird, irregular words, and their phrases are longer than they need to be.
3. Why Do the "Messy Chefs" Exist?
If efficiency is so important, why haven't these languages fixed their menus?
- The "Frequent Word" Theory: In English, we say "Twelve" instead of "Ten-Two." This is an irregularity. But "Twelve" is a very common word. The paper suggests that in languages like Dhivehi or Kashmiri, the "weird" words aren't just for the teens (11-19); they go all the way up to 99.
- The Metaphor: Imagine a city where the main roads are wide and smooth (efficient), but the side streets are full of potholes and detours (inefficient).
- The researchers found that in these "messy" languages, the potholes are everywhere, not just on the side streets.
- They speculate that maybe these irregularities stick around because they help people recognize numbers faster (like a unique logo on a package), or perhaps they are just historical leftovers that haven't been "smoothed out" yet.
The Big Takeaway
The main message of this paper is: Nature isn't always perfectly efficient.
For a long time, scientists thought all languages were like Swiss Army Knives—perfectly designed tools where every part has a specific, efficient function. This paper shows that some languages are more like Grandma's Tool Shed: full of useful tools, but also full of weird, rusty, one-of-a-kind gadgets that don't quite fit the system, yet everyone in the family still uses them because they've always been there.
In short:
- Old View: All languages are perfectly optimized to be short and simple.
- New View: Many languages are actually quite messy and inefficient, carrying around a lot of "extra baggage" (irregular words) that doesn't help them communicate faster.
- Why it matters: It reminds us that languages aren't just logical machines; they are living things shaped by history, culture, and human habit, not just by the need to be efficient.
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