Does a Bigger Alphabet Give AI a Bigger Mind?

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The 652 million Question:

Does a Bigger Alphabet Give AI a Bigger Mind?

A tale of two languages, 26 letters, 32 letters, and numbers too large to picture.

Shuffle the Alphabet

Here's a classic bar trick from mathematics: shuffle a deck of cards. Any order you get has, almost certainly, never existed before in the history of the universe. That's because 52 cards can be arranged in 52! ways — a number with 67 digits.

Now imagine the alphabet as a deck of cards.

English hands you 26. Persian hands you 32. And the number of ways to arrange each one — to shuffle the entire alphabet — is where things get wild.

The Math Nobody Told You Was Beautiful

A factorial (written with an exclamation point) just means "multiply every number down to 1." So 26! is:

26 × 25 × 24 × ... × 2 × 1

The result?

  • 26! ≈ 4 × 10²⁶ — a 4 followed by 26 zeros. This is more than the number of stars in the observable universe.
  • 32! ≈ 2.6 × 10³⁵ — a number so large it makes the star count look cozy.

Every one of these is a possible "universe" built from that alphabet — every possible ordering, every possible foundation for words yet unwritten.

The Floor and the Ceiling

Here's a fun way to frame it. Suppose you're comparing alphabets with between 26 and 32 letters. Then:

  • English is the floor — the smallest possible universe in this range. The greatest lower bound.
  • Persian is the ceiling — the largest. The least upper bound.

So how far apart are the floor and the ceiling?

652 million. Roughly the population of Europe.

For every single way to arrange the English alphabet, Persian offers a Europe's worth of alternatives. The gap isn't a gap — it's a chasm with its own weather.

The Guessing Game

Here's another way to feel the difference. Play 20 Questions with the alphabet: I pick a letter, you guess it with yes/no questions.

  • With 26 letters, you need about 4.7 questions per letter. You get five questions but never quite use them all.
  • With 32 letters, you need exactly 5. Every question works perfectly. No wasted bits.

Half a question sounds trivial. But it compounds. Write 100 characters, and Persian's alphabet allows about a billion times more possible strings than English. The advantage doesn't add up — it multiplies.

The Plot Twist: Your AI Doesn't Care (Much)

So a Persian-language AI lives under a higher ceiling. Case closed?

Not quite. Three reality checks:

1. AI models don't read letters. They read tokens — chunks of words, like "under" or "-ing." Both English and Persian models end up with dictionaries of roughly 50,000–250,000 of these chunks. At the level where the computation actually happens, the two languages walk in looking almost identical in size.

2. Real language is gloriously repetitive. The theoretical space of 26! arrangements is mostly empty wilderness that no one ever visits. Actual English text carries only about 1–1.5 bits of true information per letter — we use a tiny corner of the available room. Both languages are heavily compressible, and they compress to nearly the same density.

3. Persian quietly fights back. Persian script typically skips short vowels — the reader's mind supplies them from context. That means each written letter carries a bit more punch, and the language claws back some of the theoretical difference all on its own.

So What Actually Sets an AI's Horizon?

If not the alphabet, then what? Three things, none of which are letter counts:

  • Context window — how much text the model can hold in mind at once
  • Parameters — how many internal knobs it has for capturing patterns
  • Training data — what it read while learning

The alphabet is the doorway. The room is built from these.

The Numbers, At a Glance

English

Persian

Letters

26

32

Alphabet arrangements

~4 × 10²⁶

~2.6 × 10³⁵

Role in our comparison

The floor

The ceiling

Guesses needed per letter

~4.7

exactly 5

Advantage per position

—

+0.3 bits, compounding

The gap between them

652,458,240 arrangements

The Takeaway

Does a 32-letter alphabet give a Persian AI a bigger sky?

Formally, yes — a ceiling floating about 652 million arrangements above English's floor, with a per-character advantage that compounds exponentially. It's a genuinely larger symbolic universe, and the mathematics is not a matter of opinion.

Practically, no — tokenization flattens the difference at the machine level, and the deep redundancy of human language means both cultures use only a sliver of their theoretical space anyway. Two models, one trained on Persian and one on English, end up with horizons far more similar than their alphabets would suggest.

There's something almost poetic in that. The canvas Persian paints on really is bigger — incomprehensibly bigger. But meaning, not symbols, is what fills the space. And it turns out that whether you write with 26 letters or 32, human language finds nearly the same amount of meaning per breath.

The canvas is bigger. The paintings come out the same size. What fills the space was never the alphabet — it was us.

Enjoyed this? The factorial is the most underrated number in everyday life — and the next time you shuffle a deck of cards, remember: you are almost certainly holding an order the universe has never seen.

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