Why you can understand so much but still can’t speak fluently (Thales’s Theorem)

A student recently wrote me:

“I can understand German when someone speaks to me, but I can’t talk.”

This one sentence captures a quiet frustration shared by so many learners.

“I understand more than I can say.”

Many learners notice this gap early on.

  • You can understand when someone speaks to you — especially if they speak slowly or clearly.
  • You recognize words and phrases.
  • You often get the meaning, even if you don’t catch every single word.

But when it’s your turn to speak — you freeze.
The words just… don’t come.

So you jump to a very logical conclusion:

“I understand more than I can say. That means there’s a gap.
So I need to close the gap.”

And then the question is:

“How do I do that?”

And again, the logic seems sound:

“I’ll close the gap by practicing more speaking.

That way, all the words I understand will become words I can say.”

That’s the strategy most learners follow.

And it’s a strategic mistake.

Why the strategy is flawed

Here’s why this logic leads to frustration:

It’s built on a false assumption — that the gap between what you understand (your passive vocabulary) and what you can say (your active vocabulary) is a problem to be solved.

But it’s not a problem.
It’s a feature of language.

Even in your native language, you understand many more words than you use.

You read a book, and every sentence makes sense.

But you wouldn’t (and couldn’t) use all those words in your daily life.

That’s because in every language, there is always a delta — a fixed distance between passive and active vocabulary.

This delta is normal. It’s constant. And it’s not something you can close.

In your native language, you don’t even notice it — because your active vocabulary is already large enough to express whatever comes to mind.

But in German, that’s exactly where the frustration kicks in: you feel the lack of words. 

You start searching for them mid-sentence, and the conversation stalls in that familiar silence while you try to piece together how to say what you mean.

The cost of the wrong strategy

Now here’s the hard truth:

If your strategy is wrong — even just 1% off —
you might spend years heading in the wrong direction.

Like a long-distance missile set 1° off course, you won’t just miss the target by a little.

You’ll miss it by miles.

That’s what happens to learners who believe they just need to “practice more speaking” to activate the vocabulary they already understand.

  • They plateau.
  • They feel stuck.
  • They begin to lose motivation — and blame themselves.

But the real issue isn’t discipline.

It’s strategy.

The real problem (and the real lever)

Let’s reframe this.

The problem in German isn’t that you understand more than you can say.

That’s always going to be true.

The real problem is that your active vocabulary is not yet big enough.

So the real question becomes:

“How do I grow my active vocabulary?”

Now, here’s the counterintuitive insight:

You can’t grow it directly.

You can’t “practice” your way into new words.
You can only use what’s already there.

And speaking practice helps you use what’s active —
…but it doesn’t create new active vocabulary.

That creation happens elsewhere.

It happens through reading.
Through listening.
Through comprehension in context (see here).

That’s what builds your passive vocabulary — the side of the system you caninfluence.

Thales’s Theorem gives the solution

Let’s make this more concrete — with the help of something you might remember from geometry class: Thales’s Theorem.

Imagine your vocabulary as a kind of inverted pyramid — or a ray diagram from geometry:

  • The top edge of the pyramid represents your passive vocabulary — the words you understand.
  • Somewhere below that, there’s a narrower section — your active vocabulary — the words you can use spontaneously.
  • The distance between the two is Delta (Δ) — a fixed gap.

Now here’s the insight — and it’s based on a principle from mathematics, Thales’s Theorem.

It tells us:

If you keep the angle constant, and you extend the top line outward,
then all other lines below it grow proportionally.

In language terms:

If the delta stays fixed, and you expand the passive vocabulary,
then your active vocabulary grows with it — automatically.

You don’t need to force anything.
You just need to extend the top line — the passive side.

That’s the real lever.

And this is the strategic shift most learners miss

Most learners say:

“I need to speak more, so I can activate the words I already understand.”

But what they don’t realize is:

You can’t “activate” what was never deeply stored.
You can’t speak words that only passed through your brain once or twice.

Speaking doesn’t add new vocabulary — it only plays with the vocabulary you already own.

So the real question becomes:

“How do I expand the vocabulary I truly own?”

And the answer is:

Repetition. In context. Through reading and listening.
Again and again. Naturally. Over time.

How passive vocabulary becomes active

You can think of it like this:

Each time you hear or read a word in a sentence, you lay down a memory trace.

One exposure doesn’t do much.
But five… seven… ten meaningful exposures?

The word becomes recognizable.
Then familiar.
Then usable.

That’s when it crosses the line — from passive to active.

You didn’t “practice” the word.
You didn’t “memorize” it.
You simply encountered it often enough — and the system took care of the rest.

So what should you focus on?

You focus on the one part you control:

  • You grow your passive vocabulary.
  • You trust that the delta stays fixed.
  • And you know that as the passive side expands,
    the active side must expand with it — just like in the Thales’s Theorem.

This is the strategic shift that moves learners out of the plateau — and into real fluency.

Not by chasing more output.
But by feeding the input system that fuels it all, the same principle behind how ChatGPT works (see here).

Final Thought

If you ever feel stuck again…
like you understand so much, but can’t speak yet…

Remember this:

You don’t need to close the gap.
You need to grow the system.

Focus on the part you control:
Read more.
Listen more.

Expose yourself to comprehensible input (see here), the kind of German you can understand, even if it’s slightly above your current level.

That’s what grows your passive vocabulary.

And as it grows, your active vocabulary rises with it — automatically.

Let the system do what it’s built to do.

Talk to you soon. Bis bald.

Gruß
Manuel

P.S. Whenever you’re ready, here are 5 ways I can help you take your German to the next level.

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