Podcast Interview: Fractal Geometry + The Language Matrix

I had the opportunity to chat with Chapman Woodriff, a polyglot and passionate language learner who travels the world learning languages.  For over 10 years he has shared his research and experiences with online viewers on Free Language (https://freelanguage.org).

Prior to recording this podcast, Chapman took his first Arabic lesson using the Tony Marsh Method. After 30 minutes he was able to carry on a simple conversation in Arabic and was hooked!  This is what he has to say about his experience.

Listen to the full podcast. 

Language follows the golden (divine) ratio

Most language learning resources focus on the process of what YOU can do to learn a language.

But what I'm interested in is how a language is an organic, living, naturally occurring phenomenon, like rivers, trees, and humans, and what that has to do with efficient language learning, as well as what it has to do with the nature of life/God/the universe (as a bonus).

The mathematician Leonardo Fibonacci used a set of numbers (Fibonacci numbers) to describe how rabbit populations expand. The numbers are 1, 2, 3, 5, 8, 13, 21, 34, ... (each number is the sum of the previous two numbers). This "golden" ratio also describes flowers, trees, rivers, seashells, galaxies, and the human face.

Language also grows this way in your mind -- particularly if you're a child. My goal is that it grow that way also in the mind of the adult.

The way it looks is that for every language you grew up speaking there are a number of situations you've experienced in which you used that language. You now draw from those situations and everything in them to speak the way you do today. Each of those situations (or topics) are like branches that grow from a single point -- that single point being whatever language you're speaking.

Each of those situations has its own branches, those being verbs that support the situation. For example when hungry, the verb is 'I want', or 'I need'; when happy, the verb is 'I feel', or 'I love'.

Finally, growing from each verb are vocabulary, such as 'food', 'milk', 'great', and 'you'--that which completes the sentence that the verb started.

At each level, the total number of points increases, the result approximating the Fibonacci scale (See visual aid at the end of this post).

And that's it. It's the tree. It's the way language grew, multiplied in your mind as a child without your consent. It happens as naturally as anything does in nature. It's golden; it's divine.

In terms of practical language learning, it means that if you want to learn a language, you have to cultivate the proper conditions for the language to grow in your mind. This involves sunlight and water (input), it involves roots (thinking in the language), it involves branches (verbs) and leaves (vocabulary). And it involves doing things in a certain order so that the process be in harmony with that golden mean.

"The Universe in a Grain of Sand"

It's said you can see the universe in a grain of sand, and that every human being is a microcosm of the universe.

In the same way, in every sentence of a language (and sometimes in just a single word), there are a number of lessons that you can extract which teach you about the language at large.

For example, the simple phrase in Brazilian Portuguese, 'Oi, tudo bem?' (Hi, everything well?), could be analyzed for its pronunciation/phonology, vocabulary, even seedlings of grammar with some imagination.

In fact, if you just say the name of a foreign language over and over again ('français, français, français', for example), it kind of sounds like you're speaking that language. In other words, it gives you a general, microcosmic representation of the language.

I think an eye for this kind of recursiveness - being able to see the proverbial forest by looking at one tree (or even just a leaf) - and the patience to do so, are among the most important skills to apply to language learning.

One of the keys to learning any skill (including language)

One of the keys to learning any skill (including language) is mastering it in its 'small but complete' form.

There are endless examples of this, here are a few:

If you can paint a single perfect flower, you can likely paint anything perfectly (not necessarily, but if you can't paint a perfect flower then it's unlikely that you can paint everything else perfectly).

If you can do the basic steps of a dance, you are on your way to dancing well.

If you know a single verb, just in first person, in past, present, and future, in the language you're learning, that's a microcosm of the grammatical system of the language.

The key is recognizing the microcosm - seeing the 'whole picture' in its small (not simple, which implies details are scrubbed) but complete form, mastering those basic steps, and allowing them to bloom.

How does the method work from beginner to advanced?

As beginners become high beginners, within about 3 hours of lessons, my Matrix begins to "zoom out" until it becomes what I call a Map of the language. The Map is a single page which shows you the complete tense/aspect matrix of the language, core verbs, an adverb timeline, questions words, pronouns, and a few other items at a glance. 

Once the Map becomes in view, the potential for conversation multiplies into a variety of topics. At that point, it's time to begin choosing the most relevant topics to you, and begin to converse on those topics in a question-answer, question-answer format. At this point, lessons feel like playing a game of tennis...back and forth, practicing conversing freely, with our Map as the basis. 

As the student becomes more and more comfortable in the "tennis game", I begin introducing techniques to better "serve", or ask questions, and better "return", or answer questions. There are defensive techniques, methods for understanding when you're not really understanding, and techniques for making the most out of what you have. 

Around this time (about 5 or 6 hours in), I introduce listening exercises that train you to deal with different native speakers when different accents and styles speaking at different speeds, and again I teach strategies to deal with those situations.

When a student is rather advanced, the lesson becomes focused on "elective"-type material such as business, or whatever sort of subjects they need, and I just provide feedback/refinement within 5 categories, which are accent, pronunciation, structure, vocabulary, and colloquial language. Poetry and phonology is also of personal interest to me.

But no matter what the students' level, Katarina, my goal is also to impart to the student an understanding of the principles that underlie each stage, so that ultimately he or she will not have to rely on anyone or anything, including me, to improve in the language, but rather can continue to learn the language by simply living in the language, and let interacting with and in the language be the true, natural teacher. 

What is the #1 most important factor in language learning?

What is the #1 most important factor in language learning?

Having the right books, class, and teacher? Learning grammar? Input first? Output first? Spaced repetition techniques? The #1 most important factor in language learning is interaction with other people.

To learn a language, you must interact with other people in the language. But how can you interact with other people in the language if you don't know the language?

To solve this problem, I developed a tool called the Language Matrix™, which is a spreadsheet grid that allows you to immediately begin conversing in any new language simply by mixing and matching building blocks, so you can learn the language by using the language, not by studying the language, similar to the way we learned our first languages as children.

I have developed my method over 12 years as an Arabic Cryptologic Linguist for the US Air Force (2005 - 2009), and a Spanish, Portuguese, Arabic, and English teacher for the FBI, Navy, NATO, and hundreds of private students.

My method is inspired by fractal geometry and Taoist philosophy, and I am grateful to my NATO Arabic student for calling the method "a miracle", and "new light in language learning".

The Earth revolves around the Sun, and you learn a language by using it

The current/past thought in language learning is that you learn a language so you can use it. But in reality you use a language so you can learn it.

It's like thinking the Sun revolves around the Earth, and not the other way around. Not true, and difficult to see at the beginning because it appears that it is the Sun that is moving - appears that you need to learn a language before you can use it.

But once you see it the way that it actually is, you can't un-see it.

Preparing yourself for a Practice Partner

You've been practicing a new language for a while, and now you've met someone who is willing to be your practice partner. He or she is a native speaker, and has suggested that you meet for coffee once a week to speak the language together.

Your lessons have been going well and you are confident, but the session left you feeling discouraged.

What happened? And what can you do to make future sessions better?

There is a good chance that your practice partner (albeit with good intentions) hurt your confidence by stopping to correct you every time you made the slightest mistake.

I was once laughed at repeatedly by a Romanian guy who was trying to teach me to say a word. He'd say it, then I'd say the exact same thing, but he was sure it laughably incorrect. I've had the same experience with various other languages.

While they may be trying to help, it really just makes you feel like you'll never be able to get by in this language, and forever sound funny or weird, which is not a good self-image to have while learning to speak a new language.

So what can be done? Try this:

Tell your practice partner (in English) before the session, that you know you have a lot of work to do in this language, and that you feel it would help to get to hear the language more. So you have prepared a list of questions in the target language that you would like to ask.

The begin to ask these pre-prepared questions, such as 'How are you?', 'How was your day?', 'What did you do?', and any other question you'd like to ask. Just listen to your partner's responses. We'll call this your INPUT practice, or listening practice.

As your partner responds, practice guessing what they're saying. You can do this through keywords, and assumption. For the occasional learning moment, ask 'What does that mean' in the target language, and take a few notes. But try not to make it too much about learning, or the conversation will end - the goal is to keep the conversation going!

When it's your turn to respond to a question (OUTPUT), rely on simple answers that you also prepared when you wrote your questions.

If your partner asks a follow-up question and you understand the question, then answer it. If you do not understand the question, then use it as a learning moment and ask 'What does that mean?' in the target language, and take a note. Then answer the question. If you need a word or to to answer, have another learning moment by asking 'How do you say ...?' in the target language, and take a note.


The entire algorithm looks like this:

INPUT (listening)

1. Ask a question.

2. Listen and practicing guessing the meaning through keywords and assumption.

3. Learning moment - ask 'What does ___ mean?' in the target language; take a note.


OUTPUT (speaking)

1. Answer in a simple, prepared way.

2. Wait for a follow-up question, or go back to step 1. of INPUT and ask a question.

3. If there is a follow-up question and you understand it, answer.

4. If you don't understand, ask 'What does that mean?' and take a note.

5. Once you understand, answer.

6. If need be, ask 'How do you say ___?', and take a note.


A real-like example might go like this:

YOU: How are you?

THEM: Good. You?

YOU: Good. How was your day?

THEM: Good, but really busy, a lot going on at work. Yours?

YOU: Good too, thanks. What did you do?

THEM: I worked all day, and after that started getting ready for the party.

YOU: What does "party" mean?

THEM: "Party" means party.

YOU: Thank you.

THEM: What did you do today?

YOU: I went to work, then had lunch, and then took a lesson.

THEM: Nice! What did you have for lunch?

YOU: How do you say "chicken"?

THEM: "Chicken" is "chicken".

YOU: I had chicken for lunch.


To summarize:

1. Prepare your questions.

2. Prepare your answers.

3. Ask a lot of questions.

4. Take a few notes.

5. Repeat often!

What really matters when learning a language?

What really matters when learning a language?

Does pronunciation matter? Does correct grammar matter, or does making yourself understood matter more? How good do you have to be before you can say you've learned the language? What does being good in a language mean? And how do you know when you've learned a language?

Every one of those questions is built on the premise that language is something you learn. Like how records are things you play, frisbees are things you throw, and whistles are things you blow, languages are things you learn, right?


Language is a thing you use.

More to the point, a language isn't even a "thing", so much as it is a system of conduits, like city streets.

It's not a "thing" that you "use", as much as it is an "avenue" that you "take".

It is a structure that stands on its own, in the minds of those who know it, and when you subscribe to it, you too can fill in the lines with your own colors.

For example, once you can say 'I feel' - which is structure - you can fill in the blank with your personalized content - your color - to say 'I feel good', or 'I feel great', or 'I feel...whatever'.

That's what language is: structure and content, constant and variable, solid line and color.

Even vowels and consonants are structure and content. Vowels, vibration, like a musical flute, are the basic structure of sound, and contain within it consonants, which are like the fingers of the flute player who changes the sound.

From syntax to sound, It's structure and content all the way down.

So how do you learn it, which is to say, how do you become a member?

The structure must be established.

The structure must be established so that it will stand alone; so that even when you aren't speaking the language, for example because you are sleeping, you could be speaking the language if you chose to because you know the language, which means the structure is still there.

And how do you build the structure?

YOU don't build the structure.

The CONTENT builds the structure.

The content itself builds the very structure that will come to hold it.

Just like how moving water carves a river into the land, each time you express a thought, it leaves its mark in your mind in the shape of the language.

Over time, the system becomes more refined, and more defined. The bends are carved into rock, rather than mud, and you can say whatever you want to say. At the extreme end, it can becomes difficult for people to change the way they speak, which makes it difficult for people to change the way they think.

But in the meantime, while you are building the structure, understand that each time you express a thought in the language you're learning, you are deepening and expanding the structure. And most importantly, in that moment you're communicating something, or using the language to some end, which is the purpose of language.

Once a thought is expressed, it blows away like the colored sand of a mandala. But as it's being expressed, it makes its impression in the rock.