AI Capabilities and Limitations

SECTION 1: Opening

## Send a Text

Long ago, my friends and I would play this game where you'd grab your phone and craft a message to a friend using only the recommended next words. Maybe you did this too.

Here's a simulator that was "trained" on a bit of content. Have a play!





      hey does anyone know how to fix the build
      i think |


  wethethat



We talked about this as if it were a "Me-bot". We knew it was recommending words based on our individual usage patterns, and we could see our voices in our personalized recommendations.

At the time, we were happy to dismiss it as tech magic. I don't think we realized how simple the algorithm might be.

Keep reading if you want to build one with me :)

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SECTION 2: Training

## "Training" Your Model

Let's train on a handful of messages. All we need to do is tally the connections between words. Let's do this one message at a time.


  1. "i think we should probably ship it"2. "i think that sounds good"3. "i think we should probably wait"4. "we should check with the team"5. "that sounds good to me"
  + Add message 1



  ### The Transition Matrix

  Add messages above to start building the matrix.




This finished map of connections between words is called a frequency table. Normalize each row and you get a probability distribution of what comes next.

The act of picking a next word based on what you have so far is called sampling. We use that same term for this process with modern language models like Claude.

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SECTION 3: Sampling

## Do Some Sampling

Using the same matrix based on 5 texts, go ahead and have a more informed play at our game. We'll show you the probabilities.


  i _


      think
      100%




The highlighted row is your current context. Pick a word from the available choices to continue.

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SECTION 4: Scale

## Scale it up

Five messages gave us a tiny matrix and a handful of predictions. What happens with more data?



    + 1 message
    + 10
    + 50
    All 222


    5messages
    17unique words
    13contexts
    24transitions
    2max options



    After "probably""should""think":



    ship _50%_


    wait _50%_

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SECTION 5: Knobs

## The knobs

When you were sampling, you could see probabilities, but you also used your instincts about which words "felt right."

If you had to write code to make those choices instead of using your gut, what encoded rule do you think would create the best result?



     Always pick the highest-probability word
     Pick semi-randomly, according to probabilities
     Pick according to probabilities, but also boost the most likely choices
     Ignore anything below a certain probability threshold
     Only consider the top N options
     Goblin mode — ignore the probabilities and pick something random

  Show me the knobs

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SECTION 6: Bridge

## The bridge

The sampling strategies you just used are more or less the same sampling constraints that developers pass to Claude. For LLMs, a few things differ.


  Markov chain
  LLM


    1 Read context
    last word: **"think"**


    1 Read context
    entire conversation so far



    2 Compute distribution
    look up one row in a table


    2 Compute distribution
    forward pass through billions of parameters — attention, embeddings, feedforward layers, residual connections, layer norms...



    3 Sample next token


        we _32%_
        the _16%_
        i _11%_




    3 Sample next token same process


        we _32%_
        the _16%_
        i _11%_





The Markov table lookup is a really simple and explainable operation. A forward pass through a neural network is quite a bit more complex. But in either case, the output is the same: a probability distribution of likely next words or tokens.

While sampling is the same, training is radically different. The exponential wall from before (vocabularyN rows) doesn't apply. LLMs trade the explainability of simply tallying words for far more context and far greater capabilities.

SECTION 7: Closing

## 100-year-old Tech

"Is this real tech?" Great question, reader.

Markov published this idea in 1906. A century later in 2010, n-gram models like this were powering next-word prediction on your phone (SwiftKey, then Apple's QuickType). Around 2015, neural networks — first RNNs, then transformers in 2017 — began to replace the table lookup approach with a learned function, and the rest is... well, it's what we're working on now.