For a while now the writing here has come in series: a set of posts that build one idea from the ground up, in order, until the whole thing stands. That format wants to be watched as much as read. A diagram that assembles itself, a value that moves through a pipeline, a bar chart of amplitudes that shifts when you apply a gate: these are easier to follow when they move. So I built a way to make them move, and the results now live on the metafunctor YouTube channel.
The videos are not a separate project. Each one is built from the same source material as the post it comes from, run through a from-scratch pipeline: Manim for the animation, narrated dialogue for the voice, and the code and math taken straight from the series text. A series landing page here embeds its full playlist, and each individual post embeds its own episode at the bottom, so you can read and watch in the same place without hunting for anything.
There are three playlists so far, twenty-seven videos in total. Here they are.
Algorithms Arise from Algebraic Structure
The Stepanov series, nine episodes: declare the algebraic structure a problem lives in, and the algorithms fall out for free.
Open the playlist on YouTube (9 episodes)
Episode list
- Algorithms Arise from Algebraic Structure
- One Algorithm, Infinite Powers
- Polynomials as Euclidean Domains
- Forward-Mode Automatic Differentiation via Dual Numbers
- Reverse-Mode Automatic Differentiation
- Semirings: One Algorithm, Six Graph Problems
- Homomorphisms: Fold Is the Universal Map
- Free Algebras: Why Lists and Polynomials Are Universal
- Lattices: Fixed Points and Tarski's Theorem
Next-Token Prediction: From Solomonoff to Transformers
The sequential-prediction series, eight episodes: what-comes-next as the foundation the whole language-model era stands on, traced from Solomonoff to the transformer.
Open the playlist on YouTube (8 episodes)
Episode list
- Why Predict the Next Symbol?
- Introduction to Sequential Prediction
- Solomonoff Induction: The Incomputable Ideal
- The Bayesian Prediction Framework
- N-gram Language Models: Counting and Smoothing
- Context Tree Weighting: Theory Meets Practice
- Neural Language Models: From RNNs to Transformers
- CTW vs. N-grams vs. Neural Language Models
Quantum Computing from Scratch, in Python
The quantum series, ten episodes: a working simulator built in NumPy from nothing, with a visual language of amplitude bars that makes interference something you can see.
Open the playlist on YouTube (10 episodes)
Episode list
- Why Build a Quantum Computer from Scratch?
- Classical Information First: The Coin Under the Cup
- What Is a Qubit? Building the First Gate
- Many Qubits and Entanglement: Tensor Products
- Circuits and Interference: Making Amplitudes Useful
- Grover's Search: Quadratic Speedup from Structured Interference
- The Quantum Fourier Transform
- Shor's Algorithm: Why RSA Has an Expiration Date
- Mixed States and the Density Matrix
- Noise, Decoherence, and Why Error Correction Is Hard
More playlists are coming, drawn from the other series on the site as I get the animation for each one right. If a series here has earned a place in your reading, it now has a version you can watch too. The plan is to keep the two in step: what gets written gets animated, and both stay pinned to the same source.
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