Long-form explorations
Essays
Ideas are more interesting when their boundaries begin to blur — especially over chai.
Applicatives in Pictures
From fmap to <*>: combining independent values that live inside a shared computational context.
Basis: Choosing Coordinates for a World
A basis is not the vector space; it is the coordinate language we choose to describe it.
Biscuits in Tea
A small manifesto for attention, curiosity, chai and the dangerous few seconds between a crisp biscuit and surrender.
Cosine Similarity: When Angle Becomes Meaning
Normalize the dot product and vector angle becomes a practical measure of similarity.
Covariance: How Variables Move Together
From scatter clouds to covariance ellipses, principal directions and positive semidefinite matrices.
Eigenvectors: Directions That Refuse to Turn
Some directions survive a linear transformation without changing direction. Those are eigenvectors.
Information Geometry: When Probability Distributions Become Points
A first walk through statistical manifolds, Fisher information and the geometry hidden inside probability.
Linear Transformations: Functions That Respect Geometry
See matrices as machines that transform entire grids rather than as rectangular tables of numbers.
Monads Without Mysticism
A practical visual introduction to >>=, do-notation and sequencing computations whose next step depends on the previous result.
Projection: The Shadow of a Vector
Orthogonal projection turns the intuitive idea of a shadow into one of linear algebra's most useful operations.
Word2Vec: When Words Acquire Geometry
How prediction turns words into points, neighborhoods and surprisingly useful directions.
The Most Important Cup of Tea in the World
Zen, attention, and the radical possibility of doing one very ordinary thing completely.
The Biscuit at the Bottom of the Cup
A very small meditation on impermanence, attachment and why every biscuit eventually loses an argument with hot chai.
The Mathematics of Dunking a Biscuit
Capillary action, porous structures, competing timescales — and the quest for the perfect dunk.
Why Functions Are Values
The first great Haskell idea: functions can be named, stored, passed around and composed like any other value.
Functors Visually
A visual and practical introduction to fmap: transform the contents while preserving the surrounding structure.
The Map Is Not the Territory
A compact reminder that every diagram, theory and mental model leaves something out.
All Models Are Wrong
Why imperfection is not a failure of modelling, but the condition that makes models usable.
Words Become Geometry
The surprising idea behind Word2Vec: words used in similar contexts become neighbours in an invisible space.
The Geometry of Roughness
Mandelbrot’s invitation to see mathematical form in clouds, coastlines, bark and lightning.
Why the Dot Product Knows the Angle
Projection, cosine and the geometric meaning hidden inside a familiar algebraic operation.
A Raag as a Space of Possibilities
A musical form is not merely a scale; it is a constrained landscape of movement, emphasis and return.