Articles

Notes on optimization, machine learning, finance, and mathematical curiosities.

Essays, research notes, and visual experiments collected over the years, filed by category — from inventory control to mathematical side paths.

Article Series

Value Chains

How value chains evolve: where the cost hides, who ends up owning the bottleneck, and what changes when the cost of a thing falls toward zero — money is the worked example.

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Evolution of Value Chains

The Law · Jun 14, 2026

The Selection Pressure: How Cost Decides Which Value Chains Survive

Every value chain is the path a human want travels from unmet to met, and at every link sits a cost. Chains evolve by selection: the cheaper, faster way of serving the same want survives and becomes the next link. The want is the constant; cost is the agent of change; the rent always relocates to whichever cost has not yet fallen — including, at the end, the human ones.

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The Evolutions · Jul 11, 2026

Fourteen Journeys: How Value Chains Actually Evolve

Fourteen industries did not travel through the same three stages. This is an evolutionary atlas of the routes they actually took—from knowledge and music to food, money, transport, and virtual worlds—and where each stands in 2026.

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Money

Category

Optimization & Learning

Algorithms that learn to decide — stochastic optimization, evolution strategies, and reinforcement learning applied to real operational systems.

Category

Mathematical Curiosities

Short mathematical side paths and visual experiments, followed for the joy of the detour.

Category

Research & Teaching

The academic record — where my research has been, where it is heading, and how I think about teaching.