Visual mathematics

📖 Distill is back ;)

The Distill journal was founded as an adapter between traditional and online scientific publishing. We believed that many valuable scientific contributions — such as explanations, interactive articles, and visualizations — were held back by not being seen as “real scientific publications.” Our theory was that if a journal were to publish such artifacts, it would allow authors to benefit from the traditional academic incentive system and enable more of this kind of work.

A numerical tour of GP and BO (DRAFT UNCORRECTED)

Authors: Joseph Morlier and Claude
Published: August 2026

Summary: This article builds that idea from scratch and ends where a lot of real design optimization currently lives: Bayesian Optimization — using a Gaussian Process not just to predict, but to decide where to sample next under a tight budget. Every figure below is generated by the same code as the source notebooks (linked throughout), and the two boxed panels are fully interactive — drag points, change kernels, click to sample a “black box,” and watch the algorithm choose its next move.

Everything on Ashby’s maps (DRAFT UNCORRECTED)

Authors: Joseph Morlier and Claude
Published: September 2026

Summary: Michael Ashby’s material-selection charts turned an abstract optimisation — choosing the best material for a function — into something an engineer could see: two properties on log–log axes, a guideline of the right slope, and the winning family lights up. This is Part 1 of a two-part note. It follows that idea through two more generations — a multi-objective value function for when one chart is not enough, and an eco-cost axis that turns the same method toward sustainability — and stops exactly where the two-dimensional chart itself starts to run out of room. Part 2, “Ashby’s Maps, Renewed,” picks up from there with a generative, learned alternative.

Ashby’s maps renewed (DRAFT UNCORRECTED)

Authors: Joseph Morlier and Claude
Published: August 2026

Summary: Part 1, “Ashby’s Maps,” followed Ashby’s method through a single log–log guideline, a multi-objective value function, and an eco-cost axis — three generations that all still ask a human to pick the axes, and all still top out at two or three properties before the picture stops helping. This second part removes that ceiling by training a variational autoencoder on the same material database and replacing “read a slope off a chart” with “follow a gradient through a learned, continuous space.” The same trained network, unchanged, then answers any material index by gradient ascent — validated case by case against the classical answer, on the two baseline structural cases worked by hand in Part 1 and on thirteen further cases beyond them.

Weight, Drag, Thrust, Range (DRAFT UNCORRECTED)

Authors: Joseph Morlier and Claude
Published: August 2026

Summary: In one sentence: TASOPT treats an airliner not as a set of weight fractions looked up from history, but as a coupled system of beam-theory structures, viscous-flow aerodynamics, and a real turbofan thermodynamic cycle, all closed by a range equation — solved together, iteratively, until the airframe, the engine, and the mission agree with each other. This page walks through each piece of that loop in the order Drela’s technical description builds it, with small interactive calculators dropped in wherever a slider teaches more than a paragraph. A companion Jupyter notebook turns the same equations into running Python code and sizes a 737-800–class narrowbody from scratch.