Why Aoliba exists
Aoliba is for people who want the map before the chapter. You look up a model by the question and the scale, then see where that model stops being good enough. Proofs and data still live in textbooks and papers.
The name
Aoliba stands for An Open Library Archive. The letters are the argument.
The three middle letters are not padding: lib is the root of library
(Latin liber, book) and the name of the repository's web/lib/,
where each model's implementation lives.
Open — the door is open
No sign-up, no install, no build step. More to the point, no pretence that every question is settled: the atlas keeps a whole layer called “cracks”, where the answers are still missing.
Library — sorted shelves
A library never asks you to read it cover to cover. Seven branches are the shelves, three layers are the floors, and the model map and picker are the catalogue.
Archive — a kept record
What separates an archive from a shelf is time. Every model carries its evidence, its verification date and its sources: checkable, and destined to age.
Open door, sorted shelves, kept record.
A table of contents says what exists. A scale says when to use it.
Courses split mechanics, electromagnetism, thermal physics, and quantum theory into chapters. They rarely put “when do I change the model?” on one page. Aoliba sorts the same material by question, precision, and dimensionless ratios.
This method is not ours
How Aoliba decides when to change models comes mainly from Sanjoy Mahajan’s tradition of approximate reasoning. In Street-Fighting Mathematics (2010) and The Art of Insight in Science and Engineering (2014) he turned divide and conquer, easy cases, lumping, dimensional analysis, and successive approximation into a practice you can train: get the order of magnitude cheaply first, then decide whether precision is worth buying.
This site follows that line: criteria are written as dimensionless numbers you can compare (De, Rm, Pe, S/ħ), every hand calculation on these pages estimates before it computes, and a model’s failure condition comes before its range of use.
What is not his: the three-layer map (foundation, cracks, in progress), the four kinds of relation between models, and the way verification status and error budgets are recorded. Those are built here, and the map form also follows the older tradition of public maps of science. The split is written out so that neither his work nor ours is credited to the wrong party.
Thanks to Sanjoy Mahajan for writing these methods down as something trainable. His course and textbook are public on MIT OpenCourseWare: The Art of Approximation (6.055J) and The Art of Insight, online edition (CC BY-NC-SA 4.0).
What you will not get here
No quizzes, no required order, and no attempt to hold every derivation. You get model limits, the relation between neighboring models, and a few demos you can drag. The calculation that has to be signed still comes from a book or a paper.