No matter what I study, I can see patterns. I see the gestalt, the melody within the notes, in everything: mathematics and science, art and music, psychology and sociology.
—Ted Chiang, Understand

Gestalt.ink is intended as a repository of general knowledge, focusing on mathematics, machine learning and physics. Its first aim is to provide an overview which is encyclopedic in style and which allows the reader to jump in at arbitrary points. Each topic is discussed using minimal preliminaries, and with the required preliminaries spelled out explicitly.

The second aim, and this is where the name comes from, is to provide understanding through different perspectives. Often, a subject like eigenvectors is explained using one derivation only. For instance: an eigenvector is a vector whose direction doesn’t change. While this is accurate and useful, there are many different ways to arrive at the same idea, and many different contexts in which eigenvectors can be used. A true understanding of what eigenvectors are, comes only after you’ve followed a few of these derivations.

This is what we’ll call a gestalt understanding: the understanding you get only from having seen different perspectives on the same thing.

A complete article will aim to provide such an understanding in a self-contained way. We’ll always start with an executive summary, so if all you need is the basics, you can get them quickly. But, ideally, the longer you keep reading, the more insight you get.

Guiding principles

The following principles guide our approach to most subjects.