About

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.

• Short to long. The assumption is always that somebody is reading with a purpose. They want to understand some subject in order to use it (possibly in some other gestalt article, possibly somewhere else). This doesn’t mean no long, careful explanations, it just means they should be preceded by shorter ones.
• Minimal and explicit dependencies. We will minimize as much as possible, how much you already need to know to understand an explanation. We will make all dependencies explicit, ideally including links to other articles. Where necessary we will re-explain required concepts in the context of the current article.
• From concrete to abstract. We will start with the most concrete form of something. For instance, we will explain linear algebra subjects using real-valued elements, abstracting to complex numbers of to general fields only later. This doesn’t mean we don’t deal in abstractions, just that we start with concrete examples and then abstract.
• Alternative perspectives. For topics that are well-covered elsewhere, we will try to offer a different way of looking at them. That is, we will not pretend that other text books and tutorials don’t exist. Instead, we will focus on what hasn’t been said about these topics yet.
• No popups, no payment. These articles will be free, there will be no ads, and they will be served in clean, minimal HTML.