Turing Machines are the classic formalization of computation, later followed by many others. In this post, I will show how to represent any Turing Machine as a nonlinear operator on an appropriate Banach space. Along the way, we’ll find interesting interpretations of things like the Halting Problem as well as connections to a cool part of Dynamical Systems theory¹.

The purpose of this post is to provide a somewhat opinionated guide to doing scientific research (mostly in machine learning) for people outside traditional research institutions. There are already several excellent guides on writing papers and how to work on research projects (see below), so I aim for it to be a complement to those that can still serve as a standalone guide. Specifically, this guide covers “basic” concepts that I’ve often seen people confused about. The last section also contains links to various tools and resources.

During the holidays I worked on a small project to make posters for a computer room in my university. Since this was essentially an exercise in artistic creativity, I thought I’d document the process of making these, as I think this is often omitted despite being (for me, at least) the most interesting part of the creative process.

Mathematics is often seen by outsiders as an austere discipline of pure reason. The goal of this post is to present an interpretation of mathematics as literal magic. More precisely, the practice of mathematics bears striking similarities (vibes) to the magical tradition known as goetia, or sorcery.

Most of modern mathematics, and as a consequence, science at large assume the existence of real numbers, pretty much as a postulate¹. Given how successful both of these have been, it might seem odd to challenge it. However, when one takes a closer look at exactly how real numbers are defined, a couple of philosophical issues arise. In particular the fact that we (mere mortals) can only meaningfully interact with countably many of them, so that almost all real numbers are beyond our grasp. The goal of this post is to articulate this problem in a mostly self-contained and accessible manner, by constructing the real numbers from the ground up, and then discussing some philosophical consequences of the previously stated fact.