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$\newcommand\F{\mathbb{F}}\newcommand\R{\mathbb{R}}\newcommand\C{\mathbb{C}}\newcommand\Z{\mathbb{Z}}\newcommand\tr{\operatorname{trace}}\newcommand\End{\operatorname{End}}$ The trace of a sqaure matrix $A$ is defined to be the sum of the elements along the diagonal. A basic fact is that for any invertible matrix $M$, \begin{equation}\tag{*} \tr(M^{-1}AM) = \tr(A). \end{equation} Let $V$ be an $n$-dimensional vector space over a field $\F$. The trace of a linear transformation $L: V \rightarrow V$ is usually defined as follows: Let $(v_1, \dots, v_n)$ be a basis of $V$. …

So you’ve got a log. Maybe its a tree that came down nearby, or maybe somebody heard you’re a woodworker and offered you a log. And you have a bandsaw. You start wondering if you can mill this log into boards yourself. Sure, you could invest in an Alaskan chainsaw mill, or you could try to find someone nearby who runs a hobby sawmill to cut it up for you. …

A long-form generative art project coming to fxhash in partnership with FAB DAO on 11th Jan 2024. This series is inspired, in the abstract, by the images I visualise when reading about quantum theory. Particularly thoughts of particles spreading out as waves and then collapsing into particles again at a moment of interaction. At the quantum scale, classical ideas of space and form come apart, replaced by concepts, probability and …

In the bustling world of Kotlin/Android development, maintaining code quality and consistency is essential. This is where linters come in, like shining knights cleaning up and polishing your codebase. But with a variety of linters available, each addressing different aspects, choosing the right ones can be like picking the perfect weapons for your coding quest.In this blog post, we'll delve into the realms of two popular Kotlin/Android linters: ktlint and …

This is an exceptionally long post detailing pretty much everything I learned at an event shortly before Christmas at Meta’s offices in San Francisco. I’ve been delayed in writing it up because of traveling back to the UK for Christmas and other commitments – and because I wanted to capture everything. It’s roughly written, and I’ll probably edit it a bit after posting. If you have questions or comments or …

The exhibition, ‘Part of the Furniture: The Library of John Bedford‘, which runs until 2nd December 2024, is focused on the library of furniture history, assembled by former antique dealer, John Bedford (1941-2019). University of Leeds The exhibition explores the … Continue reading →

Today was a good day. More of that this year, please.

These popped up on Mastodon, and they’re both clever and silly. I will explain them, but in white text so you can skip that part. The first one goes back at least five years; I don’t know the originator. Darth Vader goes into a bakery and orders three breads and two apple tarts. Why? PAIN PAIN PAIN TARTE TATIN TARTE TATIN Note: Read aloud, this sounds like the Imperial March. …

Create a stunning, 12” Jacob's Ladder Afghan Square with this free crochet pattern and stitch a breathtaking geometrical motif. The post X Marks the Spot: Make This Captivating & Fun Jacob’s Ladder Afghan Square Now appeared first on Jessie At Home.

A few years ago, we interviewed Jen Cardello for Finding Our Way, and she shared that her team (UX Research) is peered with “market research, behavioral economics, brand, and advertising research, and customer loyalty” in an independent Insights team. The idea was for research to avoid a functional bias, so that it couldn’t be “weaponized” by marketing or design. And while UX Research is still typically found within a UX/Design …

As you drive from Málaga airport through the Málaga mountains into the interior of Andalusia, just before the Antequera junction where the roads branch off to Seville, Córdoba and Granada, a compact cluster of houses looks down from a hilltop along the way. Traditional Andalusian white houses, standing shoulder to shoulder, coming together as a single closed settlement, as if they were preserving an old story. I give in to …

I had such fun making Rodd’s Trigg Shorts for New Year’s Eve that I decided to make another pair. I’ve had this chambray in my stash for a few years, thinking it might make a nice pair of shorts. And guess what? It does! I asked the Snook if I needed to make any size adjustments, and the only thing he asked for was a slightly bigger waistband when fully …

Each of the three stories collected in Weasels in the Attic is linked by the narrator and his friend Saiki sharing a meal, meals that seem to become a focal point for broader currents at play. The stories may appear quiet on the surface, but there is an unsettling sense of more going on (or perhaps more being meant) beneath that façade. In the first story, ‘Death in the Family’, …

Roadmap 2024 A lot of the podcasts I listen to, and quite a few of the blogs I read, encourage you to pick a touchstone word for the year. I’ve never done that before, but I’m going to try it this year. My word for 2024 is “Simplicity”. I’m going to try to use this word to guide my decisions and actions for the year, both in my personal life …

This morning, OpenAI launched the GPT Store: a simple way to browse and distribute customized versions of ChatGPT. GPTs – awkwardly named to solidify OpenAI’s claim to the trademark “GPT” – consist of a custom ChatGPT prompt, an icon, and optionally some reference data or hookups to external APIs. In the coming weeks, OpenAI will also start paying developers based on usage of their GPTs. While GPTs may prove useful …