Area and volume of hypersphere cap

A spherical cap is the portion of a sphere above some horizontal plane. For example, the polar ice cap of the earth is the region above some latitude. I mentioned in this post that the area above a latitude φ is where R is the earth’s radius. Latitude is the

Random points in a high-dimensional orthant

In high dimensions, randomly chosen vectors are very likely nearly orthogonal. I’ll unpack this a little bit then demonstrate it by simulation. Then I’ll look at what happens when we restrict our attention to points with positive coordinates. *** The lengths of vectors don’t contribute to the angles between them,

Better Programming Monthy Reads — Issue #94

Better Programming Monthy Reads — Issue #94Hey everyone,Hope your August is off to a good start. Last month, we saw the overhaul of the Medium Partner Program, which included stronger incentives for quality-focused writing, the sunset of the referral program, the removal of the 100-follower requirement as a prerequisite, and more. Medium’s Buster

What Is “Production-Grade” Software?

We’ve all seen the phrase “production-grade” software, but what does that actually mean? Are we setting our apps up for failure?One of my favorite things to do is build “proof of concepts”. They are quick little apps that show a business problem can be solved in a certain way. They’re quick

Jukebox Diffusion

An AI tool for conditional music generationCreated using Deforum Stable DiffusionIt hit me with a sickening severity one night. While I stood staring down at a sink full of unwashed dishes, a feeling of nausea overwhelmed me. I had spent the day chasing down a single elusive error in a

Strategy for Engineering Managers

What is the next move?A chess game generated using MidJourneyEngineering Managers (EMs) have their sights focused on execution and people. They are working to ensure their team is achieving its goals and that their reports are on the right growth path. And that is plenty. Keeping a team running smoothly while

Why Are We Arguing? 3 Tools for Structuring Conflict in Teams

Photo by Sarah Kilian on UnsplashA healthy relationship with conflict is at the heart of all high-performing teams (and organisations). It’s pivotal to setting principles, making decisions, and delivering value. But when conflict so easily intermingles with a plethora of social dynamics, it’s often squandered.Circular, high-level, and unactionable conversations are typically

Complete C# Masterclass

Cosine similarity does not satisfy the triangle inequality

The previous post looked at cosine similarity for embeddings of words in vector spaces. Word embeddings like word2vec map words into high-dimensional vector spaces in such a way that related words correspond to vectors that are roughly parallel. Ideally the more similar the words, the smaller the angle between their

What a truly engaged engineer looks like

Image generated using MidjourneyI think it is fair to say that at this point, we all know that the stereotype of an engineer coding in a dark room, burning the midnight oil, has become painfully outdated and ridiculous. We haven’t internalized in the industry, yet that engineering productivity is less