The modern musical scale is seven notes spaced unevenly. Why seven notes? Why are they spaced unevenly? The reason is because we need to include the most important harmonic aside from the octave: the fifth.

It seems like a great idea, but even the most notable immediate-mode GUI turns out to be retained-mode under the hood.

After thinking about the nature of Civilization in my non-standard definition, I have come to the conclusion that the problem of creating Civilization is one of the things Christianity is concerned with.

Rationally, the Four Spiritual Laws gospel seemed like it ought to be good news, but it never actually felt like it. Now I think that is because it is only a piece of the original gospel. Certainly not in a universalist way, but rather it is missing the depth and context that make it good news.

I present an algorithm for subsampling with a non-integer step and compare execution time with two other common algorithms.

During the coronavirus pandemic many conservative Christians have been upset that wearing a mask is trampling their rights. Jesus was God, and he did not demand his rights to reverence, worship, and obedience, but came to serve. The way of Jesus is giving up our rights and serving others.

Struggles getting my app icon to show up on macOS 10.13 using CMake resulted in this documentation of the app bundle and Info.plist file.

This is a collection of C++ libraries I have discovered that I'm probably going to forget about before I need them, so I'm writing them down.

Today I implemented a simple login screen, the kind any app is going to have.  It took me most of the day.  It's surprising how much there is to consider.  And despite being a software developer for twenty years, I still found a few things I forgot as a result of writing this up!

Outlining a 3D object is harder than you'd think it ought to be, and one of the common suggestions produces terrible results. The solution is to render the object into a texture and post-process the results on top of the scene.

Bezier curves always sounded like something only mathematically-minded, skilled professionals who wrote Path Routines for operating systems could implement. It turns out that the reason they are used so much is they are so simple. I show how to evaluate Bezier curves and surfaces, and provide code to generate the Utah teapot.

Native English speakers think that English is phonetic, that is: look at a word and you know how to say it; say and word and you know how to write it. Well, read some third grade papers, or talk to someone who had to learn English as a second language. It's just not true.

Why did God create family? Family is so fundamental to our lives that we never think to question it, but wouldn’t it be so much more efficient if it did not take 20 years of nurturing to produce an adult?

I have always been kind of sympathetic with the Pharisees. When I read the Old Testament, Jesus does not look like the Messiah I would expect after reading the descriptions, and the prophetic passages often seem to be recognizable as a Messianic prophecy only after the fact.  So why was it that Jesus expected the Pharisees to recognize that he was the Messiah?

What is the goal of the Christian life?  I mean, what are we doing this Christian life for, and how will we know if we succeed?  Until I thought about writing this article, I had never formally asked the question, yet all Christians have an answer to this question lurking back there somewhere.  Our answer to this question will drive our lives on a fundamental level, so it behooves us to actually ask this question.

While I was on the ministry line today at church, three college-age girls came up for prayer as they each go back to their non-believing families who are opposed to their faith.  They didn't give details, but it was clear that the relationship is a struggle.

Charismatics say that hunger "pulls down from heaven." But what is spiritual hunger, exactly? How do you get it, and how would you create it in others?

The Creation story tends to get interpretted through our opinion of how old we think the Earth and the Universe are. If we set aside our assumptions and use proper hermeneutics, we get a different result than either of the two main competitors.