Alex Strinka

Look at the Moon, and you’ll see that it changes over time. It goes through phases, in a regular cycle. New, crescent, half, gibbous, full, gibbous, half, crescent, and back to new.

It's a common misconception that the phases of the moon is caused by the shadow of the Earth. While the shadow of the Earth does sometimes darken the Moon, that's called an eclipse and it only happens a couple times a year.

So, what does cause it? The short answer is that it's our perspective of the illuminated half of the moon as it moves around us. Perfectly clear, right? Let's break that down.

First, the Moon doesn't generate its own light. It's illuminated by the sun. Here's an experiment you can do at home. Take a ball, go into a windowless room, and turn on a single lamp. Notice that the side of the ball that's facing the lamp looks brighter than the half that's facing away. The side that's facing away isn't completely dark, because there's light bouncing off the walls, but there are no walls in space. The Moon is lit up by the Sun in the same way as the ball is lit up by the lamp.

Half of the Moon is lit up, and half is dark. That's always the case, even during the full moon (except during an eclipse). So, why doesn't it always look like it's half lit up?

Go back to the ball in the room. If you stand between the ball and the lamp (but without getting in the way and casting a shadow) and you look at the ball, what do you see? The illuminated half of the ball. You can't see the dark half, because it's on the other side of the ball.

If you stand so that the ball is between you and the lamp, then you can only see the dark side, because now that's the side that's facing you. And if you stand off to the side, you can see part of the ball that's illuminated, and part that's dark.

Here's a diagram of what I just described. The light source is the yellow circle with rays on the right. The half of the ball facing the light is illuminated. The half facing away is dark. There are three observers. A only sees the light half of the ball. B only sees the dark half. C sees half of each.

Of course, the Earth doesn't revolve around the Moon. the Moon revolves around the Earth, but the principle is the same. When the Moon is between the Earth and the Sun, we see the dark half, so it's a new moon. When the Moon is on the other side of the Earth, we see the illuminated half, so it's a full moon. When the Moon is off to the side, we see some of each.

An implication of this is that you can't see any phase at any time of day. You'll never see a crescent moon at midnight, for example. Because in order for the Moon to appear crescent, it has to be closer to the Sun than the Earth, and at midnight, you're facing directly away from the sun. A full moon rises as the Sun sets, and sets as the Sun rises. A new moon rises and sets at about the same time as the Sun.

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Well, what is a sandwich?

I’m sure you can come up with a reasonable definition, and many people have, but is that definition really what you have in mind when you think of a sandwich? Is that definition the way you first learned to identify a sandwich, or did the definition come later, based on a concept you were already familiar with?

For me personally, I don’t determine if something is a sandwich by checking if it meets a given set of necessary and sufficient conditions. I just check if it’s like a sandwich.

In the philosophy of language, there are two types of definition: intensional and extensional. Intensional definitions are the kind we normally talk about, a concise set of necessary and sufficient conditions that determine whether something is a member of a category. Extensional definitions are given by pointing out specific examples and hoping that you can figure out the connection between the examples.

Intensional definitions are great, because they’re easy to communicate, easy to check and unambiguous. But extensional definitions are what we use for most of the concepts we use daily. What’s the definition of a door, a chair, a car, a cat? You can come up with intensional definitions for those things, but they’ll almost certainly include things that aren’t in the category, exclude things that are, be difficult to apply, or all three.

This is the basic idea behind exemplar theory, which says that we evaluate whether an object belongs to a category by comparing it to known examples of that category. Under this paradigm, you might say that a hot dog is a non-typical member of the sandwich category. Or, depending on your understanding of exemplar sandwiches, maybe you’d say that a hot dog is a somewhat sandwich-like non-sandwich.

But more importantly, what’s the point of the category in the first place? A whale is a mammal, not a fish, and that’s an important distinction to a biologist studying phylogeny. But if you’re a fisherman, maybe all you care about is whether it lives in the ocean, in which case it would make sense to group fish and whales together, both separate from horses. Neither category is wrong, they’re just more or less useful to certain applications.

So, what’s the point of the sandwich category? What are you going to use the answer for?

If you don’t know algebra, it will be hard to learn calculus. If you don’t know arithmetic, it will be hard to learn algebra, and even harder to learn calculus. That’s because calculus builds on the concepts of algebra and arithmetic, and you can’t build on a concept you’re not already familiar with. This is the basic idea behind inferential distance.

The problem of inferential distance applies to, well, just about everything. Almost everything you know, every idea you have, relies on simpler concepts. Even something simple like “France is a country” relies on simpler concepts, like what the word “country” means and what it means for something to be a country.

This is one of the biggest difficulties of explaining something. In order to explain something to someone, you need to build off the concepts they already have and start with the most basic concepts they don’t already have. To do that, you need to figure out which concepts are which.

That’s not always easy, because some of the concepts you already know might seems so obvious to you that you don’t realize you need to explain them. If you’re trying to explain Newtonian physics to a flat-earther, you might not realize you need to explain what the word “down” means.

It’s even harder when you’re writing a blog on the internet, trying to explain something to a faceless audience. Everyone has a different set of concepts they’re starting with, so no single explanation will work for everyone. If you start with concepts that are too advanced, then you won’t reach people who don’t already know the starting concepts. And if you start with concepts too simple, you’ll come across as boring or condescending to other people.

What’s more, for many topics the foundational concepts might not be straightforward facts, but controversial opinions. For example, utilitarian and deontological ethics are based on two very different ideas of what the words “good” and “right” mean. In such cases, it’s very common for people to talk past each other, because they don’t realize their basic assumptions are different.

Fruitful communication relies on finding and bridging that inferential distance. I don’t know of any reliable way of doing that. My only advice is listen and don’t assume you know what your interlocuter means.

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“Don’t reinvent the wheel” is the standard advice. And I think that it’s usually good advice. Most of the time, it’s a waste of time and effort to redo something that’s already been done, if you can just reuse the existing thing instead. Most of the time, but not always. As I said in my introduction, sometimes it’s good to reinvent the wheel. Here I'll discuss some of the reasons to do so.

One of the best reasons is for learning. That’s the primary reason I’m doing it with this blog. The best way to learn is by doing. Studying how someone else achieved something is great, but by doing it yourself, you’re forced to engage with it at a deeper level, which gives you a better understanding of what goes into it.

Another reason is if the existing wheel doesn’t do what you want it to do. In this case, it’s still usually better to start with what already exists and figure out how to modify it to fit your needs. But sometimes you just need to restart from the ground up. A good example of this is git. Linus Torvalds created git because none of the existing source control management systems that existed at the time met his needs, so he built his own.

Reinventing the wheel can also mitigate the risks of having a monoculture. In agriculture, it’s common to grow a single species in a field. This is efficient, but also fragile. If there’s a disease, it can easily wipe out the whole field. This idea applies to technology too. For example, if many people use the same operating system, it’s easier to develop software that they can all use. But if that operating system has any vulnerabilities, then everyone who uses it is exposed in the same way. Having multiple co-existing systems can also be beneficial by encouraging competition and enabling cross-pollination of ideas. In this case, the benefit of reinventing the wheel is not just for the person or organization doing it, but for the community as a whole.

All of this is from the perspective of software development, where reusing existing technology is especially easy, but I think these same basic ideas apply to other fields too.

I made this animation a few months ago. To be clear, I just made the animation. The music is Chance by Kai Engel.

I've been interested in geometric art since high school, which is why I made AlDraw. Animated geometric art is a fairly natural step further. It's a step I took a long time making, because animation is complicated and hard.

I decided to make something like this while listening to Daft Punk's Motherboard. I didn't make an animation for that song for reasons of copyright. Fortunately, there's the Free Music Archive, which is where I found Kai Engel's work. I already used that site to find music for my timelapse videos. Fortunately, this song is perfect for this kind of animation.

I made the animation using SVG animation. Most image formats, like PNG, JPG and GIF are raster based, which means they store an image by encoding the information about the color of each pixel. SVG on the other hand is vector based, which means it stores the image by encoding information about geometric objects, for example by specifying the endpoints and thickness of a line. That makes it ideal for the kind of geometric designs you can make with AlDraw, and the kind of geometric shapes this animation uses.

Likewise, most video formats store an animation by storing discrete frames. SVG animation works by letting you specify how a value varies over time. For example, you can say that a line that extends from (x1, y1) to (x2, y2) at time t1 moves to (x3, y3), (x4, y4) at time t2, and between t1 and t2, the values will be interpolated. So, SVG animation is a natural choice for making a geometric animation like this.

Unfortunately, SVG animation isn't widely supported. Most browsers will display them, but they don't include any kind of playback controls. I don't know of any video players that can play SVG animations, and even most SVG editors don't support SVG animation. So, what I wanted to do was write the SVG and then convert it into a more common video format like MP4.

But there's no software that does that. Or at least, there wasn't. So I made my own. That code is pretty bad. It's inelegant, it's inefficient and it doesn't support half of what SVG animation can do. But it's enough to make this video. Someday, I might work on improving and expanding it.

As for actually writing the SVG, and in particular, timing everything just right, that was a lot of hard work. I used an audio-editing application called Audacity to see the exact timing of each note. My wife, Molly, helped too.

You can download the SVG file here.

All told, I spent about five months working on it. About two just on the svg-to-video program, and about three on the animation itself. I didn't keep track of the amount of time I actually spent working on it, but it was probably something around 200 hours.