Alex Strinka

There are two kinds of eclipses. A lunar eclipse in when the Earth casts a shadow on the Moon, making the Moon appear dark. A solar eclipse is when the Moon casts a shadow on the Earth. The people who are in the shadow will the see the Moon block the Sun, making the Sun dark. The picture above is one I tookd during a total solar eclipse.

In my previous post, I said that a full moon is when the Earth is between the Sun and the Moon. And as you might expect, a lunar eclipse can only happen during a full moon. But we get a full moon about once a month, and lunar eclipses only happen about twice a year. Why isn't there a lunar eclipse every month?

The explanation requires some 3D geometry, which can be hard to visualize. So, to help, I've made some interactive 3D models. To start, here's a model showing the Earth's orbit around the sun. You can click and drag to rotate it. Note that it's not to scale to make it easier to see. The grid is just to visualize the plane that the orbit lies on.

The Earth moves around the Sun in a circle, with the Sun at the center. (Technically, it's not actually a circle and the Sun isn't quite at the center, but that's a close enough approximation for now.) That circle lies on a plane, called the ecliptic. The ecliptic doesn't move, at least not significantly.

The Moon orbits the Earth on a circle too, but the plane of the Moon's orbit doesn't line up with the plane of the Earth's orbit. This is called the inclination of the Moon's orbit. You can adjust the slider to see how different inclinations look. The actual inclination of the Moon's orbit is about 5 degrees.

You can see how when the Moon is just slightly inclined, it's possible for it to be on the far side of the Earth, but not in Earth's shadow. But now, you might be wondering, how can there ever be an eclipse?

Well, as the Earth moves around the Sun, the plane of the Moon's orbit changes very little. (A process called nodal precession causes the plane to spin around the Earth, but it happens slowly.) This next model shows what the Moon's orbit looks like as the Earth moves around the Sun.

If you adjust both the Earth's and Moon's positions to 90 degrees, you can see the Moon will be in Earth's shadow no matter its inclination. This is why we get about two lunar eclipses per year.

This model also helps demonstrate why solar eclipses are less common than lunar eclipses. Since the Moon is smaller than the Earth, it has to be that much closer to being perfectly lined up. Furthermore, the Moon's shadow can't cover the entire Earth, so only a small portion of the Earth can see a solar eclipse when it does happen.

Because the above models aren't to scale, they might give the wrong impression about the actual sizes and distances of the solar system. So the next model is the same as the last one, except it's to scale. If you can't see anything, zoom in.

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.

Image source

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.

Image source

“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.