Alex Strinka

Stack Of Doom
A screenshot of Civilization IV

This post is about Civilization IV, a computer game that's over fifteen years old, and has had two director successors. As always, I strive to maintain my reputation for tackling topical issues.

First, a recap of the relevant game mechanics. In Civ IV, different types of military units get various bonuses. For example, a spearman gets a bonus against mounted units, so in a battle between a spearman and a chariot, the spearman will usually win. An axeman gets a bonus against melee units, so in a battle between an axeman and a spearman, the axeman will usually win. And a chariot gets a bonus when attacking axemen, forming a nice rock-paper-scissors setup.

Furthermore, you can stack multiple units on the same tile. Every unit still moves and fights individually though. When you attack a stack of units, the unit that has the highest chance of victory will defend. So, say there's a stack consisting of one spearman and one axeman. If you attack it with a chariot, the spearman will defend. If you attack it with a spearman or an axeman, the axeman will defend. As you can see, well-composed stacks of units are difficult to attack.

And there's no limit to the number of units you can have in a stack, so generally, it's most effective to put all of your troops together in one giant stack, making what's called a "Stack of Doom". Unless there's a significant tech difference, the only way to reliably counter a stack of doom is with another stack of doom. This is understandably frustrating, and it can make combat a little bit uninteresting.

Civ V dealt with this problem by introducting "One Unit Per Tile". You can only have one single military unit in a tile. In my opinion, One Unit Per Tile is far worse than Stacks of Doom, both from a gameplay perspective and from a realism perspective. Here's an article that talks about some of the problems with One Unit Per Tile.

Here are my ideas for how to fix Civ IV's Stack of Doom:

  1. More collateral damage. Typically, when you attack a stack of units, only the one defending unit takes any damage. But some units, like catapults and cannons, and also the Chinese unique unit do collateral damage, which means they can do damage to other units in the stack. My first suggestion is to simply make more units inflict collateral damage, and make collateral damage more harmful.
  2. More targeting. Targeting is a concept that exists in Civ IV, but is only used by a single unit. The Khmer unique unit is the ballista elephant. Like standard war elephants, it gets a bonus against mounted units, but unlike any other unit in the game it targets mounted units, which means that if it attacks a stack with any mounted units, one of the mounted units will be the defender. My second suggestion is to make more units have this ability.
  3. Flanking. This is a new concept that doesn't exist in Civ IV. (There is a concept with the same name, but that's just a special version of collateral damage.) The idea is that if you attack an enemy unit, and there's a friendly unit directly adjacent to the enemy, but not on the same tile as the attacker, then the attacker gets a bonus.
  4. Attacks of Opportunity. This one I'm less confident about. It's another concept that doesn't exist in Civ, but it is related to Zones of Control, a concept that existed in Civ I and II. In those games, if you had a unit that was adjacent to an enemy unit, you could attack or you could retreat, but you couldn't move your unit to another tile that's also adjacent to an enemy unit. It was really restrictive, which I think it why it was removed in later games. My idea here is to reintroduce that, but less restrictively. You can still move around an enemy unit, but doing so would give the enemy an attack of opportunity. In other words, they would get a free shot at your unit, and your unit wouldn't get a shot at them.

All these suggestions are intended to work with Civ IV's existing combat system, but they would require making other changes for balance. The existing units that do collateral damage and targeting would need to be buffed in some way to distinguish them. And since defending a city requires putting a stack of units in it, there would need to be a way of countering these abilities in a city. Perhaps defensive structures like walls and castles could reduce or nullify these abilities. You would probably also need to change the costs, strengths and abilities of various units, and maybe add and remove some.

Sturgeon's Law

According to Theodore Sturgeon, "Ninety percent of everything is crap". I think that's worded a bit too strongly. I would say something more like, the majority of everything is low quality. Of course, there's no objective way to evaluate quality, but I think that's true in most cases, by most standards.

Why is this? I think it's because there are far more ways for a work to be bad than for a work to be good, and it takes skill to reliably produce quality work. It's like a dart board. Most throws won't hit the bullseye, unless you're really good at darts.

Some individuals are particularly skilled, and produce mostly high quality work. Ninety percent of plays may be crap, but not ninety percent of plays written by Shakespeare. And more generally, while the majority of everything is low quality, a carefully selected subset of everything doesn't have to be.

I think this is part of the reason some people perceive recent works as being worse than older ones. When you look at old books, movies, music, etc., you typically find the ones that we still read, watch and listen to today. When you look at recent books, movies, songs, etc., you're more likely to see a representative sample. The latter will be worse, but only because it hasn't been winnowed by time.

A seemingly paradoxical implication of this law is that by increasing output, you increase the amount of both low quality work and high quality work. The relative proportion doesn't have to stay constant, though. In fact, it could move in either direction. For example, the proportion of high quality work can increase by an artist getting more skillful through practice. Or it could decrease by removing a selection barrier that had been in place before.


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.

This interactive 3D model requires javascript to be enabled.

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.

This interactive 3D model requires javascript to be enabled.

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.

This interactive 3D model requires javascript to be enabled.

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.

This interactive 3D model requires javascript to be enabled.

Why does the Moon have Phases?
The phases of the moon

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.

Is a Hot Dog a Sandwich?
A hot dog

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?

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