Tuesday, November 22, 2011

Extraordinary Evidence

"Extraordinary claims require extraordinary evidence" -Carl Sagan
Some people don't like this quote. They say it's too subjective. There's no objective standard of what's extraordinary. And other rather silly objections.

I would generalize the saying to be something more like this: "All claims require the appropriate amount or degree of evidence.".

The ordinariness/extraordinariness of a claim is not a binary feature, but rather a sliding scale. If I said I had eggs for breakfast this morning, that's a perfectly ordinary claim. You'd probably need no more evidence than my word to believe it. If I said I saw a zebra in my backyard, that's a little bit extraordinary, since they don't live anywhere near here. You'd probably need a photograph, or a news story about a zebra that escaped from a zoo to believe it. If I said I saw a unicorn, that's even more extraordinary. You'd probably need to see the real live thing to believe that. If I said neutrinos can go faster than light, that's even more extraordinary and will require lots more evidence. And then of course, there's always God, which is about the most extraordinary claim imaginable.

Another important thing to note is that belief too is not a binary value. Rather, it's degree of certainty. Probability. Which is nice, because that means this saying can be formalized by using Bayes' Theorem.

Bayes' Theorem is a mathematical formula that lets you calculate how probable you should consider a hypothesis after seeing some evidence, given your prior probability of that hypothesis, how likely you are to see that evidence if the hypothesis were true, and how likely you are to see that evidence if the hypothesis were false.

How extraordinary a claim is, is simply how low your prior for it was. This doesn't totally eliminate claims of subjectiveness, but it's no less subjective than any other belief, and if you're doing Bayes right, it's really a lot less subjective.

And how extraordinary evidence is, is simply how much more likely that evidence is to occur if the claim were true than if the claim were not true.

Going back to my examples, the prior probability for me eating eggs for breakfast is relatively high. You already know from past experience that eggs exist and that people commonly eat them for breakfast. So the evidence doesn't need to be very strong. I'm more likely to say something if it's true than if it's false, but lying isn't unheard of.

The prior probability of me seeing a zebra in my backyard is lower. You still know that zebras exist, but you also know they don't live in the wild here. So, on just my word, it might seem more likely that I'm lying than that I actually saw a zebra. The prior probability for the unicorn is even lower, because you already know they don't exist. A photograph isn't sufficient here because it's more likely that I faked it than that unicorns actually exist.

Saturday, November 5, 2011

Stronghold 3

The original Stronghold was an excellent game. It's easily the best castle building game I've played (though that's not really saying a lot) and even outside that relatively narrow genre, it's still one of my favorite games. So, I was very excited about Stronghold 3, which came out just a couple weeks ago.

Unfortunately, Stronghold 3 has been very disappointing.

When it first came out, it was buggy as all hell. It was pretty much unplayable. Fortunately, some patches have been released. They're now on version 1.2.24396. It's not usually a good sign when the version number is in the tens of thousands. That's a lot of bug fixes.

But at least now you can actually click on things, and your troops will go where you tell them. (Well, most of the time. My guys still occasionally get stuck on nothing, but ordering them backwards and forwards again will usually get them unstuck. (Sadly, that's still better than it was before))

But even without the bugs, it's still disappointing. The change from earlier games that I dislike the most is happiness. As with earlier games, if happiness is above a certain level, peasants will come to the castle, and the higher the happiness, the faster the come. Conversely,  the further below that level, the faster the peasants will leave. However, in earlier games, influences on happiness level were related to the rate of change of happiness. Raising taxes wouldn't make the peasants unhappy, it would make them unhappier and they would keep getting unhappier until you did something else to make them happier. In Stronghold 3 the influences on happiness are direct, and immediate. This can make for an unfortunate situation if anything happens to your farmers. If you run out of food, people will immediately start leaving the castle, and the farmers can't be replaced.

Another thing I don't like is that strongholds seem a lot less strong in this game. In earlier games, archers on top of walls or towers had an incredible advantage over those on the ground. They could shoot farther, and they got some protection against enemy arrows. In this game, there's no protection from enemy attacks. Enemy arrows never miss and bounce off a crenelation. And though there is a range enhancement, it's pretty small. In fact, archers on a wall instead of a tower don't seem to get any extra range at all.

Beyond the big things, there are lots of little irritations too. For example, peasants eat a lot. You can only attach a wall to the very end of another wall, not in the middle for a T-shape. Troops default formation is no formation. Etc.

Stronghold 3 isn't all bad. There are a few things I like about it. One is what they've done with housing.  In earlier games, it didn't matter where you put hovels, so it made sense to make them far away from the rest of the castle. That way, they wouldn't get in the way, and they wouldn't be in harms way when enemies attacked. But it also wasn't very realistic. Now, the closer you put your hovel to the keep, the more people it can hold.

Another thing I like is that now you don't place buildings on a grid, and they can rotated very finely.