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Suppose you're trying to teach someone calculus. Before they can learn calculus, they have to learn algebra. Before they can learn algebra, they have to learn arithmetic. This is the basic idea of inferential distance - background knowledge needed the understand the matter at hand.
Put this way, it looks simple, maybe not even worth talking about. But it's more subtle than that. To start with, arithmetic, algebra and calculus aren't single subjects. They're a whole bunch of related but still different subjects, which need to be learned independently. The learn integration, you have to learn differentiation, before that you have to learn limits, before that functions, variables, division, mulitplication, subtraction, addition... And don't forget the really fundamental things like what a number is.
And that's the really tricky part of inferential distance. There are a lot of things you know that you don't know you know. That is to say, you know them so well, it doesn't even occur to you to that someone else might not know it. Things that are so fundamental to your point of view that they're invisible to it. And so when you try to explain something to someone, you accidentally skip over a bunch of inferential steps, resulting in misunderstanding and each party will walk away thinking the other is stupid or crazy.
Consider a biologist talking to a creationist. They might try to explain the evidence for evolution, but before the creationist can understand that, they have to understand what evidence means, how science works, maybe even something as simple as why truth is important...
Tuesday, February 28, 2012
Friday, February 17, 2012
A Defense of Government
This is a summarization of an essay by my girlfriend.
According to the market model of society the efficient distribution of products and services is attained through the direct exchange between and response of self-interest driven individuals. Since individuals seek to maximize returns and minimize costs, exchanges occur only when mutually beneficial; therefore, the market inherently optimizes the societal good. For this to work, several conditions must be met: individuals must act independently and only try to maximize their own utility; there must be perfect information about, competition for, and free movement of goods; and all the costs and benefits must be known and contained to the exchange. There are situations where not all of these conditions are met, which prevents the market from working efficiently.
One such example is that of public goods, which breaks the condition of perfect competition. Public goods are things that no one can be excluded from, such as water quality or national defense. Since no one can be excluded from using it, there is no way for providers to get a return on its production, even if there is a demand for it so the demand will not be met. The government can correct this inefficiency by using taxes to provide the good.
Another example is when an exchange produces externalities, which are when costs or benefits affect other uninvolved parties. An example of a positive externality is vaccination, where even the unvaccinated are protected from disease by herd immunity. An example of a negative externality is pollution, where poor water and air quality affect everyone, not just the ones who make the pollution. Since the decision makers involved do not bear all the costs and benefits, they are not taken into account, and the market either produces too much of something (in the case of negative externalities) or too little (in the case of positive externalities). The government can create regulations which can impose a cost or benefit to internalize the externalities. For example, a tax can be imposed on polluters, or vaccinations can be subsidized.
Another case where there is not adequate competition is for natural monopolies, when goods are produced most efficiently by a single supplier. This gives an advantage to the first or largest supplier and with insufficient competition, the monopoly can charge more than the good is worth. The government can step in by running the monopoly as a public utility or by regulating the price, quality and quantity of the good.
An efficient market requires everyone have perfect knowledge of their potential options. There are many situations where the participants involved do not have accurate or equal amounts of information. There is usually some cost in obtaining information, and information can be deliberately withheld. The government can reduce the cost of information by funding research, and can reduce information asymmetries by making information public.
Even in a perfectly efficient economy, some people will be unable to compete for resources, such as the young, the old and the disabled. There is no economic incentive to provide care for those who can offer little or nothing in return. The government can provide welfare to establish a baseline minimum quality of life.
According to the market model of society the efficient distribution of products and services is attained through the direct exchange between and response of self-interest driven individuals. Since individuals seek to maximize returns and minimize costs, exchanges occur only when mutually beneficial; therefore, the market inherently optimizes the societal good. For this to work, several conditions must be met: individuals must act independently and only try to maximize their own utility; there must be perfect information about, competition for, and free movement of goods; and all the costs and benefits must be known and contained to the exchange. There are situations where not all of these conditions are met, which prevents the market from working efficiently.
One such example is that of public goods, which breaks the condition of perfect competition. Public goods are things that no one can be excluded from, such as water quality or national defense. Since no one can be excluded from using it, there is no way for providers to get a return on its production, even if there is a demand for it so the demand will not be met. The government can correct this inefficiency by using taxes to provide the good.
Another example is when an exchange produces externalities, which are when costs or benefits affect other uninvolved parties. An example of a positive externality is vaccination, where even the unvaccinated are protected from disease by herd immunity. An example of a negative externality is pollution, where poor water and air quality affect everyone, not just the ones who make the pollution. Since the decision makers involved do not bear all the costs and benefits, they are not taken into account, and the market either produces too much of something (in the case of negative externalities) or too little (in the case of positive externalities). The government can create regulations which can impose a cost or benefit to internalize the externalities. For example, a tax can be imposed on polluters, or vaccinations can be subsidized.
Another case where there is not adequate competition is for natural monopolies, when goods are produced most efficiently by a single supplier. This gives an advantage to the first or largest supplier and with insufficient competition, the monopoly can charge more than the good is worth. The government can step in by running the monopoly as a public utility or by regulating the price, quality and quantity of the good.
An efficient market requires everyone have perfect knowledge of their potential options. There are many situations where the participants involved do not have accurate or equal amounts of information. There is usually some cost in obtaining information, and information can be deliberately withheld. The government can reduce the cost of information by funding research, and can reduce information asymmetries by making information public.
Even in a perfectly efficient economy, some people will be unable to compete for resources, such as the young, the old and the disabled. There is no economic incentive to provide care for those who can offer little or nothing in return. The government can provide welfare to establish a baseline minimum quality of life.
Sunday, January 29, 2012
Reality is Objective
Reality is objective. What's true is true for everyone, regardless of what people believe.
You'd think this would be obvious. And yet, it comes up. Particularly in debates about the supernatural. People will say things like "Well, maybe ghosts don't exist for you, but they do exist for me." I've never seen anyone apply this sort of reasoning when doing something mundane, like say, crossing the street. No one ever says "That bus might exist for you, but it doesn't exist for me." People know there either is a bus there, or there isn't, regardless of what they believe, and if they want to not get hit by it, they ought to have beliefs which match objective reality.
I think the idea that reality is different to different people might come from the thought that our senses are infallible. If I see something, that means it's there. If I see something, and someone else sees something different, well our realities must be different. But our senses aren't infallible, and we frequently see or hear things that aren't there, or fail to see or hear things that are.
It seems to me much easier to explain occasional discrepancies in our perceptions in an objective reality than to explain the ubiquitous consistency of our perceptions. How often do people disagree about whether it's day or night, whether they're inside or outside, whether they're sitting or standing, whether there's a bus in the road or not? If reality were subjective, why would such consistency be so common?
You'd think this would be obvious. And yet, it comes up. Particularly in debates about the supernatural. People will say things like "Well, maybe ghosts don't exist for you, but they do exist for me." I've never seen anyone apply this sort of reasoning when doing something mundane, like say, crossing the street. No one ever says "That bus might exist for you, but it doesn't exist for me." People know there either is a bus there, or there isn't, regardless of what they believe, and if they want to not get hit by it, they ought to have beliefs which match objective reality.
I think the idea that reality is different to different people might come from the thought that our senses are infallible. If I see something, that means it's there. If I see something, and someone else sees something different, well our realities must be different. But our senses aren't infallible, and we frequently see or hear things that aren't there, or fail to see or hear things that are.
It seems to me much easier to explain occasional discrepancies in our perceptions in an objective reality than to explain the ubiquitous consistency of our perceptions. How often do people disagree about whether it's day or night, whether they're inside or outside, whether they're sitting or standing, whether there's a bus in the road or not? If reality were subjective, why would such consistency be so common?
Wednesday, January 4, 2012
Justified True Belief?
Epistemology is the branch of philosophy interested in the study of knowledge. One of the foundational questions of epistemology is "What does it mean to know something?". A common answer is that knowledge is justified true belief. In order to know something, you have to believe it, have a good reason for believing it and it has to actually be true.
That sounds pretty good, but there are problems with it. It's possible to construct scenarios in which all three conditions are apparently met, but it doesn't seem like anything was "known".
There's also the question of what counts as justification. But I think there's another, more fundamental, problem with this definition. One I don't think I've ever seen anyone else point out.
No definition of knowledge should include the condition of being true.
To do so is to make the term inapplicable in any situation remotely resembling real life. The reason for that is because of the answer to another fundamental question of epistemology: "Is it possible to be absolutely certain of something?". The answer to that is no. (Of course, others disagree, and I should probably write another post explaining why I think that.) All we can do is get more and more evidence for something, getting closer and closer to 100% certainty, but never actually reaching it.
In toy examples, whether a given fact is true or not is simply assumed/given. So if a hypothetical character has a justified belief, we can say whether that character knows it or not, because of our god-like omniscience. But in real life, no one has that omniscience.
Consider the same question - Is a belief knowledge or not - applied to yourself. Do I know the sun will rise tomorrow, or do I just believe it? Well, I certainly think it's true that the sun will come up. I wouldn't believe it if it I didn't think that, tautologically. But if that's the standard, then I ought to consider every belief I have to be knowledge. If I didn't believe they were true, I wouldn't believe them.
And if we apply that standard to other people, then our evaluations of whether someone else knows something or merely believes it, simply becomes a question of whether they agree with you or not.
I propose a simpler definition: Knowledge is belief that is held with a high degree of confidence.
This definition fits very well into a Bayesian framework. Degree of confidence is simply probability. If you believe something is true with a probability greater than, say, 99.9%, you can be said to know it. This also handily deals with the question of what counts as justification - that's just Bayesian evidence.
That sounds pretty good, but there are problems with it. It's possible to construct scenarios in which all three conditions are apparently met, but it doesn't seem like anything was "known".
There's also the question of what counts as justification. But I think there's another, more fundamental, problem with this definition. One I don't think I've ever seen anyone else point out.
No definition of knowledge should include the condition of being true.
To do so is to make the term inapplicable in any situation remotely resembling real life. The reason for that is because of the answer to another fundamental question of epistemology: "Is it possible to be absolutely certain of something?". The answer to that is no. (Of course, others disagree, and I should probably write another post explaining why I think that.) All we can do is get more and more evidence for something, getting closer and closer to 100% certainty, but never actually reaching it.
In toy examples, whether a given fact is true or not is simply assumed/given. So if a hypothetical character has a justified belief, we can say whether that character knows it or not, because of our god-like omniscience. But in real life, no one has that omniscience.
Consider the same question - Is a belief knowledge or not - applied to yourself. Do I know the sun will rise tomorrow, or do I just believe it? Well, I certainly think it's true that the sun will come up. I wouldn't believe it if it I didn't think that, tautologically. But if that's the standard, then I ought to consider every belief I have to be knowledge. If I didn't believe they were true, I wouldn't believe them.
And if we apply that standard to other people, then our evaluations of whether someone else knows something or merely believes it, simply becomes a question of whether they agree with you or not.
I propose a simpler definition: Knowledge is belief that is held with a high degree of confidence.
This definition fits very well into a Bayesian framework. Degree of confidence is simply probability. If you believe something is true with a probability greater than, say, 99.9%, you can be said to know it. This also handily deals with the question of what counts as justification - that's just Bayesian evidence.
Tuesday, December 13, 2011
AlDraw Wiki
Ever wish there were a wiki focused on AlDraw for you to learn from and contribute to? No, I didn't really think so. Nonetheless, it now exists - behold, AlDraw Wiki!
Right now there's not a lot of stuff specific to AlDraw. I've been focusing on the Construction techniques category. I have instructions on simple techniques, such as how to construct a midpoint, intermediate, such as how to inscribe a circle in a triangle and advanced, such as how to construct a circle that passes through two given points and is tangent to a given line. And I'm adding more every day.
Is something confusing or unclear? Ask and I'll write it better. Do you see a mistake I made? Edit it!
Edit: I've just added the pentagon. This page describes both how to construct a pentagon inscribed in a circle (which is easy to find elsewhere online) and also how to construct a pentagon from a given side length (which is harder to find elsewhere).
Right now there's not a lot of stuff specific to AlDraw. I've been focusing on the Construction techniques category. I have instructions on simple techniques, such as how to construct a midpoint, intermediate, such as how to inscribe a circle in a triangle and advanced, such as how to construct a circle that passes through two given points and is tangent to a given line. And I'm adding more every day.
Is something confusing or unclear? Ask and I'll write it better. Do you see a mistake I made? Edit it!
Edit: I've just added the pentagon. This page describes both how to construct a pentagon inscribed in a circle (which is easy to find elsewhere online) and also how to construct a pentagon from a given side length (which is harder to find elsewhere).
Tuesday, November 22, 2011
Extraordinary Evidence
"Extraordinary claims require extraordinary evidence" -Carl SaganSome 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.
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.
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