If You Can't Explain It...

There is a common saying with a variety of forms that generally goes like this:

If you can't explain it simply, you don't understand it well enough.

You do not really understand something unless you can explain it to your grandmother.

If you understand something, you can explain it in its simplest form.

If you can't explain it to a six year old, you don't understand it.

I disagree with this saying. The ability to explain something well is a skill separate from the thing you're trying to explain.

Consider a watchmaker who can make intricate watches that work correctly, but who can't tell you why certain pieces go where they do. Not only can he build watches, but he can also innovate designs to make them better. Does he understand watchmaking? Clearly, he does, otherwise he wouldn't be able to make them work at all. His inability to explain is a problem with his communication skills, not a problem with his understanding.

Further, how difficult something is to explain depends not only on how well you understand it and how good you are at explaining, but also who you're explaining it to. This is the concept of inferential distance. It's a lot easier to explain calculus to someone who understands algebra than it is to explain it to someone who doesn't even understand arithmetic.

And if you're really good at certain forms of communication, you can explain something that you don't understand at all (though not correctly).

Equality of Opportunity

But there's a fundamental question on the meaning of "fairness." Does fairness mean everybody makes the same amount of money? Or does fairness mean everybody gets the opportunity to make the same amount of money?
-Rick Warren

This is a common thing among right-wingers, talking about how the left wants equality of outcome, but the right wants equality of opportunity. But it's not true.

I don't think anyone is especially interested in achieving either of those things (though democrat positions are a little closer to it). If you were really interested in having equality of opportunity, you know what one of the first things you should do is?

Ban private schools. Or at least make it so everyone can get in regardless of how much money their parents have, which would effectively just make them public schools. A better education means more and better opportunities. That's hardly equal, and it's not like it's poor kids' fault that they have poor parents.

But no one wants something like that. And I can't blame them. It's a bit too Harrison Bergeron, making things worse to make them more equal. Nonetheless, allows private schools allows inequality of opportunity.

Beyond that, "It takes money to make money". By accepting inequality of outcomes, you're accepting inequality of opportunity. A person who has spare money lying around can invest it, and make more with it. A person living paycheck to paycheck doesn't have that opportunity.

And that's only a couple of examples of how our system supports inequality of opportunity. There are lots more if you look, and those ones don't help the poor much either.

Cultural Invisibility

Have you ever noticed that your own culture is invisible to you?

I think the most obvious example of this is accent. When you hear someone with a different accent speak, you notice their accent. It sounds weird and different to you and you recognize it as an accent. But when you speak, or you hear someone with the same accent as you, you don't notice it. It just sounds like they're talking normally and it doesn't even register that that's an accent too. But it's not hard to realize that you do have an accent, you just don't notice it.

Pretty much every cultural trait is the same. Consider for example social signalling. When someone from a different social group than you signals something, it looks like a waste of money. When you do it, you don't even realize that's what you're doing.

Your culture is the baseline against which all others are judged. Anything that differs from your culture is weird and unusual. Anything that's the same is just the way things are supposed to be.

Inferential Distance

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...

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.

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?

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.