“Any intelligent fool can make things bigger, more complex, and more violent. It takes a touch of genius—and a lot of courage—to move in the opposite direction.” —E.F. Schumacher

1. Pretend to teach a concept you want to learn about to a student in the sixth grade.
2. Identify gaps in your explanation. Go back to the source material to better understand it.
3. Organize and simplify.
4. Transmit (optional).

“If you can’t reduce a difficult engineering problem to just one 8-1/2 x 11-inch sheet of paper, you will probably never understand it.” —Ralph Peck
如果你不能把一个困难的工程问题简化的8-1/2 x 11英寸的纸上，你可能无法理解他。

“The person who says he knows what he thinks but cannot express it usually does not know what he thinks.” —Mortimer Adler
 如果一个人说他懂但不能表达，那通常是他还没有想明白。

“See that bird? It’s a brown-throated thrush, but in Germany it’s called a halzenfugel, and in Chinese they call it a chung ling, and even if you know all those names for it, you still know nothing about the bird. You only know something about people: what they call the bird. Now that thrush sings, and teaches its young to fly, and flies so many miles away during the summer across the country, and nobody knows how it finds its way.”
“看见那只鸟了吗？”它是一只褐喉鸫，德国人叫它halzenfugel，中国人叫它黑喉画眉，就算你知道所有的名字，你对这只鸟一无所知。你仅仅知道人们怎么叫这只鸟。现在那只thrush唱歌，教它的小鸟飞，它夏天飞很远，穿过国家，但是没人知道它怎么认得路的。

“Perhaps I can make the difference a little clearer this way: if you ask a child what makes the toy dog move, you should think about what an ordinary human being would answer. The answer is that you wound up the spring; it tries to unwind and pushes the gear around.

What a good way to begin a science course! Take apart the toy; see how it works. See the cleverness of the gears; see the ratchets. Learn something about the toy, the way the toy is put together, the ingenuity of people devising the ratchets and other things. That’s good.”
也许我可以把这个事说的更清楚点：如果你问一个小孩什么让这个玩具移动，你应该想想一个正常的成年人会怎么回答。这个答案是你将弹簧卷起来，弹簧要伸展开然后推动齿轮转动。
这是科学课程的一个好的开头！把toy单独拿出来，看看它怎么工作。看看灵巧的齿轮，看看棘轮，学习这个玩具，玩具组装方式，人们的创造性的发明了棘轮和其它的东西。这就很好。

“We take other men’s knowledge and opinions upon trust; which is an idle and superficial learning. We must make them our own. We are just like a man who, needing fire, went to a neighbor’s house to fetch it, and finding a very good one there, sat down to warm himself without remembering to carry any back home. What good does it do us to have our belly full of meat if it is not digested, if it is not transformed into us, if it does not nourish and support us?” —Michel de Montaigne
我们基于信任拿了别人的知识和见解，这是懒惰和肤浅的。我们要把他们变成自己的。我们就像一个需要火的人，我们去了邻居取火，然后找到一个好地方坐下来烤火，然而忘记了带火回家。如果我们的肚子填满了肉，但是没有消化掉，没有任何东西转化给自己，没有任何东西滋养我们，那这么做没有任何好处。

“My trick that I use is very easy. If you ask him intelligent questions—that is, penetrating, interested, honest, frank, direct questions on the subject, and no trick questions—then he quickly gets stuck. It is like a child asking naive questions. If you ask naive but relevant questions, then almost immediately the person doesn’t know the answer, if he is an honest man. It is important to appreciate that.
我的伎俩很容易使用，如果你问他聪明的问题---这是一个精辟的、感兴趣的、诚实的、坦率的、直截了当的问题，而不是诡计多端的问题——然后他很快就会陷入困境。它就像一个孩子问天真的问题。如果你问天真又相关的问题，那么很可能很快这个人就说不知道答案，如果他说一个诚实的人。 意识到这一点非常重要。

And I think that I can illustrate one unscientific aspect of the world which would be probably very much better if it were more scientific. It has to do with politics. Suppose two politicians are running for president, and one goes through the farm section and is asked, “What are you going to do about the farm question?” And he knows right away—bang, bang, bang.


Now he goes to the next campaigner who comes through. “What are you going to do about the farm problem?” “Well, I don’t know. I used to be a general, and I don’t know anything about farming. But it seems to me it must be a very difficult problem, because for twelve, fifteen, twenty years people have been struggling with it, and people say that they know how to solve the farm problem. And it must be a hard problem. So the way that I intend to solve the farm problem is to gather around me a lot of people who know something about it, to look at all the experience that we have had with this problem before, to take a certain amount of time at it, and then to come to some conclusion in a reasonable way about it. Now, I can’t tell you ahead of time what conclusion, but I can give you some of the principles I’ll try to use—not to make things difficult for individual farmers, if there are any special problems we will have to have some way to take care of them, etc., etc., etc.””

“I would like to mention a somewhat technical idea, but it’s the way, you see, we have to understand how to handle uncertainty. How does something move from being almost certainly false to being almost certainly true? How does experience change? How do you handle the changes of your certainty with experience? And it’s rather complicated, technically, but I’ll give a rather simple, idealized example.
几乎确定是错变为几乎是对，，如何改变你对经验的肯定（如何否定你的经验？）

You have, we suppose, two theories about the way something is going to happen, which I will call “Theory A” and “Theory B.” Now it gets complicated. Theory A and Theory B. Before you make any observations, for some reason or other, that is, your past experiences and other observations and intuition and so on, suppose that you are very much more certain of Theory A than of Theory B—much more sure. But suppose that the thing that you are going to observe is a test. According to Theory A, nothing should happen. According to Theory B, it should turn blue. Well, you make the observation, and it turns sort of a greenish. Then you look at Theory A, and you say, “It’s very unlikely,” and you turn to Theory B, and you say, “Well, it should have turned sort of blue, but it wasn’t impossible that it should turn sort of greenish color.”

So the result of this observation, then, is that Theory A is getting weaker, and Theory B is getting stronger. And if you continue to make more tests, then the odds on Theory B increase. Incidentally, it is not right to simply repeat the same test over and over and over and over, no matter how many times you look and it still looks greenish, you haven’t made up your mind yet. But if you find a whole lot of other things that distinguish Theory A from Theory B that are different, then by accumulating a large number of these, the odds on Theory B increase.”

“A professor, I think somewhere in Virginia, has done a lot of experiments for a number of years on the subject of mental telepathy, the same kind of stuff as mind reading. In his early experiments the game was to have a set of cards with various designs on them (you probably know all this, because they sold the cards and people used to play this game), and you would guess whether it’s a circle or a triangle and so on while someone else was thinking about it. You would sit and not see the card, and he would see the card and think about the card and you’d guess what it was. And in the beginning of these researches, he found very remarkable effects. He found people who would guess ten to fifteen of the cards correctly, when it should be on the average only five. More even than that. There were some who would come very close to a hundred percent in going through all the cards. Excellent mind readers.

A number of people pointed out a set of criticisms. One thing, for example, is that he didn’t count all the cases that didn’t work. And he just took the few that did, and then you can’t do statistics anymore. And then there were a large number of apparent clues by which signals inadvertently, or advertently, were being transmitted from one to the other.

Various criticisms of the techniques and the statistical methods were made by people. The technique was therefore improved. The result was that, although five cards should be the average, it averaged about six and a half cards over a large number of tests. Never did he get anything like ten or fifteen or twenty-five cards. Therefore, the phenomenon is that the first experiments are wrong. The second experiments proved that the phenomenon observed in the first experiment was nonexistent. The fact that we have six and a half instead of five on the average now brings up a new possibility, that there is such a thing as mental telepathy, but at a much lower level. It’s a different idea, because, if the thing was really there before, having improved the methods of experiment, the phenomenon would still be there. It would still be fifteen cards. Why is it down to six and a half? Because the technique improved. Now it still is that the six and a half is a little bit higher than the average of statistics, and various people criticized it more subtly and noticed a couple of other slight effects which might account for the results.

It turned out that people would get tired during the tests, according to the professor. The evidence showed that they were getting a little bit lower on the average number of agreements. Well, if you take out the cases that are low, the laws of statistics don’t work, and the average is a little higher than the five, and so on. So if the man was tired, the last two or three were thrown away. Things of this nature were improved still further. The results were that mental telepathy still exists, but this time at 5.1 on the average, and therefore all the experiments which indicated 6.5 were false. Now what about the five? . . . Well, we can go on forever, but the point is that there are always errors in experiments that are subtle and unknown. But the reason that I do not believe that the researchers in mental telepathy have led to a demonstration of its existence is that as the techniques were improved, the phenomenon got weaker. In short, the later experiments in every case disproved all the results of the former experiments. If remembered that way, then you can appreciate the situation.”

“That brings me to the fourth kind of attitude toward ideas, and that is that the problem is not what is possible. That’s not the problem. The problem is what is probable, what is happening.

It does no good to demonstrate again and again that you can’t disprove that this could be a flying saucer. We have to guess ahead of time whether we have to worry about the Martian invasion. We have to make a judgment about whether it is a flying saucer, whether it’s reasonable, whether it’s likely. And we do that on the basis of a lot more experience than whether it’s just possible, because the number of things that are possible is not fully appreciated by the average individual. And it is also not clear, then, to them how many things that are possible must not be happening. That it’s impossible that everything that is possible is happening. And there is too much variety, so most likely anything that you think of that is possible isn’t true. In fact that’s a general principle in physics theories: no matter what a guy thinks of, it’s almost always false. So there have been five or ten theories that have been right in the history of physics, and those are the ones we want. But that doesn’t mean that everything’s false. We’ll find out.”

“A lot of scientists don’t even appreciate this. In fact, the first time I got into an argument over this was when I was a graduate student at Princeton, and there was a guy in the psychology department who was running rat races. I mean, he has a T-shaped thing, and the rats go, and they go to the right, and the left, and so on. And it’s a general principle of psychologists that in these tests they arrange so that the odds that the things that happen by chance is small, in fact, less than one in twenty. That means that one in twenty of their laws is probably wrong. But the statistical ways of calculating the odds, like coin flipping if the rats were to go randomly right and left, are easy to work out.

This man had designed an experiment which would show something which I do not remember, if the rats always went to the right, let’s say. He had to do a great number of tests, because, of course, they could go to the right accidentally, so to get it down to one in twenty by odds, he had to do a number of them. And it’s hard to do, and he did his number. Then he found that it didn’t work. They went to the right, and they went to the left, and so on. And then he noticed, most remarkably, that they alternated, first right, then left, then right, then left. And then he ran to me, and he said, “Calculate the probability for me that they should alternate, so that I can see if it is less than one in twenty.” I said, “It probably is less than one in twenty, but it doesn’t count.”

He said, “Why?” I said, “Because it doesn’t make any sense to calculate after the event. You see, you found the peculiarity, and so you selected the peculiar case.”

The fact that the rat directions alternate suggests the possibility that rats alternate. If he wants to test this hypothesis, one in twenty, he cannot do it from the same data that gave him the clue. He must do another experiment all over again and then see if they alternate. He did, and it didn’t work.”

“The next kind of technique that’s involved is statistical sampling. I referred to that idea when I said they tried to arrange things so that they had one in twenty odds. The whole subject of statistical sampling is somewhat mathematical, and I won’t go into the details. The general idea is kind of obvious. If you want to know how many people are taller than six feet tall, then you just pick people out at random, and you see that maybe forty of them are more than six feet so you guess that maybe everybody is. Sounds stupid.

Well, it is and it isn’t. If you pick the hundred out by seeing which ones come through a low door, you’re going to get it wrong. If you pick the hundred out by looking at your friends, you’ll get it wrong, because they’re all in one place in the country. But if you pick out a way that as far as anybody can figure out has no connection with their height at all, then if you find forty out of a hundred, then in a hundred million there will be more or less forty million. How much more or how much less can be worked out quite accurately. In fact, it turns out that to be more or less correct to 1 percent, you have to have 10,000 samples. People don’t realize how difficult it is to get the accuracy high. For only 1 or 2 percent you need 10,000 tries.”

“Now, looking at the troubles that we have with all the unscientific and peculiar things in the world, there are a number of them which cannot be associated with difficulties in how to think, I think, but are just due to some lack of information. In particular, there are believers in astrology, of which, no doubt, there are a number here. Astrologists say that there are days when it’s better to go to the dentist than other days. There are days when it’s better to fly in an airplane, for you, if you are born on such a day and such and such an hour. And it’s all calculated by very careful rules in terms of the position of the stars. If it were true it would be very interesting. Insurance people would be very interested to change the insurance rates on people if they follow the astrological rules, because they have a better chance when they are in the airplane. Tests to determine whether people who go on the day that they are not supposed to go are worse off or not have never been made by the astrologers. The question of whether it’s a good day for business or a bad day for business has never been established. Now what of it? Maybe it’s still true, yes.

On the other hand, there’s an awful lot of information that indicates that it isn’t true. Because we have a lot of knowledge about how things work, what people are, what the world is, what those stars are, what the planets are that you are looking at, what makes them go around more or less, where they’re going to be in the next 2,000 years is completely known. They don’t have to look up to find out where it is. And furthermore, if you look very carefully at the different astrologers they don’t agree with each other, so what are you going to do? Disbelieve it. There’s no evidence at all for it. It’s pure nonsense.

The only way you can believe it is to have a general lack of information about the stars and the world and what the rest of the things look like. If such a phenomenon existed it would be most remarkable, in the face of all the other phenomena that exist, and unless someone can demonstrate it to you with a real experiment, with a real test, took people who believe and people who didn’t believe and made a test, and so on, then there’s no point in listening to them.”
也就是说你都不知道星座怎么在运行，怎么玩占星术？想搞清楚是不是占星术是不是真的，要做实验，如果都做了试验了，还需要占星术干啥呢？