## 光过玻璃是一件多么神奇的事情啊

\begin{align}
\rho^{c} = p_{1} \left|1\right\rangle\left\langle 1\right| + p_{2} \left|2\right\rangle\left\langle 2\right| \\
\rho^{q} = \left(\sqrt{p_{1}} \left|1\right\rangle + \sqrt{p_{2}} \left|2\right\rangle\right)\left(\sqrt{p_{1}} \left\langle 1\right| + \sqrt{p_{2}} \left\langle 2\right|\right) \\
= p_{1} \left|1\right\rangle\left\langle 1\right| + p_{2} \left|2\right\rangle\left\langle 2\right| + \sqrt{p_{1}p_{2}}\left(\left|1\right\rangle\left\langle 2\right| + \left|2\right\rangle\left\langle 1\right|\right)
\end{align}

## 能看到光是多么神奇的事情啊

\begin{align}
\rho^{c} = \frac{1}{Z}\int d\Omega \left|\theta, \phi\rangle\langle \theta, \phi\right| \\
\rho^{q} = \frac{1}{Z}\left(\int d\Omega \left|\theta, \phi\right\rangle\right)\left(\int d\Omega \left\langle \theta, \phi\right|\right)
\end{align}

## Feynman有意思的话

Science Quotes by Richard P. Feynman

## 关于理解型学习

“I learned very early the difference between knowing the name of something and knowing something.”
― Richard Feynman

“They didn’t put two and two together. They didn’t even know what they knew. I don’t know what’s the matter with people: they don’t learn by understanding, they learn by some other way — by rote or something. Their knowledge is so fragile!”
― Richard Feynman

“What I cannot create, I do not understand.”
― Richard Feynman

“Study hard what interests you the most in the most undisciplined, irreverent and original manner possible.”
― Richard Feynman

“Nobody ever figures out what life is all about, and it doesn’t matter. Explore the world. Nearly everything is really interesting if you go into it deeply enough.”
― Richard Feynman

“The highest forms of understanding we can achieve are laughter and human compassion.”
― Richard Feynman

“When it came time for me to give my talk on the subject, I started off by drawing an outline of the cat and began to name the various muscles.
The other students in the class interrupt me: “We know all that!”
“Oh,” I say, “you do? Then no wonder I can catch up with you so fast after you’ve had four years of biology.” They had wasted all their time memorizing stuff like that, when it could be looked up in fifteen minutes.”
― Richard Feynman, Surely You’re Joking, Mr. Feynman!: Adventures of a Curious Character

“Words can be meaningless. If they are used in such a way that no sharp conclusions can be drawn.”
― Richard Feynman, The Meaning of It All: Thoughts of a Citizen-Scientist

“You see, I get so much fun out of thinking that I don’t want to destroy this pleasant machine that makes life such a big kick.”
― Richard Feynman, Surely You’re Joking, Mr. Feynman!: Adventures of a Curious Character

“That was a very good way to get educated, working on the senior problems and learning how to pronounce things.”
― Richard Feynman, Surely You’re Joking, Mr. Feynman!: Adventures of a Curious Character

“I learned from my father to translate: everything I read I try to figure out what it really means, what it’s really saying.”
― Richard Feynman, ‘What Do You Care What Other People Think?’: Further Adventures of a Curious Character

## 关于批判性思维（和第一部分“理解型学习有联系”，和独创性有联系）

“The first principle is that you must not fool yourself and you are the easiest person to fool.”
― Richard Feynman

“Religion is a culture of faith; science is a culture of doubt.”
― Richard Feynman

“I would rather have questions that can’t be answered than answers that can’t be questioned.”
― Richard Feynman

“Of course, you only live one life, and you make all your mistakes, and learn what not to do, and that’s the end of you.”
― Richard Feynman, Surely You’re Joking, Mr. Feynman!: Adventures of a Curious Character

“What Do You Care What Other People Think?”
― Richard Feynman, Surely You’re Joking, Mr. Feynman

“In general, we look for a new law by the following process: First we guess it; then we compute the consequences of the guess to see what would be implied if this law that we guessed is right; then we compare the result of the computation to nature, with experiment or experience, compare it directly with observation, to see if it works. If it disagrees with experiment, it is wrong. In that simple statement is the key to science. It does not make any difference how beautiful your guess is, it does not make any difference how smart you are, who made the guess, or what his name is — if it disagrees with experiment, it is wrong.”
― Richard Feynman

“We absolutely must leave room for doubt or there is no progress and there is no learning. There is no learning without having to pose a question. And a question requires doubt.
― Richard Feynman

“Curiosity demands that we ask questions, that we try to put things together and try to understand this multitude of aspects as perhaps resulting from the action of a relatively small number of elemental things and forces acting in an infinite variety of combinations”
― Richard Feynman, The Feynman Lectures on Physics vols 1-2

“Have no respect whatsoever for authority; forget who said it and instead look what he starts with, where he ends up, and ask yourself, ‘Is it reasonable?'”
― Richard Feynman

## 关于科学和艺术、生活

“I have a friend who’s an artist and has sometimes taken a view which I don’t agree with very well. He’ll hold up a flower and say “look how beautiful it is,” and I’ll agree. Then he says “I as an artist can see how beautiful this is but you as a scientist take this all apart and it becomes a dull thing,” and I think that he’s kind of nutty. First of all, the beauty that he sees is available to other people and to me too, I believe. Although I may not be quite as refined aesthetically as he is … I can appreciate the beauty of a flower. At the same time, I see much more about the flower than he sees. I could imagine the cells in there, the complicated actions inside, which also have a beauty. I mean it’s not just beauty at this dimension, at one centimeter; there’s also beauty at smaller dimensions, the inner structure, also the processes. The fact that the colors in the flower evolved in order to attract insects to pollinate it is interesting; it means that insects can see the color. It adds a question: does this aesthetic sense also exist in the lower forms? Why is it aesthetic? All kinds of interesting questions which the science knowledge only adds to the excitement, the mystery and the awe of a flower. It only adds. I don’t understand how it subtracts.”
― Richard Feynman

“A poet once said, ‘The whole universe is in a glass of wine.’ We will probably never know in what sense he meant it, for poets do not write to be understood. But it is true that if we look at a glass of wine closely enough we see the entire universe. There are the things of physics: the twisting liquid which evaporates depending on the wind and weather, the reflection in the glass; and our imagination adds atoms. The glass is a distillation of the earth’s rocks, and in its composition we see the secrets of the universe’s age, and the evolution of stars. What strange array of chemicals are in the wine? How did they come to be? There are the ferments, the enzymes, the substrates, and the products. There in wine is found the great generalization; all life is fermentation. Nobody can discover the chemistry of wine without discovering, as did Louis Pasteur, the cause of much disease. How vivid is the claret, pressing its existence into the consciousness that watches it! If our small minds, for some convenience, divide this glass of wine, this universe, into parts — physics, biology, geology, astronomy, psychology, and so on — remember that nature does not know it! So let us put it all back together, not forgetting ultimately what it is for. Let it give us one more final pleasure; drink it and forget it all!”
― Richard Feynman

“Poets say science takes away from the beauty of the stars – mere globs of gas atoms. I too can see the stars on a desert night, and feel them. But do I see less or more? The vastness of the heavens stretches my imagination – stuck on this carousel my little eye can catch one – million – year – old light. A vast pattern – of which I am a part… What is the pattern, or the meaning, or the why? It does not do harm to the mystery to know a little about it. For far more marvelous is the truth than any artists of the past imagined it. Why do the poets of the present not speak of it? What men are poets who can speak of Jupiter if he were a man, but if he is an immense spinning sphere of methane and ammonia must be silent?”
― Richard Feynman

“Physics is like sex: sure, it may give some practical results, but that’s not why we do it.”
― Richard Feynman

“Physics is to math what sex is to masturbation.”
― Richard Feynman

“– and pompous fools drive me up the wall. Ordinary fools are alright; you can talk to them and try to help them out. But pompous fools – guys who are fools and covering it all over and impressing people as to how wonderful they are with all this hocus pocus – THAT, I CANNOT STAND! An ordinary fool isn’t a faker; an honest fool is all right. But a dishonest fool is terrible!”
― Richard Feynman, Surely You’re Joking, Mr. Feynman!: Adventures of a Curious Character

“… it is impossible to explain honestly the beauties of the laws of nature in a way that people can feel, without their having some deep understanding of mathematics. I am sorry, but this seems to be the case.”
― Richard Feynman, The Character of Physical Law

“I believe that we must attack these things in which we do not believe. Not attack by the method of cutting off the heads of the people, but attack in the sense of discuss. I believe that we should demand that people try in their own minds to obtain for themselves a more consistent picture of their own world; that they not permit themselves the luxury of having their brain cut in four pieces or two pieces even, and on one side they believe this and on the other side they believe that, but never try to compare the two points of view. Because we have learned that, by trying to put the points of view that we have in our head together and comparing one to the other, we make some progress in understanding and in appreciating where we are and what we are. And I believe that science has remained irrelevant because we wait until somebody asks us questions or until we are invited to give a speech on Einstein’s theory to people who don’t understand Newtonian mechanics, but we never are invited to give an attack on faith healing, or on astrology — on what is the scientific view of astrology today.”
― Richard Feynman, The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman

“They didn’t put two and two together. They didn’t even know what they knew. I don’t know what’s the matter with people: they don’t learn by understanding, they learn by some other way — by rote or something. Their knowledge is so fragile!”
― Richard Feynman
）的。另外，独创性我觉得比创新性好，只要独创就行，不一定是新的，例如旧的东西的新的角度的理解和看法，完全重新发明一遍旧的东西，在学习过程中，都是很有意义的。

## 附几个小品

“After reading the salary, I’ve decided that I must refuse. The reason I have to refuse a salary like that is I would be able to do what I’ve always wanted to do- -get a wonderful mistress, put her up in an apartment, buy her nice things.. . With the salary you have offered, I could actually do that, and I know what would happen to me. I’d worry about her, what she’s doing; I’d get into arguments when I come home, and so on. All this bother would make me uncomfortable and unhappy. I wouldn’t be able to do physics well, and it would be a big mess! What I’ve always wanted to do would be bad for me, so I’ve decided that I can’t accept your offer.”
― Richard Feynman

“I think the educational and psychological studies I mentioned are examples of what I would like to call cargo cult science. In the South Seas there is a cargo cult of people. During the war they saw airplanes land with lots of good materials, and they want the same thing to happen now. So they’ve arranged to make things like runways, to put fires along the sides of the runways, to make a wooden hut for a man to sit in, with two wooden pieces on his head like headphones and bars of bamboo sticking out like antennas—he’s the controller—and they wait for the airplanes to land. They’re doing everything right. The form is perfect. It looks exactly the way it looked before. But it doesn’t work. No airplanes land. So I call these things cargo cult science, because they follow all the apparent precepts and forms of scientific investigation, but they’re missing something essential, because the planes don’t land.”
― Richard Feynman, Surely You’re Joking, Mr. Feynman! Adventures of a Curious Character

“It was a kind of one-upmanship, where nobody knows what’s going on, and they’d put the other one down as if they did know. They all fake that they know, and if one student admits for a moment that something is confusing by asking a question, the others take a high-handed attitude, acting as if it’s not confusing at all, telling him that he’s wasting their time… All the work they did, intelligent people, but they got themselves into this funny state of mind, this strange kind of self-propagating “education” which is meaningless, utterly meaningless.”
― Richard Feynman, Surely You’re Joking, Mr. Feynman!: Adventures of a Curious Character