专栏首页一个会写诗的程序员的博客What do we mean by “understanding” something?

What do we mean by “understanding” something?

In this chapter, we shall examine the most fundamental ideas that we have about physics—the nature of things as we see them at the present time. We shall not discuss the history of how we know that all these ideas are true; you will learn these details in due time. 在这一章中,我们将考察我们对物理学最基本的观点,即我们现在所看到的事物的本质。我们不应讨论我们如何知道所有这些想法都是真实的历史;你将在适当的时候了解这些细节。

The things with which we concern ourselves in science appear in myriad forms, and with a multitude of attributes. For example, if we stand on the shore and look at the sea, we see the water, the waves breaking, the foam, the sloshing motion of the water, the sound, the air, the winds and the clouds, the sun and the blue sky, and light; there is sand and there are rocks of various hardness and permanence, color and texture. There are animals and seaweed, hunger and disease, and the observer on the beach; there may be even happiness and thought. Any other spot in nature has a similar variety of things and influences. It is always as complicated as that, no matter where it is. 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. 我们在科学中所关注的事物以各种形式出现,并具有多种属性。例如,如果我们站在岸边看海,我们会看到水,波浪破碎,泡沫,水的晃动,声音,空气,风和云,太阳和蓝天,还有光;有沙子,有各种坚硬和永久的岩石,颜色和质地。有动物和海藻,有饥饿和疾病,还有海滩上的观测者;甚至可能有幸福和思想。自然界的任何其他地方都有相似的事物和影响。不管它在哪里,它总是那么复杂。好奇心要求我们提出问题,我们试着把事物放在一起,试着理解这许多方面,因为它们可能是由相对较少的基本事物和以无限多种组合作用的力量的作用而产生的。

For example: Is the sand other than the rocks? That is, is the sand perhaps nothing but a great number of very tiny stones? Is the moon a great rock? If we understood rocks, would we also understand the sand and the moon? Is the wind a sloshing of the air analogous to the sloshing motion of the water in the sea? What common features do different movements have? What is common to different kinds of sound? How many different colors are there? And so on. In this way we try gradually to analyze all things, to put together things which at first sight look different, with the hope that we may be able to reduce the number of different things and thereby understand them better. 沙子不是岩石吗?也就是说,沙子也许只不过是一堆非常小的石头?月亮是块大石头吗?如果我们了解岩石,我们还会了解沙子和月亮吗?风是空气的晃动,类似于海水的晃动吗?不同的动作有什么共同的特点?不同的声音有什么共同点?有多少种不同的颜色?等等。这样我们就逐步地分析所有的事物,把乍一看不一样的东西放在一起,希望能够减少不同事物的数量,从而更好地理解它们。

A few hundred years ago, a method was devised to find partial answers to such questions. Observation, reason, and experiment make up what we call the scientific method. We shall have to limit ourselves to a bare description of our basic view of what is sometimes called fundamental physics, or fundamental ideas which have arisen from the application of the scientific method. 几百年前,人们发明了一种方法来寻找这些问题的部分答案。观察、推理和实验构成了我们所谓的科学方法。我们必须把自己局限于对有时被称为基础物理学的基本观点的简单描述,或是对由于应用科学方法而产生的基本观点的简单描述。

What do we mean by “understanding” something? We can imagine that this complicated array of moving things which constitutes “the world” is something like a great chess game being played by the gods, and we are observers of the game. We do not know what the rules of the game are; all we are allowed to do is to watch the playing. Of course, if we watch long enough, we may eventually catch on to a few of the rules. The rules of the game are what we mean by fundamental physics. Even if we knew every rule, however, we might not be able to understand why a particular move is made in the game, merely because it is too complicated and our minds are limited. If you play chess you must know that it is easy to learn all the rules, and yet it is often very hard to select the best move or to understand why a player moves as he does. So it is in nature, only much more so; but we may be able at least to find all the rules. Actually, we do not have all the rules now. (Every once in a while something like castling is going on that we still do not understand.) Aside from not knowing all of the rules, what we really can explain in terms of those rules is very limited, because almost all situations are so enormously complicated that we cannot follow the plays of the game using the rules, much less tell what is going to happen next. We must, therefore, limit ourselves to the more basic question of the rules of the game. If we know the rules, we consider that we “understand” the world. “理解”是什么意思?我们可以想象,构成“世界”的这一系列复杂的运动物,有点像是一场伟大的象棋游戏,由众神来下棋,我们是这个游戏的观察者。我们不知道游戏规则是什么,我们只允许看比赛。当然,如果我们观察的时间足够长,我们最终可能会掌握一些规则。游戏规则就是我们所说的基础物理。然而,即使我们知道每一条规则,我们也可能无法理解为什么在游戏中会做出某个特定的动作,仅仅因为它太复杂,我们的思想也很有限。如果你下国际象棋,你必须知道学习所有的规则是很容易的,但往往很难选择最好的棋式,也很难理解为什么一个棋手会像他那样移动。这在本质上是如此,只是更多;但我们至少可以找到所有的规则。实际上,我们现在没有所有的规则。(偶尔会发生一些我们仍然不明白的事情,比如卡斯林)除了不知道所有的规则外,我们真正能用这些规则解释的东西是非常有限的,因为几乎所有的情况都非常复杂,我们无法用规则来遵循游戏的规则,更别提接下来会发生什么了。因此,我们必须把自己局限于游戏规则这一更基本的问题上。如果我们知道规则,我们认为我们“了解”这个世界。

How can we tell whether the rules which we “guess” at are really right if we cannot analyze the game very well? There are, roughly speaking, three ways. First, there may be situations where nature has arranged, or we arrange nature, to be simple and to have so few parts that we can predict exactly what will happen, and thus we can check how our rules work. (In one corner of the board there may be only a few chess pieces at work, and that we can figure out exactly.) 如果我们不能很好地分析这个游戏,我们怎么知道我们“猜测”的规则是不是真的正确呢?大致来说,有三种方式。首先,可能存在这样的情况:自然已经安排好了,或者我们安排好了自然,变得简单,并且只有很少的部分,我们可以准确地预测将要发生的事情,因此我们可以检查我们的规则是如何工作的。(棋盘的一角可能只有几个棋子在下,我们可以准确地计算出来。)

A second good way to check rules is in terms of less specific rules derived from them. For example, the rule on the move of a bishop on a chessboard is that it moves only on the diagonal. One can deduce, no matter how many moves may be made, that a certain bishop will always be on a red square. So, without being able to follow the details, we can always check our idea about the bishop’s motion by finding out whether it is always on a red square. Of course it will be, for a long time, until all of a sudden we find that it is on a black square (what happened of course, is that in the meantime it was captured, another pawn crossed for queening, and it turned into a bishop on a black square). That is the way it is in physics. For a long time we will have a rule that works excellently in an overall way, even when we cannot follow the details, and then some time we may discover a new rule. From the point of view of basic physics, the most interesting phenomena are of course in the new places, the places where the rules do not work—not the places where they do work! That is the way in which we discover new rules. 检查规则的第二个好方法是使用从规则派生的不太具体的规则。例如,棋盘上主教移动的规则是只能在对角线上移动。我们可以推断,无论采取多少行动,某位主教都将永远站在红场上。所以,在不了解细节的情况下,我们总是可以通过找出主教的动议是否总是在一个红场上来检验我们对该动议的看法。当然,在很长一段时间内,直到我们突然发现它在一个黑广场上(当然,发生的事情是,在这段时间里,它被俘虏了,另一个棋子被划到皇后区,它变成了一个黑广场上的主教)。物理学就是这样。很长一段时间,我们会有一个整体上运行良好的规则,即使我们不能遵循细节,然后有一段时间我们可能会发现一个新的规则。从基础物理的角度来看,最有趣的现象当然是在新的地方,规则不起作用的地方不是规则起作用的地方!这就是我们发现新规则的方式。

The third way to tell whether our ideas are right is relatively crude but probably the most powerful of them all. That is, by rough approximation. While we may not be able to tell why Alekhine moves this particular piece, perhaps we can roughly understand that he is gathering his pieces around the king to protect it, more or less, since that is the sensible thing to do in the circumstances. In the same way, we can often understand nature, more or less, without being able to see what every little piece is doing, in terms of our understanding of the game. 判断我们的想法是否正确的第三种方法相对粗糙,但可能是其中最有力的一种。也就是说,粗略的估计。虽然我们可能无法解释为什么阿列克辛会移动这一块,但我们大概可以理解,他是在国王周围收集他的作品,或多或少地保护它,因为在这种情况下,这是明智的做法。同样地,我们也可以或多或少地理解自然,而不必从我们对游戏的理解中看到每一个小片段在做什么。

At first the phenomena of nature were roughly divided into classes, like heat, electricity, mechanics, magnetism, properties of substances, chemical phenomena, light or optics, x-rays, nuclear physics, gravitation, meson phenomena, etc. However, the aim is to see complete nature as different aspects of one set of phenomena. That is the problem in basic theoretical physics, today—to find the laws behind experiment; to amalgamate these classes. Historically, we have always been able to amalgamate them, but as time goes on new things are found. We were amalgamating very well, when all of a sudden x-rays were found. Then we amalgamated some more, and mesons were found. Therefore, at any stage of the game, it always looks rather messy. A great deal is amalgamated, but there are always many wires or threads hanging out in all directions. That is the situation today, which we shall try to describe. 起初,自然界的现象大致分为几类,如热、电、力学、磁、物质性质、化学现象、光或光学、x射线、核物理、引力、介子现象等。然而,目的是把完整的自然界看作一组现象的不同方面。这就是基础理论物理的问题,今天要找到实验背后的规律,把这些课程合并起来。从历史上看,我们总是能够把它们融合在一起,但随着时间的推移,新事物被发现了。当突然发现x光片时,我们融合得很好。然后我们又合并了一些,发现了介子。因此,在游戏的任何阶段,它总是看起来相当混乱。有很多是合并的,但总有许多电线或线挂在各个方向。这就是今天的情况,我们要试着描述一下。

Some historic examples of amalgamation are the following. First, take heat and mechanics. When atoms are in motion, the more motion, the more heat the system contains, and so heat and all temperature effects can be represented by the laws of mechanics. Another tremendous amalgamation was the discovery of the relation between electricity, magnetism, and light, which were found to be different aspects of the same thing, which we call today the electromagnetic field. Another amalgamation is the unification of chemical phenomena, the various properties of various substances, and the behavior of atomic particles, which is in the quantum mechanics of chemistry. 合并的一些历史性例子如下。首先,学习热学和力学。当原子运动时,运动越多,系统包含的热量就越多,因此热量和所有温度效应都可以用力学定律来表示。另一个巨大的融合是发现了电、磁和光之间的关系,发现它们是同一事物的不同方面,我们今天称之为电磁场。另一个融合是化学现象、各种物质的各种性质和原子粒子的行为的统一,这是化学的量子力学。

The question is, of course, is it going to be possible to amalgamate everything, and merely discover that this world represents different aspects of one thing? Nobody knows. All we know is that as we go along, we find that we can amalgamate pieces, and then we find some pieces that do not fit, and we keep trying to put the jigsaw puzzle together. Whether there are a finite number of pieces, and whether there is even a border to the puzzle, is of course unknown. It will never be known until we finish the picture, if ever. What we wish to do here is to see to what extent this amalgamation process has gone on, and what the situation is at present, in understanding basic phenomena in terms of the smallest set of principles. To express it in a simple manner, what are things made of and how few elements are there? 当然,问题是,是否有可能把一切都融合起来,仅仅发现这个世界代表了一件事情的不同方面?没人知道。我们只知道,当我们继续,我们发现,我们可以合并块,然后我们发现一些不适合的块,我们继续努力把拼图拼凑在一起。是否有有限数量的碎片,是否甚至有一个边界的拼图,当然是未知的。除非我们完成这幅画,否则永远不会知道。我们在这里要做的是,看看这一合并进程在多大程度上继续下去,以及目前的情况如何,以便用最小的一套原则来理解基本现象。用一种简单的方式来表达,事物是由什么构成的,有多少元素?

参考链接

https://www.feynmanlectures.caltech.edu/I_02.html

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