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说一说白居易《浪淘沙》中的“浪” 2017-04-09 10:31:41

说一说白居易《浪淘沙》中的“浪”

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白居易有两首《浪淘沙》的诗中所提到的“浪”有些有趣的物理意义:

 

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白浪茫茫与海连,平沙浩浩四无边。
暮去朝来淘不住,遂令东海变桑田。

 

一泊沙来一泊去,一重浪灭一重生。
相搅相淘无歇日,会交山海一时平。

+++++++++

 

这里的“浪”应该就是指“波浪”或即“水波”。从“一重浪灭一重生”这一句的描述来看,白居易对水波的传播及变化应该是作了很仔细的观察思考的。“一重浪灭一重生”可以说是比较精准地描述了他所观察到的海浪(或即水波的一种)的传播变化。当然估计他不知道他所观察到的“一重浪灭一重生”其实对应着两种不同的物理过程。

 

波动及其传播是物质的一种很普遍的运动形式。声音通过“声波”传播,光线则通过“电磁波”传播,水面的扰动则可以通过“水波”从扰动源传播开去。我们往平静的水池塘里扔一块石头,就可看到一圈圈的同心圆水波向外传播开去。在波动的传播过程中,有些波的波形或即波峰与波谷之间的相对位置能基本维持不变。在学术上,这些波动通常就被称为“非频散波”。象声波和光波就可认为是“非频散波”。也正是声波、光波的这非频散特性,我们可以在不同的地方听到同样声调的声音或看到同一色彩的画面。但水波恰恰正是所谓的“频散波”。它的波形在传播过程中快速变化。变化最快的就是所谓的“深水波”,而“浅水波”则变化极慢或几乎不变。

 

“白浪茫茫与海”中的“浪”应该就是指的深水波。种波的播特性与水池塘里扔了石之后所看到的一圈圈向外播开去的同心水波是相同的。在种情形下,你若试图用眼睛紧盯着某一波峰,看它如何随时间向前行,你会发现那个波峰会在你眼皮底下很快消失,而新的波峰会在水面的平静突然冒出来。正是白居易中所的“一重浪一重生”的象。流体力学家James Lighthill在他的名著《Waves in Fluids》中“一重浪一重生”的一深水波的象作了更致、精彩的描述:

 

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Lighthill, M. J., 1978: Waves in Fluids. Cambridge University Press, London and New York, 504 pp.

 

It is extremely instructive to watch those outside waves. Anyone observing, however carefully, the progress of one of the crests will suddenly lose sight of it! It seems an optical illusion at first; the possible result of mistaken identity between that crest and the next one coming along behind, to which the observer's gaze is now transferred; but then this next crest, too, disappears! Meanwhile, crests are coming along thick and fast behind. Indeed, at the inside edge of the concentric pattern, new crests are appearing ‘from nowhere’; that is, from the now calmed central water. [p. 240]

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这里再顺带多说一句。James Lighthill上面描述中的“Meanwhile, crests are coming along thick and fast behind”其实就对“长江后浪推前浪”的确切解释。此外,紧接着的“前浪死在沙滩上”很明显是文科生的恶搞(或是把长江里的前浪同死在沙滩上的海浪给搞混淆了)。真正的理科生应该很清楚那长江前浪之死是由于波的频散特性而导致的消失,与沙滩没有一毛钱的关系。

 

白居易对海浪在不同情况下的传播变化应该都进行了仔细的观察思考,从而得出了“一重浪灭一重生”的一般概念。他也把这一概念用在了平坦的海滩上所见到的海浪。“一泊沙来一泊去”所描述的应该是在或接近海滩上行进的浅水波对沙滩上沙粒的作用。浅水波的频散作用很弱。这时,你若用眼睛紧盯着某一很靠近平缓沙滩的行进波峰的话,你应该可以盯住它很长一段时间。但这时由于水深变化所引起的所谓非线性作用会使得波峰渐渐变陡而导致波峰的破裂或破碎,并进而导致波峰的完全消失。自然,这一由波峰的破碎过程而导致的消失与前述由波的频散而导致的消失其本质是不同的。特别,此时在“一重浪灭”之后又出现的“一重生”并非是从平静水面上突然冒出来的新的波峰,而是随后跟着的已有的波峰继续前行而已。

 


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作者:coolboy 留言时间:2017-04-16 11:46:52

The above example by R. Feynman on a comprehensive view or a broad knowledge of a true scientist was on the beauty of a flower. While looking at a flower, there will be many related issues coming into a scientist’s mind that would inspire his/her pondering. However, the original discussion started from the poet Bai, Juyi (白居易) who made careful observations while standing at the seashore and arrived at a scientific conclusion on the behavior of ocean waves (“一重浪灭一重生”). Feynman’s example was nice but can we also provide an example of what a scientist would think about in addition to ocean waves while standing on the seashore? There is a good book on my bookshelves that gives the answer to this question:

Trefil, J., 1984: A Scientist at the Seashore. Charles Scribner’s Sons, New York, 208 pp.

There are 14 chapters in the book that discuss many different but related topics:

1. Look at All That Water

2. The Salt Salt Sea

3. The Tides

4. The Search for Planet X

5. The Back of the Moon

6. Making Waves

7. The Surf

8. Bubbles in the Foam

9. The Shape of the Wave

10. Queen Anne’s Pudding

11. Of Beaches and Baseballs

12. Castles in the Sand

13. Sailing Ships and Skeletons

14. Skipping Stones.

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作者:coolboy 留言时间:2017-04-16 11:41:23

I argued above that the Lighthill’s text gave a vivid description on the behavior of deep-water waves observed by a Chinese poet Bai, Juyi (白居易:772–846) shown in his well-known poem (“一重浪灭一重生”). This is an interesting example showing that sometimes a poet or an artist, through his careful observations to a natural phenomenon, is able to draw insightful scientific conclusions. Of course, in my opinion, the major difference between an artist and a scientist on scientific research or knowledge is that the former generally possesses, if any, only sporadic knowledge whereas a true scientist sees and thinks the world comprehensively, systematically, and logically. A well-known example is given by physicist Richard Feynman’s view on the beauty of a flower:

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Feynman, R. P., 1988: “What Do You Care What Other People Think?” Further Adventures of a Curious Character. Penguin Books Canada Ltd, Ontario, 255 pp.

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. But then he’ll say "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." 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 might not be quite as refined aesthetically as he is, I can appreciate the beauty of a flower. But at the same time, I see much more about the flower than he sees. I can imagine the cells inside, which also have a beauty. There’s beauty not just at the dimension of one centimeter; there is also beauty at a smaller dimension.

There are the complicated actions of the cells, and other processes. The fact that the colors in the flower have evolved in order to attract insects to pollinate it is interesting; that means that insects can see the color. That adds a question: does this aesthetic sense we have also exist in lower forms of life? There are all kinds of interesting questions that come from a knowledge of science, which only adds to the excitement and mystery and awe of a flower. It only adds. I don't understand how it subtracts.

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