THOUGHTS ON MIND AND ON STYLE

随风而逝

 

SECTION I: THOUGHTS ON MIND AND ON STYLE	第一编：关于精神和文风的思想
The difference between the mathematical and the intuitive mind.—In the one, the principles are palpable, but removed from ordinary use; so that for want of habit it is difficult to turn one's mind in that direction: but if one turns it thither ever so little, one sees the principles fully, and one must have a quite inaccurate mind who reasons wrongly from principles so plain that it is almost impossible they should escape notice.	几何学精神与敏感性精神的区别——在几何学，原则都是显然可见的，但却脱离日常的应用；从而人们由于缺乏运用习惯，很少能把脑筋放到这上面来，但是只要稍一放到这上面来，人们就会充分看出这些原则的；对于这些巨大得几乎不可能被错过的原则，若竟然也推理错误，那就一定是精神根本谬误了。
But in the intuitive mind the principles are found in common use and are before the eyes of everybody. One has only to look, and no effort is necessary; it is only a question of good eyesight, but it must be good, for the principles are so subtle and so numerous that it is almost impossible but that some escape notice. Now the omission of one principle leads to error; thus one must have very clear sight to see all the principles and, in the next place, an accurate mind not to draw false deductions from known principles.	但是敏感性精神，其原则就在日常的应用之中，并且就在人人眼前。人们只需要开动脑筋，而并不需要勉强用力；问题只在于有良好的洞见力，但是这一洞见力却必须良好；因为这些原则是那么细微，而数量又是那么繁多，以致人们几乎不可能不错过。可是，漏掉一条原则，就会引向错误；因此，就必须有异常清晰的洞见力才能看出全部的原则，然后又必须有正确的精神才不致于根据这些已知的原则进行谬误的推理。
All mathematicians would then be intuitive if they had clear sight, for they do not reason incorrectly from principles known to them; and intuitive minds would be mathematical if they could turn their eyes to the principles of mathematics to which they are unused.	因而，凡是几何学家只要能有良好的洞见力，就都会是敏感的，因为他们是不会根据他们已知的原则做出谬误的推理的；而敏感的精神若能把自己的洞见力运用到那些自己不熟悉的几何学原则上去，也会成为几何学家的。
The reason, therefore, that some intuitive minds are not mathematical is that they cannot at all turn their attention to the principles of mathematics. But the reason that mathematicians are not intuitive is that they do not see what is before them, and that, accustomed to the exact and plain principles of mathematics, and not reasoning till they have well inspected and arranged their principles, they are lost in matters of intuition where the principles do not allow of such arrangement. They are scarcely seen; they are felt rather than seen; there is the greatest difficulty in making them felt by those who do not of themselves perceive them. These principles are so fine and so numerous that a very delicate and very clear sense is needed to perceive them, and to judge rightly and justly when they are perceived, without for the most part being able to demonstrate them in order as in mathematics, because the principles are not known to us in the same way, and because it would be an endless matter to undertake it. We must see the matter at once, at one glance, and not by a process of reasoning, at least to a certain degree. And thus it is rare that mathematicians are intuitive and that men of intuition are mathematicians, because mathematicians wish to treat matters of intuition mathematically and make themselves ridiculous, wishing to begin with definitions and then with axioms, which is not the way to proceed in this kind of reasoning. Not that the mind does not do so, but it does it tacitly, naturally, and without technical rules; for the expression of it is beyond all men, and only a few can feel it.	因而，某些敏感的精神之所以并不是几何学家，就在于他们根本未能转到几何学的原则方面来；而某些几何学家之所以并不是敏感的，就在于他们并没有看到自己面前的东西，就在于他们既然习惯于几何学的简洁的原则，并且只是在很好地看出了并掌握了他们的原则之后才能进行推论，所以他们在敏感性的事物方面就茫然自失了，因为它们的原则是不容这样来掌握的。这些原则几乎是看不见的，我们勿宁是感到它们的而不是看到它们的；那些自己不曾亲身感到过它们的人，别人要想使他们感到，那就难之又难 了。这类事物是如此之细致而又如此之繁多，以致于必须有一种极其细致而又十分明晰的感觉才能感受它们，并根据这种感受做出正确公允的判断来；但却往往不能用几何学里那样的秩序来加以证明，因为我们本来就不是以这种方式获得这些原则的，也因为那样尝试的话，就会是一桩永无止境的事了。我们必须在一瞥之下一眼看出整个的事物来而不能靠推理过程，至少在一定程度上是这样。因此就很少有几何学家是敏感的，或者敏感的人而是几何学的了；这是由于几何学家要想几何学式地对待那些敏感的事物，他们要想从定义出发，然后继之以定理，而这根本就不是这类推论的活动方式，于是他们就把自己弄得荒唐可笑了。这并非是说我们的精神没有在进行推论，但它却是默默地、自然而然地、毫不造作地在进行推论的；因为它那表现是超乎一切人力之外的，而它那 感受也只能属于少数人。
Intuitive minds, on the contrary, being thus accustomed to judge at a single glance, are so astonished when they are presented with propositions of which they understand nothing, and the way to which is through definitions and axioms so sterile, and which they are not accustomed to see thus in detail, that they are repelled and disheartened.	相反地，敏感的精神既已习惯于这样一眼看去就下判断，所以——当人们向他们提出了为他们所毫不理解的命题，而深入这些命题又要经过许多如此之枯燥乃至他们根本就不习惯于那样仔细地加以观察的定义和原理时——，他们就会那么惊愕失措，以致于望而却步并且感到灰心丧气了。
But dull minds are never either intuitive or mathematical.	但谬误的精神却永远既不能成为敏感的人，也不能成为几何学家。
Mathematicians who are only mathematicians have exact minds, provided all things are explained to them by means of definitions and axioms; otherwise they are inaccurate and insufferable, for they are only right when the principles are quite clear.	因而，那些仅仅不外是几何学家的几何学家虽则具有正确的精神，却需我们以定义和原理向他们解说清楚一切事物；
And men of intuition who are only intuitive cannot have the patience to reach to first principles of things speculative and conceptual, which they have never seen in the world and which are altogether out of the common.	否则他们就会荒谬得不能容忍，因为他们只有依据说得清清楚楚的原理才能是正确的。

jiajiashiwo

貌似是那个叫啥 思想录 书里的？

随风而逝

 

There are different kinds of right understanding; some have right understanding in a certain order of things, and not in others, where they go astray. Some draw conclusions well from a few premises, and this displays an acute judgment.	有各种不同的正确意识；有的人在某一序列的事物上，但在其它序列方面则否，在那些方面他们是胡说八道。
Others draw conclusions well where there are many premises.	有的人能从少数的原则得出结论，这也是意识的一种正确性。另有人能从含有大量原则的事物中得出结论。
For example, the former easily learn hydrostatics, where the premises are few, but the conclusions are so fine that only the greatest acuteness can reach them.	例如，有的人很理解水的种种作用，而关于水的原则却是很少的；然而其结论又是如此之精致，那是非有极大的正确性办不到的。
And in spite of that these persons would perhaps not be great mathematicians, because mathematics contain a great number of premises, and there is perhaps a kind of intellect that can search with ease a few premises to the bottom and cannot in the least penetrate those matters in which there are many premises.	而这些人却未必因此就是伟大的几何学家；因为几何学是包含大量原则的，而精神有一种性质却可能是这样：即，它固然很能钻研少数原则的深处，然而却一点也不能钻研那些含有大量原则的事物。
There are then two kinds of intellect: the one able to penetrate acutely and deeply into the conclusions of given premises, and this is the precise intellect; the other able to comprehend a great number of premises without confusing them, and this is the mathematical intellect. The one has force and exactness, the other comprehension. Now the one quality can exist without the other; the intellect can be strong and narrow, and can also be comprehensive and weak.	因而便有两种精神：一种能够敏锐地、深刻地钻研种种原则的结论，这就是精确性的精神；另一种则能够理解大量的原则而从不混淆，这就是几何学的精神。一种是精神的力量与正确性，另一种则是精神的广博。而其中一种却很可能没有另一种；精神可以是强劲而又狭隘的，也可以是广博而又脆弱的。