亨利·庞加莱
亨利·庞加莱 ，法国数学家、天体力学家、数学物理学家、科学哲学家。庞加莱的研究涉及数论、代数学、几何学、拓扑学、天体力学、数学物理、多复变函数论、科学哲学等许多领域。
他被公认是19世纪后四分之一和二十世纪初的领袖数学家，是对于数学和它的应用具有全面知识的最后一个人。庞加莱在数学方面的杰出工作对20世纪和当今的数学造成极其深远的影响，他在天体力学方面的研究是牛顿之后的一座里程碑，他因为对电子理论的研究被公认为相对论的理论先驱，是“批判学派”代表人物之一。
ARTICLE SHARING
The genesis of mathematical creation is a problem which should intensely interest the psychologist. It is the activity in which the human mind seems to take least from the outside world, in which it acts or seems to act only of itself and on itself, so that in studying the procedure of geometric thought we may hope to reach what is most essential in man's mind...
数学创造的源头是一个应该引起心理学家强烈兴趣的问题。在数学创造活动中，人类的思维似乎对外界的依赖最少，且只对人类自身或只在人类自身上发挥作用，因此，在研究几何思想的过程中，我们希望寻得人类思维中必不可少的东西。
A first fact should surprise us, or rather would surprise us if we were not so used to it. How does it happen there are people who do not understand mathematics? If mathematics invokes only the rules of logic, such as are accepted by all normal minds; if its evidence is based on principles common to all men, and that none could deny without being mad, how does it come about that so many persons are here refractory?
第一个事实会使我们感到惊讶——或者更确切地说——如果我们不太习惯它的话，我们便会感到惊讶：怎么会有人无法理解数学呢？如果数学仅仅调用逻辑的规则，比如一些所有正常人都会接受的规则；如果它的论据是基于一种对所有人来说都很普遍，而且正常人都不会去否认它的原则，那么怎么会有那么多人深陷其中呢？
That not every one can invent is nowise mysterious. That not every one can retain a demonstration once learned may also pass. But that not every one can understand mathematical reasoning when explained appears very surprising when we think of it. And yet those who can follow this reasoning only with difficulty are in the majority; that is undeniable, and will surely not be gainsaid by the experience of secondary-school teachers.
不是每个人都能进行创造性的工作，这是很正常的。此外，也不是每个人都能记住学习过的例子。与之不同且令人惊讶的是，并不是每个人都能理解数学推导的过程。事实上，大多数人都很难跟上推导的节奏，这是不可否认的，当然，一个有经验的中学老师肯定也会同意这点。
And further: how is error possible in mathematics? A sane mind should not be guilty of a logical fallacy, and yet there are very fine minds who do not trip in brief reasoning such as occurs in the ordinary doings of life, and who are incapable of following or repeating without error the mathematical demonstrations which are longer, but which after all are only an accumulation of brief reasonings wholly analogous to those they make so easily. Need we add that mathematicians themselves are not infallible?...
让我们更进一步：在学习数学或研究数学时，为什么会出错？理智的头脑不应该犯逻辑谬误，有好头脑的人也不会被困在简短的推导中，因为对他们来说这就像处理日常事务一样简单，然而这些人却不能无误地跟上数学推导和演算的节奏，但这些数学演示毕竟只是简单推理的累积，完全类似于他们能够轻易得出的结论。难道说数学家们也做不到这点吗？
The answer seems to me evident. Imagine a long series of syllogisms, and that the conclusions of the first serve as premises of the following: we shall be able to catch each of these syllogisms, and it is not in passing from premises to conclusion that we are in danger of deceiving ourselves. But between the moment in which we first meet a proposition as conclusion of one syllogism, and that in which we reencounter it as premise of another syllogism occasionally some time will elapse, several links of the chain will have unrolled; so it may happen that we have forgotten it, or worse, that we have forgotten its meaning. So it may happen that we replace it by a slightly different proposition, or that, while retaining the same enunciation, we attribute to it a slightly different meaning, and thus it is that we are exposed to error.
在我看来，答案是显而易见的。想象一长串的三段论，第一个三段论的结论可以作为下一个三段论的前提：我们将能够抓住每一个三段论，而我们并不是在从前提过渡到结论的过程中有欺骗自己的危险。但是，从我们第一次把一个命题当作一个三段论的结论，到我们偶然又把它当作另一个三段论的前提，在这段时间里，链条上的几个环节已经展开了。因此，我们可能会忘记它，或者更糟的是，我们已经忘记了它的含义。 我们可能会用一个稍微不同的命题来代替它，或者在保留相同的发音的同时，我们赋予它略有不同的含义，因此我们面临错误。
Often the mathematician uses a rule. Naturally he begins by demonstrating this rule; andat the time when this proof is fresh in his memory he understands perfectly its meaningand its bearing, and he is in no danger of changing it. But subsequently he trusts hismemory and afterward only applies it in a mechanical way; and then if his memory failshim, he may apply it all wrong. Thus it is, to take a simple example, that we sometimesmake slips in calculation because we have forgotten our multiplication table.
数学家经常使用一条规则。自然地，他一开始就证明了这一规则；当他对这一证明记忆犹新时，他完全理解它的意义和含义，没有改变它的危险。但后来他相信了自己的记忆，之后只是机械地运用它；如果他的记忆出错了，他可能会用错。举一个简单的例子，我们有时会因忘记乘法表而计算失误。
According to this, the special aptitude for mathematics would be due only to a very surememory or to a prodigious force of attention. It would be a power like that of the whistplayer who remembers the cards played; or, to go up a step, like that of the chess-playerwho can visualize a great number of combinations and hold them in his ~emory. Everygood mathematician ought to be a good chess player, and inversely; likewise he should bea good computer. Of course that sometimes happens; thus Gauss was at the same time ageometer of genius and a very precocious and accurate computer.
根据这种说法，数学的特殊天赋只能归因于非常可靠的记忆力或惊人的注意力。这种能力就像打牌的人能够记住所打的牌一样，或者更进一步，就像下棋的人能够想象出大量的组合并将它们牢牢记住一样。每个优秀的数学家都应该是人优秀的棋手，反之亦然，同样，他也应该是一个优秀的计算机高手。当然这种情况有时也会发生，因此，高斯既是一位天才的几何学家，同时又是一台非常早熟和精确的计算机。
As for myself, I must confess, I am absolutely incapable even of adding without mistakes... My memory is not bad, but it would be insufficient to make me a good chess-player. Why then does it not fail me in a difficult piece of mathematical reasoning where most chess-players would lose themselves? Evidently because it is guided by the general march of the reasoning. A mathematical demonstration is not a simple juxtaposition of syllogisms, it is syllogisms placed in a certain order, and the order in which these elements are placed is much more important than the elements themselves. If I have the feeling, the intuition, so to speak, of this order, so as to perceive at a glance the reasoning as a whole, I need no longer fear lest I forget one of the elements, for each of them will take its allotted place in the array, and that without any effort of memory on my part.
我必须承认，对于我来说，我没法准确无误地做加法运算。我的记忆力也不差，但我并不是一个好的棋手。那么为什么大多数棋手会迷失在数学推导中而我却不会？显然，下棋时的推理是由普遍的、一般的推导来引导的。但数学证明并不是简单地把三段论并列起来，而是把三段论按一定的顺序排列，而这些排列的顺序比思考某一个具体的三段论要重要得多。如果我有这样的感觉，或者说直觉，对于这个三段论的顺序，我看一眼就能对整个推导过程略知一二，那么我根本不用担心会忘记其中一个的一个具体步骤，它们自动就会被分配到一个序列中，这不需要我动用任何记忆。
We know that this feeling, this intuition of mathematical order, that makes us divine hidden harmonies and relations, cannot be possessed by every one. Some will not have either this delicate feeling so difficult to define, or a strength of memory and attention beyond the ordinary, and then they will be absolutely incapable of understanding higher mathematics. Such are the majority. Others will have this feeling only in a slight degree, but they will be gifted with an uncommon memory and a great power of attention. They will learn by heart the details one after another; they can understand mathematics and sometimes make applications, but they cannot create. Others, finally, will possess in a less or greater degree the special intuition referred to, and then not only can they understand mathematics even if their memory is nothing extraordinary, but they may become creators and try to invent with more or less success according as this intuition is more or less developed in them.
我们知道，这种感觉，这种对于数学顺序的直觉，使我们能够预知到隐藏在其中的和谐与联系，这种直觉不是每个人都能拥有的。有些人既没有这种难以定义的微妙感觉，也没有超乎寻常的记忆力和注意力，那么他们就绝对无法理解高等数学，大多数人都是这样。另一些人可能只是在很小的程度上有这种感觉，但他们被赋予了罕见的记忆力和巨大的注意力，他们能一个接一个地记住细节，他们能理解数学，有时也能应用，但他们不能创造。最后，另一些人，他们或多或少地拥有这种特殊的直觉，即使他们的记忆力并不超群，他们也可以理解数学，甚至可能成为创造者。他们在数学创造上获得成就的大小与他们的这种直觉被开发了多少相对应。
In fact, what is mathematical creation? It does not consist in making new combinations with mathematical entities already known. Anyone could do that, but the combinations so made would be infinite in number and most of them absolutely without interest. To create consists precisely in not making useless combinations and in making those which are useful and which are only a small minority. Invention is discernment, choice.
事实上，什么是数学创造？它不在于用已知的数学实体进行新的组合。任何人都可以这样做，但这样得到的组合在数量上将会是无限的，而且其中的大多数都是我们完全不感兴趣的。创造就是不做无用的组合，而只做那些有用的，这往往只是少数的组合。因此，创造是洞察力和选择。
It is time to penetrate deeper and to see what goes on in the very soul of the mathematician. For this, I believe, I can do best by recalling memories of my own. But I shall limit myself to telling how I wrote my first memoir on Fuchsian functions. I beg the reader's pardon; I am about to use some technical expressions, but they need not frighten him, for he is not obliged to understand them. I shall say, for example, that I have found the demonstration of such a theorem under such circumstances. This theorem will have a barbarous name, unfamiliar to many, but that is unimportant; what is of interest for the psychologist is not the theorem but the circumstances.
现在是时候深入探究，看看在数学家的灵魂深处究竟发生了什么。为此，我相信，通过回顾我的记忆，我能做到最好。但我将仅限于叙述我是如何写出我的第一本关于 Fuchsian 函数的回忆录的。请读者原谅，我将使用一些专业用语，但不必吓唬自己，因为你们不需要去理解它们。例如，我将会说，我已经找到了这个定理在这种情况下的证明，而这个定理有一个吓人的名字，很多人都不熟悉，但这并不重要；心理学家感兴趣的不是定理，而是环境。
For fifteen days I strove to prove that there could not be any functions like those I have since called Fuchsian functions. I was then very ignorant; every day I seated myself at my work table, stayed an hour or two, tried a great number of combinations and reached no results. One evening, contrary to my custom, I drank black coffee and could not sleep. Ideas rose in crowds; I felt them collide until pairs interlocked, so to speak, making a stable combination. By the next morning I had established the existence of a class of Fuchsian functions, those which come from the hypergeometric series; I had only to write out the results, which took but a few hours.
在15天的时间里，我努力证明不可能有任何类似于我后来称之为 Fuchsian 函数的函数。那时我很无知；每天我坐在工作桌前，待上一两个小时，尝试各种组合，但都没有结果。一天晚上，与我的平时习惯相反，我喝了黑咖啡，这让我无法入睡。想法成群涌现；我感觉到它们相互碰撞，直到成对地相互连锁，可以说，形成一个稳定的组合。到第二天早上，我已经确定了一类 Fuchsian 函数的存在性，它们来自超几何级数；我只需写出结果，这只花了几个小时。
Then I wanted to represent these functions by the quotient of two series; this idea was perfectly conscious and deliberate, the analogy with elliptic functions guided me. I asked myself what properties these series must have if they existed, and I succeeded without difficulty in forming the series I have called theta-Fuchsian.
随后，我想用两个级数的商来表示这些函数；这个想法是完全有意识，且深思熟虑的，与椭圆函数的类比指导着我。我问自己，如果这些级数存在，它们一定具有什么性质，我毫不费力地成功构造出了我称之为 theta-Fuchsian 的级数。
Just at this time I left Caen, where I was then living, to go on a geologic excursion under the auspices of the school of mines. The changes of travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go some place or other. At the moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as, upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for conscience's sake I verified the result at my leisure.
就在这个时候，我离开了我当时居住的卡昂，在矿山学校的赞助下进行一次地质考察。旅行的变化使我忘记了数学工作。到了科孔茨，我们便坐上公共马车，到什么地方去。就在我踏上这一步的时候，我突然想到，我用来定义富克斯函数的变换与那些非欧几里得几何的变换是相同的，尽管在此之前，我似乎没有任何想法来为这个想法铺平道路。我没有证实这个想法，当时我没有时间，因为我一在公共马车上坐下，就继续着已经开始的谈话，但我觉得这是完全肯定的。我回到卡昂后，跟随内心的想法，在闲暇时刻从容不迫地验证了一下结果。
Then I turned my attention to the study of some arithmetical questions apparently without much success and without a suspicion of any connection with my preceding researches. Disgusted with my failure, I went to spend a few days at the seaside, and thought of something else. One morning, walking on the bluff, the idea came to me, with just the same characteristics of brevity, suddenness and immediate certainty that the arithmetic transformations of indeterminate ternary quadratic forms were identical with those of non-Euclidean geometry.
然后，我把注意力转向了一些算术问题，显然没有多大成功，也没有想到这与我之前的研究有任何联系。我对我的失败感到厌恶，去海边呆了几天，想了些别的事情。一天早上，我走在悬崖上，突然有了一个想法，它和非欧几何一样，具有简洁、突然性和立即可确定的特点，它是一个不定三元二次型的算术变换。
Returned to Caen, I meditated on this result and deduced the consequences. The example of quadratic forms showed me that there were Fuchsian groups other than those corresponding to the hypergeometric series; I saw that I could apply to them the theory of theta-Fuchsian series and that consequently there existed Fuchsian functions other than those from the hypergeometric series, the ones I then knew. Naturally I set myself to form all these functions. I made a systematic attack upon them and carried all the outworks, one after another. There was one, however, that still held out, whose fall would involve that of the whole place. But all my efforts only served at first the better to show me the difficulty, which indeed was something. All this work was perfectly conscious.
回到卡昂后，我对这个结果进行了思考，并推导出了结果。二次型的例子告诉我，除了超几何级数对应的群之外，还存在 Fuchsian 群；我发现我可以将 theta-Fuchsian 级数的理论应用于它们，并且因此，除了来自超几何级数的函数之外，还存在我当时知道的 Fuchsian 函数。很自然地，我构造出了所有的这些函数。我对他们进行了系统的攻破并一个接一个地承担了所有的工作。然而，还存在着一个问题，解决不了它会使所有努力白费。但是，我所有的那些仅在一开始时起作用的努力，使我更清楚地看到了困难，这的确是件了不起的事。所有这些工作都是在完全有意识的情况下进行的。
Thereupon I left for Mont-Valérien, where I was to go through my military service; so I was very differently occupied. One day, going along the street, the solution of the difficulty which had stopped me suddenly appeared to me. I did not try to go deep into it immediately, and only after my service did I again take up the question. I had all the elements and had only to arrange them and put them together. So I wrote out my final memoir at a single stroke and without difficulty.
于是我去了Mont-Valérien，我要在那里服完兵役，所以我的工作完全不同。一天，我在街上走着，突然想到了解决这个使我停下来的难题的办法。我并没有试图立即深入研究，在我服役之后，我才重拾这个问题。我有了所有的元素，只需要把它们排列起来，然后把它们放在一起。于是，我毫不费力地一笔一划地写出了最终的回忆录。
I shall limit myself to this single example; it is useless to multiply them...
我将仅限于讨论这个例子，举再多的例子是无用的......
Most striking at first is this appearance of sudden illumination, a manifest sign of long, unconscious prior work. The role of this unconscious work in mathematical invention appears to me incontestable, and traces of it would be found in other cases where it is less evident. Often when one works at a hard question, nothing good is accomplished at the first attack. Then one takes a rest, longer or shorter, and sits down anew to the work. During the first half-hour, as before, nothing is found, and then all of a sudden the decisive idea presents itself to the mind...
在这个例子中，最引人注目的是这种突然式启发的出现，这是长期的、潜意识的前置工作的明显迹象。在我看来，这种潜意识的工作在数学创造中的作用是无可争辩的，在其他不那么明显的情况下，也会发现它的痕迹。当一个人努力解决一个难题时，往往一开始就没有什么好的结果。然后或长或短地休息一会儿，再坐下来重新开始工作。在最初的半小时里，就像以前一样什么也找不到，然后突然间，一个决定性的想法出现在脑海里……
There is another remark to be made about the conditions of this unconscious work; it is possible, and of a certainty it is only fruitful, if it is on the one hand preceded and on the other hand followed by a period of conscious work. These sudden inspirations (and the examples already cited prove this) never happen except after some days of voluntary effort which has appeared absolutely fruitless and whence nothing good seems to have come, where the way taken seems totally astray. These efforts then have not been as sterile as one thinks; they have set agoing the unconscious machine and without them it would not have moved and would have produced nothing...
关于这种潜意识工作的条件，还有一点值得注意的是：潜意识工作有可能出现在有意识工作之前，也有可能出现在一段有意识的工作之后。对于我们要解决的问题，这样的潜意识工作肯定是富有成效的。如果没有经过几天自发的努力，这些突然的灵感(前面提到的例子证明了这一点)永远不会出现，而之前有意识工作中的努力似乎毫无结果，似乎没有任何好处，所走的路似乎完全错误。但这些努力也并非像人们想象的那样毫无结果；它们启动了这台无意识的机器，没有它们（指有意识的工作），机器就不会移动，也不会产生任何东西……
Such are the realities; now for the thoughts they force upon us. The unconscious, or, as we say, the subliminal self plays an important role in mathematical creation; this follows from what we have said. But usually the subliminal self is considered as purely automatic. Now we have seen that mathematical work is not simply mechanical, that it could not be done by a machine, however perfect. It is not merely a question of applying rules, of making the most combinations possible according to certain fixed laws. The combinations so obtained would be exceedingly numerous, useless and cumbersome. The true work of the inventor consists in choosing among these combinations so as to eliminate the useless ones or rather to avoid the trouble of making them, and the rules which must guide this choice are extremely fine and delicate. It is almost impossible to state them precisely; they are felt rather than formulated. Under these conditions, how imagine a sieve capable of applying them mechanically?
这就是事实。现在说说从这之中我们不得不接受的东西，潜意识，或者说，潜意识的自我在数学创造中扮演着重要的角色，这是我们所说的。但通常潜意识自我被认为是完全自动的。现在我们已经知道，数学工作不是简单的机械工作，它无法由机器完成，无论这台机器多么完美。数学工作不仅仅是一个应用规则的问题，也不仅仅是一个根据某些固定的法则进行最多的组合的问题。这样得到的组合将是非常多的，无用的且累赘的。创造者的真正工作是在这些组合中进行选择，以消除无用的组合，或者更确切地说，避免创造出它们，因为这很麻烦，而指导这种选择的规则是非常精细和细致的。要精确地描述它们（指潜意识的指导）几乎是不可能的，它们是一种感觉，没法形式化地表达出来。你能够想象出一个能够自动将这些组合筛选出来的筛子吗？
A first hypothesis now presents itself; the subliminal self is in no way inferior to the conscious self; it is not purely automatic; it is capable of discernment; it has tact, delicacy; it knows how to choose, to divine. What do I say? It knows better how to divine than the conscious self, since it succeeds where that has failed. In a word, is not the subliminal self superior to the conscious self? You recognize the full importance of this question...
现在出现了第一个假设：潜意识的自我并不亚于意识的自我、它不是完全自动的、它有辨别能力、它机智且细腻、它懂得如何选择，如何占卜。我该说什么？它比有意识的自我更懂得如何占卜，因为它在有意识失败的地方成功了。总而言之，潜意识的自我难道不高于意识的自我吗？你意识到了这个问题的全部重要性……
Is this affirmative answer forced upon us by the facts I have just given? I confess that, for my part, I should hate to accept it. Re-examine the facts then and see if they are not compatible with another explanation.
通过我刚才所讲的事实，能给出这个肯定的回答吗？我承认，就我而言，我不愿接受它。然后重新检查这些事实，看看它们是否与另一种解释不一致。
It is certain that the combinations which present themselves to the mind in a sort of sudden illumination, after an unconscious working somewhat prolonged, are generally useful and fertile combinations, which seem the result of a first impression. Does it follow that the subliminal self, having divined by a delicate intuition that these combinations would be useful, has formed only these, or has it rather formed many others which were lacking in interest and have remained unconscious?
可以肯定的是，这种经过长时间的无意识工作后，以一种突然的顿悟的方式出现在头脑中的组合，通常都是有用的、丰富的组合，这似乎是第一印象的结果。这是否意味着，潜意识的自我，究竟是已经通过一种微妙的直觉推测出这些组合是有用的，所以只形成了这些组合，还是在这过程中也形成了许多无用的组合，但它们被留在了潜意识中？
In this second way of looking at it, all the combinations would be formed in consequence of the automatism of the subliminal self, but only the interesting ones would break into the domain of consciousness. And this is still very mysterious. What is the cause that, among the thousand products of our unconscious activity, some are called to pass the threshold, while others remain below? Is it a simple chance which confers this privilege? Evidently not; among all the stimuli of our senses, for example, only the most intense fix our attention, unless it has been drawn to them by other causes. More generally the privileged unconscious phenomena, those susceptible of becoming conscious, are those which, directly or indirectly, affect most profoundly our emotional sensibility.
从另一种角度来看，所有的组合都是由潜意识自我的自动性形成的，但只有有趣的组合才会进入意识领域。这仍然很神秘。在我们潜意识活动的上千个产物中，有一些能够跨过门槛走进意识，而另一些则被留在了潜意识中，这是什么原因呢？是一个简单的机会赋予这种通向意识的特权吗？显然不是。例如，在我们所有的感官刺激中，除非被其他原因吸引，否则只有最强烈的刺激能吸引我们的注意力。更普遍地说，那些拥有特权的无意识现象，就是那些容易变得有意识的现象，是那些直接或间接地最深刻地影响我们的情感敏感性的现象。
It may be surprising to see emotional sensibility invoked à propos of mathematical demonstrations which, it would seem, can interest only the intellect. This would be to forget the feeling of mathematical beauty, of the harmony of numbers and forms, of geometric elegance. This is a true esthetic feeling that all real mathematicians know, and surely it belongs to emotional sensibility.
在数学论证上提到情感敏感性可能会使人感到惊讶，因为数学论证似乎只与智力有关。但这样说的话就忽略了数学之美，忽略了数与形的和谐、几何的优雅。而这是所有真正的数学家都能感受到的一种真实的美感，所以这当然也属于情感上的感性。
Now, what are the mathematic entities to which we attribute this character of beauty and elegance, and which are capable of developing in us a sort of esthetic emotion? They are those whose elements are harmoniously disposed so that the mind without effort can embrace their totality while realizing the details. This harmony is at once a satisfaction of our esthetic needs and an aid to the mind, sustaining and guiding. And at the same time, in putting under our eyes a well-ordered whole, it makes us foresee a mathematical law... Thus it is this special esthetic sensibility which plays the role of the delicate sieve of which I spoke, and that sufficiently explains why the one lacking it will never be a real creator.
那么，是什么数学实体让我们能够赋予它们美丽和优雅的特性，哪些数学实体能够在我们身上发展一种审美情感？是那些被和谐地摆放的元素，这样头脑才可以毫不费力地拥抱它们的整体，同时掌握细节。这种和谐既满足了我们的审美需要，又帮助了我们思考，使我们能够跟上节奏并提供指导。同时，在审视这些有序的整体时，我们预见了一个数学定律……因此，正是这种特殊的审美敏感性发挥了我之前所说的精致的筛子的作用，这充分解释了为什么没有它的人永远无法成为一个真正的创造者。
Yet all the difficulties have not disappeared. The conscious self is narrowly limited, and as for the subliminal self we know not its limitations, and this is why we are not too reluctant in supposing that it has been able in a short time to make more different combinations than the whole life of a conscious being could encompass. Yet these limitations exist. Is it likely that it is able to form all the possible combinations, whose number would frighten the imagination? Nevertheless that would seem necessary, because if it produces only a small part of these combinations, and if it makes them at random, there would be small chance that the good, the one we should choose, would be found among them.
然而，所有的困难并没有消失。有意识的自我是狭隘且受限的。至于潜意识自我，我们不知道它的局限性，这就是为什么我们不太情愿做出之前的假设，因为它似乎可以在很短的时间内产生许多组合数量，比意识自我一生中所能产生的组合数量还要多。然而，潜意识的局限性问题仍然存在。它是否可能形成所有可能的，超乎你想象之多的组合？这似乎必需的，因为如果它只产生这些组合中的一小部分，如果它只是随机产生这些组合，那么在这些组合中找到我们需要的那个好的组合的概率就很小。
Perhaps we ought to seek the explanation in that preliminary period of conscious work which always precedes all fruitful unconscious labor. Permit me a rough comparison. Figure the future elements of our combinations as something like the hooked atoms of Epicurus. During the complete repose of the mind, these atoms are motionless, they are, so to speak, hooked to the wall...
也许我们应该向最初有意识工作的阶段寻求解释，它总是先于所有卓有成效的无意识劳动。请允许我做一个粗略的比较。把我们未来的组合元素想象成伊壁鸠鲁的钩状原子。在思想完全休息的时间内，这些原子是静止的，可以说，它们是挂在墙上的……
On the other hand, during a period of apparent rest and unconscious work, certain of them are detached from the wall and put in motion. They flash in every direction through the space (I was about to say the room) where they are enclosed, as would, for example, a swarm of gnats or, if you prefer a more learned comparison, like the molecules of gas in the kinematic theory of gases. Then their mutual impacts may produce new combinations.
另一方面，在一段明显的休息和无意识的工作期间，它们中的某些原子会脱离墙壁，开始活动。它们在封闭的空间（我正想说房间）中向各个方向闪去，就像一群蚊子，或者，如果你喜欢更有学问的比较，就像气体运动学理论中的气体分子。然后，它们的相互影响可能产生新的组合。
What is the role of the preliminary conscious work? It is evidently to mobilize certain of these atoms, to unhook them from the wall and put them in swing. We think we have done no good, because we have moved these elements a thousand different ways in seeking to assemble them, and have found no satisfactory aggregate. But, after this shaking up imposed upon them by our will, these atoms do not return to their primitive rest. They freely continue their dance.
初期有意识工作的作用是什么？显然是调动其中的某些原子，把它们从墙上解下来，使它们摆动起来。我们认为我们没有做得很好，因为我们以成千种不同的方式设法把这些元素集合起来，但没有找到令人满意的集合。但是，在我们的意志强加于它们这种震动之后，这些原子并没有回到它们原始的静止状态。它们自由地继续它们的舞蹈。
Now, our will did not choose them at random; it pursued a perfectly determined aim. The mobilized atoms are therefore not any atoms whatsoever; they are those from which we might reasonably expect the desired solution. Then the mobilized atoms undergo impacts which make them enter into combinations among themselves or with other atoms at rest which they struck against in their course. Again I beg pardon, my comparison is very rough, but I scarcely know how otherwise to make my thought understood.
现在，我们的意志不会随机选择它们，而是追求一个完全坚定的目标。因此，被动员的原子不是所有的原子，而是那些我们期望能够产生令人满意的解的原子。然后，受力运动的原子受到冲击，使得在运动的原子之间或在运动过程中与其他静止原子碰撞而形成组合。再说一遍，请原谅我这个比较粗略的比喻，但我找不到更好的比喻了。
However it may be, the only combinations that have a chance of forming are those where at least one of the elements is one of those atoms freely chosen by our will. Now, it is evidently among these that is found what I called the good combination. Perhaps this is a way of lessening the paradoxical in the original hypothesis...
无论如何，唯一有机会形成的组合中，至少有一种元素是由我们自由选择的原子组成的。显然，在这些组合中找到了我所说的良好组合。也许这是一种减少原假设中自相矛盾之处的方式……
I shall make a last remark: when above I made certain personal observations, I spoke of a night of excitement when I worked in spite of myself. Such cases are frequent, and it is not necessary that the abnormal cerebral activity be caused by a physical excitant as in that I mentioned. It seems, in such cases, that one is present at his own unconscious work, made partially perceptible to the over-excited consciousness, yet without having changed its nature. Then we vaguely comprehend what distinguishes the two mechanisms or, if you wish, the working methods of the two egos. And the psychologic observations I have been able thus to make seem to me to confirm in their general outlines the views I have given.
最后，我想补充的是：当我做出如前所述的自我观察时，我谈到了一个激动的夜晚，当时我忘我地工作着。这种情况很常见，我提到的这种异常的大脑活动不需要物理刺激引发。在这种情况下，这种无意识工作有可能被过度兴奋的意识察觉到，但并没有改变它无意识工作的本质。这样，我们就大概地了解到是什么将这两种机制区分开，如果你愿意，也可以说是两种自我的工作方法。在我看来，我所做出的这些心理观察似乎证实了我给出的观点。
Surely they have need of [confirmation], for they are and remain in spite of all very hypothetical: the interest of the questions is so great that I do not repent of having submitted them to the reader.
当然，以上的观点仍需要证实，尽管上述的所有内容都是假说，但它们确实存在，这些问题是如此有趣，以至于我无悔地将它们交给读者。
龙大量化
联系客服
