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CHAPTER VI
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OF SPACE

23. WHAT ARE WE SUPPOSED TO KNOW ABOUT IT.—The plain man may admit that he is not ready to hazard a definition of space, but he is certainly not willing to admit that he is wholly ignorant of space and of its attributes. He knows that it is something in which material objects have position and in which they move about; he knows that it has not merely length, like a line, nor length and breadth, like a surface, but has the three dimensions of length, breadth, and depth; he knows that, except in the one circumstance of its position, every part of space is exactly like every other part, and that, although objects may move about in space, it is incredible that the spaces themselves should be shifted about.

Those who are familiar with the literature of the subject know that it has long been customary to make regarding space certain other statements to which the plain man does not usually make serious objection when he is introduced to them. Thus it is said:—

(1) The idea of space is necessary. We can think of objects in space as annihilated2, but we cannot conceive space to be annihilated. We can clear space of things, but we cannot clear away space itself, even in thought.

(2) Space must be infinite. We cannot conceive that we should come to the end of space.

(3) Every space, however small, is infinitely4 divisible. That is to say, even the most minute space must be composed of spaces. We cannot, even theoretically, split a solid into mere1 surfaces, a surface into mere lines, or a line into mere points.

Against such statements the plain man is not impelled5 to rise in rebellion, for he can see that there seems to be some ground for making them. He can conceive of any particular material object as annihilated, and of the place which it occupied as standing6 empty; but he cannot go on and conceive of the annihilation of this bit of empty space. Its annihilation would not leave a gap, for a gap means a bit of empty space; nor could it bring the surrounding spaces into juxtaposition7, for one cannot shift spaces, and, in any case, a shifting that is not a shifting through space is an absurdity8.

Again, he cannot conceive of any journey that would bring him to the end of space. There is no more reason for stopping at one point than at another; why not go on? What could end space?

As to the infinite divisibility of space, have we not, in addition to the seeming reasonableness of the doctrine9, the testimony10 of all the mathematicians12? Does any one of them ever dream of a line so short that it cannot be divided into two shorter lines, or of an angle so small that it cannot be bisected?

24. SPACE AS NECESSARY AND SPACE AS INFINITE.—That these statements about space contain truth one should not be in haste to deny. It seems silly to say that space can be annihilated, or that one can travel "over the mountains of the moon" in the hope of reaching the end of it. And certainly no prudent13 man wishes to quarrel with that coldly rational creature the mathematician11.

But it is well worth while to examine the statements carefully and to see whether there is not some danger that they may be understood in such a way as to lead to error. Let us begin with the doctrine that space is necessary and cannot be "thought away."

As we have seen above, it is manifestly impossible to annihilate3 in thought a certain portion of space and leave the other portions intact. There are many things in the same case. We cannot annihilate in thought one side of a door and leave the other side; we cannot rob a man of the outside of his hat and leave him the inside. But we can conceive of a whole door as annihilated, and of a man as losing a whole hat. May we or may we not conceive of space as a whole as nonexistent?

I do not say, be it observed, can we conceive of something as attacking and annihilating14 space? Whatever space may be, we none of us think of it as a something that may be threatened and demolished15. I only say, may we not think of a system of things—not a world such as ours, of course, but still a system of things of some sort—in which space relations have no part? May we not conceive such to be possible?

It should be remarked that space relations are by no means the only ones in which we think of things as existing. We attribute to them time relations as well. Now, when we think of occurrences as related to each other in time, we do, in so far as we concentrate our attention upon these relations, turn our attention away from space and contemplate16 another aspect of the system of things. Space is not such a necessity of thought that we must keep thinking of space when we have turned our attention to something else. And is it, indeed, inconceivable that there should be a system of things (not extended things in space, of course), characterized by time relations and perhaps other relations, but not by space relations?

It goes without saying that we cannot go on thinking of space and at the same time not think of space. Those who keep insisting upon space as a necessity of thought seem to set us such a task as this, and to found their conclusion upon our failure to accomplish it. "We can never represent to ourselves the nonexistence of space," says the German philosopher Kant (1724-1804), "although we can easily conceive that there are no objects in space."

It would, perhaps, be fairer to translate the first half of this sentence as follows: "We can never picture to ourselves the nonexistence of space." Kant says we cannot make of it a Vorstellung, a representation. This we may freely admit, for what does one try to do when one makes the effort to imagine the nonexistence of space? Does not one first clear space of objects, and then try to clear space of space in much the same way? We try to "think space away," i.e. to remove it from the place where it was and yet keep that place.

What does it mean to imagine or represent to oneself the nonexistence of material objects? Is it not to represent to oneself the objects as no longer in space, i.e. to imagine the space as empty, as cleared of the objects? It means something in this case to speak of a Vorstellung, or representation. We can call before our minds the empty space. But if we are to think of space as nonexistent, what shall we call before our minds? Our procedure must not be analogous17 to what it was before; we must not try to picture to our minds the absence of space, as though that were in itself a something that could be pictured; we must turn our attention to other relations, such as time relations, and ask whether it is not conceivable that such should be the only relations obtaining within a given system.

Those who insist upon the fact that we cannot but conceive space as infinite employ a very similar argument to prove their point. They set us a self-contradictory task, and regard our failure to accomplish it as proof of their position. Thus, Sir William Hamilton (1788-1856) argues: "We are altogether unable to conceive space as bounded—as finite; that is, as a whole beyond which there is no further space." And Herbert Spencer echoes approvingly: "We find ourselves totally unable to imagine bounds beyond which there is no space."

Now, whatever one may be inclined to think about the infinity18 of space, it is clear that this argument is an absurd one. Let me write it out more at length: "We are altogether unable to conceive space as bounded—as finite; that is, as a whole in the space beyond which there is no further space." "We find ourselves totally unable to imagine bounds, in the space beyond which there is no further space." The words which I have added were already present implicitly19. What can the word "beyond" mean if it does not signify space beyond? What Sir William and Mr. Spencer have asked us to do is to imagine a limited space with a beyond and yet no beyond.

There is undoubtedly20 some reason why men are so ready to affirm that space is infinite, even while they admit that they do not know that the world of material things is infinite. To this we shall come back again later. But if one wishes to affirm it, it is better to do so without giving a reason than it is to present such arguments as the above.

25. SPACE AS INFINITELY DIVISIBLE.—For more than two thousand years men have been aware that certain very grave difficulties seem to attach to the idea of motion, when we once admit that space is infinitely divisible. To maintain that we can divide any portion of space up into ultimate elements which are not themselves spaces, and which have no extension, seems repugnant to the idea we all have of space. And if we refuse to admit this possibility there seems to be nothing left to us but to hold that every space, however small, may theoretically be divided up into smaller spaces, and that there is no limit whatever to the possible subdivision of spaces. Nevertheless, if we take this most natural position, we appear to find ourselves plunged21 into the most hopeless of labyrinths22, every turn of which brings us face to face with a flat self-contradiction.

To bring the difficulties referred to clearly before our minds, let us suppose a point to move uniformly over a line an inch long, and to accomplish its journey in a second. At first glance, there appears to be nothing abnormal about this proceeding23. But if we admit that this line is infinitely divisible, and reflect upon this property of the line, the ground seems to sink from beneath our feet at once.

For it is possible to argue that, under the conditions given, the point must move over one half of the line in half a second; over one half of the remainder, or one fourth of the line, in one fourth of a second; over one eighth of the line, in one eighth of a second, etc. Thus the portions of line moved over successively by the point may be represented by the descending24 series:

1/2, 1/4, 1/8, 1/16, . . . [Greek omicron symbol]

Now, it is quite true that the motion of the point can be described in a number of different ways; but the important thing to remark here is that, if the motion really is uniform, and if the line really is infinitely divisible, this series must, as satisfactorily as any other, describe the motion of the point. And it would be absurd to maintain that a part of the series can describe the whole motion. We cannot say, for example, that, when the point has moved over one half, one fourth, and one eighth of the line, it has completed its motion. If even a single member of the series is left out, the whole line has not been passed over; and this is equally true whether the omitted member represent a large bit of line or a small one.

The whole series, then, represents the whole line, as definite parts of the series represent definite parts of the line. The line can only be completed when the series is completed. But when and how can this series be completed? In general, a series is completed when we reach the final term, but here there appears to be no final term. We cannot make zero the final term, for it does not belong to the series at all. It does not obey the law of the series, for it is not one half as large as the term preceding it—what space is so small that dividing it by 2 gives us [omicron]? On the other hand, some term just before zero cannot be the final term; for if it really represents a little bit of the line, however small, it must, by hypothesis, be made up of lesser25 bits, and a smaller term must be conceivable. There can, then, be no last term to the series; i.e. what the point is doing at the very last is absolutely indescribable; it is inconceivable that there should be a very last.

It was pointed26 out many centuries ago that it is equally inconceivable that there should be a very first. How can a point even begin to move along an infinitely divisible line? Must it not before it can move over any distance, however short, first move over half that distance? And before it can move over that half, must it not move over the half of that? Can it find something to move over that has no halves? And if not, how shall it even start to move? To move at all, it must begin somewhere; it cannot begin with what has no halves, for then it is not moving over any part of the line, as all parts have halves; and it cannot begin with what has halves, for that is not the beginning. What does the point do first? that is the question. Those who tell us about points and lines usually leave us to call upon gentle echo for an answer.

The perplexities of this moving point seem to grow worse and worse the longer one reflects upon them. They do not harass27 it merely at the beginning and at the end of its journey. This is admirably brought out by Professor W. K. Clifford (1845-1879), an excellent mathematician, who never had the faintest intention of denying the possibility of motion, and who did not desire to magnify the perplexities in the path of a moving point. He writes:—

"When a point moves along a line, we know that between any two positions of it there is an infinite number . . . of intermediate positions. That is because the motion is continuous. Each of those positions is where the point was at some instant or other. Between the two end positions on the line, the point where the motion began and the point where it stopped, there is no point of the line which does not belong to that series. We have thus an infinite series of successive positions of a continuously moving point, and in that series are included all the points of a certain piece of line-room." [1]

Thus, we are told that, when a point moves along a line, between any two positions of it there is an infinite number of intermediate positions. Clifford does not play with the word "infinite"; he takes it seriously and tells us that it means without any end: "Infinite; it is a dreadful word, I know, until you find out that you are familiar with the thing which it expresses. In this place it means that between any two positions there is some intermediate position; between that and either of the others, again, there is some other intermediate; and so on without any end. Infinite means without any end."

But really, if the case is as stated, the point in question must be at a desperate pass. I beg the reader to consider the following, and ask himself whether he would like to change places with it:—

(1) If the series of positions is really endless, the point must complete one by one the members of an endless series, and reach a nonexistent final term, for a really endless series cannot have a final term.

(2) The series of positions is supposed to be "an infinite series of successive positions." The moving point must take them one after another. But how can it? Between any two positions of the point there is an infinite number of intermediate positions. That is to say, no two of these successive positions must be regarded as next to each other; every position is separated from every other by an infinite number of intermediate ones. How, then, shall the point move? It cannot possibly move from one position to the next, for there is no next. Shall it move first to some position that is not the next? Or shall it in despair refuse to move at all?

Evidently there is either something wrong with this doctrine of the infinite divisibility of space, or there is something wrong with our understanding of it, if such absurdities28 as these refuse to be cleared away. Let us see where the trouble lies.

26. WHAT IS REAL SPACE?—It is plain that men are willing to make a number of statements about space, the ground for making which is not at once apparent. It is a bold man who will undertake to say that the universe of matter is infinite in extent. We feel that we have the right to ask him how he knows that it is. But most men are ready enough to affirm that space is and must be infinite. How do they know that it is? They certainly do not directly perceive all space, and such arguments as the one offered by Hamilton and Spencer are easily seen to be poor proofs.

Men are equally ready to affirm that space is infinitely divisible. Has any man ever looked upon a line and perceived directly that it has an infinite number of parts? Did any one ever succeed in dividing a space up infinitely? When we try to make clear to ourselves how a point moves along an infinitely divisible line, do we not seem to land in sheer absurdities? On what sort of evidence does a man base his statements regarding space? They are certainly very bold statements.

A careful reflection reveals the fact that men do not speak as they do about space for no reason at all. When they are properly understood, their statements can be seen to be justified29, and it can be seen also that the difficulties which we have been considering can be avoided. The subject is a deep one, and it can scarcely be discussed exhaustively in an introductory volume of this sort, but one can, at least, indicate the direction in which it seems most reasonable to look for an answer to the questions which have been raised. How do we come to a knowledge of space, and what do we mean by space? This is the problem to solve; and if we can solve this, we have the key which will unlock many doors.

Now, we saw in the last chapter that we have reason to believe that we know what the real external world is. It is a world of things which we perceive, or can perceive, or, not arbitrarily but as a result of careful observation and deductions30 therefrom, conceive as though we did perceive it—a world, say, of atoms and molecules31. It is not an Unknowable behind or beyond everything that we perceive, or can perceive, or conceive in the manner stated.

And the space with which we are concerned is real space, the space in which real things exist and move about, the real things which we can directly know or of which we can definitely know something. In some sense it must be given in our experience, if the things which are in it, and are known to be in it, are given in our experience. How must we think of this real space?

Suppose we look at a tree at a distance. We are conscious of a certain complex of color. We can distinguish the kind of color; in this case, we call it blue. But the quality of the color is not the only thing that we can distinguish in the experience. In two experiences of color the quality may be the same, and yet the experiences may be different from each other. In the one case we may have more of the same color—we may, so to speak, be conscious of a larger patch; but even if there is not actually more of it, there may be such a difference that we can know from the visual experience alone that the touch object before us is, in the one case, of the one shape, and, in the other case, of another. Thus we may distinguish between the stuff given in our experience and the arrangement of that stuff. This is the distinction which philosophers have marked as that between "matter" and "form." It is, of course, understood that both of these words, so used, have a special sense not to be confounded with their usual one.

This distinction between "matter" and "form" obtains in all our experiences. I have spoken just above of the shape of the touch object for which our visual experiences stand as signs. What do we mean by its shape? To the plain man real things are the touch things of which he has experience, and these touch things are very clearly distinguishable from one another in shape, in size, in position, nor are the different parts| of the things to be confounded with each other. Suppose that, as we pass our hand over a table, all the sensations of touch and movement which we experience fused into an undistinguishable mass. Would we have any notion of size or shape? It is because our experiences of touch and movement do not fuse, but remain distinguishable from each other, and we are conscious of them as arranged, as constituting a system, that we can distinguish between this part of a thing and that, this thing and that.

This arrangement, this order, of what is revealed by touch and movement, we may call the "form" of the touch world. Leaving out of consideration, for the present, time relations, we may say that the "form" of the touch world is the whole system of actual and possible relations of arrangement between the elements which make it up. It is because there is such a system of relations that we can speak of things as of this shape or of that, as great or small, as near or far, as here or there.

Now, I ask, is there any reason to believe that, when the plain man speaks of space, the word means to him anything more than this system of actual and possible relations of arrangement among the touch things that constitute his real world? He may talk sometimes as though space were some kind of a thing, but he does not really think of it as a thing.

This is evident from the mere fact that he is so ready to make about it affirmations that he would not venture to make about things. It does not strike him as inconceivable that a given material object should be annihilated; it does strike him as inconceivable that a portion of space should be blotted32 out of existence. Why this difference? Is it not explained when we recognize that space is but a name for all the actual and possible relations of arrangement in which things in the touch world may stand? We cannot drop out some of these relations and yet keep space, i.e. the system of relations which we had before. That this is what space means, the plain man may not recognize explicitly33, but he certainly seems to recognize it implicitly in what he says about space. Men are rarely inclined to admit that space is a thing of any kind, nor are they much more inclined to regard it as a quality of a thing. Of what could it be the quality?

And if space really were a thing of any sort, would it not be the height of presumption34 for a man, in the absence of any direct evidence from observation, to say how much there is of it—to declare it infinite? Men do not hesitate to say that space must be infinite. But when we realize that we do not mean by space merely the actual relations which exist between the touch things that make up the world, but also the possible relations, i.e. that we mean the whole plan of the world system, we can see that it is not unreasonable35 to speak of space as infinite.

The material universe may, for aught we know, be limited in extent. The actual space relations in which things stand to each other may not be limitless. But these actual space relations taken alone do not constitute space. Men have often asked themselves whether they should conceive of the universe as limited and surrounded by void space. It is not nonsense to speak of such a state of things. It would, indeed, appear to be nonsense to say that, if the universe is limited, it does not lie in void space. What can we mean by void space but the system of possible relations in which things, if they exist, must stand? To say that, beyond a certain point, no further relations are possible, seems absurd.

Hence, when a man has come to understand what we have a right to mean by space, it does not imply a boundless36 conceit37 on his part to hazard the statement that space is infinite. When he has said this, he has said very little. What shall we say to the statement that space is infinitely divisible?

To understand the significance of this statement we must come back to the distinction between appearances and the real things for which they stand as signs, the distinction discussed at length in the last chapter.

When I see a tree from a distance, the visual experience which I have is, as we have seen, not an indivisible unit, but is a complex experience; it has parts, and these parts are related to each other; in other words, it has both "matter" and "form." It is, however, one thing to say that this experience has parts, and it is another to say that it has an infinite number of parts. No man is conscious of perceiving an infinite number of parts in the patch of color which represents to him a tree at a distance; to say that it is constituted of such strikes us in our moments of sober reflection as a monstrous38 statement.

Now, this visual experience is to us the sign of the reality, the real tree; it is not taken as the tree itself. When we speak of the size, the shape, the number of parts, of the tree, we do not have in mind the size, the shape, the number of parts, of just this experience. We pass from the sign to the thing signified, and we may lay our hand upon this thing, thus gaining a direct experience of the size and shape of the touch object.

We must recognize, however, that just as no man is conscious of an infinite number of parts in what he sees, so no man is conscious of an infinite number of parts in what he touches. He who tells me that, when I pass my finger along my paper cutter, what I perceive has an infinite number of parts, tells me what seems palpably untrue. When an object is very small, I can see it, and I cannot see that it is composed of parts; similarly, when an object is very small, I can feel it with my finger, but I cannot distinguish its parts by the sense of touch. There seem to be limits beyond which I cannot go in either case.

Nevertheless, men often speak of thousandths of an inch, or of millionths of an inch, or of distances even shorter. Have such fractions of the magnitudes that we do know and can perceive any real existence? The touch world of real things as it is revealed in our experience does not appear to be divisible into such; it does not appear to be divisible even so far, and much less does it appear to be infinitely divisible.

But have we not seen that the touch world given in our experience must be taken by the thoughtful man as itself the sign or appearance of a reality more ultimate? The speck39 which appears to the naked eye to have no parts is seen under the microscope to have parts; that is to say, an experience apparently40 not extended has become the sign of something that is seen to have part out of part. We have as yet invented no instrument that will make directly perceptible to the finger tip an atom of hydrogen or of oxygen, but the man of science conceives of these little things as though they could be perceived. They and the space in which they move—the system of actual and possible relations between them—seem to be related to the world revealed in touch very much as the space revealed in the field of the microscope is related to the space of the speck looked at with the naked eye.

Thus, when the thoughtful man speaks of real space, he cannot mean by the word only the actual and possible relations of arrangement among the things and the parts of things directly revealed to his sense of touch. He may speak of real things too small to be thus perceived, and of their motion as through spaces too small to be perceptible at all. What limit shall he set to the possible subdivision of real things? Unless he can find an ultimate reality which cannot in its turn become the appearance or sign of a further reality, it seems absurd to speak of a limit at all.

We may, then, say that real space is infinitely divisible. By this statement we should mean that certain experiences may be represented by others, and that we may carry on our division in the case of the latter, when a further subdivision of the former seems out of the question. But it should not mean that any single experience furnished us by any sense, or anything that we can represent in the imagination, is composed of an infinite number of parts.

When we realize this, do we not free ourselves from the difficulties which seemed to make the motion of a point over a line an impossible absurdity? The line as revealed in a single experience either of sight or of touch is not composed of an infinite number of parts. It is composed of points seen or touched—least experiences of sight or touch, minima sensibilia. These are next to each other, and the point, in moving, takes them one by one.

But such a single experience is not what we call a line. It is but one experience of a line. Though the experience is not infinitely divisible, the line may be. This only means that the visual or tactual point of the single experience may stand for, may represent, what is not a mere point but has parts, and is, hence, divisible. Who can set a limit to such possible substitutions? in other words, who can set a limit to the divisibility of a real line?

It is only when we confuse the single experience with the real line that we fall into absurdities. What the mathematician tells us about real points and real lines has no bearing on the constitution of the single experience and its parts. Thus, when he tells us that between any two points on a line there are an infinite number of other points, he only means that we may expand the line indefinitely by the system of substitutions described above. We do this for ourselves within limits every time that we approach from a distance a line drawn41 on a blackboard. The mathematician has generalized our experience for us, and that is all he has done. We should try to get at his real meaning, and not quote him as supporting an absurdity.

[1] "Seeing and Thinking," p. 149.

点击收听单词发音收听单词发音  

1 mere rC1xE     
adj.纯粹的;仅仅,只不过
参考例句:
  • That is a mere repetition of what you said before.那不过是重复了你以前讲的话。
  • It's a mere waste of time waiting any longer.再等下去纯粹是浪费时间。
2 annihilated b75d9b14a67fe1d776c0039490aade89     
v.(彻底)消灭( annihilate的过去式和过去分词 );使无效;废止;彻底击溃
参考例句:
  • Our soldiers annihilated a force of three hundred enemy troops. 我军战士消灭了300名敌军。 来自《现代汉英综合大词典》
  • We annihilated the enemy. 我们歼灭了敌人。 来自《简明英汉词典》
3 annihilate Peryn     
v.使无效;毁灭;取消
参考例句:
  • Archer crumpled up the yellow sheet as if the gesture could annihilate the news it contained.阿切尔把这张黄纸揉皱,好象用这个动作就会抹掉里面的消息似的。
  • We should bear in mind that we have to annihilate the enemy.我们要把歼敌的重任时刻记在心上。
4 infinitely 0qhz2I     
adv.无限地,无穷地
参考例句:
  • There is an infinitely bright future ahead of us.我们有无限光明的前途。
  • The universe is infinitely large.宇宙是无限大的。
5 impelled 8b9a928e37b947d87712c1a46c607ee7     
v.推动、推进或敦促某人做某事( impel的过去式和过去分词 )
参考例句:
  • He felt impelled to investigate further. 他觉得有必要作进一步调查。
  • I feel impelled to express grave doubts about the project. 我觉得不得不对这项计划深表怀疑。 来自《简明英汉词典》
6 standing 2hCzgo     
n.持续,地位;adj.永久的,不动的,直立的,不流动的
参考例句:
  • After the earthquake only a few houses were left standing.地震过后只有几幢房屋还立着。
  • They're standing out against any change in the law.他们坚决反对对法律做任何修改。
7 juxtaposition ykvy0     
n.毗邻,并置,并列
参考例句:
  • The juxtaposition of these two remarks was startling.这两句话连在一起使人听了震惊。
  • It is the result of the juxtaposition of contrasting colors.这是并列对比色的结果。
8 absurdity dIQyU     
n.荒谬,愚蠢;谬论
参考例句:
  • The proposal borders upon the absurdity.这提议近乎荒谬。
  • The absurdity of the situation made everyone laugh.情况的荒谬可笑使每个人都笑了。
9 doctrine Pkszt     
n.教义;主义;学说
参考例句:
  • He was impelled to proclaim his doctrine.他不得不宣扬他的教义。
  • The council met to consider changes to doctrine.宗教议会开会考虑更改教义。
10 testimony zpbwO     
n.证词;见证,证明
参考例句:
  • The testimony given by him is dubious.他所作的证据是可疑的。
  • He was called in to bear testimony to what the police officer said.他被传入为警官所说的话作证。
11 mathematician aoPz2p     
n.数学家
参考例句:
  • The man with his back to the camera is a mathematician.背对着照相机的人是位数学家。
  • The mathematician analyzed his figures again.这位数学家再次分析研究了他的这些数字。
12 mathematicians bca28c194cb123ba0303d3afafc32cb4     
数学家( mathematician的名词复数 )
参考例句:
  • Do you suppose our mathematicians are unequal to that? 你以为我们的数学家做不到这一点吗? 来自英汉文学
  • Mathematicians can solve problems with two variables. 数学家们可以用两个变数来解决问题。 来自哲学部分
13 prudent M0Yzg     
adj.谨慎的,有远见的,精打细算的
参考例句:
  • A prudent traveller never disparages his own country.聪明的旅行者从不贬低自己的国家。
  • You must school yourself to be modest and prudent.你要学会谦虚谨慎。
14 annihilating 6007a4c2cb27249643de5b5207143a4a     
v.(彻底)消灭( annihilate的现在分词 );使无效;废止;彻底击溃
参考例句:
  • There are lots of ways of annihilating the planet. 毁灭地球有很多方法。 来自辞典例句
  • We possess-each of us-nuclear arsenals capable of annihilating humanity. 我们两国都拥有能够毁灭全人类的核武库。 来自辞典例句
15 demolished 3baad413d6d10093a39e09955dfbdfcb     
v.摧毁( demolish的过去式和过去分词 );推翻;拆毁(尤指大建筑物);吃光
参考例句:
  • The factory is due to be demolished next year. 这个工厂定于明年拆除。
  • They have been fighting a rearguard action for two years to stop their house being demolished. 两年来,为了不让拆除他们的房子,他们一直在进行最后的努力。
16 contemplate PaXyl     
vt.盘算,计议;周密考虑;注视,凝视
参考例句:
  • The possibility of war is too horrifying to contemplate.战争的可能性太可怕了,真不堪细想。
  • The consequences would be too ghastly to contemplate.后果不堪设想。
17 analogous aLdyQ     
adj.相似的;类似的
参考例句:
  • The two situations are roughly analogous.两种情況大致相似。
  • The company is in a position closely analogous to that of its main rival.该公司与主要竞争对手的处境极为相似。
18 infinity o7QxG     
n.无限,无穷,大量
参考例句:
  • It is impossible to count up to infinity.不可能数到无穷大。
  • Theoretically,a line can extend into infinity.从理论上来说直线可以无限地延伸。
19 implicitly 7146d52069563dd0fc9ea894b05c6fef     
adv. 含蓄地, 暗中地, 毫不保留地
参考例句:
  • Many verbs and many words of other kinds are implicitly causal. 许多动词和许多其他类词都蕴涵着因果关系。
  • I can trust Mr. Somerville implicitly, I suppose? 我想,我可以毫无保留地信任萨莫维尔先生吧?
20 undoubtedly Mfjz6l     
adv.确实地,无疑地
参考例句:
  • It is undoubtedly she who has said that.这话明明是她说的。
  • He is undoubtedly the pride of China.毫无疑问他是中国的骄傲。
21 plunged 06a599a54b33c9d941718dccc7739582     
v.颠簸( plunge的过去式和过去分词 );暴跌;骤降;突降
参考例句:
  • The train derailed and plunged into the river. 火车脱轨栽进了河里。
  • She lost her balance and plunged 100 feet to her death. 她没有站稳,从100英尺的高处跌下摔死了。
22 labyrinths 1c4fd8d520787cf75236b4b362eb0b8e     
迷宫( labyrinth的名词复数 ); (文字,建筑)错综复杂的
参考例句:
  • I was engulfed in labyrinths of trouble too great to get out at all. 我陷入困难的迷宫中去,简直无法脱身。
  • I've explored ancient castles, palaces, temples, tombs, catacombs and labyrinths. 我曾在古堡、古皇宫、古神庙、古墓、地下墓穴和迷宫中探险。
23 proceeding Vktzvu     
n.行动,进行,(pl.)会议录,学报
参考例句:
  • This train is now proceeding from Paris to London.这次列车从巴黎开往伦敦。
  • The work is proceeding briskly.工作很有生气地进展着。
24 descending descending     
n. 下行 adj. 下降的
参考例句:
  • The results are expressed in descending numerical order . 结果按数字降序列出。
  • The climbers stopped to orient themselves before descending the mountain. 登山者先停下来确定所在的位置,然后再下山。
25 lesser UpxzJL     
adj.次要的,较小的;adv.较小地,较少地
参考例句:
  • Kept some of the lesser players out.不让那些次要的球员参加联赛。
  • She has also been affected,but to a lesser degree.她也受到波及,但程度较轻。
26 pointed Il8zB4     
adj.尖的,直截了当的
参考例句:
  • He gave me a very sharp pointed pencil.他给我一支削得非常尖的铅笔。
  • She wished to show Mrs.John Dashwood by this pointed invitation to her brother.她想通过对达茨伍德夫人提出直截了当的邀请向她的哥哥表示出来。
27 harass ceNzZ     
vt.使烦恼,折磨,骚扰
参考例句:
  • Our mission is to harass the landing of the main Japaness expeditionary force.我们的任务是骚乱日本远征军主力的登陆。
  • They received the order to harass the enemy's rear.他们接到骚扰敌人后方的命令。
28 absurdities df766e7f956019fcf6a19cc2525cadfb     
n.极端无理性( absurdity的名词复数 );荒谬;谬论;荒谬的行为
参考例句:
  • She has a sharp eye for social absurdities, and compassion for the victims of social change. 她独具慧眼,能够看到社会上荒唐的事情,对于社会变革的受害者寄以同情。 来自辞典例句
  • The absurdities he uttered at the dinner party landed his wife in an awkward situation. 他在宴会上讲的荒唐话使他太太陷入窘境。 来自辞典例句
29 justified 7pSzrk     
a.正当的,有理的
参考例句:
  • She felt fully justified in asking for her money back. 她认为有充分的理由要求退款。
  • The prisoner has certainly justified his claims by his actions. 那个囚犯确实已用自己的行动表明他的要求是正当的。
30 deductions efdb24c54db0a56d702d92a7f902dd1f     
扣除( deduction的名词复数 ); 结论; 扣除的量; 推演
参考例句:
  • Many of the older officers trusted agents sightings more than cryptanalysts'deductions. 许多年纪比较大的军官往往相信特务的发现,而不怎么相信密码分析员的推断。
  • You know how you rush at things,jump to conclusions without proper deductions. 你知道你处理问题是多么仓促,毫无合适的演绎就仓促下结论。
31 molecules 187c25e49d45ad10b2f266c1fa7a8d49     
分子( molecule的名词复数 )
参考例句:
  • The structure of molecules can be seen under an electron microscope. 分子的结构可在电子显微镜下观察到。
  • Inside the reactor the large molecules are cracked into smaller molecules. 在反应堆里,大分子裂变为小分子。
32 blotted 06046c4f802cf2d785ce6e085eb5f0d7     
涂污( blot的过去式和过去分词 ); (用吸墨纸)吸干
参考例句:
  • She blotted water off the table with a towel. 她用毛巾擦干桌上的水。
  • The blizzard blotted out the sky and the land. 暴风雪铺天盖地而来。
33 explicitly JtZz2H     
ad.明确地,显然地
参考例句:
  • The plan does not explicitly endorse the private ownership of land. 该计划没有明确地支持土地私有制。
  • SARA amended section 113 to provide explicitly for a right to contribution. 《最高基金修正与再授权法案》修正了第123条,清楚地规定了分配权。 来自英汉非文学 - 环境法 - 环境法
34 presumption XQcxl     
n.推测,可能性,冒昧,放肆,[法律]推定
参考例句:
  • Please pardon my presumption in writing to you.请原谅我很冒昧地写信给你。
  • I don't think that's a false presumption.我认为那并不是错误的推测。
35 unreasonable tjLwm     
adj.不讲道理的,不合情理的,过度的
参考例句:
  • I know that they made the most unreasonable demands on you.我知道他们对你提出了最不合理的要求。
  • They spend an unreasonable amount of money on clothes.他们花在衣服上的钱太多了。
36 boundless kt8zZ     
adj.无限的;无边无际的;巨大的
参考例句:
  • The boundless woods were sleeping in the deep repose of nature.无边无际的森林在大自然静寂的怀抱中酣睡着。
  • His gratitude and devotion to the Party was boundless.他对党无限感激、无限忠诚。
37 conceit raVyy     
n.自负,自高自大
参考例句:
  • As conceit makes one lag behind,so modesty helps one make progress.骄傲使人落后,谦虚使人进步。
  • She seems to be eaten up with her own conceit.她仿佛已经被骄傲冲昏了头脑。
38 monstrous vwFyM     
adj.巨大的;恐怖的;可耻的,丢脸的
参考例句:
  • The smoke began to whirl and grew into a monstrous column.浓烟开始盘旋上升,形成了一个巨大的烟柱。
  • Your behaviour in class is monstrous!你在课堂上的行为真是丢人!
39 speck sFqzM     
n.微粒,小污点,小斑点
参考例句:
  • I have not a speck of interest in it.我对它没有任何兴趣。
  • The sky is clear and bright without a speck of cloud.天空晴朗,一星星云彩也没有。
40 apparently tMmyQ     
adv.显然地;表面上,似乎
参考例句:
  • An apparently blind alley leads suddenly into an open space.山穷水尽,豁然开朗。
  • He was apparently much surprised at the news.他对那个消息显然感到十分惊异。
41 drawn MuXzIi     
v.拖,拉,拔出;adj.憔悴的,紧张的
参考例句:
  • All the characters in the story are drawn from life.故事中的所有人物都取材于生活。
  • Her gaze was drawn irresistibly to the scene outside.她的目光禁不住被外面的风景所吸引。


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