十维空间

Tenth Dimension
0. A point (no dimension)
点(无维)
We start with a point. Like the ―point‖ we know from geometry, i t has no size, no dimension. It’s just an imaginary idea that indi cates a position in a system.
我们从一个点开始。

几何上的―点‖，没有尺寸，没有体积。

它只是想象中的某个系统里的某个位置。

1. The first dimension –a line
第一维-线
A second point, then, can be used to indicate a different positio n, but it, too, is of indeterminate size. To create the first dimensi on, all we need is a line joining any two points. A first dimensio nal object has length only, no width or depth.
用第二个点来表示另一个位置，它也没有固定尺寸。

我们只需要用一条线把两个点连接起来，就创造了第一个维度。

一维物体只有长度，没有宽度和深度。

2. The Second Dimension –A Split
第二维-分叉
If we now take our first dimensional line and draw a second line crossing the first, we’ve entered the s econd dimension. The obj
ect we’re representing now has a length and a width, but no de pth. To help us with imagining the higher dimensions, we’re goin g to represent our second dimensional object as being created u sing a second line which branches off from the first.
如果我们拿出我们的一维线，然后画第二条线穿过第一条，我们就进入了二维空间。

现在，我们要表示的物体就有了长度和宽度，但是没有深度。

为了帮助我们更好地理解更高的维度，我们把第二条线作为第一条线的分叉来表示我们的二维物体。

Now, let’s imagine a race of two-dimensional creatures called ―Fl atlanders‖. What would it be like to be a Flatlander living in their two-dimensional world? A two-dimensional creature would have only length and width, as if they were the royalty on an impossi bly flat playing card. Picture this: a Flatlander couldn’t possibly h ave a digestive tract, because the pipe from their mouth to their bottom would divide them into two pieces!
现在，让我们来设想一种叫做―平面人‖的二维生物。

平面人是怎样生活在二维世界里的呢？二维生物只有长度和宽度，就像一套诡异的扑克牌中的J,Q,K。

设想一下，一个平面人绝对不可能有消化道，因为从嘴到屁股的管道会把他们切成两半。

And a Flatlander trying to view our three-dimensional world woul d only be able to perceive shapes in two-dimensional cross-secti ons. A balloon passing through the Flatlander’s world, for instanc e, would start as a tiny dot, become a hollow circle which inexpl icably grows to a certain size, then shrinks back to a dot before popping out of existence. And we three-dimensional human bein gs would seem very strange indeed to a Flatlander.
如果一个平面人去观察三维世界，他就只能从二维面的垂直方向去辨识
图像。

假如一个气球穿过平面人的世界，开始（那平面人观察到的）会是一个小点，然后它会从一个难以辨认的小圈变成一个够大的圈，在（整个球）通过平面世界之前，它又会慢慢缩回成一个小点。

对一个平面人来说，我们三维生物看起来肯定很奇怪。

3. The Third Dimension –A Fold
第三维-折叠
Imagining the third dimension is the easiest for us because ever y mo ment of our lives that is what we’re in. A three dimensional object has length,
width, and height. But here’s another way to describe the third d imension: if we imagine an ant walking across a newspaper whi ch is lying on a table, we can pretend that the ant is a Flatland er, walking along on a flat two-dimensional newspaper world. If t hat paper is now folded in the middle, we create a way for our Flatlander Ant to ―magically‖ disappear from one position in his t wo-dimensional world and be instantly transported to another. W e can imagine that we did this by taking a two-dimensional obje ct and folding it through the dimension above, which is our third dimension. Once again, it’ll be more convenient for us as we i magine the higher dimensions if we can think of the third dimen sion in this way: the third dimension is what you ―fold through‖ t o jump from one point to another in the dimension below.
想象一个三维空间对我们来说是最容易的，因为我们无时无刻不生活在这样的空间里。

三维物体有长度，宽度，高度。

但这还有另一种描述三维空间的方式：想象一只蚂蚁要爬过一张铺在桌上的报纸，我们可
以把它当作一只平面蚁，在一个平的二维报纸世界里行走。

如果报纸从两边对折，我们可以制造一条路让我们的平面蚁魔法般地从二维世界中的一处消失，然后立即出现在另一处。

我们这样做是靠在一个更高的维度里把二维物体折叠，这个更高的维度就是第三维。

为了便于我们理解更高的维度，我们可以这样理解第三维度：在第三维度里，你可以通过―折叠‖从一个点跳至另一个点。

雷龙翻译
4. The Fourth Dimension –A Line
第四维-线
Okay. The first three dimensions can be described with these w ords: ―length, width, and depth‖. What word can we assign to th e fourth dimension? One answer would be, ―duration‖. If we thin k of ourselves as we were one minute ago, and then imagine o urselves as we are at this moment, the line we could draw from the ―one-minute-ago version‖ to the ―right now‖ version would b e a line in the fourth dimension. If you were to see your body i n the fourth dimension, you would be like a long undulating sna ke, with your embryonic self at one end and your deceased self at the other. But because we live from moment to moment in t he third dimension, we are like our second dimensional Flatlande rs. Just like that Flatlander who could only see two-dimensional cross-sections of objects from the dimension above, we as three -dimensional creatures can only see three-dimensional cross-secti ons of our fourth-dimensional self.
前三个维度可以被描述成―长度，宽度，深度‖。

那我们用什么表述第四个维度？一种答案是―时长‖。

我们设想一个一分钟前的自己，然后设想一个此刻的自己，我们就可以在第四维度中的―一分钟前的我‖和―现在的我‖之间画一条线。

如果你能在第四维度里看到你的身体，你看起来
就想一条绵延不断的长蛇，一头是胚胎时的自己，一头是嗝儿屁的自己。

我们在第三维度中总是一刻接一刻地活着，所以看起来就像二维的平面人一样。

平面人看高一维的物体时只能从二维面的垂直角度看到它的二维形状，我们三维生物看四维的自己时，只能从垂直角度看到自己的三维形状。

（我们只能观察到四维时空中，某一时刻的自己——译注）
5. The Fifth Dimension –A Split
第五维-分叉
One of the most intriguing aspects of there being one dimension stacked on another is
that down here in the dimensions below we can be unaware of our motion in the dimensions above. Here’s a simple example: if we make a Möbius strip (take a long strip of paper, add one t wist to it and tape the ends together) and draw a line down the length of it, our line will eventually be on both sides of the pap er before it meets back with itself. It appears, somewhat amazin gly, that the strip has only one side, so it must be a representat ion of a two-dimensional object. And this means that a two-dime nsional Flatlander traveling down the line we just drew would en d up back where they started without ever feeling like they had left the second dimension. In reality, they would be looping and twisting in the third dimension, even though to them it felt like th ey were traveling in a straight line.
再加一个维度发生的最有趣的事情就是在加它以前我们从来没考虑过自己的行为（对观察的影响）。

举个简单的例子：如果我们做一个魔比斯环（拿一个长纸条，弯曲以后将首尾粘连在一起）沿着它的长度方向画线。

这条线会划过纸的两面并最终回到起点。

你会惊讶地发现这个
环只有一面，这可以看作一个二维物体。

如果一个平面人沿我们刚才画下的线行走，当他回到原点时并没有意识到他离开了二维面。

他们会感觉自己一直走的是直线，但实际上它在三维空间里被环接并扭曲了。

The fourth dimension, time, feels like a straight line to us, movin g from the past to the future. But that straight line in the fourth dimension is, like the Möbius strip, actually twisting and turning i n the dimension above. So, the long undulating snake that is us at any particular moment will feel like it is moving in a straight line in time, the fourth dimension, but there will actually be, in th e fifth dimension, a multitude of paths that we could branch to a t any given moment. Those branches will be influenced by our o wn choice, chance, and the actions of others.
第四维度，时间，在我们感觉起来就是条直线，从过去到未来。

但在四维空间里的一条直线就像条魔比斯环，在更高一层的维度上被环接、扭曲。

在第四维中，我们这条起伏的长蛇会感觉沿时间直线行走。

但实际上，在第五维中，在任何一刻都有无数个分支。

这些分支的产生受到我们的选择、机会和别人的行为的影响。

Quantum physics tells us that the subatomic particles that make up our world are collapsed from waves of probability simply by t he act of observation. In the picture we are drawing for ourselve s here, we can now start to see how each of us are collapsing the indeterminate wave of probable futures contained in the fifth dimension into the fourth dimensional line that we are experienci ng as ―time‖.
量子物理告诉我们由于观察行为导致的波函数坍塌形成的亚原子粒子构成了我们世界（哈哈，发现自己明白这段话什么意思了——猥琐的译者注）。

在图中，我们把自己画在这儿，我们现在可以看见我们是怎样把第五维中涵盖可能未来的不确定波坍塌至第四维直线上形成我们
所感知的―时间‖。

6. The Sixth Dimension –A Fold
第六维-折叠
What if you wanted to go back into your own childhood and visi t yourself? We can imagine folding the fourth dimension through the fifth, jumping back through time and space to get there. Bu t what if you wanted to get to the world where, for
example, you had created a great invention as a child that by n ow had made you famous and rich? We can imagine our fourth-dimensional selves branching out from our current moment into t he fifth dimension, but no matter where you go from here the ―g reat child inventor‖ timeline is not one of the available options in your current version of time -- ―you can’t get there from here‖ -- no matter how much choice, chance, and the actions of others become involved.
如果你想回到你的童年去见你自己会怎么样？我们可以想象通过第五维折叠第四维，让我们穿越时间和空间回到那里。

如果你想去一个世界，在那里由于你儿时所进行的一项伟大的发明创造使你现在变得很牛很
富有，会如何呢？想象第四维中的我们从这里向第五维分叉，可无论你从这里怎么走，―牛X的少年发明家‖这条时间线都不会出现在你如今的可选线路里——―你不可能从这到那儿‖——无论受到多少选择、机会、别人的行动的影响都没戏。

There are only two ways you could get to
that world –one would be to travel back in time, somehow trigg
er the key events that caused you to come up with your inventi on, then travel forward in the fifth dimension to see one of the possible new worlds that might have resulted. But that would be taking the long way. The shortcut we could take would involve us folding the fifth dimension through the sixth dimension, which allows us to instantly jump from our current position to a differe nt fifth dimensional line.
只有两种方法可以让你到达那个世界：一种是做时间回溯旅行，引发一些会导致你想出发明的关键事件，然后在第五维中向前旅行，观察因这些事件所产生的新世界。

但这太麻烦了。

更快的方法是我们在第六维中折叠第五维，让我们从现在所处的五维线跳至另一条五维线。

7. The Seventh Dimension –A Line
第七维-线
In our description of the fourth dimension, we imagined taking th e dimension below and conceiving of it as a single point. The fo urth dimension is a line which can join the universe as it was o ne minute ago to the universe as it is right now. Or in the bigg est picture possible, we could say that the fourth dimension is a line which joins the big bang to one of the possible endings of our universe.
在我们描述第四维时，我们把低于它的维度看成了一个独立的小点。

第四维就成了一条从一分钟前的宇宙到现在的宇宙的线。

如果我们把尺度放的大点，我们可以说四维就是一条从大爆炸到我们宇宙可能结局的一条线。

Now, as we enter the seventh dimension, we are about to imagi ne a line which treats the entire sixth dimension as if it were a single point. To do that, we have to imagine all of the possible t
imelines which could have started from our big bang joined to al l of the possible endings for our universe (a concept which we often refer to as infinity), and treat them all as a single point. S o, for us, a point in the seventh dimension would be infinity –al l possible timelines which could have or will have occurred from our big bang.
现在，假设我们进入第七维，我们就可以把整个第六维看成一个独立的点。

这样做的话，我们就必须设想所有可能的时间线，它包括了宇宙从大爆炸起点和最终可能的终点（这个概念我们一般看做无限），然后我们把这些点全部看做独立的点。

那么，对我们来说，第七维将会是无限的，它包含了从大爆炸开始应该有的、将会有的所有时间线。

8. The Eighth Dimension –A Split
第八维-分叉
When we describe infinity as being a ―point‖ in the seventh dime nsion, we are only imagining part of the picture. If we’re drawing a seventh dimensional line, we need to be able to imagine wha t a different ―point‖ in the seventh dimension is going to be, bec ause that’s what our line is going to be joined to. But how can there be anything more than infinity? The answer is, there can b e other completely different infinities created through initial conditi ons which are different from our own big bang. Different initial c onditions will create different universes where the basic physical laws such as gravity or the speed of light are not the same as ours, and the resulting branching timelines from that universe’s b eginning to all of its possible endings will create an infinity whic h is completely separate from the one which is associated with our own universe. So the line we draw in the seventh dimension
will join one of these infinities to another. And, as boggling as t he magnitude of what we are exploring here might be, if we wer e to branch off from that seventh dimensional line to draw a line to yet another infinity, we would then be entering the eighth di mension.
当我们把无限描述成第七维中的一个―点‖ 时，我们只是想到了这个图像的一部分。

如果我们画一条七维线，我们就必须去想象七维中一个不同的点会变成什么样子，因为那正是我们所在的线将要通过的地方。

但有什么能比无限更多呢？答案是：通过一个不同于我们的大爆炸的起始条件，产生的一个完全不同的无限。

不同的起始条件会创造出不同的宇宙。

这些宇宙中，重力、光速这些基本物理量和我们不一样，从这个宇宙开始产生的所有分支到它所有可能性的结局的时间线所构成的无限和我们的宇宙也八竿子打不着。

所以，当我们在第七维中画线的时候会把这些无限中的某个点和另一点连起来。

先不管我们在这里讨论的问题在数量级上是多么的纠结，如果我们从一条七维线上分叉，画向另一个无限，我们就进入了第八维。

9. The Ninth Dimension –A Fold
第九维-折叠
As we’ve explored already, we can jump from one point in any dimension to another simply by folding it through the dimension above. If our ant on the newspaper were a two-dimensional Flatl ander, then folding his two-dimensional world through the third di mension would allow him to magically disappear from one locatio n and appear in a different one. As we’re now imagining t he nin th dimension, the same rules would apply –if we were to be ab
le to instantaneously jump from one eighth dimensional line to a nother, it would be because we were able to fold through the ni nth dimension.
就像我们先前解释的，我们要从任何一个维度的一点跳至该维度的另一点，只须在高它一级的维度上对其进行折叠。

如果那只报纸上的蚂蚁是一个二维的平面人，在第三维度里折叠它的二维世界，就可以让它奇迹般地从一点消失，接着出现在另一点。

让我们在第九维中继续这样想，同样的规则应该适用——如果我们想从一条八维线瞬移至另一条，那么就移吧，我们可以把两者在第九维中叠在一起。

10. The Tenth Dimension –A Point?
第十维-点?
Before we discussed the first dimension, we could say that we fi rst started out with dimension
zero, which is the geometrical concept of the ―point‖. A point ind icates a location in a system, and each point is of indeterminate size. The first dimension then, takes two of these ―points‖ and j oins them with a line.
在我们讨论第一维之前，我们是从零维开始的，一个几何意义上的―点‖。

一个表示系统中某个位置的点，大小不确定。

第一维就是拿出这样的
点来然后用线连起来。

When we imagined the fourth dimension, it was as if we were tr eating the entirety of three-dimensional space in a particular stat e as a single point, and drawing a fourth-dimensional line to ano ther point representing space as it is in a different state. We oft
en refer to the line we have just drawn as ―time‖.
当我们想象第四维时，我们把处于一个特殊位置的整个三维空间看成
了一个点，然后用一条四维线把它和代表一个不同位置宇宙的另一个点
连起来。

我们通常把这条线叫做―时间‖。

Then in the seventh dimension, we treated all of the possible ti melines which could be generated from our big bang as if this were a single point, and imagined drawing a line to a point repr esenting all of the possible timelines for a completely different u niverse. 而后，在第七维中，我们把大爆炸产生的所有可能的时间线当
做一个点，然后画了一条线将它和代表另一个完全不同的宇宙中所有可
能时间线的点连起来。

Now, as we enter the tenth dimension, we have to imagine all o f the possible branches for all the possible timelines of all the p ossible universes and treat that as a single point in the tenth di mension. Whew! So far, so good. But this is where we hit a roa dblock: if we’re going to imagine the tenth dimension as continui ng the cycle, and being a line, then we’re going to have to ima gine a different point that we can draw that line to. But there’s no place left to go! By the time we have imagined all possible ti melines for all possible universes as being a single point in the tenth dimension, it appears that our journey is done.
现在，我们进入了第十维，我们要把所有可能的宇宙的所有时间线的
所有分支看做一个十维点。

嗬！很快很不错！但是我们又撞上了另一个
路障：如果我们继续按这个循环思路去想象第十维，画线，我们就必
须去想象另一个点，好让我们连上它。

但没戏了！我们已经把所有可能
的宇宙的所有可能的时间线看做了十维中的一个点，看起来我们可以
歇着了。

雷龙翻译
In String theory, physicists tell us that Superstrings vibrating in t he tenth dimension are what create the subatomic particles whic h make up our universe, and all of the other possible universes as well. In other words, all possibilities are contained within the t enth dimension, which would appear to be the concept we have just built for ourselves as we imagined the ten dimensions, built one upon another.
在弦理论中，物理学家告诉我们，第十维的超弦振动创造了构成我们宇宙的亚原子，其他宇宙也是如此。

换句话说，所有的可能性都包含在第十维中。

这会成为一个基本概念，我们一级接一级地想象直至第十维就用到了它。