手机APP下载

您现在的位置: 首页 > 英语听力 > 英语演讲 > TED-Ed教育演讲 > 正文

探索其他维度

来源:可可英语 编辑:max   可可英语APP下载 |  可可官方微信:ikekenet

We live in a three-dimensional world where everything has length, width, and height.

我们生活在一个三维世界里,每件物体都有长度,宽度和高度。
But what if our world were two-dimensional?
但是如果我们的世界是二维的呢?
We would be squashed down to occupy a single plane of existence, geometrically speaking, of course.
我们会被压扁,只存在于一个平面,当然,只是从几何的角度来看。
And what would that world look and feel like?
那么,那个世界看上去和感觉上又是怎样的呢?
This is the premise of Edwin Abbott's 1884 novella, Flatland.
这就是埃德温·艾勃特1884年的中篇小说《平面国》中的假设。
Flatland is a fun, mathematical thought experiment that follows the trials and tribulations of a square exposed to the third dimension.
平面国是一个有趣的数学思想实验,叙述一个正方形在历经第三维度的时候遇到的种种考验与磨练。
But what is a dimension, anyway?
但什么是维度呢?
For our purposes, a dimension is a direction, which we can picture as a line.
从我们的角度出发,一维是指一个方向,我们可以想成一条线。
For our direction to be a dimension, it has to be at right angles to all other dimensions.
把我们的方向当作是一维,它必须与所有其他的维度都形成直角。
So, a one-dimensional space is just a line.
所以,一维空间就是一条线。
A two-dimensional space is defined by two perpendicular lines, which describe a flat plane like a piece of paper.
二维空间由两条相互垂直的直线所定义,它们建构了一个平面,就像一张纸一样。
And a three-dimensional space adds a third perpendicular line, which gives us height and the world we're familiar with.
三维空间,增加第三条垂直线,它提供我们高度及那个我们熟悉的世界。
So, what about four dimensions? And five? And eleven?
那四维呢?五维呢?甚至十一维呢?
Where do we put these new perpendicular lines?
我们要将这些新的垂直线放在哪呢?
This is where Flatland can help us. Let's look at our square protagonist's world.
这就是平面国可以帮助我们的地方。让我们来看一下正方形主角的世界。
Flatland is populated by geometric shapes,
平面国居住着各种几何图形,
ranging from isosceles trianges to equilateral triangles to squares, pentagons, hexagons, all the way up to circles.
从等腰三角形、等边三角形、正方形、五边形、六边形、一直到圆形。
These shapes are all scurrying around a flat world, living their flat lives.
这些图形都在一个平面的世界上到处跑来跑去,过着它们平面的生活。
They have a single eye on the front of their faces,
在它们脸的前方有一只眼睛,
and let's see what the world looks like from their perspective.
让我们来看看从它们的角度上这个世界看起来像什么样。
What they see is essentially one dimension, a line.
实质上它们看到的是一维,也就是一条线。
But in Abbott's Flatland, closer objects are brighter, and that's how they see depth.
但是在艾勃特的《平面国》中,距离更近的物体更加明亮,这就是它们如何察觉深度的。
So a triangle looks different from a square, looks different a circle, and so on.
所以,一个三角形看上去就和一个正方形不同,和圆形不一样,等等。
Their brains cannot comprehend the third dimension.
它们的大脑无法理解第三维度。
In fact, they vehemently deny its existence because it's simply not part of their world or experience.
其实,它们强烈地否认它的存在,因为那不是它们的世界的一部分,它们也没有经历过。
But all they need, as it turns out, is a little boost.
但是它们所需要的,事实证明,是一点小鼓励。

探索其他维度

One day a sphere shows up in Flatland to visit our square hero.

有一天,一个球体出现在平面国中,拜访我们的正方形男主角。
Here's what it looks like when the sphere passes through Flatland from the square's perspective, and this blows his little square mind.
这是当球体经过平面国时看起来的样子。从正方形的角度来看,这完全颠覆了它小小正方形的观念。
Then the sphere lifts the square into the third dimension,
然后,那个球体把正方形举起来,进入了第三维度,
the height direction where no Flatlander has gone before and shows him his world.
高度上升了,到了平面国中的形状们从来没去过的地方。
From up here, the square can see everything:
从这个高度,正方形可以看到所有事物:
the shapes of buildings, all the precious gems hidden in the Earth,
建筑物的形状、所有隐藏在地球中珍贵的宝物,
and even the insides of his friends, which is probably pretty awkward.
甚至于它朋友的内部,这可能有点尴尬。
Once the hapless square comes to terms with the third dimension,
一旦这个正方形适应了第三个维度,
he begs his host to help him visit the fourth and higher dimensions,
它央求球体帮助它看到第四个或更高的维度,
but the sphere bristles at the mere suggestion of dimensions higher than three and exiles the square back to Flatland.
但球体对于超过三维的看法感到非常生气,并把正方形逐回平面国。
Now, the sphere's indignation is understandable.
球体的愤怒是可以理解的。
A fourth dimension is very difficult to reconcile with our experience of the world.
第四维度很难和我们在这世界的经历达成一致。
Short of being lifted into the fourth dimension by visiting hypercube, we can't experience it, but we can get close.
我们不可能被一个超立方体举起,被带到第四个维度。我们无法体验到,但我们可以接近。
You'll recall that when the sphere first visited the second dimension,
回想一下,当球体第一次来到二维世界时,
he looked like a series of circles that started as a point when he touched Flatland,
它看上去像一连串的圆形,当它在平面国落地时,它看上去像一个点,
grew bigger until he was halfway through, and then shrank smaller again.
一直变大,直到它一半的体积陷进地面,然后又开始变小。
We can think of this visit as a series of 2D cross-sections of a 3D object.
我们可以把这个看做一个三维物体的一系列二维横截面。
Well, we can do the same thing in the third dimension with a four-dimensional object.
我们可以用同样的方法从一个三维世界看一个四维物体。
Let's say that a hypersphere is the 4D equivalent of a 3D sphere.
比如,一个超球体是一个四维物体,等同于三维的球体。
When the 4D object passes through the third dimension, it'll look something like this.
当这个四维物体经过第三维度时,它会看起来像这样。
Let's look at one more way of representing a four-dimensional object.
我们来看看另一个表现四维物体的方式。
Let's say we have a point, a zero-dimensional shape.
我们有一个点,这是一个零维图形。
Now we extend it out one inch and we have a one-dimensional line segment.
现在我们把它延伸到一英寸,于是我们有了一个一维线段。
Extend the whole line segment by an inch, and we get a 2D square.
把整个线段向外延伸一英寸,于是我们得到一个二维正方形。
Take the whole square and extend it out one inch, and we get a 3D cube.
把整个二维正方形向外延伸一英寸,于是我们得到一个三维立方体。
You can see where we're going with this.
你可以看见我们做了什么。
Take the whole cube and extend it out one inch,
把整个立方体向外延伸一英寸,
this time perpendicular to all three existing directions, and we get a 4D hypercube, also called a tesseract.
这一次与所有存在的三个维度相互垂直,然后我们得到一个超立方体,也叫四维超正方体。
For all we know, there could be four-dimensional lifeforms somewhere out there,
我们都知道,可能有四维生物存在于某个地方,
occasionally poking their heads into our bustling 3D world and wondering what all the fuss is about.
偶尔探头到我们繁忙的三维世界,看看有什么大惊小怪的事情。
In fact, there could be whole other four-dimensional worlds beyond our detection,
事实上,可能有其他的四维世界,超越我们所能察觉的范围,
hidden from us forever by the nature of our perception.
因为我们感知的能力导致我们永远看不到。
Doesn't that blow your little spherical mind?
这有没有彻底颠覆你的三维观念?

重点单词   查看全部解释    
boost [bu:st]

想一想再看

vt. 推进,提高,增加
n. 推进,增加

联想记忆
perpendicular [.pə:pən'dikjulə]

想一想再看

n. 垂直线 adj. 垂直的,直立的,陡峭的

联想记忆
premise ['premis]

想一想再看

n. 前提
vt. 提论,预述,假设

联想记忆
perspective [pə'spektiv]

想一想再看

n. 远景,看法,透视
adj. 透视的

联想记忆
perception [pə'sepʃən]

想一想再看

n. 感知,认识,观念

 
plane [plein]

想一想再看

adj. 平的,与飞机有关的
n. 飞机,水平

 
exposed [iks'pəuzd]

想一想再看

adj. 暴露的,无掩蔽的,暴露于风雨中的 v. 暴露,

 
dimension [di'menʃən]

想一想再看

n. 尺寸,次元,容积,维度,范围,方面
vt

联想记忆
describe [dis'kraib]

想一想再看

vt. 描述,画(尤指几何图形),说成

联想记忆
cube [kju:b]

想一想再看

n. 立方体,立方
vt. 求 ... 的立方

 

    阅读本文的人还阅读了:
  • 什么是阅读障碍? 2018-02-09
  • 用漂白剂、酸和砂纸来确保种子长大? 2018-02-11
  • 如何阅读音乐 2018-02-14
  • 揭秘单词Fizzle的出处 2018-02-16
  • 英文复数名词简史 2018-02-18
  • 发布评论我来说2句

      最新文章

      可可英语官方微信(微信号:ikekenet)

      每天向大家推送短小精悍的英语学习资料.

      添加方式1.扫描上方可可官方微信二维码。
      添加方式2.搜索微信号ikekenet添加即可。