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If I want to turn this globe into a flat map, I’m going to have to cut it open.
想把这个球形地图变成平面地图的话，我得把它割开
In order to get this to look anything like a rectangle.
要让它大致变成一个长方形的模样
I've had to cut it in places.
我还得割开好几个地方
I've had to stretch it so that the countries look all wonky.
再加上来回拉扯，那么拉完以后，国家的形状就变了
And even still, it's almost impossible to get it to lie flat.
即便如此，感觉还是不能把它弄成一个平面图
And that right there is the eternal dilemma of map makers:
这恰好也是地图制造商们一直头疼的问题
The surface of a sphere cannot be represented as a plane
球体的表面无法展开成平面
without some form of distortion.
除非发生扭曲
That was mathematically proved by this guy a long time ago.
这个家伙很早就证明了这一点
Since around 1500s, mathematicians have set about creating algorithms
早在16世纪，数学家们就想通过运算
that would translate the globe into something flat.
把球体表面变成平面
And to do this, they use a process called projection.
为此，他们还用了所谓的“投影”
Popular rectangular maps use a cylindrical projections.
大家通常使用的长方形地图用的是圆柱投影
Imagine putting a theoretical cylinder over the globe
试想，把一个圆柱套在一个球体表面
and projecting each point of the sphere onto the cylinder’s surface.
然后把球体上的每个点都投射到圆柱表面
Unroll the cylinder, and you have a flat, rectangular map.
把圆柱摊开，就得到了一张平面的长方形地图
But you could also project the globe onto other objects,
然而，球形地图也可以投射到其他物体上
and the math used by map makers to project the globe
而且，地图制造商们所用的投影公式
will affect what the map looks like once it’s all flattened out.
会影响地图摊开后的形状
And here’s the big problem:
问题就在这里：
Every one of these projections comes with trade offs in shape, distance, direction and land area.
每一次投影都会受形状、远近、方向以及投影面积的影响
Certain map projections can be either misleading or very helpful
所以，投影出来的地图要么很有用，要么很容易引起误解
depending on what you are using them for.
具体要看你想用它做什么
Here’s an example.
举个例子
This map is called the Mercator projection.
这个地图叫墨卡托投影
If you’re American, you probably studied this map in school.
如果你是美国人，那你很可能在学校里学过这张地图
It’s the projection Google Maps uses.
谷歌地图用的就是这个投影
Mercator projection is popular for a couple of reasons.
墨卡托投影之所以大受欢迎有如下几个原因
First, it generally preserves the shape of the countries.
首先，它基本上保持了各个国家的形状不变
Brazil on the globe has the same shape as Brazil on the Mercator projection.
地图上巴西的形状就和巴西本身的形状完全吻合
But the real purpose of the Mercator projection was navigation
然而，墨卡托投影原本是为了航海之用。
it preserves direction,
这一投影还保证了方向的正确性
which is a big deal if you are trying to navigate the ocean with only a compass.
对靠罗盘在海上航行而言，地图方向正确至关重要
It was designed so that a line drawn between two points on the map
墨卡托投影发明之初是让地图上两点之间的连线
would provide the exact angle to follow on a compass to travel between those points.
能够让船在其间航行时给罗盘提供准确的航向
If we go back into a globe, you can see that this line is not shortest route.
回到球形地图上，我们就会发现，这条线路其实并不是航程最短的线路
But it at least provides a simple, reliable way to navigate across oceans.
但它至少能给海上航行提供一个简便、可靠的航向
Gerardus Mercator, who created the projection in the 16th century,
公元16世纪，（荷兰地图学家）墨卡托发明了这一投影法
was able to preserve direction by varying the distance between latitude lines
通过改变纬线之间的距离，
and also making them straight, creating a grid of right angles..
将纬线拉直，墨卡托得以在地图上标出正确的方向
But that created other problems.
但这也引起了别的问题
Where Mercator fails is its representation of size.
墨卡托地图的尺寸是不准确的
Look at the size of Africa as compared to Greenland.
我们不妨比较一下非洲和格陵兰岛的大小
On the mercator map they look about the same size.
墨卡托投影地图上，两个板块大小差不多
But look at a globe for Greenland’s true size,
然而，看看球形地图上格陵兰岛的实际大小
and you’ll see it’s way smaller than Africa.
你会发现，它其实比非洲小得多
By a factor of 14 in fact.
实际上只是非洲的1/14大小
If we put a bunch of dots onto the globe that are all the same size,
如果我们在球形地图上画上很多大小相同的圆点
then we projected as a mercator map, we would end up with this.
然后把它们投影到墨卡托地图上，投影结果会是这样
The circles retain their round shape but are enlarged as they get closer to the poles.
虽然圆点的形状没变，但越靠近两极，圆点越大
One modern critique of this is that
现代有一种说法是
the distortion perpetuates imperialist attitudes of European domination over the southern hemisphere
这一变形使得欧洲主导南半球的帝国主义心态更加猖獗
The Mercator projection has fostered European imperialist attitudes for centuries
数百年来，墨卡托投影助长了欧洲的帝国主义心态
and created an ethnic bias against the third world. Really?
导致欧洲人对第三世界产生了种族偏见，真的吗
So if you want to see a map that more accurately displays land area,
所以，如果你想要一张尺寸更准确的地图
you can use the Gall-Peters projection, which is called an equal-area map.
那么你可以选择高尔-彼得斯投影，这一投影据的尺寸据说跟实际情况比较一致
Look at Greenland and Africa now.
来看非洲和格陵兰岛
The size comparison is now accurate. Much better than the mercator.
现在大小比例已经很准确了，比墨卡托投影好多了
but it’s obvious now the country shapes are totally stretched.
但很明显，各个国家的形状已经完全扭曲了
Here are those dots again
再来看这些圆点
so that we can see how the projection preserves area while totally distorting shape.
看得出来，这一投影保证了各个圆点的面积，但形状彻底被扭曲了
Something happened in the late 60s
上个世纪六十年代晚期发生了一件
that would change the whole purpose of mapping and the way we think about projections.
足以改变制图目的以及我们看待投影的方式的事情
Satellites orbiting our planet started sending location and navigation data
绕地卫星开始
to little receiver units all over the world.
给世界各地的接受设备发送位置和导航信息
Today, orbiting satellites of the navigating satellites system
如今，导航卫星系统的绕地卫星
provide round-clock, ultra-precise position from space to units everywhere in any kind of weather.
已经能够风雨无阻从太空往任何地方的设备发送时事的超高精度的定位信息了
This global positioning system wiped out the need for paper maps
全球定位系统淘汰了
as a means of navigating both the seas and the sky.
曾经用于航空和航海导航的纸质地图
Map projection choices became less about navigational imperatives
如今，地图投影关注的不再是制作导航必须的地图
and more about aesthetics, design, and presentation.
而是地图的美感、设计和展示
The mercator map, that vital tool of pre-GPS navigation,
在前GPS的导航时代，墨卡托地图曾发挥了至关重要的作用
was shunned by cartographers who now saw it as misleading.
如今却因为容易引人误解而被制图者纷纷抛弃
But still, most web mapping tools like Google maps use the mercator.
然而，包括谷歌地图在内的大部分网络地图仍在使用墨卡托投影地图
this is because the Mercator’s ability to preserve shape and angles
这是因为，墨卡托地图准确的形状和角度下
makes close-up views of cities more accurate --
我们能够更准确地获取城市的细节
a 90 degree left turn on the map is a 90 degree left turn on the street that you’re driving down.
地图上的直角左转表示到了街头就要左转
The distortion is minimal when you close up
即便是放大之后变形也是可以忽略不计的
But on a world map scale, cartographers rarely use the mercator.
然而，就世界规模的地图而言，制图者们还是很少用墨卡托投影
Most modern cartographers have settled on a variety of non-rectangular projections
大部分当代制图者选用的都是各种
that split the difference between totally distorting either size or shape.
在完全改变大小或完全改变形状之间妥协的非直角投影
In 1998 The National Geographic Society adopted The Winkel tripel projection
1998年，国家地理协会选用了温克尔投影
because of it’s a pleasant balance between size and shape accuracy.
因为这种投影在形变和大小之间找到了一个很好的平衡点
But the fact remains that there is no one right projection.
然而，还是没有一种完全正确的投影方式
cartographers and mathematicians have created a huge library of available projections,
制图者和数学家们设计了大量的投影方式
each with a new perspective on the planet and each useful for a different task.
每一种都带来了新的希望，每一种在完成某种任务时都很有效
The best way to see what the earth really looks like is to look at a globe.
要想看地球真实的样子，最好还是看球形地图
But as long we use flat maps, we will deal with the tradeoffs of projections,
因为只要用平面地图，投影时就有需要折衷的地方
Just remember: there’s no right answer.
记住了，没有一个投影方案是完全正确的
