Good points here. Only many other limitations apply when building an actual tower, so you would probably need a lot of engineering to design a tower even remotely close to that height that can be built before it collapses. If that kind of thing was so easy the carbon nano-tubes fiber cable for the space elevator would be a reality and we would be sending packages to the ISS at almost no cost. But if you take a look at the ideas for the project, you'll find the amazing problems they are trying to solve just to be able to say: Ok, we can do it. Let's build it! http://en.wikipedia.org/wiki/Space_elevator