Having just finished Arthur C. Clarke's "The Fountains of Paradise", Clarke seems to make a distinction between starting construction of a space elevator from geosynchronous orbit and working on our way down until we hit a point on Earth and constructing starting from Earth and going up.
My question is, is there a difference between the two? Theoretically speaking, is starting from GEO and coming down different or even easier than starting from Earth and just building a really tall building and going up? It seems to me that starting from the surface and going up might be easier. We don't even have to restrict ourselves to the equator. Is there some fundamental difference or a deep physical reason why one works better than the other?
Building a really really tall building/space elevator (36,000 km up) from the surface seems to work just as well because the top of the building/elevator will be "in sync" with its base on the surface, no? Effectively behaving like geosynchronous even away from the equator at higher latitudes? Its not like the top will be "moving" at different speeds than its base hence the elevator breaks. I thought only free-bodies such as satellites will have different speeds depending on their height in orbit because they are constantly "falling". If something is connected to the surface via a rigid solid body then it will move at the same rotational speed as its base point on the surface of the Earth.