Relatively speaking, the length-to-width ratio of the elevator would be thinner than any hair. It's just hard for me to visualize something so long and skinny being able to resist the kind of lateral stress it would face. Maybe if it were built in a cone shape up to, say, the stratosphere...but that would take a *lot* of carbon.

Of course, if we were able to suck enough carbon out of the atmosphere, that would solve two problems at once....