[chriswarbo]

We can build massive steel towers (e.g. https://en.wikipedia.org/wiki/X-Seed_4000 would be 4km tall), but they would still be nowhere near space (one common definition of reaching space is https://en.wikipedia.org/wiki/K%C3%A1rm%C3%A1n_line which is at 100km).

A space elevator would reach at least 36,000km to hit geostationary orbit ( https://en.wikipedia.org/wiki/Geostationary_orbit ). Most designs are even longer, to provide a counterweight.

No known material could support a tower that tall (towers need compressive strength; elevators need tensile strength). It would need to rely on 'active support' or 'dynamic structures', like a space fountain ( http://www.orbitalvector.com/Orbital%20Travel/Space%20Founta... )

[asib]

A friend of mine who studies engineering told me that masonry has infinite compressive strength meaning, in theory, it's possible to build monumental structures out of stone.

[chriswarbo]

The base needs to be large enough to support the weight, so you get less of a tower and more of a mound (like the great pyramids).

We can get to about 9km using stone by climbing Mount Everest.