That's BTW an old Russian idea. The key concept of the space elevator appeared in 1895 when Russian scientist Konstantin Tsiolkovsky was inspired by the Eiffel Tower in Paris to consider a tower that reached all the way into space, built from the ground up to an altitude of 35,790 kilometers (22,238 mi) above sea level (geostationary orbit).[6] He noted that a "celestial castle" at the top of such a spindle-shaped cable would have the "castle" orbiting Earth in a geostationary orbit (i.e. the castle would remain over the same spot on Earth's surface). http://en.wikipedia.org/wiki/Space_elevator
Well, yes, but with a liberal interpretation of the word "cruise", that would be 100% accurate. Indians were indeed the first to employ self-propelled artillery in a truly effective military capacity. Probably not in Vedic days, but certainly against the British: http://en.wikipedia.org/wiki/Mysorean_rockets.
It's interesting to note that much of the tradition of western rocketry is descended from captured and reverse-engineered Mysorean rockets. And most of the rest of the western tradition of rocketry is descended from half-crazed Russian mystics and Egyptian ceremonial magicians. But that's another story entirely...
Did you read the Wikipedia article they linked to? It was experience fighting against rockets in India that led the British to develop the Congrave Rocket, which was made famous in the "Rocket's Red Glare" line in the US National Anthem. Britain might have had military rockets at some point before that, but they hadn't used them for at least a century before that point.
India wasn't as backwards as you might suppose, there were lots of areas of technology they were very good at such as chemistry and metalurgy. After the Battle of Plassey, I believe, the British captures a number of Indian cannons and found that they were better than the guns that the British had. Of course, they all had different bores and it was too logistically difficult to keep that many different kinds of ammunition, so the British just destroyed them. Which, I think, goes a long way towards illustrating the actual reasons the British ended up ruling India.
So long as you don't require the tether to be stationary and to meet up with a stationary point on the ground, you can have a space elevator with materials we already have.
> That made no sense. How you can have a space elevator if it's not geo-stationary?
Apparently, you didn't read. The tether rendezvous is with a pod carried by a hypersonic spaceplane, not the ground. The tether can be spun, to make the ground speed of the tether-end even slower. Rendezvous slows down the spinning tether and lowers its orbit, but it can be boosted between rendezvous using very high ISP motors like ion thrusters, which dramatically lowers the amount of fuel to be lifted.
You didn't actually say what materials are strong enough for this (that we can actually produce without bankrupting whole countries).
Spectra and Kevlar have the required tensile strength for many proposed configurations. There is the added complication of dealing with ions, free radicals, and radiation, however.
Apparently, you are pedantic with terminology. So call it a "Skyhook" and read the HASTOL links. Kevlar is strong enough for some configurations, but none we'd be anxious to use.