>Does any one here have any architectural insight to a question I have? If I
>were to begin building a simple structure merely to achieve it's epitome of
>height, what should it be built of, (not considering the future of
>nanotubes, but what could be used now) how high would it reach and how thick
>would the structure have to be in width?
Well, the sky is not the limit if you are willing to throw enough mass at it. A weak material can simply be piled up to any height. 100Km using dirt? No problem if you have the mass of a continent to work with! The question you might be asking is "What is the highest practical structure one can build". Practical here is usually defined as "a building that can pay for itself", such as office space. The biggest problem with building tall office buildings seems to be the elevators. The cables get very long, and you need a lot of elevators to service all those long trips up and down. A surface to volume ratio scaling problem, I think.
But if you just want to build a very inspiring sculpture (an idea that has tickled me now and then), you could build miles high - if someone would pay for all that material. Taken to the limit, I believe you wind up with a taper ratio for a given material that allows you to build to geosynchronous orbit (and then some, to balance the mass). The taper ratio is (experts correct me here, I'm guessing) the ratio of the cross sections of the thick part to the thin end. Such a "skyhook" is possible with current materials (carbon fiber) but the taper ratio is so bad that we couldn't afford the mass of material until we have diamondoid or buckytube cable.
If you support the structure from below, I believe plain old steel and concrete could be built up for miles - again, tapered, wide at the base.
I did some calculations once for another approach. Build a tapered, hollow carbon fiber tube. Pressurize the inside with hydrogen - to enormous pressure, enough so that the tube is never in compression vertically. Specifically, the taper is set so that from the top view, the area of a given length of tube provides enough "lift" from the internal pressurization to support that length. Just a thought experiment, but, one might build a second, straight tube up the center, and evacuate it. Now you can electrically accelerate into space without that pesky atmosphere getting in the way. Reaching 100Km or more with a 1Km wide base was not a problem by my calculation, if I remember correctly. That was fifteen years ago, so I'm vague on the width of the base. But, again, geosync altitude was possible if totally impractical. In the real world, side forces such as wind might set the taper ratio. To say nothing of earthquakesthe taper would probably make a nice continuously shifting acoustic impedance for ground waves, causing the structure to whip to shreds at some height (literally, whip, as in those tapered leather things that go supersonic at the end for the same reason).
I want to see a sculpture built in some geologically stable desert, say, in Utah. A single hand, reaching up for the sky, about a mile or two high. Clouds forming and clinging to it at altitude some times, or the fingers disappearing into the cloud deck. Perhaps, if built where there is a predictable cloud deck height, the hand is opened out as if supporting the clouds. This is worth a few billion, don't you think? Why not embarrass the Egyptians and their piddly pyramids?