LAST EDITED ON Jun-06-06 AT 05:10 PM (EDT)
 
>Take a sphere approximately one AU in diameter.
>
>On the inside of that, a hemispherical dome roughly 12,000 kilometers
>across, say, just wouldn't even be much of a pimple. Plenty of space
>to drop a pseudo-content, a few oceans, and such, and have it have a
>nice horizon.

I doubt that they would engineer it to be a half-dome; too much wasted space on the inside (not that a dyson sphere isn't a massively huge waste of space, at least for the first several millenia, until expansion really sets in...), and it would make it rather difficult to "expand" and connect to the next pseudo-continent that would eventually be constructed without a lot of divirting through the surface of the sphere itself.

I have thought of the pseudo-continent as rather flat, kind of like nebraska or the southwest, but on a grand scale. The actual inside circumference at 1AU would be 584 million miles, btw. Using some rough trig, if the (for purposes of the math, perfectly circular) pseudo-continent had a diameter of 12,000 km and was perfectly flat edge to edge (discounting mountains and such, just mean thickness) it would be about .54 km thick in the center. Bump that up to 2 km or so and give it a nice, gradual curve towards the inner surface of the sphere and you have a horizon, no problems, although one much flatter and more like the great plains that what someone from new england or the south would think of as a horizon. And it would be fairly easy for that scale of engineering to bring the next pseudocontinent up to it and create an ocean in between to get rid of the low spots when it is time to expand, and with the distances involved the transition should still look 'normal' to someone from a planet.

{On a tangent using these numbers (113 million square kilometeres, btw), and assuming that there is as much land proportionally on the pseudo-continent as there is on earth, it can probably support a half-billion to a billion sentients easily. (New Avalon is quoted as having a population of 20 million, most living quite comfortably). Probably a lot more, but that gets into environmental arguments, so lets use a billion. Easy to work with. As 1 degree of radius inside the sphere is something approaching three and a third trillion square miles or almost 9 trillion square kilometers (VERY rough math, don't shoot me for the fudge factors, please), that small section of the sphere could support almost 7.9 million times that population, or 7.9 million billion. 7.9 quadrillion? Even if I muffed the numbers somewhat, 6 to 7 quadrillion would still probably be reasonable. That's in a 1 degree by 1 degree section of the the Zeta Cygni sphere. Just something I was thinking of while cruching numbers.}

EDIT: got some of my labels crossed, all the math is done in miles, not km like I originally had, so had to redo a couple of numbers. Allows for even more people, actually. And it's double-checked this time.

And hell yes, it's granular detail, but I was almost a US Navy Nuke operator. We overthink things, its an occupational (and personal) trait.