>But if you want to build a giant fuckoff "this thing is relatively
>thick and solid EVERYWHERE all the way around" one like the one from
>Star Trek, then you're talking an absolute nightmarish amount of
Fine, let's actually math this out. I'm going to take Niven's word for it that the required strength is on the order of the strong force, because that conveniently means the required density is that of nuclear matter, which is 4e+11 kilograms per cubic centimeter. Multiply that by the surface area of a sphere with radius 1AU and you get 1e+41 kilograms of material per meter of solid thickness. Or, in more useful units, 6e+10 solar masses per meter.
That's on the order of one-eighth of the entire galaxy's mass for a 1m-thick shell, which is basically what you were saying, but which should also raise a gigantic red flag, because the Schwarzchild radius of that much mass is on the order of 1100 AU—in other words, if you attempt to build it that heavy it will immediately collapse into a black hole.
(Flipping that around, to avoid building a black hole by mistake, the mass of the sphere plus everything within it needs to be less than about 50 million solar masses, and if we use all of that for the shell of nuclear matter we get ... 0.8 mm.)
I don't see that it makes sense to build the entire Dyson shell out of solid nuclear matter, though. If the goal is meteor shielding, why not have an outer layer of ordinary steel, or ice, or anything else that can absorb orbital-velocity impacts and is cheap to replace? The impossibly strong part just needs to be the structural skeleton, thick enough to support itself plus everything you hang off of it, and I'm prepared to handwave that this is thin enough that you only need one or two solar masses' worth.
But you've definitely convinced me that this is not Baby's First Kardashev II Construction Project. :-)