But isn't it easier to keep the tech up when your looking over what amounts to one big city instead of whole state or country? Also doesn't things like solar panels and even windmills help also. As for future generations I assume the kids go to schools much like our schools so the knowledge of the old world I assume is being passed along in that way also.
It's easier to keep the tech up when that one city is being supported by stockpiles and you only need a few spares at a time.
It isn't any easier ten years later when the spares have run out and you've got no way to make any more. Doesn't matter that it's only one city.
It's true that it'd make a huge difference to maintain records of old-world technology and educate the next generation with it. But recreating that technology is another story. Look at what it'd take to manufacture microchips.
Wikipedia said:
Wafers are formed of highly pure, nearly defect-free single
crystalline material, with a purity of 99.9999999% (
9N) or higher. One process for forming crystalline wafers is ... a cylindrical
ingot of high purity monocrystalline semiconductor, such as silicon or
germanium, called a
boule, is formed by pulling a
seed crystal from a
melt. Donor impurity atoms, such as
boron or
phosphorus in the case of silicon, can be added to the molten
intrinsic material in precise amounts in order to
dope the crystal, thus changing it into an
extrinsic semiconductor of
n-type or
p-type. The boule is then
sliced with a wafer saw (a type of
wire saw), machined to improve flatness, chemically etched to remove crystal damage from machining steps and finally
polished to form wafers. The size of wafers for photovoltaics is 100–200 mm square and the thickness is 100–500 μm. Electronics use wafer sizes from 100 to 450 mm diameter.
So, first you have to recreate the means to create silicon crystals that are 99.9999999% pure. You'd have to recreate the means to dope the crystals with boron or phosphorus ... except first you'd have to recreate the process to extract those elements in the first place. You'd have to have the tools to build a wafer saw to the appropriate degree of fineness ... except first you need to find out what a wafer saw's made of and refine those alloys and materials. And of course you need the chemical knowledge to mix up the acids and other materials for cleaning, texturing and etching. Get ready to build a chemistry lab first.
Oh, and this work has to be performed in a sterile environment. Get ready to manufacture bunny suits with gloves and clear faceplates, respirators, and a work facility maintaining constant positive air pressure.
Oh, and all these steps require a microscope to see what you're doing. To build one of those, you need appropriate knowledge of glassmaking, grinding, and polishing, with an appropriate background in optics. Get ready to build a glassmaking facility first.
And that doesn't count the steps to build the microscope's controls and adjustment mechanisms, which require a high degree of precision. Get ready to build a machine shop first.
This is the absolute minimum required to make exactly one thing: a microchip. Can you really envision making it, knowing that first you have to reconstruct the entire infrastructure of the civilization that invented it? Now imagine trying to figure out all this stuff from a
book — because all the experts in all these fields have either been eaten, or they're walking around with their faces hanging off. Theoretically possible? Yes. Likelihood of success? Questionable.
How much manpower and brainpower do you throw at it? How much do you really have to spare, compared to the needs of survival? At what point do you give up when you realize that you simply can't support the infrastructure you want? Or, if you succeed in manufacturing a microchip: Do you know what to do with it once you've made it?
Of course, if that's too hard, maybe you could go back to the 1950s and recreate the infrastructure to manufacture transistors.
Or, if you can't support 1950s infrastructure, you could go back to the 1910s and recreate the infrastructure to manufacture vacuum tubes.
See the regression?
It's certain that in the long term, your post-ZA civilization will only settle out at the tech level they can provably maintain (once the stockpiles run out). No more than that, regardless of how many books they have.
Alexandria settled out at the 19th century.
Could the Commonwealth achieve higher? Probably. But not the 21st.