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As part of my ongoing 'Floating Society' (new thing, floating islands made out of handwavium floating above a habitable planet) worldbuilding project, I'm asking whether a society with technology comparable to current human tech could develop with extremely limited land area. Assume that they cannot just find a place with more land.
To put it more simply, can a society develop 21st century technology while having only an area of a large Earth island to settle on?
They could not advance very much.
The crux of the matter is they inherently lack abundant resources. If they're floating on a island with nothing but a free-fall under them, they have extremely limited access to raw materials. Resources and materials like wood, coal, oil, metal, radioactives, silicon, etc.
You actually might expect their technology level to decrease over time. Any mined metal weapons or tools that are lost over the side of the island are gone for good. So while they may have had some metal to make strong tools in the past, they will have quickly mined it, then lost or destroyed it.
Take a look at Easter Island for what can happen to a civilization on a relatively small island with limited resources.
Development of current technology is going to depend heavily on how many people you can put on this island. When the occasional backyard tinkerer who comes up with a new product, it takes lots of money to turn that invention into a product. Every widespread technological innovation in history has happened in an environment where it is economically viable to sell it. This is true for commercial and military products.
Consider the following example with plastics: Sam, the inventor comes up with a new plastic thingy that will solve everyone's problems. Money at this point hasn't mattered. However, to create the tooling to pressure inject the plastic costs 1,000,000 ISK. If the market for the plastic thingy is only 1000 people (because there's only 1000 people to be sold to) then each thingy will cost at least 1000 ISK to make up just the tooling costs. This doesn't include materials, admin overhead, marketing or a healthy profit for any investors, so the cost per thingy will be at least 2000 ISK. That product just isn't worth it.
However, if there 100 million people in the plastic thingy market then the tooling costs per person are 1 ISK per thingy. The very high one-time costs just disappear when spread across large markets.
(This also explains why China is such a huge draw for large multinationals. For the longest time there was no market in China but now there are tens of millions of newly middle-class people who want goods and services. Markets that size are just too big to ignore.)
Consider how large the market must be to support modern semiconductor manufacturers who spent many hundreds of billions in capital investments in the last five years. And that's just one small section of the larger economy.
Market size has a huge impact on how much technological innovation can be afforded and in what area that innovation happens.
I'm not clear why they could not land on the planet below and mine whatever resources they need, either to expand their island or build new ones.
In fact, even with current technology and knowledge, it is on the outside bounds of possibility to terraform a planet like Mars to make it fully habitable by human beings. Of course they would have to be very patient human beings, since with current technology and knowledge it would take about a millennium for the bulk of the terraforming to be complete...
Given the very small resource base people on an island will be starting with, terraforming an entire planet may not be possible, but setting up mining camps on the surface, placing a dome over top and gradually expanding the usable surface area, resource base and numbers of people will gradually bring you to the point where your economy is large and robust enough to bootstrap the terraforming process.
To understand why the economy needs to be large and diverse enough to do this, you should read the essay "I Pencil" (http://www.econlib.org/library/Essays/rdPncl1.html), which explains why even such a seemingly simple object as a 2B pencil requires the industrial infrastructure of the world to be affordable and ubiquitous.
So to undertake any advanced projects, or even to remain at their present stage of development, they will need to look to ways of expanding from their island habitat and command the resources of the planet below.
