I think you are far over-stretching the limits of technological wishful thinking. There is no guarantee that any technological knowledge will ever allow making a space ship like the enterprise or a flying elephant.
It is in fact perfectly possible to imagine impossible things. For example, it is easy to imagine a solar powered commercial car. Picture a Ford Mustang, but it uses no gas: all its energy comes from the solar panels on its surface, and it goes just as fast as a normal Ford. Have it in your mind ? But yet, it is never gonna happen, because there is simply not enough surface on a car to yield from the sun the kind of energy you can get from a few litters of gasoline. Better technology, like better solar panel, won't do, because we can at most yield 100% of what sun light falls on the car, which is something we can compute and it's not enough by several orders of magnitude. Yet, we had it firmly imagined in our mind, if we close our eyes we can almost see it.
So what happened here? Spinoza would say we had an incomplete idea of a solar car. An incomplete idea is an idea which, by lack of analysis does not match reality. We can have a vague idea of something unreal, but as soon as we try to detail it, to figure how it could happen we reach a contradiction.
The same would happen with a flying elephant, or Pegasus the famous flying horse: as soon as we analyse what kind of wing span, what kind of muscles would be necessary to fly those hundreds of kilos, what kind of lungs, heart and diet would be required to feed those muscles, we have to recognize that the end result would look nothing like the flying elephant we had in our mind.
On the other hand, there is no shortage of things that exist and yet nobody has a complete, adequate idea of. Just think of a very complex system like the space shuttle: no one has a complete idea of the whole shuttle from the general concepts to the gritty details like the length and diameter of each pipe in the engines, or how those pipes are made.
So we can see that ideas and things are disjointed: there are things nobody has a proper idea of, and there are ideas related to no existing thing. An idea of a flying elephant might exist, but a flying elephant does not.