But at the same time if we would collect all the uncertainties in our models/simulations/calculations etc in a variable u. What happens as u->0 ? Shouldn't the gap between 2 and 3 go to zero? That would mean that enough knowledge about a technology is equivalent to actually possessing the technology.
All the uncertainties? If we had infinite evidence that the implementation will work the way you want it to then you could do this. So in this case "enough knowledge" effectively means infinite knowledge - everything about the construction process down to the quantum level and all of the (infinitely many) logical implications of your evidence. Actually, you arguably need more than that to make u go to 0.
So the conclusion ends up being that having infinite knowledge about everything that might affect the implementation is equivalent to having the technology. That doesn't hold at all. If you knew that much about the implementation and all the related issues you would have vastly more power at your disposal than if you just had access to a sensible plan that happens to work (even though you're not 100% certain about its soundness).
I don't know what the purpose of this post is, but there is a difference between research and development. Basically the gap between 1 and 2 is research and between 2 and 3 is development. Both are important but they follow different rules and need to be managed differently. It's impossible to research until you know exactly everything and it's likewise impossible to start development out in the blue.
Here's a little thing I wrote down a couple of years back:
Question: Does the following statements represent three different stages of technological development or does two of them represent the same stage? In some sense it should boil down to how we define the word 'technology', or at least its relation to 'knowledge'.
The key is how to handle 'know' in the second statement. One could argue that no matter how sure we are on how to construct it (down to every detail), statement three is still superior since we have actually one functioning reactor to show. But at the same time if we would collect all the uncertainties in our models/simulations/calculations etc in a variable u. What happens as u->0 ? Shouldn't the gap between 2 and 3 go to zero? That would mean that enough knowledge about a technology is equivalent to actually possessing the technology.
EDIT: The utility of having a reactor is of course higher than knowing how to construct one, so if we measure technological level as a function of the utility gained from that technology then the resolution is trivial.