(1) We can do it (maybe for some time) but never thought of it.
- The ancient Romans had polyhedral dice and writing. They could have invented roleplaying games. Why did it take until 1970 for Dungeons & Dragons?
- Similarly, Romans and Egyptians could have fashioned the parts for a low quality bicycle. Wikipedia has the first bicycle in 1817.
The classic simple machines are the lever, wheel & axle, pulley, inclined plane, wedge and screw. Is there an undiscovered one?
(2) We can't do it today, but it should be here soon. Maybe it's just too expensive, or needs the next generation of tech evolution, or needs us to make a fundamental change in society.
- Supersonic business jet is clearly possible, but utterly un-economical.
- Some people would put self-driving cars here, as they feel they're close. It might even be possible today if we switched to central traffic control and designated pedestrian crossings, and didn't let humans drive at all.
- Full AI, as in synthetic intelligences, are in this category for anyone who doesn't believe that consciousness comes from the Divine.
- I put anti-gravity here because of the current contradtion between relativty and quantum mechanics. We're clearly missing the theory that connects the two and there's a lot of scope for new physics in this area.
- Building a galactic dyson sphere? That requires so much time, material and energy that anyone who can do this probably needs #5. It becomes hard to make predictions at this level.
- Faster than light travel. If this ever works, then all of modern physics goes in the bin. We can open the Unicorn pen and let them out to play.
- EDIT: Violation of the second law of thermodynamics. The total entropy of an isolated system can never decrease. I personally think this is the single most unlikely thing to proven wrong and the best example of type #5. (After feedback by "Old School")