Something in this last post got my brain a whirring, and it is not the consensual chop busting exercise.
You initial post has to do, as I see it, with the following promise: the next leap forward in understanding may use an extra human intelligence as a catalyst.
For example, a few centuries ago, some folks argued about the fact, or demonstrability, of the flat versus round earth. When did we "KNOW?" Well, for certain, when Magellan's last ship came back, "we KNEW," but the analytical "understanding" of how it should work predated Magellan's concrete proof.
You opening question struck me as a little ambiguous, in that I am not sure if you imply an enabling role, or more of a "gotta pull you through by your nose" role for said alien, or "I can do it, and you will understand even if you can't duplicate the act" role.
We can ideate any number of things "that are not yet" and we are aware that things that once seem impossible, or contrary to the knowledge of the day, are possible after future synthesis of varying branches of knowledge. (Example: A Tornado Fighter aircraft in Napoleons Time. Possible in time, not possible at the time . . .) In some cases, such as the FTL travel, we either do not trust our theories, cannot as yet provide them with sufficient proof, or we appear to run into barriers that either are visible, like the known speed of sound barrier once was in fluid dynamics, or are less apparent. The question is, are the barriers seen now as "impenetrable" as the sound barrier once was for aircraft design? (Our man made bullets already were exceeding the speed of sound, so we knew it could be done, just not sure on what scale. Again, the analytical lead the practical.)
What "Eureka" will lead to a breakthrough in something like the hovercraft I describe in my post further down? At present, our analytical tools may point to them being un makeable.
The problem with not having done all the work our selves is that the so called Eureka could create a frustrating series of "pulled by the nose" steps presented to us by the alien being. Even if he showed that he could do it or make it, that might not give us what you are asking for.
Let us say that the alien is a lot like us, but can sense, or see, nuances in magnetic and gravitational fields with the sort of amplification and resolution you and I get when we smell or hear.
When he gets to explaining hovercraft to us, he discusses, for example, how you just follow the orthoganal field conversion path, tending toward the miopegal shift, and he then gives tips on what intensity or angle of flow a good or bad path tends to look like.
What then ensues is the need to get us to be able, either naturally (what, he splutters, you mean you humans don't have a miopegal organ within your spines that sense these things through your hair follicles?) or artificially, to be able to detect those naturally occurring phenomenon and exploit them accordingly.
This is akin to the challenge in teaching a blind man with no feet how to land a tail dragging biplane. All of your descriptive skill, and the fact that you can do it, may not allow him to achieve what you can: Even if you can do it yourself and prove it can be done. A coarse example, but it touches on the entire discussion above.
Is your question a mattter of a third party clearing up a matter we would eventually get in time, or a matter of identifying one of our incorrect assumptions or laws (our flat earth) and thus create an enlightenment where our normal process allows us to follow a different path fruitfully?
Or, is your question asking what could he show us that we could understand but not necessarily do?
The entering argument was unclear to me, so I was left to ponder any number of follow on questions. Therefore, I did.
Here, have a beer, that was thirsty work!!