"Any sufficiently advanced technology is indistinguishable from magic." That's one of Arthur C. Clarke's Three Laws. Nowadays it's often cited by those who wish to advance the idea that magic exists, which would probably make the author pull out his hair, assuming he were alive today and had hair to tug. In fact, Clarke was making a point about our perception of things: specifically, that our perception is constrained by the limitations in our knowledge and reasoning ability, and that perception is most decidedly not reality.
If you could show a Harrier jet to a person from the stone age, he/she would almost certainly see it as magical, or divine, or maybe demonic. The exact flavor would depend on his/her cultural matrix and its predisposition to frame the inexplicable in one way or another, but the essence is the same. If, on the other hand, you were to show a Harrier jet to someone from the late 19th or early 20th century, it would more likely be understood as some technology that was a leap or two beyond what they knew...but that was still somewhere along that path. Barring some kind of rare genius, they wouldn't be able to understand how you got from the flight technologies they knew to the Harrier jet -- but there's a good chance that they would be able to imagine that such a path existed, and moreover, that it consisted of successive steps, each building on the knowledge and understanding gained previously. And at the same time, there would have been people from that same era, even from that same culture, who thought it was all magic.
So it's really in how your mind works. To some people, pretty much anything beyond their current understanding is magic; to others, it's understandable -- it's just not understood yet. I'm firmly in the latter camp. I don't understand knot theory, but I did study linear algebra (and did a rather awesome job if I do say so myself), so I have total confidence that I could fill in the intervening steps and learn knot theory. And I don't understand much about aikido, but I do have some understanding of a few basic things, and I think I can figure out the steps as time goes on. I don't see the need to mystify any of it, and furthermore, I don't think that an endorsement IHTBF is in any way an endorsement of mysticism -- quite the opposite. It can be, and IMO often is, a copout -- an avoidance of filling in as much information as can be filled in without the "feel" dimension. But certainly, you can get to the point where only the "feel" dimension will provide that last bit of data. But it IS data, not magic.