I think we have digressed too far from cold Fusion to post under that thread.
Sam: As far as I understand this stuff, your ideas about the uncertainty principle are right on track. The wave/particle duality business is another matter.
By the way, I hesitate to call myself either a mathematician or a physicist. I know a lot about both due to having taken some college courses. Also, back in the prehistoric Mainframe era I did a lot of programming of math, engineering, & physics applications (as well as various other applications). Since these were new applications back then, I had to get involved in discussions with people who really were mathematicians, physicists, engineers, et cetera. They really understood the subject matter, but knew zip about programming. Interacting with them got me interested in reading up on the frontiers of math & physics. Compared to an average guy at the ski lodge, I am both a mathematician and a physicist. Compared to the real math/physicist, I am an average guy at the ski lodge.
I sometimes suspect that the uncertainty principle is easier to understand if merely stated over and over again without further explanation: "The more accurate is your knowledge of the momentum, the less accurate is your knowledge of position & vice versa." At least I always get more confused by further explanation. I am pretty sure that there is some formula which states that the product of the two errors in measurement is equal to a constant. It's the implications which seem to require lots of explanation. Are you aware that there are various other uncertainty relationships? For example: There is a time/energy uncertainty principle, which I think is related to the momentum/position principle.
As far as I can tell, the hotshots in Quantum Theory really seem to believe that entities like photons & electrons can behave either like wave phenomena or like particle phenomena, but not both at the same time. If you set up apparatus to measure wave properties, they really seem to act like waves. If you set up apparatus to measure particle properties, they really seem to act like particles. The two sets of properties are such that an entity cannot have both at the same time. There have been some Scientific American articles on this subject which are truly mind-boggling and too complex to describe here. All sorts of complex experiments have been devised to try to "fool" a Quantum entity and make it show a wave and a particle property at the same time. It never does.
When you read a carefully written article by an expert (not edited by a tech-writer), he seems to avoid talking about the entities being waves or being particles: They talk about measuring wave properties and measuring particle properties. Same with the uncertainty principle: Their language seems to talk about "knowledge" (or measurements) of momentum & position properties, but they avoid actually saying that a particle has a position or has momentum. It suggests that they really think that our Classical World concepts only approximate the Quantum World properties.
You run into a lot of strange statements by the Big Thinkers. Einstein once said something like "Isn't obvious that momentum is a real quantity while mass is a construct of the human mind used to make it easier to think about various laws of physics?".
