The Heisenberg uncertainty principle is more than a mathematical oddity; there was an article in Philosophy Now which illustrates the point:
http://philosophynow.org/issues/45/Bohr ... t_and_Zeno
The main thrust is that there are practical reasons why you cannot know both position and momentum. I've reproduced part of the article here, which should give the gist:
"At the heart of quantum theory lies the Heisenberg Uncertainty Principle, the thrust of which is that certain conjugate properties, position and momentum for instance, cannot both be measured to a totally accurate degree of precision at once. If we choose to measure perfectly the position of an electron, we then lose accuracy regarding its momentum. We could choose instead to accurately measure its momentum, but then we cannot be exactly sure of its position. This promotes the seemingly untenable situation of an electron that has neither well-defined position nor momentum until we come to measure it. In effect, what we choose to measure in some way determines the characteristics of the electron. Hardly surprising that Einstein, Planck et al found this unacceptable.
In defending quantum theory against Einstein’s many thought experiments, Bohr would repeatedly emphasise the practicality of any experiment. When Einstein proposed his famous Clock in a Box experiment [see box], it was not enough that he propose we weigh the box before and after the photon’s escape. Bohr was insistent we specify exactly how we do the weighing. Only once it is made clear that a spring or some such device must be used does it become clear how the uncertainty will manifest itself. It was not enough to argue in principle. For Bohr the practicalities had to be explicit."
This is the box referred to:
"A box containing a clock is swimming with photons; the clock being connected to a shutter which covers a hole in the wall of the box. The apparatus is designed so that the clock will briefly open the shutter at a specified time, allowing just one photon to escape. Einstein argued that by weighing the box before and after this specified time, we can calculate the energy of the photon, since mass=energy. As we know the time the photon escaped (we specified this before the experiment) we have broken the Uncertainty Principle – the time and energy of a particle are a conjugate pair that according to quantum theory, we cannot have exact knowledge of, both at once.
All well and good in principle, came Bohr’s response, but how do we actually weigh the box? Suppose we suspend it from a spring in a gravitational field. Then obviously the box, clock and all, has to move in the gravitational field; that’s how weighing works. But according to Einstein’s own general theory of relativity, clocks run at different rates depending on their position within a gravitational field, so we cannot be exactly sure of how fast the clock is running. This uncertainty is just enough to comply with Heisenberg’s principle. Bohr is said to have been not a little amused that he had turned Einstein’s own theory against him."