Heisenberg's uncertainty principle
The math is a way of describing things that happen in the real world. You might imagine that it would be easy to get both the exact position of something and its exact mass, path, and speed at the same time. However, in reality you have to do two things to get your answer. If you are measuring the position and momentum of a bullet that is stuck in a cliff of a great mountain somewhere, it is a simple matter. The mountain does not appear to be going anywhere, and neither is the bullet. So its position is known and its velocity is 0, so its momentum is also 0. But if the bullet is somewhere between a gun and a target, it will be difficult to get its position at any given time. The best we may be able to do is to take its picture using a camera with a very fast shutter. But a single squeeze of the shutter would give you only one thing, the bullet's position at time t. To get the momentum we might put a block of paraffin in the bullet's way and measure how the block of paraffin moved when it stopped the bullet. Or, if we knew the bullet's mass, we might take a sequence of two pictures, compute the velocity by knowing the difference between the two positions of the bullet and the time between its two appearances. However we do it, we need to measure mass and position and time between appearances. We end up making at least two measurements to get to x and p. In that case we have to choose which measurement to make first, and which to make second. It seems to make no difference which order our measurements are made in. Measuring the bullet's mass and then measuring its positions twice, or measuring the bullet's positions twice and then recovering the bullet and measuring its mass would not make any difference, would it? After all, we have not done anything to the bullet when we weigh it or when we make photographs of it.