To supplement Cagey's reply -
If you imagine a jump rope, consider the travel of the rope in the center vs. near the handles. The rope travels a lot further in the middle than at the ends, despite the frequency (the number of rotations per time period) being the same at all points along the rope. The same is true of a guitar string. The way the string disturbs the magnetic field of the pickup is different at various distances from the end of the string. This is why the same note played on a Strat has a different timbre depending on which pickup you have selected.
Now, IANAE (I Am Not An Engineer), but I know that this is complicated by the interaction of the pickups with each other. If you have two pickups of roughly equal strength, but one is wound and polarized the reverse of the other, common mode rejection operates to eliminate not just 60 cycle hum, but also other stuff that both pickups are receiving identically, resulting in the "quack" of the in-between positions. You'll need to get Cagey or Mayfly or line6man or one of our other resident engineers to give you more than that.
I found these neat things as I was verifying whether I was about to grossly misstate something:
How waves on a string behave:
http://www.acoustics.salford.ac.uk/feschools/waves/standing_waves.php
Common mode rejection (the phenomenon underlying humbucking pickups):
http://en.wikipedia.org/wiki/Common-mode_rejection_ratio
Pickups generally:
http://en.wikipedia.org/wiki/Pickup_(music_technology)
Humbuckers in particular:
http://en.wikipedia.org/wiki/Humbucker