The explanation I have waited my whole potato growing life for is on this thread (if I copied it right

).
http://www.idigmygarden.com/forums/showthread.php?t=15350&page=4&highlight=potatoes
Someone gives directions how to keep potatoes productive as they grow, through hilling or tower method. I would copy it here but I don't know protocols.
Okay, I'm going to quote this part:
...constantly hill the plant so that only 3 or 4 leaves are ever exposed, the underground stem will continue to produce stolons. Do that over a 6-week period with tires and you could conceivably end up with 2' of tuber production. Miss several days early and allow the true stem to develop and you would probably find 2' of nothing but stem.