Travelers are always advised to stay on the path if they go through Mirkwood. For, as Bilbo experienced long ago, if one strays off of the path, one may encounter such horrors as giant, talking spiders. Luckily for Bilbo, he found his way back to the path, and he was even luckier it was the right one.
If Bilbo had gone farther, he may have found more than just spiders. Centaurs have been seen, and sometimes, even giants. If one goes far enough, he may find the other path. If he were to follow this path out of the woods, he would find, to his great surprise, not the Lonely Mountain but rather a castle. A different world entirely.
Mirkwood, otherwise known as the Forbidden Forest, is a gateway between two worlds.
There are some who know its paths well and frequent the other world often. It was in this way that Gandalf and Dumbledore became great friends. Whenever one required the assistance of the other or had a confounding problem to solve, they would summon the other. And off they would traipse into the forest.
Many times they would meet for tea in the afternoon, but sometimes they assisted each other on quests. When Gandalf was hunting Sméagol, Dumbledore helped him. Dumbledore also had Gandalf's assistance in locating several of Voldemort's Horcruxes. To this day their friendship is confidential and only their most trusted allies know about it.
There are some, of course, who know the paths of the forest, but not of Gandalf and Dumbledore's friendship. Wood-elves, mostly, and the centaurs. The spiders live in that sort of in-between world: neither Mirkwood nor the Forbidden Forest, and yet both worlds at once.
The magic of the forest was set in place by Elves long ago, long before the days of Dumbledore or Gandalf. But—and it was perhaps by chance—these two wizards became best of friends, and neither of them knew the twist of fate that would bring them closer than ever.
