WHAT?! You still remember that evil abomination?
... Now I'm gonna have nightmares for another week >_<!...here you can have the apple back... *silently steals a more ripe version with the other hand... and flies for the hills*
So putting that all into the picture, we now surmise that Ryuk is bored enought to try out something that's radically new and therefore, owing to reasons of his own, tricks the shinigami king into believing that rules should be written down in the book and also steals a book for his own purpose...namely shoving it down into the human world... Now the other facts that we already know are that shinigami are intricately related to humans simply because it is the drain of a human life that actually prolongs a shinigami's life. There seems to be no other species that is effective enough to keep a shinigami alive. Further, it is only humans who have special names to identify themselves, us being a sentient specieies. For e.g. even if I name a sheep "John" to all other sheep all he would be is "Baaa"!
and you can't write that on a death note because it doesn't identify John from any of the other sheep. Further, it is only love and sacrifice for a human that actually "kills" a shinigami... that's another connection to the human world. And with all these in mind ryuk sets off to the human dimention because...
... he's sneaky enough to have a purpose bigger than just stealing ripe apples! Maybe he really wants to die...maybe death to a shinigami is actually a release! The only way to do it is to live out your years or to sacrifice yourself for a human being...both of which ordinary shinigami wouldn't do because of their greed!