Three Wishes And Thrice Three Lives

Today's burning questions both revolve around animation, as a result of the current explosion of interest in the works of Disney that my fellow mathematicians seem to be suffering.

The first question is by far the most involved. It concerns the conclusion of my favourite Disney film of all, Aladdin. Taken as a whole, it's close to perfect: funny and sweet and technically impressive, with the two best villains Disney has produced (though I grant that Shan Yu was far more menacing, and Gaston has the best evil theme going), and a very strong set of songs into the bargain. The ending, however, always winds me up, because it requires to believe that everyone involved has miraculously turned into an idiot, all except the Sultan, who has miraculously stopped being an idiot.

For those who have forgotten (or who, unforgivably, have never seen it) Aladdin is forced to choose between two options for his final wish. He can either become a prince once again, so as to marry his true love (does anyone in Disney films take more than 72 hours to decide who they'll spend the rest of their lives with?), or he can free the genie, as he promised. I realise that the intent here is to demonstrate that by choosing to free the genie Aladdin is demonstrating that strength of character is worth more than wealth or social standing, but this is somewhat undermined by the knowledge that he could easily just wish to become royalty once more and then hand the lamp to Jasmine, who could then free the genie herself. This, as I say, is then compounded by the Sultan suddenly realising he can change any law he chooses in any case, but that is somewhat more forgivable (he may only have realised due to Aladdin the importance of character over wealth, or perhaps Jafar had been deliberately preventing any potential marriage in an attempt to avoid getting the chop from a new Sultan). It's the first point that really rankles.

Of course, handing the lamp to Jasmine is only one potential way out. They could have used wishes from Jafar's genie, for example. That, though, assumes that he wouldn't find some way to trick them out of what they were asking for (hardly an uncommon tack for mischievous djinns to take). Passing on the lamp would make more sense. Or would it? Do the things you ask a genie for remain after they've been freed? They certainly outlive the lamp being passed on, but that's a different thing. The fact that Aladdin is neither transported to the Cave of Wonders nor instantly drowned once the genie loses his shackles likewise suggests not, but motion and creation are clearly not the same.

I guess you can patch together an explanation that makes sense, though if one of the most important scenes in your movie only works according to rules you haven't bothered to describe at all, you're doing something badly wrong. In any case, the question of what happens when a genie is freed is of critical importance, because it raises another conundrum, if a genie's creations survive its freedom, then are infinite wishes in fact possible?

BigHead and I discussed this at length over our lunchtime caffeine (because that is how we roll), and between us came up with the following. Consider the four rules of the genie. You can't wish for more wishes, and you can't have anyone killed/fall in love with you/rise from the dead. However, we know full well that a wish can make you into a genie. So what's to stop three people getting their hands on a magic lamp and trying the following? Person 1 has two wishes of whatever kind they wish, and then wish to be a genie. Person 2 gets one wish, then spends his second freeing the initial genie (which, admittedly, you don't need to do for this to work, but it's kind of a nice gesture, y'know?) and his last one on turning himself into a genie.

Person 3 gets one wish for themselves, uses their second wish to free Person 1, and then with their final wish they become a genie. Person 1 can now free Person 2, get one wish of whatever kind they choose, and then become a genie again, and so on the cycle goes.

Pretty neat, huh? There are two potential issues here. Whether a genie be freed and turned into a person simultaneously ("I wish you were a free human!") is one, though that doesn't matter as long as a free genie can themselves make wishes (you'd eventually have to end the cycle in order to get yourself free and human, but by that time you can have made an arbitrarily large number of wishes; so who cares?). The other potential stumbling block is the possibility that the genies operate some kind of union/hive mind, and one can only ever receive three wishes from them, irrespective of how many you have met.

Still, it's a nice little cheat, no?

Also, my second, rather shorter question is this: does anyone know of any cartoon, ever, in which a cat is killed and stays dead?