Well, I think it comes down to excitement. I mean why do humans need to be entertained or do anything? Most animals are more or less content to exist. They have enough food, shelter, etc... and they still feel the need to do something. To some extent I think this is part of self awareness and consciousness. The inabillity to be satisfied with mere existance and the desire to fill it with something.
Truthfully I do not think that violence alone interests people, typically the violence that people are entertained by has some context to it. A fight for survival, justice, or the promotion of the values of one's culture. Most people find violence entertaining within the context of an action movie. In general people shooting each other in of itself isn't going to entertain people, there has to be some framework to justify it.
When it comes to things like Horror movies, it's usually the concepts and ideas that are involved that are the entertainment, the violence is just part of it. If I made a 90 minute movie of some guy with knives on his fingers stabbing people in a featureless white room with no dialogue, plotline, or anything but that, I doubt anyone would really want to watch the fake finger stabbing. However properly framed with a storyline, and an unusual plot about a dead man who becomes pure dreamstuff and kills people in their sleep, that basic premise became the foundation for one of the longest running, and most successful, horror movie franchises of all time.
Even when it comes to movies like "Saw" without the mystery and the ongoing storyline it wouldn't work. In the first movie the whole idea of the people waking up in the puzzle and such captured the imagination. Everything else has been variations on that theme. The death machines are a big part of it, as are the results when people fail, but if someone just made a movie about people getting killed in torture machines with nothing else to it, I don't think it would find a wide audience.
When it comes to things like an arena, personal combat is perhaps the ultimate competitive proving ground. I think there is more appeal to watching things like boxing or the UFC than a couple of guys beating on each other. This is why so much time is spent by people gathering statistics, comparing fighting styles, and performance records, and training techniques, and everything else. The spectacle is the contest.
The thing is though that back in Rome they had things like wrestling and pugilism. But in a non-lethal sport with rules there are always questions about who would have won if those rules didn't apply. Mortal combat answered those questions, either for those who volunteered, or for slaves trained and forced to fight (at which point it also became a contest between trainers).
I personally believe Sanity is defined by the state of mainstream society. When someone is "insane" they are greatly deviating from accepted standards. As such I do not think a desire for entertainment, and excitement, manifested as violence within a theme or competition is unusual. It's not "sick". Rather I'd think someone who is a complete
pacifist or does not derive satisfaction from such things is the one who is actually "insane". Of course things CAN go in the other direction as well, someone who actually kills people for no other reason than their entertainment is also insane.
I guess what I'm saying is that it's not the violence in of itself. If violence by itself was inherantly entertaining nobody would ever turn off a movie with violence in it as a bad movie. Yet it happens all the time.
Now on another level one can start talking about the base desires of humanity and how everyone has really "evil" repressed thoughts and such, but I think that goes beyond what your talking about.
Basically for your essay I'd simply point out the bit about excitement, and how violence is only seen as entertaining within a proper creative framework, which is why horror movies and such survive, but you also see plenty of movies and video games that are absolutly loaded with violence that nobody winds up liking because the framework is bad and they just blow chips.
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