The titular problem is a mathematical conundrum from Newtonian physics that is often equally applicable to other areas of physics and it boils down to the near impossibility of telling the future positions of three moving bodies all of which exert gravitational forces on eachother (such as the Sun, Earth and Moon).
The same problem of relativity arises when writing about the relationships - and especially related motivations - of three characters. Quite aside from confusions over pronouns - resolved generally by replacing them with their proper nouns, it makes for confusing, clunky and multi-claused sentences. I'm going to try to build the simplest possible example. Alice, Bob and Chris are friends. Chris and Bob are both in love with Alice, but Bob is prepared to give up Alice to make Chris happy.
"Alice loved Bob and Chris equally, but she knew that Bob's friendship with Chris was important to him - maybe more important than his feelings for her. That increased her tenderness towards Bob when she was with Chris, but Bob's affection for his friend often made her feel even more tenderness for him."
This is already horribly knotty. (Imagine how much worse it would be if all three were men!) But its knottiness actually creates an opportunity for the patient writer - I tend to think that this kind of issue is created by the writer being in a hurry to explain the situation. The opportunity it creates is one of extending the narrative, by presenting the relationship in a narrative structure. The writer who really wants to take the bull by the horns here will devote a chapter to establishing this three way relationship. If it isn't that kind of story (and it might not be), then you should at least devote a couple of paragraphs to it, and present it as narrative, giving yourself time to explain each relationship separately. A good setting for this might be an incident where Alice and Bob are alone together, and Bob is relating some past experience of his with Chris. Alice can react to what Bob says by comparing it with something that Chris has previously said to her - and concludes that she needs to tread carefully, since it is Bob and Chris' affection for eachother that makes them both so attractive to Alice.
Furthermore, by setting up the relationship through narrative, you will engage the reader's attention much better, and get him involved in the relationship, and get him to care about what happens - something that you won't get through plain exposition.
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