Love Theory: Vector calculus and objectoriented programming 
[Nov. 29th, 200508:52 pm]
Napkin Philosophy

Add little arrows above a and b if you wish, but I don't know how to do that in html.
This our model of the two people in the relationship:
λ_{a} = (τ_{b}, ι_{b}, λ_{b}) λ_{b} = (τ_{a}, ι_{a}, λ_{a})
That is, a person's love for the other person (i.e. a's love for b) is dependent on how they view b's traits (τ_{b}), how a views interactions with b (ι_{b}) and how a perceives b loves them (λ_{b}). There was some disagreement about where to put _{a} and _{b}, but I figured keeping them uniform for the vectortuple set would be a good idea.
Furthermore, the third term in the 3tuple must be changed, we found out, since person a can not know the lambda factor of the other person. I'll get to that later (1).
We considered how this could be modeled with recurrence equations (a la Algorithms), but that was doomed to failure since we have two different equations that rely on each other AND time, instead of just one equation referring to itself over time (e.g., a_{n} = a_{n1} + a_{n2}).
All we know is that we need to model λ(t) (2), so we can derive the integral, ∫λdt and the derivative λ'  the satisfaction in the relationship, and the "direction" the relationship is heading, respectively.
Issues:
 Derive an objectoriented (OO) model of subjects a and b with private data(τ_{other} and &iota_{other}) and public methods (used by the other subject to find out information, like how much they like them  some function used by the other subject to get an estimate of λ_{other}).
 Model λ(t) in a definitive format  recurrence equation, otherwise recursive, or nonrecursive.
 Figure out the starting points (in time) for all of the members of the equation and how they relate to each other. What we know at this point is that, if S(x) is the starting point for variable x, then S(λ_{b}) > S(ι_{a}) > S(τ_{a}).
 ι depends on λ, but we don't know how yet.
 In the OO model, the interactions between the objects with the public functions is timebased and happens oneatatime and this should, ideally, get rid of the need for recursion, if we can figure out when the time variable is going to change, since the references between the objects (a and b) seem to be at the same time.
λ > λ  ^ <
 Each object, in the above model (a and b), has a "cache" which stores inforamtion about the other object that affects or "filters" their perception of the data collected from the other object.
 Find a logical basis for this model's premises and theorems. Very important!


