The Chow-Faronius Emotional Bank(something similar to it has most likely been introduced already) is a very simple model for describing the growth of feelings (or emotional values) of a relationship. The model can then be extended to describe even more complicated matters.
Assume that we have a person P, with a set I containing all pieces (discrete) of information about person P. We will now define a function E, that assigns a real number (an emotional value) to every piece of information i.
Definition: For all i belonging to I, we can define a function E that assigns a real number to every i. The image E(i, t) is called the "emotional value" of the information. The t is for time, and shows that the emotional value of something can change over time.
The emotional value is a scalar describing how "emotionally charged" every piece of information is. A natural choice of the range of E(i) is the interval (0, 1), but the function can be defined for any interval on the real axis, and so that a high value corresponds to a high emotional significance. For instance, for most people the E(your name, independent of time) is lower than E(your cat, this morning).
The thing about relationships (with friends, relatives, colleagues, lovers, etc...) is that by spending time with them, you share information, and this information has emotional values. Like a bank where you can invest your money in different shares and funds, people invest emotional values of information in other people and their relationships, and then you may get a good return or a bad one, depending on coincidences and the person. The more emotional valued information you share, the more you can earn on it (due to rates of the bank).
It is also due to this model that you get more hurt if someone close to you. Actually "closeness to someone" could be defined from having the function E(i, t). Closeness could be measured as the sum of all the information you have shared E(i,t). Of course this is only relative to another relationship and its closeness, and it would be very difficult to define an intrinsic way of defining how much you will have chosen so that you become friends.
Corollary: "Love" is just a special instance of a relationship and sharing emotional values.
Of course, one might say that by doing things you might improve your relationship with someone, and one might argue that this is not just abstract information, but a more thorough investigation will reveal to you that by doing things with someone, you actually just change the emotional value of information that have already been sent. Eg. Lovers might do things for each other to heighten the value of the information that they are affectionate.
Some more advanced extensions to this model is the fact that there is a probabilistic factor of the growth of relationships, and that some possible might not happen if the people involved feel that the risk of losing is too great. The last of these is easily treated with Game Theory and the one before is described by a stochastic model, simmilar to Brownian motion. But treating these, is a more advanced subject.
