The Friendship Index

I've been wondering what are the ingredients of a good friendship. Since I left Secondary School, throughout my JC and especially army days, I've come to realise that people we meet in life come and go, and good friendships is very often a result of favourable circumstance.

There are times when I meet people with the same mind and enjoy being with, but circumstances prys our paths apart, and we end up going our seperate ways. Other times, especially in army, I have been put with people whom I might not usually click very well with under normal conditions, but because we share a common experience, we become very good friends.

Friendships are also a function of Chemistry and Physics. It is quite common for people to use the term Chemistry to describe how well two people get along with each other... And physics? Well, it's the amount of effort (work done) each party puts into a friendship ;)

I have attempted to put in all these factors into an equation coined "Friendship Index". This index measures how good a friendship between two parties, Alice (denoted by a) and Bob (denoted by b), is. The larger the value the better friends they are. Ok, this equation is largely nonsense, as the values here cannot be determined quantitatively at all. It is simply my attempt at expressing how I feel each of these factors affects friendship. But i guess it can have applications in a game involving friendships...

The function F(a,b), the Friendship Index between Alice and Bob, is defined as,

where
c_f is the favourable circumstance (yuo3 yuan2 factor) - the circumstances forcing Alice and Bob to interact even though they do not make an effort to.
c_u is the unfavourable circumstance (mei2 yuo3 yuan2 factor)- the circumstances hindering Alice's and Bob's Efforts at an interaction, the smaller the number, the more unfavourable the circumstance.
E_a and E_b measure Alice's and Bob's Efforts at an interation respectively.
A_a and A_b measure the Affinity of Alice towards Bob and Bob towards Alice respectively - How much pleasure Alice gains from interaction with Bob, and vice versa.


An anotomy of the Friendship Index

The Interaction Opportunity Index, measures the amount of interation between Alice and Bob. Heavily dependent on circumstance, but can be affected by effort. However it's effectiveness requires that both parties play their part, and that there is no overwhelmingly unfavourable circumstances.

The Mutual Affinity Index, measures how much both parties gain from an interaction. This value increases with larger A_a and A_b, but is maximum for a constant sum A_a + A_b when A_a and A_b are equal, and zero if either party does not like the other.

Thus when you take the product of how much interaction they have and how much they gain from each interaction, you get how good a friendship is :p