# Lewin's equation - expanded A physicists reading of an equation in social psychology.

I recently came across a discussion about Lewin's equation. In short it is an equation  within social psychology used to describe people's behaviour,

B = f(P, E) (1)

where B is a person's behavior, P is the person and E is the environment.

Which is fine and dandy. But if we think a bit more closely about the factors, we will see they are not completely independent. E.g. a person's environment will to a large extent be shaped by both your own and other people's behaviour, in addition to a natural component, so we can write the environment factor as

E = f(N, B1, B2,..., Bn). (2)

In the same way, a person, if you look upon this as a process that happens over time, is shaped by both a natural (genetic) factor (no matter how you are raised you will behave differently from an anteater raised the same way), and an environmental factor shaped by both the natural environment, and - again - other people's behaviour over the entire course of a person's development. We can mark this as an integral from t=0, ~birth of the person in question, to t=T, the time in question.

In this developmental model, all factors, with exception of the genetic one  will in turn be functions of time, and we will get an equation

P(T) = f(G, 0T (N(t), B1(t), B2(t),...,Bn(t))). (3)

If we are to combine these two formulas, we can replace the P and E factors and get something like

B1(T) = f(N(T), B1(T), B2(T),...,Bn(T), G, 0T (N(t), B1(t), B2(t),...,Bn(t))). (4)

This is a more complex equation, but it does not hide the (strong) interdependencies of the factors in the original Lewin's equation. Does it help us in discussing behaviour? I'm not so sure, but acknowledging the complexities of the problem and the huge simplification in Lewin's equation is perhaps also of some help?

Endnotes:
 A scientist would probably rather reformulate it as Lewins function, however without any specific function.
 One could argue this is also not the case as genetics is not as completely set in stone as previously thought, but it will do as an approximation and the most effects of e.g. activating genes at specific times will be encompassed by other factors.