Wednesday, November 3, 2010

On Being Stuck at a Local Optimum

It seems that my seven years of engineering school were not a total waste.  For they have given me ways to think about life's problems that might otherwise not have occured to me, such as the distinction between global and local optima.  ("Optima" is the plural of "optimum", which means "the best" place.)

My contention (from looking at my own life and the lives of others) is that we humans often get stuck at a local optimum, and that we lack the faith or the initiative to seek for the global optimum.  There are reasons for this.

In the accompanying plot, the vertical axis could be anything you seek in life (e.g., happiness), or anything you wish to eliminate from your life (e.g., fear).  I have drawn the curve so that the lower you are on the curve, the better things are for you.  The horizontal axis indicates things in your life over which you have direct or indirect control.

Picture yourself at the point labelled "Local Optimum".  As far as you can tell, things are going as well as can be expected.  How do you know this?  You know it by sensing the gradient (or slope) to the left and right of your position.  If you move to the left, the curve goes up (meaning: your life gets a bit worse).  If you move to the right, the curve also goes up (your life gets worse in that direction also).  So, it seems logical to stay where you are.  Right?

Well, perhaps not.  There may be some much better point (the Global Optimum) where your life would be much happier.  But there are two problems:

(1)  You probably cannot see the Global Optimum.  You may only be able to see for a short distance in either direction from your present location.

(2)  Even if you know it is there, your life has to get worse (or at least, harder) before it gets better.  There will be sacrifice (moving far up on the curve) before things begin to improve.

Of these two problems, I think that the first is by far the worse.  Without a vision of a better place, it is not easy (and, perhaps, not advisable) to set off to find it.  This calls for faith, and for the vision of another, who can see both your position and the Global Optimum.  The second problem is still daunting for some.  One knows of and believes in the existence of the Global Optimum (or even some better Local Optimum), but one seems unable to gather the required strength to climb the hills necessary to reach it.  This part calls for courage.

Maybe you fancy yourself to be at your life's Global Optimum; I do not.  Today, let us catch a vision of how our lives could be better, more glorifying to God.  And let us start climbing.