Local Maxima

This is Andrew’s dad writing.  Andrew is taking a brief vacation from blogging, but he will be back.

The genetic mechanisms that govern species adapting to new conditions is a powerful concept.  In addition to its influence as an explanation for how human beings came to be, it has inspired programmers looking for imaginative ways to solve difficult problems with computers.  The idea of many computerized “individuals” in a “species” optimizing a “gene” – I quoted all these words because their correspondence to our actual DNA is purely conceptual – has led programmers to mimic the natural evolution of species.

One serious problem this genetic programming approach runs into is local maxima. Maybe a good way to understand, without trying to remember high school math, is to imagine a bug climbing a tree.  On any branch of the tree, there is the point that is the highest off the ground.  But only the highest point on the highest branch is the global maximum.  All the other high points, on each of the branches, are what we could call local maxima.

If instead of a bug climbing a tree, a programmer sets up generations of individual units, and enforces survival of the fittest individuals, the local maxima can wreck the solution.  After a while, the individuals that are at the local maxima “beat out” all the others, and so the computer program gives as its answer not the highest point of the tree, but only the highest point of the branch where the individuals started.  Why not start at the highest branch?  Because if you knew that, you wouldn’t need to run the program—you would already know the answer.

This is also the problem with the “pursuit of happiness,” as Andrew briefly wrote about in his article on The Good Place.  If all we humans do is try to be happy, we will perhaps find a local maximum, and at that point will be able to climb no higher.  Mind altering substances might make a person happy, but after a while, the notion of having reached a “local maximum” becomes cruelly apparent.  It’s not just drugs, though:  sex, power, eating, and pretty much anything that just tickles our pleasure centers will not work for an eternity.

God, like a programmer, looks at us and is trying to help us find that highest point.  Rather than using survival of the fittest, God leads us through dry places and valleys in the shadow – unhappy places all – because to get higher, sometimes, you have to go further down first.  Many bugs just never find the top of the tree.  But God will lead us, if we will follow, to the highest point, even if we first walk through the valley of the shadow of death.

Ironically, it is our success in localized happiness that has made our situation more difficult.  Earlier generations of Christians, though they may not have expressed it in terms of computer simulations, certainly understood the idea of following God even through dry places. As the false miracles of technology sing their songs, we have followed them in our pursuit of happiness away from God and to the local maxima where we are stuck.

Viewed from this angle, widespread drug abuse makes more sense.  Once you have found something that makes you happier than anything else you can think of at the moment, who other than God will get you to abandon your local maximum?

2 thoughts on “Local Maxima”

  1. I enjoyed read the post. Allan Bloom talk about local minima in a similar way. Here is a quote from _The Closing of the American Mind_:

    > My concern here is not with the moral effects of this music—whether it leads to sex, violence or drugs. The issue here is its effect on education, and I believe it ruins the imagination of young people and makes it very difficult for them to have a passionate relationship to art and thought that are the substance of liberal education…. In my experience, students who have had a serious fling with drugs—and gotten over it—find it difficult to have enthusiasms or great expectations. It is as though the color has been drained out of their lives and they see everything in black and white. The pleasure they experienced in the beginning was so intense that they no longer look for it at the end, or as the end.

    Bloom translated and taught Plato’s _Republic_. In that book, Plato says the philosopher kings know the enjoyment the rational part of the psyche can afford and thus they avoid Hedonism, which he thought was a local maximum.

    1. I had forgotten that passage in Bloom, but you brought it back to mind. I remember a high school assembly with a recovering heroin addict that was supposed to scare us straight. I wouldn’t have used “seeing in black and white” at the time, but the expression captures the thought perfectly.

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