The Stopping Problem
I have a method for making symmetrical images. It's not very hard if you know elementary geometry and how to use an image manipulating system like Photoshop or the GIMP. Once i have achieved a picture I can apply the method to that and get another picture. I can repeat that process indefinitely and produce a series of related pictures. The problem is - when do I stop?
It gets worse. With each stage I can play with color and get many variations of the same image. When do I stop?
I worked as a studio assistant for an artist once. He faced the same issue. He always wanted to make one last change. A couple of times I had the picture in a crate to ship to a gallery and I had to say - Arnold - This picture is done! as I screwed down the cover.
Jasper Johns had a method for making pictures. You do something and then you carry on like that till you are done. He never did say how one could tell when a picture was done.
In practice I don't actually decide that a series of pictures is done. Something else catches my attention and I start a new series. What I notice is that when I look at the individual pictures in a series I can't really say which is 'the best'. They are on a sort of aesthetic plateau though individual viewers have their own preferences.
A variation on the stopping problem might be to ask who is the greatest artist?
When I was in art school people would mock the idea that collectors chose pictures that harmonized with their couch. But that is a way of solving the stopping problem and making a choice..
The Mandelbrot Set is created by recursively repeating a certain calculation until certain conditions are met. What if the conditions are never met? The algorithm solves that by just counting the number of repeats and stopping when there have been X repetitions.
In 1938 Alan Turing established the Halting Problem as a fundamental limit in computer science. The problem was to determine whether a particular bit of code would ever go into an infinite loop. That is, the code would never halt and present a result. Turing proved formally that that was impossible.
Years ago my TRS80 would lock up periodically - that is - the software would get stuck in some sort of infinite loop. These days that happens much less often. But the solution to the Halting Problem wasn't writing better debugging code. It was coming to know from experience which kinds of code were vulnerable to infinite loops. An evolutionary approach rather than an analytic one.
Nature has a way of solving the stopping problem. Things reproduce. Lots of things have no internal limit that keeps them from reproducing indefinitely. Instead there are external limits like starvation or even overfishing.
Overfishing might be another example of a stopping problem. I remember when red snapper was plentiful and cheap. There was nothing to stop the fishers from hauling in the last one which stopped the overfishing in a way. I don't know if red snapper is actually extinct but I haven't seen it in stores for many years.
One might think that issues like global warming are examples of a stopping problem. We know the danger and see the results but the ol algorithm just keeps chugging along.
What do you think?
I present regular philosophy discussions in a virtual reality called Second Life.
I set a topic and people come as avatars and sit around a virtual table to discuss it.
Each week I write a short essay to set the topic.
I show a selection of them here.