A Very Long Straight Line

I’ve been multitasking in an interesting way. Sort of. I’ve reached a certain point with some computations I am doing that I cannot go beyond by analytic means. LinePlotThis means that I can’t extract the physics I need by doing algebra and other exact manipulations on paper any more. Progress can continue however by using numerical means, employing a computer to solve the highly non-linear equations and extract the juice. There are several steps involved, and ultimately, I want to determine how a certain physical quantity depends on another physical quantity. (I’m sparing you the trouble of knowing what the details of the physical quantities are, since it does not matter for the thing I am trying to tell you. It relates to quantum field theory, gravity, and string theory, which connects the two.)

I can see that dependence quite clearly if I simply plot a graph of one versus the other, and in this case I need the computer to work out what the points on that graph are. I actually don’t know the answer for the cases I really am interested in, nobody does (that’s why it is research!), and so that’s what I want to find. I want lots of points to get a nice smooth graph, so the computer has to compute a lot of points, and I need to run it for a long time since I want it to compute the points very accurately. So I wrote a program (in Maple) to work on the problem, studying just one […] Click to continue reading this post