Power laws and log-log plots II.

Back again to power laws. After some more googling, I found an even more important piece of blogging by Cosma Shalizi: Speaking Truth to Power About Weblogs, or, How Not to Draw a Straight Line. The title says it all: just don't play with power law distributions by fitting straight lines to log-log plots, because chances are that you will get a reasonably looking line and R squared will be relatively large, but that still does not mean that there is a power law distribution. Shalizi is complaining about papers in statistical physics and complexity theory that do such things -- well, he should see what is going on in sedimentary geology, where somebody invented the 'segmented power-law distributions' and now everybody who is measuring bed thicknesses is fitting not one, but two or even more straight lines to log-log plots of cumulative distributions. It's utter nonsense, even more so than with a single straight line, but it looks very sophisticated and regular, and people keep doing these plots and all kinds of fancy interpretations based on them (earthquakes, self-organizing criticality, confinement, erosion, etc.). If it plots as a straight line - fine, it's a power law, we explained everything. If it does not plot as a straight line -- well, just fit two straight lines and talk about two populations, and how the original power-law distribution has been modified by erosion, confinement, etc. - and we explained everything again. I know I am also guilty of some of this in my thesis, but at least I have never done the segmented power law plots.

Just for the records: here is a link to my paper in Sedimentology. Overall I am fairly happy with it, I haven't changed my mind about most of the things I have written about in this paper, unlike with many other subjects I have done some work on.

Power laws and log-log plots I.

Did a bit of reading today on power law distributions, just to refresh my memories from three years ago when I was writing my thesis. And found some interesting papers and notes on the web, e.g., this one. I think we are still far from being able to use bed thickness distributions in a useful, predictive way, even though this has become a popular subject among turbidite experts. One of the problems is that it is easy to play with the distributions (e.g., take an initial power-law distribution and modify it by amalgamation), but things are probably a lot more complicated and cannot be explained just with amlagamation and basin topography. The other problem is that power-law distributions and their exponents cannot be assessed by fitting a straight line to an exceedence probability plot, as it is explained here. This method is bound to give erroneous estimates when dealing with a single distribution, but it is close to meaningless when people want to break out two different populations by fitting not one, but two lines to the exceedence probability plot.

Well, I guess that is enough about power laws for today.

A nice quote from "The Scientists" about Kepler and Galileo:

He was a man of his time, poised between the mysticism of the past and the logical science of the future, but whose stature as a voice for reason stands even higher in the context of a world where princes and emperors still depended on the prognostocations of astrologers, and where his own mother was tried for witchcraft. At the same time Kepler was carrying out his great work, an even more powerful voice of scientific reason was being heard further south in Italy, where although there was as mutch superstition and religious persecution as in central Europe, at least there was some measure of stability and the persecution always came from the same Church.

A few new things I am the happy owner of: John Gribbin's "The Scientists" and a Nikon D70. The former seems to be a great reading (I only got to the first scientist, Galileo, but I hope the whole thing will be of similar quality), the latter takes amazing pictures. I was just fed up with low-resolution, blurry, color-challenged digital photos I was taking with the old Sony DSC-S85. I even had problems taking sharp photos with the self-timer (that is, when I was not holding the camera).

But I am absolutely delighted with the Nikon D70. I came back a couple of weeks ago from the Canadian Rockies, and most of the pictures I took with the Nikon are technically flawless - I mean if there is anything is wrong with them, that's obviously my fault. For the first time, I tried an online printing service - Sony's Imagestation.com -, and the prints look great, both in terms of resolution and color. Of, course, the Canadian Rockies are not bad photographic subjects, especially if the weather is as good as it was during my stay there.