Siliceous and Delicious

Managed no work at all this weekend, in spite of having a Saturday alone with Kati in DC. Not much to say about it other than that I really, really didn’t feel like working, and jumped upon every excuse not to do it—laundry, grocery shopping, newspaper reading, relaxing, and watching TV on Saturday; sleeping in, Kati time, going for a walk in the sun and the last episode of Downton Abbey on Sunday. Anything but work.

I tried not to let this cast a cloud on my Monday, however; headed out on my scheduled run and was at my desk, ready to work, at 9am. The starting of work was delayed by a little over an hour, since Andy’s intern Sarah showed up and begged for fulfillment of an earlier promise (not as empty as I had hoped, it turned out) to show her how to set up macros to set scale and insert scale bars on the photos she’s taking with the microscope camera system. It was a time sink but she was very grateful, and I felt (for a change) extremely competent. I may have failed to produce anything of academic value (so far) in the many years I’ve spent in graduate school, but I’ve certainly picked up a lot of skills and general knowledge along the way—including how to write macros for ImageJ.

In a strange way then, this was an hour well spent, since I returned to my desk feeling much more chipper and motivated than I had been earlier that morning, peeling myself from the bed and cursing the fact that it was a holiday yet I wouldn’t be able to take time off, without extreme guilt, i.e. no time off until the thesis is done. Fortunately, I’m well placed to get myself there now.

Spent a good few hours working here and there though Pierre and Nicole and Alexandre came by to visit, and took me to lunch, and in the end I figured it was no good hanging around at work since I was mostly distracted anyway, and headed back home with Kati. Back here, made some real progress on the next set of plots, showing the various measures of disparity. First, mean pairwise distance:

Then, convex hull volume (showing the effect of increasing the number of dimensions considered when calculating the volume, strictly speaking the hypervolume—in 3, 4, … up to 10 dimensions):

The results for convex hull volume are shown normalized (to the largest value in each set of calculations) since the absolute values get smaller with the addition of each dimension. This makes sense, considering the coordinates on all axes are between -1 and 1—an area of a square of side length 0.2, for example, is 0.04, a cube of the same side length is 0.008, a hypercube in 4 dimensions 0.0016, etc.

In any case, regardless of the number of PCO axes considered, the convex hull volumes tell a totally different story from the pairwise distances. Pairwise distances are pretty much indistinguishable, with the exception of the Early Cretaceous. Convex hull volume, on the other hand, shows a definite increase with time. What gives?