A 60 second exposure capturing a chair and its shadow in moonlight.

I've been keeping track of certain statistics in the grand tours for a while now.

I just updated the table with the 2010 results.

A few observations:

• The correlation between prologue rank and final gc rank was lower than any year I have
  calculated it for, with the exception of 1997. This might be a result of the limited time trials and/or the rather intense mountain stages.
• The percentage finishing, 87%, was the same as last year, and ties the record among the
  years I've calculated. I am a bit surprised at this, since it seemed like there was a particularly large number of crashes. Perhaps there was less illness?
• The winning margin and the 10th place final gc gap were both rather small. Does this indicate an "easy" tour, or a hotly contested tour?
• Petacchi won the green jersey, with the lowest GC ranking since at least 1994.
• Charteau's KOM win makes three years in a row with the KOM winner not winning a stage.

A pencil (HB) drawing from a LOC photograph.

Two more drawings from Drawing in Ink class.

The first, a copy of a van Gogh. The idea here is to vary line weight, detailing, and other aspects to create the impression of depth.

This one is a copy of a Ruisdael. This was my very first attempt to use wash (diluted ink applied with brushes). I had a very hard time with this, particularly since I had difficulty getting the dilutions the way I needed them.

I took some pictures of a young woman hooping at Cal Anderson park over the weekend. Here is the result of one photo.

Today was my first day of my Drawing in Ink class at Gage. I made two drawings.

The first is a copy of a drawing by Raphael of Michelangelo's David.

The second is a rubber ducky, drawn from "life".

(Click the drawings for larger versions at Flickr.)

I think I'm off to a good start.

I rode 171 km yesterday. I found a route on Bikely.com, basically this one, except that (a) the Green River trail is closed, so I rode the Interurban trail instead, and (b) I missed lots of turns, so there was quite a bit of improvisation and backtracking. This probably account for the added length; I had been shooting for 160 km.

I met a couple at a gas station/convenience store in Black Diamond. They were riding fully loaded touring bikes. They told me they'd landed at SeaTac from Norway yesterday and were headed to Boston, Massachusetts; they planned to take 35 to 45 days. I was very impressed, and failed to help them decide on a route to Cle Elum, because, really, who knows how to get to Cle Elum?

The worst thing on the ride was a big brown furry dog dead on the shoulder, with his entrails strewn across a good chunk of the road. That 'bout made me cry, 'especially as I was going the wrong way at the time, and had to back track past the poor thing. I later saw a small snake in much the same condition; as it wasn't a mammal, I wasn't quite as moved.

This ride took a little under 7 hours. I've noticed that I can feel great up to about 5 or 5.5 hours, but then start getting a little low. There were strange aches in the last hour, including something like a side stitch, under my left rib cage.

I ate quite a bit during the ride, including half of a peanut-butter-and-grape-jelly sandwich, which I think perked me up for the first half hour of my last hour on the bike. Fig bars, alternating with clif bars and the clif "mojo" bars, seems pretty awesome.

It's time now to clean the bike up. I've been neglecting this since I want to replace the chain when I clean the bike, and I didn't want to replace the chain until I got this long ride out of the way. I'm complicated that way.

Another applet at OpenProcessing.

A new applet at OpenProcessing. I used recursion for the first time in decades. I think it came out nice.

Just a short comment.

If we let f(n,k) be the sum of the divisors of n, each raised to the k power, then the highly composite numbers are those n which are record setters for k=0. For k=1, we get the highly abundant numbers, and for k=-1 we get the superabundant numbers.

A curious question to consider is the set of k values for which a given n is a record setter.

I just calculated that 672 is a record setter for 0 < k < 0.3705405845106956751517917 using Pari/GP. Note that k>0, so 672 is not highly composite, but minimally so (I haven't actually checked that, but it is certainly a record setter down to tiny positive k, yet not for k=0).

Plouffe's Inverter gives me nothing on this 0.3705.. number. It's certainly some solution of a ridiculous exponential sum equation.

Here's more (correct) digits just for fun: 0.3705405845106956751517917005244140444958735486823441966658021494
305594049833761245395005733860464257