days of driving

i'm back from colorado. i didn't get to do nearly what i wanted while i was out west. but here's a few pictures of colorado from the drive home.

cheesy through the windshield picture. but the fog looked really cool.

headwaters of the rio grande. with aspen trees. and some fir trees.

reprise of the rio grande headwaters. this time zoomed in. rio grand pyramid is the peak in the background.

next summer. for real. 14 308 feet. 9th highest peak in the lower 48. 6th highest in colorado. highest in the san juan range. uncompahgre.

overall i have to say i am a bit disappointed with my vacation. i didn't get to go fossil hunting and i didn't get to climb any 14ers in colorado. i did get to go fishing a couple of times, and i also got to drive through some country i hadn't seen before. up through lake city and up to crested butte and then through gunnison and canon city was really beautiful. if i could find a job there i think i'd move somewhere like that. pueblo and kansas i hadn't seen before...but seeing them doesn't get to be on the list of trip highlights. talk about a lot of nothing. next big trip should be out to lake powell in november...and i'm thinking of going to see have heart's last show in boston in about a month. i could pay quinn and courtney a visit while i'm up there.

williams creek

uncle vee and i went to williams creek reservoir this evening. the fishing wasn't any good but it's still one of my favorite places. i forgot my camera though, so no pictures. it is a beautiful place...and there are some old growth ponderosa pines there...4ish feet at the base. i love trees like that. back when i lived out here i climbed one at the williams creek campground that was about 120 feet tall and 5 feet at the base. maybe the coolest tree i ever climbed. sadly i forgot my camera that day too. i left it in my car at the shop so it spent the day there instead of documenting large trees. oh well...worse things have happened.

echo canyon

did a little fishing tonight with vee...we only caught one that we kept, a little rainbow trout. we caught a bunch of little (shorter than 5 inches) largemouth bass and a couple of bluegill and pumpkin seed, but it was still fun.

this is a picture of echo canyon reservior. not very big. southern san juan mountains in the background.

oh but plans can fall through as so often they do

well...here i am stuck in salt lake. i was supposed to be off finding fossils today with my cousin, but his car broke down and he has had to rewrite a report for work. so i'm pretty bored until thursday. i'm staying at his mom's house and am trying to help her with a bunch of genealogy stuff and also trying to keep from being bored out of my mind. i did at least make it up to logan to get my bike, and i had the presence of thought to bring my bike shoes (no helmet or gloves though) so once i get some air in the tires i'll probably try to head up city creek canyon. jeff says there are some decent trails up there. if i'm honest i'm a little worried about riding up the canyon though...i haven't been biking in about 6 months. i get a pretty good workout at work...lots of lifting and carrying and dragging and pulling myself up trees...but it isn't really the sustained cardiovascular workout you get from running or riding a bike. but we'll see how it goes. plus the weather is nice and cool for the next couple of days.

the not-so-high seas

Went sailing on Saturday with Keith and a couple of other people. The winds weren't very good...we topped out at about 3 knots. But it was a beautiful afternoon and a nice sunset.

Ospreys.

Looking aft from the front of the boat.

Me with the furled jib behind me.

Sunset.

We sail from a harbor in Annapolis. Unfortunately some of the kids that came along didn't want to be out sailing too late, and since we got a late start we only made it as far as the bay bridge. We'll try again in 3 more weeks.

math is for nerds

Not that anyone is horribly interested in nerdy math stuff...but here's what a spanning tree is.

The image above is what we mathy people call a graph. It consists of a vertex set and an edge set. Vertices are points (zero-cells, if you really want) and edges are lines (one-cells). So you have a bunch of lines and a bunch of dots...and now you play connect the dots. That's a graph.

A tree (in math) is a graph with no closed loops. Here's a tree:

Note that this tree contains no closed polygons. That's what makes it a tree. Just like trees in the real world, generally.

A spanning tree is a subset of a graph. Specifically, a spanning tree contains the vertex set and enough of the edge set to keep all connected subsets of the graph connected. (Connected = you can draw it without picking up your pencil. And you're allowed to cross lines and draw back over lines you already drew.) The above tree is, in fact, a spanning tree for the graph up at the top. Here's a picture of them together.

Note that spanning trees are not unique. Here's another one for the graph at the top.

And again with the original graph superimposed:

On the second spanning tree I decided to go for the "without lifting the pencil, crossing lines, or drawing back over what you already drew" method.

Anyhow, that's what a spanning tree is. They play a significant role in Bass-Serre theory and graphs of groups. I'm not going to try to explain either. If you really want you can search for Bass-Serre theory on wikipedia. It's on there.

And I'm terribly clever for naming my blog "spanning trees" because I do tree work. Like the leafy things with bark and trunks. I'll get some pictures of that soon.

And I also promise that this blog won't be exclusively about math. Or tree work.