"There are dark shadows on the earth, but its lights are stronger in the contrast."

The above quote from the Pickwick Papers seems particularly apt given the rather dark clouds that have been coming and going all week (and that sent us to the basement Thursday with a tornado warning). I still appreciate actually having weather though :-)

Earlier this week I decided that we needed cookies. Since discovering in Budapest that I could make fine cookies without the bother of carefully measuring things out, I have almost exclusively been making "variations on approximation cookies." Now, given this style of baking I am never quite sure how long the cookies are going to take to bake and I am well aware of the fact that different ovens have different cooking times - but they usually take ~10-12 minutes. Less than 5 minutes after putting the first tray of cookies in the oven the apartment began to smell of popcorn (why the burning bottoms of cookies smells like popcorn I have yet to figure out)... They were definitely still edible, but their bottoms were rather blackened. I turned the oven down from "350" to "300" and gave it time to readjust the temperature before putting in the second tray - 12 minutes later the cookies were still slightly gooey. I took them out anyway and they /mostly/ set up nicely as they cooled and ended up being really soft. I think I need to experiment more with baking cookies longer at a lower temperature. I also need to remember to be really careful when dealing with the oven here...

Friday night a group of us from the REU walked into downtown Springfield (roughly the same distance that it is from Mudd to the Village) to find dinner. After wandering around for a while (which reminded me rather strongly of wandering up and down Raday in Budapest) we finally decided to eat at Trolleys and sat outside so that we had a view of the square. My chicken sandwich was good, though not spectacular, but it was served with sweet potato fries. I was slightly skeptical of the fries when I saw them on the menu (the time Mudd's dining hall tried to make them they seasoned them with salt and pepper, it really didn't work) but decided to try them anyway. I'm really glad I did - they were fantastic. I was through about half of them before I finally figured out that they had sprinkled them with cinnamon :-)

While we were eating dinner we discovered that there were local bands giving a free concert on the square later in the evening, so we ended up hanging out on the square in downtown Springfield listening to the music and people watching.

• an old bearded guy sitting right up by the stage who was /really/ into all of the music regardless of the style
• a group of three middle aged cowboys complete with cowboy hats and holsters with varied combinations of knives and guns
• plenty of little kids climbing on the big geometric sculpture and playing in the fountain
• a guy handing out glowsticks to any kid brave enough to go ask for one
• a group of students who didn't seem to know how to get clothes that fit and liked baseball caps with spikes
• and the list could go on and on

In short there was a rather large spectrum of people all gathered on the square.

When being less social and not doing math I have been doing a lot of reading. Having finished the Pickwick Papers (incidentally, Springfield has consecutive streets named Pickwick and Weller...), I started and have finished a collection of Dickens's Christmas writings and started Bleak House. I'm finding that I really enjoy Dickens. He manages to draw me into the story while maintaining the feeling that I am sitting with the narrator listening to him/her tell me the story. This latter impression is built by the small digressions and comments clearly directed at the reader that do not typically appear in novels. I was especially amused by Dickens's digression on idioms at the beginning of A Christmas Carol:

Old Marley was as dead as a door-nail.
Mind! I don't mean to say that I know, of my own knowledge, what there is particularly dead about a door-nail. I might have been inclined, myself, to regard a coffin-nail as the deadest piece of ironmongery in the trade. But the wisdom of our ancestors is in the simile; and my unhallowed hands shall not disturb it, or the Country's done for. You will therefore permit me to repeat, emphatically, that Marley was dead as a door-nail.

I have also been entertained by all of the allusions to various nursery rhymes in Bleak House and slightly surprised at how many of them I recognize before having them pointed out in the notes (and that I have found at least one that is not in the notes at all).

Now, it has been requested that I explain what exactly one does when doing "Math research." The simplest possible answer I can give is "math", but that is probably not a very satisfying answer. There are a few different kinds of broad things that count as math research (and this list is probably not exhaustive)

• Start with a problem that someone else has come up with but that no one knows the answer to and try to find the answer.
  
• Alternately, it is sometimes good to take a problem that we know the answer to and find a new way to get to the solution. This sort of thing is useful in mathematics since it can often give us a new way of looking at mathematical structures and lead to new insights.
  
• There are some areas of math that have been around since ancient times that are fairly well explored and understood. There are also areas of math and mathematical objects where things are named after mathematicians who are still alive today. In these areas it is quite possible to find interesting questions that no one has thought to ask and to then try to answer them.

My particular research this summer falls into some combination of the first and last of the above categories. I spent a good bit of the first week here learning about the theory of Local Rings and looking at the kinds of questions that my adviser for the summer has been interested in. From this we have come up with a vague question for me to attack - and working toward that is producing smaller more manageable problems to understand and solve. In particular, I am trying to understand the relationship between the zero divisor graph of finite local rings and the zero divisor graph of their corresponding graded ring.

I have been thinking about how to explain the general idea of what I am doing without using such technical terms, but I'm not quite there yet. I shall continue working on that :-)