In the last week and a half or so, I did not keep up with my blog because I was trying to get the most out of my time in Paris.
One Wednesday evening while I was sitting in my bed back at Cite Universitaire, I was struck by a thought. I should try to do something new and interesting every night that I am in Paris. For some reason, it had not occurred to me that I had not been taking advantage of the evenings to visit Paris. My adventurousness paid off- I had many exciting experiences during the last week and a half of my time in Paris.
My first adventure took me to the gaudy red light district of Paris. Among other things, the Montmartre district contains the iconic Moulin Rouge, more sex shops than anybody could every want, and what seemed to be strip clubs. I wondered what these clubs were and I even had some people approach me and invite me in. However, I had different aspirations. Under the title of "Offbeat Ways to See Paris," my tour guide suggested the Musee d'Eroticisme. As the name suggests, this museum is devoted to the artistic expression of sexuality. I can understand that many people may be uncomfortable with such a place, but I wanted to push my boundaries. While it was shocking at times, the museum had a lot to offer: from ancient African sculptures depicting sex to the history of prostitution in France, Musee d'Eroticisme communicated a view of sexuality, dispirate from the reserved attitudes in the United States. In many African tribes, sexuality and particularly sexual organs are an integral part of many of their traditions. For instance, the male penis is important in many rituals signifying the passage into manhood. The history of prostitution in France was even more interesting. I do not know what the laws are like now, but prostitution was a legal, thriving business in 19th century France. Opulent brothels contained beautiful, ornate sculptures beds. However, the glamor of the Parisian brothel masked a sinister system. Many of the women in these brothels started out poor. They wanted to make money to live a normal life. However, the brothels often took a large percentage of the revenue so these women would be stuck in brothels for many years. Many women became depressed. Another fascinating aspect is that a substantial number of women turned to lesibianism. Surrounded by a sexual environment, these women turned to each other for support. It is a touchy subject, but the commentary suggested that the main factor in these relationships was a mutual hatred of men that resulted from their work. While the Musee d'Eroticisme would be shocking and appalling to many Americans, I was glad that I pushed my boundaries to go to such a place and see different views of sexuality.
My next adventure brought me to the Fleche d'Or, a vibrant and popular establishment that has alternative and rock concerts nightly. While I enjoyed the music, my conversations with people there was the most rewarding part of the evening. As I have discussed earlier, I am fascinated by stepping into other subcultures - if only for an evening - and learning about these people. As far as I can see, the alternative scene tends to favor art, creativity and the humanities. One may think that in being an avid mathematician and scientist, I would have little to say to these people. I find such a view insulting.
The humanities and the sciences have much more in common than one might think. Lest I digress too much, I will briefly discuss my thoughts on the subject. First, both areas are concerned with the quality of expression. I am no expert, but in the Humanities, the method of expression is central to any piece of writing. From the language, to the structure, the writer carefully crafts their expression and meaning. In the same light, communcation is vital to the scientist as well. While one can do great work, the goal of science is to create new knowledge and share it with the world. As such, most senior scientists spend most of their time finding ways to communicate their work to others while the graduate students actually carry out the experiments. As a more mundane example, when preparing for a presentation of this summer's work, I spent many hours thinking about how to convey my work in a way that was both complete and understandable. It is a real challenge to look at a topic from someone else's perspective. Second, all important scientific work is an expression of creativity and novel thinking just as artistic masterpieces are as such due to their originality and questioning of established artistic practices. I think that part of the reason for the thought that mathematics is mechanical comes from a lack of inspired teachers. To put the typical mathematics education in context, I will give an analogy. Before you create a painting, you have to know your tools. You have a canvas, a brush, paints, and a place to mix the paints. You may have a variety of colors and brushes. After knowing your materials, you take to the canvas. There are many different strategies for putting paint on a canvas. You can use broad, wavy strokes or fine and precise ones. These technical aspects of painting to an artist are the high school mathematics coures to an engaged and lively mathematician. Such a researcher is not concerned with the routine aspects of calculus, but has a grander purpose. As the types of brush strokes to not make a masterpiece, algorithmic calculations do not make great mathematics. While the artist is trying to express emotion and capture the human condition, the mathematician aspires to grand goals. He or she seeks understanding in enigmatic problems, and eventually finds order in chaos. The people who end up pursuing theoretical math have a wildly different introduction to the subject. As a high school student, my best experiences with math involved making my own problems. While it is easy to solve problems when you are told the solution technique, it takes a much greater ability to create challenging questions. You need to not only understand the concepts, but be able to combine them in a new and interesting way. For instance, one problem that I created used a 3d visualization of a cube in order to answer the question: if three people arrive at some time between 12 and 1, and wait for 20 mins, will they see each other? Regardless, with these type of experience, it is clear that math would be appealing to me whereas the people who are only exposed to boring, mechanical math never touch the subject after their classes end.
Forgive my diversion, but I have been thinking a lot about how to communciate why I love math and science to others. Really, the long and short of it is that I talked to these people about art and what they liked about it. The first woman that I talked to was a freelance artist that had her work featured internationally. Having just finished an exhibition in Paris, she was soon to fly off to New York and then Portland to be present at two showings of her work. It was fun to hear about her art and we also discussed France-America cultural differences. Additionally, she explained to me that the impact of most art is inseparable from an understanding of the contemporary thought about art. Thus, she argued, many modern art pieces have more merit than a dilitante could observe. Did I mention that we spoke only in French! Such a conversation is why I am happy that I know French! I regret that I did not have this perspective when I was learning the language in high school. My bad attitude towards languages back then led me to not get nearly as much out of my classes as I could have. The next woman that I talked to was a student whow as a around my age. The most notable part of our conversation is that she explained that the modern art that she liked evoked a certain emotion in her. She would be impressed by the creativity and departure from reality that her favorite artists evoked. Anyways, the music was generally good. The first band was an energetic, intense rock/alternative band. The second band was somewhat boring, but I enjoyed it as a relaxing conclusion to my great night of conversations-entirely in French-with the artsy people who are a part of the rock-alt. subculture.
During my next night, I found myself biking across Paris with the most American Americans that I had seen during the trip. It seemed as if the people who embodied negative stereotypes that Europeans have of Americans. The boisterious, aggressive and culturally unaware lot of us visited "touristy" Paris with the FatTire Bike Tours. Right off the bat, our negative tendancies were encouraged by the guides. "Domination" shouted the guide. "We must dominate the road when we bike." A couple from New York, a group of 10 students who came to Paris to drink and party, and another family took to this midset right away. As we left, excited exclimations of the word "Domination" echoed through the Parisian streets. The most extreme example of the our outrageous attitudes was that on the streets, we were near a taxi. Since he wanted to get through us, he revved his engine and produced black smoke. He was immediately met with jeers from our group and one guy went so far as to stick his head into the taxi and swear the guy out. "What the hell is your f-ing problem?"
I should say that I am being a tad bit melodramatic. While the Americans annoyed me a bit, I still had a good time on the trip. I enjoyed tasty, yet over-priced ice cream. I got to bike through Paris and I saw many of the large attractions. We ended the trip with a beautiful boat ride down the Seine, while indulging in some nice French wine. I could write a few more paragraphs about why I didn't like these people and why I distanced myself from them on the tour, but suffice it to say our conversations were characterized by a stark lack of things in common and superficial discussions about the places that we are from and that we knew people shared the same hometowns.
Over the weekend, I visited my uncle Harold, aunt Meg, and younger cousin Hannah in Grenoble. My uncle is a Physics professor at Duke University but he spends a few months in Paris collaborating with French collegues. It is unfortunate that I have not gotten to see my cousins much, but, by the end of the summer, I will have seen then three times. After getting picked up at the train station, we had a delicious 'french' lunch. We had a large collection of french cheeses, two types of pate and some fruit. Next, we explored Grenoble. I enjoyed taking in the atmosphere of another French town. As Grenoble is in a valley, there are beautiful, awe-inspiring mountains in all directions. Later in the day, we took the gondola to the top of one of the mountains. I enjoyed looking over the city and seeing all the other mountains that surrounded the valley. In general, I loved the company of my cousins and they are welcoming, accomodating and thoughtful people. One amusing nugget of information is that the defensive structures that we explored atop the mountains, while they were well preserved, the reason for that was because they never saw any fighting. Thus while it was great to see these old fortifications, the only reason that they were so well-perserved was that the tumultuous French history had not touched this area. Later in the evening, we had a nice dinner at a lebanese restaurant. While it seemed that we did not get good service due to being American, the food was delicious and filling.
The next day, my uncle had to had to leave early to go to a conference so I spent the day with the gals. We decided to go a French revolution museum in a nearby town. Despite a car ride that seemed very stressful for the two of them, we eventually got to a small town that had been taken over by a French Revolution weekend. Many of the locals dressed in historical clothing while others enacted historical scenes. We briefly walked through a carnival-like area where you could take a picture of yourself with your head in a guillotine and throw balls at the nasty and oppressive French kings. I remaked to myself that while it seemd that many French people were proud of the historical overthrow of the monarchy, the French revolution was nasty, violent and epitomized the horrors that people can commit. For instance, there was a murder where somebody had their skin lascerated, lead and acid were poured into the crevices, and four ropes tied to each of his limbs were tugged by horses until he was split into four pieces. I don't know what to say about that to express how crazy it was to hear about such practices. Anyways the museum was fun and we got to learn a fair amount of history. Overall, I had a lot of fun on my trip with my cousins and I will be glad to see them again in a few weeks at a family reunion!
After I came back to Paris, I was tired and took a night off from doing cool things. However, I soon returned to experience the excited of the Parisian evenings. I went to an immaculate performance of Vivaldi's Four Seasons at La Sainte Chapelle. The church was unbelievible. Stained glass windows adorned for one's entire field of vision and everything else was golden and ornate. I was exteremely impressed by the precision and skill of the violinists. I felt strong emotions when hearing the sounds of the harmonious and energetic violinists reverberate around me. I have so much more respect for these artists than the popular musicians of today. In total, I felt like I was able to appreciate a performance of classical music and I hope that I will find time to attend more masterful performances.
The next evening, I decided to do some exploring. I started by walking next to the Seine. For a month during the summer, they bring in sand so there is a sort of beach on the side of the water. Spanned by beautiful bridges and surrounded by monumental buildings, the Seine passes through the heart of Paris. From the grotesque faces adorning Pont Neuf to the small plaque marking the execution of the last of the knights templar, the area was a treasure trove of French history. After wandering around a while, the sun set and I stumbled upon a fantastic street performance in front of Notre Dame. To begin, a man with a torch came and put some liquid in his mouth. Then after a few moments of waiting for dramatic effect, he blew a fantastic fire from his mouth! After a few smaller acts, a man came out with balls that were in fire and he held them by strings. He twirled the balls of fire with finesse. (See here: http://www.youtube.com/watch?v=Av8g8NNkKbk ). In the finale, he took firecrackers attached to strings and twirled them around. While similar, there was an incredible effect where he was surrounded by sparks. I enjoyed this night a lot because I just explored and I stumbled upon something fantastic! In the subsequent evenings, I did not do a whole lot more than explore and take it easy. I was preparing my final presentation. However, the last day, I had a moving experience at a number of French Museums.
Per the suggestion of my father, I went to Musee d'Orsay to see the impressionism paintings. More than any of my other museum experience, I felt emotions when I saw the paintings. As somewhat of a surprise, my favorite paintings were the realist and naturalist paintings. In particular, I found the following painting of Jesus at the cross moving (see http://iconsandimagery.blogspot.com/2011/03/calvary.html). As described by the audio tour that I used throughout my visit, the jesus was depicted more like a human that was feeling intense pain. From his facial expression, his body dangling from his arms and his gaunt legs, everything about the painting is screaming out pain and anguish. Apparently this depiction of christ was so controversial that it was removed from the exhibition that had originally commissioned the work. I also enjoyed the impressionist paintings. The most enjoyable part for me is that I recognized most of the impressionist artists and their styles. As always, I liked the Van Gogh paintings and in particular, I find his self-portrait to be fantastic! I could spend a long time examining his facial expression. One other point was that I decided to pay for an audio tour and that certainly made the experience better for me. It was a lot of fun to hear the descriptions of the paintings. Most of them were reasonable in pointing out the main features of the art without going too over the top with flowery descriptions. Afterwards, I headed to the Musee de l'Orangerie to see the Monet waterlilies. At this point, I was pretty tired from having walked around Musee d'Orsay for about two hours so I was glad to be able to sit. Specially designed for the waterlilies, two oval rooms light by soft rays from the sun were specialy designed to display the Monet paintings. It was enjoyable to sit and just appreciate the paintings. For me, I felt like the colors were pleasing for some of the paintings but not others. Somewhat surprisingly, the museum had a great collection of art in addition to the Monet paintings. One of my favorite paintings was a Renoir painting of a girl learning how to play piano. I liked the soft curves of their faces and their gentle expressions that I bought a copy of this painting for my dorm room. There was also a surprisingly large collection of Picasso paintings. While he painted many nudes, a type of art that would seem to be intimate, the expressions of the women were very distant. I spent a long time deciding which poster I wanted to buy. They did not have the specific waterlilies that I liked the most and the colors seemed off in the prints that they had. So I finally decided on the Renior painting that I described earlier. In total, I enjoyed my trip a lot. In addition to liking the audio guide, I experienced more emotion that these museums that I have at any other art exhibit.
This post is already ridiculously long. So I am going to write later about some more general conclusions about my trip. Suffice it to say, I had a great time in Paris, so much so, that I did not feel the need to do anything crazy or special the last night that I was there. I had a relaxed evening where I packed and watched some youtube videos.
Saturday, July 30, 2011
Tuesday, July 19, 2011
Crazy Awesome Weekend!
I feel bad that I have been getting behind on the blog, but I have been very busy.
To put it succinctly, the reason that I enjoyed this weekend so much was that I got to meet a lot of new people. I had positive interactions with these people and my effort to make eye contact with people when I talk to them is seeming to increase the quality of my interactions with people.
Last Wednesday, I took the GRE. I did well enough so that the general GRE will not hurt my applications to any physics program. I am pleased to have that done with. After the test was over, I went to the Gardens near the Louvre and explored a bit.
That evening, one of my friends, Steven, invited me to come hang out. It was very spontaneous and I enjoyed it a lot. I met his sister, and a girl named Ippa, an awesome person from Finland. We went by the Eiffel tower at night and took touristy pictures. They were generally a lot of fun to hang out with.
The next day was Bastille day. I went with the same group as the previous night and my roommate, Bakari, to the Eiffel tower. There were a crazy amount of people there! It was so busy that there were some people who staked out a seat in the bushes. We had a picnic with cheese, tomatoes, olives, and bread. Afterwards, Steven and I played some frisbee. It was dangerous because there were so many people. A random girl, who I later got to talk to more, joined our game. Victoria is a student from Texas who goes to Yale and she plays frisbee. Later on that afternoon, we were playing ninja, and a group of American high school students joined in. So for the rest of the afternoon, in addition to our group of 5 people, we had another 8 or so new people that we just met. We did a lot of fun things including following people in a line. We also played the crowd-surfing game: we sit in a line, and then somebody jumps on the line and we use our hands to carry them to the end of the line. When we did this, a lot of people were looking at us. Under the supervision of their parents, some little kids decided to go down our crowd-surfing line. I had to leave early so I did not see the fireworks, but regardless it was quite an awesome day.
The next day, my friend Mike came to visit. He got here early and we had a very long day of fun touristy stuff. Throughout the days, I had a lot of fun hanging out with Mike. He came to Paris with about 10 other people from his program. I had a lot of fun meeting all of them. We started with a 3 hour walking tour of Paris. It was free, but we had to pay a tip at the end. The guide was very quirky and funny. She made a lot of pop-culture references and cheesy jokes, which I enjoyed. She had a lot of cool stories to tell about the landmarks that we saw. One particular one is that there is a bridge that has the faces of drunk noblemen that amused King Henry the 4th.
Afterwards, she brought us to a place to eat. I got to talk to one of Mike's friends here for a while so that was pretty fun for me as I got a chance to practice my eye contact and conversation skills. In the evening, we went to the Louvre. I got to see more new things and some old things. Even later that day, we decided to go to the Eiffel tower and climb up it.
It is a bit of a long story, but some of Mike's friends were 'couch-surfing'. This is where you sleep in the house of some person that you do not know that volunteers their home. It is free but obviously there is some risk involved. Anyways, so since we were also with part of Mike's group, they were trying to find their host. So it turned out that their host also happened to be going up the Eiffel tower that night. Johann was a very cool guy. At first, I was unsure why somebody would have random people come to his house, but he said that he got to practice his English and Spanish and he got to meet a lot of cool people. There were also three girls from the Czech Republic that just graduated from high school and one of Johann's friends from France came along.
Again, I had a lot of fun meeting these people. At first it was a bit awkward because I seemed like an idiot since I did not know where the Czech Republic was and I also got that country confused with Czechoslovakia. But after those initial bumps, I was able to start up conversation with them. It is really a ton of fun to talk to foreigners because you can talk about cultural differences forever. They were very cool to hang out with.
It was fun to climb up the eiffel tower. You can take the stairs 2/3 of the way and then you have to pay more to take a lift to the top. We got a really beautiful view of the city from up there! I did not have my camera, but some other people took a bunch of pictures. I am considering going up again. After a long and awesome day, Mike and I went back to sleep.
We slept in, but then we resumed an exciting day of touristy stuff. We saw the Arc de Triomphe. Then Mike and I decided to go to the Montmartre area. The basilique du sacre coeur stands atop the highest place in Paris. There is an unbelievably beautiful view of the city from up there. It was cool to see the city in the day time and to contrast that with the night time view that we had seen the previous evening from the top of the Eiffel tower.
The area is famed for having many of the great French artists and thinkers. Although the area has become somewhat overrun with tourism, there is still a nice, old feeling to the area. It is a fun area because there are a lot of artists (who are now pandering to tourists) and a lot of people who will make caricatures of you. We walked down to the more gaudy part of Montmartre. Next to the Moulin Rouge, there are a lot of sex shops and strip clubs. I did not get to explore this area, but randomly, we ran into some of Mike's friends. It was a really strange coincidence.
After this, Mike and I headed back to make some pasta. Again, it was cool to hang out with Mike and do all of these touristy things. The host of the couch-surfers was hosting a party so we planned to go. It ended up being pretty hard to get to because we had to take a train and then a bus to get there. The party was pretty cool. There were a number of other people to meet including another two people from Poland. They were doing some drinking games that were okay but I really didn't drink much. But I have gotten to the point where I will have a little bit just since that is what is polite in the situation. It was a lot of fun to talk to these people. One particularly good conversation was with the Czech girls where we talked about the holidays in our countries. One oddity was that these girls had taken an American culture class so they knew the stories behind Thanksgiving and Martin Luther King day better than I do! Mike and I stayed out pretty late and so the bus had stopped. We took a taxi back which ended up costing us 25 euros each. It was pretty expensive, but it was late and I just wanted to get back. It was worth it because it was really fun to hang out with these people.
Mike headed out on Sunday, and I just took it easy. It was such a fun weekend for me! The main thing that I saw is that I really enjoyed meeting new people. It felt good that people were responsive and it seemed that they were interested in talking to me. Also there is just something about making eye contact with people that makes the conversations more enjoyable - somehow I feel more of a connection when I do that. I liked how spontaneous the weekend was and a lot of the most fun aspects of the trip were not really planned way in advance. Also I was glad that I went out on a limb and spent two hours somewhat late at night in order to go to a party where I didn't really know the host.
Another aspect is that I felt like I got to meet a different sort of subculture - that is to say the people who couch surf. It seems that you have to be trusting of others and generally laid-back and able to handle a lot of bumps along the way. The polish girls were saying that they had done a lot of couch surfing where most of their experiences were good but one was really, really bad. Their host played music late in the night and even watched porn while they were around. I feel like I have meet other people who seem like they belong to this subculture- some college students from the AMSP camp come to mind. I wonder if I will be able to connect with people like this when I get back to college. I feel like most of use at WashU are very locked into our friend group and that most people do not do things along these lines... There is something about these people who go around on very little money, touring and meeting lots of new people that is attractive to me. However, I doubt that I will find myself in that type of situation in the future where I can be such a person.
Anyways, I took it easy for the next few days and dealt with some issues. It just occurred to me that I do not have that many more nights left so I really need to take advantage of my evenings. However that is for another post...
To put it succinctly, the reason that I enjoyed this weekend so much was that I got to meet a lot of new people. I had positive interactions with these people and my effort to make eye contact with people when I talk to them is seeming to increase the quality of my interactions with people.
Last Wednesday, I took the GRE. I did well enough so that the general GRE will not hurt my applications to any physics program. I am pleased to have that done with. After the test was over, I went to the Gardens near the Louvre and explored a bit.
That evening, one of my friends, Steven, invited me to come hang out. It was very spontaneous and I enjoyed it a lot. I met his sister, and a girl named Ippa, an awesome person from Finland. We went by the Eiffel tower at night and took touristy pictures. They were generally a lot of fun to hang out with.
The next day was Bastille day. I went with the same group as the previous night and my roommate, Bakari, to the Eiffel tower. There were a crazy amount of people there! It was so busy that there were some people who staked out a seat in the bushes. We had a picnic with cheese, tomatoes, olives, and bread. Afterwards, Steven and I played some frisbee. It was dangerous because there were so many people. A random girl, who I later got to talk to more, joined our game. Victoria is a student from Texas who goes to Yale and she plays frisbee. Later on that afternoon, we were playing ninja, and a group of American high school students joined in. So for the rest of the afternoon, in addition to our group of 5 people, we had another 8 or so new people that we just met. We did a lot of fun things including following people in a line. We also played the crowd-surfing game: we sit in a line, and then somebody jumps on the line and we use our hands to carry them to the end of the line. When we did this, a lot of people were looking at us. Under the supervision of their parents, some little kids decided to go down our crowd-surfing line. I had to leave early so I did not see the fireworks, but regardless it was quite an awesome day.
The next day, my friend Mike came to visit. He got here early and we had a very long day of fun touristy stuff. Throughout the days, I had a lot of fun hanging out with Mike. He came to Paris with about 10 other people from his program. I had a lot of fun meeting all of them. We started with a 3 hour walking tour of Paris. It was free, but we had to pay a tip at the end. The guide was very quirky and funny. She made a lot of pop-culture references and cheesy jokes, which I enjoyed. She had a lot of cool stories to tell about the landmarks that we saw. One particular one is that there is a bridge that has the faces of drunk noblemen that amused King Henry the 4th.
Afterwards, she brought us to a place to eat. I got to talk to one of Mike's friends here for a while so that was pretty fun for me as I got a chance to practice my eye contact and conversation skills. In the evening, we went to the Louvre. I got to see more new things and some old things. Even later that day, we decided to go to the Eiffel tower and climb up it.
It is a bit of a long story, but some of Mike's friends were 'couch-surfing'. This is where you sleep in the house of some person that you do not know that volunteers their home. It is free but obviously there is some risk involved. Anyways, so since we were also with part of Mike's group, they were trying to find their host. So it turned out that their host also happened to be going up the Eiffel tower that night. Johann was a very cool guy. At first, I was unsure why somebody would have random people come to his house, but he said that he got to practice his English and Spanish and he got to meet a lot of cool people. There were also three girls from the Czech Republic that just graduated from high school and one of Johann's friends from France came along.
Again, I had a lot of fun meeting these people. At first it was a bit awkward because I seemed like an idiot since I did not know where the Czech Republic was and I also got that country confused with Czechoslovakia. But after those initial bumps, I was able to start up conversation with them. It is really a ton of fun to talk to foreigners because you can talk about cultural differences forever. They were very cool to hang out with.
It was fun to climb up the eiffel tower. You can take the stairs 2/3 of the way and then you have to pay more to take a lift to the top. We got a really beautiful view of the city from up there! I did not have my camera, but some other people took a bunch of pictures. I am considering going up again. After a long and awesome day, Mike and I went back to sleep.
We slept in, but then we resumed an exciting day of touristy stuff. We saw the Arc de Triomphe. Then Mike and I decided to go to the Montmartre area. The basilique du sacre coeur stands atop the highest place in Paris. There is an unbelievably beautiful view of the city from up there. It was cool to see the city in the day time and to contrast that with the night time view that we had seen the previous evening from the top of the Eiffel tower.
The area is famed for having many of the great French artists and thinkers. Although the area has become somewhat overrun with tourism, there is still a nice, old feeling to the area. It is a fun area because there are a lot of artists (who are now pandering to tourists) and a lot of people who will make caricatures of you. We walked down to the more gaudy part of Montmartre. Next to the Moulin Rouge, there are a lot of sex shops and strip clubs. I did not get to explore this area, but randomly, we ran into some of Mike's friends. It was a really strange coincidence.
After this, Mike and I headed back to make some pasta. Again, it was cool to hang out with Mike and do all of these touristy things. The host of the couch-surfers was hosting a party so we planned to go. It ended up being pretty hard to get to because we had to take a train and then a bus to get there. The party was pretty cool. There were a number of other people to meet including another two people from Poland. They were doing some drinking games that were okay but I really didn't drink much. But I have gotten to the point where I will have a little bit just since that is what is polite in the situation. It was a lot of fun to talk to these people. One particularly good conversation was with the Czech girls where we talked about the holidays in our countries. One oddity was that these girls had taken an American culture class so they knew the stories behind Thanksgiving and Martin Luther King day better than I do! Mike and I stayed out pretty late and so the bus had stopped. We took a taxi back which ended up costing us 25 euros each. It was pretty expensive, but it was late and I just wanted to get back. It was worth it because it was really fun to hang out with these people.
Mike headed out on Sunday, and I just took it easy. It was such a fun weekend for me! The main thing that I saw is that I really enjoyed meeting new people. It felt good that people were responsive and it seemed that they were interested in talking to me. Also there is just something about making eye contact with people that makes the conversations more enjoyable - somehow I feel more of a connection when I do that. I liked how spontaneous the weekend was and a lot of the most fun aspects of the trip were not really planned way in advance. Also I was glad that I went out on a limb and spent two hours somewhat late at night in order to go to a party where I didn't really know the host.
Another aspect is that I felt like I got to meet a different sort of subculture - that is to say the people who couch surf. It seems that you have to be trusting of others and generally laid-back and able to handle a lot of bumps along the way. The polish girls were saying that they had done a lot of couch surfing where most of their experiences were good but one was really, really bad. Their host played music late in the night and even watched porn while they were around. I feel like I have meet other people who seem like they belong to this subculture- some college students from the AMSP camp come to mind. I wonder if I will be able to connect with people like this when I get back to college. I feel like most of use at WashU are very locked into our friend group and that most people do not do things along these lines... There is something about these people who go around on very little money, touring and meeting lots of new people that is attractive to me. However, I doubt that I will find myself in that type of situation in the future where I can be such a person.
Anyways, I took it easy for the next few days and dealt with some issues. It just occurred to me that I do not have that many more nights left so I really need to take advantage of my evenings. However that is for another post...
Monday, July 11, 2011
Weekend in the Loire Valley and Upcoming GRE
Puffy white clouds with a light grey lining and the beautiful sky blue accumulated near the horizon from above while the vibrant trees, gushing river approached the horizon from below. The view from atop the Chinon castle in the Loire valley was fantastic. The spirits of the former Kings of the castle and the simple watchmen are alive and well in my imagination as I imagine them standing beside me on the top of the tallest tower of the chateau.
If I had known what was about to come, I would not have been so grumpy the morning of the departure. Waking up at 5:45 is not my favorite thing to do! This past Saturday, a couple of friends and I decided to go on an adventure to see the redoubtable chateaus of the infamous French kings. Our train ride to Onzain, a small town in the Loire valley was uneventful.
Despite a bit of trouble deciding which direction was north, we soon found our way to an International garden festival. It was typical of many art exhibits - the artists displayed a multitude of creative ideas while still spoon-feeding the novice art critic unnecessarily florid language and amusingly broad claims about the consequences of their work. For instance, a collection of plants in oil barrels was claimed to evoke a sense of awareness of the imminent shortage of oil. Regardless, I was pleased with by the creative idea of having trees connected to life support, yet I smirked when I read that such an expression was redolent of the fragility of our biosphere. However the beauty of the flowers was untainted by the trite descriptions that tarnished the rest of the garden. I enjoyed taking many pictures of the varied flowers.
Home to a forceful castle that has suffered the damages of time, the small town of Chinon was our next stop on our weekend tour of the Loire Valley. In addition to the awe-inspiring beauty of the valley, the dilapidated castle gave me an intense feeling of being in a place with a rich history. We proceeded to check into the Hotel named after Agnes Sorel. A mistress of one of the owner's of the chateau, she had the distinct honor of being just a secret passage away from the king. With an appetite for history already wet by this morsel of French history, I was excited to elevate myself to the height of the castle that overlooked the city. Joan of Arc's visit to the castle in 1429 where she gained the respect of the current Dauphin of France, Henry VII, was one of the most enjoyable pieces of history. By recognizing the disguised Dauphin among a group of his courtiers, she gained his trust, which eventually led him to accede to her wish of him declaring himself king. As I mentioned earlier, the view from atop the castle was marvelous.
After a rejuvenating night of at the hotel, we set out to visit another chateau. While this castle had pristine gardens and most of the extravagant decorations intact, the hordes of tourists at Chenonceau swarming like ants over a tasty morsel of bread inhibited my ability to imagine myself in the midst of the historical figures that once lived at Chenonceau. The castle had a rich history dominated by greedy kings and seductive women. Kings constantly repossessed the beautiful chateau, Diane de Poitiers exercised power using her womanly ways on King Henry II, and Catherine de Medici who eventually overcame Diane's siren-like influence over the King.
After a nice trip back, I have resigned myself to more GRE studying. I am pleased about my improvement on the verbal section but more importantly, I feel like my writing has improved significantly in the course of practicing for the GRE essay sections. While not vital, varied sentences, sophisticated language and clear structure can allow one to achieve higher scores on the analytical writing sections. I take the test Wednesday. I expect to achieve a score that will not hurt my physics graduate school applications. I wonder if I will continue to write in this fashion after the test has passed. Hopefully the enjoyment of writing in a florid manner will help me continue to write well.
If I had known what was about to come, I would not have been so grumpy the morning of the departure. Waking up at 5:45 is not my favorite thing to do! This past Saturday, a couple of friends and I decided to go on an adventure to see the redoubtable chateaus of the infamous French kings. Our train ride to Onzain, a small town in the Loire valley was uneventful.
Despite a bit of trouble deciding which direction was north, we soon found our way to an International garden festival. It was typical of many art exhibits - the artists displayed a multitude of creative ideas while still spoon-feeding the novice art critic unnecessarily florid language and amusingly broad claims about the consequences of their work. For instance, a collection of plants in oil barrels was claimed to evoke a sense of awareness of the imminent shortage of oil. Regardless, I was pleased with by the creative idea of having trees connected to life support, yet I smirked when I read that such an expression was redolent of the fragility of our biosphere. However the beauty of the flowers was untainted by the trite descriptions that tarnished the rest of the garden. I enjoyed taking many pictures of the varied flowers.
Home to a forceful castle that has suffered the damages of time, the small town of Chinon was our next stop on our weekend tour of the Loire Valley. In addition to the awe-inspiring beauty of the valley, the dilapidated castle gave me an intense feeling of being in a place with a rich history. We proceeded to check into the Hotel named after Agnes Sorel. A mistress of one of the owner's of the chateau, she had the distinct honor of being just a secret passage away from the king. With an appetite for history already wet by this morsel of French history, I was excited to elevate myself to the height of the castle that overlooked the city. Joan of Arc's visit to the castle in 1429 where she gained the respect of the current Dauphin of France, Henry VII, was one of the most enjoyable pieces of history. By recognizing the disguised Dauphin among a group of his courtiers, she gained his trust, which eventually led him to accede to her wish of him declaring himself king. As I mentioned earlier, the view from atop the castle was marvelous.
After a rejuvenating night of at the hotel, we set out to visit another chateau. While this castle had pristine gardens and most of the extravagant decorations intact, the hordes of tourists at Chenonceau swarming like ants over a tasty morsel of bread inhibited my ability to imagine myself in the midst of the historical figures that once lived at Chenonceau. The castle had a rich history dominated by greedy kings and seductive women. Kings constantly repossessed the beautiful chateau, Diane de Poitiers exercised power using her womanly ways on King Henry II, and Catherine de Medici who eventually overcame Diane's siren-like influence over the King.
After a nice trip back, I have resigned myself to more GRE studying. I am pleased about my improvement on the verbal section but more importantly, I feel like my writing has improved significantly in the course of practicing for the GRE essay sections. While not vital, varied sentences, sophisticated language and clear structure can allow one to achieve higher scores on the analytical writing sections. I take the test Wednesday. I expect to achieve a score that will not hurt my physics graduate school applications. I wonder if I will continue to write in this fashion after the test has passed. Hopefully the enjoyment of writing in a florid manner will help me continue to write well.
Monday, July 4, 2011
Visit to Geneva
Despite a rocky start, I had a great time visiting Switzerland this weekend. I had trouble getting money and the other people on the trip didn't want to lend me any. But after using euros to get swiss francs, I had a great time looking at the waterfront in Geneva and exploring the old quarter. The next day, I did more of the same: I went on a cruise, had a drink by the water, and had fondue in the old quarter.
My trip started early (for me)! Our TGV train left at around 8 am, so we needed to wake up before 7 am to take the RER to the TGV station. The Gare de Lyon station was very impressive. I wish that I had taken some more time to marvel at the high ceiling but we were in a rush to get on the train. Also since this was a new way of traveling, I didn't feel as comfortable taking time to look around: I wanted to get into my seat as quickly as possible.
I enjoyed riding the train as something different. The train was about 15 cars long and there was a little bar in the middle. I didn't go walking around but it was cool to see a nice train. The ride was very smooth and it was nice to not have to worry about having to prepare for landing. I didn't realize that the train stopped multiple times before going to Geneva so I almost got off at an incorrect stop but luckily I realized just as I stepped off the train that I was not, in fact, in Geneva yet.
Arriving at Geneva was a bit tense for me as I didn't have money and the other students weren't helpful. So we got there and my debit card did not work at the machines because my pin number was too long. I also have a credit card but that is not too useful because it does not have a pin number at all and I don't know if I informed that bank that I would be in Geneva. Regardless, I didn't have any money but the other people didn't want to withdraw extra money and have me pay them back. I could have been more forceful but I asked a couple people directly and they shrugged off my request. One thing that complicated matters was that the rest of the group was planning to go to CERN and I was not interested in that so I was planning to do my own thing in Switzerland.
Regardless, they more or less left on their trip. I was pretty annoyed. I walked to the hotel to try to get my room but it was not clean yet so I went around and looked for ATMs. Eventually, it occured to me that I had 60 euros so I could exchange those for swiss francs. So once I did that, I felt a lot better but I was still in a rancorous mood. Meanwhile, one other student in our group, Steven, had arrived earlier and he was supposed to meet me at the hotel. There were some communication problems with him and the rest of the group, but suffice it to say that we met up and there were not too many problems. The hotel gave me my room without too much trouble.
As I said, this was a rocky start, but after getting settled and getting some money, the trip became much better for me. Steven and I walked around and explored. We walked around the edge of the lake and had a good time seeing the water, the boats, and the nice parks in the area. Among other things, we got to see a number of sculptures, fountains and the famed garden clock.
The old neighborhood, with cobblestone walkways and ivy growing on the old looking walls, had an enjoyable atmosphere. There was an old church that was playing music using the bell tower. We explored a lot of cool shops. In addition to an extravagant chocolate store and a neat modern art store, we saw a scientific antique store. It was closed but in the window I saw a set of teeth that used to be used to teach dentists and a collection of microscopes. The rest of the day was pretty uneventful.
The next day, I wandered around on my own and had a great, relaxing day. First, I went to wander around the park. I ended up finding a cruise that went around lake Geneva. In addition to getting a great view of the 140 m high water jet, the cruise gave me a beautiful view of the water and the ice-capped mountains. While I was sitting down on the top deck of the boat, I had a conversation with a family from Nigeria. They had recently moved from Nigeria to live in Geneva. Their daughter was very cute when she was excited about seeing Mont Blanc.
Afterwards, I wanted to relax a bit so I went to a place where I could look at the water and I got a glass of red wine. I sat around, did some GRE vocab and just looked at the water. I think that I have taken a liking to the European idea of sitting and just relaxing. I feel that our trips are always so rushed and I like to just sit around and relax.
Then I returned to the old quarter and walked around a bit. I wanted to get some type of Swiss meal. In my travels, I stumbled upon the Geneva Art and History museum. It was a free day since it was the first of the month - what luck! There were surprisingly few people there but I had a good time looking around in a quiet atmosphere. For some reason, they did not want me to talk pictures, even if I did not use flash. Another oddity was that of the 20 or so people that I saw there, there were no other men. I wonder if this means anything about women taking more time to appreciate art.
After that, I had fondue at a place that I scoped out earlier. It was a very relaxing meal and I enjoyed the Gruyere cheese. There were little birds fluttering about, hopping from table to table. I suspected that they were looking for a tasty piece of bread! The waitress took away the last bit of my bread before I could offer it to the birds.
I went to the train station and sat around for a while since I was early. The train ride was quite nice because I ended up in first class seating. They served us a nice meal. One strange aspect of the trip was that the train was, in my opinion, eerily quiet. Desiring to practice my French, I decided that I wanted to speak with the person across the row from me. I felt weird but I kept vacillating. I kept thinking over and over how I would initiate the conversation: "Bonjour" no "Bonsoir" "Mademoiselle" .. "Parlez-vous Francais?" ... Should I use "tu?" "Parles-tu Francais?" She has an iPod on, will she hear me? Is she sleeping? What if she doesn't speak French? Could I practice my french with you? "Est-ce que je pourrais practiquer mon francais avec vous (tu?)?" Is it too weird to start a conversation like that?... This went on for a while so I spoke to Kevin, one of the kids in my program for a while since that felt safer to me. Fortunately, I did get up the courage to start up a conversation.
I ended up talking (mostly) in French for about an hour with this Russian woman, until the train arrived. In high school, I didn't really see the reason for learning French. However, I can now see the reason. It is very fun to be able to talk to people in French and to hear their opinions on things. This woman was from Russia, was studing business in France and was planning to go to Geneva after she receives her degree. It is cool to meet these people who are so comfortable living internationally! I asked her about how she perceived the US and what stereotypes she had heard - this is a question that I commonly ask. One thing she mentioned is that she felt like Americans had a narrow view of Russians - people from Russians are drunk all the time, poor from communism, wearing the Russian Ushanka hats, etc. This was interesting to me because I do not know anything about contemporary Russia. She also said that she thought that going to Russia would be a much larger culture shock for me than me visiting Europe. I tried to ask her what she meant but she just said that I had to see what it is like for myself. All in all, I had a fun trip. I certainly see the benefits of striking up conversation with others but it is hard to find people who are willing to talk.
My trip started early (for me)! Our TGV train left at around 8 am, so we needed to wake up before 7 am to take the RER to the TGV station. The Gare de Lyon station was very impressive. I wish that I had taken some more time to marvel at the high ceiling but we were in a rush to get on the train. Also since this was a new way of traveling, I didn't feel as comfortable taking time to look around: I wanted to get into my seat as quickly as possible.
I enjoyed riding the train as something different. The train was about 15 cars long and there was a little bar in the middle. I didn't go walking around but it was cool to see a nice train. The ride was very smooth and it was nice to not have to worry about having to prepare for landing. I didn't realize that the train stopped multiple times before going to Geneva so I almost got off at an incorrect stop but luckily I realized just as I stepped off the train that I was not, in fact, in Geneva yet.
Arriving at Geneva was a bit tense for me as I didn't have money and the other students weren't helpful. So we got there and my debit card did not work at the machines because my pin number was too long. I also have a credit card but that is not too useful because it does not have a pin number at all and I don't know if I informed that bank that I would be in Geneva. Regardless, I didn't have any money but the other people didn't want to withdraw extra money and have me pay them back. I could have been more forceful but I asked a couple people directly and they shrugged off my request. One thing that complicated matters was that the rest of the group was planning to go to CERN and I was not interested in that so I was planning to do my own thing in Switzerland.
Regardless, they more or less left on their trip. I was pretty annoyed. I walked to the hotel to try to get my room but it was not clean yet so I went around and looked for ATMs. Eventually, it occured to me that I had 60 euros so I could exchange those for swiss francs. So once I did that, I felt a lot better but I was still in a rancorous mood. Meanwhile, one other student in our group, Steven, had arrived earlier and he was supposed to meet me at the hotel. There were some communication problems with him and the rest of the group, but suffice it to say that we met up and there were not too many problems. The hotel gave me my room without too much trouble.
As I said, this was a rocky start, but after getting settled and getting some money, the trip became much better for me. Steven and I walked around and explored. We walked around the edge of the lake and had a good time seeing the water, the boats, and the nice parks in the area. Among other things, we got to see a number of sculptures, fountains and the famed garden clock.
The old neighborhood, with cobblestone walkways and ivy growing on the old looking walls, had an enjoyable atmosphere. There was an old church that was playing music using the bell tower. We explored a lot of cool shops. In addition to an extravagant chocolate store and a neat modern art store, we saw a scientific antique store. It was closed but in the window I saw a set of teeth that used to be used to teach dentists and a collection of microscopes. The rest of the day was pretty uneventful.
The next day, I wandered around on my own and had a great, relaxing day. First, I went to wander around the park. I ended up finding a cruise that went around lake Geneva. In addition to getting a great view of the 140 m high water jet, the cruise gave me a beautiful view of the water and the ice-capped mountains. While I was sitting down on the top deck of the boat, I had a conversation with a family from Nigeria. They had recently moved from Nigeria to live in Geneva. Their daughter was very cute when she was excited about seeing Mont Blanc.
Afterwards, I wanted to relax a bit so I went to a place where I could look at the water and I got a glass of red wine. I sat around, did some GRE vocab and just looked at the water. I think that I have taken a liking to the European idea of sitting and just relaxing. I feel that our trips are always so rushed and I like to just sit around and relax.
Then I returned to the old quarter and walked around a bit. I wanted to get some type of Swiss meal. In my travels, I stumbled upon the Geneva Art and History museum. It was a free day since it was the first of the month - what luck! There were surprisingly few people there but I had a good time looking around in a quiet atmosphere. For some reason, they did not want me to talk pictures, even if I did not use flash. Another oddity was that of the 20 or so people that I saw there, there were no other men. I wonder if this means anything about women taking more time to appreciate art.
After that, I had fondue at a place that I scoped out earlier. It was a very relaxing meal and I enjoyed the Gruyere cheese. There were little birds fluttering about, hopping from table to table. I suspected that they were looking for a tasty piece of bread! The waitress took away the last bit of my bread before I could offer it to the birds.
I went to the train station and sat around for a while since I was early. The train ride was quite nice because I ended up in first class seating. They served us a nice meal. One strange aspect of the trip was that the train was, in my opinion, eerily quiet. Desiring to practice my French, I decided that I wanted to speak with the person across the row from me. I felt weird but I kept vacillating. I kept thinking over and over how I would initiate the conversation: "Bonjour" no "Bonsoir" "Mademoiselle" .. "Parlez-vous Francais?" ... Should I use "tu?" "Parles-tu Francais?" She has an iPod on, will she hear me? Is she sleeping? What if she doesn't speak French? Could I practice my french with you? "Est-ce que je pourrais practiquer mon francais avec vous (tu?)?" Is it too weird to start a conversation like that?... This went on for a while so I spoke to Kevin, one of the kids in my program for a while since that felt safer to me. Fortunately, I did get up the courage to start up a conversation.
I ended up talking (mostly) in French for about an hour with this Russian woman, until the train arrived. In high school, I didn't really see the reason for learning French. However, I can now see the reason. It is very fun to be able to talk to people in French and to hear their opinions on things. This woman was from Russia, was studing business in France and was planning to go to Geneva after she receives her degree. It is cool to meet these people who are so comfortable living internationally! I asked her about how she perceived the US and what stereotypes she had heard - this is a question that I commonly ask. One thing she mentioned is that she felt like Americans had a narrow view of Russians - people from Russians are drunk all the time, poor from communism, wearing the Russian Ushanka hats, etc. This was interesting to me because I do not know anything about contemporary Russia. She also said that she thought that going to Russia would be a much larger culture shock for me than me visiting Europe. I tried to ask her what she meant but she just said that I had to see what it is like for myself. All in all, I had a fun trip. I certainly see the benefits of striking up conversation with others but it is hard to find people who are willing to talk.
Things at work
Anyway, I thought that I should put an update about the stuff that I have been doing at work.
I wrote a somewhat long, mathematical post on the issue of recovering an unknown function given some information about it: http://www.artofproblemsolving.com/blog/53857
I also looked into the simulated annealing algorithm, a method that my lab currently uses, and wrote about it as well: http://www.artofproblemsolving.com/blog/53958
(I think that I will put the more math related posts on my art of problem solving blog).
I have been reading a lot of papers about the "Needle Optimization Technique," a method that is specifically designed for designing multilayer mirrors.
I am preparing a presentation on the work that I did on the Kramers-Kronig relations.
I wrote a somewhat long, mathematical post on the issue of recovering an unknown function given some information about it: http://www.artofproblemsolving.com/blog/53857
I also looked into the simulated annealing algorithm, a method that my lab currently uses, and wrote about it as well: http://www.artofproblemsolving.com/blog/53958
(I think that I will put the more math related posts on my art of problem solving blog).
I have been reading a lot of papers about the "Needle Optimization Technique," a method that is specifically designed for designing multilayer mirrors.
I am preparing a presentation on the work that I did on the Kramers-Kronig relations.
Wednesday, June 29, 2011
American Stereotypes and Starting a new Project
Last night, I spoke with a number of students from other countries and enjoyed discussing the way that they saw America. It is a bit of a long story, but suffice it to say that I ended up in a conversation with a Canadian, a Russian, three French people, and a bunch of the people in my program. I learned about their views on American stereotypes, American culture, and American foreign policy.
The Russian man told me that many Russians like South Park because that show freely expresses ideas. He liked a lot of American movies but I had not heard of many of them. The only one that I recognized was the Imaginarium of Doctor Parnassus.
According to the French man, there was support for the war in Afghanistan and he pointed to the fact that the French military is there as well. He repeatedly pointed to situations where the French and US military were working together. He also pointed out that England and France needed the large military of the US to be able to have a presence in many countries at once. He was strongly against the war in Iraq and he pointed out that there are many ruthless dictators all over the world so why did the US choose Iraq in particular.
I enjoyed conversing with these people in a mixture of French and English. I tried to listen to their conversations in French but again they would generally speak too fast for me to understand. I also feel like they did not speak loud enough for me to hear them unless they were talking to me directly (perhaps I need to continue to try to clean out my ears).
Lastly, these people had intelligent views on stereotypes. When I first asked the question about stereotypes, all of them said something to the effect of we know that those aren't true so we don't like to say them. They had met people from the US and they did not fit their stereotype. But after they insisted, they told me about how Americans can be loud. They also pointed to Texans.
At lunch today, I discussed stereotypes with the people that I work with. They were much more willing to tell us about American stereotypes. One of the more interesting ones is the idea that Americans do not have any culture. So when I think of American culture, I think of movies, TV shows and food. However, when they spoke of culture, they thought of art and history. I thought that was an interesting difference.
One big update from work is that it seems to me that the project that I was working on during the start of the summer is not going to work out. Basically, I was looking into a measurement technique and it seems that the method will not be useful to the lab. So I am going to stop working on this project soon and I will be moving on to another project for the rest of the summer. I will be looking into improving their optimization algorithms for the mirrors that they are using. I am pretty excited about this project because it is something that I have been wanting to learn about for a while.
I feel good about experience so far because I am accustomed to difficulty in research and I still learned useful things. After doing research last summer and struggling through physics labs this year, I am comfortable with research not going smoothly. Additionally, I feel like I learned a lot from this experience. I learned matlab and got experience searching for and sifting through literature for my project. More than anything, I am happy to start a new project.
The Russian man told me that many Russians like South Park because that show freely expresses ideas. He liked a lot of American movies but I had not heard of many of them. The only one that I recognized was the Imaginarium of Doctor Parnassus.
According to the French man, there was support for the war in Afghanistan and he pointed to the fact that the French military is there as well. He repeatedly pointed to situations where the French and US military were working together. He also pointed out that England and France needed the large military of the US to be able to have a presence in many countries at once. He was strongly against the war in Iraq and he pointed out that there are many ruthless dictators all over the world so why did the US choose Iraq in particular.
I enjoyed conversing with these people in a mixture of French and English. I tried to listen to their conversations in French but again they would generally speak too fast for me to understand. I also feel like they did not speak loud enough for me to hear them unless they were talking to me directly (perhaps I need to continue to try to clean out my ears).
Lastly, these people had intelligent views on stereotypes. When I first asked the question about stereotypes, all of them said something to the effect of we know that those aren't true so we don't like to say them. They had met people from the US and they did not fit their stereotype. But after they insisted, they told me about how Americans can be loud. They also pointed to Texans.
At lunch today, I discussed stereotypes with the people that I work with. They were much more willing to tell us about American stereotypes. One of the more interesting ones is the idea that Americans do not have any culture. So when I think of American culture, I think of movies, TV shows and food. However, when they spoke of culture, they thought of art and history. I thought that was an interesting difference.
One big update from work is that it seems to me that the project that I was working on during the start of the summer is not going to work out. Basically, I was looking into a measurement technique and it seems that the method will not be useful to the lab. So I am going to stop working on this project soon and I will be moving on to another project for the rest of the summer. I will be looking into improving their optimization algorithms for the mirrors that they are using. I am pretty excited about this project because it is something that I have been wanting to learn about for a while.
I feel good about experience so far because I am accustomed to difficulty in research and I still learned useful things. After doing research last summer and struggling through physics labs this year, I am comfortable with research not going smoothly. Additionally, I feel like I learned a lot from this experience. I learned matlab and got experience searching for and sifting through literature for my project. More than anything, I am happy to start a new project.
Sunday, June 26, 2011
Exploring Opera, Time with cousins, Pantheon, and GRE
I have been busy so I will be breaking things up:
In exploring the area around Opera, a touristy area, I was able to discover many fascinating shops. To give some background, I have a bunch of traveler's checks. It is somewhat of a pain to use these, but it ended up being nice to have some since my debit card got frozen since I made a train reservation to Switzerland. Anyways, I went from one bank to another in order to find where I could exchange them. Eventually, somebody suggested that I go to the Opera train stop. Right as I emerged from the metro stop, I was greeted with the hustle and bustle of tourists clamoring over the beautiful Opera house building. I walked around and took a number of pictures. The currency exchanges in the area are blatantly in the business to rip off tourists as some places charged 10 percent plus a fee of 5 euros. After going to about 5 places, I found an exchange where the fee was only 2 percent. Since I went all the way out here, I decided to go walking around. I explored a number of children's shops. My wanderings let me to a passage with a number of cool shops. My favorite was an oriental antiquities shop. They had such an amazing collection: there were ivory, gold and wood sculptures in addition to a large collection of jewelry, tapestries, and oriental weapons! As I have concluded in the past, wandering away from the tourist traps has led to some of my best experiences here.
In walking through the Louvre slowly and enjoying a long dinner with my cousins, I saw again that I get more out of what I do by experiencing it slowly. So my aunt, uncle, and younger cousin, Meg, Harold, and Hannah, respectively visited Paris this weekend. First, we went to the Louvre. I was happy to see that my family members were happy with going through the Louvre slowly. I felt like I was able to appreciate the art more than when I went with other kids. Among other things, we discussed the progression of perspective as shown by portraits of the baby Jesus. The Louvre is just so amazing. Each section of the Louvre might as well be its own museum. We also slowly perused at paintings from smaller European countries. I enjoyed looking closely at the paintings and at least attempting to appreciate all of the work that went into each masterpiece. After that, we went out to dinner to a place that specialized in the cuisine from the Auvergne region. We enjoyed a long meal with an appetizer, main dish, dessert and some wine. I feel like I can enjoy a good bottle of wine with a meal now. It was nice to have a slow dinner for a change where we were able to talk. I hope to go on one or two more nice dinners like this where I get to try food from a new region. The only difficulty is that there is no way that I could read the menu: my aunt and uncle who have extensive experience in french cuisine still struggled to read the menu.
It is a bit harder to draw any conclusions about my travels today, but suffice it to say that it reinforces the point that I like to go through things slowly and I was pleased to see that some, but not many, of the students feel similarly. We started by going to some gardens. One particular person in our group planned the trip so we more or less went to see what she saw. It was hot and bright so I didn't particularly enjoy the gardens. It would have been nice to have a picnic though. Then we continued on to the Pantheon- a majestic building that contains the remains of some of Paris's "great men." Boasting large sculptures, frescos depicting hordes of people and ceilings that went hundreds of feet into the air, the inside of the pantheon was awe-inspiring. The lower level of the building contained a crypt that housed many of the influential thinkers of Paris. At this point, we split up and we each went around and looked at who we wanted to. I was able to read the French descriptions and although I was not able to understand everything, I was able to get the gist of the descriptions. Seeing these people makes me desire to know more French history and philosophy. Another notable point is that of the hundred or so people interred in the Pantheon, there are only two women. I also enjoyed reading about the history of building the Pantheon and how it had been used over the years.
My GRE preparation is going along smoothly and I am starting to notice that it is impacting my thinking in a positive way. I have been looking at a lot of vocabulary and I have a little notebook where I write all the words and definitions so that I can study them wherever I go. I feel that I am recognizing a lot of words in the practice materials that I am doing but I have trouble free-recalling the words that I am working with. The other major area of preparation is on the essay portion. I am working with a tutor and he has had a lot of helpful suggestions. It seems to me that if you write a straight-forward essay, then you get a 4. In order to make the essay better, you need to situate your argument in some context. For instance, I spoke about current problems necessitating generalists in the context of renaissance scientists. Further, by mixing in some impressive vocabulary, you can push your score to a 5 or 6. Really the idea is that you want to set yourself apart in some way with a flourish of your vocabulary and historical knowledge. I feel like it is a up to luck whether or not I can think of some historical or artistic example in order to situate my essay. Overall, I think all of this is a bit silly because I think straightforwardly, but I can see how these elements make an essay stronger. Additionally, I have to focus on writing strong introductory sentences and creating fluid transitions. I am pleased with how my preparation is going.
That's that for now. The weeks are pretty busy with work and I am having a lot of good experiences over the weekends. Next weekend I am going to Switzerland!
In exploring the area around Opera, a touristy area, I was able to discover many fascinating shops. To give some background, I have a bunch of traveler's checks. It is somewhat of a pain to use these, but it ended up being nice to have some since my debit card got frozen since I made a train reservation to Switzerland. Anyways, I went from one bank to another in order to find where I could exchange them. Eventually, somebody suggested that I go to the Opera train stop. Right as I emerged from the metro stop, I was greeted with the hustle and bustle of tourists clamoring over the beautiful Opera house building. I walked around and took a number of pictures. The currency exchanges in the area are blatantly in the business to rip off tourists as some places charged 10 percent plus a fee of 5 euros. After going to about 5 places, I found an exchange where the fee was only 2 percent. Since I went all the way out here, I decided to go walking around. I explored a number of children's shops. My wanderings let me to a passage with a number of cool shops. My favorite was an oriental antiquities shop. They had such an amazing collection: there were ivory, gold and wood sculptures in addition to a large collection of jewelry, tapestries, and oriental weapons! As I have concluded in the past, wandering away from the tourist traps has led to some of my best experiences here.
In walking through the Louvre slowly and enjoying a long dinner with my cousins, I saw again that I get more out of what I do by experiencing it slowly. So my aunt, uncle, and younger cousin, Meg, Harold, and Hannah, respectively visited Paris this weekend. First, we went to the Louvre. I was happy to see that my family members were happy with going through the Louvre slowly. I felt like I was able to appreciate the art more than when I went with other kids. Among other things, we discussed the progression of perspective as shown by portraits of the baby Jesus. The Louvre is just so amazing. Each section of the Louvre might as well be its own museum. We also slowly perused at paintings from smaller European countries. I enjoyed looking closely at the paintings and at least attempting to appreciate all of the work that went into each masterpiece. After that, we went out to dinner to a place that specialized in the cuisine from the Auvergne region. We enjoyed a long meal with an appetizer, main dish, dessert and some wine. I feel like I can enjoy a good bottle of wine with a meal now. It was nice to have a slow dinner for a change where we were able to talk. I hope to go on one or two more nice dinners like this where I get to try food from a new region. The only difficulty is that there is no way that I could read the menu: my aunt and uncle who have extensive experience in french cuisine still struggled to read the menu.
It is a bit harder to draw any conclusions about my travels today, but suffice it to say that it reinforces the point that I like to go through things slowly and I was pleased to see that some, but not many, of the students feel similarly. We started by going to some gardens. One particular person in our group planned the trip so we more or less went to see what she saw. It was hot and bright so I didn't particularly enjoy the gardens. It would have been nice to have a picnic though. Then we continued on to the Pantheon- a majestic building that contains the remains of some of Paris's "great men." Boasting large sculptures, frescos depicting hordes of people and ceilings that went hundreds of feet into the air, the inside of the pantheon was awe-inspiring. The lower level of the building contained a crypt that housed many of the influential thinkers of Paris. At this point, we split up and we each went around and looked at who we wanted to. I was able to read the French descriptions and although I was not able to understand everything, I was able to get the gist of the descriptions. Seeing these people makes me desire to know more French history and philosophy. Another notable point is that of the hundred or so people interred in the Pantheon, there are only two women. I also enjoyed reading about the history of building the Pantheon and how it had been used over the years.
My GRE preparation is going along smoothly and I am starting to notice that it is impacting my thinking in a positive way. I have been looking at a lot of vocabulary and I have a little notebook where I write all the words and definitions so that I can study them wherever I go. I feel that I am recognizing a lot of words in the practice materials that I am doing but I have trouble free-recalling the words that I am working with. The other major area of preparation is on the essay portion. I am working with a tutor and he has had a lot of helpful suggestions. It seems to me that if you write a straight-forward essay, then you get a 4. In order to make the essay better, you need to situate your argument in some context. For instance, I spoke about current problems necessitating generalists in the context of renaissance scientists. Further, by mixing in some impressive vocabulary, you can push your score to a 5 or 6. Really the idea is that you want to set yourself apart in some way with a flourish of your vocabulary and historical knowledge. I feel like it is a up to luck whether or not I can think of some historical or artistic example in order to situate my essay. Overall, I think all of this is a bit silly because I think straightforwardly, but I can see how these elements make an essay stronger. Additionally, I have to focus on writing strong introductory sentences and creating fluid transitions. I am pleased with how my preparation is going.
That's that for now. The weeks are pretty busy with work and I am having a lot of good experiences over the weekends. Next weekend I am going to Switzerland!
Sunday, June 19, 2011
Notre Dame, ENSTA Party, Wine Tasting, Musee Rodin and redeeming qualities of the GRE
So this might be a long post... I have been feeling pretty busy lately so I have been putting of this blog. So
Last weekend, most of the group went to Marseilles. The rest of us who stayed in Paris had a relaxing weekend and we tried to catch up on sleep. On Sunday, I went to Notre Dame. While I enjoyed seeing the amazing stained glass windows, I was somewhat saddened by way that the church had become so touristy. The windows were fantastic as ever. Given that the church was completed by 1345, I am impressed by the ability of the French people at the time to construct such a fantastic building. Granted, it took about 200 years to complete, but the windows and all of the sculptures were amazing. Again, I found the impact of the tourism to be displeasing. The area was flooded by tourists taking pictures and everywhere you looked, there were little trinkets that you could buy. There were also advertisements for the church's program to help other countries spread about that were asking for donations. Of course I am not religious but I picture a church as a place where one would go to get closer to god and not an institution that fawns over tourists.
I have been busy studying for the GRE so I did not do that much during the week. However, on Thursday night, I went to a party with some of the students who welcomed us to Paris when we first arrived. It was the last hurrah before their final exams started so the event was understandably crazy - they held a shopping cart race where they threw water ballons, pies, milk and many other strange things at the competitors. My favorite part of the party was talking to the french students. I described the various things that I have been doing in Paris to them and some of my general impressions of Paris all in French! Everybody was very friendly and spoke slower to me in French so I was able to understand them. I left a lot earlier than most of the people who went to the party so I missed some fun things but overall it was a great time. I am glad that I decided to go.
This Saturday, I went to a wine tasting with most of the other students. My goal was to attempt to see what people like about good wines. The "Tour de France of Wine" featured six wines from around France and an expert wine maker to explain the wines. Overall, it was a good experience. I enjoyed hearing about the technique of wine tasting - one of the more pompous things that one can do- and the amazing amount of skill that goes into making great wines. You can read about it more online, but proper wine tasting involves many steps. One starts by looking at the color and viscosity of the wine from which you can predict certain properties of the wine. Then one swirls the wine to let out some of the aromas and to oxidize some of the wine. Then you taste a little wine and swish it about in your mouth. There are different stages of the taste which some pompously entitle the attack phase, the evolution phase, and the finish. Our particular guide did not use these terms but they came up frequently on the internet. I was impressed with how there were subtle differences in the tastes of the wines. I felt that the wines were okay but I have never had that much wine so perhaps it is not a taste that I have acquired yet. I felt that I got some appreciation for the work that goes into making the wines but I still don't quite see why people find wine to be so fantastic. After drinking all of that wine, I felt the alcohol a bit but I again I didn't really like the feeling of being a bit tipsy. I felt like I was talking a bit louder than normal and that my balance wasn't quite the same but I still felt as outgoing and the same levels of social anxiety (which is typically quite low for me) as I normally do. This was a good experience for me but it didn't change my views that much on drinking - others seem to enjoy it a lot but I don't have much of a desire to drink. I am glad to see that my extreme aversion to alcohol at the start of college has relaxed to a more reasonable view.
Today, I went to Musee Rodin because I wanted to see the place that so many people have recommended to me. I was glad to go to a smaller museum where I could both appreciate fantastic pieces of art and not be overwhelmed by too many pieces of art. After you enter, there is a beautiful outdoor courtyard that displays some of Rodin's more famous works. Among others, the thinker, the gates of hell, and the three shades are situated in a beautiful garden. Rodin was able to capture emotion in his sculptures - the main quality by which I judge art. Inside a renovated hotel, there was a sizable collection of Rodin's other sculptures and a few other paintings like a Van Gogh painting and a Renoir painting as well.
The trip was more relaxed than usual because I went with one other student who has a similar energy level to mine. I liked that we went through the art relatively slowly and that we were able to see pretty much all of the art in three hours. I have found it very overwhelming to go to the Louvre where there are so many masterpieces that I cannot really appreciate any of them. In the future, I do want to go to a museum and do an audio tour. Even though I went through this museum slowly, I could have spent much more time reading about the history. I feel that I have to have at least one museum experience where I take a sufficient amount of time to learn about the history. In order to accomplish this, I think that I need to go alone because it does not seem like this appeals to the people in our group.
So a quick update on the GRE. I have been continuing to study an hour or two a day. I feel that my preparation is going pretty well but it would be nice to have more time. I can pay $50 to move my test day to as late as July 13th (whereas I am currently planning to take in June 27th). As I see it, the reason to take it now is that I would be able to do more fun things during the rest of my trip. The upside is that I would certainly do better on the test if I had two more weeks to prepare. Additionally, I do feel that what I am doing is useful. I should be able to formulate a clear and organized argument in a short amount of time. I should feel comfortable deconstructing an argument. I should have the ability to read through a dense passage and quickly determine the structure and the purpose of the author. I will make this decision in the next few days. I do wish that I had more experience doing these things at college but I have not taken that many humanities classes.
That's all for now.
Last weekend, most of the group went to Marseilles. The rest of us who stayed in Paris had a relaxing weekend and we tried to catch up on sleep. On Sunday, I went to Notre Dame. While I enjoyed seeing the amazing stained glass windows, I was somewhat saddened by way that the church had become so touristy. The windows were fantastic as ever. Given that the church was completed by 1345, I am impressed by the ability of the French people at the time to construct such a fantastic building. Granted, it took about 200 years to complete, but the windows and all of the sculptures were amazing. Again, I found the impact of the tourism to be displeasing. The area was flooded by tourists taking pictures and everywhere you looked, there were little trinkets that you could buy. There were also advertisements for the church's program to help other countries spread about that were asking for donations. Of course I am not religious but I picture a church as a place where one would go to get closer to god and not an institution that fawns over tourists.
I have been busy studying for the GRE so I did not do that much during the week. However, on Thursday night, I went to a party with some of the students who welcomed us to Paris when we first arrived. It was the last hurrah before their final exams started so the event was understandably crazy - they held a shopping cart race where they threw water ballons, pies, milk and many other strange things at the competitors. My favorite part of the party was talking to the french students. I described the various things that I have been doing in Paris to them and some of my general impressions of Paris all in French! Everybody was very friendly and spoke slower to me in French so I was able to understand them. I left a lot earlier than most of the people who went to the party so I missed some fun things but overall it was a great time. I am glad that I decided to go.
This Saturday, I went to a wine tasting with most of the other students. My goal was to attempt to see what people like about good wines. The "Tour de France of Wine" featured six wines from around France and an expert wine maker to explain the wines. Overall, it was a good experience. I enjoyed hearing about the technique of wine tasting - one of the more pompous things that one can do- and the amazing amount of skill that goes into making great wines. You can read about it more online, but proper wine tasting involves many steps. One starts by looking at the color and viscosity of the wine from which you can predict certain properties of the wine. Then one swirls the wine to let out some of the aromas and to oxidize some of the wine. Then you taste a little wine and swish it about in your mouth. There are different stages of the taste which some pompously entitle the attack phase, the evolution phase, and the finish. Our particular guide did not use these terms but they came up frequently on the internet. I was impressed with how there were subtle differences in the tastes of the wines. I felt that the wines were okay but I have never had that much wine so perhaps it is not a taste that I have acquired yet. I felt that I got some appreciation for the work that goes into making the wines but I still don't quite see why people find wine to be so fantastic. After drinking all of that wine, I felt the alcohol a bit but I again I didn't really like the feeling of being a bit tipsy. I felt like I was talking a bit louder than normal and that my balance wasn't quite the same but I still felt as outgoing and the same levels of social anxiety (which is typically quite low for me) as I normally do. This was a good experience for me but it didn't change my views that much on drinking - others seem to enjoy it a lot but I don't have much of a desire to drink. I am glad to see that my extreme aversion to alcohol at the start of college has relaxed to a more reasonable view.
Today, I went to Musee Rodin because I wanted to see the place that so many people have recommended to me. I was glad to go to a smaller museum where I could both appreciate fantastic pieces of art and not be overwhelmed by too many pieces of art. After you enter, there is a beautiful outdoor courtyard that displays some of Rodin's more famous works. Among others, the thinker, the gates of hell, and the three shades are situated in a beautiful garden. Rodin was able to capture emotion in his sculptures - the main quality by which I judge art. Inside a renovated hotel, there was a sizable collection of Rodin's other sculptures and a few other paintings like a Van Gogh painting and a Renoir painting as well.
The trip was more relaxed than usual because I went with one other student who has a similar energy level to mine. I liked that we went through the art relatively slowly and that we were able to see pretty much all of the art in three hours. I have found it very overwhelming to go to the Louvre where there are so many masterpieces that I cannot really appreciate any of them. In the future, I do want to go to a museum and do an audio tour. Even though I went through this museum slowly, I could have spent much more time reading about the history. I feel that I have to have at least one museum experience where I take a sufficient amount of time to learn about the history. In order to accomplish this, I think that I need to go alone because it does not seem like this appeals to the people in our group.
So a quick update on the GRE. I have been continuing to study an hour or two a day. I feel that my preparation is going pretty well but it would be nice to have more time. I can pay $50 to move my test day to as late as July 13th (whereas I am currently planning to take in June 27th). As I see it, the reason to take it now is that I would be able to do more fun things during the rest of my trip. The upside is that I would certainly do better on the test if I had two more weeks to prepare. Additionally, I do feel that what I am doing is useful. I should be able to formulate a clear and organized argument in a short amount of time. I should feel comfortable deconstructing an argument. I should have the ability to read through a dense passage and quickly determine the structure and the purpose of the author. I will make this decision in the next few days. I do wish that I had more experience doing these things at college but I have not taken that many humanities classes.
That's all for now.
Tuesday, June 14, 2011
Simulation Working? Yes Practical? No
So I have finally gotten the simulations to work. To review, here is the idea:
I have a design of a multilayer mirror (eg. 4 nm of one substance, 3 of another...). Then we have a program that can simulate the reflectivity and the phase delay of that mirror. The goal of my program is to take simulated reflectivity data and use that to calculate phase using the Kramers-Kronig relationship, and compare that to the simulated phase delay.
As you can see, the results are pretty good. Over a wide range of energies, the two graphs are quite close. But there are still a lot of problems to deal with. As I have mentioned before, there are complex frequencies with zero reflectivity that come into the KK relation. They must be taken into account.
The algorithm that I wrote to find these was effective and found two complex zeros E1=97.0+0.5i and E2=68.7+3.6I. This method requires you to know the magnitude of the reflectivity for complex frequencies. Of course this is not practical so I will be looking into how others have attacked this problem.
The other issue to mention is that I used quite a large energy range in this calculation. (The simulated data was 10 eV to 120 eV in steps of 0.5 eV. Then the data used to calculate the KK relation was 10 eV to 100 eV with steps of 1 eV). I will have to play around with the energy range in order to achieve something practical. Also the energy range has a significant impact on the graph so I will look into what gives an accurate result.
Another complication to mention is that the calculation is actually off by a factor of pi. This has to do with the fact that the complex zeros introduce a factor of pi for frequencies that have a real part that is much larger than the real part of the zero.
Just for myself, it is important to note that this was a good exercise in debugging. Basically, I needed to find the simplest thing to test in my program and work up. It occurred to me that I could think of a simple function to plug into my numerical integrator that would allow me to check if it was working. This helped me work out a few problems. Next, I realized that I did not take the logarithm of the reflectivity so I eventually realized that when looking at my code. The complex zeros would have been hard to know about if I hadn't read a fair number of papers (many of the papers on this subject don't really mention them).
I have a design of a multilayer mirror (eg. 4 nm of one substance, 3 of another...). Then we have a program that can simulate the reflectivity and the phase delay of that mirror. The goal of my program is to take simulated reflectivity data and use that to calculate phase using the Kramers-Kronig relationship, and compare that to the simulated phase delay.
As you can see, the results are pretty good. Over a wide range of energies, the two graphs are quite close. But there are still a lot of problems to deal with. As I have mentioned before, there are complex frequencies with zero reflectivity that come into the KK relation. They must be taken into account.The algorithm that I wrote to find these was effective and found two complex zeros E1=97.0+0.5i and E2=68.7+3.6I. This method requires you to know the magnitude of the reflectivity for complex frequencies. Of course this is not practical so I will be looking into how others have attacked this problem.
The other issue to mention is that I used quite a large energy range in this calculation. (The simulated data was 10 eV to 120 eV in steps of 0.5 eV. Then the data used to calculate the KK relation was 10 eV to 100 eV with steps of 1 eV). I will have to play around with the energy range in order to achieve something practical. Also the energy range has a significant impact on the graph so I will look into what gives an accurate result.
Another complication to mention is that the calculation is actually off by a factor of pi. This has to do with the fact that the complex zeros introduce a factor of pi for frequencies that have a real part that is much larger than the real part of the zero.
Just for myself, it is important to note that this was a good exercise in debugging. Basically, I needed to find the simplest thing to test in my program and work up. It occurred to me that I could think of a simple function to plug into my numerical integrator that would allow me to check if it was working. This helped me work out a few problems. Next, I realized that I did not take the logarithm of the reflectivity so I eventually realized that when looking at my code. The complex zeros would have been hard to know about if I hadn't read a fair number of papers (many of the papers on this subject don't really mention them).
Saturday, June 11, 2011
Versailles
So the main thing that I want to talk about in this post is my trip to Versailles.
When we first got to Versailles, we were greeted with a regal statue of Louis the 14th. Then we saw the brilliant golden fences. I was amazed at how much gold there was everywhere. This palace is really a testament to the wealth of the French monarchs (and perhaps a warning about their extreme arrogance...).
So the line to get in was very long. We decided that it would be a good idea to pretend that we were students from the EU. That way we would get free admission. I didn't like this idea too much but they didn't give us that hard a time even though we didn't actually have identification from another country- we used our international students cards. Luckily they didn't know that University of Michigan wasn't in the EU...
My overall reaction to the palace was that it was unbelievable that such a palace exists. The extravagance is almost impossible to describe. One of the more impressive aspects is that there were fabulous statues everywhere. Also the rooms of the king and queen were really outrageous (the queen won out on the most opulent room... good for her?!)
I think a general theme in many of the trips that we've been taking is that there is just so much to appreciate and we don't have the time to really appreciate the sites. I would love to learn all about the history of Versailles and the psychology behind the man who made it so extravagant. I felt like we rushed through all of the exhibits. Another theme that I've noticed is that my general historical knowledge is lacking. Many sculptures are related to Greek mythology and many paintings depict stories from the bible. It would be nice to have enough knowledge of these things to be able to recognize that a sculpture is showing, for instance, the abduction of Persephone.
But even though I am recognizing a lack of knowledge, I doubt that I will take steps to learn more about these areas. I just feel that I am too busy. I think that I would like to go back to some of these places on my own in the future. I would like to do the audio tours. I would enjoy learning more about the history of the paintings.
Another general conclusion about these trips is that I value relaxing. In accordance with the French style pace of life, I love to just sit down and enjoy looking around. I was pleased that I was able to convince our group to sit on the grass for about a half hour. I hope that I will get to do more relaxing in the future.
Socially, I feel that I am striking a good balance. I appreciate that people seem to respect the fact that I want to carefully balance my time and that I need to factor in GRE studying. From my perspective, it seems like I am able to do things with other people every few days. For instance, I have been making pasta for myself for the past few nights, but I took one night off to go to dinner with the group at the on campus cafeteria in order to hang out. Overall, it seems like I am over thinking these things and that I am getting along with the group. I really did have a good time at Versailles and a big part of it was doing touristy things with the other people here.
Anyways, I have two more days this weekend to do fun things. Half of the students in the program are going to southern France. So hopefully the rest of us will do some fun things as well. But most of all, I am looking forward to sleeping in tonight.
Another aside is that I do feel like my GRE preparation is going well. I took a computer adaptive test through princeton review and I hit my goal on the verbal. The essays didn't seem to go so well. I had trouble thinking about ideas for the essay and I didn't start out with a solid outline. Furthermore, I got nervous throughout the essay since the ideas were not coming together well. Also in general, I have to work on the essay that is to evaluate an argument. I do this so rarely now in a formal sense that I am not sure how to structure the essay. I have been doing a lot of vocab and I think that helps me get handful of questions correct on the verbal. The most helpful thing in studying is just getting familiar with the question types and how to go about them.
Another thing that has been on my mind related to the GRE is that I feel that the test prep sites negatively impact poorer people. $450 effectively gets you an increase of 100 to 200 points (out of 800). Granted you have to put in the time, but if that is prohibitively expensive for you, then you are at a huge disadvantage. It is too bad that they don't offer better free test materials. Luckily I have been able to find enough practice materials to last me until I take the test in about two weeks.
When we first got to Versailles, we were greeted with a regal statue of Louis the 14th. Then we saw the brilliant golden fences. I was amazed at how much gold there was everywhere. This palace is really a testament to the wealth of the French monarchs (and perhaps a warning about their extreme arrogance...).
So the line to get in was very long. We decided that it would be a good idea to pretend that we were students from the EU. That way we would get free admission. I didn't like this idea too much but they didn't give us that hard a time even though we didn't actually have identification from another country- we used our international students cards. Luckily they didn't know that University of Michigan wasn't in the EU...
My overall reaction to the palace was that it was unbelievable that such a palace exists. The extravagance is almost impossible to describe. One of the more impressive aspects is that there were fabulous statues everywhere. Also the rooms of the king and queen were really outrageous (the queen won out on the most opulent room... good for her?!)
I think a general theme in many of the trips that we've been taking is that there is just so much to appreciate and we don't have the time to really appreciate the sites. I would love to learn all about the history of Versailles and the psychology behind the man who made it so extravagant. I felt like we rushed through all of the exhibits. Another theme that I've noticed is that my general historical knowledge is lacking. Many sculptures are related to Greek mythology and many paintings depict stories from the bible. It would be nice to have enough knowledge of these things to be able to recognize that a sculpture is showing, for instance, the abduction of Persephone.
But even though I am recognizing a lack of knowledge, I doubt that I will take steps to learn more about these areas. I just feel that I am too busy. I think that I would like to go back to some of these places on my own in the future. I would like to do the audio tours. I would enjoy learning more about the history of the paintings.
Another general conclusion about these trips is that I value relaxing. In accordance with the French style pace of life, I love to just sit down and enjoy looking around. I was pleased that I was able to convince our group to sit on the grass for about a half hour. I hope that I will get to do more relaxing in the future.
Socially, I feel that I am striking a good balance. I appreciate that people seem to respect the fact that I want to carefully balance my time and that I need to factor in GRE studying. From my perspective, it seems like I am able to do things with other people every few days. For instance, I have been making pasta for myself for the past few nights, but I took one night off to go to dinner with the group at the on campus cafeteria in order to hang out. Overall, it seems like I am over thinking these things and that I am getting along with the group. I really did have a good time at Versailles and a big part of it was doing touristy things with the other people here.
Anyways, I have two more days this weekend to do fun things. Half of the students in the program are going to southern France. So hopefully the rest of us will do some fun things as well. But most of all, I am looking forward to sleeping in tonight.
Another aside is that I do feel like my GRE preparation is going well. I took a computer adaptive test through princeton review and I hit my goal on the verbal. The essays didn't seem to go so well. I had trouble thinking about ideas for the essay and I didn't start out with a solid outline. Furthermore, I got nervous throughout the essay since the ideas were not coming together well. Also in general, I have to work on the essay that is to evaluate an argument. I do this so rarely now in a formal sense that I am not sure how to structure the essay. I have been doing a lot of vocab and I think that helps me get handful of questions correct on the verbal. The most helpful thing in studying is just getting familiar with the question types and how to go about them.
Another thing that has been on my mind related to the GRE is that I feel that the test prep sites negatively impact poorer people. $450 effectively gets you an increase of 100 to 200 points (out of 800). Granted you have to put in the time, but if that is prohibitively expensive for you, then you are at a huge disadvantage. It is too bad that they don't offer better free test materials. Luckily I have been able to find enough practice materials to last me until I take the test in about two weeks.
Thursday, June 9, 2011
Things are Coming Together...
Things that I did today:
(Got Principal Value Integral Package to work)
So today, I got a matlab package to work that integrates principal value integrals. The code was written poorly but I adjusted it so that I could pass a function handle to the method that did the integration. From what I can see, the integral does not contribute much to the phase. The larger contributions seem to come from the extrapolation terms.
(Thoughts about extra terms due to complex zeros of R)
In the actual phase graph, there seems to be a jump discontinuity. Looking at the equation for the phase, it seems like this is due to a complex zero in the reflectivity. (The arctan term gives a jump discontinuity if the real part is small).
(Learning how to Calculate Reflectivity)
Anyways, now I've been looking into the code that lets you calculate the reflectivity. The relevant topic is called "the transfer matrix method" (see http://en.wikipedia.org/wiki/Transfer-matrix_method_(optics) ). The idea is that if you have a layered structure, you look at the electric field and the derivative of E with respect to the normal to the surface and the propagation of the waves can be described by multiplying the E, dE/dz vector by a matrix.
(Derivation of KK Relations)
Also one question that came up yesterday is why are the complex zeros of reflectance relevant in the equation. So the derivation of the KK relationship using complex variables is very nice and can be found here: http://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relation (see derivation). The basic idea is that you take a contour integral of f(omega')/(omega'-omega) that goes along the real axis and then a semicircle in the upper half of the complex plane (with a little indent around omega). If there are singularities, you have to surround those with little loops to take them into account when you deform the integration contour.
(Algorithm to find complex zeros)
So I adjusted the program that is used to calculate reflectivity given a frequency so that it can pass it into a root finding algorithm. I wonder if I will be able to find the zeros of this function.
Anyways, I feel pretty good about my project because I am understanding things and I have a lot of things that I can do.
(Got Principal Value Integral Package to work)
So today, I got a matlab package to work that integrates principal value integrals. The code was written poorly but I adjusted it so that I could pass a function handle to the method that did the integration. From what I can see, the integral does not contribute much to the phase. The larger contributions seem to come from the extrapolation terms.
(Thoughts about extra terms due to complex zeros of R)
In the actual phase graph, there seems to be a jump discontinuity. Looking at the equation for the phase, it seems like this is due to a complex zero in the reflectivity. (The arctan term gives a jump discontinuity if the real part is small).
(Learning how to Calculate Reflectivity)
Anyways, now I've been looking into the code that lets you calculate the reflectivity. The relevant topic is called "the transfer matrix method" (see http://en.wikipedia.org/wiki/Transfer-matrix_method_(optics) ). The idea is that if you have a layered structure, you look at the electric field and the derivative of E with respect to the normal to the surface and the propagation of the waves can be described by multiplying the E, dE/dz vector by a matrix.
(Derivation of KK Relations)
Also one question that came up yesterday is why are the complex zeros of reflectance relevant in the equation. So the derivation of the KK relationship using complex variables is very nice and can be found here: http://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relation (see derivation). The basic idea is that you take a contour integral of f(omega')/(omega'-omega) that goes along the real axis and then a semicircle in the upper half of the complex plane (with a little indent around omega). If there are singularities, you have to surround those with little loops to take them into account when you deform the integration contour.
(Algorithm to find complex zeros)
So I adjusted the program that is used to calculate reflectivity given a frequency so that it can pass it into a root finding algorithm. I wonder if I will be able to find the zeros of this function.
Anyways, I feel pretty good about my project because I am understanding things and I have a lot of things that I can do.
Wednesday, June 8, 2011
Continued Research Ideas
One paper that I have found seems to be helpful in that it discusses using the KK relations for a thin film. The generalized relation that takes into account the singularities that occur for complex frequencies is
Theta_R(omega)= - omega/Pi INT [0,Infinity] (ln R(omega') )/(omega'^2-omega^2)d omega'
+ 2 SUM arctan (omega-a_j)/b_j
where a_j+i* b_j are the zeros of R(omega).
(1) These zeros are difficult to find experimentally. I wonder if I can modify the code for the simulation in order to allow for complex frequencies. (I do not know what the equations are like but it seems at least possible to do this).
Some other things that are important to do are:
(2) Think of an appropriate way to extrapolate in the LOW frequency region. The issue is that even outside the region where the mirror that I am working with was optimized, there is some significant reflection in the 10 to 30 eV range. My professor said that this isn't too surprising because in addition to the peaks that come from constructive interference, the metals that they use just reflect those frequencies. Experimentally, this could be problematic because you can only go so low with the energies in the synchrotron. Regardless, I hope to get some sort of bound on the error that this produces.
For now, it seems like it is appropriate to assume that reflectivity is a constant in the high frequency region since that is a small contribution. One thing that I am not sure about, however, is how the phase acts for large x. Regardless, I should be able to get a bound on the error that comes from the HIGH frequencies.
Another nice thing that I figured out today is that instead of writing a code to integrate the cauchy principal value integrals, I was just able to find a method that should be able to do it for me. The code is written somewhat poorly so I am working on getting that to work correctly.
All in all, I do feel good about this project. It is quite a challenge, but it is important for this lab to be able to measure the phase delay for their mirrors so I am contributing something. Hopefully I will be able to get my program to do a better job of predicting the phase. If the few things that I am doing don't work, I will go to more papers and see how they approached this problem.
Theta_R(omega)= - omega/Pi INT [0,Infinity] (ln R(omega') )/(omega'^2-omega^2)d omega'
+ 2 SUM arctan (omega-a_j)/b_j
where a_j+i* b_j are the zeros of R(omega).
(1) These zeros are difficult to find experimentally. I wonder if I can modify the code for the simulation in order to allow for complex frequencies. (I do not know what the equations are like but it seems at least possible to do this).
Some other things that are important to do are:
(2) Think of an appropriate way to extrapolate in the LOW frequency region. The issue is that even outside the region where the mirror that I am working with was optimized, there is some significant reflection in the 10 to 30 eV range. My professor said that this isn't too surprising because in addition to the peaks that come from constructive interference, the metals that they use just reflect those frequencies. Experimentally, this could be problematic because you can only go so low with the energies in the synchrotron. Regardless, I hope to get some sort of bound on the error that this produces.
For now, it seems like it is appropriate to assume that reflectivity is a constant in the high frequency region since that is a small contribution. One thing that I am not sure about, however, is how the phase acts for large x. Regardless, I should be able to get a bound on the error that comes from the HIGH frequencies.
Another nice thing that I figured out today is that instead of writing a code to integrate the cauchy principal value integrals, I was just able to find a method that should be able to do it for me. The code is written somewhat poorly so I am working on getting that to work correctly.
All in all, I do feel good about this project. It is quite a challenge, but it is important for this lab to be able to measure the phase delay for their mirrors so I am contributing something. Hopefully I will be able to get my program to do a better job of predicting the phase. If the few things that I am doing don't work, I will go to more papers and see how they approached this problem.
Tuesday, June 7, 2011
A post that ended up being mostly about food
As discussed before, I feel like I have been very busy - I have a lot to balance: learning french, doing research, socializing with the other people in my program, getting settled in my living area and studying for the GRE.
Just to summarize a few notable experiences,
Yesterday, I went with two other people on a "pasta-venture." My goal was to get a pan, pasta, and some toppings. We took the train and bus to a very large supermarket (called a hypermarche/). Carrefour is basically the French Walmart. It was a lot of fun to go around and see the all of the different food sections. There was a huge cheese section, a fish section, etc. Another cool area was the french book area. There were a lot of children's books. I spent about 15 minutes reading Winnie the Pooh (or Winnie l'Ourson). It was fun to read but I did not recognize some of the grammar structures. It was 10 euros so I didn't buy it but I do have fond memories of Winnie the Pooh from when I was younger! Another fun feature of the store is that they had moving walkways to go upstairs so you could take your shopping cart. The surrounding shopping center had these as well.
When I went to the checkout, apparently I almost bought a 50 euro pot. I also didn't weigh my bananas. So I was able to use my french to say no thanks. Apparently I misread the label for the pot and it actually cost 20 euros only if I bought 50 vignettes whatever that means. I was able to get another pot.
Another thing that I have been doing is that I have been trying different French cheeses. I have always eaten a lot of cheese and so it has been fun to explore different kinds. At my lunch, I have been getting a little cheese with each meal. I also bought some cheese from the store. So far, I have had Camembert, Brie, and Roquefort. The last cheese there is one of the moldy cheeses that is supposed to be quite strong but I thought it was tasty. Tomorrow, I hope to try Munster. I also bought "mimolette jeune". It looks like cheddar but I haven't tasted it yet. I hope to continue to try different french cheeses.
Tonight, I was successful in using my pot to cook pasta and I put some cheese on it (emmental). After looking this up, it is just what we refer to as Swiss cheese. I also got two other pasta sauces. One is a tomato sauce with Ricotta, and another is tomato sauce "basquaise" I just chose it randomly when I was there. Apparently it is a sauce with tomatoes and hot peppers. All in all, I am looking forward to making more pasta!
I have been trying to spend less money lately in general so I think that I will be doing well now that I am settled. For breakfast, I have a few cereal bars (they were quite cheap at that store), for lunch, it is subsidized so that is cheap, and dinner will be cheap with the pasta. I will go out occasionally but not everyday like I was doing at the start of the trip.
Also I am not sure if I have talked about the lunch at work. So basically, around 12, the whole lab moseys over to the lunch area. There is typically a long line so we talk a bit. When you are in line, you pick up a tray and put various dishes on your plate. A typical lunch for me includes: a hot plate with a meat and rice or pasta, a small salad, some fruit, a dessert (I have gotten a variety of things such as fruit with pudding or a piece of pie), some cheese, and a roll or two of bread. I enjoy lunch very much and the food is subsidized for students so that all costs around 2.50 euros! It is cool how balanced the meals are here. You have a lot of small plates instead of just one large dish of food.
So thats about that. I haven't been sleeping too well so I should be getting to bed now. Yesterday, I stayed up late doing some GRE studying since I haven't been keeping up with my studying goals. I really felt it at work so I hope to get at least 7 hours of sleep tonight.
Just to summarize a few notable experiences,
Yesterday, I went with two other people on a "pasta-venture." My goal was to get a pan, pasta, and some toppings. We took the train and bus to a very large supermarket (called a hypermarche/). Carrefour is basically the French Walmart. It was a lot of fun to go around and see the all of the different food sections. There was a huge cheese section, a fish section, etc. Another cool area was the french book area. There were a lot of children's books. I spent about 15 minutes reading Winnie the Pooh (or Winnie l'Ourson). It was fun to read but I did not recognize some of the grammar structures. It was 10 euros so I didn't buy it but I do have fond memories of Winnie the Pooh from when I was younger! Another fun feature of the store is that they had moving walkways to go upstairs so you could take your shopping cart. The surrounding shopping center had these as well.
When I went to the checkout, apparently I almost bought a 50 euro pot. I also didn't weigh my bananas. So I was able to use my french to say no thanks. Apparently I misread the label for the pot and it actually cost 20 euros only if I bought 50 vignettes whatever that means. I was able to get another pot.
Another thing that I have been doing is that I have been trying different French cheeses. I have always eaten a lot of cheese and so it has been fun to explore different kinds. At my lunch, I have been getting a little cheese with each meal. I also bought some cheese from the store. So far, I have had Camembert, Brie, and Roquefort. The last cheese there is one of the moldy cheeses that is supposed to be quite strong but I thought it was tasty. Tomorrow, I hope to try Munster. I also bought "mimolette jeune". It looks like cheddar but I haven't tasted it yet. I hope to continue to try different french cheeses.
Tonight, I was successful in using my pot to cook pasta and I put some cheese on it (emmental). After looking this up, it is just what we refer to as Swiss cheese. I also got two other pasta sauces. One is a tomato sauce with Ricotta, and another is tomato sauce "basquaise" I just chose it randomly when I was there. Apparently it is a sauce with tomatoes and hot peppers. All in all, I am looking forward to making more pasta!
I have been trying to spend less money lately in general so I think that I will be doing well now that I am settled. For breakfast, I have a few cereal bars (they were quite cheap at that store), for lunch, it is subsidized so that is cheap, and dinner will be cheap with the pasta. I will go out occasionally but not everyday like I was doing at the start of the trip.
Also I am not sure if I have talked about the lunch at work. So basically, around 12, the whole lab moseys over to the lunch area. There is typically a long line so we talk a bit. When you are in line, you pick up a tray and put various dishes on your plate. A typical lunch for me includes: a hot plate with a meat and rice or pasta, a small salad, some fruit, a dessert (I have gotten a variety of things such as fruit with pudding or a piece of pie), some cheese, and a roll or two of bread. I enjoy lunch very much and the food is subsidized for students so that all costs around 2.50 euros! It is cool how balanced the meals are here. You have a lot of small plates instead of just one large dish of food.
So thats about that. I haven't been sleeping too well so I should be getting to bed now. Yesterday, I stayed up late doing some GRE studying since I haven't been keeping up with my studying goals. I really felt it at work so I hope to get at least 7 hours of sleep tonight.
Collecting thoughts on Research
My first attempt to calculate the phase from the simulated reflectivity data did not seem to work so I am going back and reading as much as I can. I am looking for ways to improve my calculation of phase.
I attempted to implement a method in matlab that integrated reflectivity data to get the phase but the results are not very good. (I took reflectivity data for every 0.1 eV (apparently this is typical for real data), created a function that interpolated those points into a smooth curve (I used a cubic spline), then I numerically integrated that using an adaptive simpson's rule routine. In order to handle the principal part integral, I removed a symmetric neighborhood of the singularity). For extrapolation, I assumed that the reflectivity was constant.
One problem: I am getting high reflectivity in regions where we wouldn't normally measure the reflectivity. I am looking at an aperiodic mirror from "Aperiodic multilayer mirrors for efficient broadband reflection
in the extreme ultraviolet". So there is reflectivity of about 0.15 in a wide region (30-80 eV) where the mirror was optimized, but there is also another peak near 10 to 20 eV. I am not sure if this is due to bad optical constants, or if this is just how their calculation worked out. Anyways this may be causing problems in my integration (and my way of extrapolating the reflectivity to low frequencies is not going to work)
So I looked at a lot of papers today. There is a ton of work that has been done in the area of using the KK relations. Here is a summary of things to do / things that I am thinking about:
1. learn more optics
a. how is the reflection coefficient derived from known constants for a multi-layer (maybe this would help me understand where the zero reflectivity points are)
b. does the reflectivity coefficient have zeros in the complex frequency plane (how can I predict their position... eg. the dielectric function for a semi-infinite substrate has its only zeros on the imaginary axis)
c. qualitatively, what is the reflectivity of a multilayer for high frequency/low frequency (so I can extrapolate correctly)
d. what effect does polarization, angle of incidence have on the calculations that I am doing?
e. is there a relationship between the complex reflectivity coefficient and the complex dielectric function
2. Kramers-Kronig relationship
a. which representation should I be using
i. real and imaginary part of a boundary condition for an analytic function are related by the Hilbert transform
ii. the transformation can be done as two Fourier transforms
b. zeros of reflectivity (for complex frequency) give rise to singularities in the integral above and result in extra terms being needed in the transformation
c. how is this derived? how can one use causality to show that reflectivity as a function of a complex variable is analytic?
3. Using matlab to do the hilbert transform numerically (there are MANY papers on this subject)
a. use of gaussian quadrature method (write integral as INT w(x) p(x) where w(x) is the weight function log x^(-1)... this may require a different program as you need high precision arithmetic for large numbers of sample points
b. write the transform of a sequence of fourier transforms and approximate as a discrete fourier transform (cooley-turkey algorithm?)
c. look into algorithms that allow one to isolate the zeros of the reflectivity as a function of a complex variable (eg. find the blaschke factors that are needed to recover a function that has singularities when it is fourier transformed...one paper suggests using transmission data?)
d. look into methods that acceleration of convergence of the integral by knowing the phase (eg. multiply subtractive KK method)
Anyways, I feel like there is SO much that I can do at the moment.
I attempted to implement a method in matlab that integrated reflectivity data to get the phase but the results are not very good. (I took reflectivity data for every 0.1 eV (apparently this is typical for real data), created a function that interpolated those points into a smooth curve (I used a cubic spline), then I numerically integrated that using an adaptive simpson's rule routine. In order to handle the principal part integral, I removed a symmetric neighborhood of the singularity). For extrapolation, I assumed that the reflectivity was constant.
One problem: I am getting high reflectivity in regions where we wouldn't normally measure the reflectivity. I am looking at an aperiodic mirror from "Aperiodic multilayer mirrors for efficient broadband reflection
in the extreme ultraviolet". So there is reflectivity of about 0.15 in a wide region (30-80 eV) where the mirror was optimized, but there is also another peak near 10 to 20 eV. I am not sure if this is due to bad optical constants, or if this is just how their calculation worked out. Anyways this may be causing problems in my integration (and my way of extrapolating the reflectivity to low frequencies is not going to work)
So I looked at a lot of papers today. There is a ton of work that has been done in the area of using the KK relations. Here is a summary of things to do / things that I am thinking about:
1. learn more optics
a. how is the reflection coefficient derived from known constants for a multi-layer (maybe this would help me understand where the zero reflectivity points are)
b. does the reflectivity coefficient have zeros in the complex frequency plane (how can I predict their position... eg. the dielectric function for a semi-infinite substrate has its only zeros on the imaginary axis)
c. qualitatively, what is the reflectivity of a multilayer for high frequency/low frequency (so I can extrapolate correctly)
d. what effect does polarization, angle of incidence have on the calculations that I am doing?
e. is there a relationship between the complex reflectivity coefficient and the complex dielectric function
2. Kramers-Kronig relationship
a. which representation should I be using
i. real and imaginary part of a boundary condition for an analytic function are related by the Hilbert transform
ii. the transformation can be done as two Fourier transforms
b. zeros of reflectivity (for complex frequency) give rise to singularities in the integral above and result in extra terms being needed in the transformation
c. how is this derived? how can one use causality to show that reflectivity as a function of a complex variable is analytic?
3. Using matlab to do the hilbert transform numerically (there are MANY papers on this subject)
a. use of gaussian quadrature method (write integral as INT w(x) p(x) where w(x) is the weight function log x^(-1)... this may require a different program as you need high precision arithmetic for large numbers of sample points
b. write the transform of a sequence of fourier transforms and approximate as a discrete fourier transform (cooley-turkey algorithm?)
c. look into algorithms that allow one to isolate the zeros of the reflectivity as a function of a complex variable (eg. find the blaschke factors that are needed to recover a function that has singularities when it is fourier transformed...one paper suggests using transmission data?)
d. look into methods that acceleration of convergence of the integral by knowing the phase (eg. multiply subtractive KK method)
Anyways, I feel like there is SO much that I can do at the moment.
Monday, June 6, 2011
matlab fatlab?
So I am at work again and I am going to write a few thoughts: Phase can be calculated from reflectivity using the the integral
phi(E)= -1/pi int 0 to infinity ln R(X/E) / (X^2 -1) dX (this is understood to be a principal part integral)
So the main issues for me are as follows:
1. We only know the function R for a limited range so we need to extrapolate it for other values of energy (frequency). For the moment, I am just assuming that R is constant outside that range. I do not know if this a reasonable assumption or how to go about saying what the reflectivity is for large frequencies.
For large frequency, I get the error as Log(R_infinity)/(2 Pi) Log | ( Emax-E)/(Emax+E) |
For small frequency, Log(R_0)/(2 Pi) Log | (E-Emin)/(E+Emin)|
R_infinity = R(E_max)
R_0=R(E_min)
2. I have to find an appropriate method of discretizing the integral that takes into account that we need to take a principal part integral.
2a. For the moment, I am using a right-side riemann sum. Perhaps I will implement simpson's rule. The disadvantage of the latter method is that it assumes equal spacing so I cannot see if the large spacing is the issue.
2b. Say we want to estimate the phase for a frequency omega. Then we need to know the reflectivity very precisely near omega. However, from what I hear from the lab, the reflectivity is measured every 0.2 eV, which I do not think is accurate enough.
Anyways, so I spent most of today trying to get the phase to predict more accurately. I had an idea that would let me integrate over the singularity. Basically, I just wanted to subtract the singularity out around a small symmetric neighborhood. This contributes nothing to the principal part integral but removes the singularity. This seemed fine but when I went to try and integrate this new function, I spent probably 3 hours trying to figure out how to get matlab to integrate this. This was pretty frustrating for me because I could have done this in 15 mins in mathematica but my lab does not use that program. I understand that this is just something that I will learn in time but I don't like having work go so slowly like this. I eventually asked one of the guys that I work with a few questions that I was able to figure it out. The main idea is that many functions need to be able to handle a vector input. I also didn't realize that when you write equations, you need to allow for vectors to work as well.
phi(E)= -1/pi int 0 to infinity ln R(X/E) / (X^2 -1) dX (this is understood to be a principal part integral)
So the main issues for me are as follows:
1. We only know the function R for a limited range so we need to extrapolate it for other values of energy (frequency). For the moment, I am just assuming that R is constant outside that range. I do not know if this a reasonable assumption or how to go about saying what the reflectivity is for large frequencies.
For large frequency, I get the error as Log(R_infinity)/(2 Pi) Log | ( Emax-E)/(Emax+E) |
For small frequency, Log(R_0)/(2 Pi) Log | (E-Emin)/(E+Emin)|
R_infinity = R(E_max)
R_0=R(E_min)
2. I have to find an appropriate method of discretizing the integral that takes into account that we need to take a principal part integral.
2a. For the moment, I am using a right-side riemann sum. Perhaps I will implement simpson's rule. The disadvantage of the latter method is that it assumes equal spacing so I cannot see if the large spacing is the issue.
2b. Say we want to estimate the phase for a frequency omega. Then we need to know the reflectivity very precisely near omega. However, from what I hear from the lab, the reflectivity is measured every 0.2 eV, which I do not think is accurate enough.
Anyways, so I spent most of today trying to get the phase to predict more accurately. I had an idea that would let me integrate over the singularity. Basically, I just wanted to subtract the singularity out around a small symmetric neighborhood. This contributes nothing to the principal part integral but removes the singularity. This seemed fine but when I went to try and integrate this new function, I spent probably 3 hours trying to figure out how to get matlab to integrate this. This was pretty frustrating for me because I could have done this in 15 mins in mathematica but my lab does not use that program. I understand that this is just something that I will learn in time but I don't like having work go so slowly like this. I eventually asked one of the guys that I work with a few questions that I was able to figure it out. The main idea is that many functions need to be able to handle a vector input. I also didn't realize that when you write equations, you need to allow for vectors to work as well.
Sunday, June 5, 2011
Visiting the Louvre and More Wanderings
The Louvre was AMAZING!! There is a seemingly endless collection of treasures. Further, the building that houses these masterpieces is equally as amazing. I wish that I know much more about the history. After going to the Centre Pompidou, it is so clear in my mind that modern art is nothing compared to the art here. There were so many sculptures and paintings that captured intensity and emotion. One of my favorite sculptures depicted a lion biting a man's leg. You could see the ferocity of the lion it his eyes and the fear in the man whose leg was getting devoured. Their entangled bodies captured the intensity of the fight. It is hard for me to see anything close to that in the art that I saw at the modern art museum.
It was impossible to appreciate everything at the Louvre. I hope to return sometime. Each tiny piece of art is the result of many hours or even years of careful craftsmanship. Further, there is a huge history behind all of the art. I was disappointed that all of the descriptions of the art were in French that was too complicated for me to understand.
This visit also makes me feel like it is somewhat pointless to visit a whole bunch of countries. There is so much to do in Paris. Seeing the details in the French culture is much more satisfying to me than rushing through a bunch of tourist attractions in other countries.
We decided to go to lunch outside the louvre to save some money. We ended up going to another street that was even move expensive. We looked at a BMW store and Louis Vuitton. The prices were so outrageous there. There was a not so fantastic looking handbag that was 25,000 euros!! I am really disgusted with anybody who buys things like that. There are so many other things that could use that kind of money. I tried to take pictures but they did not like that too much. After that, we came back to the Louvre but the line to get back in literally stretched a fourth of a mile. So we just wandered around for a bit.
It is hard to keep up with the blog because so much is going on. In other news, yesterday, I spent most of the day studying while the others went out. I felt pretty good about this because I got a fair amount done.
Also here are some pictures that I took at centre pompidou (modern art) and of cite universitaire (the place that I am living now).
Centre Pompidou and Cite Universitaire
http://www.facebook.com/media/set/?set=a.2159398021917.2101909.1155513641&l=c959a8756b
It was impossible to appreciate everything at the Louvre. I hope to return sometime. Each tiny piece of art is the result of many hours or even years of careful craftsmanship. Further, there is a huge history behind all of the art. I was disappointed that all of the descriptions of the art were in French that was too complicated for me to understand.
This visit also makes me feel like it is somewhat pointless to visit a whole bunch of countries. There is so much to do in Paris. Seeing the details in the French culture is much more satisfying to me than rushing through a bunch of tourist attractions in other countries.
Louvre (see picture descriptions for more detail about my day):
http://www.facebook.com/media/set/?set=a.2159452143270.2101910.1155513641&l=f431ca771c
We decided to go to lunch outside the louvre to save some money. We ended up going to another street that was even move expensive. We looked at a BMW store and Louis Vuitton. The prices were so outrageous there. There was a not so fantastic looking handbag that was 25,000 euros!! I am really disgusted with anybody who buys things like that. There are so many other things that could use that kind of money. I tried to take pictures but they did not like that too much. After that, we came back to the Louvre but the line to get back in literally stretched a fourth of a mile. So we just wandered around for a bit.
It is hard to keep up with the blog because so much is going on. In other news, yesterday, I spent most of the day studying while the others went out. I felt pretty good about this because I got a fair amount done.
Also here are some pictures that I took at centre pompidou (modern art) and of cite universitaire (the place that I am living now).
Centre Pompidou and Cite Universitaire
http://www.facebook.com/media/set/?set=a.2159398021917.2101909.1155513641&l=c959a8756b
Friday, June 3, 2011
Some feelings while in Paris
One thing that I wanted to blog a bit about was my mood. When we started the program, they showed us the happiness curve. It starts out erratic, then you go through a period of happiness due to being in new surroundings. Then there is a low when you start missing home and eventually, you get acclimated to the new country and it is similar to other places.
Anyways, I would say that I am in the erratic stage now. For the most part, I have been having a great time with seeing all that there is to see in France. I enjoy seeing the city but more importantly I have enjoyed interacting with French people. Too bad that I don't have time to do some type of French class. I feel like I am solidifying my French knowledge but I am not learning that many new things. But one thing that has been getting to me a bit is that I do feel like is that my social situation is unstable and that I have to put a lot of effort into that.
One example is that when we are in a group, I feel like I need to be loud otherwise my voice gets drowned out. In general, I am a person who likes to talk to people one on one. I feel like I have had good small group conversations with people but in the larger group I am sometimes quiet. This is not that different from other parts of my life but I do wish that I was more dynamic in a group setting at times. I remember one particular instance where some of us went out to rue de mouffetard and I was just quiet and I didn't feel like I had a good way to break into the conversation. For some reason, I was not in a very good mood.
One thing that is somewhat related is that I am not sleeping particularly well (I am averaging around 7 hours). I anticipated this earlier in the trip but now that it is happening, I am not sure that I am going to do much about it. When I am tired, I am less likely to speak up.
Looking at how I've been feeling, it is a bit strange that I have been so concerned with these small social issues. In the past, these things have not been on my mind. One aspect of it for me is that I feel like my relationships with the people on this trip are changing quickly (I know a few people that I have changed the way that I am acting around them a lot since the start of the trip). The main insecurity for me is that I don't want to feel like I don't have anybody to go around with.
In a related note, I have to be very careful with how I manage my time. I have been devoting a lot of time to social activities. I am taking the GRE general test on the 27th so I really do need to study for that more than I have been doing. I also feel that I haven't quite been doing as much as I could be on my research. One of the things that I have noticed is that it takes us a really long time to get dinner and I do not get that much done during the evenings. I think that until the 27th, I need to not be going out most of the time. I have some reservations about doing this because of the social issues that I mentioned above. I am glad that I chose that date though because I can then just be done with all of that and enjoy the rest of the summer.
In a bit unrelated note, I have noticed that I really do enjoy a bit of alone time. Tonight, I just sifted through my emails and watched a few starcraft videos. This was relaxing for me and I do like to have time with my thoughts. We are always running around and I think that it is great to have some personal relaxing time.
As always, there is way too much for me to talk about. Next time, I will talk more about my travels in the past few days and some things about research. Hopefully I get to do a practice GRE tomorrow morning...
Anyways, I would say that I am in the erratic stage now. For the most part, I have been having a great time with seeing all that there is to see in France. I enjoy seeing the city but more importantly I have enjoyed interacting with French people. Too bad that I don't have time to do some type of French class. I feel like I am solidifying my French knowledge but I am not learning that many new things. But one thing that has been getting to me a bit is that I do feel like is that my social situation is unstable and that I have to put a lot of effort into that.
One example is that when we are in a group, I feel like I need to be loud otherwise my voice gets drowned out. In general, I am a person who likes to talk to people one on one. I feel like I have had good small group conversations with people but in the larger group I am sometimes quiet. This is not that different from other parts of my life but I do wish that I was more dynamic in a group setting at times. I remember one particular instance where some of us went out to rue de mouffetard and I was just quiet and I didn't feel like I had a good way to break into the conversation. For some reason, I was not in a very good mood.
One thing that is somewhat related is that I am not sleeping particularly well (I am averaging around 7 hours). I anticipated this earlier in the trip but now that it is happening, I am not sure that I am going to do much about it. When I am tired, I am less likely to speak up.
Looking at how I've been feeling, it is a bit strange that I have been so concerned with these small social issues. In the past, these things have not been on my mind. One aspect of it for me is that I feel like my relationships with the people on this trip are changing quickly (I know a few people that I have changed the way that I am acting around them a lot since the start of the trip). The main insecurity for me is that I don't want to feel like I don't have anybody to go around with.
In a related note, I have to be very careful with how I manage my time. I have been devoting a lot of time to social activities. I am taking the GRE general test on the 27th so I really do need to study for that more than I have been doing. I also feel that I haven't quite been doing as much as I could be on my research. One of the things that I have noticed is that it takes us a really long time to get dinner and I do not get that much done during the evenings. I think that until the 27th, I need to not be going out most of the time. I have some reservations about doing this because of the social issues that I mentioned above. I am glad that I chose that date though because I can then just be done with all of that and enjoy the rest of the summer.
In a bit unrelated note, I have noticed that I really do enjoy a bit of alone time. Tonight, I just sifted through my emails and watched a few starcraft videos. This was relaxing for me and I do like to have time with my thoughts. We are always running around and I think that it is great to have some personal relaxing time.
As always, there is way too much for me to talk about. Next time, I will talk more about my travels in the past few days and some things about research. Hopefully I get to do a practice GRE tomorrow morning...
More Paris
So there are just way too many things to talk about so I will try to be brief. We moved into our new living area, "Cite universitaire". The goal of this place is to house international students studying in Paris. Most of the major countries have a house. We live in the German house. The room is somewhat bare bones. We have to walk down the hallway to go to the bathroom and shower. I have never lived in dorm like this but it will not be that big a deal. Honestly, I hope to spend as little time as possible in the room. The cite universitaire campus is really nice. I have taken a lot of pictures of the different buildings. There is also a lot of open space for relaxing or playing sports.
Yesterday, we went to centre pompidou. I am not a big fan of modern art but it was fun to see. One trend that seemed new to me is that the modern art pieces included sound as well as visuals. One of my favorite pieces involved a bunch of mirrors hanging down from the wall and the way that they were situated allowed for you to see multiple images of yourself. I enjoyed reading some of the descriptions of the art work. One of the funniest was something along the lines of: this artist's trademark is to paint alternating white and colored stripes that are approximately 8.7 cm. Then the piece of art was just a wall painted in stripes. But I suppose if this guy can tell a good enough story to sell his art, good for him.
Another cool thing that I did was that I played some frisbee with french people at Cite. They were very nice to me and allowed me to play. They didn't speak very much english but we got along fine. They invited me to play with them again (they play every thursday evening). In the near future, I hope to go around and talk to more people at Cite. The people there are especially friendly.
Another interesting thing is that Thursday was a holiday so most French people take Friday off as well. There are not that many people in the lab and most of the eateries in the area where I work were closed.
Anyways, onto research:
I feel a bit intimidated by my project because I feel that there has been a lot of work done on it already. However, I know that isn't the correct attitude so I will continue to read more papers. Even if I don't get any results, I think that I will learn how to make progress on a difficult problem. For now, I am playing around with matlab because I want to use some simulated data. I prefer using mathematica but knowing how to use matlab would be a good skill for me to have. I have spent most of the day wrestling with matlab. At the moment, my goal is to write matlab code that allows me to convert simulated reflectivity data into phase data. I can compare this phase data with simulated phase data. So far, my results are not that good but that is not much of a surprise.
Yesterday, we went to centre pompidou. I am not a big fan of modern art but it was fun to see. One trend that seemed new to me is that the modern art pieces included sound as well as visuals. One of my favorite pieces involved a bunch of mirrors hanging down from the wall and the way that they were situated allowed for you to see multiple images of yourself. I enjoyed reading some of the descriptions of the art work. One of the funniest was something along the lines of: this artist's trademark is to paint alternating white and colored stripes that are approximately 8.7 cm. Then the piece of art was just a wall painted in stripes. But I suppose if this guy can tell a good enough story to sell his art, good for him.
Another cool thing that I did was that I played some frisbee with french people at Cite. They were very nice to me and allowed me to play. They didn't speak very much english but we got along fine. They invited me to play with them again (they play every thursday evening). In the near future, I hope to go around and talk to more people at Cite. The people there are especially friendly.
Another interesting thing is that Thursday was a holiday so most French people take Friday off as well. There are not that many people in the lab and most of the eateries in the area where I work were closed.
Anyways, onto research:
I feel a bit intimidated by my project because I feel that there has been a lot of work done on it already. However, I know that isn't the correct attitude so I will continue to read more papers. Even if I don't get any results, I think that I will learn how to make progress on a difficult problem. For now, I am playing around with matlab because I want to use some simulated data. I prefer using mathematica but knowing how to use matlab would be a good skill for me to have. I have spent most of the day wrestling with matlab. At the moment, my goal is to write matlab code that allows me to convert simulated reflectivity data into phase data. I can compare this phase data with simulated phase data. So far, my results are not that good but that is not much of a surprise.
Wednesday, June 1, 2011
Another Day of Research
So I am really getting started on my research. I am pleased that I will be doing a challenging project. To review, there is a mathematical relationship between the reflectivity and the delay (phase delay) of a mirror. Strictly speaking, this relationship requires that we know the reflectivity for all frequencies in order to determine the phase for a particular frequency. As it is not practical to measure the reflectivity for all phases, I am looking to approximate that relation so that the reflectivity only needs to be measured over a band. Also our lab builds mirrors by making layers of different metals. The lab uses a matlab program to optimize the depths of the layers. I am interested in learning how this program works.
Things to do:
1. continue to try to understand papers given to me and look at other papers that I have found on this subject
2. understand the matlab code used to simulate the reflectivity (this is more of a personal goal)
2a. learn about the simulated annealing algorithm
3. use simulated reflectivity data to estimate phase
3a. understand better what typical reflectivity data looks like for multilayer mirrors and see where the major contributions come from in terms of the
Today, I continued to read over the papers that one of the professors gave me. Now I am going to be more specific. So given a mirror, we can define a complex number called reflectivity, r(omega). This is a function of frequency. The magnitude of this complex number is the amplitude of the reflected wave divided by the input amplitude. The phase of this complex number is equal to the phase delay of the pulse after it is reflected. So it turns out that defining a complex reflectivity in this way has a number of nice properties. This is somewhat obvious, but if we write the input pulse in complex number form, then to transform that pulse (in the frequency domain), we just multiply by the reflectivity. So if we have a pulse in the time domain, we just Fourier transform it, multiply by the reflectivity, and then inverse fourier transform.
The other property that is really nice is that r(omega) is an analytic function (we extend omega to allow for complex frequencies) except at isolated points for Im(omega)>0. I am not quite sure why this is so. It may be arguable due to "causality arguments" but I am not sure. Anyways, experimentally, it is relatively easy to calculate R(omega) := |r|^2. So we know the magnitude but not the phase. We do a bit of a trick, we note that f(w) = ln r(w) = (1/2) ln R(w)+i phi(w) where phi(w) denotes the phase as a function of frequency. Since r is an analytic function, so is its logarithm. Now we know that the real an imaginary parts of a complex analytic function are related. This relation involves an integral from w=0 to infinity.
The formula that lets us calculate the imaginary from the real part requires that the real part be well behaved. In general, this is not a valid assumption so we need to do some normalization procedures in order to make the integral converge. As far as I can see, doing this requires some general knowledge of the function. Ex. for a semi infinite medium, the reflectivity for large frequencies is a real constant. Here, the integral diverges as ln(constant not equal to 1) is nonzero. So we divide out this constant and use that normalized reflectance to calculate the phase. I will write more about this when I get to it.
Things to do:
1. continue to try to understand papers given to me and look at other papers that I have found on this subject
2. understand the matlab code used to simulate the reflectivity (this is more of a personal goal)
2a. learn about the simulated annealing algorithm
3. use simulated reflectivity data to estimate phase
3a. understand better what typical reflectivity data looks like for multilayer mirrors and see where the major contributions come from in terms of the
Today, I continued to read over the papers that one of the professors gave me. Now I am going to be more specific. So given a mirror, we can define a complex number called reflectivity, r(omega). This is a function of frequency. The magnitude of this complex number is the amplitude of the reflected wave divided by the input amplitude. The phase of this complex number is equal to the phase delay of the pulse after it is reflected. So it turns out that defining a complex reflectivity in this way has a number of nice properties. This is somewhat obvious, but if we write the input pulse in complex number form, then to transform that pulse (in the frequency domain), we just multiply by the reflectivity. So if we have a pulse in the time domain, we just Fourier transform it, multiply by the reflectivity, and then inverse fourier transform.
The other property that is really nice is that r(omega) is an analytic function (we extend omega to allow for complex frequencies) except at isolated points for Im(omega)>0. I am not quite sure why this is so. It may be arguable due to "causality arguments" but I am not sure. Anyways, experimentally, it is relatively easy to calculate R(omega) := |r|^2. So we know the magnitude but not the phase. We do a bit of a trick, we note that f(w) = ln r(w) = (1/2) ln R(w)+i phi(w) where phi(w) denotes the phase as a function of frequency. Since r is an analytic function, so is its logarithm. Now we know that the real an imaginary parts of a complex analytic function are related. This relation involves an integral from w=0 to infinity.
The formula that lets us calculate the imaginary from the real part requires that the real part be well behaved. In general, this is not a valid assumption so we need to do some normalization procedures in order to make the integral converge. As far as I can see, doing this requires some general knowledge of the function. Ex. for a semi infinite medium, the reflectivity for large frequencies is a real constant. Here, the integral diverges as ln(constant not equal to 1) is nonzero. So we divide out this constant and use that normalized reflectance to calculate the phase. I will write more about this when I get to it.
Tuesday, May 31, 2011
Some more Research Related Stuff
I will talk about a few things in this post: (1) Initial thoughts on my research project, (2) other things that I have been doing at work, and (3) some other reading that I have been doing that is optics related.
So the main idea of my project is as follows: say you have a mirror and you shine light at it. There are two things that happen. First, only a percentage of this light is reflected. Second, the light is delayed. The amount of reflection and delay differ for different frequencies (i.e. red light and blue light are reflected differently). It is easy to measure reflectivity but it is hard to measure delay. There is a (somewhat complicated) relationship between these two quantities. The issue is that to calculate delay from reflectivity, you must know the reflectivity for all different frequencies. My current understanding is that my goal is to approximate the delay using only some (but not all) knowledge of the reflectivity. (Ex. you might get a pretty accurate answer by just using the reflectivity data for visible light and not other frequencies like ultraviolet).
Overall, I am pleased with this project. It combines theory and experiment in a nice way for me. The approximations that I will need to make require me to both know a lot of math and understand the trends in the actual reflectivity data. The math that I have learned in the past year that is related to approximating integrals and integral transforms may be useful for my projection. Additionally, the approximations that I make will require me to understand the trends of the actual data. I will have to know what data can easily be measured and what areas cannot be neglected even if it would be mathematically convenient to do so.
Anyways, at my first real day of work. Franck introduced us to a program called IMD that simulates multilayer mirrors. For now, we are just looking at a periodic mirror of Mo and a-Si. We are varying the number of times we repeat layers of those two substances, the ratio of those two substances, the thickness of the period and the roughness (i.e. there is some error involved in making the mirrors so we introduce some error into the sizes of the layers). Then we are looking at the reflectivity as a function of wavelength. By bragg's law, we know that the maximum should be around double the period of the multilayer mirror.
Another thing that I noticed yesterday is that when you look at these plots, there is a maximum and the center, but then there are local maxima on the higher wavelength side of the global max. After playing around with this, I noticed that when you increase the number of layers, then the number of ripples increases. When you change the incidence angle, the ripples are on different sides of the central maximum. This isn't too important, but it was fun to play around with a bit. In order to see the ripples, you have to put the reflectivity on a log scale.
I also asked more about automating the process of using the program to simulate the multilayer mirrors. It would be nice to generate a reflectivity graph, then feed that result into a loop, and then adjust the layers with some method and then see what the new reflectivity would be. Apparently one of the people here made a program that simulates the reflectivity in matlab. Depending on the nature of my project, it might be worthwhile for me to either learn matlab or to learn how to make the program in mathematica.
After we played around with things, our professor came in and talked to us for a bit. I hope that he continues to check up on us and see how we are doing. He seems very knowledgable about the program that we were using. He also explained complex reflectivity to me. The idea is that if you have a light pulse that reflects off a surface, then you get the same frequency with a different amplitude and phase. It turns out that if you represent the incoming wave as a complex exponential, then the math works out nicely and when you divide the outgoing complex exponential by the incoming exponential, you get a complex number whose magnitude is the ratio of the amplitudes and the argument is the phase difference. This is an interesting representation.
I have been having so many experiences that I haven't had the time to talk about the physics related stuff that I have been doing. For the past few days, I have been taking some time to read a long paper on general attosecond physics. The main thing that it talked about was the specifics behind high harmonic generation and the simulated raman scattering schemes for generating short pulses. I focused more on the high harmonic generated because it seems like my lab is going to focus on that light in that range.
The other interesting things that I have been reading about involve measuring these attosecond pulses. Since they are so short, you need to generate new methods to measure them. One idea is streaking. So what I read about was that you have a light pulse and you send that through a photocathode. This knocks off electrons. Then you have a rapidly varying electric field and so the electrons excited by the start of the pulse are moved a different amount by the electric field than the electrons excited by the electric field later in the pulse. This converts the image of the pulse into electrons. The intensity of the pulse is measured through the number of electrons. I don't think that this can be done with attosecond pulses because a professor said that this is more useful on the order of picoseconds. I am not sure if there are streaking cameras that can measure attosecond pulses. However, apparently these apparatuses are very expensive.
The other stuff that I have been reading about is related to the methods of FROG and SPIDER. (Again we see the crazy acronyms that have become standard in this area of physics). FROG stands for frequency resolved optical gating. I don't really understand what this is doing, but here are some general ideas. This method splits the beam up into two parts. Then one can use mirrors so that the second pulse is delayed in a controlled fashion. Then the pulses are able to interact in a nonlinear medium. I asked the professor/researcher that has been showing me around about this.
So some things that he explained to me were as follows: There is a model of a medium where we consider the atoms like little oscillators. When you subject these oscillators to an external EM field, they oscillate with the same frequency as the field however there is a phase delay. These oscillators emit photons at the same frequency. Since this is happening over many little oscillators, this accumulated phase delay over a distance can just be thought of as the light pulse traveling slower in the medium. Then he proceeded to talk about in a nonlinear medium that at the start, the potential for an electron is parabolic as we might expect from a first order Taylor expansion but when we get into higher order terms, the potential becomes wider than one might expect. That is to say, if the external EM field has a high amplitude, then there is a nonlinear effect and there is an additional phase delay because the potential widens. So the idea here is that if the amplitude changes as a function of position, then the wave separates itself. Loosely speaking, you could imagine that if you have a known pulse and an unknown one, then when you put it through this nonlinear medium, you could deduce something about the unknown pulse based on how much it slows down.
The FROG says that given two split pulses where we vary the time delay, then we can find the autocorrelation of the original pulse. However, there is something additional that we can get that is more than an autocorrelation. The things that I do not understand are: what are we physically measuring when we do the frog experiment. I asked John a bit about this and he gave me the explanation above that vaguely, you can imagine that in a nonlinear medium, you get some terms that are the product of the electric fields instead of just the sum. Another thing that I don't understand is what information you can extract from the autocorrelation of an electric field.
There is also something called SPIDER. I need to read more about this, but the idea is that it is another method that is used to measure the pulses. One of the problems of these methods that some people have problems with is that you are using your own signal to probe the signal. All of these things are fuzzy in my head now but it seems that it isn't that important that I understand them for my project.
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