It’s strange to look back and read my initial blog. It feels like I wrote it such a long time ago.The first was that I wanted to learn a lot of Italian. I must admit that for the longest time I felt like I was not reaching this goal, like I was not working hard enough. It’s only been in the past two or three weeks that I’ve really realized how much I’ve learn. My spelling is still horrible, I can’t remember the rules, I feel like as far as class goes I’m still confused, but when it comes to talking to people I understand a lot of what they say. It’s amazing how much I’ve habituated myself to hearing it. I can understand announcements in the train station, many of the questions people ask in shops or while they’re out, and mostly I am finding that I am finally understanding random little bits and pieces of people’s conversations. I have definitely progressed in Italian in a manner very different than I learned French or even the little bit of Spanish I know. I have appreciated having the ability to see just how much comes to you simply by listening and learning a few verbs. If I could do this trip over however, I would have studied some before I came.
The second was to learn about my Catholic heritage. I really have done this too. I know a lot more about the day to day practice of Catholicism than ever. However, I also have realized a lot about my own personal beliefs and how they relate. I share a lot of beliefs with Catholics. I already knew this to some extent but this trip has proven it even further. I’ve also been noticing how, as much as religion is a touchy subject for most people, it really isn’t for me. I really feel like I’ve heard it all before, as much as I think I might be too young to say that. People can be really insulting and I don’t even get upset. I guess I’m just to the point where I think people who say insulting things like that atheists have nothing to prevent them from committing murder are, well ,as wrong as someone who thinks that the Earth is flat. I’m beginning to find harsh, uneducated religious arguments amusing. Perhaps, I should be more alarmed, I’m not sure. I’ll certainly defend people who need defended. However, otherwise I think I’ll just let their boat sail off the edge of the Earth.
Apart from all that, I would say that I’m definitely more aware and comfortable with the person that I am. Travelling brings out a different side of people, and I’ve noticed things about myself that I’ve never noticed before. I guess most of these things are private but the basic just is I think I’m going to be even more mature after this. Ok, now that I’ve shared probably too much with everyone, all I can really say is grazie e arrivederci a Rome. This has definitely been the experience of a lifetime.
venerdì 9 ottobre 2009
More Fibonacci
Fibonacci sequence is one of life’s most interesting mathematical mysteries. The basic mathematical definition of the Fibonacci sequence is basically is that it starts with 0 and 1 and that every number after that equals the sum of the previous two numbers {0, 1, 1, 2, 3, 5, 8, 13, 21…}. The Fibonacci sequence is one of several recursive sequences, which means simply that it follows the rule that to get the next number one simply finds the sum of the previous two. The name Fibonacci comes from Leonardo Pisano Bigollo the son of Bonacci, a merchant trader with Africa. His most important contribution to mathematics was not the Fibonacci sequence that he is famous for; his greatest achievement was bringing Arabic Numerals to Europe. His father was a merchant and in Bigollo’s travels with him, he learned that Arabic Numerals functioned much better than Roman ones. Overtime, people remembered him only as the son of Bonacci or Fibonacci and not by his proper name which did not even have Bonacci in it. Fibonacci, although it was not the proper name was still the first mathematician to bring to light how the sequence reoccurred in nature.
The Fibonacci first noticed in the mating system of rabbits. Fibonacci noticed how rabbits multiplied and that the first month there would be 1 pair of rabbits, then the second month the female would be pregnant but there’d still only be 1 pair of rabbits. By the second month there would be 2 pairs of rabbits, the third month only one set of rabbits would be able to reproduce so there would only be 3 pairs of rabbits, so on and so on always following the sequence where a number would always add up to the previous two numbers. Since this discovery and actually even before it, mathematicians have found the Fibonacci sequence recurring in different places throughout nature.
It had been for a long time observed even in the doctrines of the Ancient Greeks, a certain aesthetically pleasing ratio that can be found in nature using the Fibonacci sequence. The ratio is formed by taken the current number over the previous number in the sequence {1/1, 2/1, 3/2, 5/3, 8/5…}. This sequence converges meaning that there is a single real number which the terms of this sequence approach more and more closely, eventually arbitrarily close. If we impose limits and assume that this sequence converges on a real number (this would be a fact that would require a proof). If we follow these rules we find that there is a simple quadratic equation to solve for x. or the golden ratio. Many things such as plant rings or the growth patterns of a snail shell fit in almost perfectly to this ratio. Even the sum of Pascal’s oblique triangles fits right into this pattern.
I think it was seeing that it fit into Pascal’s triangle that made me wonder, is this really a magical divine number for beauty or is it a sort of coincidence that these numbers follow this pattern. Another words, are these numbers simply golden because they are proportionate or is that not sufficient enough an explanation? There are some things that don’t fit the golden ratio, some flower’s petals do not fit the ratio perfectly. However, I guess I’ve never truly thought about whether everything has a mathematical explanation before or not. To me, if the very makings of the universe can somehow all be worked out into perhaps several mathematical sequences, well I’m not sure if I’d think that was divine or not. It remains amazing to me that everything from the Pantheon, to the works of Leonardo Di Vinci, to the United Nations building in New York used the golden ratio and the Fibonacci numbers in its creation.
The Fibonacci first noticed in the mating system of rabbits. Fibonacci noticed how rabbits multiplied and that the first month there would be 1 pair of rabbits, then the second month the female would be pregnant but there’d still only be 1 pair of rabbits. By the second month there would be 2 pairs of rabbits, the third month only one set of rabbits would be able to reproduce so there would only be 3 pairs of rabbits, so on and so on always following the sequence where a number would always add up to the previous two numbers. Since this discovery and actually even before it, mathematicians have found the Fibonacci sequence recurring in different places throughout nature.
It had been for a long time observed even in the doctrines of the Ancient Greeks, a certain aesthetically pleasing ratio that can be found in nature using the Fibonacci sequence. The ratio is formed by taken the current number over the previous number in the sequence {1/1, 2/1, 3/2, 5/3, 8/5…}. This sequence converges meaning that there is a single real number which the terms of this sequence approach more and more closely, eventually arbitrarily close. If we impose limits and assume that this sequence converges on a real number (this would be a fact that would require a proof). If we follow these rules we find that there is a simple quadratic equation to solve for x. or the golden ratio. Many things such as plant rings or the growth patterns of a snail shell fit in almost perfectly to this ratio. Even the sum of Pascal’s oblique triangles fits right into this pattern.
I think it was seeing that it fit into Pascal’s triangle that made me wonder, is this really a magical divine number for beauty or is it a sort of coincidence that these numbers follow this pattern. Another words, are these numbers simply golden because they are proportionate or is that not sufficient enough an explanation? There are some things that don’t fit the golden ratio, some flower’s petals do not fit the ratio perfectly. However, I guess I’ve never truly thought about whether everything has a mathematical explanation before or not. To me, if the very makings of the universe can somehow all be worked out into perhaps several mathematical sequences, well I’m not sure if I’d think that was divine or not. It remains amazing to me that everything from the Pantheon, to the works of Leonardo Di Vinci, to the United Nations building in New York used the golden ratio and the Fibonacci numbers in its creation.
mercoledì 7 ottobre 2009
Circe Transforms Picus into a Woodpecker
Unfortunately, I was unable to find a picture of this late 15th to early 16th century painting by Garofalo Ferrara, so it was difficult at best to find information on this blog. The most I could find were Italian websites, that did not have pictures and did not make sense when they were translated.
From what I could tell this painting was an excellant example of an early mistake in prospective drawing as there appear to be clear lines acrossed the pages going horizontally and not vanishing at all. The picture appears to be in rows up close, although the perspective appearance is fairly decent as you get further away. I would've thought this painting was fantastic had I not been looking for it. The error put it closer to our first attempts to draw vanishing points in my high school art class. It creates these layers that make it look very unrealistic.
Vanishing points was probably one of my favorite aspects from art class, however, I think in part because I cannot bring myself, for the most part, to critique artists who are doing a much better job than I would. I also found myself having trouble with the religious paintings because I spent along time debating how big babies or figures such as Jesus and the Virgin Mary should be. I lost track of the vanishing points.
From what I could tell this painting was an excellant example of an early mistake in prospective drawing as there appear to be clear lines acrossed the pages going horizontally and not vanishing at all. The picture appears to be in rows up close, although the perspective appearance is fairly decent as you get further away. I would've thought this painting was fantastic had I not been looking for it. The error put it closer to our first attempts to draw vanishing points in my high school art class. It creates these layers that make it look very unrealistic.
Vanishing points was probably one of my favorite aspects from art class, however, I think in part because I cannot bring myself, for the most part, to critique artists who are doing a much better job than I would. I also found myself having trouble with the religious paintings because I spent along time debating how big babies or figures such as Jesus and the Virgin Mary should be. I lost track of the vanishing points.
lunedì 5 ottobre 2009
We saw some unbelieveable artwork...
I’ve said before that I’ve decided that for the most part I agree with Leonardo Da Vinci, in the value of painting versus sculpting because you can do so much more with a painting than a sculpture. However, I am also someone who loves things with deep meaning, especially if that deep meaning is share by millions of people. It is for this reason, I think, that one of the most incredible statues we visited on this trip was the ancient bronze one of St. Peter in St. Peter’s Basilica in Vatican City.
The statue is of St. Peter sitting atop a marble see from the early renaissance, a tiara around his head, holding high the keys to the kingdom of Heaven and giving a blessing and preaching to those below. I sits upon an alabaster base that was executed by Carlo Marchionni in 1757. The statue is clothed in amice, alb, stole, red cope and a ring so that it practically seems to come to life. The most amazing thing is how worn down his right foot is from the centuries of pilgrims rubbing them. Pilgrims rubbed and kissed the foot of St. Peter praying that he’d be merciful and open the gates of Heaven to them if they died during the pilgrimage. Today, I’ve noticed the legend is changing as many guided tours come through the museum. People are saying that his right foot is good luck or to rub it for an important prayer. Many people rub his foot and pray that they will get into Heaven but I think that most people no longer consider dying during the pilgrimage as a serious option the way they would’ve during the Middle Ages. I walked up and touched the foot and you could feel its power. The thought of so many people praying and believing in what St. Peter’s statue represents is incredible to me.
Behind it, there is what appears to be a beautiful brocade draping but it is actually a mosaic. Above the mosaic is a portrait of Pope Pius IX, the first Pope in nineteen centuries to hold the throne longer than St. Peter himself. St. Peter held the throne for twenty-five years and Pope Pius IX reined for 31. Tradition holds that the mosaic and the portrait are insuperable from the statue. To me its amazing either of these men could’ve lived long enough for that. However, I never really thought that a Pope reining longer than St. Peter would make him noteworthy enough to get his portrait directly behind St. Peter’s statue. I would imagine that after nineteen centuries people were beginning to think twenty-five years was the Divine limit.
A great mystery also surrounds the statue relating to who created it, as well as the epoch in which it was created. Datings range from as early as the fourth century and as late as the fourteenth century. Tradition has it that the statue was commissioned by St. Leo the Great as a token of gratitude for defeating Attila. This legend also says that the statue was made of the metal from a previous statue made by Giove Capitolino. In reality however, the oldest historical information on the work only dates back to the fifteenth. Currently, it is almost the unanimous opinion of historians that the author of the statue is more likely than not Arnolfo di Cambio(c. 1300) the artist who created the tabernacles of St. Paul and St. Cecilia, and the sacellum of Bonifacius VIII in the Constantinian Basilica. The snail like curls of the hair and beard are found in famous Arnolfian works and match thirteenth century Classicism.
Overall I found the whole of St. Peter’s Basilica to be absolutely incredible. I loved having the opportunity to see the Cathedral that is the most important in all of Catholicism. This statue is, of course, one of the most important works of art in the entire basilica. However, I find it amazing how everything in the Basilica has its own legend and story. Everything from the keys, to the tiara, to the picture behind the statue has its own history and symbolism. The year the statue was made really isn’t that important, it’s the energy behind it that is absolutely incredible.
The statue is of St. Peter sitting atop a marble see from the early renaissance, a tiara around his head, holding high the keys to the kingdom of Heaven and giving a blessing and preaching to those below. I sits upon an alabaster base that was executed by Carlo Marchionni in 1757. The statue is clothed in amice, alb, stole, red cope and a ring so that it practically seems to come to life. The most amazing thing is how worn down his right foot is from the centuries of pilgrims rubbing them. Pilgrims rubbed and kissed the foot of St. Peter praying that he’d be merciful and open the gates of Heaven to them if they died during the pilgrimage. Today, I’ve noticed the legend is changing as many guided tours come through the museum. People are saying that his right foot is good luck or to rub it for an important prayer. Many people rub his foot and pray that they will get into Heaven but I think that most people no longer consider dying during the pilgrimage as a serious option the way they would’ve during the Middle Ages. I walked up and touched the foot and you could feel its power. The thought of so many people praying and believing in what St. Peter’s statue represents is incredible to me.
Behind it, there is what appears to be a beautiful brocade draping but it is actually a mosaic. Above the mosaic is a portrait of Pope Pius IX, the first Pope in nineteen centuries to hold the throne longer than St. Peter himself. St. Peter held the throne for twenty-five years and Pope Pius IX reined for 31. Tradition holds that the mosaic and the portrait are insuperable from the statue. To me its amazing either of these men could’ve lived long enough for that. However, I never really thought that a Pope reining longer than St. Peter would make him noteworthy enough to get his portrait directly behind St. Peter’s statue. I would imagine that after nineteen centuries people were beginning to think twenty-five years was the Divine limit.
A great mystery also surrounds the statue relating to who created it, as well as the epoch in which it was created. Datings range from as early as the fourth century and as late as the fourteenth century. Tradition has it that the statue was commissioned by St. Leo the Great as a token of gratitude for defeating Attila. This legend also says that the statue was made of the metal from a previous statue made by Giove Capitolino. In reality however, the oldest historical information on the work only dates back to the fifteenth. Currently, it is almost the unanimous opinion of historians that the author of the statue is more likely than not Arnolfo di Cambio(c. 1300) the artist who created the tabernacles of St. Paul and St. Cecilia, and the sacellum of Bonifacius VIII in the Constantinian Basilica. The snail like curls of the hair and beard are found in famous Arnolfian works and match thirteenth century Classicism.
Overall I found the whole of St. Peter’s Basilica to be absolutely incredible. I loved having the opportunity to see the Cathedral that is the most important in all of Catholicism. This statue is, of course, one of the most important works of art in the entire basilica. However, I find it amazing how everything in the Basilica has its own legend and story. Everything from the keys, to the tiara, to the picture behind the statue has its own history and symbolism. The year the statue was made really isn’t that important, it’s the energy behind it that is absolutely incredible.
domenica 4 ottobre 2009
Four Rivers
I found Gian Lorenzo Bernini’s Fountain of the Four Rivers to be one of his more intriguing works. The Fountain of the Four Rivers is world renowned and found in the Piazza Navona in Rome. The fountain is of considerable size and is the central fountain in the piazza. This is mainly because it incorporates the central Egyptian Obelisk. The fountain incorporates a god representing four rivers from 4 continents. The Ganges represents Asia, the Nile for Africa, the Danube for Europe, and the Rio de la Plata for the Americas. Each carries traits that are metaphors and allegories such as the Nile’s head being drape in a cloth showing how no one at the time knew where the head of the river was.
This Fountain also has a very interesting historical background. First, this fountain was designed by Bernini for a competition he was never invited to enter. He had made his share of enemies and someone made sure the Pope did not invite Bernini to enter. A prince whose wife was the Pope’s niece persuaded Bernini to enter the contest anyway. When his design was unveiled in a place where the Pope could see it, Bernini’s rivals could not persuade Pope Innocent X away. This fountain was also built at the people’s expense at a time when bread was scarce. The people wanted the money to go to food instead of beautiful fountains. Of course, decent was dealt with in the usual fashion, the Pope had the writers who spoke out against him arrested. Overall, I enjoyed the Bernini tour despite my tired legs from our tours from the previous day. This was well worth it.
This Fountain also has a very interesting historical background. First, this fountain was designed by Bernini for a competition he was never invited to enter. He had made his share of enemies and someone made sure the Pope did not invite Bernini to enter. A prince whose wife was the Pope’s niece persuaded Bernini to enter the contest anyway. When his design was unveiled in a place where the Pope could see it, Bernini’s rivals could not persuade Pope Innocent X away. This fountain was also built at the people’s expense at a time when bread was scarce. The people wanted the money to go to food instead of beautiful fountains. Of course, decent was dealt with in the usual fashion, the Pope had the writers who spoke out against him arrested. Overall, I enjoyed the Bernini tour despite my tired legs from our tours from the previous day. This was well worth it.
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