January 30, 2007
This documentary tells the trial of Brenton Butler, a 15 year-old black high school student who was arrested in Jacksonville, Florida, in 2000, for the murder of a tourist white woman. There is nothing special from a technical point of view about how the story is shown, in that respect the documentary feels like a larger version of the true crime series shown on Court TV.
Other than that, this is one of those stories that one should watch and think about. During the trial we see how the police did not appear to conduct anything resembling a serious investigation; Butler was arrested two hours after the crime, was intimidated and physically threatened into signing a confession and it mattered little that his family accounted for him at the time of the murder. Lacking almost any evidence, the officers involved in the case still insist on their conclusions, unwilling to admit a mistake. The victim’s husband’s visual identification of Butler is the only evidence the police has, and the defense attorneys also shed doubts on its accuracy.
Jean-Xavier de Lestrade, the director, specializes in documentaries about justice and what he calls societal taboos. Murder was awarded the Oscar for Best Documentary of 2001.
The Wikipedia page on the case has some updates.
January 30, 2007
All about Eve was awarded the Oscar for Best Picture of 1950, competing against Sunset Blvd. Both movies deal with similar topics; in both we see an ageing actress dealing with an industry that favors the young. While Sunset Blvd. deals directly with Hollywood, All about Eve sets the story within the theater industry. Anne Baxter plays Eve, a young woman who idolizes Margo Channing, the character played by Bette Davis. Marilyn Monroe has also a small role. Little by little we discover how Eve is unscrupulously setting herself as the next great actress, by lying to and manipulating Margo, her friends, and the press.
The script is excellent, the acting is spotless, and the final scene is unforgetably beautiful. The whole story is quite enjoyable. The only detail I didn’t like was how DeWitt, the theater critic, devolves in a crucial scene into a cartoon villain. Except for this, this is a subtle and carefully crafted movie, and even though I thoroughly enjoyed Sunset Blvd., it is not hard to see why Eve was favored by the Academy.
January 30, 2007
We concluded the proof that Matiyasevich sequences are Diophantine. This involved a delicate analysis of congruences satisfied by terms of these sequences.
It follows that exponentiation is Diophantine. Using exponentiation, we can now proceed to code finite sequences, the key idea behind both the proof of undecidability of the tenth problem and of the incompleteness theorems.
January 25, 2007
I enjoy Steven Soderbergh’s movies, overall. I think he is one of the few mainstream American directors who is constantly trying to innovate, to experiment, and being as prolific as he is, the results tend to be a treat. (There are a few exceptions, of course.)
The good German is shot as if it had been made in the late forties or early fifties. If nothing else, it is a good exercise in style, much more rewarding than remaking Psycho. The story, a noir, concerns an American, his German old flame, Berlin during the Postdam peace conference, and a lot of hypocrisy from almost everybody involved. There is an obvious homage to Casablanca at the end, which I found charming. The musical score works differently from how music is treated nowadays, it is much more present in the sense that it has a shape and a theme and it is almost another character, but it is not intrusive or distracting. Thanks to having watched Sunset Boulevard recently, and a few days later, All about Eve, this was clear to me, although music works differently in these films from how it does in The Good German. (I’ve also recently watched The cabinet of doctor Caligari and Nosferatu, where music plays yet a completely different role.) The camera angles and even the cameras used are in the style of the period, and swipe cuts to shift scenes are common.
Not just the style, but the story itself was interesting. It is clearly a contemporary movie in goals and narrative, with a more daring agenda than a film from the period would have been able to portray. As for the actors, it was very nice to contrast Cate Blanchett’s character with the one she plays in Notes on a scandal; Tobey Maguire plays a character very different from those I am used to seeing him play; and George Clooney was excellent, of course. Very good.
January 25, 2007
Douglas Bruce finds himself one day riding the subway in New York without knowing where he is going. In fact, he doesn’t know where he is, he doesn’t recognize any of the buildings. Panic sets in once he realizes he doesn’t know where he took the train, or even his own name. Doug suffers total amnesia, a rare condition in which one forgets everything about one’s life. Well, this is not exactly true: He knows how to talk, and when in the hospital someone asks him to sign, he remembers his signature. This strange and fascinating condition is explored in this documentary that uses footage shot by Doug himself and directed by his (former) friend Rupert Murray.
I found the documentary quite interesting, but I also found it wanting in several respects. Part of it may be due to the simple fact that we still know very little about how memory works, so surprisingly little time is devoted to hard data, to what may be happening—as for why it is happening, nobody knows. Some hypotheses are mentioned, and as the story progresses we get some clues. But part of the problem with the story I think is due to what I perceive as a shortcoming of the director: There are questions that do not get asked, some that beg to be asked, and why they are not seems to be because everybody is so fascinated by what is happening that they assume that filming it is enough. Part of it I think is due to the friendship between Doug and Mr. Murray. Mr. Murray seems to go out of his way to make Doug feel comfortable, while obviously the subject matter may make him uncomfortable. So, at the end of the day, I find the final product a bit awkward. There are a few extras in the DVD that leave me feeling the same (at least there is consistency); I missed (being in Vienna) the controversy on the veracity of the story, so the short section addressing it didn’t mean much to me. There is a long section explaining how a sequence was shot. I found it very curious that the director put so much thought into the visual look of the final product instead of trying to add a bit more substance to it.
I like explorations of memory, and mental problems intrigue me to no end. So this was a good movie overall. It complements well other documentaries in similar subjects, like anterograde amnesia, the disease that Memento popularized. I had the fortune of watching in 2004 an excellent documentary by Koreeda Hirokazu about one such case in Japan, Without memory.
January 25, 2007
Due Thursday, February 1 at 1:00 pm.
The second pdf contains some hints for problem 3.
January 25, 2007
The core of the proof of the undecidability of the tenth problem is the proof that exponentiation is Diophantine. We reduced this to proving that certain sequences given by second-order recurrence equations are Diophantine. These are the Matiyasevich sequences: For ,
for all .
We began the proof that they are Diophantine by analyzing some of the algebraic identities their terms satisfy.
- Unsolvable problems, by M. Davis. In Handbook of mathematical logic, J. Barwise, ed., North-Holland (1977), 567-594.
January 23, 2007
We reviewed the statements of the first, second and tenth problems of the list presented by Hilbert during the International Congress in 1900. The tenth problem (undecidability of Diophantine equations) will be our immediate focus. The goal is to show that any r.e. set is Diophantine. The undecidability of the halting problem will give the result. Then we will use this characterization as part of the proof of the incompleteness theorems.
Diophantine sets are closed under conjunction and disjunction. `Easy’ number theoretic relations and functions (e.g., being divisible by, the least common multiple) are Diophantine.
January 18, 2007
Due Thursday, January 25 at 1:00 pm.