A Mind for Madness

Musings on art, philosophy, mathematics, and physics


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Economics Anyone?

Maybe I’ve been reading too much Pynchon, and the paranoia is starting to set in, but is anyone else in conspiracy theory mode right now? I usually laugh off conspiracy theories, because people have to pull in all sorts of random tiny details from all over to try to get their theory to work. In this case, it is just blatantly in our faces.

Think about the timing for this economic crisis to happen. Think about it. If this is not some sort of crazy conspiracy designed for some reason, then it is without a doubt the most amazing coincidence I’ve ever experienced.

What are some reasons someone might design this? I think the most plausible is that the Republicans have basically spent 8 years making themselves look completely incompetent. Now they need to get re-elected somehow. What is a good way to do that? Well, right before the election there should be an economic crisis, then the Republicans draw up this great (i.e. lousy) solution and save the day restoring some hope that they can do something right. Luckily by the time we realize it is was not a solution at all, the election will be long over.

Unforeseen catch: The House doesn’t play along because the proposed solution is crap.

Another less likely possibility is that they somehow need to take the pressure off Palin. Divert the attention of the voter to the fact that this person is probably the most ignorant and unintelligent person in all of American history to be considered for one of the top two positions. This possibility isn’t as likely, since it is such short notice and possibility 1 allows for a good two years of planning this.

Thoughts on the timing? Coincidence or no?


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Zeros of Analytic Functions

A strange property of analytic functions is that the zeros are isolated. I don’t remember the proof I originally learned of this fact, but today I saw a really interesting topological way to do it. It makes sense now.

More precise formulation: If \Omega\subset\mathbb{C} is a connected open set, then \{z: f(z)=0\} consists of isolated points if f is analytic on \Omega. (Oops, I started writing this up and realized that I need to trivially throw out the case where f\equiv 0.

Proof: Let U_1=\{a\in\Omega : \exists\delta>0, \ f(z)\neq 0 \ on \ 0<|z-a|<\delta\} and let U_2=\{a\in\Omega : \exists\delta>0, \ f(z)\equiv 0 \ on \ 0<|z-a|<\delta \}. Reformulating the setup we see that U_1 means: if f has a zero, it is isolated since f is nonzero on a punctured disk (meaning the zero must be the punctured part). Also U_2 is just the regions that f has non-isolated zeros.

It is straightforward to check that both U_1 and U_2 are open (just choose \delta‘s sufficiently small to stay inside the declared sets). Also we have that U_1\cap U_2=\emptyset and I now claim \Omega=U_1\cup U_2.

This seems obvious, but should be pinned down in some sort of argument. Let z_0\in\Omega. We claim that there is a punctured disk about z_0 such that either f\equiv 0 on the disk or f\neq 0 anywhere on the disk. By analyticity, we have a power series convergent on some radius r>0 about z_0, i.e. f(z)=\sum_{n=0}^\infty a_n(z-z_0)^n on |z-z_0|<r.

Suppose a_k is the first nonzero coefficient (by not being equivalently zero, this must exist). Then f(z)=\sum_{n=0}^\infty a_{n+k}(z-z_0)^n=(z-z_0)^{-k}\sum_{n=k}a_n(z-z_0)^n. So since the series converges in 0<|z-z_0|<r and since f is continuous we can choose 0<\delta<r small enough so that |f(z)-f(z_0)|=|f(z)-a_k|<\frac{|a_k|}{2}. This clearly shows that f(z)\neq 0 on 0<|z-z_0|<\delta else we’d have |a_k|<\frac{|a_k|}{2}. So either there is a punctured disk on which f is non-zero, or the f has no first non-zero coefficient making it zero everywhere on that first disk |z-z_0|<r proving the claim.

The properties U_1\cap U_2=\empty and \Omega=U_1\cup U_2 (along with both sets being open) combine to give that either U_1=\emptyset or U_2=\emptyset by the connectedness of \Omega. This simply means that all the zeros are isolated since we ruled out the alternative of being equivalently zero.

This goes to show how remarkably different analytic on \mathbb{C} is to continuous on \mathbb{R}. In fact, even infinitely differentiable functions on \mathbb{R}. Bump functions play a crucial role in many areas of analysis and they are smooth functions with compact support meaning that outside of a bounded they are zero. An entire class of important functions violates this property that analytic functions are guaranteed to have.


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SSS 4

This is bad when I only have one post between my SSS’s. Today: What is social interface theory? This is fairly interesting. For all practical purposes it is the study of how humans interact with machines (namely computers). First off, how can we humanize the interface of a computer *insert Ubuntu joke here*? There are blatant ways of doing it such as having a CGI face talk to you. There are lots of subtle ways of doing it. These are the interesting things that lead to the next question.

How does having a more human interface affect how people interact with computers? For instance, are people more or less likely to tell the truth if they feel a human is surveying them? Can the type of human interface sway what people do? This relates back to the first part now. This is essentially a new type of advertising. Now the idea is to sway how people act (consuming products?) without them realizing they are being swayed by using those subtle humanization techniques.

Basically I’ve defined what social interface theory is by bringing up some of the questions that it studies.


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The Past Few Days

Well, I did not pass my prelim. This is perfectly acceptable as I did not think I had passed. Luckily I found out that I had three significantly correct, and four is a pass, so I wasn’t too far off. Darn you classical analysis! Give me topology or algebra, just not analysis.

In other news, it is great to have students try hard, but sometimes too hard is just plain annoying. I’ve had one email me three times today to verify things like proper format for the homework. I understand that some teachers are very concerned with this, but I for one am not. If you somehow give some sort of indication as to which problem you are doing, and I can read it, that is good enough for me. (OK, so I may be a little annoyed if you stick to those bare minimum requirements, but you get the point).

I finished Libra by Don DeLillo. It was good, but if you want to do a DeLillo I would definitely look to White Noise or even possibly Underworld before this one. It was rather dry. It also had ridiculous amounts of recurrent ideas from his other novels (which may be why I didn’t like this one as much). Everyone smokes Lucky Strikes in Libra. This plays a major role in Underworld. The line “Hidell means don’t tell” surfaces in many many forms throughout. This is one of my favorite aspects of DeLillo’s writing. This same thing happens with the line “Who will die first?” in White Noise. The JFK assassination/the Zapruder film of it plays a major role in Underworld. It is the entirety of the plot in Libra. Recycling ideas is fine, but I feel like DeLillo is really stuck on certain things.

The one really, really great thing was the film Quiet City. I can’t believe films like this are dismissed due to their low budget, lack of plot, and hard-to-watch “arty” shots. The film was utterly brilliant in capturing the reality of an entire generation. The things people do and say are so spot on that it was scary to think there was a script involved. These are the types of films that should be archived and saved as great. One hundred years from now, people will look back and say, “I wonder what life was like then…” They will look to our mainstream cinema and will not learn the truth. It is misleading what is being saved as classic and indicative of our time. Oh well, that is a rant for another time. In the meantime, watch this film to understand what I’m talking about! I will without a doubt rant about it later. A whole post of films that I think should be archived as brilliant vignettes of modern society!


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SSS 3

I’m starting to not like how aware of how fast weeks go by with this weekly SSS thing. Today we take a look at an author you’ve probably never heard of (I certainly hadn’t): Kia Abdullah. She is a Muslim British-Asian writer. She has one book and another in the works. It is called Life, Love, and Assimilation.

The book came out in 2006 and explores some issues that brought controversy. She grew up in Tower Hamlets in London and the book is based on the drug problem there. It is interesting to note that she got her bachelors in computer science before deciding to be a writer.


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Alan Ball…Towelhead

The blogosphere has been mighty quiet on the academic front (probably due to the start of the academic year). I have fallen prey as well. Last night I went to the screening of Alan Ball’s new film Towelhead and I’d like to set the record straight. There is a lot of nonsense going on out in the web about this film. First off, I think Ball is probably the best writer out there for the acting medium. He did Six Feet Under, American Beauty, and probably lesser known Five Women Wearing the Same Dress. In general, he writes about profoundly touchy subjects in a very human way. He never forgets to incorporate a very ironic at times, very quirky at others, sense of humor.

On to the subject at hand. Towelhead is no exception. People have been claiming that this is extremely graphic, should be considered “kiddie porn,” is racist, etc. I can’t imagine these reviewers were watching the same film as me. This is purely conservative propaganda. The film has a very strong anti-racist message. As in the typical Ball fashion, though, the racist in the film is unexpected, apparently giving the unsuspecting viewer the idea that the message is racist? I can’t figure out the psychology there.

Next: The claim that this is “child pornography”. The very first thing that we should note is that the main content of the film is an exploration of the psychological problems of a 13 year old girl that gets raped. Anyone that considers child rape as the same thing as pornography probably shouldn’t be let into movie theaters. Secondly, these people have very vivid imaginations, since the claim that “very little is left to the imagination” is also false. If the concept of the film wasn’t so serious, then this film could almost get away with an under R rating. I was sort of baffled at how much was left to the imagination. Whenever the girl was naked there was always, always something there to hide her neck down. Whenever a sex scene occurred, you almost never saw both people. They were done through cuts, so usually only three seconds or so were shown of the beginning and then it would cut to after the scene.

In conclusion, there is no denying that it truly was one of the more disturbing movies I’ve ever seen. It was extremely dark, yet had moments in which the theater couldn’t stop laughing. Ball can really lighten the mood and make these subject matters much more watcher friendly. The hype about child pornography is just that, hype. You will be disturbed, but you don’t have to worry about extremely graphic scenes. It is almost The Bell Jar-esque in its ability to put yourself in the victim’s place and understand why the character behaves in the way she does.

I highly recommend this to fans of Ball, but if you didn’t like his earlier stuff, this is sort of a more extreme version of it, so I wouldn’t recommend it to you.


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SSS 2

I shall from this point forward use the abbreviation SSS for Strange Sunday Specials. Today we examine music. Slainte Mhath is a band from Cape Breton (how exciting, I’ve always wanted to visit). Apparently they fuse genres of Celitc, dance, funk, and electronica. This sounds rather innovative so I may need to check them out. Unfortunately, if I like them they are no longer a band as of 2005.

As a sidenote not included in the wikipedia article, the band name translates to “good health.”

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