## Middlesex by Jeffrey Eugenides

I’ve always had some sort of aversion to this book. I never understood why it was so universally acclaimed by everyone I spoke to. The main plot is about two siblings that get married and have a child, who then goes on to marry his first cousin, who then has a child that is a hermaphrodite due to the genetic mutations passed on from incest. The story just never seemed to be the kind that all people can relate to.

So as usual with a book post, I want to touch on lots of things I thought about during the reading of the book without going into much detail on any of them. The other aspect of this post is to make some sort of argument that will get people to read the book even if they are sort of put off by the content.

The narrator is the hermaphrodite. So let’s address this right off the bat. He is born and raised as a female, even though he is genetically essentially a male. So a transformation takes place over the course of the book from Callie (female) to Cal (male). To me the “hermaphrodite nature” of the book is to completely miss the point. It seems more of a device to indicate transformation from being confused about your identity and sexuality to becoming more comfortable with yourself and accepting yourself for who you are. It is a device to indicate coming of age. It exists for literary reasons, and to me, this seems to be the only reason it exists. I believe everyone will be able to identify with Cal in a deep way.

The structure of the book is really effective as well. Cal is an adult narrating his family history. The “current” timeline is usually about the first paragraph or so of the chapter and then the chapter flashes back. Over time you start to better understand Cal’s current motivations and life. Due to having both male and female sex organs, Cal has spent his life very closed off. He is afraid of telling people, so never really let’s anyone in. To me, this is the most profound aspect of the book. Again, instead of the hermaphrodite aspect of the book alienating readers, it actually creates a universal situation. Everyone has a past and some secrets they are afraid of. This “current” timeline gives the book this edge: a story about finding someone who will accept these aspects of you. It is risky and scary to let someone get close to you, but if you are honest about yourself and they accept you as this person, the pay-off is much greater than living closed off.

As with The Virgin Suicides, Jeffrey Eugenides writes fantastically beautiful prose. He seems to be much better in this book, though. He quickly jumps around in style to perfectly set up and mimic exactly what the content of the sentences are trying to say. Some paragraphs I think of as just heart-wrenching snippets of truth. Of course, I didn’t mark them, so it will be hard to find now. But here is one I randomly opened to:

It occured to me today that I’m not as far along as I thought. Writing my story isn’t the courageous act of liberation I had hoped it would be. Writing is solitary, furtive, and I know all about those things. I’m an expert in the underground life. Is it really my apolitical temperament that makes me keep my distance from the intersexual movement? Couldn’t it also be fear? Of standing up. Of becoming one of them.

Still, you can only do what you’re able. If this story is written only for myself, then so be it. But it doesn’t feel that way. I feel you out there, reader. This is the only kind of intimacy I’m comfortable with. Just the two of us, here in the dark.

Another aspect of the book is about chance and how much of our lives are out of our control. The book often reads like Pynchon. It is full of reference, statistics, and facts. This is a very effective way of addressing the question of whether our lives are just the lump sum of determined information, or is there something more. This aspect of the book is hard to describe. It is very implicit and never explicitly addressed. It always is lurking there in the hard factual data that seems to be competing with the flowery undetermined prose around it. From which does Cal’s life get its meaning? This seems to also be the reason we follow three generations of this family. The point seems to be setting up the fact that all these things happen that directly affect and determine Cal’s life before he is even born. There seems to be one part of the book that tries to give a definitive answer, but I won’t spoil that plot point.

I could go on forever, so I’ll try to wrap it up. I didn’t even touch on comparisons to and use of Greek mythology. Or any of the great world and American historical events going on in the background, always subtly affecting everyone.

Overall, I can’t recommend this book enough. It raises the big questions in a new way. It is funny. It forces you to examine your own life. It is about learning to accept yourself and others. It is about the struggle between succumbing to all the predetermined genetic, scientific, political and historical forces working against you and actually living your life and overcoming these forces. It is about societal norms. It is about falling in love. There are so many instances that I thought it was reading my mind. There were other moments I knew it wasn’t, because it helped me figure out something I was struggling with. It is about the messiness of life. It is universal.

## Music 2009

I may as well post this today since it is done. I’ve officially relistened to everything I got this year and ranked it. I’m going to do two new things this year. First off, I need to explain a little about how my taste in music (and art in general) has changed drastically. I’ll start with a quote from Franz Kafka

I think we ought to read only the kind of books that wound and stab us. We need the books that affect us like a disaster, that grieve us deeply, like the death of someone we loved more than ourselves, like being banished into forests far from everyone, like a suicide. A book must be the axe to the frozen sea inside us.

I’ve sort of lost interest in things that don’t really affect me. I still get and listen to lots of technically amazing musicians who are doing great original things. If this were last year Andrew Bird would probably be in the top 5 because there is no denying that he wrote some of the most complicated and original music this year. He is a phenomenal violin player and shows this off as well. But his songs sort of lack any real meaning.

Let’s face it. I’m a very moody person. I like to have music that hits a huge range of emotions, so that I can find something to sympathize with me no matter my mood.

So without furthur ado, the top 10:

1. The Antlers – Hospice
2. Imogen Heap – Ellipse
3. Land of Talk – Fun and Laughter
4. Loney, Dear – Dear John
5. Doves – Kingdom of Rust
6. The Swell Season – Strict Joy
7. Wilco – Wilco (The Album)
8. Regina Spektor – Far
9. Grizzly Bear – Veckatimest
10. The Decemberists – The Hazards of Love

The honorable mentions:
Dirty Projectors – Bitte Orcha
M. Ward – Hold Time
Sunn O))) – Monoliths & Dimensions

Now the ordering here was made with some consideration, but it shouldn’t be taken too seriously. Everything above I thought was all around great. Essentially no bad songs. All original creative things. All technically great things with a good deal of emotional content.

The middle ground stuff:
Andrew Bird, Neko Case, Dan Deacon, Tortoise, Dodos, Animal Collective, F**k Buttons, Duncan Sheik, Other Lives

These had really good aspects and had some aspects I didn’t really like. All worth getting in my opinion, but not as well rounded as the top list. For instance, I think the songs on Neko Case or Animal Collective are the best of those groups when they are good. But when they are bad, they are some of the worst either have put out. This dichotomy could not be overlooked. Actually having to skip songs on an album is a major turn-off for me.

The subpar group is as follows:
Bon Iver, Yeah Yeah Yeahs, The Field, Mount Eerie

These were not worth getting in my opinion, but not totally completely horrible. I enjoy some songs and aspects, but not enough to make the “middle ground” list.

The bottom three I’ll go back to ranking:
Worse: Holopaw – Oh Glory, Oh Wilderness
Worst: Heartless Bastards – The Mountain

Other than The Antlers, everything on the top 10 I expected to be there. They’ve all impressed me in the past. So mostly my surprises are in the realm of disappointments. I’ve already said this, but for the most part I was severely disappointed this year. The other surprise was sort of Loney, Dear. I only got this because he was touring with Andrew Bird. After a few listens I thought I had gotten everything to get to it. To my surprise 8 months later, I was still not bored of it.

My biggest disappointment has to be Bon Iver. He was number 1 last year and was very close to bottom three this year. Another big disappointment was Holopaw. This was bottom three. The first time I heard this group was at a party, and it was on in the background. Music people and non-music people alike were so drawn to its greatness that there were constant comments and asking who it was. I’ve never seen anything like that occur since.

I’ll leave this post here. I didn’t rank a top 10 list for individual songs, but I probably should have. If anyone would like me to elaborate more on specific placements, just comment, I’d be happy to. Also, if there are things you thought were great but I missed, I’d love to hear about it.

## Associated Primes II

Today we’ll continue towards a primary decomposition for modules. First, I’ll list two facts without proof that may come up (they are quite straightforward to prove if you want to try). If R is any ring and $0\to M'\to M\to M''\to 0$ is an exact sequence of $R$-modules, then $Ass(M)\subset Ass(M')\cup Ass(M'')$. Secondly, if $R$ is a Noetherian ring and $M$ a non-zero finite $R$-module, then there is a chain $0=M_0\subset M_1\subset \cdots \subset M_n=M$ of submodules of $M$ such that for each $i$ we have $M_i/M_{i-1}\simeq R/P_i$ with $P_i\in Spec R$.

I don’t remember, but I may have even proved that second one when talking about Artin-Rees. Now let $R$ be Noetherian and $M$ a finite $R$-module.

I) $Ass(M)$ is finite. We induct on the length of the chain in the second fact. Suppose this is true for all $M$ having a chain of the above form of length $n-1$. If $N$ is a finite module with a chain of length $n$, then since $R$ is Noetherian and $N_{n-1}$ is a submodule it is also finite. So by the inductive hypothesis, $Ass(N_{n-1})$ is finite. Now consider the exact sequence $0\to N_{n-1} \to N \to N/N_{n-1}\to 0$. By the first fact $Ass(N)\subset Ass(N_{n-1})\cup Ass(N/N_{n-1})$. But the chain has the condition that $N/N_{n-1}\simeq R/P$ for some $P\in Spec(R)$. Since $Ass(R/P)=\{P\}$ we have that the cardinality of $Ass(N)$ can increase by at most one from the cardinality of $Ass(N_{n-1})$ which was finite.

II) $Ass(M)\subset Supp(M)$. Suppose $P\in Ass(M)$. Then $M$ contains a submodule isomorphic to $R/P$ (it is just the image of the hom $r\mapsto r\cdot x$ and apply first iso theorem). So $0\to R/P\to M$ is exact, so when we localize we still have an exact sequence $0\to R_P/PR_P\to M_P$. Since $R_P/PR_P\neq 0$, $M_P\neq 0$ which means $P\in Supp(M)$.

III) The set of minimal elements of $Ass(M)$ coincides with the minimal elements of $Supp(M)$. Well, (II) gave one inclusion so suppose $P\in Supp(M)$ is a minimal element. Then since $M_P\neq 0$ by the last post we get that $Ass(M_P)\neq \emptyset$. But we also figured out a formula for this set $Ass(M_P)=Ass(M)\cap Spec(R_P)\subset Supp(M)\cap Spec(R_P)=\{P\}$. Thus by non-emptyness we must have $P\in Ass(M)$.

Recall when we working in the Zariski topology on $Spec(R)$. We have an operator on ideals $V(I)=\{p\in Spec(R) : p\subset I\}$, and the Zariski closed sets of $Spec(R)$ are precisely those sets that are of the form $V(I)$ for some $I$.

So by definition of this operator, if $P_1, \ldots , P_r$ are the minimal elements of $Supp(M)$, then $Supp(M)=V(P_1)\cup \cdots \cup V(P_r)$. Another property of the topological space $Spec(R)$ is that a subspace is irreducible if and only if it is $V(\frak{p})$ for some minimal prime $\frak{p}$. So if we think of $Supp(M)$ as a closed subspace of $Spec(R)$, then the irreducible components are precisely $V(P_i)$. We call the $P_i$ the isolated associated primes of M. The other associated primes are called embedded primes.

Due to the above geomtric interpretation of what isolated and embedded primes are, the terms make sense. An isolated prime gives you full irreducible component of $Supp(M)$ whereas an embedded prime gives some embedded subspace of the component generated by the prime it lies over.

I’ll finish with the new definitions. Suppose $N\subset M$ is a submodule. Then we call $N$ a primary submodule if for all $r\in R$ and $x\in M$ we have the condition $x\notin N$ and $rx\in N\Rightarrow r^nM\subset N$ for some $n$.

The above condition is equivalent to the condition: if $r\in R$ is a zero-divisor for $M/N$, then $r\in \sqrt{(ann(M/N)}$. Showing these are equivalent is immediate when you write out what the definitions of all these things are. This shows that the property of being primary is dependent only on the quotient module $M/N$.

Sorry to end on some definitions, but I think if I do another theorem this post will become too long.

## Associated Primes I

I’d like to go over associated primes in general rather than just the Noetherian ring form of primary decomposition of ideals. The natural generalization is to modules, since ideals are sub-modules over the ring treated as a module over itself. We’ll need to define a few things first.

Let M be an R-module. Let P be a prime ideal of R. Then we call this an associated prime of M if $P=ann(x)$ for some $x\in M$. The set of associated primes is denoted $Ass_R(M)$ (since R will be understood, we’ll just drop that from here on).

Now suppose $I\subset R$ an ideal. Then the elements of $Ass(A/I)$ are called the “prime divisors” of I.

Now we’ll get some basics out of the way. Suppose that R is Noetherian. First off, $Ass(M)\neq \emptyset$ when $M\neq 0$. We show this by showing that any maximal element of the family $\mathcal{F}=\{ann(x) : 0\neq x\in M\}$ is an associated prime. This is an important fact on its own.

Note that all we really are trying to show is that a maximal element of $\mathcal{F}$ is prime as an ideal, since it will already be of the form $ann(x)$. Let $A\in\mathcal{F}$ be a maximal element. Suppose $A=ann(x)$ and that $ab\in A$ and that $b\notin A$. Then $abx=0$ but $bx\neq 0$. Thus $ann(x)\subset ann(bx)$. But by maximality, $ann(x)\subset ann(bx)$. Thus $ann(x)=ann(bx)$ which means $a\in A$. Thus $A$ is prime and hence an associated prime of M.

The other fact we need is that the set of zero-divisors for M is precisely the set $\displaystyle \bigcup_{P\in Ass(M)}P$.

If $a\in \displaystyle \bigcup_{P\in Ass(M)}P$, then this just says there is some $x\in M$ such that $a\in ann(x)\Rightarrow ax=0$ and hence $a$ is a zero-divisor. The reverse inclusion just uses the previous fact. Let $a$ be such that $ax=0$ for some $x$. So we have $a\in ann(x)$. Then take a maximal element $P\in\mathcal{F}$ containing $ann(x)$. By the last fact $P\in Ass(M)$ and hence $a\in \displaystyle \bigcup_{P\in Ass(M)}P$.

For the theorem of the day, you may need a refresher on the spectrum of a ring, and on localization.

We no longer assume R is Noetherian. Let $S\subset R$ be multiplicative, and $N$ an $R_S$-module. Viewing $Spec(R_S)\subset Spec(R)$, then we have $Ass_R(N)=Ass_{R_S}(N)$. In general, if $R$ is Noetherian, then for any R-module M, we have $Ass(M_S)=Ass(M)\cap Spec(R_S)$.

Let $x\in N$. Then $ann_R(x)=ann_{R_S}(x)\cap R$. This is just because the elements of R that kill x, are just the fractions that kill x that are “actually” in R. This immediately gives us one inclusion, since if $P\in Ass_{R_S}(N)$ then $P\cap R\in Ass_R(N)$.

Now suppose $Q\in Ass_R(N)$. Then there is some $x\in N$ such that $Q=ann_R(x)$. Thus $x\neq 0$ giving $Q\cap S=\emptyset$. Thus $QR_S\in Spec(R_S)$ with $QR_S=ann_{R_S}(x)$. This proves the first statement.

We now show the second statement about M. Suppose $P\in Ass(M)\cap Spec(R_S)$. Thus we again get that $P\cap S=\emptyset$ and $P=ann_R(x)$ for some non-zero $x\in M$. Suppose that that $(r/s)x=0$ in $M_S$. Thus there is some $t\in S$ such that $trx=0$ in $M$. But we’ve already noted that $t\notin P$ and $tr\in P$, thus by primality $r\in P$. So $PR_S=ann_{R_S}(x)$. Thus $PR_S\in Ass(M_S)$ giving one inclusion.

For the reverse, suppose $Q\in Ass(M_S)$. By clearing the denominator we can assume that for a non-zero $x\in M$ we have $Q=ann_{R_S}(x)$. Let $Q^c=Q\cap R$. Then $Q=Q^cR_S$. We have that $Q^c$ is finitely generated since $R$ is Noetherian, so there is some $t\in S$ such that $Q^c=ann_R(tx)$. Thus $Q^c\in Ass_R(M)$ which gives the reverse inclusion.

A nice little corollary is that for Noetherian rings a prime ideal $P\in Ass_R(M)$ if and only if $PR_P\in Ass_{R_P}(M_P)$.

## Dune

Bear with me. I’m going to attempt to do my Dune post as a single post, but there probably two theses worth of ideas in here. Well, the plane trip across the country allowed me the time needed to read most of Dune. I’ll start out by saying that this book was very challenging for me at first. There is a very complicated system and hierarchy set up. There are families and alliances and sworn enemies. There are traitors. There are lots and lots of confusing names. The book essentially throws you in and although the first 100 pages or so are very slow in what I imagine is the author’s mercy at trying to catch you up, it makes for tough reading.

The other tough part is that it is incredibly dense. It is like reading Wittgenstein’s Philosophical Investigations. There are only 100 aphorisms because you are supposed to stop and think after each one. This kept happening to me, except that it was a novel and so I probably wasn’t supposed to do that. Anyway, I hit a critical point when I was on the plane and had these two ideas about what the book was actually about, but my history isn’t very good and so I had no way to check. I also couldn’t see if other people had come up with this or not. So I just started testing it against everything I read, and it fit way too well to not have at least crossed the author’s mind. This also made the book way more exciting to read.

Here goes. The first thing I thought was that Dune was a metaphor for the Middle East. I immediately checked when the book was published, and it said 1965. This was rather unhelpful because I couldn’t even be sure which countries existed in the Mid East in that year, yet alone what sort of political things were going on. I haven’t really researched it because I wanted to at least get this post out there. So I apologize if this is way off base.

First off, the book takes place on Arrakis…a desert. Does this sound like “Iraq” to anyone (for future reasons, I actually think that Arrakis is Saudi Arabia in this metaphor)? The natives are the Fremen and they have a tribal society. What are some common strange names that keep appearing. Muad’Dib or Kwisatz Haderach and even at one point Rhamadan. Do these have an Arabic flare to them or am I imagining it? Alright, so this one can be resolved with a quick google search. Kefitzat Haderech is Hebrew for “short cut”, and the made up word means “shortening of the way”. Well, those are all things that got me thinking about this, but they are sort of the fluff of this argument.

The real thing was that the universe seems completely dependent on the “spice”. So the spice is the metaphor for oil. All the conflict is essentially based around possession of the spice. Here comes a spoiler if you haven’t read it. But to solidify the metaphor beyond a doubt, the spice is created by some chemical underground process that happens to dead gigantic worms (maybe they don’t have to be dead, this was unclear to me). Um, what is oil (re: fossil fuels)? It is just decomposition of buried organisms in a particularly well-suited environment.

Some things I still haven’t figured out that will take a bit of researching of what was going on at the time are who the families/people are. I’m assuming that the Atreides are a country and the Harkonnens are another country. Who would have Herbert have thought of as the “good guys” at that time and who the “bad guys?” I don’t think the U.S. had a big involvement yet, so it probably wouldn’t be one of them. The emperor sort of presides over all the families (re: countries), but seems to have no power in controlling them. Is this the UN? Also, is this just a metaphorical retelling of events, or did he take it further and insert some sort of warning/message about the situation? This brings me to my next topic.

I thought the only really clear overriding message was one of religion. I guess I can pitch this at two different levels. The more dramatic level is that religion is invented by people in order to control people. Whether you believe this or not, there is no doubt this was an intention of Herbert. I wish I had quotations on hand, but it is repeated time and time again that the Bene Gesserit invented legends and myths to create the religion of the Fremen a long time ago so that when this time came it could be exploited for their protection. Paul is some sort of messiah figure that most religions have, but he also clearly exploits this to gain power.

The less dramatic religious message seems to be that religion and politics need to stay as separate as possible. When people believe they are doing things for a religious cause, then they will stop at nothing since the cause is far greater than their mere earthly bodies. In particular, wars waged with religious overtones break from any sense of a “just war” (whatever that is). The end of Dune talks about women, children, and elderly throwing themselves onto swords so that the men can get in actually kill the other side. The Fremen are often so feared as fighters because they have no reason to fear death with the assurance of an afterlife.

I’ll stop here. I’m sure there are holes and errors, and I purposely skipped details and quotes. But a first sketch of these arguments is now out there for criticism. Be gentle, remember this was my first time through the book. It is possible a second reading would make me embarrassed that I ever thought this.

## Almost Music List 2009

It is approaching that time again where I re-listen to every album I got this year and rank them. This will be much easier when I’m sitting around twiddling my thumbs at my parent’s house over break. I’ll probably also blog about associated prime decompositions. But until then, I though it would be interesting to see how I feel about the list I made last year.

The old list is here. Well a first glance at the top 10 a few things immediately jump out at me. I’d definitely pull Bon Iver from the number 1 spot and completely remove Son Lux, MGMT, and Extra Life from the top 10. Son Lux is the only of those that I’ve listened to since last December.

My top 5 in some order (possibly not the one I’m going to list) would probably be Land of Talk, NIN, The Dodos, Lightspeed Champion, and The Helio Sequence. I still have to admit that Bon Iver was the most affecting and moving album created last year and still deserves top 10, but it didn’t last the way these other ones did.

I must admit right up front that this year has not been a great music year for me. I’ve been listening to things on my last year’s list and even further back more often than stuff created this year. Lot’s of my favorite artists put out new albums, and they repeatedly disappointed me.

I can without a doubt say that my favorite couple of albums I listen to a lot year are not going to be reviewed because they came out several years ago. One of these artists being Joanna Newsom which I’ve blogged about a few times. I also have standard fallbacks like Interpol and Radiohead that just never get old. There have been a lot of “best of the decade” lists, and all three of these artists would definitely make that list if I were to do one.

I’m very much dreading having to sit through some of these again. But maybe I’ll be surprised now that they’ve had time to sit. I also might as well list the four albums I just never got around to getting that were really high on my list: Zs Music of the Modern White, WHY? Eskimo Snow, Blakroc (self-titled), and The Fiery Furnaces I’m Going Away.

I’ll definitely get them at some point, but I don’t like to just start listening to something and then quickly make a judgment call. More on this later.