ChapterZero

Rome, or the awesomest HBO original series, evar!

Filed under: General — Alex @ 2:08 am 8/29/2008

If, like me, the first time you heard about Rome was in connection with the infamous well-endowed slave, you probably didn’t think much of the show. After my Netflix subscription, though, I started renting the first episode of a lot of series that I would otherwise not have put forth effort to obtain: Rome, Weeds, Wired, etc.; Rome was the only one that I found interesting enough to rent more of.

Beyond the cinematic eye candy– it was filmed in beautiful period reconstructions in the Italian countryside–, the ubiquitous sex scenes, and casual full frontal nudity, Rome is incredibly well written. The storylines, which center mostly around the Julii family: Atia, Octavia, and Octavian, and the two soldiers Titus Pullo and Lucius Vorenus, cover from the rumblings between Pompeii and the Senate with Julius Caesar that leads to him marching on Rome to the suicides of Cleopatra and Marc Antony.

My favorite character is perhaps Atia, the resident psychopath– as in ‘lying, exploitive, arrogant, sexually promiscuous, and lacking empathy and remorse’. She has Octavia’s husband killed because she feels that he’s beneath their station, and when Octavia, who knows her mother, asks her if she was behind his death, she manipulates Octavia into feeling guilty. When Caesar occupies Rome she forces the breakup of Caesar (her uncle) and his lover because she feels the relationship is holding Caesar back from taking to the field to crush his opposition. Atia humiliates the same lover by hiring ruffians to kill her palanquin bearers, strip her naked, cut her hair off, and leave her on the streets. She does a lot more deliciously bitchy things, and through it all seems to think she’s doing nothing wrong. Maybe it’s because of this twisted innocence that you feel bad for her when her actions turn back on her.

I was going to say more, but I can’t do the series justice. Just go get it; you won’t be disappointed.

Possibly relevant posts:

Real Analysis and Fourier theory (3/4/2005)
cooped up (9/13/2006)
Red seas under Red Skies (8/19/2008)

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Modern textbooks are over designed

Filed under: General — Alex @ 11:41 pm 8/26/2008

When did textbooks start being replaced by particolored monstrosities? I can imagine textbook marketers get excited over the additional appendices, and in-chapter supplements, and case studies showing ‘real world applications’, and highlight boxes, and end of chapter bulleted lists of important points, and outline boxes for each definition, and several figures per page, and that on top of it all each separate feature has its own color for quick identification… but I can’t imagine that readers are nearly as enamored of that clutter.

Remember the good old days when books used one color of ink– black–, and one font family, and because they cost so much, figures didn’t make the cut unless they were actually worth 1000 words? When textbooks didn’t need user manuals? I wasn’t around then, but I learned calculus from a book written in those times, and it outshines any modern calculus textbook I’ve seen with all their educational accoutrements. Likewise Feller far outshines any more modern probability text I’ve come across. Paradoxically, having to work within relatively spartan printing resources helped those authors to focus more on the content of the material than the presentation. It also seems that they were less worried with soft-selling their material: those texts have more gravitas than modern pulpy textbooks.

I wish we could return to those times. Or failing that, I wish I could locate an introductory macroeconomics text that doesn’t induce a migraine after reading several pages.

Possibly relevant posts:

Another visit to the library… (6/13/2002)
What is Dell doing? (7/15/2007)
My summer plans (5/15/2004)

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I’m a bad black person too

Filed under: General — Alex @ 10:56 am

I started running again on Sunday night. Between sucking down cold air for the past couple of mornings and nights, and leaving my overhead fan on at night to avoid overheating, and thereby having a constant stream of air rushing over my neck, I’m dealing with a sore throat. So, I decided to spend the day at home — theoretically, I can do my work here just as well,and I’ll be in range of all my lozenges and fluids.

Anyhow, I started off my morning by checking out my blog roll backlog. Jam Donaldson did a post on the Black in America series on CNN on her Conversate is not a Word blog. At the time, I wanted to see this, but not having cable, I would have to youtube it, or otherwise stream it, and it’s just not that crucial to me. So I guess I’m a bad person too? I’ve seen several of these types of shows, and I don’t usually learn anything worthwhile, or hear any good suggestions, so I don’t think I’ve missed anything major.

On the humorous side, this was one of the comments on Jam’s post. Is this sarcasm, or is she serious?:

Quesha on 25 Jul 2008 at 2:20 am #

i haven’t watched it…but i did dvr it. i want to check out how we are being portrayed for the white folks.

it would be interesting if the next big program was called “being white in america.” now i know most sitcoms are predominately white, as are “reality” shows. but i want to know how they really live. gimme their secrets. let me see into their houses and their true thoughts and feelings. actually i want to tape them when they don’t know that they are being taped.

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A really old entry (3/14/2002)
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Comments (1)

Probabilistic Tools

Filed under: Mathematics — Alex @ 10:36 pm 8/25/2008

Today one of the first years studying for his qualification exams asked me a question that he came across on a previous year’s probability qual: If people are removed from couples, what is the expected number of remaining couples?

Give it a shot, then see under the cut for my solution

(more…)

Possibly relevant posts:

Probability tricks (11/28/2006)
Probablistic Integrals (10/27/2006)
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QOTD: What if the chinese had labour unions?

Filed under: General — Alex @ 8:40 pm 8/22/2008

As far as old white guys go, Bill Moyers is one of my favorites.

Question of the day: communism is supposed to be all about workers’ rights, right? My question is, what would happen if the soi-disant ‘communist’ Chinese government encouraged (or at least allowed) the formation of labour unions?

Possibly relevant posts:

Reverse Racism? (11/27/2005)
Two Unsatisfactory Theories of Government (10/4/2002)
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Comments (1)

Red seas under Red Skies

Filed under: General — Alex @ 11:01 am 8/19/2008

I finally got the sequel to The Lies of Locke Lamora yesterday; I was so excited about it finally being available in paperback, and so enamored of its prequel, that I picked it up without even reading the blurb. Then I got home, read the blurb, and steeled myself for a more typical novel about the ‘larcenous exploits of a band of daring thieves’:.

The Lies of Locke Lamora followed some momentuous events in the lives of a band of young priests, recruited from among the most talented and incorrigible of the orphans of the city of Camorr, whose rather unorthodox sacrament is thievery. The sequel follows the surviving priests, who have fled to another city, and according to the blurb, is about their attempt to swindle from the most reknown of the city’s gambling houses, a place where those caught cheating are guaranteed a swift, sure death.

The twist is that someone knows about their background and their plot, and is out to ‘make them pay for their sins’… Granted, his first book was off the hook, so Lynch could probably breathe new life into the old troupe of the gentlemen rogues, but if this was truly as deep as the book got, the result would definitely not be anywhere near as delicious as The Lies of Locke Lamora.

Luckily, it turns out that the sin being referred to is one from The Lies of Locke Lamora. Without giving too much away, before they fled the city, they avenged themselves on a bondsmage who killed some of their friends. They would have liked to kill him, but the Bondsmagi are a unique force in their world: they maintain a monopoly on magical ability by killing mages who attempt independent practice; their magic grants them some terrible abilities, like being able to voodoo puppet anyone whose name they know. Consequently, they can do what they will when they will without fear of retribution– the murder of a bondsmage led to the casual destruction of a city once– and will do pretty much anything for anyone who can afford their services.

Apparently, the Bondsmagi don’t like what was done to one of their own … So, an exciting premise. One as puzzling as that of the prequel: how can they possibly survive against the Bondsmagi?

Possibly relevant posts:

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Complexification of the Rademacher comparison theorem?

Filed under: Mathematics — Alex @ 12:00 pm 8/18/2008

Recall the Rademacher comparison theorem:

Let $F: \R^+ \rightarrow \R^+$ be an increasing, convex function, $T \subset \R^n$ be a compact set, and $\varphi_i$ be real contractions such that $\varphi_i(0) = 0$ , then

$\displaystyle \mathbb{E} F\left(\frac{1}{2} \sup_{t \in T} \left| \sum_{i=1}^n \epsilon_i \varphi(t_i) \right| \right) \leq \mathbb{E} F\left( \sup_{t \in T} \left| \sum_{i=1}^n \epsilon_i t_i \right| \right),$

where $\epsilon_i$ are independent Rademacher (Bernoulli $\pm 1$ ) variables.

Intuitively, replacing with the identity, this says that if we shrink the coordinates and then take random Bernoulli averages, the expected value of the maximum deviation is going to be less than that for the original coordinates. Therefore, it makes sense to expect that an appropriately modified version of this theorem holds for the case where $T \subset \C^n$ and the $\varphi_i$ are complex contractions.

In one version of a proof (see “Comparison Theorems, Random Geometry and Some Limit Theorems for Empirical Processes” by Ledoux and Talagrand), an intermediate step is to show that

$\displaystyle \mathbb{E} F\left( \sup_{t \in T} \left| \sum_{i=1}^n \epsilon_i |t_i| \right| \right) \leq 2 \mathbb{E} F \left( \sup_{t \in T} \left| \sum_{i=1}^n \epsilon_i t_i \right| \right)$

and their main tool for doing this is a bijection $\theta_t : \{\pm 1\}^n \rightarrow \{\pm 1\}^n$ which satisfies, for a given $t \in T$

$\displaystyle \left| \sum_{i=1}^n \epsilon_i |t_i| \right| \leq \left| \sum_{i=1}^n \theta(\epsilon)_i t_i \right|.$

They prove such a $\theta_t$ exists without explicitly specifying it, using the marriage theorem.

If I could somehow generalize this to the complex case, i.e. find a bijection $\theta_t : \{\pm 1\}^n \rightarrow \{\pm 1\}^n$ which satisfies the above, I’d have at least this intermediate inequality. (As it turns out, this inequality is all I need for my applications, since we only use $\varphi_i = | \cdot |$ .) But the question is, is it even reasonable to expect this?

Possibly relevant posts:

One direction in Khintchine’s inequality for Rademacher sums (9/26/2008)
Dr. Singh’s Take on the Fourier Unicity Theorem (via Invariant Subspaces) (6/17/2005)
The other direction in Khintchine’s inequality for Rademacher sums (9/26/2008)

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Correct in spirit, but not so much mathematically

Filed under: General — Alex @ 9:20 pm 8/17/2008

“Love is like pi - natural, irrational, and very important”
-Lisa Hoffman

I mean, everyone knows that irrationality is so not natural.

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Orson Scott Card is a homophobe

Filed under: General — Alex @ 3:03 pm 8/13/2008

I’ve been silent for a long time, but after reading about Orson Scott Card’s ridiculous position on gay marriage, I feel compelled to say something. Like, wtf would Ender or Bean say? Did you think about that Mr. Card? WTF would Ender or Bean say? The article correctly points out the utter lack of reasoning in Card’s so-called arguments, and the comments have a nice supplementary discussion on judicial activism. Why is it that they only call it judicial activism when they disagree?

Getting back to business, I plan to post in a short while on using truncation to estimate expectations of random variables: this turns out to be a powerful and simple technique for answering several of the questions I’ve posted over the past few weeks, like finding the asymptotic behavior of $\mathbb{E} \sqrt{\text{Bin}(n,\frac{1}{2})$ without using the delta method, or showing that $\max_{k=1, \ldots, n} e_k$ grows like $\log(n)$ where e_k are Exp(1) random variables.