A Mind for Madness

Musings on art, philosophy, mathematics, and physics


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What is Speedrunning?

In honor of AGDQ 2015 (to be explained shortly), I thought I’d do a short post on speedrunning. I assume most of my readers are entirely unaware of this concept. Speedrunning is the act of beating a video game as quickly as possible.

The first surprising thing I’d like to get across is: if you have a favorite video game, then there is probably a whole community of people who have dedicated hundreds of hours (many, many more for some games) to figuring out how to beat it as quickly as possible.

When people decide to start “running” a game, it will usually look like someone who is familiar with the game doing it as fast as possible. As people explore glitches and route possibilities, the game will look less and less like you remember. To give you a feel for how impressive the times have become, The Legend of Zelda: Ocarina of Time usually takes on the order of 30-40 hours to beat. The world record is now 18 minutes and 10 seconds. If you spent every waking moment of the next month learning to do this, you still wouldn’t come close.

What makes this interesting? I think there are at least two fascinating aspects. The first is the thrill of wondering what is possible and then seeing someone achieve it. This is similar to when people wondered if a four-minute mile was possible. It seemed like maybe it was, but no one was quite sure. Then Roger Bannister dedicated his life to doing it and finally achieved it.

The other interesting aspect is the beauty of seeing a perfect performance. This is similar to gymnastics. Sure the tricks are amazing, but let’s face it, there are tons of people who can do really cool tricks that aren’t in the Olympics. At the top level, the distinguishing feature is that they can execute the routine to near perfection.

This is also what distinguishes top speedrunners. Some speedruns might take a new person a few days to learn, some might take a few months, but without serious dedication for many, many months (often years) you will come nowhere near the times the top runners get. This is because you must develop consistency at executing everything to perfection.

I’ll just list some resources now, because a whole book could be devoted to this topic.

The main place where the records (along with video) can be found is speedrun.com. If you want to check out speedruns as they are done live, see Speed Runs Live. This is a page to organize people’s live streams of their speedrun attempts. The reddit community is a pretty friendly place to ask questions (for example, “I’m interested in where to learn how to do such and such glitch I saw in such and such speedrun, can anyone help?”).

Right now AGDQ 2015 (Awesome Games Done Quick) is happening. AGDQ is a yearly fundraiser for a charity. For a week, some of the top speedrunners will perform games live 24 hours/day for about a week. People call in and donate money for the Prevent Cancer Foundation. Last year they raised over a million dollars for the organization. Go check it out if this sounds interesting!


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Sadness in Sia’s “Chandelier”

Unless you’ve been under a rock, you’ve probably heard Sia’s single “Chandelier” off her new album 1000 Forms of Fear. She’s had some commercial success in the past, but this song broke into the top 10 on the Billboard 100 and seems to be everywhere. I’ve been sitting on this post and decided now was good timing, because I imagine this song will blast from many speakers tonight at New Year’s Eve parties as some sort of uplifting dance song.

In the past, Sia has had most success in indie scenes because of the subtle deepness to her lyrics and complicated tonal and harmonic aspects to the songwriting. At first glance, this song seems to go against this history with a purely pop appeal. This post will be an attempt to show that lyrically there is still the depth of her past material.

Let’s start with the reason I think the song blew up in the first place. If you ask someone for the lyrics, they will probably only remember the chorus:

I’m gonna swing from the chandelier, from the chandelier
I’m gonna live like tomorrow doesn’t exist
Like it doesn’t exist
I’m gonna fly like a bird through the night, feel my tears as they dry
I’m gonna swing from the chandelier, from the chandelier

These lyrics have a mostly uplifting feel to them. Live life to the fullest. Go out and party. Do things that are out of your comfort zone. Seize the day. This feeling is backed by the soaring melody and general good feeling of a pop song.

The verse lyrics go by fast and are generally easy to miss. The opening already gives away that the song is not as cheery as one might imagine:

Party girls don’t get hurt
Can’t feel anything, when will I learn?
I push it down, push it down

I’m the one “for a good time call”
Phone’s blowin’ up, ringin’ my doorbell
I feel the love, feel the love

There is an implication here that the main girl is some party girl or even a prostitute. She puts up a front of always having a good time. She is happy and can’t get hurt. In fact, she has put up such a shield that she can’t feel anything. She pushes the bad feelings down.

The next part is “1, 2, 3, 1, 2, 3, drink/Throw ‘em back ’til I lose count.” This girl uses alcohol in a severely unhealthy way to numb her feelings. She gives the impression of going out and having fun, but she is depressed.

The other half of the chorus is:

But I’m holding on for dear life, won’t look down, won’t open my eyes
Keep my glass full until morning light, ’cause I’m just holding on for tonight

Now swinging from the chandelier has a double meaning. It isn’t symbolic of living an unconventional, free life to the fullest. It seems here to be symbolic of near catastrophe. She is barely holding on. She can’t even look at what she’s doing.

“I’m just holding on for tonight” is carefully worded. On the one hand it can mean that she’s holding on for the night. She will make it through. The darker interpretation is that she will only hold on for tonight. Once the night is over she will let go into death (possibly overdose?). The way Sia says that sentence over and over at the end of the song implies this darker interpretation.

If you aren’t convinced yet, the second verse drives this interpretation home:

Sun is up, I’m a mess
Gotta get out now, gotta run from this
Here comes the shame, here comes the shame

The night was not a fun party at all. She’s ashamed of the acts she performed and wants to run away from it. In case you haven’t heard it, here’s the music video:


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Mathematical Reason for Uncertainty in Quantum Mechanics

Today I’d like to give a fairly simple account of why Uncertainty Principles exist in quantum mechanics. I thought I already did this post, but I can’t find it now. I often see in movies and sci-fi books (not to mention real-life discussions) a misunderstanding about what uncertainty means. Recall the classic form that says that we cannot know the exact momentum and position of a particle simultaneously.

First, I like this phrasing a bit better than a common alternative: we cannot measure perfectly the momentum and position simultaneously. Although, I guess this is technically true, it has a different flavor. This makes it sound like we don’t have good enough measuring equipment. Maybe in a hundred years our tools will get better, and we will be able to make more precise measurements to do both at once. This is wrong, and completely misunderstands the principle.

Even from a theoretical perspective, we cannot “know.” There are issues with that word as well. In some sense, the uncertainty principle should say that it makes no sense to ask for the momentum and position of a particle (although this again is misleading because we know the precise amount of uncertainty in attempting to do this).

It is like asking: Is blue hard or is blue soft? It doesn’t make sense to ask for the hardness property of a color. To drive the point home, it is even a mathematical impossibility, not just some physical one. You cannot ever write down an equation (a wavefunction for a particle) that has a precise momentum and position at the same time.

Here’s the formalism that lets this fall out easily. To each observable quantity (for example momentum and position) there exists a Hermition operator. If you haven’t seen this before, then don’t worry. The only fact we need about this is that “knowing” or “measuring” or “being in” a certain observable state corresponds to the wavefunction of the particle being an eigenfunction for this operator.

Suppose we have two operators {A} and {B} corresponding to observable quantities {a} and {b}, and it makes sense to say that {\Psi} we can simultaneously measure properties {a} and {b}. This means there are two number {\lambda_1} and {\lambda_2} such that {A\Psi = \lambda_1 \Psi} and {B\Psi = \lambda_2 \Psi}. That is the definition of being an eigenfunction.

This means that the commutator applied to {\Psi} has the property

{[A,B] = AB\Psi - BA\Psi = A\lambda_2 \Psi - B \lambda_1 \Psi = \lambda_2\lambda_1 \Psi - \lambda_1\lambda_2 \Psi = 0}.

Mathematically speaking, a particle that is in a state for which it makes sense to talk about having two definite observable quantities attached must be described by a wavefunction in the kernel of the commutator. Therefore, it never makes sense to ask for both if the commutator has no kernel. This is our proof. All we must do is compute the commutator of the momentum and position operator and see that it has no kernel (except for the 0 function which doesn’t correspond to a legitimate wavefunction).

You could check wikipedia or something, but the position operator is given by {\widehat{x}f= xf} and the momentum is given by {\widehat{p}f=-i\hbar f_x}.

Thus,

\displaystyle \begin{array}{rcl} [\widehat{x}, \widehat{p}]f & = & -ix\hbar f_x + i\hbar \frac{d}{dx}(xf) \\ & = & -i\hbar (xf_x - f - xf_x) \\ & = & i\hbar f \end{array}

This shows that the commutator is a constant times the identity operator. It has no kernel, and therefore makes no sense to ask for a definite position and momentum of a particle simultaneously. There isn’t even some crazy, abstract purely theoretical construction that can have that property. This also shows that we can have all sorts of other uncertainty principles by checking other operators.


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Favorite Books I Read in 2014

I said I would do this last time. Here’s a list of my favorite books that I read this year. Note that it may look like this list is meant to be “Favorite Books from 2014,” but it is a fluke that so many were actually published in 2014.

I did the Goodreads challenge to complete 40 books this year (and I will be successful). This gives you some idea of how big the pool was. I plan to use modified versions of reviews I’ve already written in case you find the same review elsewhere and think I copied. In no particular order:

1. The Imperfectionists by Tom Rachman.

I’ll start with a caveat that I read this book entirely on plane trips. In some sense, this is more a collection of short stories than a novel. But the characters in the stories all work at the same newspaper. This means as you read more and more, characters you’ve already met start making their appearances and it feels more like a novel.

The characters are bizarre in a fascinating way. Each of the stories felt unique, and some even fell into Borges-esque scenarios (a woman reads the newspaper in its entirety everyday, but one day is missing and she can’t move on until it gets found which leads to an endless bureaucratic mess through the inner workings of the paper).

The book is full of surprises and turns with each character. I thoroughly enjoyed it.

2. Zeus is Dead: A Monstrously Inconvenient Adventure by Michael G. Munz.

This book is absolutely hilarious. It is simultaneously a murder mystery, classic hero quest, and old school comedy. This may seem impossible, but the combination is seamless.

Let’s start with the comedy. This is not your modern, tasteless humor that will seem dated in 10 or 20 years when the trend dies. This comedy goes back to the timeless masters. The setup is masterfully done with verbal misdirection, odd and surprising combinations, and goofy situations. Even puns. But have no fear if you’re the type to groan at a pun. They are used in conjunction with other techniques, so once you’re laughing for another reason, the pun slides right in for effect.

On to the mythology. From reading other reviews, I was a little afraid that I needed to be an expert on mythology. Don’t be afraid! The characters are introduced in layers with excellent pacing. All you need to know about them will be explained in the book. Only once you have time to get used to them are new characters introduced. It works wonderfully. Plus, there is guide in the back if you need it. You won’t need it.

You probably should be somewhat familiar with common tropes from these genres (as most people who read books will be), because a lot of the humor comes from the characters (and narrator) being fully aware of the tropes and cliches they fulfill. The self-awareness of the book is crucial to it working properly. Otherwise it might come across as a blind mash-up.

Munz shows us he knows what he’s doing by carefully keeping the tradition in some parts and radically departing at others. Weaving all these threads together could have been a catastrophe in less deft hands, but it seamlessly stays together and seems natural here. Most importantly, the book will immediately draw you in with a fun, original premise and keep you in the whole way through.

3. The Bone Clocks by David Mitchell.

Don’t come to this one expecting something totally different. This is classic David Mitchell. Think of Cloud Atlas. It is a sprawling epic story with some slight supernatural elements but a healthy dose of realism. Each section jumps ten years and changes character point of view.

Each character’s voice is fully distinct and developed. The politics can be a bit heavy handed at times, and cutting the entire last section would greatly improve the book (there is nothing (I mean nothing!!) worse in literature than an extended denouement).

Overall, it is a fun, engaging read even if slightly predictable at times.

4. 10:04 by Ben Lerner.

In order to appreciate Ben Lerner’s new book, one must be proprioceptive, a word used often in the book, to the writing style which includes appositives, those clarifying comments between commas, and beginning sentences with subordinate clauses, but one must also grapple with long compound sentences; only to reach the end and find new punctuation that extends the sentence even more.

More seriously, this novel is excellent. Be warned. One could argue that the character and plot development are not strong and do not propel the book forward in the way of the classic novel form. This should not be a criticism in the same way that such a criticism would be seen as nonsense if given of Whitman’s poetry.

The book raises big questions about art and life. There’s no attempt to force some correct answer down your throat. The point is to get you to think about them.

5. For Kings and Planets by Ethan Canin.

I recommend this one with reservation, because outside of the above 4 books, everything else I read this year is a 4 star review or lower, but I wanted this list to have 5 things on it.

The plot setup might make you groan: a pristine, naive midwestern boy goes to the big city for college and is seduced into the dark ways of the rich, city boy. Sound familiar?

But forget about that for a second, because that’s where everyone’s review seems to get stuck. Underneath this trope, which should be considered a device to deliver the story and message, is a heartbreaking struggle that came right at a time I wanted to hear it.

The main character grapples in no uncertain terms, but beautiful prose, with the great questions. What do you do if you don’t succeed at your dream? How long do you keep trying before settling? Is there ever a way to compromise on such things without losing a part of yourself? What does it mean to live a meaningful life?

This novel handles these questions better than any in my recent memory.


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Thoughts on William Gibson’s Pattern Recognition

If you couldn’t tell, I’ve been trying hard to get a post out every Wednesday. I also haven’t done any book reviews in a long, long time. This is because I’ve been trying to keep everything organized on goodreads, so when I finish a book I write a quick review and give it a rating there.

This week I drew a blank for a post. I recently finished William Gibson’s Pattern Recognition, so it seemed fitting to say a few words about it here. To set the stage, here’s a quick plot synopsis. A girl named Cayce has the skill to identify logos that will succeed in advertising.

You should think of this as a speculative fiction thing and not an intuition she has developed through years of practice. For instance, her parents discovered it when she was a child and had a violent nauseous reaction to some particularly bad logos. Now she consults with firms as a freelancer. She has the ability to “recognize patterns” in culture.

Anyway, a mysterious collection of short video clips keeps getting found on the internet and a cult following happens. No one knows where they came from, how people are finding them, or who is making them. A key point is that they are universally appealing and moving works of art.

These video clips lead us to one of the major themes of the book. If we abstract the video clips, this gives us the major thematic questions: In a digital age, bombarded by information, how can we know who is creating what we see/read? Is it part of a larger set of data and being selectively skewed to bias us? How do we know where to go to get “real” information?

Cayce is approached by an ad agency to investigate who is producing the video footage. This adds to those earlier questions, because where some people see untarnished art, other people see an opportunity to skew and manipulate using it. If that ad agency succeeds, can we ever tell? I think this is an important and difficult question for our time (and note that he published the book in 2003 before internet tailored advertising was “a thing”).

Overall, I found the premise of Cayce’s skill and the spot on cultural commentary to be the high point of the book. It kept me interested and brought to the forefront of my thoughts important questions. Let’s move on to the points I didn’t like as much.

At first, I found the style of the book to be clever, fast-paced, and ultra-modern. Gibson uses the present tense, and he “evolves” the language to drop the subject of the sentence when understood. This fun style didn’t stay fun for long. It turned choppy and grating. I assume the intent was to create a sense of fast-paced, forward motion, but in the long run it did the opposite.

Somewhere along the way, the plot turned to a huge Pynchonesque ultra-conspiracy as Cayce uncovered more and more information. I’ll admit that it plays in with the theme that we never know who is controlling our media, but overall it wasn’t convincing.

It works in Pynchon, because his style is so complex and intense that it plays into the mindset of uncovering the conspiracy. As I pointed out already, Gibson’s style is the opposite. It is simplistic to the point of creating sentence fragments.

By the end of the book, I had to will myself to read it. The style plus the conspiracy plot points made it a slog. Overall, I enjoyed it and gave it a 4/5 on goodreads. It is inventive and original and raises lots of important questions. But I have to recommend it with reservation (I’ll probably do a top 5 books I read this year with my real recommendations).


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Composers You Should Know Part 3

My relationship to today’s composer is much different than the previous two. The previous ones I have been listening to and following for ten years or more. I found this one recently, because I was listening to Sirius XM’s classical channel and heard something magnificent come on. I looked the composer up and found her.

Jennifer Higdon is writing some of the most inventive music I’ve heard. She has the ability to write in a huge variety of styles: bluegrass, beautiful lush orchestrated pieces, avant-garde experimentation, and more … often all rolled into a single piece.

There are several really interesting facts about her life. The first one is that she started late in music. I spent my youth around stressed out high school students who had “only” a few pages of musical accolades who feared they had already missed out on the chance of a profession in music. They were already 15 and hadn’t finished writing their second symphony which put them way behind their idols.

Jennifer Higdon didn’t even pick up an instrument until 15 and hadn’t started composing until 21! Now she is one of the most successful living composers. She currently holds the Milton L. Rock Chair at the Curtis Institute of Music and has had numerous commissions from the top orchestras and performers. She has won basically all the top prizes and awards for composition as well.

Her doctorate was under George Crumb at the University of Pennsylvania (though I hear almost no Crumb influence in her work and think that extracting it would be an awesome music theory Ph.D. if anyone is interested). The piece I want to talk about is her violin concerto (I’m using the Hilary Hahn recording). The piece won the 2010 Pulitzer Prize (I swear I’ll try to avoid the Pulitzer next time).

The piece opens with the main theme on the violin. The orchestral accompaniment is a collection of disjointed, broken upper register parts with chimes and what possibly sounds like harmonics on the violin. The solo part contrasts with this nicely, but the power of Higdon is first noticeable when the orchestra accompaniment switches to a sustained part. The bottom comes in for the first time, and the effect is chilling.

The positioning and style choices in the juxtaposition of contrasts is what made me fall in love with the first piece and seek out more. I’ve since learned that this is a characteristic in many of her pieces. One moment the soloist is playing rapid, technical passages, the next she has long flowing lines.

The transitions are spot on. You can think about the different sections and wonder how you get from one to the next. But in the moment of listening, the flow works, and you don’t notice the section breaks unless you are intended to notice them. When she intends you to notice, then it is quite an experience. The set up contrasts are often the most moving moments of the piece.

The violin concerto is quite difficult to describe, because its sound is so unique. It sounds vaguely atonal yet always feels fully tonal. It sounds foreign while maintaining the feeling of familiarity. The second movement is fascinating, becuase it opens as the standard “slow movement,” but once the solo comes in it quickly shifts to a much more urgent and pressing feel.

The movement does a wonderful job at maintaining an undercurrent of passive beauty while the motion of the solo picks up intensity over top of it. This tension allows the piece to build to a huge sense of relief when the tension releases. This type of thing isn’t possible with a more traditional approach to the middle movement.

The last movement is more traditional in that it provides an awesome, showy finish. It reminds me a bit of the end to Shostakovich’s first violin concerto. It is technical with interesting moody, modal tonalities coming in and out throughout.

Overall, this is a fantastic piece you should check out. I will definitely continue to follow what Jennifer Higdon does and familiarize myself with more of her work. This is a composer you should definitely know if you are into orchestral works but not so familiar with modern works.

I should have been doing this in the previous posts, but here’s a link to the first movement:


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Composers You Should Know Part 2

Obviously this series could go on every week for the next year, so I’ll have to determine how far to take this. Recall that I’m trying to expose people to important living and working composers they may never have heard of. I’m not so sure about today’s choice, because in my circles he is a name people know.

Aaron Jay Kernis is someone you must familiarize yourself with if you haven’t heard of him. He studied under John Adams at the San Francisco Conservatory and with several other people at Yale and the Manhattan School of Music. He has won more prizes, awards, and commissions than anyone I know of.

Let’s not focus on that stuff and instead get to the music. Stylistically he is often said to be neo-Romantic or post-Romantic with some minimalist influences. I’m not sure I agree, or could even explain what that is supposed to mean exactly.

The key thing I love so much about his music is how unfamiliar and original the chord progressions and melodies are without losing musicality. You could always create something new by using some random process to make the note choices for you, but that is the furthest thing from what is happening here.

Despite being engaging and interesting from the originality standpoint, the music still can be moving or heartrendingly beautiful. This is remarkable, because so much of music composition is setting up expectations and using familiar ideas to elicit certain responses in people. Kernis has the ability to do this after throwing away the conventions.

He is a magnificent orchestrator. He often produces wonderful and strange textures that are in constant flux and propel the music forward. The piece I’d recommend to hear all of these aspects is the second movement of the Second Symphony. It is moving, beautiful, and utilizes the orchestral textures while simultaneously being ominous and unfamiliar.

With how good his orchestral works are, I still think that his chamber works are where he excels the most. His second string quartet made him the youngest composer to win the Pulitzer. That piece is magnificent, but my favorite work of his of all time is still the first string quartet.

The first string quartet is usually listed under Musica Celestis if you want to find it. I think the Lark Quartet might have the only recording. I used to listen to this piece on repeat when I was in high school. It was without question one of the definitive pieces that made me want to be a composer. I’ve listened to it probably hundreds of times.

The first movement is aptly named “Flowing,” because the main first theme is a soaring, flowing melody. The piece is extremely dense and chaotic at parts. As I said before, it will feel very unfamiliar in terms of melodic lines, chord progressions, and even form, but it is more in an originality way rather than alienating. It still sounds natural.

The second movement “Adagio” is the movement I listen to the most. It starts slow and beautiful with long sustained, open chords. This is one of those deeply moving pieces. In the middle, the climax is shocking in its power.

He starts a low ascending pattern that climbs up higher and higher, getting faster and faster, to an intensity that is almost unbearable. Then the opening, chilling chord progression comes back while the intensity in the first violin lingers just a tad too long. I’ve never heard anything quite like it, and I found the effect so amazing that when I was younger I often tried to imitate it myself when I wrote pieces.

It only works if the performer is ready to fully put themselves out there. If you don’t go for it one hundred percent, then it will sound awkward because of how exposed it all it. Luckily, the Lark Quartet pull it off perfectly, and they will leave you with chills at the end of it.

One of the remarkable things about the string quartets is how large they can sound. He writes in a way that maximizes the medium’s potential. At times it is hard to tell whether it is a full string orchestra or just a quartet (there is a string orchestra version of the Adagio I just wrote about, but I think it isn’t as good, because the exposedness of that section needs to be one on a part to feel that way).

Anyway, I could go on like this all day about his music. If you haven’t heard of him, you should definitely check out some of his works, especially the first string quartet.

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