A Mind for Madness

Musings on art, philosophy, mathematics, and physics


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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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Thoughts on NaNoWriMo

If you didn’t know, November is National Novel Writing Month (NaNoWriMo). The goal, in my understanding, is to motivate someone who has always wanted to write a novel to actually sit down and do it. You have a daily writing goal of 1667 words per day. If you meet this goal, you will have produced a 50,000 word novel in one month.

I successfully did this in 2010, and I decided to do it this year as well (though I decided about 5 days into the month, and I still haven’t made up my 8,000 word deficit). I’ve been trying to meet my Wednesday blog goal in addition, so this is going to be a short and poorly edited post.

I’d like to give an analogy with running a half-marathon (something I did for the first time last month). To be successful at either of these tasks, it is something you have to want to do. If you don’t actually want to put the work in, then nothing I say after this point will matter.

So now we’ve established that you want to write the novel. In this case, NaNoWriMo is an excellent opportunity for you. I’ll give a list of helpful things NaNoWriMo provides.

Impediment to Writing a Novel 1: You have no pressure to sit down and do the work.

Solution: If you sign up on the NaNoWriMo webpage, make a profile, tell people you are doing it, have the website give you word count deadlines, etc, this external pressure gives you incentive to do it.

Now maybe adding stress to your life with extra artificial deadlines, or your family continually asking you how its going, isn’t the healthiest thing in the world. But it is only a month, and then you can choose to never think about it again if you want.

I think of this in the analogy as signing up for the half-marathon. I had started training programs many, many times in my life but always quit well before the day of the race. I think this was because there was no pressure to complete the program once it got tough. I could drop out with no consequences. If you sign up, then your name is out there, you put some money down to do it, people you’ve told get excited for you and would be let down if you dropped out.

Impediment to Writing a Novel 2: Working through slow or difficult writing periods, i.e. staying motivated when you hit the wall.

Solution: NaNoWriMo provides an enthusiastic community. No matter where you live, there are probably lots of people who meet up and do “write-ins.” When you are feeling down, you can post this in a message board, and get tons of helpful tips to stay motivated. When other people post, you can be the one to provide cheery feedback.

I think you can’t underestimate the feeling of doing this in a community. There’s something about being in a group of thousands of people who are doing the same thing at the same time.

This is similar to the half-marathon. You can’t imagine the number of times I thought to myself, “If all of these people can do it, then I definitely can do it. They can’t all be special superhumans.” The race itself is full of nonstop positive feedback. Similarly, you get all sorts of motivational and positive feedback from famous authors in your email throughout the process.

When you find yourself thinking that you can’t keep up this pace of words per day, it is nice to think that most of the people participating are just normal people like you, and if they can do it, so can you. You can even meet many of them and bond over the experience.

Now on to some of the downside of NaNoWriMo (why have I not ended this post yet? I still have over 3,000 words to write today in addition to this…). I guess one could ask what is the point? In some sense, you produce a terrible rough draft of about a third of a typical novel length.

Here’s a thought experiment. Suppose you want to publish your novel. This means that if you work at this furious pace for two more months after NaNoWriMo has ended, then you will have a rough draft. I personally estimate editing something to take about 3 times longer than it took to write.

This means that you can’t really consider NaNoWriMo to be an intense experience, because you have to keep it up for a full year if you want to even start sending it out to places, which might take several more years. There have been famous examples of people doing this, but I think one downside to NaNoWriMo is that it gives people a false sense of how much work producing a novel is.

If you want to go all the way to publication, it is like running six marathons, but only having the excitement and support for the first half-marathon. This isn’t necessarily a problem if you understand what you are getting into when you start, but if it is your first time, it is easy to fall prey to the hype and not realize that at the end of the whole thing, you have basically nothing that you can show people (please don’t make people read your unedited 50,000 words that spewed out of you at this rapid pace (even if they beg you for it!)).

So why do it? I guess you could ask why do anything? It gives you a real sense of accomplishment if you succeed. It is cathartic to produce. It is a community building exercise. It teaches you a lot about yourself. It can be extremely fun to invent the plot twists. It exercises your creative muscles. It gets you away from TV and mindlessly clicking through cat videos on youtube in your spare time. Plus, I plan on publishing mine someday.

I think there is a way to link my progress bar to WordPress. I’ll try to do that so that I can stay accountable to you all as well.


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Composers You Should Know Part 1

I figured I would start a series on important living composers that most people are probably unaware of. I think a lot of symphony orchestras do a disservice by sticking to the classics. Even people that regularly attend orchestra performances have a hard time naming more than a handful of living composers outside of those that have made a bit of fame through movie scores (John Corigliano or Philip Glass come to mind).

It is a strange state of affairs if you consider any other artistic medium. An art connoisseur would have no problem listing living artists ad nauseum or an avid reader would have no problem listing living authors (and not just popular bestsellers). The blame can be spread over many sources, but it doesn’t help that the major orchestras shy away from new music. Public education doesn’t include it, either.

The person I’ve picked for today has been in the news a lot recently. Can you guess from that alone? John Luther Adams won the Pulitzer Prize for music this year (did you know there was a Pulitzer for music?) for his work Become Ocean. As such, a lot of people have written about it, but I’ll give my own take in a bit. You may be thinking, “Ah, but I have heard of this person!” Make sure you are not confusing John Luther Adams with the minimalist composer John Adams (also recently in the news for his controversial opera The Death of Klinghoffer).

John Luther Adams lives in Alaska, and this has been a major influence on his music. His pieces are often about some aspect of nature. Become Ocean fits into a larger program of the composer to create pieces about all the elements. This one is about water, but he has an earlier piece, Inuksuit, based on earth and one that has come out since then, Sila: The Breath of the World about air. I expect to see a piece about fire in the near future.

I have avoided reading much about Become Ocean, so I could write this without being influenced by other people’s reviews and interpretations. The Seattle Symphony comissioned the piece and premiered it in June of last year. Of course, when thinking about what an orchestral representation of the ocean would sound like, it is hard not to think of Debussy’s attempt with La Mer. You should get that out of your head, because this work is very different. Despite how much I love La Mer, I have to admit that Adams’ representation is brilliant.

Most of the work is quiet and almost zen-like. You can hear the gentle waves with short, scalar and arpeggio patterns up and down, up and down. It is hard to know for certain without a score, but it sounds like a piano keeps this ostinato going for the entire piece. On top of these waves are long, held notes tying the whole thing together with a dark murkiness.

This is most of the piece, and it may sound boring to you, but consider the following. The sun is setting, and you are sitting on the edge of a dock looking out over the ocean watching it. The repetitive waves transfix you, and you lose 45 minutes out there. It is beautiful and wonderful, not boring. That is this piece.

The piece, as a whole, continually shifts and moves. It has long, slow builds to magnificent climaxes. These moments are chilling in the strength and power, just as the ocean has the power to be a destructive force. It is amazing that the piece can seem so static, yet have so much underlying motion in the same way that changing your attention on the ocean can make it seem static or turbulent.

If you don’t listen to much modern music, then this would be a good place to start. The piece does not have a large barrier to entry like a serialist composition or quarter-tone piece or something with lots of references. Anyone can sit down and instantly be captured by the beauty. It will take a good deal of patience, though. There’s no melody or anything to command your attention. Like all great art, it requires some effort on the listener’s part. But that effort is well worth it.But that effort is well worth it.


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An Introduction to Metal for People Who Like “Good Music” Part 2

It has been 2 years since I did Part 1. That has a broader introduction which I suggest you start with. This is intended as a minor follow up. Most of the great composers since 1900 have pushed the boundaries of what we consider music. This is part of what makes them great. Their music takes time and effort to properly digest and understand. Keep this in mind when you are first exposed to the bands below.

1. Blotted Science is a band fronted by Ron Jarzombek. They use a lot of polyrhythms and 12 tone technique. Anyone who thinks of early Schoenberg as worthwhile should check this band out. It is not the extreme serialism of Boulez and Babbit. There is still a clear tonal center. Jarzombek uses 12 tone rows in a different way. Here’s a sample: Vermicular Asphyxiation.

2. Behold… the Arctopus is one of the many projects of Colin Marston. It was difficult to pick which of his bands to include on this list. I will warn you before you click on the sample, this is probably the most extreme avant garde music on this list. This band writes extraordinarily complicated music. One could write Ph.D. theses on them. It is all completely composed and not just people playing random notes as fast as humanly possible like some imagine. There is a ton of structure and development. It is impressive as anything you will find in the classical world. Here’s a sample: Exospacial Psionic Aura.

3. Meshuggah is a Swedish band well-known for revolutionizing metal. They are probably the most influential band on modern metal. If you doubt the seriousness of this bands compositional technique, then look no further than the top music theory journal for an analysis of their polyrhythms: Music Theory Spectrum, Vol. 29, Issue 2. A classically trained musician would cry if they saw this sheet music and had to hold it together in a performance. Enough said, here’s a sample: I

4. Between the Buried and Me is a progressive metal band. They are hard to describe because they use all sorts of styles in their music. You’ll find lots of technical sections, chromaticism, slow melodic parts, jazz influences, and more. Their albums are often huge concepts that tell a story. This makes listening to them feel like a metal opera. Here’s a sample: Telos (if you find the beginning too intense, skip to around 3:30 for a more jazz influenced part).

I could do a whole series on prog metal, because that genre is based around the idea of chromaticism and technique. It is almost a direct translation of Liszt or Paganini to metal. Other prog bands I think are good are Archspire, Cynic, Leprous, Intronaut and the Ocean. We could also continue with the avant metal scene with bands like Jute Gyte (crazy use of semi-tones) and Normal Love. But let’s move on.

5. Burzum is a one man black metal band by Varg Vikernes. There is a controversy surrounding this band, but he remains one of the foundational pillars of black metal. Black metal cannot be summarized easily here. It is unlike the previous bands. The focus is not on technique but atmosphere. Black metal is about creating a turbulent, icy, lonely atmosphere and living within nature. It has a philosophy behind it which rejects the excesses of the more popular death metal. Here’s a sample: Naar Himmelen Klarner.

6. At the Gates were pioneers in the early death metal scene. They write dense music with a lot of counterpoint and interesting melody. Their songs have purpose with a lot of cultural criticism. Don’t fear the label “death metal.” This term has come to mean something quite different than it once did. I recommend With Fear I Kiss the Burning Darkness in general, but here’s a sample: Primal Breath.

I might do another of these before too long, but I think that’s enough to contemplate for now. Nothing on this list can be absorbed without spending a lot of time with it.


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The Role of Genre in Game Interpretation

This essay is a bit late. I wrote it about three months ago, so it rehashes tons of things from the past months of posts as if they never occurred. Still, I think the example is nice. We’ve been thinking about genre and interpretation of literature. But if we take seriously the idea that games can be art, then the same methods of interpretation still apply.


Game critics jump at the opportunity to place games in the nice neat box of its genre. Still, there has been a growing trend to shrug off genre as useless due to the diversity of modern games that push boundaries. We will examine the idea that the utility of genre identification is not in its descriptive power, but its use for artistic interpretation.

It is true that no label will ever perfectly fit any given game. But if this were a viable argument to forgo genre as useless, then it would have caught hold in the world of literary criticism by now. Instead, we find that genre is still a useful means to understand literature. The idea is ancient and can be found in Aristotle’s Poetics, but the (post-Derrida) resurgence can be traced back to at least Gérard Genette’s famous 1979 essay The Architext: An Introduction.

Roughly, Genette defines poetics as the art and science of interpreting a text by situating it in the proper context of similar texts. The similarities come from stylistic and thematic concerns among other things. This group of similar texts is what we call a genre. Some narratologists, such as Genette, argue that one must establish the context to obtain a proper understanding and interpretation. In other words, if we want to interpret a work of art, then identifying its genre is not only useful, but necessary.

This might sound shocking to most people, because (American) high schools teach that great works of art stand on their own. There is no right or wrong way to interpret. I can read The Catcher in the Rye, be moved by it, and formulate my own opinions without ever considering the genre in which it resides. Great art should be universal and not dependent on surrounding works.

This viewpoint is valid, but limited in scope. Consider the following thought experiment. You read a book on Abraham Lincoln. You are not told the genre or author. I now reveal that the book was a collection of journal entries by a friend of Abraham Lincoln. This exposes a set of ways to interpret the book. If I told you it was a biography released by a reputable academic press last year, then I open a different set of interpretations. For example, both are trying to convey factual information, but we should be more skeptical of stories found in one person’s journal.

Now, if I told you it was a work of historical fiction, then a new set of possibilities arises. Major people, places, and events form a factual framework for the story, but the bulk of the plot will be fiction. We might expect to find other literary devices such as symbols and themes which put a particular spin on the events. Identifying the genre was enough to open and close various ways to interpret the book, because we are familiar with the genre’s conventions.

This example also shows us that the author’s intent is important, because we want to know whether we are reading true statements. Art isn’t always as egotistical as we want to believe: I felt this; I think it means that. David Foster Wallace often referred to experiencing great literature as building a relationship between author and reader. Art fails if one side tries to be selfish.

Communication is vital for a successful relationship. Understanding only comes if the reader is familiar with the genre in the same way that cultural context can change the meaning of oral communication. Familiarity with conventions and tropes allows the reader to see the manner in which it deviates. According to Genette, these deviations will have significance for interpretation. Only by putting a work in the context of its genre can we hear what the artist is saying.

By now you’ve guessed how this relates to games. Games serving as an artistic medium is a recent development. Sophisticated dialogue on interpreting games is in its infancy, and attempting to port established literary theory to the discussion is almost non-existent. The point is not that genre theory or poetics is the “right” way to frame these conversations, but that it gives us one established lens of interpretation from a multitude of literary theories.

It is futile to produce a full-scale analysis here (Genette took several books to analyze Proust), but let’s consider one familiar example: Braid. In this case, we have an unambiguous genre. Braid is a puzzle platformer in the sense that the player jumps between platforms and solves puzzles. The most significant innovation is that getting to platforms and solving puzzles requires time manipulation.

If we want to interpret the game, poetics tells us that we should give time special status. You might think at this point, “Duh! The game is about time manipulation, and we didn’t need to know the genre to come to that conclusion.” But you would be wrong, because you are biased and know that time manipulation is not a characteristic of the genre. If the genre typically used this mechanic, then we’d have no reason to give special status to time in our analysis. So identifying and understanding the genre gave us information to bring to our interpretation of the game.

We should not be hasty in our attempts to render genre useless merely because many recent games defy clean classification. Genette (and Hirsch) allowed for the definition of genres to change and grow over time. New ones can be constructed where no old ones fit. The Braid example may not have convinced you, but genre analysis can be a useful tool for interpretation of games in more subtle and abstract settings. We should move past the simplistic notion that genre is purely descriptive. It can also be interpretive.


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Validity in Interpretation Chapter 5

You know the drill by now. These are just notes from my reading of E.D. Hirsch, Jr.’s Validity in Interpretation. We have finally reached the last chapter. The main thrust of this last chapter is on how to tell whether our interpretation is valid. It rehashes a lot of stuff we’ve already covered, and it gives some examples of putting the theory to use.

The first point is that we can often trick ourselves into self-validating an invalid interpretation. Hirsch doesn’t use the term, but this is a direct rephrasing of confirmation bias to literary interpretation. If we go into a text thinking it must mean something, then try to find confirmation of this interpretation, we will always find it and will overlook conflicting evidence. This is not the correct way to validate an interpretation (or anything for that matter!).

We are led back to the hermeneutic circle, because some of the evidence will only appear after a hypothesis about the interpretation has been formed. In the next section, Hirsch doesn’t say this, but he essentially argues for a Bayesian theory of interpretation. The process of validation is to take all the hypotheses and then figure out which one is most likely correct based on the evidence. As new evidence comes in, we revise our view.

All that matters are the relative probabilities. Sometimes two interpretations are equally likely, and then we say both are valid. The point is not to have one victorious theory, but to have a way to measure how likely each is in terms of the others.

Personal Note: Whenever someone brings up probabilistic reasoning in the arts (or even history) the same sorts of objections get raised. The assignment of a probability is arbitrary. You can make up whatever priors you want to skew the results in favor of your pet interpretation. These are very recent debates that came decades after this book was published. Surprisingly, Hirsch gives the same answers to these objections that we still give.

First, we already speak in probabilities when analyzing interpretations. I think it is “extremely unlikely” that the word “plastic” means the modern substance in this 1744 poem, because it hadn’t been invented yet. It is “likely” that this poem is about the death of a loved one, because much of Donne’s work is about death. These statements assign relative probabilities to the likelihood of the interpretation, but they try to mask this.

By clearly stating what we are doing, and coming up with actual quantities that can be disputed and argued for, we make our reasoning more explicit and less likely to error. If we pretend that we are not dealing with probabilities, then our arguments and reasoning become sloppy.

As usual, when determining probabilities, we need to figure out the narrowest class that the work under consideration fits in. A good clarifying example is the broad classification of women vs men. Women live longer on average than men. But when we pick a specific woman and a specific man, it would be insane to argue that the woman will probably live longer based only on that broad class. If we note that the woman is a sedentary smoker with lung cancer, and the man is an Olympic marathon runner, then these narrower classes improve our probability judgments.

This was the point of having an entire chapter on genre. We must analyze the intrinsic genre of a work to find the narrowest class that it fits in. This gives us a prior probability for certain types of interpretation. Then we can continue the analysis, updating our views as we encounter more or less evidence.

Hirsch then goes on to talk about the principle of falsifiability as we know it from science. Rather than confirming our hypothesis, we should come up with plausible evidence that would conclusively falsify the interpretation. He goes on to give a bunch of subtle examples that would take a lot of time to explain here. For simplicity, we could go back to the plastic example. If a poem dates before 1907, then any interpretation that requires the substance meaning of the word plastic is false.

He ends the section by reminding us that we always have to think in context. There are no rules of interpretation that can be stated generally and be practical in all situations. There are always exceptions. The interpretive theory in this book is meant as a starting point or provisional guide. This is also true of all methods of interpretation (think of people who always do a “Marxist reading” or “feminist reading” of a text).

I’ll end with a quote:

“While there is not and cannot be any method or model of correct interpretation, there can be a ruthlessly critical process of validation to which many skills and many hands may contribute. Just as any individual act of interpretation comprises both a hypothetical and a critical function, so the discipline of interpretation also comprises the having of ideas and the testing of them.”


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Validity in Interpretation Chapter 4

We are back with the next set of notes on E.D. Hirsch, Jr.’s Validity in Interpretation. This chapter is on Understanding, Interpretation, and Criticism. I found it to be the least interesting as a whole. It mostly involved clarifying some terms related to interpretation.

The first section is about the diversity of interpretations. If there is a notion of valid/invalid for an interpretation, how can there be so many? Is only one correct? The answer is that we should welcome these diverse interpretations, because they all contribute to understanding. A key idea that is repeated throughout this chapter is that understanding comes before interpretation. We must understand what the author means before we can put our explanation into words.

Different interpretations can agree on the author’s meaning, in which case our understanding is deepened. Conflict only arises when two interpretations disagree on what the author means. Sometimes the difference might only be aspects of the same traits. Hirsch gives an example of two people looking at the same building from different angles. They might describe the building in radically different ways, but they are still describing the same thing.

The next two sections are where the terminology begins. I’ll distill the definitions here.

Understanding: The construction of meaning. A silent, internal affair.

Interpretation: The explanation of meaning. This almost always contains criticism and significance claims, but should be kept separate as a theoretical matter. Interpretation is an art, because the interpreter must convey their understanding accurately using terms that are familiar to their audience.

Significance: A perceived relationship between the verbal meaning and something else. We usually cannot artificially isolate significance from the above two acts, because these relationships aid us in coming to an understanding of a text.

Criticism: The explanation of significance. Thus, criticism is to significance as interpretation is to understanding.

Judgment: The act of perceiving significance. “One understands meaning; one judges significance.” This can include value judgments, but could also be purely descriptive.

Even though Hirsch is largely concerned with interpretation for the book, he emphasizes that criticism is important because it shows us why a work has value. He turns to the idea of intrinsic criticism for the next section. This starts with a brief retrospective. After the early 20th century logical positivists took hold of criticism, the literary community rebelled and tried to formulate a literary form of criticism. This was a useful advancement, but Hirsch wants to do better.

The theorists argued that the only way to properly judge a literary work is on literary grounds. For example, it is wrongheaded to judge the value of a poem on how well it would serve as a newspaper headline. The only fair way to judge a poem is in how well it succeeds as a poem. New problem: this is not a good way to judge a poem, because there is no agreed upon notion of what a poem is.

This is where intrinsic criticism comes in. We must make our judgments according to the nature of the work, but we cannot come into the work assuming we know what those standards are. We must look to the work itself to determine its nature. Judging by extrinsic criteria will be called extrinsic criticism. The theorists argue that extrinsic criticism is always wrongheaded.

Hirsch points out that it can be a useful tool sometimes. Being forced to limit yourself to intrinsic criticism is, well, limiting. The critic has a duty to judge by extrinsic criteria if she believes the purpose of the author to be misguided. For example, an essay may be extremely unclear and vague, but the arguments of the author well-known. If the intended argument is faulty, then it is reasonable to critique it. This is extrinsic, because the intended argument cannot be parsed from the poorly written essay itself.

A more concrete example is Gadamer’s famous work on interpretation Truth and Method. Gadamer wrote about how the historicity of understanding affects interpretation. Hirsch criticizes it for not concerning itself with validity. This form of extrinsic criticism is judging the assumptions on which the work was written. Hirsch believes Gadamer succeeded in his intended purpose, but that his purpose was faulty in this matter.

He ends with a plea for critical freedom. At the time this was written, the established schools of thought argued for a very limited “literary” internal criticism (*cough* New Criticism). The main point they try to make is that anyone is free to criticize a work using any method, but it is not valid to evaluate the work on the arbitrary grounds that the critic makes up. For example, one should not evaluate Paradise Lost as a poor work on the grounds that it does not contribute to the history of mathematics.

Hirsch gets around this by saying that extrinsic criticism shouldn’t be arbitrary. A good critic understands what the intent and values of the author are, and can make a case for a reweighing of those priorities. This isn’t a question of limiting the critic, but merely one of appropriateness. To totally ignore the purpose of the author is to misunderstand the work, and hence you cannot possibly present a valid interpretation (the explanation of your understanding). A critic must found their argument on valid interpretation.

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