A Mind for Madness

Musings on art, philosophy, mathematics, and physics


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Validity in Interpretation Chapter 2

I thought my last post would be the only one on this topic. Then I realized, if I’m reading the book, why not just take notes on it and post them? My goal is to give a good enough summary so that later, if I want to recall what was in a particular chapter, I can figure it out from this. I’ll also try to be explicit where I’m adding my own thoughts (which should be minimal).

Chapter 2 begins with a positive argument for developing a notion of validity in interpretation. The first chapter addressed common objections. This one begins by pointing out that one major purpose of art is to expand your mind with other people’s thoughts and actions and to feel what others have felt. If we take the usual modern approach that anything can mean anything to anyone, then you have a Rorschach inkblot test and will only encounter yourself.

Chapter 2 is all about showing that the author’s intended verbal meaning provides a viable principle for measuring the validity of an interpretation. Hirsch states that such a principle must be determinate, reproducible, and able to deal with the problem of implication. The subsections of the chapter deal with each of these.

First, we need to know what is meant by verbal meaning. Hirsch says, “Verbal meaning is whatever someone has willed to convey by a particular sequence of linguistic signs and which can be conveyed (shared) by means of those linguistic signs.” He explains how verbal meaning is variable and context dependent, but not indeterminate. For example, we should be careful of “the Humpty-Dumpty effect” (based on the scene in Through the Looking Glass where Humpty-Dumpty insists his name means the shape that he has). We can’t just say words at random and expect them to mean something because we claim they do.

The next section is on whether we can actually reproduce the intended meaning. First, he admits that interpreters can misunderstand an intended meaning, but the fact that mistakes happen does not invalidate the idea of reproducibility. It is a logical fallacy to argue that something is impossible in theory by pointing to a specific example. The person that objects has to demonstrate that such misunderstandings always occur. Hirsch points out that we will never know such a thing, and hence it cannot be used as a valid objection.

The most common objection to reproducibility comes from the empirico-psychologistic notion of perception which says that we never encounter anything in real life. We merely encounter our perception of things. For example: That isn’t a table you see, but your perception of the table. This type of objection disappears if you are careful in distinguishing meaning vs significance (a central theme of the whole book). Verbal meaning is the thing itself (the table or the author’s intended meaning), and significance is your relationship to the thing (your perception of the table or your particular reading of the text).

There is also a radical historical skepticist objection to reproducibility which says that we can never understand the writings of a different time period, because we do not have the linguistic, cultural, and so on perspective for a proper understanding of the verbal meaning. This radical form of criticism should not be confused with the healthy version (which Hirsch admits is true) that an interpreter will always encounter some difficulties if the culture is too far removed.

Personal note: The odd thing about the radical skeptic view is how backwards it has often proved to be in reality. How many times have we seen a poet or writer be completely misinterpreted and torn down by their contemporaries only to be better understood by later generations? This is especially true of really old texts in which we have a good general understanding of the culture and etymology of words that people living at that time never could have known.

The next concept Hirsch moves to is determinacy. Determinacy is necessary to share meaning, because something without boundaries would have no identity to share with someone. He upgrades his terminology, “Now verbal meaning can be defined more particularly as a willed type which an author expresses by linguistic symbols and which can be understood by another through those symbols.”

A type is defined to be something that has boundary and can be fully understood through one instance, but can always be represented by more than one instance. My example: The concept of snow is a type, because the word “snow” is an instance that has that verbal meaning. Another, different instance would be “that white stuff that falls from the sky in winter.” Both instances have the same verbal meaning, and the verbal meaning can be recovered in full from any instance.

Personal note: I think of this in terms of computer science. You can make a class in object oriented programming, and you can make instances of that class. One instance may not have enough information to recover what the class contains, so this is not a type…it is a class (Hirsch uses the same terms but isn’t thinking of computer science).

The next section is about the difference between unconscious and symptomatic meanings. The main point is that verbal meaning may contain things that come subconsciously. Verbal meaning does not contain things are unintended due to symptoms of something else. The example is a boy who has a tell when he lies. The tell is symptomatic of not wanting to lie, but it is not part of the verbal meaning of the lie. The tell changes our interpretation to something that was not verbally intended by the boy, and that’s why we should not include it.

Personal note: Something makes me feel funny about this section. Even though the example makes it clear why we do not want symptomatic meaning to influence our interpretation, nothing will be that clear in pure writing. I’m not sure in practice it is ever possible to determine the difference between symptomatic and unconscious meaning. Suppose a story has sexist undertones the author is not aware of. Do we consider this symptomatic of the author’s sexism or is it an unconscious intended part of the story? Since we are allowed to include symptomatic meaning in the significance of the work, maybe this doesn’t matter very much.

There is then another section on the difference between meaning and subject matter which we discussed last time. The last section is about implication. (Personal note:) This seems a thorny issue given little space, so I hope it comes up again later. The main point is that implication is a learned convention, because it relies on the reader’s past experience with a given shared type. He explains it by analogy: an implication belongs to a meaning as a trait belongs to a type.

That ends the chapter. The next chapter is about genre and context which should be interesting.


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On Validity in Interpretation

I have two volumes of critical theory, and an excerpt that appears in both of them is a selection from E.D. Hirsch, Jr.’s Validy in Interpretation. I just got the full book, because I’m fascinated by the argument. This is one of those things where I’ve made a complete reversal of opinion over the course of this blog. Let’s start at the beginning.

If you’re unfamiliar academic literary criticism, there was a period of time starting around the early 40’s (still kind of going on) where literary theorists thought a text could stand on its own. It began with Wimsatt and Beardsley’s The Intentional Fallacy, which argued that the intention of the author shouldn’t matter when interpreting a text. The text would make you feel something. The symbols and themes would mean something to you. And that was how it should be, since you were the one doing the interpreting.

That description is an oversimplification, because these were complicated academic papers making these arguments. The nail in the coffin of the author came a bit later with Barthe’s Death of the Author. This school of thought was roughly associated with something called “New Criticism.” The New Critics argued for doing close readings of a text, and this came to dominate the scene so much that we were all taught this as the only way to analyze literature.

It is extremely difficult to get out of this mode of thinking, because we were taught to think this way in school. When talking about literature, we are told there are no wrong answers. We can come up with a theory of what the book is about and then find passages to support it. We get an A if we do this successfully. What is interesting is that despite the fact that this is what people will publicly espouse, everyone secretly believes that there are wrong answers.

The whole point of this post was to point out that we recognize some interpretations as nonsense even if they are well-supported. But we’ve been taught this New Criticism stuff so thoroughly that it becomes impossible to call someone out on it. This is because most people aren’t familiar with a philosophy of literature that allows you to talk about valid versus invalid interpretations. Isn’t the whole point of an interpretation that it is personal and can change from person to person? I say no. If a text can mean anything to anyone, then it doesn’t really mean anything.

Hirsch gives us a way out of this bind with Validity in Interpretation, published in 1967. The excerpt I’ve read is the first chapter, and it is brilliant. Before going on to describe a positive theory of validity, he first goes through and dispels the common objections to a notion of validity for interpretation. That’s what the rest of this post will be. Note that Hirsch’s argument is a whole chapter of a book, so I can’t do it justice here. I just want to give an overview.

Counterargument 1: The meaning of the text changes (throughout time), even to the author. Thus, the original intention of the author should be irrelevant.

This is obviously nonsense. The example used to support this is of authors that reject their old work. But it isn’t the meaning of the text that has changed, but the author’s attitudes or opinions. If the meaning had changed with the author, then the author would have no need to reject it. In this example, the changed author still recognizes the original meaning as the meaning.

Counterargument 2: It doesn’t matter what the author means, only what the text says.

To expand on this argument a bit, it often appears in a different form: an author may intend something, but not have the technique to effectively convey that meaning. This is part of the argument in The Intentionally Fallacy. A text must be evaluated on what it does and not on what the author intends it to do.

We must pull apart a few distinct concepts here. If the point is evaluation, then the intention is important. We can’t evaluate whether the author effectively conveyed their meaning without first knowing their intended meaning. The other concept is meaning.

The only way to successfully argue that authorial intent doesn’t matter is to find examples where there is a consensus that a text meant one thing and the author intended something different. The New Critics use this example as a thought experiment, but in reality no such example exists. Even if these examples were abundant, then we wouldn’t need to have a theory of interpretation at all, because everyone would agree to the valid interpretation confirming the fact of validity in interpretation.

Counterargument 3: We can never truly know what the author meant, because we are not the author.

Implicitly, this argument is asking: why bother trying something that is an impossibility? First, we don’t have to be the author to claim that a certain proposed meaning is highly improbable. To take Beardsley’s own example, a poem in 1744 in reference to God, “He raised his plastic arm.” We know beyond all doubt that “plastic” was not intended to mean the material that wasn’t invented yet.

All a theory of validity involving authorial intent is trying to do is bring up a range of possible valid meanings. There can be interpretations that hit every part of the spectrum from highly likely to literally impossible (as the above example). We get around the problem of knowledge of the author’s internal states by using probabilities.

One more thing. Certainty is also impossible in science, but that doesn’t mean it is not worthwhile to try to understand what is happening in the universe around us. Similarly, being certain of what the author intended is impossible, but it is still worthwhile to try to reconstruct the possible intentions.

Counterargument 4: The author often doesn’t even know what they mean.

The example given is that Kant claimed to understand Plato better than Plato himself. This is a subject/meaning confusion. Kant doesn’t understand what Plato meant better than Plato. He better understands the subject matter.

The other example is where someone makes a compelling case that an author had an unconscious meaning that came out in the artistic process, but was not intended. Hirsch beautifully counters by asking, “How can an author mean something he did not mean?” In other words, things that come out from subconscious processes are still part of the author’s meaning.

That’s it. All common objections to authorial intent and validity in interpretation have been dealt with. Hirsch can proceed to constructing the theory. I’m quite excited to read it!


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Narrative Voice vs Narrative Perspective

I’ve been on a bit of a Gérard Genette kick lately. If you don’t know who he is, then you probably haven’t studied much narrative theory. He is mostly known for his work on structuralism, but I’ve never really found the structuralists that interesting or compelling. Genette’s other major work was to almost single-handedly invent the foundations for modern narrative theory (in the 70’s).

It is true that Booth’s Rhetoric of Fiction (from which the idea of “show don’t tell” originated) came first. But until Genette’s groundbreaking Narrative Discourse: An Essay in Method it wasn’t really thought that the narratology could be applied to anything more than simple, contrived examples. Genette clarified the terms we use today like “voice” and “mood” and showed how they can be used to examine actual complex literature (he used Proust’s In Search of Lost Time).

Today I want to pull out an interesting concept from Narrative Discourse. The concepts of narrative voice and narrative perspective tend to get lumped together as the “point of view” in inattentive analysis, yet the distinction is important and clear in contemporary literature.

To illustrate the distinction, let’s consider an example. I write a story with a third-person limited viewpoint about a child growing up. There is a clear main character, and we only see things from his “point of view.” Now what if I tell you that the narration is done through a set of journal entries from the child’s mother. Nothing about the story itself has changed, but it seems the “point of view” should be the mother.

The confusion comes from conflating two distinct notions. The first is narrative perspective. In our example, the narrative perspective is the child. Genette would say the story is “focalized” through the child, because the story unfolds with the child as the main character. The other concept is narrative voice. The voice of the narration in our example is the mother.

I think most people are probably comfortable with the distinction between voice and perspective, because these ideas have become universal. That’s why it is kind of surprising that it wasn’t until somewhat recently (in comparison to how long writers have been using the distinction) that we actually had terms to talk about them.

Of course, you can intentionally make these the same, but this tends to be more work than keeping them separate. You often hear, “You must develop/find your voice as a writer.” If you use your own voice for the narration, which will come most naturally, then the narrative voice is you and not the main character. To write in the main character’s voice will take a tremendous effort, because you have to overcome all of your own natural tendencies and stick to a consistent fictional voice.

Also, notice how much complexity can enter into a work merely by being aware of this distinction. There is a narrator, who could be a fully fleshed out fictional character, and there are one or more focal lenses to the narration. The narrator can learn of various events in a certain order. Then they can relay those events in a different order, which could be totally different from the order in which they happen to the main characters.

The main characters will have feelings and emotional reactions to events. The narrator can have totally different ones. The narrator can try to skew the telling of events due to their reaction. As you see, keeping the voice and perspective separate can be a useful tool for making complex and rewarding fiction. In fact, all the complexities listed here can be found as fairly standard technique these days.

If you are interested in isolating various elements of narrative such as voice and perspective, then I definitely recommend looking at this classic work.


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Verbs of Being and the Past Progressive Tense

Everyone gets told to “show, don’t tell” at some point in their education. Today I want to talk about an equally important (and related) piece of advice that rarely gets taught. In fact, many people go through their whole lives and don’t even notice this. Until you’re told to look for it, you might miss it entirely, because in speech it sounds so natural.

If you write something in past tense, then you will undoubtedly use the word “was.”

Example: I was in my room reading a book, when there was a knock on my door.

Take a moment and answer the question: does this sound fine to you? Before we begin, I need to point out that sometimes “was” is the best option. There is no need to blindly expunge all verbs of being out of your writing. The thing I look for is whether something is happening. “To be” is static. If someone is doing something in the sentence, why not make them do it with the appropriate verb? In other words, make the action happen!

First off, replacing “was” with the active verb brings the action of the sentence more vividly to the reader’s imagination (i.e. it shows the action rather than telling the action). Also, it naturally varies the sentences. If most of your sentences read “blah was blah,” then it gets boring.

A related issue is the past progressive tense. This takes the form “was verb-ing.” I was sitting in my room. I was reading a book. Then I heard that someone was knocking on my door. If you are already on the lookout for “was,” this should be no problem to detect. Sometimes it is subtle to identify. In the example, “I was in my room reading” uses past progressive, but I split the infinitive to make it harder to catch. Rearranging makes this clearer: I was reading in my room.

The past progressive suffers from the same types of problems as before. It gets repetitive, and it implies inaction.

There are two main ways I use to get rid of these constructs. First, I identify the active verb. Second, I add details. Strangely, these passive expressions almost always appear when you haven’t sufficiently described the scene. In the first part of the example sentence, the active verb was “read.” In the second part, the active verb was “knock.” One way to fix the sentence is to add some detail and use the right verbs.

Edited example: I sat down in my room, excited to crack open Annie Dillard’s The Living, when someone knocked on my door.

Part of producing clear, vivid writing involves a long, tedious process of weeding these constructs out wherever possible. There exists unprofessional writing (like this blog post) which maybe goes through one or two revisions. But most of professional quality writing is rewriting and editing. I think it is easy to forget how dedicated you have to be to get everything just right. Your first draft will have these problems, and that’s fine. You can’t be worried about that upfront or else you will never write anything.

I want to show an example to illustrate that great writers are constantly aware of the problems listed in this post. I love Annie Dillard and I am reading The Living right now. I’ll use a random number generator to pick a page (to emphasize I didn’t tailor the example) and give you the first full paragraph.

Eustace and Clare worked together often, and hunted the hills and fished the river together, and smoked their pipes, resting their eyes on the wide river or the drowsing fields. Resolution burned in Eustace and made him grave and sincere; gaiety and hopefulness animated Clare and blew him about. Clare’s view that a man could enjoy this life eased Eustace’s urgency to succeed, and moderated his mental habit of measuring himself, his material gains and losses, against the doubt and dread of his parents, and Minta’s parents …

(OK, I ended it early because it was long). Notice the verbs: worked, hunted, fished, smoked, resting, burned, made, animated, blew, enjoy, eased, moderated, … There isn’t one verb of being or past progressive tense in there. A sad state of affairs is that sometimes a mark of great writing is that you don’t notice it. Now that I’ve taken the time to examine a paragraph like this, I can’t even imagine the effort that went into it. Yet most people, including myself, will normally read through it without a second thought.

I thought hard about what to contrast this with, because I don’t have much on my bookshelves that I could be confident made the errors I listed above. I chose Ayn Rand’s Atlas Shrugged.

There were glaring lights inside, a few tired salesgirls among a spread of deserted counters, and the screaming of a phonograph record being played for a lone, listless customer in a corner. The music swallowed the sharp edges of Taggart’s voice: he asked for paper tissues in a tone which implied that the salesgirl was responsible for his cold. The girl turned to the counter behind her, but turned back once to glance swiftly at his face. She took a packed, but stopped, hesitating, studying him with peculiar curiosity…She gasped like a child at a burst of firecrackers; she was looking at him with a glance …

I have to say, it isn’t terrible. The first sentence is in past progressive, and we get one “was” in the middle. I couldn’t resist adding the next sentence after the dialogue which had a “was looking.” That first sentence could be altered, and then it would be a less awkward tense change to the simple past tense:

The lights glared inside. He saw a few tired salesgirls among a spread of deserted counters and heard the screaming of a phonograph record being played for a lone, listless customer in a corner.

I admit it isn’t much better, but that’s part of the point of this post. Sometimes it takes a great deal of effort to get even one sentence to be clear and active and to fit stylistically with everything else. The difference between a good writer and a great writer is often that the great writer has the stamina and dedication to question the strength of every word and sentence. They don’t settle for fixing most of them. Anyway, I have no idea how this turned into a pep talk being great, so I’ll end here.


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Thoughts on Permadeath

I hate to return to this topic so soon, but it has been awhile since I’ve blogged and I’ve been reading a bit about it. Back here I blogged about why playing roguelike games can be a gratifying and important experience if you’ve never tried it before. I want to step back from the genre in general and focus in on just one feature.

Recall that permadeath (shorthand for “permanent death”) is a game mechanic where once you die you must start the whole game over again. Even within hardcore roguelike gamers and game developers there has been a lot of controversy surrounding this mechanic. Isn’t it unfair if someone puts in 12 hours of work, and then a random event outside of their control makes them start all over again? Right at the very end. It seems punishingly unfair.

Well, let’s consider a thought experiment which I think exemplifies the purpose of permadeath. Imagine you are going to a job interview, but you live in an alternate universe where you can set a clock and time travel back to that point in time. You set the clock right before the interview. You go into the interview. You are way too passive and modest and some other person that exhibited more ambition gets the job.

No big deal. You travel back in time, and you take the opposite approach. You go all out with your risky self-promotion. You seem like a jerk that won’t fit the team, so you don’t get the job. You travel back in time. Each time you try new things based on the feedback you got from your last attempt. You never feel any pressure to get it right, because you can keep trying until something works. There’s no real penalty for doing poorly. Finally, you get the job.

This is exactly how save points work in a game. Maybe in real life you think this type of thing would be great, but notice what it does to a game. All of a sudden, a challenge presented in the game that you were supposed to think about and develop the skills to get past no longer functions in that way. You lose all motivation to try to get it right the first time. It is no longer challenging, because you can keep repeating it and seeing what went wrong until you calibrate a success. You are virtually guaranteed to be successful.

This type of success can feel mildly rewarding, because you still made progress and got better until you were good enough to get through that part. But you have no sense of real danger or excitement or real accomplishment when you play this way. What does success even mean if there is no risk of failure? You could try act as if you didn’t save, but it won’t create the same effect. The point of the permadeath mechanic is to get your blood pumping with excitement that if you make one wrong move you could lose everything. It is far more exciting to be living on the edge like that.

Permadeath makes you take your time and plan your strategies carefully. You can’t just blindly spam a bunch of attempts until something works. When you get good enough at the game to succeed, it is a real success. Puzzles and challenges are actually puzzles and challenges in the sense that you need to solve them to get through them. There’s no guess and check.

There are of course varying degrees of save points, but in the extreme scenario above, I think the case is clear. It is hard to get the gamer to experience any sense of danger or reality with excessive save points. On the other extreme, permadeath tends to elicit anxiety and fear just walking around an empty corridor. In some cases, this may not be desirable for your game.

I’m not saying one way or another is better or worse. I just wanted to explain what I think the game mechanic’s purpose is. Sometimes it is quite inappropriate. There have been tough platformers that I never would have gotten very far in if they had permadeath. This is to say that even though I find permadeath to be a very rewarding way to play a game, it doesn’t serve its purpose in some genres.

To tie this back to roguelikes, I think this is really the perfect genre for permadeath. The reason is that roguelike games tend to have a massive amount of randomly generated content. Your starting stats, items, character, etc are all random. The rooms and level layouts are random. The enemies you fight are random.

This means that when you die and start all over again, you aren’t just repeating the exact same thing over and over again. Each playthrough gives you a totally new game. Permadeath would be quite tedious and obnoxious if you had to keep playing the same content over and over again. I think that would be a misuse of it. Save points serve a good purpose in that case. If you’ve demonstrated you can get through a certain part, why make the player do it again if it is exactly the same?

If you want to see other opinions, here is a 203 comment discussion on the topic.


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Pushing Children to Early Career Choices

I’m staying with my in-laws right now, and they watch America’s Got Talent. As the show went on, I started to get more and more disturbed by the things some of these 11- and 12-year-olds were saying. They were saying things like, “I’ve been working my whole life for this moment.” Or they would say, “This is important for my career.” I don’t remember the exact phrases, but they were acting like the entire rest of their life was planned for them already.

I don’t like the pressure these children are feeling. They think that they will let everyone in their lives down if they don’t use their talent to become super famous. They feel like they will somehow be a failure at anything less than winning this thing. I know because I’ve been there.

This means that I also know that it might not be the parent’s fault at all. Sometimes it doesn’t matter how many times a parent says that it is okay to do whatever you want, or that they will support you no matter what career you want. I can say from experience that words can’t easily overcome all the subtle external environmental factors.

When I was young I started gymnastics and excelled quickly at it. In high school I competed nationally and even sometimes internationally. I wasn’t the best at that level, but I was still fairly young and I won the New York state championship one year. Here were the types of pressure I felt that were not parental, but my parents probably had no idea they existed. If I were to quit, then I would let my coach down, my teammates down, the family members that kept telling me I would be in the Olympics someday, random people in my hometown that thought I would bring the town fame, and on and on.

This type of pressure that no one even realized they were exerting (they were expressing how proud they were of me and how excited they were for my future) kept me doing it for much, much longer than I wanted to. Luckily, I got up the courage to quit at some point. It was a total shock to everyone, because they couldn’t see that I had grown to hate it. They confused me being good at it with me being passionate about it. To this day I still don’t “miss it” like everyone assumes.

I understand that there is a fine line that must be walked which is probably very difficult for parents of talented children. If your child shows promise in singing, how far should you let it take over their life? You don’t want to discourage them from practicing if they actually do love doing it. You don’t want to discourage them from working hard. You don’t want them to quit if they are merely having a bad week or month. Let’s face it. Sometimes it is tedious, discouraging, hard work to get better at something. It is easy to confuse this with disliking it.

You also don’t want to force them into a career in it before they are ready to make that decision (which honestly I don’t see how you could be ready for that decision until at least college age). All these things are very difficult to tell without being inside the person’s head. Even asking them bluntly how they feel about it might not get an honest response if they are feeling a lot of pressure. I know. I used to lie about it.

There is also the issue that people think that if you aren’t a famous musician (or mathematician, etc) by a certain age, then you will never be famous. First, that is false. More importantly, I’m not sure why being famous is thought of as a measure of success. Heck, I’m not even sure being able to make a living at music should be the sole measure of success. There are lots of people who enrich their lives with their talents as a hobbies, and this is a far better path for them. Making it a career would have made them hate it.

I don’t really have any proposed solution to this (or reason for writing about it other than that it was on my mind today), and I know it is a tough issue. Still, I felt quite disturbed to hear these children express these concerns that I used to have. I wish I could tell them that they can still do whatever they want, and what they want might be something they haven’t even heard of yet. You might disappoint some people when they find out you stopped pursuing it as a career, but you can’t let that dictate your life.


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Preventing Fragmentation with Paging

Since I’ve been on a bit of a computer science kick lately (I even made a new “computer science” category to tag posts with) I thought I would do a follow up to my post on fragmentation. I’ll summarize it so you don’t have to go reread it. If you try to put stuff in memory in the most naive way by just looking for the first place it fits, then you end up with huge amounts of fragmentation (wasting around 33% of your available space). I also said that no modern operating system would do it this way.

To appreciate how great this idea I’m about to describe is, just take a moment and try to think of a different way of doing it. When I learned about this, I actually tried and was stumped. Any algorithm I thought of was very similar to the first-fit one and left lots of external fragmentation. My hint is that the solution has no external fragmentation at all, and it requires a radically different way of thinking about the situation.

As far as I know, all modern operating systems solve the problem using something called paging. The idea is actually really simple, even though the implementation can be quite confusing at first. The idea is that you use something called a page table which keeps track of where everything is located. This allows you to physically break everything up so that they all can fit right next to eachother and you’ll have no external fragmentation.

Even though one chunk could then be spread all over the place physically, the page table allows you to logically think of it as one chunk, because you just look at the page table and read the addresses contiguously. Let’s just look at an example. A page is just some fixed small size. Let’s suppose we want to put something that takes three pages of space into memory.

Maybe there’s not 3 consecutive pages left in memory, but there’s still a room if you don’t look consecutively. The first 3 pages are taken, but then there are two available places, then another is taken, but then there is room for the last page:

In some sense this is still the first-fit algorithm, but now the chunks are all the same size and we break everything into those chunks first. We then just start sliding the pages in wherever they fit without ever having to worry about fitting the whole thing together.

You can use the page table to look up where the pages were placed in physical memory. It is really clever, because as a user you can still think of things as single units, but you never (externally) waste any space. There will still be a small amount of internal fragmentation which comes from things not being perfect multiples of the sizes of pages, but this will be minuscule comparatively.

Anyway, that’s all for today. I didn’t want to leave you all hanging. I’m sure you were all dying to know how your computer got around the problem I raised in that post.

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