Let the Gushing Begin

While spending 90 hours with Persona 3, and 75 hours with Persona 4, at a steady rate of two hours a night, four or so nights a week, I've had plenty of time to consider how I should praise these games. There has been much talk about how Persona 3 and 4 are unique among JRPGs, and why they should be seen as pinnacles for a flagging genre. I think it would be better to say that any gamer should break out their PS2 and give these a try, regardless of your feelings toward JRPGs. In many ways, Persona 4 has more in common with a Studio Ghibli movie than Final Fantasy. Clare and I have enjoyed these games tremendously (they are great games to play with a partner), and I plan on spending multiple posts elaborating on what makes them so good.

Both Persona 3 and 4 are excellent games. Unlike a lot of reviewers, I don't like to spend most of my time talking about all the minor improvements that each new iteration of a series makes. Suffice it to say that if you only have time to play one of these games, and they are long games, play Persona 4. They have entirely separate stories with different settings (and a single event that connects them, as a fan service), and according to one man's opinion, the improvements are worth something.For this reason, I'm going to spend most of my time talking about Persona 4, although there are interesting and important differences in setting and plot between the two games that I hope to talk about.

To save time, I'm also going to assume some familiarity with the basic mechanics and premise of the game. Reading through this spoiler-free description at HG101 is worth your time if you haven't played either of these games before; there are really no other games I'm aware of in the states that I can effectively compare these to.

With that out of the way, I'm going to list three aspects of Persona 4 that make it a special game for me. Then my plan is to spend one post elaborating further on each of these aspects, with maybe a conclusion post at the end. Here goes:

1. It's Japan, stupid!

Growing up as a fan of video games, I've learned that good localizations really do make all the difference. And though translations have gotten a lot better in the last five or ten years, way too many publishers try to pull the rug over our eyes about where a game originated, by replacing all references to Japanese culture with obvious American substitutions.

One of the few upsides of the diminishing market for Japanese games in the states is that those games that do make it over here are less afraid to show themselves for what they are to a more dedicated audience. Atlus is smart enough to figure out that Persona 3 and 4's rich grounding in Japanese culture was much more of an asset than a liability.

It doesn't do it justice to say simply that Persona 4 is set in Japan. Yes, you will learn many surprising facts about Japanese holidays, the rigid school system (6 days a week, with frequent testing), delicious-sounding food (P3 set Clare and I on a search for good ramen in Portland), and the complex meanings of the different Japanese signifiers (which are completely untranslatable).


What makes P4 so unique and fascinating is that it is not a game about Japan, it is a game about Japanese people, who live in this culture and deal with these conventions. Your character experiences the pressure to get good grades in a school that posts the test scores of each student publicly. He risks embarrassment to show affection and perhaps have a relationship in front of disapproving adults. In its own implicit way, the game also confronts expected gender roles and homosexuality. All of these issues get reflected in the "other" world, in the bizarre nature of the enemies you fight (the game is similar to Earthbound in this respect). This leads into my second point:

2. Escaping the Representation-ist Philosophy

As we all know, RPGs started on the table top, as a way for adolescents to become heroes in a fantasy setting. The mechanics, dice-rolling and all, were simply a means to simulate the chance elements that factor into a real-life (or fantastical) battle.

These days it's popular to call JRPGs derivative and uninnovative, but historically they have made one important development in the RPG form that Western developers have been slow to pick up on. They liberated the RPG mechanic from it's representation-ist origins. The kind of battles that take place in P4 make no sense realistically; you're looking at a bunch of kids carrying fans and baseball bats surrounding something called a "Fickle Papillons" (bunch of butterlies) and a "Chaos Fuzz" (crazy cop-gorilla hybrid). The battles that these simulate (in their own way) take place in the real world, with real-life enemies like depression and anxiety.

Plenty of JRPGs before P4 use interesting symbolism in the enemy design, but P4 is uniquely explicit in this regard (this is one way in which P4 excels P3 as well). The Personas that emerge from each character (as evil Shadows to be confronted) create their own worlds that reflect their own personal conflicts. The main insight that allowed the Persona series to be born from the giant Shin Megami Tensei juggernaut is that the demons that the characters control in those games are a lot like the inner kind that any high school student deals with.

3. A Sense of Time

One of my favorite aspects of Mother 3 is that for a very long time, the game is centered around different characters in a single community. Unlike so many RPGs, Mother 3 gave you a firm sense of home, something worth protecting (which also makes the surprise ending a lot more interesting).

P4 gives you more than a home, it gives you a normal life. No matter how serious the situation gets (and like many RPGs, the world is in peril), you will always be just a normal student to those around you. And God help you if you ever skip school.


Instead of progressing through places, P4 progresses through time, and the game is driven by a kind of rigid schedule. Some people complain about the level of grind in P3 and P4 (something that's offset by playing with a partner), but sticking in one place has some definite upsides. Characters can have roles more complex than a class type and a backstory; you're friends can have families, they can feel trapped in their jobs (many of which are inherited). Characters can be allowed to develop on their own instead of letting a constant change of venue drive them along.

Anyways, I hope to go into more detail soon. Till next time.

Screenshots from HG101, and 1up.

What a Mathematican Does 101

My girlfriend is a biologist. I've noticed that introducing oneself as a biologist is a fairly good conversation starter. You don't have to be an expert in genetics or cellular biology to have an opinion about evolution or cloning. Even talking about your pet's strange behavior is fair game.

I am a mathematician. When I introduce myself as a mathematician, the response usually falls into one of three categories:

1. The "Oh, you must be pretty smart" response. I know people mean well, but I did not go into mathematics to impress people. Indicative of a larger problem, specifically the impression that you have to be a genius (usually some kind of detached savant) to work or take an interest in the subject. Also, hard to respond to. (I lean towards "Smart enough to work at Starbucks.")

2. The "I was bad at math in school" response. One of my professors told us once of a time when someone (I think a delivery man) nearly broke into tears when the professor introduced himself as a mathematician. The delivery man had such a traumatic and humiliating algebra class that just the mention of the subject sent him into shivers. It's true that most people are not as emotional about it. They mention their time in school because that is their only exposure to math, and the only way they can relate to me.

I can only sympathize and explain that math is a lot more stimulating when it's not a set of tools to be applied to boring problems. Though I did not struggle at math in high school, I didn't really enjoy it either, and I have a lot of sympathy with this perspective. I was a political science major until I realized how different math is in college (at least at Reed, where I was not forced to take two years of calculus before I could study something more fun).

3. Quietly and quickly moving to a different subject. This is by far the most common response.
Sad, but preferable to the first two.

A response I have never gotten, though I would love to get it, is "What does a mathematician actually do?" People do not usually ask this question, either because they are not interested or too embarrassed, although there is nothing to be embarrassed about. I didn't know the answer to this question until after I took two years of college math. Math professors don't usually tell you, because they're more concerned with helping you pass whatever class you're taking (and I'd never been brave enough to ask). However, it is a really important question, partly because there are so many misconceptions, many of which I fell victim to.

How would I answer this question? The short answer that I lean towards lately is "I study worlds that aren't real."

Most colleges group math with other sciences, and I understand the logic behind this. Besides the fact that science uses tools from math, both mathematicians and scientists observe things and make and test hypotheses. There are two differences.

Firstly, the things I observe are not facts about the world in which we live, but about worlds which are purely hypothetical. I study worlds like the world of natural numbers, the world of geometry, or the world of set theory. It is okay to call them models, but they don't necessarily "model" anything about the real world, or at least that is not the context in which I, as a mathematician, study them. Certainly, physicists or computer scientists might be interested in the conclusions I draw, but those are just applications and not the subject itself.

Secondly, unlike a scientist's conclusions, my conclusions can be completely verified, such that they can never be refuted. This is because certain axioms are true in these worlds, as well as certain rules of logic which let me derive things from them. Most people would say I assume the axioms, but I have a slight problem with the word "assume". I prefer to say that I am studying precisely that world in which these axioms are true. How do I know that there is such a world? Because I know that there are statements that can be derived from these axioms; in a certain sense, I am only dealing with language. (I choose to sidestep the Platonist-Antiplatonist debate about mathematical reality that pops up in math philosophy.)

Of course, what I have just stated sounds tremendously boring. It needs to be noted that a mathematician is not interested in all statements that can be derived from these axioms; one could tell a computer to derive statements for me, but the vast majority of these would be meaningless gibberish that no one could care less about. The statements that I am interested in are ones that are either useful for their applications, or just aesthetically pleasing (and the two go together far more often than not).

What does it mean for a fact about a hypothetical world to be aesthetically pleasing? Often, the worlds we're interested in can be visualized in interesting ways. Not just in terms of a picture, but in terms of examples from real life. But visualizations alone don't quite do it justice. Some facts we just want to be true; something we expect should be true by thinking of examples, but can't quite figure out why, until we do, which is gratifying. Some facts are very surprising, and they might help us conceptualize something we thought we had no hope of grasping. Some facts make connections between two worlds that seemed separate.

Part of being a mathematician is deciding what deserves to be studied; and like any scientist, we should be able to explain why the topic we've chosen is interesting, or just beautiful. There is an artistic aspect to math, just as there is a philosophical aspect.

Anyways, I hope to say more about certain aspects of the mathematician later. Comment if you have any questions.

Morte and Murray

Can a man ever change his nature, even if he lived forever? Wouldn't he just make the same mistakes over and over again? If so, immortality would be a curse.

Two works come to mind that approach this question head-on, with very different conclusions. One is Planescape: Torment, the dark, brilliant 1999 computer RPG. The other is Groundhog Day, the 1993 philosophical comedy with Bill Murray.


In both works, the protagonist must repeat the same actions endlessly, but for different reasons. In Groundhog Day, Phil Connors (Murray) is cursed to wake up at 6:00 on February 2nd every day for infinity. In P:T, the Nameless One (he has forgotten his name long ago) has had his mortality removed. He can die, but he will eventually regenerate. If the death is harsh enough, he'll lose his memories, and the game starts after such an experience. You'll soon find out that there's virtually nothing you can do that you haven't already done thousands of times.


Thus both characters are immortal, although neither can truly progress until they change their nature. It's fun to watch Murray's character evolve over the course of the movie, from joy at the lack of consequences, to despair at his predicament, and eventually to selflessness and thus his redemption. Many see the movie as a religious parable, but I think it's rather the pressures of a mainstream release that necessitate a happy ending. It's a great movie (Murray is excellent), and definitely thought-provoking, but as a morality tale it provides a fairly simple prescription; to change your surroundings you must change yourself.

The Nameless One's goal is equally simple, yet nearly impossible: he wants to die (an ironic premise for an RPG, to say the least). The game stresses that there is no simple epiphany that will allow him to do this. Over the long course of his life, he has had many personalities, from saint to deranged psychotic. No matter how strong or smart he gets, he's been stronger and smarter, and it hasn't helped him one bit.

Here's my favorite experience in the game, and a pretty major spoiler (although nothing should stop you from playing this game). You learn that you were first cursed by a hag for failing to answer a riddle correctly, "What can change the nature of a man?" This point comes up repeatedly, and you have plenty of time to prepare the correct response to her question. When you finally meet her again, she does indeed ask it a second time, and you carefully pick the answer from an extensive list. But there is no right answer! The riddle is a ruse; you were cursed because you asked to be cursed, and the hag did so because she once loved you. There are no ultimate truths, and the only demon haunting you is yourself.

One crude but effective summarization of existentialism is that only you can give meaning to a life that has none intrinsically. It takes Connors years (presumably) to give meaning to a single day. The Nameless One's curse is that his life can never have meaning. That's why the question "What can change the nature of a man?" is a joke. The Nameless One has no hope of changing his nature, because he has no intrinsic nature (that's why he's nameless).

Connors eventually breaks free from his cycle, and the Nameless One (with a LOT of effort) dies and falls to the underworld. I find the endings of both works to be more ambiguous than they seem. What's really to stop Connors from falling into the same ego-centric habits on February 3rd?

In the Planescape universe, death is not a ticket to oblivion. The underworld is engaged in an eternal war between chaotic evil and ordered evil (perhaps one of the most dismal allegories for human existence). The Nameless One has broken his own cycle, only to find that the world itself has its own cycle which is far more dire. If Groundhog Day is hopelessly optimistic, than perhaps Planescape: Torment is hopelessly pessimistic.

No matter which conclusion you favor, Groundhog Day and Planescape: Torment each deserve more than the status of cult classic. P:T is especially underrated these days, and any RPG fan should definitely take a look.

Linearity vs. Spoilability: Part 2

This is a continuation of last week's linearity post.

2. Some games are much more spoilable than others

Last year, one of the recurring topics in the circle of game blogs I read is that of spoilers. Michael Abbott (who you should read, by the way) started it going with a post in which he complained that the community was being stifled by the fear of giving away plot details, even rather mundane ones, when discussing a game. Essentially, he said that this shouldn't be a big deal; indeed, most movie or book reviews assume that it's impossible to evaluate something without, well, talking about it.

A flurry of comments ensued. One of the more interesting ones was from Clint Hocking, lead designer of Far Cry 2 and a good game theorist to boot. He said that while it was possible to spoil a game's story, that's not really spoiling the game itself, which consists of a set of mechanics. Hocking questioned whether you could ever really spoil the mechanics of a game, which are generally assumed to be open knowledge.

As a designer, Hocking is interested in replaced fixed stories told through cutscenes with stories told through the player's point of view, so there's a motive behind his question. Setting all that aside though, it's not quite correct to say that game mechanics are never spoilable. I'm going to go through a few examples of this, many of which were brought up by commenters responding to Hocking.

Many games have mechanics that evolve in ways that surprise the player. The first, although probably not the best, thing that comes to mind is the grav gun in Half-Life 2. You probably won't find anyone who hadn't heard about the grav gun before playing the game, but nonetheless it is a mildly spoilable fact. Experimenting with it and finding new ways to use the grav gun is a fun experience, and if someone had listed all these ways out to me beforehand, I would've missed out on that.

One could argue that the basic mechanic of Half-Life 2 is that of a fairly conventional first-person shooter, the particular guns you use are simply variations on this mechanic, which is in itself not spoilable. But that's like saying that the story of Half-Life 2 is really just your basic tale of good vs. evil, or one man versus a vast government conspiracy, and thus it's not really spoilable either. Besides, some games really do change the fundamental mechanic. Imagine if someone had not told you that you will become a Jedi after the first couple levels of Jedi Knight 2. That would completely change your experience of that game. I think one of the reasons that Hocking doesn't consider mechanics spoilable is because it's conventional to spoil them anyway. (I'm not saying that's wrong; I take Abbott's position that there shouldn't be restrictions on the way we talk about games. But it is fair to say that knowing certain things about a game does change the way you experience it.)

Once I started thinking about this, it became clear that spoilability (by which I mean mechanic-spoilability, not story-spoilability) is already a criterion we use for games, though a bit subconsciously. Think about what defines a strategy game, for instance. One of the key characteristics of a strategy game in my mind is that it has little to no spoilability. Like chess, we know what the rules are; the game consists of applying them with skill. Similarly, certain puzzle games like Tetris are in no way spoilable. (It is important to specify the type of spoilability. For instance, one of the key rewards of playing Command and Conquer, at least for me, is watching the FMV cutscenes after each level, and I wouldn't want those spoiled. Obviously, that has nothing to do with the game mechanics.)

These types of games occupy one end of a spectrum. Slightly more spoilable are the types of games I mentioned earlier, in which the mechanics undergo small (HL2) to big (JK2) changes. How do we tell just how spoilable these games are? Pretty simple, really. Pick a game, and make up a story about what you did in this game. Not what your character did (your character is involved in the narrative), but how you as the player interacted with this game. Be as specific as you need to be to give someone a good impression of what you did; don't be abstract. Then think about whether this information would affect someone who knew nothing about the game yet.

You'll find that story-spoilability and mechanic-spoilability are usually correlated, but not always. The Xenosaga series (along with most modern RPGs) is highly story-spoilable but not very mechanic-spoilable.

What games are the most spoilable in terms of mechanics? Adventure games, almost by definition. In fact, I think the decline in adventure games has a lot less to do with linearity and a lot more to do with spoilability, and this is a connection I want to explore in Part 3.

Bite-Sized Bloggie Treats

While you await the second half of my series on linearity, here's one big collection of mini-posts; stuff that isn't important or interesting enough for a whole post, but which I've been thinking about nonetheless: some of these may receive greater-sized elaborations later.

Tales of Monkey Island

I played adventure games all through my childhood, but didn't play through the Monkey Island series until I was in college (save for the black sheep of the series Escape from Monkey Island, which my friend P. and I played and loved on the PS2 in high school). This is one of my greater embarrassments as a gamer. The series is, of course, a pinnacle of the genre.

I can, and undoubtedly will, go on at length about my perspective on adventure games. But right now, after recently finishing Tales of Monkey Island, a few comments.

Unsurprisingly, the game feels less like Monkey Island 5, and more like Sam and Max Season 2 1/2. It shares the same cartoony graphical style, many of the same voice actors (who were relatively easy to recognize), and shares the same philosophy when it comes to puzzles. Which isn't really a bad thing, because the Sam and Max seasons are my favorite adventure games of the past five years (perhaps longer). Telltale's found a formula that sells adventure games in an unfriendly market, and funny, clever ones at that.

But Tales isn't as good as Sam and Max. It's not nearly as funny, which is again not surprising. Sam and Max is probably the funniest series I've ever played; it's worth the full price of admission just for the privilege of clicking the cursor on all the random objects and hearing their responses. Tales trades out the pure inanity of SaM for a stronger narrative. This would be fine, except Monkey Island is a series with ghost pirates, talking skulls, and a protagonist who's afraid of porcelain. It's hard to get super-invested in plot points like Morgan's love for Guybrush, or the possible betrayal of the Voodoo Lady.

And Tales doesn't have what redeemed the earlier games in the series from a not-too-serious plot: strong puzzle design that's both challenging and fair. This isn't really Telltale's fault: they need to pitch to a casual-aligned market that's not looking for real stumpers. Plus the episodic format limits the size of each location, so the player usually stumbles onto the solution to each puzzle without really having to think.

All things considered, I still recommend the game: it's still pretty funny, there are still some clever puzzles, and the writing is good. But I'm more excited about SaM Season 3.

Shadow of the Colossus:

( Sidenote: I started to play through Final Fantasy Tactics, but playing two full-length RPGs at the same time proved to be a bit much, so I set it aside for the time being. Hopefully, I'll get back to it after Clare and I get through Persona 4.)

I don't usually buy games I've already played, but I had to make an exception here. Since I finished Ico for the first time a year or so ago, this game has been on my mind a lot, and I finally bought it last week.

When I first played it, I pretty much rushed through all the colossi without really exploring the landscape. This time around, I'm taking my time; the game rewards a curious mindset. There's so much about this game that's worth thinking about. Right now, I want to point you to an excellent article that explores the conception of 'place' in this game.

Persona 4:

I'll have a lot, and I mean a LOT, to say about this game and its predecessor when Clare and I get done with it. How much do we like this series? We spent 90+ hours on Persona 3 in a period of three to four months. We emerged from it absolutely exhausted. Within a month or two, we didn't think twice about starting the fourth game. It's that good.

Labyrinth:

This is not a video game, but lately I've spent more time on it recently than any actual video game. Only recommended for people who like riddles, to the point that they are willing to agonize for days over them. For me, it's more dangerous than any drug. I think I'll have more to say about this on my upcoming post on spoilability.

Be careful; it can take over your life.

Well, that's all I got for now. Till next time!

Linearity vs. Spoilability: Part 1

In the last post, I talked a bit about why linearity and replayability are not well-correlated. Since I wrote that, I've been rethinking the whole notion of linearity in games, and concluded that it's not very useful. Much more useful in my opinion is the notion of 'spoilability', which I came up with last week.

My original intention was just to summarize my whole argument in one post, since it's fairly easy to explain. But I got a little sidetracked after getting part of it done a few days ago. So it's become a series. Here's part 1:

1. Linearity isn't a very useful concept.

This shouldn't come as a surprise, since I think the use of the word 'linear' in game reviews and criticism has dropped quite a bit over the past few years. Despite this, I think there's still a perception that nonlinearity is important, because it's the key characteristic that differentiates games as a form of storytelling from movies or books. And in an obvious sense, that's true. After all, those forms generally have a beginning, an end, and one conventional means by which to pass from the former to the latter. But what does it mean to call a game linear?

Usually, we use the term when we find a game too restrictive in one way or another. Prince of Persia: The Sands of Time is a good example. The main character has a wide range of fun acrobatic moves, yet in each room there's usually only one path that will not lead him to his death. This makes PoP more of a puzzle game than some players would have liked. So when we call the game 'too linear', we might be referring to this fact. Or we might be referring to the game's overarching narrative. After all, the game never gives us any choice in releasing the Sands of Time and causing all hell to break loose; I believe that takes place in a cutscene.

So we might differentiate between story-linearity and game-linearity. Still, there is no easy way to quantify these concepts, even in the most clear-cut examples. For instance, Knights of the Old Republic constantly offers you dialogue options that directly affect various character stats. Yet like many RPGs, there are only two viable paths for your character: the transcendent, inscrutable light Jedi or the greedy, asshole dark Jedi. As soon as you decide who you want to be, it's painfully obvious (except in interesting ambiguous cases which are far too rare) which lines to select in every single dialogue tree. This makes the game all too linear and even boring, which is the main reason I've never finished it.

Lots of games offer choices, but some choices aren't really choices at all. Some choices are explicit, and some, like Silent Hill 2's, aren't. There are games like Morrowind, where the main narrative can be avoided, but never really diverges once you decide to continue with it. What about free-form games like Civilization? Some would say they are completely non-linear given the range of possibilities. However, in narrative terms, Civ is really quite simple. You start with a society, it grows, and then either it dies or everyone else's does.

Again, I think a lot of game writers have figured out that 'linear' is an outdated term. But here's my idea, which DOES get at the real issue that people usually refer to when they use that word:

NEXT TIME: Spoilability!

A Straight Line of a Different Kind

Contra III is a 30 minute game that has lasted me over a month. The game has 6 levels, and none of them will take a skilled gamer more than a few minutes. But that's an easy enough thing to say. Yesterday I was overjoyed when I made it to the fifth level for the first time.

So why have I stuck with it for so long? It's true that I am a more patient gamer than ever before. I avoid using the word 'hardcore', since I respect gamers of all types, but it's true that patience and diligence count for something with this type of game. Ten years ago, I dedicated myself to adventure games because I was sick of game overs, but now I can't get enough of them.

The real reason is that Contra III is very fair. Like the Castlevania series, it's very well-crafted. I die often, but each time I know where I went wrong and how to do better next time. Unlike the Castlevania series, it's also a great adrenaline rush no matter how many times I play it.


Like most classic platformers and run'n'guns, Contra III is as linear as a game could possibly be, for good reason. Each difficult boss such as the one above (which was the hardest for me so far) has one crucial weakness: it's forced to act the same way every single time. If it didn't, I'd have given up. Linearity keeps hard games like this replayable.

Linearity and Replayability

At the time, the most common reason given for the decline of adventure games in the late 90's is their linearity. Adventure games had strong, coherent narratives that play out like movies, and this kept the games from being replayable. Players wanted more agency in their games; the future of video games was more choice, more non-linearity.

But if nonlinearity equals replayability, then why are completely linear games like Contra so endlessly replayable? One could argue that I'm not really replaying Contra III, since I haven't beaten it yet. But I have beaten Castlevania, and I keep coming back to it. It provides challenging, hypnotizing gameplay with no real time commitment. That seems to me to be the definition of replayable.


As far as adventure games go, I've replayed the Gabriel Knight series more than any other games I can think of. I've played the third game at least five times. (In fact, they're more fun when you don't get stuck on every puzzle.) It's like rewatching a favorite movie.

Some games are not very replayable to me, even when there are choices involved. Silent Hill 2 is probably my favorite console game, and there was a time when I wanted to see all six endings, which requires you to play the game six times. To this day, I've only seen two of them, for a number of reasons. Firstly, the game gets less scary when you replay it; less to do with linearity than with the horror genre itself. Secondly, the game is unique in that the endings reflect how you've chosen to play the game (do you use first aid often, how close do you stick to Maria?) and so it's tricky to force the game to a specific ending.




The third reason is more relevant to this discussion, since I generally feel this way about games with choice. To me, my first ending will always be my ending. Even though I did not consciously choose it, it is how I would've wanted the game to end (it is arguably the 'best' ending for the character). Two of my friends got a different ending (a more tragic one) that they are both happy with. When I force the game to end a different way, it feels like I'm making that choice...well, not really a choice. So I choose not to replay it, and savor my version of the story.

So in certain ways, linear games are more replayable and nonlinear games are less so. There's more to be said here, so...next time.

Screenshots from MobyGames, as if it wasn't obvious.

Remember When We Used to Get Nostalgic About Games?

So I couldn't finish Rocket Knight Adventures. Not because it was too difficult. Nor did I lose interest; it's still one of my favorite Genesis games. No, I couldn't finish it because my Genesis started freezing up, at random points late in the game. I'd blame the age of the system, but I remember this kind of thing happening on a sports game I used to have, College Football 1995 in, well, 1995.

I bought RKA used, a couple weeks ago, at one of the nicer retro game shops in town. I'd been looking for it specifically since I heard it praised on 1up's Retro Game Blog a while back. It was 5 bucks. Most of the games I pick up these days are under ten.


This is the first thing I saw after the Konami logo. The Rocket Knight (this game never explicitly uses his name Sparkster, at least as far as I got into it) pulls out his sword from behind him with a 'ching'. As soon as I heard it, something struck me about this game that I couldn't put my finger on. I watched the short intro, got to the menu, and started up a new game.

As soon as the Stage 1-1 song started playing (you can listen to a lot of the music here, which I recommend, because it's one of my favorite things about this game), it hit me. I'd definitely played this game before. Everything about it was familiar.

In the Genesis's heyday, I only owned three or four games. The vast majority of the games I played I rented at a mom'n'pop video store in my hometown called American Video (which closed up shop shortly after Hollywood Video came to town). American Video had pretty spotty selection, but chances are this is where I came across the game about a dog in a suit of armor with a rocket on his back. Well, at least he has a dog's nose, but the prehensile tail makes it more likely he's a monkey. Whatever.

Discovering that you've played a game over ten years ago is a bizarre experience. (In fact, the same thing happened to me when I played Dynamite Headdy recently, which is somewhat remarkable since that game sold poorly here in the States.) Video games, particularly those with dated sound cababilities, have a knack for burying themselves deep in your subconscious. I'd be interested if anyone else has had this experience. But ultimately, it's not something I seek out.

You might think that as a retro gamer, I enjoy playing games from my own past. For the most part, this is not true. This is because the majority of games I played 'back in the day' were pretty awful. The number of awful-to-mediocre movie or TV-licensed 16-bit platformers is truly staggering. I do actually remember the first three games (in order) I owned for my Genesis:

1. Lion King. Actually not that bad - it was a pack-in with my Genesis. A little short.
2. Home Alone 2. Laying clever traps for Joe Pesci and Daniel Stern sounds like fun at first, but after Joe trips over the water fountain spill for the sixteenth time, it gets wearisome.
3. Batman Forever. By far the worst of the bunch. Simple goons take forever to kill, and your subweapons are harder to activate than MK fatalities. Plus you have to hear Jim Carrey say "Riddle me this, Riddle me that" at least 30000 times. At least there are no bat-nipples.

All things considered, it's a wonder I keep my Genesis at all, instead of booting it out the window for giving me such awful memories.

As you can probably tell, nostalgia ranks pretty low on my list of reasons for being a retro gamer. So what are those reasons?

1. Price - No, I haven't played Suikoden 2. Most old games really are very cheap. And they usually work. And NES save batteries last a lot longer than you think.
2. Knowledge about what's good - I've always thought the best time to get a console is when the next one is coming out. I may have to rethink that, since the current generation is sticking around for a while.
3. Good games stay good. Now surely some games don't age well, while others are ahead of their time, and these are important and interesting issues. There will always be trends, and they tell us something. But games wouldn't be worth much as a medium if we let it stand that all our best games of today would become unplayable in ten years.

I have no special gripe with today's games. I do wish there were fewer space marines, but all generations have their quirks. I'm still very interested in where games are going, but I guess that's tempered since I'm generally a little late to the action.

Oh yeah, you should play Fallout 3. Good game.

Next time: ANYTHING but another Sega Genesis post, I promise.

Screenshot from mobygames.com.

Why Good Mathematicians Make Mistakes (Part 2):

In my last post, I described why I think Legendre was so determined to prove the Parallel Postulate from the other axioms. Legendre knew where the faults in his proofs were, but he believed they could be overcome if we allow some basic assumptions to be made about straight lines. Indeed, he wrote explicitly that the problems we have with this postulate are due to the "imperfection of the common language and to the difficulty of giving a good definition of a straight line."

What Legendre didn't know is that the difficulty is not particular to the "common language," but that there simply is no way to define a straight line (or for that matter, a line itself or a point) without making reference to another model, that is itself undefined. Generations of mathematicians before Legendre had tried to give a simple, self-contained definition, but the clearest of all is, in my opinion, the very first one we have, which predates Euclid.

In the Parmenides, Plato gives what is believed to be the common definition of contemporary geometers: a straight line is one in which the middle covers the ends. Of course, we cannot be sure about these things, but this is the only way anyone's been able to make sense of this:

If you, yes you, put your eye in the middle of a straight line, then you wouldn't be able to see anything of the line but the point where you put your eye.

Modern mathematicians should be up in arms at this point; giving a definition that refers to a previous model is one thing, but a definition that refers to reality, to a human being, is unconscionable. In fact, Euclid's revolutionary act was to remove the human from the divine realm of mathematics. So here's Euclid's stumper of a definition:

A straight line is one which lies evenly on the points on it.

If you're like me, then you should be wondering, what is this shit? I thought there must be a translation issue here. So I looked at the source (Did I mention I took two years of ancient Greek in college? Liberal arts schools are great.) and here's what I found. Sorry, fellow Greek scholars, but you're just going to have to accept a poor transliteration until I can figure out how to use Greek characters in Blogspot:

"ex isou tois eph' eautes semeiois keitai" (lies evenly on the points on itself)

The ambiguity is in the 'ex isou', which literally means something like 'in an equal way'. The phrase can either be taken with 'keitai' (lies evenly on the points on itself) or 'tois semeiois' (sits on its evenly spread out points). What's the difference? Here I turned to Thomas Heath's 1908 edition of Euclid, what may still be the standard source on interpreting Euclid in Greek, if only because both reading Euclid and learning ancient Greek have been in serious decline since education stopped being so aristocratic.

Anyways, he says that the first translation might mean that a straight line looks the same no matter which point you look at; you'd be hard pressed to tell the difference between picking one point or another, since the line 'around it' will look the same. The second translation depends on what you mean by 'evenly spread out points'. He might mean that a curve amounts to a kind of 'bunching' of points. But nobody really knows. Proclus, the earliest commentator on Euclid, gives the least convincing interpretation of all; that a straight line measures out the smallest distance between two points. (Here I guess 'ex isou' is taken to mean 'of equal measure? I don't know.) It's pretty obvious why Euclid is the only one who gives this definition, and Greeks afterwards go back to Plato's definition.

Ironically, Platonism may have been the reason that Euclid changed to this vague and pretty meaningless definition. If Euclid was a Platonist (he is believed to have studied at the Academy), then it makes sense that he would have attempted to remove all traces of the material world from his geometry. I've been spent more than a bit of time studying Plato, so I find this pretty fascinating. I've always held the suspicion that Plato had mathematics in mind when he invented 'forms'. If so, then it's pretty interesting that Euclidean geometry suffers from some of the same issues with Platonism as more general philosophy does:

Does the form of a straight line exist in the world of the forms? If so, then it would be pure in itself; it wouldn't make reference to anything else. But then it would be impossible to describe it.

There are bigger Platonic problems with lines than the fact that lines may not exist in nature (or that no one can draw them perfectly straight). Euclid's failure and the failure of so many mathematicians exemplify the fact that even the idea of a line isn't sensible unless we give it some kind of context, a place to live like a real two-dimensional vector space.

I've always thought of myself as a mathematical Platonist, but after thinking about these issues, I'm not so sure.

Next time: Rocket Knight Adventures!!

Why Good Mathematicans Make Mistakes

So my girlfriend and I have started doing math again in our spare time (she's a biologist who's a good sport). The story begins when I discovered the awesome text Mathematical Masterpieces, which sent me on a search for it's prequel Mathematical Expeditions, which is geared towards lower-division undergrads so that I could read through it with Clare (any opportunity to do math with a partner is appreciated, since it's a lonely game in general). Both books talk about individual math topics through a math-historical perspective; each chapter has you reading original sources in chronological order in order to learn about, say, Fermat's Last Theorem or set theory. It's interesting stuff, and it doesn't shy away from real math like a lot of math history does. There desperately needs to be more historical context in the standard math education.

Anyways, the first chapter which Clare and I started reading talks about the development of hyperbolic geometry after generations of mathematicians failed to prove the independence of Euclid's "Parallel Postulate" from his other axioms. At the very beginning of Book I of Euclid's Elements, Euclid first defines a point, a line, and all the standard objects that Euclidean geometry is made of. I'll say more about this later. Then he gives five axioms for geometry. The first three basically say that all objects that should exist do: there's a line between every two points, a circle with any radius and center, and any finite line can be extended infinitely. Pretty non-controversial. The fourth one says that all right angles are equal, which sounds weird, but really just gives him the right to compare angles at all. The fifth one is a doozy (here I'm kind of paraphrasing):

If a line crosses two other lines, in such a way that the interior angles on the same side add to less than two right angles, than the two lines will converge on that side.

This is Euclid's Parallel Postulate, often just called Euclid's Postulate. (Here's the way I think of it. Take two lines, and two points, one on each of the lines. If at those points, the lines look like they're going to converge, than they will.) And that's it. Euclid then lists five "common notions", which are also axioms, but really for math in general. Stuff like equality is transitive, and the whole is greater than the part.

Anyways, from the moment that Euclid wrote it, this postulate was pretty controversial. Our earliest commentator mentions it, and tries to do away with it. On the one hand, it looks ugly. Turns out there are a lot of nicer statements that are equivalent. I was always taught it as this:

Given a line and a point off the line, there's only one line parallel to this line through the point.

Euclid almost certainly knew this equivalence, but phrased it in a way that he could work with more easily. It's his book.

Here's the more important issue: why is it even necessary? We all know what a straight line is, so assuming we have straight lines, we know that if they're coming towards each other, they're going to meet. We shouldn't need to take this an axiom, because it is inherent to the very notion of a straight line. This was the thought of pretty much every mathematician until the nineteenth century, and trying to prove it from the other postulates was a big deal, one of the great unsolved problems. Even Euclid lays out the Elements in such a way as to get as far as he can without using it, proving 26 theorems before he makes use of it.

From a modern perspective, the question is whether the fifth axiom is independent of the others. This was not the perspective of mathematicians prior to the discovery of hyperbolic geometry. The historical perspective was, this axiom must depend on the others, and we have to prove it. In Mathematical Expeditions, you read a source from the last major mathematician to believe in this dependence, Adrien-Marie Legendre. Legendre gave a number of proofs, and believed that each one was correct even when the flaws were pointed out to him. With each proof, he tried to make it simpler, make it the follow the same clear form of logic that Euclid himself used. Legendre is a smart guy; he solved some problems in number theory that Euler couldn't figure out, and he gave birth to the theory of elliptic functions, which makes him partly responsible for the solution to Fermat's Last Theorem. So why couldn't he or other mathematicians at the time acknowledge that they might be wrong about this?

The book answers this with a number of theories, and they're all pretty insightful. There's a cute historical argument that basically says that in an unstable world, mathematics, especially Euclid, was a torch-bearer for eternal, implacable stability, and the possibility of alternate geometries did not sit well. But I want to add a couple of my own theories, which I'm sure have been brought up many times before:

In modern math logic, one of the most fundamental ideas is the distinction between a syntactic model and a system of semantic logical statements that might be applied to that model. In our heads, we have a perfect visual model for Euclidean geometry. So did Euclid, and that's what he set out to work with. But Euclid wasn't working syntactically, he's working with a semantic system, and thus he needed to start somewhere. I get the sense after reading Legendre that even as late as 1792, this distinction was not well-known. I think he had serious problems with the notion that one would start with this awkward postulate and then prove how a straight line behaves, rather than the other way around. Reading one of his "proofs", you can see that he knows exactly where the flaw is, even adding a footnote with an explanation of why one should take his necessary assumption (which, too, was equivalent to the parallel postulate) as given. It's an assumption that one is perfectly willing to accept if one has the visual model in mind, but it's laughably easy to spot if one is working semantically. Smart mathematicians of then and now did not lay out axioms and figure out things to prove from them; they used intuition and insight, reverting to semantics when they need to convince others.

There's another more philosophical issue that is, I think, more to the point, and perhaps the real reason why Legendre was so adamant. That is that a 'straight line' is a perfectly intuitive notion that has no fundamental definition. I can see I'm going a little bit overboard for today, so I'll talk about this tomorrow.

A Sega Genesis Discussion (with 100% more 'tude)

One embarrassing fact about me: I own seven game consoles. Not counting handhelds. (Interesting fact #2: None of those are current generation. Yup, I'm poor.) So you can say that I'm a guy that likes console games.

It was not always this way. This is because the very first console I received, one very special Christmas in 1994 (I think), was the Sega Genesis. Looking back on it, I think I can say that if my parents had decided to get me an SNES, I would probably know a lot less than I do about PC adventure games.

It's not that the Genesis is a bad system; in fact, it was Sega's most successful console by a long shot. It broke the NES's long-standing dominance over the hearts of gamers and forced Nintendo to design a follow-up. For one or two years there, it was king. Unfortunately for the Genesis, Nintendo did pull through with a console that was better than it in every way; the SNES had better graphics, the most popular franchises, and more third-party support than you can shake a stick at. To be a Sega child was to be a spiteful one, and I didn't stick with the Genesis for very long.

Both today and then, the problem with the Genesis is that it's hard to know what games for it are any good; there are precious few franchises you can count on. When I was a kid, I stuck with crappy movie-licensed games because I didn't know any better. Now that I have the internet to inform me, what are the best Genesis games I've played? (Note I haven't gotten to any of the good Sega RPGs yet)

1. The Sonic games. Recently, I replayed 1,2,3, and Knuckles, beating them all for the first time. Yup, I was bad at platformers. Sonic 3 is actually my favorite, although they're all great.
2. The Treasure classics: Gunstar Heroes, Dynamite Headdy, Alien Soldier (not released in US). Gunstar Heroes is perhaps my absolute favorite. I could not put down the controller when I first played this.
3. Rocket Knight Adventures (hope to talk about this game later, once I beat it)

And that's pretty much it; still one of my least favorite consoles. But I have to say that the games on this list pretty much all demonstrate the Genesis' trademark, which Sega endlessly promoted with its blue furry mascot: character. These platformers/run'n'guns are so good because each level is filled to the brim with colorful backgrounds, multi-sprite multi-phase bosses, and a fun well-utilized gameplay mechanic. And they all have pretty good soundtracks. I love my NES, but the Genesis went a long way to make games exciting, and that's still true today.

You know you're a technophobe...

...when your mom invites you to join Facebook. True story. I am horrible with social networking sites. Probably because I'm horrible at social networking. So this blog is a concession, in a sense.

But I do have things to say! Mainly about retro games, math, and whatever bit of consumable media I've just enjoyed. And delicious meals.

They say blogs are going out of style, so...hello world. This is for those who enjoy the above things, and those friends I've lost touch with over the years.