Instead of a straightforward platformer relying on skill, in Castlevania II you level up and explore an “open” world with lots of secrets before confronting Dracula when you feel appropriately powered up. There’s an added soft time limit, where you have to navigate the overworld efficiently lest you take too long to kill Dracula and die immediately afterwards in the ending. (I think the biggest obstacle to this is the grinding at the beginning, honestly: you need enough money to get the items to access the first mansion, and I took a really long time to do that.) As usual I hate stairs.

I had fun looking for the secrets and dropping garlic in graveyards and the like, though I must note I was playing with a patch that fixed the poor English translation, so the hints were far less confusing. Also, even though there is a time limit, it freezes in the mansions, so you can grind the infinitely respawning enemies there…the developers did stop you from leveling up on weak enemies, though, which was kind of sad XD. The correct strategy for the boss battles is “toss sacred flame at them so they stop moving repeatedly”. If you have enough hearts, guaranteed to work.

I suppose the game was meant to be replayed several times — the first time, you take a really long time trying to figure out where everything is, and on later iterations you can immediately perform some steps while figuring out how to optimize your route or discovering more secrets.

• yay scifi setting! Yay female protagonist! Yay first-person dungeon exploration with an atlas system in case you are lost!
• the consult system is SO HELPFUL. forgot what you were doing after some time not playing? just press L1 and hear Myau be like “it’s time to go to the corona tower!!!!” You still have to write stuff down because consult doesn’t tell you WHERE anything is, just that you have to find it next. Also it’s cute to see the characters banter!
• the difficulty is not too bad, especially with some grinding. However, the encounter rate is ASS. I did do some early leveling on Dezoris when I got the spaceship, but other than that, I naturally leveled up as I was walking around because I would hit an enemy every few steps. Also, as with FF1, once you get the Caduceus, the game gets way easier because you have free healing. Paired with heal crystals for everyone, you end up at full health after most fights. (Admittedly, I did finish the game at level 96, so I was also benefiting from taking less damage. I think the PS Cave walkthrough recommended running from everything in the last few dungeons and then beat the boss at level 60…)
• fights get repetitive. Also, attack animations fairly slow. Before the Caduceus, my strategy for most fights was to spam AoE from Lutz/Myau/Tyrone (w/gun) and Alisa awkwardly hits one enemy. When I ran out of MP, I would teleport back to nearest city, heal up, and try again. After the Caduceus, my strategy for most fights was to just attack with everyone except Lutz and have Lutz heal where necessary. Boss fights become “Myau casts Warla and Mawarla on loop because their effects expire after 3 turns, Lutz heals when needed, Alisa + Tyrone attack” and praying that this is the last turn I have to repeat those actions. I guess if the game were harder, I would have needed more of a brain and that would have its own set of problems, but whatever.
• I never actually use the collabo system because I was too scared of my crystals breaking. Apparently you can use it to cheese some bosses if you buy enough crystals, but w/e
• Because of how damage is calculated, at the end of the game multi-hit weapons are the way to go – you’ll have so much base attack that it pays to attack twice with a weapon with like 90 less attack than the single hit!
• Unsurprisingly, I went from “how am I so poor” at the start to “I am sitting on piles of money with nowhere to spend it” at the end.
• Item management SUCKS. Items DON’T STACK. I just want to keep 99 potions. I was pretty conservative with item use, then I ran out of inventory, so I started using items as soon as I got them to accommodate.
• Music was fairly good, not too repetitive.
• Story was a bit anticlimactic – Baya Malay onwards is fairly linear, you beat La Shiec, and are unceremoniously dropped into a new dungeon with pulsating flesh walls that is entirely linear. Dark Falz has no villain monologue, you just yeet him. I enjoyed the pre-Baya Malay parts way more – getting to talk with all the townspeople and learn about the planets, running around fetching items (the Dezoris sequence especially, adding the liar/truth teller trick was fun). Alisa’s reveal as princess was not really foreshadowed?? You’re just like ah yes, I see she was a royal all along, that doesn’t change anything and beat La Shiec. Kind of annoying that you have to repeatedly talk to people and in the right order to trigger more story events.

We've evolved from the one-man party to a three-man party that are distant descendants of the DQI protagonist. We also encounter the descendant of the DQI villain and can later visit Alefgard, the DQI continent. The gameplay has also evolved! With more allies and monster groups, there's more flexibility in battle. We get to sail around the whole map and teleport.

My main memory of the game is when your team gets to Rhone, the last area of the game, the difficulty spikes tremendously. That's mitigated by a couple hours of grinding, but it was kind of demoralizing XD

First, I want to talk about gacha games in general. I sort of swore off gacha games in graduate school as I realized that I did not want to play live service, microtransaction-based games that relied on FOMO for time-limited events, an endless story that would never actually resolve, and resource-gated grinding. Yes, at the start you have these exciting systems to learn, you get tons of free pulls for cool characters, and you progress fairly quickly, but soon enough you spend most of your time hitting the autobattle button and a little bit of it team-building or trying harder content. Plus, the episodic nature of main story and events means that not only do you forget what happened 4 months ago during the last lore-relevant event, the writers have probably also changed and forgotten about some vaguely foreshadowed story beat. Also, at any point the developers might add some mechanic that invalidates half the meta (and thus whatever you were grinding towards). Getting to play a “finished” game on a private server fixes all these issues and lets you focus on the good parts — it's great! All the story and game mechanics are final, even if the story's coherence is still somewhat doubtful at times. The server devs can set the banners to whatever they want, which in DL's case is either rotating banners or all banners organized by type, so there's no longer pressure to pull because a collab character is super good but vanishing in a week, or something. The community is still there, and more passionate than ever. And both private servers have ways to speed up grinding and progression; for example, one offers a free 10-pull every day, and the other drops the premium currency on every quest. You can really play at your own pace while still enjoying the game with others and getting those dopamine hits from the gacha or from progression.

In fact, playing DL has made me recall that one of the things I really loved about gacha games which I feel is rarely replicated in single-player games is the way progression works. There's a set of things to do — progressively harder content, new game modes, etc. — and although there is a meta, for the free-to-play player (and really, everyone who isn't a whale) your life is basically trying to optimize your play around your gradually improving personal constraints and basking in slowly hitting progression milestones regardless. Maybe you rerolled for that one broken character, but you still have to cobble together a team around them using whatever else you've got. Sure, eventually you'll get everyone, but for now, there's a lot of satisfaction in managing to put together a jank but workable team that can still challenge hard content. Maybe your fire team only has B and C-tier units, but that doesn't mean they can't synergize into something greater than the sum of their parts. Maybe you finally finished getting the materials for a weapon, and you get to revel in your temporary badassery until you run up against another wall, hence more grinding. Maybe you just do your dailies and one day you pull that character you've really wanted. The almost roguelike nature of how you advance through the game is great because, unlike roguelikes, you don't lose everything when you die, and in theory keeping at it for long enough means you'll be pretty good. In the past, I would always worry that I wasn't doing “enough” with my limited energy or resources, but I realize now that, regardless of all those exhortations to spend just a little more money to get things a little faster, all I should do is show up and play however I want. Modulo end of service, everything will come in time.

OK, now let's talk about Dragalia Lost. First of all, the music is fire. DAOKO has a ton of range and basically all the songs are hits. I got the soundtrack album on my second day of playing. Second, it's very different from Shironeko Project. Yes, the controls are the same, you pay resources to unlock nodes to strengthen your characters, and you construct buildings that boost your stats, but everything else plays quite differently. In no particular order:

• Dragalia Lost is really meant to be played with other people. All the quests have your whole team on the screen attacking and using skills at the same time, and most can be challenged either solo or co-op. The bosses have mechanics that would be familiar from MMOs, such as requiring players to stack on each other to reduce damage, baiting AoE attacks, trapping one of the players in a prison, etc. To mitigate AI failings on mechanically harder quests, AI-controlled characters (which is the norm if you're playing solo) take reduced damage and are actually exempt from some attacks.

• Some aspect of progression comes from pulling stronger characters and dragons, and there are some gacha pulls that are quite broken. However, quite a lot of it is due to weapons and wyrmprints, which are mostly gated behind grinding. The weapon progression is linear and also depends on how much content you clear; generally, you challenge the next tier of content using weapons from the previous tier. Meanwhile, wyrmprints are used to give characters extra passives, and you can equip up to eight (!) on a character, so that's a lot of space to customize and create synergies across your team.

• Skills cannot be spammed. Instead of MP, you charge a skill by attacking enemies, and cannot generally store multiple charges, and there is some care required to time skill usage correctly. Also, in later challenge quests, the dangerous boss attacks cannot be dodged with skills, so you actually have to have some mechanical skill.

• There's some feeling that the storyline is actually relevant to the other content. You unlock more challenge quests that are storyline bosses as you progress, and some story content is locked behind appropriate progression in other areas, such as leveling up the castle and smithy. The story characters get alternate versions that are actually good! And the story actually wrapped up, though this is partially due to the writers trying to do so when end of service was announced.

• The power creep is present, but pretty measured. It's mitigated somewhat by introducing an extra 20 nodes (“mana spiral”) to older units. The main creep is not stats, but just much more utility from later characters, but even older units can hold their own.

I have two main complaints about the game: that having dragons are really important, probably more than good units because units have wyrmprints and you need to pull dupes for dragons, and that Kaleidoscape is way too long for the randomized rewards you get. Seriously — 80 of basically the same set of floors?? Besides that, I am having a lot of fun and would highly recommend!

Things I like: – the backlight is really helpful. Now I can also see the screen at night or on planes/trains, but without sacrificing how the screen gets brighter under the sun. – the color is not totally accurate (it looks better with the backlight), but just having the option to add colored notes and highlights makes my notes clearer. I also appreciate being able to see the color in puzzles and books. – there's no longer stretching or compressing of my writing at the very top and bottom of the tablet. – larger screen size = bigger font on my PDFs and more space for notes – because of the cloud syncing, all I had to do was set up and connect the reMarkable to wifi to get all my notebooks and PDFs to appear.

Things I dislike: – I have one dead pixel when I turn on my backlight :( It's on the lower middle part of the screen, so I'm usually not looking there, but sometimes I end up fixating on it – the tablet seemed to heat up after consecutive hours of use. I'm guessing I could get about 16 hours of battery life out of it, since when I was at my conference, I was writing on the tablet for about 4 hours a day and the battery would go to around 70-75%. – I still don't understand how the calligraphy pen works. – there's no option to select some handwriting and change its color (or if there is, I haven't found it yet)

Is it worth $580 (plus the $50 extra for Marker plus), considering I already have the reMarkable 2?

Controller Input

IMPORTANT: press all the buttons, then F3 so Mednafen detects all analog joysticks. My 8bitdo M30's left and right shoulders were apparently analog joysticks.

Then, press Alt-Shift-N, where N should be replaced by the controller port you're mapping, and you'll be prompted to press buttons. You have to do each one twice to confirm you're done and move onto the next one. This should save your settings to your config file.

If you want to manually set joystick buttons, there's no official documentation, but: * the joystick's ID is printed when you start mednafen. * in mednafen.cfg or a console-specific config file, set the relevant gamepad's controls: each one should be joystick [id] followed by either button_[n] or, if it's an axis, abs_[n][-|+]. I think the -|+ indicates polarity. e.g. ss.input.port1.gamepad.down joystick 0xblah abs_1+ (and up would be abs_1-). * To find the button and axis numbers, I used another program that used SDL input (e.g. Ares); you can also write yourself a little SDL program that detects presses and prints out info. Let me know if there's something more convenient.

Here's the full configuration for my M30 (with joystick ID omitted)

;ss, Virtual Port 1, Digital Gamepad: A
ss.input.port1.gamepad.a joystick button_0

;ss, Virtual Port 1, Digital Gamepad: B
ss.input.port1.gamepad.b joystick button_1

;ss, Virtual Port 1, Digital Gamepad: C
ss.input.port1.gamepad.c joystick button_10

;ss, Virtual Port 1, Digital Gamepad: DOWN ↓
ss.input.port1.gamepad.down joystick abs_1+

;ss, Virtual Port 1, Digital Gamepad: LEFT ←
ss.input.port1.gamepad.left joystick abs_0-

;ss, Virtual Port 1, Digital Gamepad: Left Shoulder
ss.input.port1.gamepad.ls joystick abs_4-+

;ss, Virtual Port 1, Digital Gamepad: RIGHT →
ss.input.port1.gamepad.right joystick abs_0+

;ss, Virtual Port 1, Digital Gamepad: Right Shoulder
ss.input.port1.gamepad.rs joystick abs_5-+

;ss, Virtual Port 1, Digital Gamepad: START
ss.input.port1.gamepad.start joystick button_6

;ss, Virtual Port 1, Digital Gamepad: UP ↑
ss.input.port1.gamepad.up joystick abs_1-

;ss, Virtual Port 1, Digital Gamepad: X
ss.input.port1.gamepad.x joystick button_2

;ss, Virtual Port 1, Digital Gamepad: Y
ss.input.port1.gamepad.y joystick button_3

;ss, Virtual Port 1, Digital Gamepad: Z
ss.input.port1.gamepad.z joystick button_9

Changing Hotkeys

Also, the pause command is mapped to the Pause button by default. Uh oh, my keyboard doesn't have that button because it's a puny laptop keyboard, and remapping a hotkey (as described in the help dialog brought up by F1) typically involves pressing the original button first, then the new button. Instead, find your config (probably ~/.mednafen/mednafen.cfg) and replace all instances of the relevant scancode (0x0 72 for Pause) with the key for the desired scancode (e.g. I mapped Space, which is 0x0 44, to pause). Save. (Or just do it for the consoles and ports you care about.)

We (by which I mean everyone, not just mathematicians) are interested in symmetries of the world around us, e.g. ways to order a finite set of letters or the symmetries of shapes (equilateral triangle, cube, circle, etc.). When you divorce symmetries from the concrete object they act on and study them as abstract symmetry groups, you get abstract algebra. This is useful – for example, \(S_3\) is both ways of ordering 3 letters and the symmetries of an equilateral triangle. Representation theory is about “putting back” the concrete object and trying to collectively study “all the different ways” a group of symmetries can act on \(n\)-dimensional space (called the representations of this group), giving you a systematic way to describe any action, which is really important because the only way these abstract symmetries show up in places is when they act on things! For example, character tables in chemistry come from realizing that molecules have symmetry groups, then using representation theory to describe how a symmetry group acts on a molecule. The mathematics underlying the standard model in physics is from representation theory of what mathematicians would call \(\text{SU}(3) \times \text{SU}(2) \times \text{SU}(1)\) (don't ask me how the physics works, I don't actually know). Moreover, there is actually a formal theorem that expresses the idea that if I told you about all the representations of a group (but I never told you what the group was), you could recover the group from this description.

Now let's try something abstract: what I've described is groups acting on vector spaces (i.e. Euclidean space). What if we could replace “vector spaces” with “a family of things that behave similarly to vector spacess but aren't vector spaces” and “group” with “whatever the correct analogue of group would be in that setting”? I didn't make this up – the physicists did when they started talking about supersymmetry groups and supervector spaces! Then we can try to understand this new setting and how it is similar to and different from our more classical examples. When I say “a family of things that behaves similarly to a vector spaces but aren't vector spaces”, a more formal term for this is a (symmetric) tensor category, and one can also define what a “group” would be in such a symmetric tensor category. Why would we be interested in studying these generalizations besides finding them intrinsically interesting (though I will admit I mostly find them intrinsically interesting)?

Well, it turns out that it's representation theory all the way down (or up). Over the complex numbers, under some mild conditions (“moderate growth”), every symmetric tensor category is secretly “the family of representations of a supergroup”. (If you remove those conditions, you get very interesting new categories, including ones that are somehow morally “representations of permutations of \(\pi\) letters or \(-2\) letters or \(3.5 – i\) letters” despite not being actually able to describe what said permutations would be.) This is a crazy statement – we've defined some new class of objects which, a priori, should be this new unexplored land, but it turns out to study them, all you need to do is understand supergroups in supervector spaces. I mean, that is hard, but it's something mathematicians and physicists have been doing for a while.

Now let's try working over a “field of characteristic \(p\)” for prime \(p\) (this is a set where you can do the same operations as you can on real or complex numbers, except you specify that \(1 + 1 + \cdots + 1\), where 1 is added \(p\) times, is 0, which means the set is strange, but it's important in number theory and cryptography and stuff). Generally, representation theory is harder over said fields. We don't know how to describe symmetric tensor categories of moderate growth in this setting, but we do have a guess – they are all secretly “the family of representations of an algebraic group in the higher Verlinde category”, where the higher Verlinde category is some massively complicated, very abstract, construction that no one really understands yet. So it would sure be great if, just like how we've already developed representation for supergroups, we could do the same thing here. And that's really hard. We have to take all these notions we take for granted in the vector space case (including notions from related fields which took centuries to develop) and figure out how they work here (or if they don't), and they all end up having super abstract definitions even when they do work. We also don't know if those definitions are the “right” ones (“right” will only really be indicated by posterity, if those definitions are able to lead to our guess being proved correct and other results following). It's all very strange and cool.

So what do I do? I study a specific higher Verlinde category called \(\text{Ver}_4^+\). It's nice, in that it has a concrete definition. It's also not nice, in that several things about this category break assumptions we take for granted classically. There's two reasons we would want to care about it:

1. In this big program I described in the previous paragraph, \(\text{Ver}_4^+\) provides a prototype to conjecture what the right definitions and theorems should be in the general case. Roughly, this is because going from vector spaces (or supervector spaces) to \(\text{Ver}_4^+\) is about having things go from working to breaking (hard to fix), whereas going from \(\text{Ver}_4^+\) to other higher Verlinde categories is about things breaking even more than they already do (hopefully not as difficult to fix).
2. It's of intrinsic interest because another way to describe this category is “supervector spaces in characteristic 2”. That is, if you naively try to define supervector spaces in characteristic 2, you just get vector spaces (which isn't bad, it's just means you don't get something new to study), but you can also try to define it in such a way that \(\text{Ver}_4^+\) pops out, and then you can try to explain how representation theory in this category is like if you “replaced \(p\) with \(2\)” in the usual \(p \ge 3\) case.

What's going to come out of this? I have no idea. Maybe it'll just be a cool thing to study. But hopefully, it will allow us to broaden our perspective even more – new abstractions make it possible for us to answer concrete questions that previously seemed opaque by providing a new framework for our thinking, like how navigating a city via written directions (“turn left at X Street”) becomes much easier when you draw a map from a birds-eye view and plot your entire route on it. And after that, who knows? One day, perhaps college students will get a nicely packaged version of all this work as an undergraduate class, not as a frontier of mathematical research, and I'd be excited to see what new things people are thinking about then.

Stuff I liked: – The text and puzzles are fairly straightforward (except that one time I got stuck in a room because you were supposed to find and open a way out before entering, which was actually clued by something earlier, but I didn't understand it). I actually read the cursive in the manual and it was helpful. – The game looks pretty good. The rooms have enough detail that you can figure out what objects to examine and there are cool little animated scenes sometimes. – The sun position or whatever indicated in the circle at the top and accompanying puzzles were a good touch. – I actually followed and remembered the story.

Stuff I liked less: – the “combat” is “take turns whacking at each other” and only happens at scripted moments. The leveling up/HP is meaningless; it is just a way to gate you from entering certain areas early. Why not find a different method (like “you didn't find the right colored jewel yet”) to prevent said entrance? – I wish there was more space for the environment. There's a lot of space around the sun indicator... – walking around was kinda jank.

Your goal is to get strong enough to beat up the 3-headed dragon. When it dies, 4 crowns are scattered across the map, and you have to find them and bring them back to your house, except that your house is now surrounded by gravestones and just getting back is really annoying. Then you pass to the next phase. Phase 1 was pretty ordinary, and phase 2 looked like a giant puzzle where there's warps everywhere and some of the houses are actually warps and I didn't have the brain space to think about how to actually get to any of the items, so I gave up.

Here’s what happened to me in phase 1: I went around and earned XP and strength and stuff until I got break. Then I broke into the bottom part of the map (the map is a torus, so that meant going up from my house) and there’s a LOT of power stones in the shape of “FALCOM” there. I picked them all up, one by one, until I had lots of attack (like 400k). Then I beat up a bunch of monsters, mostly one-shotting, until I had lots of XP. Because your HP is set to your XP when you get back to your house, I ended up with a bunch of HP too. Eventually, I upped my attack to about 500k, and beat up the dragon; because of my high XP, it wasn’t doing any damage to me. Then I had to deal with getting -10’d by all the enemies near my house while gathering up the crowns (ALSO one by one). It was fascinating but IDK if I really want to play 2 (which seems to have more strange mechanics, including a prohibition on powerleveling and separate levels for magic and each weapon, according to Wikipedia). I think I prefer Ys...

Magic of Scheherzade – I don't know how to feel about having BOTH action combat on the overworld AND random encounters when moving between screens.

The Guardian Legend – it seemed fine, but also like just another Zelda clone, except in a sci-fi setting.

Drakkhen – I didn't understand how combat worked. I just saw my characters running around the screen?? Sorryyy

Wonder Boy III: The Dragon's Trap – I missed a room when I was mouse man and became really sad.

A Boy and His Blob: Trouble on Blobolonia – the title seemed very cute, but I couldn't get used to the controls. :(

Lagoon – the combat is like if Ys and Zelda had a child, but it took the worst attributes of both, by which I mean you have a really short sword, so you can only hit enemies if you stand less than a tile away from them, but you still have to press a button to use your sword. At that point can't we just have bump combat?? This also means fighting the bosses is basically whether or not you can consistently position yourself like 2 pixels away from the boss when it's vulnerable, stab it, and repeat. I actually got through 1 or 2 bosses before deciding it wasn't worth it.