Thursday, June 30, 2016

The Physics of King Kai's Planet

I've been a Dragon Ball kick lately. This post had me floored. There's analyzing a series you like, and then there's analyzing a series you like. This falls firmly into the latter category.  I found it while reading leavemywife's let's play of Dragon Ball Z: Attack of the Saiyans, which you should read. It's a good let's play of a good game.

"Seriously, you folks start talking about physics but don't even take your calculator out?

To do calculations with the gravity we need to know the gravity of the planet and the size.

The surface gravity is simple. 10g, or 10 x 9.8 m/s^2 = 98 m/s^2.

For the size, I went to the Dragon Ball Wiki. It says that King Kai's car is a 1957 Red Chevrolet Bel Air. According to Wikipedia, that car has a length of 195.6", or almost 5 meters.

The scale seems to differ a bit between the anime and the game, but I'll go with a picture from this game. It won't change much anyway.

As you can see, the diameter of the planet is about six and a half times the length of the car. That makes 32.5 meters. The radius is half the diameter, 16.25 meters. By the way, that's a tiny house.

Now, we can use the formule g = GM / r^2, with g being the surface gravity, G the gravitational constant, M the mass of the planet in kg, and r the radius in meters. Let's rewrite that. M = g*r^2 / G.
Filling it in: M = 98 * 16.25^2 / 6.674E-11 = 3.88E14 kg
That's a rather big number, but it doesn't tell us that much by itself. But we can use it to calculate a mean density of the planet. Density is simply mass divided by volume.

The volume of a sphere is given by (4/3)pi*r^3. For King Kai's planet, that is 17974 cubic meters.
The density is 3.88E14 kg / 17974 m^3 = 2.16E10 kg / m^3 or roughly 21.6 billion kg / m^3. For the Americans, that's about 1.35 billion pounds per cubic foot. Imagine lifting a block of that stuff.

Anyway, that density is in the same order of magnitude as a white dwarf. That's a very dense, relatively small star that has almost burned out. As it completely burns out, which can take hundreds of billions of years, it might turn into a black dwarf, with similar properties except that it doesn't glow. Its matter is in a 'degenerate' state, meaning that the atoms are so close together they don't act in a way we're used to. The only reason a white/black dwarf is stable is because it is about as heavy as our sun. This gives it so much gravity that it can keep itself together.

King Kai's planet weighs many, many, many orders of magnitude less than our sun. This means that in reality, this planet would immediately blast apart in an enormous explosion.

Of course you could try to prevent this by using a different kind of mass distribution. Put something much denser in the center, and make the outer layers a bit less dense. For instance, put a neutron star or a black hole in the center, those are both much denser than a white dwarf.

The thing is, this wouldn't be stable either. Either the black hole is too strong, the gravity is way higher than 10g, and everything is sucked in, or it's not strong enough and the planet explodes (or if it's exactly in between, the inner part would be sucked in while the outer part would be blasted away).

The only way I can think of to make a planet like this keep together is by using some magical "forcefield" that prevents it from flying apart. The force required for such a thing would be incomprehensibly large. And you need to keep applying it every nanosecond.

Oh by the way, if King Kai's planet were possible, the small size distorts gravity so much that Goku's head would experience significantly less gravity than his feet. Enough to make anyone feel a bit... lightheaded."

Post credit goes to user Carbon Dioxide. Now that's dedication.

Wednesday, June 29, 2016

Warrior of the Future, Trunks: A Case Study of Wasted Potential

We all have the experience of thinking a certain character is great when they're introduced. Maybe they have one episode where they're the highlight, but then they stick around for the rest of the show without ever doing anything important again. Maybe they're falsely hyped up to be integral to the plot of the show and then subsequently drop off the face of the earth, or end up never doing anything substantial. Maybe they do participate in the plot, but not in the way that you thought or wanted them to.

A prime example of this, for me, is Future Trunks from Dragon Ball Z.

His arrival on the scene is one of the most captivating moments in the entire series. He comes out of nowhere and decides to face down Frieza, the most powerful enemy we've seen up until that point, and not only wins, but takes him - and his father, for that matter - down effortlessly, and with style. Not only that, but this purple haired badass can go Super Saiyan, something that very recently we've only seen Goku, the hero, able to accomplish, and only through immense turmoil. Also, he had a sword. Nobody else had used a sword in the Z portion of the series up until this point. (Gohan had one as a kid, but that hardly counts).

His intrigue doesn't end with his stylish appearance. He's introduced as Vegeta's son (!) from the future (!!) and his mother is Bulma (!!!) His future is a post apocalyptic wasteland, and he and Gohan were the only survivors, fighting against not one, but two threats far greater than Frieza ever was. He's come back in time to set things right, and he's going to fight alongside the heroes we know to help fix the future that went wrong.

Except he doesn't ever really do anything again, really. From the moment he comes back in the Android arc to the moment the Cell arc is over, the only thing of note he does is A) Allow Cell to enter their timeline inadvertently and B) Fight Cell and lose, making a fool of himself in the process. He gets a cool design overhaul with Saiyan armor like his father and a ponytail, but it doesn't do him any good, and he goes back to his original style eventually anyway.

To be fair, it's not at all Trunks' fault that he doesn't get to shine during the Android and Cell story arcs, and unlike the other Z Fighters (I'm looking at you, Vegeta and Goku) he is trying his hardest at all times and never wants to prolong fights for any superficial reasons. He has the drive to finish the fight, without any of the Saiyan love for battle that so often bites them in the end. This is a pretty consistent trait of his from his introduction up through his latest appearance in Dragon Ball Super, which is part of what makes him stand out so much from the other characters in the series. I'm rambling a bit: the reason he doesn't get to shine is because his signature weapon - his sword - breaks early on in the story, leaving him without any real style of his own, and his one real moment in the spotlight has him using a form of Super Saiyan that is largely useless. This was to show Trunks' respect for his father and his pride, as well as Vegeta's knack for what's useful in a fight; Vegeta realized the form was useless right away, showing us that as powerful as Trunks may be, he is still naive and inexperienced. You can't blame him. Unlike Goku and Vegeta, he hasn't had any formal training, and also unlike those two, he is only a seventeen year old kid.

I'm sure that, if pushed to the same extent that Gohan was during his fight with Cell, he could have easily taken his place as the first Saiyan to reach Super Saiyan 2. But, that isn't how things played out, and Gohan needed his moment in the sun. This mysterious warrior from the future that was able to kill Frieza so easily is shoved to the side for the rest of the series. He does get one more moment of glory in his own timeline when he kills the Androids, but for all intents and purposes he did almost nothing to help the Z Fighters actually fight the Androids beyond giving them the heads up that they exist. Dragon Ball is notorious for sidelining its characters, but you'd think someone like Trunks would fare better than he did. His present timeline counterpart - the much less appealing Kid Trunks - does far more than he ever did, even if he never received the same level of praise and popularity as his future counterpart.

I will say, even though his last act in Z was the equivalent of returning to the first area and fighting level 5 monsters when you are level 50 in an RPG, he again showed his brutal efficiency and no nonsense fighting style, making his exit from the series just as stylish as his entrance.

Now that Trunks is back in the latest arc of Super, I hope he gets his chance to be useful. He's already shown that he took out his timeline's incarnations of Dabura, who was around Perfect Cell's level of strength, and the wizard Babidi, as well as reached Super Saiyan 2 on his own. In addition, he's apparently learned to channel ki through his sword, shooting a blade beam at new villain Black. He's definitely no slouch, and he's already shaping up to be a key figure in the story.

Poor Trunks. His future can't seem to catch a break. I'm glad he's back, but there's one thing that bugs me. Why is his hair suddenly blue!?

Thursday, June 23, 2016

Riding the Zelda Wave: A Link Between Worlds Retrospective

The Legend of Zelda: Breath of the Wild's E3 reveal has everyone in a Zelda mood. With that in mind, I thought it would be a good time to revisit one of the more popular incarnations of Hyrule... or rather, its direct sequel.

Let me start off by saying two things: one, I am a HUGE fan of Link to the Past, to the point of absurdity (it was one of my first video games), so I came into this not expecting it to surpass the original. Two, I enjoyed it my first time around, but not as much as other 2D Zeldas, such as the Oracle duology or The Minish Cap. Overall, I found it to be a disappointment, even if I had fun with the game.

This time I played on Hero Mode, and it makes all the difference. Normal mode is simply too easy. Hero mode requires you to stay on your toes. You die. You become more engaged with the game. It's harder than LttP, but still closer to it in difficulty than Normal Mode. Hero Mode makes the game fun.

The map is completely derivative of LttP, at least the map of Hyrule, but that's also where its charm lies. It's fun to go back and visit the old locations again, and see new faces and subtle changes to certain areas. The desert being walled off and only visited later as part of Lorule's dungeons was a nice change of pace and a creative way to design a new dungeon in an old area. I also like how they didn't reuse the dungeons from LttP; even the ones you visit again, like the Tower of Hera, are totally different in their design.

Lorule is a hauntingly beautiful world and, in my personal opinion, much more enjoyable than the series' other parallel universe of Termina. I love its use of purples and blues, and it's visually distinct enough that it doesn't feel like a retread of LttP's Dark World at all. My only complaints with Lorule are that A) The name is a really stupid pun and B) Despite what I just said, it's also true that it's too similar to the Dark World to believe that it's a totally different place. Regardless, it was a very enjoyable experience and the second set of dungeons were very creative.

The portrait mechanic is something I initially didn't like, as I felt it was too much of a departure from LttP's mechanics, but this time around I really warmed up to it. Zelda is at its best when it takes a gimmick and runs with it, whether it be time travel, transformative masks, changing the seasons, ocean traversal, or whatever - and this game not only take Link to the Past's alternate world travelling gimmick, but also adds one of its own with the portrait wall crawling. It added its own unique flair to solving puzzles and felt like a fresh experience.

The rental system, on the other hand, was a nice idea in concept. I don't dislike it. The non-linearity it offers is as refreshing as the new portrait mechanic. However, it also took away the charm of finding a new weapon in a dungeon, and renting items over and over again when you die could get tedious. Despite the tedium of re-renting items upon your death, Hero Mode made the concept more fun, as in Normal Mode you are never in any real danger of losing your items and there is much more of an incentive to save up rupees to buy them.

I also very much liked the upgrades and how they were performed - finding lost Maiamais was one of my favorite things to do. It took the collectathon concept and made it feel substantial by giving you a useful reward for every ten Maiamais that you find. The Maiamais were also adorable.

Spoilers follow.

The story was more absent than it has been in recent Zeldas, but more present than it was it was the classic games, which was a nice compromise between new and old. Hyrule's cast of characters was relatively bland, but where the game really shone brightest was in the inhabitants of Lorule and the story behind their kingdom and its Triforce. Hilda and her last minute betrayal were well done - I never saw it coming the first time around, and she was effective as an empathetic villain.

The ending makes her entire scheme seem intellectually bankrupt, however, as Link and Zelda use Hyrule's Triforce to wish Lorule's back into existence. Why didn't Hilda do this from the beginning? Ravio and his existence as the "other Link" is probably my favorite plot twist in any Zelda game, if only for the fact that we technically get to see an incarnation of Link speak. Yuga was... ok, I guess. Ganon, Demise, Ghirahim, Zant and Vaati were all more interesting villains than he was. Yuga came off as kind of a clown.

Lorule's "Triforce trio" was ultimately a refreshing new take on the three characters we've grown attached to over the course of several games, and their subdued personalities were a thematically appropriate inverse for a world that had its own Triforce shattered. Ravio lacked courage, Hilda lacked wisdom, and Yuga lacked power.

Overall, it was a fantastic game, and a nice return to the "Fallen Hero" timeline of the original games. Perhaps Nintendo will visit it again in the future? One can hope.

Sunday, June 19, 2016

Quick Look: Gungnir, Dept. Heaven Episode IX

What a neat little gem of a game this is.

This game is a strategy RPG through and through - Final Fantasy Tactics and Tactics Ogre have their fingerprints all over this game. However, it also has a unique flair to it that only developer Sting could bring to the table - their RPGs always stand out as different from most, and this game is no exception. You don't get more experience for killing blows, for example: experience is gained from acting, whether it be using potions, attacking, etc. The game has its own twist on the grid based, turn based battle system where you can force your character to move when they're fatigued at the expense of their max HP for that battle. You can choose any member of your team to move on your turn, rather than wait for a specific unit to become ready for battle. You can also choose your "ace" at the beginning of battle, and, depending on who you choose, the units in your army will receive different bonuses. Even with the trademark Sting flair, however, this game plays much more traditionally than their usual titles, which is somewhat disappointing coming off of the one-of-a-kind Riviera, but also refreshing for fans thirsty for traditional tactics games.

Pictured here are the four supporting members that you can choose to support your "ace" unit getting ready to sortie.
The story is what you'd expect from a SRPG, and not quite what you'd expect from that art style. If you're coming off of the lighthearted Riviera, it's kind of jarring how much darker this plot is by comparison. You play as Giulio, a persecuted minority in an evil empire who is A) the son of a rebel hero B) the younger brother of a revolutionary leader and C) the successor of the Norse-inspired magical spear, Gungnir. You're set up for greatness in every way, but at the same time you also start at the very bottom of society. The first battle is you and your friends raiding a caravan for food. You're not much better than low-life bandits, although Giulio himself has a noble undertone to his actions and words that will no doubt bloom into something substantial later on in the story. The story delves into supernatural elements very early on, as soon as you're introduced to the spear Gungnir. It has a Valkyrie Profile-esque tone to it, with the afterlife and even a valkyrie warrior taking the stage at various points. It's not quite as sweeping or gripping as FFT or TO, but I would go so far as to say that it comes very close, and I would even go so far as to call it a very good story. If you like the typical SRPG storylines, play this game. Despite the supernatural twinge, it is still a relatively grounded plot and no more invested in the fantastical than FFT was with its Zodiac Stones.

Ragnus, protagonist Giulio's older brother and revolutionary leader, makes a grim inquiry.
This is also, incidentally, Episode IX in the Dept. Heaven series, which also includes:

Riviera, the Promised Land
Yggdra Union
Knights in the Knightmare

It supposedly takes place in the same universe as those games, despite sharing almost no similarities.

Overall, the bottom line is this: this game is an unsung gem of the PSP's library, and it's well worth playing if you like Japanese RPGs, strategy RPGs, or Sting/Atlus games. If you can check even one of those boxes off, this game is worth your time, even if the others don't usually appeal to you.