Vacation theorising

I am currently enjoying some vacation, so it’s the perfect time to take a break from theorising about black holes and theorise about Game of Thrones instead. Here are three (not too scientific) theories for how the story may continue. Beware, there may be spoilers (for the books and the show), and dragons, below.

1 The dragon has three heads

The most active area of Game of Thrones theorising has been Jon’s parentage. The last series confirmed that Jon is not the illegitimate son of Ned Stark, possibly the most honourable man in Westeros, but is instead Ned’s nephew. Jon is the son of Lyanna Stark and Rhaegar Targaryen. Ned hid Jon’s identity to hide him from King Robert, who tried to kill all the Targaryens to protect his rule (presumably Jon would have been safe after joining the Night’s Watch and recounting his right to any titles). Jon’s true identity means that we now know of two extent Targaryens: Jon and (his aunt) Daenerys.

Is there a third?

The Burninator

Trogdor Targaryen? (credit: Homestar Runner)

In the House of the Undying, Daenerys has a vision telling her that the dragon has three heads. She needs three riders for her dragons. Before his death, Maester Aemon worries about who the three will be, realising that he is too old.

The books have introduced Aegon, a character (originally known as Young Griff), who claims to be the son of Rhaegar Targaryen and Elia Martell. Aegon was meant to have been killed as a baby by the Mountain, but perhaps he could have been smuggled out and swapped for another unfortunate infant?

I think Aegon is likely a fake, probably a pawn in the schemes of Varys and his old friend  Illyrio Mopatis. We know they are definitely up to something. Daenerys is warned of a mummer’s dragon, which I think implies that this Aegon is a fake.  Furthermore, since Aegon has not appeared in the show, I think it’s safe to say that his plot line is an non-essential complication.

If we give up on Aegon, who else is there? There is one other character we know who is fascinated by dragons, who has even dreamt of them (and did a good job of petting them in the show): Tyrion. Tywin often complained that he could not prove that Tyrion was not a Lannister. Yet, the two seem much alike in intellect and temperament. Tywin is indeed Tyrion’s father in that he is the man that raised him. However, it is possible that Tyrion’s biological father was the Mad King Aerys. Aerys was known to have a liking for Joanna Lannister, perhaps he took advantage while she was at court? This would make Tyrion Daenerys’s elder brother.

Jon Snow, Daenerys Targaryen and Tyrion Lannister

Family portrait? (credit: EW)

The existence of multiple Targaryens might be relevant to the prophesy of The Prince That Was Promised/Azor Ahai. A woods-witch, prophesied that The Prince would come from the line of Aerys and his sister Rhaella. Prophesies aren’t reliable, but I think all three could be in the running. There are ways to interpret all the various other prophesied properties to fit the various characters, but I wonder if the prophesy could be describing all of them?

The most interesting aspect to me is Azor Ahai’s sword Lightbringer, which sounds like exactly the weapon needed to defeat the Others. Azor Ahai killed his wife to make the sword. Daenery’s burnt Khal Drogo to hatch her dragons: they’d be a good weapon against the forces of winter. Jon sacrifices Ygritte to save the Night’s Watch: when joining the Watch, men vow to be “the sword in the darkness”. Tyrion, despite his performance at the Battle of the Blackwater (which included setting the sea of fire), is not much of a fighter. He drinks and knows things. His weapon is his intellect, so what could Lightbringer be in his case? Tyrion strangled Shae with the necklace of the Hand of the King: perhaps his counsel will be what wins the great war.

2 The Seven

The world of George R R Martin definitely contains magic and religion, but it is less clear if there are gods. Just as prophesies are unreliable, so is divine intervention. While miraculous events do happen, it is not clear if these are as a results of the gods, or just a coincidence. I think we are meant to be left unsure if any faith is correct.

While there are miracles that can be assigned to the Old Gods (the magic of the Children of the Forests and Bran’s abilities), R’hllor the Lord of Light (the resurrections of Jon and Beric Dondarrion, and the deaths of Joffrey, Balon Greyjoy, and Robb) and the Drowned God (the resuscitation of the drowned men and Victarion Greyjoy’s success), there is a conspicuous absence of intervention from the Seven, the gods of the majority religion of Westeros (although the church has intervened many times).

My theory is that characters representing the Seven will play an important role in the culmination of the story, such that looking back, it will appear that they guided events.

Seven of Nine

Do the Borg control the Iron Throne? (credit: Paramount)

The question is then who will serve the various roles?

The Father judges. Ser Davos often celebrates how just Stannis is. However, Stannis is not a great father. In fact, it is Ser Davos who is often talked Stannis into doing the right thing, and Ser Davos who cares more children (both Stannis’ and his own). While imprisoned, he writes letters to his sons, in an example of parenting not seen elsewhere. Therefore, Ser Davos is my leading choice as the Father.

The Mother embodies mercy. There are many mothers in the books (Cersei, Catelyn, etc.) but none too merciful. However, I think there is an obvious candidate: the Mother of Dragons, Mhysa of Yunkai. Daenarys is merciful and compassionate.

The Warrior offers protection and courage. There are many notable warriors like Brienne or the Hound who could fit, but I think the best fit is Jaime. Brienne strictly follows her vows and the Hound shuns all notions of knightly honour, neither quite representing the full range of roles that a warrior must serve. Jaime, however, had to pick between his vow of loyalty to the king and his loyalty to his father: Cersei’s younger brother accepted the dishonour of being a kingslayer rather than letting the people of King’s Landing burn. He also better knows the cost of battle, having lost his hand, ironically meaning that he has lost the ability to fight.

The Smith mends broken things. There aren’t too many makers in Westeros (most do the opposite). Gendry is the only real choice. Perhaps he will mend the House of Baratheon? Gendry is my only pick who has not been the point-of-view character for a chapter so far—if he does get a chapter, it could be an indication that he has some future importance.

The Maiden embodies young women, and perfectly matches Sansa.

The Crone gives wisdom and guidance, and is the most difficult to place as (i) few characters live to old age, and (ii) most make terrible life choices. In the books, Brienne prays for the Crone to lead her way as she searches for Sansa, and she is told the Crone will light her way by a Sparrow. Her path leads her to Lady Stoneheart, who is described as having hair as “white and brittle as a crone’s”. However, Stoneheart has not appeared in the show, so perhaps someone else will fill this role? (Maybe Melisandre, who is old enough, if she can get off Arya’s list—although she may need to convert her faith).

Finally, the Stranger is death. I think Arya is the Stranger. The Stranger is identified with the Many-Faced God, whose temple Arya apprenticed in and where she learnt to change her face. While the rest of the Seven are either male or female, the Stranger is neither: Arya is often mistaken for a boy or disguises herself as such. There is also the fact that people on her list keep on dying—the Hound managed to survive his seemingly fatal wounds after Arya removed him from the list, so perhaps she can withhold death too?

Arya’s fit to the Stranger gave me this idea. I think it is neat enough to work, but the difficulty in finding a fit for the Crone might undermine it. It’s perhaps not surprising that there are counterparts to the Seven given that they are meant to represent the different aspects of life.

Assuming that it is the case, there is one possible consequence. The Seven-Pointed Star tells of how the Seven crowned the first king of the Andals. Perhaps the seven characters will crown the new king of Westeros—it will not be one of them. (Daenerys has conquered much of Essos, so perhaps she’ll retire to rule that from a house with a red door, or perhaps she’ll be the queen?) Excluding the seven leaves many candidates, like Jon and Little Finger. The first king of the Andals was Hugor of the Hill. Tyrion travelled under the pseudonym of Hugor Hill; if he were the son of Aerys, he would have a claim…

3 The Faceless Man’s Mission

We first meet Jaqen H’ghar as a prisoner being taken to the Wall. Arya frees him, and after he repays his debt to her he disappears.

In the prologue of A Feast for Crows, we meet Pate, a novice at the Citadel. Pate hates sharing his name with Pate the Pig Boy. He meets an Alchemist, who shares the same description as how we last saw Jaqen. At the end of the prologue, Pate falls to the ground. We’re not sure what happens to him, but given that every other prologue point-of-view character ends up dead, I’d bet he’s been poisoned.

When Sam finally makes it to the Citadel, he meets Marwyn the Mage, a maester who studies magic. Amongst his students is a novice, who introduces himself as Pate “like the pig boy”. I think this change in character indicates that Jaqen has adopted Pate’s face.

So what is Jaqen up to?

I’ve always thought it odd that a Faceless Man, a great assassin who is a master of  disguise, would get caught and imprisoned by the guards of King’s Landing. Perhaps he was in prison because he wanted to be, because it would allow him to establish an identity at the Wall? If Jaqen wanted to go to the Wall, but is now in the Citadel, whatever he was after must have moved too. Maester Aemon is dead of old-age, no-one would hire a Faceless Man for Gilly, and while Sam’s father hates him, I doubt he would go to the expense of a Faceless Man (he’d be happy enough to arrange an accident himself).  So Jaqen may be after something Sam and Gilly brought with them. There are Maester Aemon’s books, there may be an important secret within them. There is also the ancient horn that Jon gave to Sam, the horn Ghost found buried with the dragonglass at the Fist of the First Men. The horn is mentioned a couple of times as one of Sam’s prized possessions, perhaps it has more significance?

I suspect that the horn could be the mythical Horn of Winter. It is ancient enough, and its burial with dragonglass (which can kill Others) suggests that it might have been used by the First Men for defence. The horn looks unimpressive, but that doesn’t mean it is insignificant.

Grails

Choose your ancient artefacts wisely (Credit: LucasFilm)

I’m pretty much certain that Jaqen is Pate, I’d give good odds that Sam’s horn has some importance; whether the two are related it a bit more of a stretch.

Of course, if this is the case, there’s still the question of who hired Jaqen and how they knew that the horn had been found?

Advertisements

How big is a black hole?

Physicist love things that are simple. This may be one of the reasons that I think black holes are cool.

Black holes form when you have something so dense that nothing can resist its own gravity: it collapses down becoming smaller and smaller. Whatever formerly made up your object (usually, the remains of what made up a star), is crushed out of existence. It becomes infinitely compact, squeezed into an infinitely small space, such that you can say that the whatever was there no longer exists. Black holes aren’t made of anything: they are just empty spacetime!

A spherical cow

Daisy, a spherical cow, or “moo-on”. Spherical cows are highly prized as pets amongst physicists because of their high degree of symmetry and ability to survive in a vacuum. They also produce delicious milkshakes.

Black holes are very simple because they are just vacuum. They are much simpler than tables, or mugs of coffee, or even spherical cows, which are all made up of things: molecules and atoms and other particles all wibbling about and interacting with each other. If you’re a fan of Game of Thrones, then you know the plot is rather complicated because there are a lot of characters. However, in a single glass of water there may be 1025 molecules: imagine how involved things can be with that many things bouncing around, occasionally evaporating, or plotting to take over the Iron Throne and rust it to pieces! Even George R. R. Martin would struggle to kill off 1025 characters. Black holes have no internal parts, they have no microstructure, they are just… nothing…

(In case you’re the type of person to worry about such things, this might not quite be true in a quantum theory, but I’m just treating them classically here.)

Since black holes aren’t made of anything, they don’t have a surface. There is no boundary, no crispy sugar shell, no transition from space to something else. This makes it difficult to really talk about the size of black holes: it is a question I often get asked when giving public talks. Black holes are really infinitely small if we just consider the point that everything collapsed to, but that’s not too useful. When we want to consider a size for a black hole, we normally use its event horizon.

Point of no return sign

The event horizon is not actually sign-posted. It’s not possible to fix a sign-post in empty space, and it would be sucked into the black hole. The sign would disappear faster than a Ramsay Street sign during a tour of the Neighbours set.

The event horizon is the point of no return. Once passed, the black hole’s gravity is inescapable; there’s no way out, even if you were able to travel at the speed of light (this is what makes them black holes). The event horizon separates the parts of the Universe where you can happily wander around from those where you’re trapped plunging towards the centre of the black hole. It is, therefore, a sensible measure of the extent of a black hole: it marks the region where the black hole’s gravity has absolute dominion (which is better than possessing the Iron Throne, and possibly even dragons).

The size of the event horizon depends upon the mass of the black hole. More massive black holes have stronger gravity, so there event horizon extends further. You need to stay further away from bigger black holes!

If we were to consider the simplest type of black hole, it’s relatively (pun intended) easy to work out where the event horizon is. The event horizon is a spherical surface, with radius

\displaystyle r_\mathrm{S} = \frac{2GM}{c^2},

This is known as the Schwarzschild radius, as this type of black hole was first theorised by Karl Schwarszchild (who was a real hard-core physicist). In this formula, M is the black hole’s mass (as it increases, so does the size of the event horizon); G is Newton’s gravitational constant (it sets the strength of gravity), and c is the speed of light (the same as in the infamous E = mc^2). You can plug in some numbers to this formula (if anything like me, two or three times before getting the correct answer), to find out how big a black hole is (or equivalently, how much you need to squeeze something before it will collapse to a black hole).

What I find shocking is that black holes are tiny! I meant it, they’re really small. The Earth has a Schwarzschild radius of 9 mm, which means you could easily lose it down the back of the sofa. Until it promptly swallowed your sofa, of course. Stellar-mass black holes are just a few kilometres across. For comparison, the Sun has a radius of about 700,000 km. For the massive black hole at the centre of our Galaxy, it is 1010 m, which does sound a lot until you release that it’s less than 10% of Earth’s orbital radius, and it’s about four million solar masses squeezed into that space.

The event horizon changes shape if the black hole has angular momentum (if it is spinning). In this case, you can get closer in, but the position of the horizon doesn’t change much. In the most extreme case, the event horizon is at a radius of

\displaystyle r_\mathrm{g} = \frac{GM}{c^2}.

Relativists like this formula, since it’s even simpler than for the Schwarzscild radius (we don’t have to remember the value of two), and it’s often called the gravitational radius. It sets the scale in relativity problems, so computer simulations often use it as a unit instead of metres or light-years or parsecs or any of the other units astronomy students despair over learning.

We’ve now figured out a sensible means of defining the size of a black hole: we can use the event horizon (which separates the part of the Universe where you can escape form the black hole, from that where there is no escape), and the size of this is around the gravitational radius r_\mathrm{g}. An interesting consequence of this (well, something I think is interesting), is to consider the effective density of a black hole. Density is how much mass you can fit into a given space. In our case, we’ll consider the mass of the black hole and the volume of its event horizon. This would be something like

\displaystyle \rho = \frac{3 M}{4 \pi r_\mathrm{g}^3} = \frac{3 c^6}{4 \pi G^3 M^2},

where I’ve used \rho for density and you shouldn’t worry about the factors of \pi or G or c, I’ve just put them in case you were curious. The interesting result is that the density decreases as the mass increases. More massive black holes are less dense! In fact, the most massive black holes, about a billion times the mass of our Sun, are less dense than water. They would float if you could find a big enough bath tub, and could somehow fill it without the water collapsing down to a black hole under its own weight…

In general, it probably makes a lot more sense (and doesn’t break the laws of physics), if you stick with a rubber duck, rather than a black hole, as a bath-time toy.

In conclusion, black holes might be smaller (and less dense) than you’d expect. However, this doesn’t mean that they’re not very dangerous. As Tyrion Lannister has shown, it doesn’t pay to judge someone by their size alone.