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The Night King’s eerie sigils on Game of Thrones could have a basis in math

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‘Not bad for the frozen undead’

Spoilers ahead for Game of Thrones, season 8, episode 1, “Winterfell.”

As we near the end of Game of Thrones, there are still a few huge mysteries left unsolved. The audience still knows relatively little about the White Walkers. Their origins were revealed in season 6, but the extent of their powers hasn’t been explained, nor have the mysterious symbols they leave behind in their bloodshed. The season 8 premiere, “Winterfell,” prominently features one of these symbols, made out of human body parts. But it’s only one of many times we’ve seen it, and there are various ways to interpret what it means.

The first time Game of Thrones associates a curious symbol with the Army of the Dead is in season 1, episode 1, “Winter is Coming” when body parts of wildings are left in a strange circle with a line through the middle. It looks like Φ. A member of the Night’s Watch uncovers this symbol in the snow and sees a wilding girl who has been pinned to a tree, dead, behind him. The imagery of a strange circle plus an additional sacrifice appears again in the premiere of season 8 when Ned Umber’s body is found pinned to a wall at the center of a spiral.

Φ is the Greek symbol, phi, which has various uses in science and mathematics. Most famously, it’s used to represent the golden ratio, which frequently appears in geometry, art, and architecture throughout history. As seen in season 1, it appears that the White Walkers are perverting the golden ratio and sending some sort of foreboding message to the humans who observe it.

The spiral we see at the end of “Winterfell” also appears to have roots in mathematics. It bears a resemblance to the Fibonacci spiral, a golden spiral whose growth factor is Φ, the golden ratio. It grows wider by a factor of Φ for every quarter turn it takes. We could interpret this as more humans being killed and absorbed into the Army of the Dead, which increases with every new slaughter.

Andrew Beveridge, a math professor at Macalester College, says the White Walker spiral goes in the opposite direction of a golden spiral, but it’s “pretty darn close” to a clockwise golden spiral. Beveridge measured the expansion of each quarter turn and found it to be 1.616, which is close to the golden spiral’s expansion factor of 1.618. “Not bad for the frozen undead,” he says. “So if you ask me: yes, the White Walkers have made seven clockwise golden spirals.” Seven is an important number in Game of Thrones lore, he says: there are seven kingdoms, seven great Houses, and seven gods in the series’ main religion.

Still, the fan theory isn’t 100 percent perfect. As for whether the first symbol seen in “Winter is Coming” is indeed Φ, Beveridge says, “I agree that it is pretty close. But I wish that either the circle didn’t complete at 11:00, or that the vertical line extended above the circle. That way it would match one of the two lower-case phi variants. I personally wouldn’t put my money down on that one.”

So far, the show’s inclusion of these weird symbols seems to be a departure from George R.R. Martin’s source novels. The books do mention of whorls and swirling patterns in dragon eggs and fabrics, but there’s no greater meaning ascribed to them. On the HBO show, though, we know that before the White Walkers started using these symbols, their creators, the Children of the Forest, had also used them — carved in stone rather than with flesh.

In season 6, Bran observed that the stones around a weirwood tree are positioned in a peculiar spiral pattern. After he spots the symbol, he sees one of the Children of the Forest, Leaf, stabbing one of the First Men with dragonglass, turning him into the first White Walker, aka the Night King. Later on in season 7, when Jon takes Daenerys down into a cave in Dragonstone, they study the ancient carvings of spirals on the walls, which were drawn by the Children of the Forest.

Showrunner David Benioff explained in a behind-the-scenes clip on season 7, episode 4 that he showrunner D.B. Weiss pulled these ideas from the real world. “These are patterns that have mystical significance for the Children of the Forest. We’re not sure exactly what they signify, but spiral patterns are important in a lot of different cultures in our world, and it makes sense that they would be in this world as well,” Benioff said. The symbols also appear naturally when Dothraki riders surround Daenerys in season 5 and in season 3 when she’s embraced by a crowd.

One fan theory suggests that the spirals symbolize magic and its proximity to humans. Others note that the symbols bear a resemblance to the Targaryen sigil’s multiple dragon heads. Another possibility is that the spirals simply signify the circle of life (and the undead). As Varys says in the season 8 premiere, while looking at Jon and Daenerys, “Nothing lasts.” There’s also the idea that history repeats itself and life is cyclical. In season 1, episode 1, Ned Stark tells Bran that the White Walkers haven’t appeared in thousands of years. Now, seven seasons later, they’re back. The symbol, in other words, could be a warning that the White Walkers will always return to make humans part of their undead army.

Update April 16th, 2:49PM ET: This article has been updated to reflect that Beveridge counted seven clockwise golden spirals.