The dragons of Game of Thrones haven’t exactly had a great run over the past couple of seasons. First went Viserion, killed by the Night King, then resurrected by the Night King as an ice dragon, then destroyed all over again during the Battle of Winterfell when Arya shanked the Night King and shattered his army of wight supremacists. Next went Rhaegal, felled just last week by Euron Greyjoy and two well-placed, apparently hypersonic mega-spears. Of Daenerys Targaryen’s scale-baby triplets, only one remains, and even that one’s likely to need some recovery time after turning King’s Landing to a smoldering ash-heap.
On the bright side, that means a smaller cottage industry will be needed to ensure that Drogon is fed and cared for without laying waste to the rest of Westeros—or so determined a trio of Maryland high school students on their way to outdueling thousands of other teams in the prestigious Mathematical Contest in Modeling (MCM).
Since 1987, the nonprofit Consortium for Mathematics and Its Applications has held the annual competition for university and high school teams across the world. Each team chooses one of three complex, open-ended scenarios and then researches and crafts a technical paper analyzing and proposing a solution. It’s a four-day slog that still impresses contest director Patrick J. Driscoll. “No matter what we craft for a problem, it’s amazing to see that anyone can do that kind of work in that short span of time,” says Driscoll, who teaches systems engineering at West Point.
While two of this year’s scenarios, known in the competition as Problems B and C, carried real-world urgency—one asked teams to configure and deploy a fleet of drones that would supplement relief medical-supply chains on Puerto Rico, the other asked them to build a model that could assess how severe the opioid epidemic in the US could become if left unabated—the third went in a distinctly Westerosi direction. Problem A involved modeling the ecological ramifications of Dany’s three dragons living on Earth.
Your team is assigned to analyze dragon characteristics, behavior, habits, diet, and interaction with their environment. To do so, you will have to consider many questions. At a minimum, address the following: What is the ecological impact and requirements of the dragons? What are the energy expenditures of the dragons, and what are their caloric intake requirements? How much area is required to support the three dragons? How large a community is necessary to support a dragon for varying levels of assistance that can be provided to the dragons? Be clear about what factors you are considering when addressing these questions.
Nearly 4,000 teams tackled the problem, among them three seniors at Richard Montgomery High School in Rockville, Maryland. Matthew Kolodner, Clarissa Xia, and Lauren Zhou had gotten their first taste of math modeling in a competition last year and formed a club at their school. After a handful of competitions on different teams, they banded together for this year’s MCM—a supergroup of sorts.
None of the three were GoT fans to begin with; their journey into cryptozoology was predicated mostly on not wanting to deal with the combinatorial complexity inherent in the other two problems. (Teams grappling with those would find “really extreme computing challenges no matter how they did it,” Driscoll says.) But Zhou, who had just finished the latest volume in Brandon Sanderson’s Stormlight Archive saga, happened to have A Game of Thrones (the first book in George R. R. Martin’s series, not the show) on reserve at the library and was more than ready to dive in. “Part of the slog of modeling is finding data, but I could read fantasy wiki pages for days—which I did,” she says.
While she read up on lore about Balerion the Black Dread, her teammates figured out which real-world animals could be used as modeling stand-ins, based on migratory behavior, bodily density, and other qualities. (They went with pterosaurs and komodo dragons.) They cleared their schedules of ski trips and friend hangs, spending the entire weekend holed up at Zhou’s house, sleepover style—”we had a potluck, my mom made a nice breakfast”—and taking advantage of a Monday holiday to get their technical paper in by the deadline.
In 23 pages, the trio begin by determining the dragons’ caloric needs (more than a million a day) and rate of growth, even explaining why they’re using a modified von Bertalanffy equation rather than an asymptotic sigmoidal curve. (Apologies to mathematicians, but I’m just noting that because it’s an enjoyably silly name.) They go on to derive the land area that would be necessary to sate a dragon’s metabolic needs while remaining environmentally sustainable; looking at apex predators in various biomes, they conclude that each dragon would need as little as 292.5 square miles for a savannah, and as much as 7,108 square miles for arctic tundra (i.e., north of the Wall). Finally, in a section on human intervention—specifically, the logistics of sustainably raising livestock for the sole purpose of being dragon-dinner—they determined that a single dragon would necessitate 1798x cows, in which x equals the minimum cows needed to survive for one day. (The cows that aren’t being devoured are growing to maturity, or just being pregnant with Drogon’s next meal.) Yes, that is a lot of cows. And a lot of land—almost 20,000 acres per cow eaten.
When the blind evaluation process began, Entry 17933 impressed the MCM judges immediately. (With 14,000 total entries to sift through, 136 volunteer judges in the US and 80 or so in China do a first pass to narrow the field down to about 120 entries for each problem, then 10 finalist judges devote an entire weekend to vetting the finalists.) “It’s extremely well-written,” Driscoll says, “but I what I really liked was they way they walked through the modeling approach: defining the problem, assumptions and justification, approach, sensitivity analysis, and then ultimately evaluating their model for strengths and weaknesses. They did that really, really well and did it in a way that really exposed the way that they were thinking about each element of the problem. That’s not the case in general for papers that we see.”
Ultimately, MCM designated 17 teams from among the 14,108 total entrants Outstanding Winners, the contest’s highest honor. Not only did Montgomery High’s team snag one of the 17 designations—the only high school to do so—but it picked up additional awards from the Mathematics Association of America and even COMAP itself. When Driscoll finally unblinded the winners and unveiled the teams behind the entries, he says, “people were astounded.”
It stands to reason that the dragon’s creator would be as well. “Although George R. R. Martin’s series A Song of Ice and Fire falls under the category ‘hard fantasy,'” wrote the students, who will be attending Stanford, Berkeley, and University of Maryland next year, “we doubt he expected this level of rigor applied to his dragons.”
