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A case of mathematical manipulation made its way to the Supreme Court this week. Gill v. Whitford is the latest court case to challenge partisan gerrymandering, the practice of warping congressional districts into convoluted shapes to win seats in the United States House of Representatives and various state legislatures.

The last time the court examined gerrymandering was 13 years ago in Vieth v. Jubelirer. The ruling ended with a cliffhanger: Justice Anthony Kennedy challenged plaintiffs to set a new standard to limit agenda-based redistricting that could be introduced to the courts at a future date. Since then, political scientists and mathematicians have been crunching the numbers, hoping to apply what could be considered abstruse research to a pervasive civic problem.

The United States Supreme Court

“It’s very rare that we find a socially-relevant cause for geometry research,” said Justin Solomon, computer scientist at MIT and member of Tufts University’s Metric Geometry and Gerrymandering Group (MGGG).

One model experts have come up with involves what's called the efficiency gap, which the court considered this week. The efficiency gap is a way to measure “wasted” votes, or all votes beyond what’s necessary to win a district. This interactive from The New York Times breaks it down. The creators of the efficiency gap have recommended that a gap of 7% or higher would be classifiable as an unconstitutional act of partisan gerrymandering.

But there are other ways math could solve the crisis. District sampling algorithms, for one, can do a lot of the work for us.

Here’s how it works. You load in basic information about a particular state, as well as district criteria defined by both the legislature and the law. Then, you formulate an algorithm that randomly generates districting plans that satisfy all the rules you impose on it. The result is a suite of districting options. 

“We’re able to generate billions of possible redistricting maps,” said Wendy K. Tam Cho, a political scientist at the University of Illinois at Urbana-Champaign. “It provides a counterfactual for the maps in dispute." In other words, if a court is trying to determine the acceptability of a district map, a single alternative map isn’t going to impress anyone.

“Maybe the existence of a billion plans is a little more convincing,” Solomon said.

Cho and Solomon warn, though, that if you’re going to use an algorithm to stop gerrymandering, you’d better trust that algorithm. 

“The computer makes the decision about how the districts are drawn,” Cho said. “If you don’t want partisan districts, you just don’t put in partisan information.” Instead, mathematicians can issue guidelines for the algorithm to follow related to “compactness” or population density. The former is a bit of a wishy-washy term (according to Cho, “the court is unwilling to give a strict definition”), but essentially compactness refers to the extent to which the shape of a district is spread out from its center. But politicians and academics alike disagree about the term’s usefulness. 

The work of mathematicians like Cho and Solomon will run parallel to the Supreme Court decision-making process. Along the way, these experts will be trying to educate the public about their methods. 

No matter what happens, gerrymandering will be difficult to rein in purely because it’s so embedded in our country’s history.

“Gerrymandering is a natural byproduct of the American political system as it was designed,” Solomon said. “This is just what happens when people are trying to defend their political and social interests.

“Regardless of the outcome of this case, we’re going to have a lot of work ahead of us.”


The Berlin Marathon was on September 24 this year, and all eyes were on Eliud Kipchoge of Kenya, who many hoped would be the first to run a “sub-2” marathon, or a marathon completed under two hours. Kipchoge finished first in 2:03:32, which didn’t set a record—but it’s still impressive. The rain and humid weather probably contributed to his less-than-optimal pace, plus a number of other factors that physiologist Wouter Hoogkamer and his colleagues at the University of Colorado, Boulder have been studying .

"By the end his shoes were probably about 100 grams heavier just because of the accumulation of water in the fabric, that might have slowed him down," Wouter said regarding Kipchoge's time. "I would suggest that he probably lost about 40 seconds there."

Cheri Blauwet is a medical doctor and a champion wheelchair racer. Check out her Secret Life of Scientists profile.

Wouter suggests Kipchoge may have been able to beat the two-hour mark at other marathons—with help from the right pair of shoes, ideal terrain, and a technique called drafting—but that he didn't. "There’s a lot of psychology happening, too," he said. "I think Kipchoge just had a mental weak moment around 30 kilometers, where, without even realizing it, he quit the race."


This week, the 2017 Nobel Prize in Physics was awarded to three scientists who, in February of last year, discovered ripples in spacetime known as gravitational waves.

Fun fact? One of the winners, Kip Thorne of the California Institute of Technology, was an executive producer and consultant on the movie Interstellar. We chatted with him about the intersection of science and culture.

Revisit some of our gravitational wave coverage on NOVA Next, and subscribe to What the Physics?!, our YouTube channel about all things physics.


We had some fun engaging in a little witty banter with Stacy Conaway on Twitter, in response to our article addressing whether or not we're in a computer simulation:

Thanks, Stacy! The article prompted a lot of discussion over on Reddit. Check out the conversation here.

NOVA's project director, Pam Rosenstein, brings us this excerpt from an article in The New York Times on climate change:

"Arctic sea ice has been in steep decline since the late 1970s, when satellite images were first used to study the region. NASA says that the extent of ice covering Arctic waters has fallen by 13 percent per decade. The 10 lowest ice minimums—measured each September, after the summer thaw—have all been recorded since 2007. Scientists say the disappearance of sea ice is largely a result of climate change, with the Arctic warming at a faster rate than any other region. This year, sea ice reached its minimum on Sept. 13, according to the National Snow and Ice Data Center in Boulder, Colo. At that point, ice covered 1.8 million square miles, or 4.6 million square kilometers, of Arctic waters. That makes this year’s minimum the eighth-lowest on record."


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And if you got the link to this newsletter elsewhere, subscribe here and check out last week's edition.

See you next week, 

Allison and the NOVA team

National corporate funding for NOVA is provided by Draper and 23andMe. Major funding for NOVA is provided by the David H. Koch Fund for Science, the Corporation for Public Broadcasting, and public television viewers.
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