The agency launched the little four-pound chopper in July 2020, with Ingenuity hitchhiking to Mars in the belly of NASA’s Perseverance rover. The tissue box-size craft made its first-ever flight in April 2021. Launched as a month-long technology demonstration, the helicopter was built to make a mere five hops to prove that powered flight is possible on the Red Planet.
Many in the American public feel a personal connection to the topic. Recent surveys find that about one quarter of Americans report having seen some kind of UFO. Research we worked on at the nonprofit, nonpartisan RAND Corporation has found clusters of UFO reports across most U.S. states over the past several decades. These constituencies—and their elected officials—can be expected to have strong feelings about UAP data and what it does or doesn’t show.
Carl Sagan popularized the maxim that “extraordinary claims require extraordinary evidence.” This advice should not be optional for policy makers. In today’s world of misinformation, conspiracy driven decision-making and sensationalist-dominated governance, our capacity for rational, evidence-based critical thinking is eroding, with deleterious consequences for our ability to effectively deal with multiplying challenges of ever increasing complexity.
One of the most influential books of this era to raise this question was The Invisible Government, written in 1964 by journalists David Wise and Thomas Ross. They opened their account with a stark declaration: “There are two governments in the United States today. One is visible. The other is invisible.” They then set out their thesis that the CIA had occasionally acted outside the authority of elected officials, and that such covert operations were not merely an instrument of U.S. foreign policy, but had actively shaped it. Though their thesis was more nuanced and narrowly focused than that of many contemporary purveyors of deep state conspiracy theories, their book provided the language and narrative apparatus that would eventually metastasize into the widespread skepticism in American society toward officialdom, and in particular toward the U.S. intelligence community.
America has always been a suspicious society, famed for its persecution of imaginary subversives, from witches to commies hiding under the bed. But that terrible history almost seems quaint today when disinformation experts agree we now live in the Golden Age of Conspiracy Theories. This movement has even swept up pop idol Taylor Swift and the 2024 election, as you may have heard, into only the latest reductio ad absurdum of the era.
.jpg?w=900)
At about the same time, Conway was exploring the idea of the universal constructor, which was first studied by American mathematician John von Neumann in the 1940s. A universal constructor is a hypothetical machine that could build copies of itself—something that would be very useful for colonizing distant planets. Von Neumann created a mathematical model for such a machine, using a Cartesian grid—basically, an extended checkerboard—as his foundation. Conway simplified the model, and it became the now famous game of Life.
Stepping into John H. Conway’s office at Princeton University is like stepping into a mathematician’s playpen. Dozens of polyhedra made of colored cardboard hang from the ceiling like mirror balls at a discotheque. Dangling among them is a Klein bottle constructed from chicken wire. Several models of crystal lattices sit beside the window, and a pyramid of tennis balls rises from the floor. At the center of it all is Conway himself, leaning back in his chair, his face obscured by oversize glasses and a bushy, gray beard. The eclectic 61-year-old mathematician is clearly in his element.
Stepping into John H. Conway’s office at Princeton University is like stepping into a mathematician’s playpen. Dozens of polyhedra made of colored cardboard hang from the ceiling like mirror balls at a discotheque. Dangling among them is a Klein bottle constructed from chicken wire. Several models of crystal lattices sit beside the window, and a pyramid of tennis balls rises from the floor. At the center of it all is Conway himself, leaning back in his chair, his face obscured by oversize glasses and a bushy, gray beard. The eclectic 61-year-old mathematician is clearly in his element.
In the early 1970s mathematician Donald Knuth spent a sabbatical with his wife in Norway. The time was meant to be spent relaxing. Yet one night he woke up his partner in a state of agitation. He urgently needed to write a book. Don’t worry, he reassured his spouse, it will only take a week. To concentrate on his writing, he reserved a hotel room just for himself in Oslo.
To visualize this, we can again use the initial example with the 50 voters (20 for red, 30 for blue) and calculate the efficiency gap for the different divisions. In the first case, when all boundaries were drawn vertically, the first and second districts (from the left) each have 10 red votes, wasting four each. The third, fourth and fifth districts, on the other hand, each have 10 blue votes, four of which are also wasted. Thus, the efficiency gap is as follows (the vertical bars indicate absolute value): |(2 x 4) – (3 x 4)|/50 = 2/25 = 0.08.