Two kinds of transformations copy the fundamental domain to the right and left, as well as to a series of ever-shrinking semicircles along the horizontal axis. These copies fill the entire upper half of the complex plane. A modular form relates the copies to each other in a very particular way. That’s where its symmetries… Continue reading Behold Modular Forms, the ‘Fifth Fundamental Operation’ of Math
The Bizarre Case of Victim F (Matthew Muller, Denise Huskins, Aaron Quinn)
Podcast: Download MYS277: The kidnapping of Victim F was like something out of a movie. Jimmy Akin and Dom Bettinelli discuss the bizarre details of the case and how it riveted the nation; the police investigation; and the ultimate, confounding truth behind what happened. Get all new episodes automatically and for free: Follow by Email… Continue reading The Bizarre Case of Victim F (Matthew Muller, Denise Huskins, Aaron Quinn)
A message from Dom Bettinelli of Starquest
Podcast: Download I need to ask for your help, but first I want to thank you for listening to StarQuest and supporting our mission of exploring the intersection of faith and pop culture. Over the past five years–since 2018–StarQuest has grown by leaps and bounds, more than at any time in our previous 12 years.… Continue reading A message from Dom Bettinelli of Starquest
Tech Companies’ New Favorite Solution for the AI Content Crisis Isn’t Enough
Thanks to a bevy of easily accessible online tools, just about anyone with a computer can now pump out, with the click of a button, artificial-intelligence-generated images, text, audio and videos that convincingly resemble those created by humans. One big result is an online content crisis, an enormous and growing glut of unchecked, machine-made material… Continue reading Tech Companies’ New Favorite Solution for the AI Content Crisis Isn’t Enough
Embracing the Messiness of Public-Private Collaboration in the Fight Against Botnets
Since the start of the Russia-Ukraine War, Russia has sponsored several Distributed Denial of Service (DDoS) attacks against Ukrainian targets, including various attacks against government and financial entities. Botnets, which are networks of computers infected with malware that an attacker controls and uses to fulfill malicious cyber activities, can be used to launch these DDoS… Continue reading Embracing the Messiness of Public-Private Collaboration in the Fight Against Botnets
The 4 Stages of Conspiracy Theory Escalation on Social Media
The following essay is reprinted with permission from The Conversation, an online publication covering the latest research. Conspiracy theory beliefs and (more generally) misinformation may be groundless, but they can have a range of harmful real-world consequences, including spreading lies, undermining trust in media and government institutions and inciting violent or even extremist behaviors. For… Continue reading The 4 Stages of Conspiracy Theory Escalation on Social Media
Winning the Tech Cold War
If world leaders learn only one lesson from the war in Ukraine, it should be that the ability to rapidly innovate—to invent, adopt, and effectively integrate new technologies—can have profound implications for combat outcomes. Outgunned and outnumbered, Ukrainians took a page from the U.S. playbook and turned to technology to gain an advantage over the… Continue reading Winning the Tech Cold War
A Tower of Conjectures That Rests Upon a Needle
The next step up in that hierarchy is the “restriction” conjecture. If it is true, so is the Kakeya conjecture. (This also means that if the Kakeya conjecture turns out to be false, the restriction conjecture can’t be true.) The restriction conjecture, in turn, is implied by the so-called Bochner-Riesz conjecture. And at the very… Continue reading A Tower of Conjectures That Rests Upon a Needle
Maui Wildires, Regulating AI, Ukraine’s Civilian Resistance: RAND Weekly Recaps
This week, we discuss the invisible damage from the Maui wildfires; improving the safety of America’s AI industry; what makes teachers of color feel a sense of belonging; Ukraine’s civilian resistance; how to increase housing affordability in New York City; and the situation of ISIS prisoners in Syria. The Vaa family escaped the deadly wildfire… Continue reading Maui Wildires, Regulating AI, Ukraine’s Civilian Resistance: RAND Weekly Recaps
‘Species Repulsion’ Enables High Biodiversity in Tropical Trees
For ecologists, tropical rainforests hold many enigmas. A single hectare can contain hundreds of tree species, far more than in forests closer to the poles. Somehow these species coexist in such dizzying abundance that, as naturalists and ecologists have sometimes noted, tropical forests can feel like botanical gardens, where every plant is something new. For… Continue reading ‘Species Repulsion’ Enables High Biodiversity in Tropical Trees