Richard Dedekind was a 19th-century mathematical giant, responsible for reshaping the field right down to its foundations. He was the first to give a rigorous definition of infinity; he also came up with the definition of the real numbers that form the basis of much of modern mathematics. In 1897, he published an investigation into… Continue reading Ninth Dedekind Number Found by Two Independent Groups
Tag: Quantum Stuff
How to Protect Yourself from Ticks and the Dangerous Diseases They Spread
Summer is the season for stone fruit, pool parties, cookouts and, increasingly for Americans, ticks. Ecologist Felicia Keesing had an uncanny sense for ticks for as long as she could remember. If one bit her, she could feel it and would quickly pluck it off with tweezers. But last year this superpower failed her when… Continue reading How to Protect Yourself from Ticks and the Dangerous Diseases They Spread
AI Promises Humanity One Last Job. Helping AI Help Humanity
From dethroning chess masters and game show champions to outperforming radiologists, the dazzling—and at times overwhelming—world of artificial intelligence raises deep questions about the future of human jobs. In the last century, our capacity to store and process data has soared, with electronics marching from the vacuum tube to the transistor to today’s semiconductor chips.… Continue reading AI Promises Humanity One Last Job. Helping AI Help Humanity
New Calculations Show How to Escape Hawking’s Black Hole Paradox
Akers had already convinced himself that the conversion program should be written in the language of quantum error correction, as Harlow had already worked out for empty space. The semiclassical interior would be the message, and the quantum exterior would be the transmission. And given that the interior seemed to grow inside a shrinking horizon,… Continue reading New Calculations Show How to Escape Hawking’s Black Hole Paradox
Selfish, Virus-Like DNA Can Carry Genes Between Species
Previous studies of horizontal transfers have often focused on the mobile genetic elements called transposons. These privileged “jumping genes” can hop around the genome of an organism by replicating themselves and inserting their copies. Their sole concern is to promote their own survival within the genome rather than the fitness of the organism, which is… Continue reading Selfish, Virus-Like DNA Can Carry Genes Between Species
This Ancient Language Has the Only Grammar Based Entirely on the Human Body
One morning in December 2004, elders and children were wandering on the shore of Strait Island in the Bay of Bengal when one of them noticed something odd. The sea level was low, and weird-looking creatures that normally inhabit the deep twilight zone of the ocean were bobbing near the water’s surface. “Sare ukkuburuko!”—the sea… Continue reading This Ancient Language Has the Only Grammar Based Entirely on the Human Body
AI Chatbots Could Help Provide Therapy, but Caution Is Needed
On Reddit forums, many users discussing mental health have enthused about their interactions with ChatGPT—OpenAI’s artificial intelligence chatbot, which conducts humanlike conversations by predicting the likely next word in a sentence. “ChatGPT is better than my therapist,” one user wrote, adding that the program listened and responded as the person talked about their struggles with… Continue reading AI Chatbots Could Help Provide Therapy, but Caution Is Needed
Math That Lets You Think Locally but Act Globally
In math, as in life, small choices can have big consequences. This is especially true in graph theory, a field that studies networks of objects and the connections between them. Here’s a little puzzle to help you see why. Given six dots, your goal is to connect them to each other with line segments so… Continue reading Math That Lets You Think Locally but Act Globally
New Proof Shows That ‘Expander’ Graphs Synchronize
Melody and Silence In the early 1990s, together with his student Shinya Watanabe, Strogatz showed that Kuramoto’s solution was not only possible, but all but inevitable, even for a finite number of oscillators. In 2011, Richard Taylor of the Australian Defense Science and Technology Organization chipped away at Kuramoto’s requirement that the graph be complete. He… Continue reading New Proof Shows That ‘Expander’ Graphs Synchronize
A New Therapy for Multiple Personality Disorder Helps a Woman with 12 Selves
When Ella time traveled in my office for the first time, I did not realize what was happening right away. She was sitting comfortably in a chair, her hands folded, her back straight and her feet flat on the floor. There was no dramatic change, no shuddering or twitching. But then I saw it: a… Continue reading A New Therapy for Multiple Personality Disorder Helps a Woman with 12 Selves