The post What Do Gödel’s Incompleteness Theorems Truly Mean? first appeared on Quanta Magazine
In 1931, by turning logic on itself, Kurt Gödel proved a pair of theorems that transformed the landscape of knowledge and truth. These “incompleteness theorems” established that no formal system of mathematics — no finite set of rules, or axioms, from which everything is supposed to follow — can ever be complete. There will always be true mathematical statements that don’t logically follow from…
The post What Do Gödel’s Incompleteness Theorems Truly Mean? first appeared on Quanta Magazine
In 1931, by turning logic on itself, Kurt Gödel proved a pair of theorems that transformed the landscape of knowledge and truth. These “incompleteness theorems” established that no formal system of mathematics — no finite set of rules, or axioms, from which everything is supposed to follow — can ever be complete. There will always be true mathematical statements that don’t logically follow from…
The post Rubin Tracks Skyscraper-Size Asteroids, Failed Supernovas, and Interstellar Visitors first appeared on Quanta Magazine
Over the years, anticipation has built for the start of observations at the Vera C. Rubin Observatory in the mountains of the Atacama Desert in Chile. Originally imagined in the mid-1990s as the Dark Matter Telescope, Rubin is designed to study our constantly moving and changing universe in greater detail than ever before. Once every few days for a decade, Rubin will take images of the entire…
The post Rubin Tracks Skyscraper-Size Asteroids, Failed Supernovas, and Interstellar Visitors first appeared on Quanta Magazine
Over the years, anticipation has built for the start of observations at the Vera C. Rubin Observatory in the mountains of the Atacama Desert in Chile. Originally imagined in the mid-1990s as the Dark Matter Telescope, Rubin is designed to study our constantly moving and changing universe in greater detail than ever before. Once every few days for a decade, Rubin will take images of the entire…
The post How the Bird Eye Was Pushed to an Evolutionary Extreme first appeared on Quanta Magazine
When an optometrist shines a bright light into your eyes, a vast, branching tree sprouts in your field of vision. This is the shadow of blood vessels. Though we normally can’t perceive them, these vessels always occlude a portion of what we see, and for an important reason. They power the retina, a thin layer of nerve tissue in the back of the eye that communicates light signals to the brain.
The post How the Bird Eye Was Pushed to an Evolutionary Extreme first appeared on Quanta Magazine
When an optometrist shines a bright light into your eyes, a vast, branching tree sprouts in your field of vision. This is the shadow of blood vessels. Though we normally can’t perceive them, these vessels always occlude a portion of what we see, and for an important reason. They power the retina, a thin layer of nerve tissue in the back of the eye that communicates light signals to the brain.
The post How Unknowable Math Can Help Hide Secrets first appeared on Quanta Magazine
Mathematicians spend most of their time thinking about what’s knowable. But the unknowable can be just as compelling. Perhaps the most famous example comes from a theorem by the logician Kurt Gödel. Gödel’s celebrated result — one of two “incompleteness theorems” he published in 1931 — established that for any reasonable set of basic mathematical assumptions, called axioms, it’s impossible to…
The post How Unknowable Math Can Help Hide Secrets first appeared on Quanta Magazine
Mathematicians spend most of their time thinking about what’s knowable. But the unknowable can be just as compelling. Perhaps the most famous example comes from a theorem by the logician Kurt Gödel. Gödel’s celebrated result — one of two “incompleteness theorems” he published in 1931 — established that for any reasonable set of basic mathematical assumptions, called axioms, it’s impossible to…
The post Will We Ever Be Able To Forecast Volcanic Eruptions Like Weather? first appeared on Quanta Magazine
In the summer of 1991, Pinatubo, a volcano in the Philippines, self-destructed. The eruption started on June 12, and three days later it culminated in a tremendous explosion. By the time pyroclastic flows — incandescent avalanches of molten rock and gas — tumbled down its sterilized slopes, Pinatubo’s peak had been obliterated and replaced by a 2.5-kilometer-wide chasm. The eruption killed more…
The post Will We Ever Be Able To Forecast Volcanic Eruptions Like Weather? first appeared on Quanta Magazine
In the summer of 1991, Pinatubo, a volcano in the Philippines, self-destructed. The eruption started on June 12, and three days later it culminated in a tremendous explosion. By the time pyroclastic flows — incandescent avalanches of molten rock and gas — tumbled down its sterilized slopes, Pinatubo’s peak had been obliterated and replaced by a 2.5-kilometer-wide chasm. The eruption killed more…
The post What Causes Lightning? The Answer Keeps Getting More Interesting. first appeared on Quanta Magazine
Before he changed the way we understand lightning on Earth, Joseph Dwyer studied the weather in more cosmic settings. Using the sensors on NASA’s Wind satellite, orbiting a million miles away, he watched flares shoot out from the sun and analyzed the particles that stream from the sun’s surface. But when he relocated to Florida around the turn of the millennium, Dwyer felt ready for something new…
The post What Causes Lightning? The Answer Keeps Getting More Interesting. first appeared on Quanta Magazine
Before he changed the way we understand lightning on Earth, Joseph Dwyer studied the weather in more cosmic settings. Using the sensors on NASA’s Wind satellite, orbiting a million miles away, he watched flares shoot out from the sun and analyzed the particles that stream from the sun’s surface. But when he relocated to Florida around the turn of the millennium, Dwyer felt ready for something new…
The post The Hidden Mathematical Dance Inside Plant Cells first appeared on Quanta Magazine
Living on light is a dangerous game. Not only do the sun’s rays carry ultraviolet waves that can snap DNA strands and degrade molecules, but they also vary wildly in intensity. Plants must endure and thrive through soft morning light and blazing summer afternoons, through shade one moment and full sun the next. Their solar calories come in a trickle — or a deluge. “Think of a cloud obscuring the…
The post The Hidden Mathematical Dance Inside Plant Cells first appeared on Quanta Magazine
Living on light is a dangerous game. Not only do the sun’s rays carry ultraviolet waves that can snap DNA strands and degrade molecules, but they also vary wildly in intensity. Plants must endure and thrive through soft morning light and blazing summer afternoons, through shade one moment and full sun the next. Their solar calories come in a trickle — or a deluge. “Think of a cloud obscuring the…
The post A Treasure Trove of Cambrian Fossils Rewrites the Story of Early Life first appeared on Quanta Magazine
Roughly 540 million years ago, toward the start of the Cambrian Period, the planet was mostly ocean, and life was both alien and vaguely familiar. Small, phallic-looking worms rummaged through ocean-floor sediments while blind swimming beasts flung out whiplike tentacles to ensnare prey. Meanwhile, early versions of mollusks and sponges populated the seafloor as jellyfish floated above.
The post A Treasure Trove of Cambrian Fossils Rewrites the Story of Early Life first appeared on Quanta Magazine
Roughly 540 million years ago, toward the start of the Cambrian Period, the planet was mostly ocean, and life was both alien and vaguely familiar. Small, phallic-looking worms rummaged through ocean-floor sediments while blind swimming beasts flung out whiplike tentacles to ensnare prey. Meanwhile, early versions of mollusks and sponges populated the seafloor as jellyfish floated above.