These and other surprising examples made it clear that mathematicians needed to prove that dimension is a real notion and that, for instance, n- and m-dimension Euclidean spaces are different in some fundamental way when n ≠ m. This objective became known as the “invariance of dimension” problem. Finally, in 1912, almost half a century after Cantor’s… Continue reading The Journey to Define Dimension
Tag: Quantum Stuff
Electric Vehicle Orders Are Zooming at Ford
Ford Motor Co. nearly tripled its electric vehicle sales last month, according to a company report. The auto giant increased its EV and hybrid sales this May by 184% compared to May 2020, marking a record number of 10,364 EVs sold in a given month, the sales report found. The significant increase is due in part to… Continue reading Electric Vehicle Orders Are Zooming at Ford
How Ancient War Trickery Is Alive in Math Today
Imagine you’re a general in ancient times and you want to keep your troop counts secret from your enemies. But you also need to know this information yourself. So you turn to a math trick that allows you to achieve both aims. In a morning drill you ask your soldiers to line up in rows… Continue reading How Ancient War Trickery Is Alive in Math Today
Any Reform of Federal Oil and Gas Leasing Must Include Environmental Justice
After four years of an agenda that favored polluters, a new day is dawning at the Department of the Interior. In March, communities across the country rejoiced in Secretary Deb Haaland’s historic confirmation to lead the biggest and most powerful land management agency in the country. Now, she’s taking the opportunity to pursue real reforms… Continue reading Any Reform of Federal Oil and Gas Leasing Must Include Environmental Justice
A Massive Subterranean ‘Tree’ Is Moving Magma to Earth’s Surface
But seismology is not omniscient. Seismic waves can detect structures within the mantle, but they cannot reveal every characteristic of those structures. “You can slow down a seismic wave by heating a material up,” said Harriet Lau, a geophysicist at the University of California, Berkeley. But a change in the rock’s mineral makeup can achieve… Continue reading A Massive Subterranean ‘Tree’ Is Moving Magma to Earth’s Surface
Neck-Zapping Gadget Reduced All-Nighter Fatigue in New Study
Instead of reaching for a cup of coffee during a graveyard shift, workers might one day hold an electric-razor-sized device to their necks. After a couple of minutes they would emerge refreshed and awake from this experience, which could come to be known as a “vagus nerve break.” The device, called gammaCore, sends a series… Continue reading Neck-Zapping Gadget Reduced All-Nighter Fatigue in New Study
Biologists Rethink the Logic Behind Cells’ Molecular Signals
The emerging picture does more than reconfigure our view of what biomolecules in our cells are up to as they build an organism — what logic they follow to create complex life. It might also help us understand why living things are able to survive at all in the face of an unpredictable environment, and… Continue reading Biologists Rethink the Logic Behind Cells’ Molecular Signals
New Radioactivity Measurement Could Boost Precision of Dark Matter Experiments
A concentration of one part per billion is like a pinch of salt in 10 tons of potato chips—and scientists can now find radioactive particles at concentrations millions of times smaller. In the Journal of Analytical Atomic Spectrometry, researchers describe successfully detecting radioactive uranium and thorium hiding among something like a million billion other atoms.… Continue reading New Radioactivity Measurement Could Boost Precision of Dark Matter Experiments
Banach-Tarski and the Paradox of Infinite Cloning
Imagine two friends hiking in the woods. They grow hungry and decide to split an apple, but half an apple feels meager. Then one of them remembers one of the strangest ideas she’s ever encountered. It’s a mathematical theorem involving infinity that makes it possible, at least in principle, to turn one apple into two.… Continue reading Banach-Tarski and the Paradox of Infinite Cloning
To Learn More Quickly, Brain Cells Break Their DNA
Faced with a threat, the brain has to act fast, its neurons making new connections to learn what might spell the difference between life and death. But in its response, the brain also raises the stakes: As an unsettling recent discovery shows, to express learning and memory genes more quickly, brain cells snap their DNA… Continue reading To Learn More Quickly, Brain Cells Break Their DNA