On Halloween in 1832, the naturalist Charles Darwin was onboard the HMS Beagle. He marveled at spiders that had landed on the ship after floating across huge ocean distances. “I caught some of the Aeronaut spiders which must have come at least 60 miles,” he noted in his diary. “How inexplicable is the cause which induces these small insects, as it now appears in both hemispheres, to undertake their aerial excursions.”
Small spiders achieve flight by aiming their butts at the sky and releasing tendrils of silk to generate lift. Darwin thought that electricity might be involved when he noticed that spider silk stands seemed to repel each other with electrostatic force, but many scientists assumed that the arachnids, known as “ballooning” spiders, were simply sailing on the wind like a paraglider. The wind power explanation has thus far been unable to account for observations of spiders rapidly launching into the air, even when winds are low, however.
Now, these aerial excursions have been empirically determined to be largely powered by electricity, according to new research published Thursday in Current Biology. Led by Erica Morley, a sensory biophysicist at the University of Bristol, the study settles a longstanding debate about whether wind energy or electrostatic forces are responsible for spider ballooning locomotion.
“What is the single most important thing that you want your readers to learn?”
Thorne: The amazing power of human mind — by fits and starts, blind alleys, and leaps of insight — to unravel the complexities of our Universe, and reveal the ultimate simplicity, the elegance, and the glorious beauty of the fundamental laws that govern it.
From the book, ‘Black Holes & Time Warps: Einstein’s Outrageous Legacy’ by Kip S. Thorne.
T=temperature
h=Plank’s constant
c=speed of light
G=Newton’s gravitational constant
M=mass of the black hole
k=Boltzmann’s constant
The equation tells us that as the mass of the black hole gets bigger, its Hawking radiation temperature gets lower.
If I do close my eyes, what is it that I picture years from now?
Like Leon said, doesn’t one need to understand that, before they’re ready to fight for their existence?
How would my future fairytale unfold?
Will I finally connect with those I deeply care for?
Will I reunite with old friends long gone?
See the ones I love find true happiness?
Maybe this future includes people I’d never dream of getting close to.
Even make amends with those I have unfairly wrong.
A future that’s not so lonely.
A future filled with friends and family.
You’d even be there.
A world I’ve always wanted.
And you know what?
I would like very much to fight for it.
As a result of new work by Amir Ali Ahmadi and Anirudha Majumdar of Princeton University, a classical problem from pure mathematics is poised to provide iron-clad proof that drone aircraft and autonomous cars won’t crash into trees or veer into oncoming traffic.
The guarantee comes from an unlikely place — a mathematical problem known as “sum of squares.” The problem was posed in 1900 by the great mathematician David Hilbert. He asked whether certain types of equations could always be expressed as a sum of two separate terms, each raised to the power of 2.
Mathematicians settled Hilbert’s question within a few decades. Then, almost 90 years later, computer scientists and engineers discovered that this mathematical property — whether an equation can be expressed as a sum of squares — helps answer many real-world problems they’d like to solve.
Yet even as researchers realized that sum of squares could help answer many kinds of questions, they faced challenges to implementing the approach. The new work by Ahmadi and Majumdar clears away one of the biggest of those challenges — bringing an old math question squarely to bear on some of the most important technological questions of the day.
$$ a^n + b^n = c^n $$
$$ n > 2 $$
Fermat’s Last Theorem states that no three integers satisfy the above equation for any integer value greater than 2.