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Descartes’ theorem & Soddy’s poem

In geometry, Descartes’ theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to three given, mutually tangent circles. The theorem is named after René Descartes, who stated it in 1643.

Descartes’ theorem was rediscovered independently in 1826 by Jakob Steiner, in 1842 by Philip Beecroft, and again in 1936 by Frederick Soddy. Soddy published his findings in the scientific journal Nature as a poem, The Kiss Precise, of which the first two stanzas are reproduced below. The first stanza describes Soddy’s circles, whereas the second stanza gives Descartes’ theorem. In Soddy’s poem, two circles are said to “kiss” if they are tangent, whereas the term “bend” refers to the curvature k of the circle.

Soddy CirclesFor pairs of lips to kiss maybe
Involves no trigonometry.
‘Tis not so when four circles kiss
Each one the other three.
To bring this off the four must be
As three in one or one in three.
If one in three, beyond a doubt
Each gets three kisses from without.
If three in one, then is that one
Thrice kissed internally.

Four circles to the kissing come.
The smaller are the benter.
The bend is just the inverse of
The distance from the center.
Though their intrigue left Euclid dumb
There’s now no need for rule of thumb.
Since zero bend’s a dead straight line
And concave bends have minus sign,
The sum of the squares of all four bends
Is half the square of their sum.

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Bird navigation: The Quantum Around You

Quantum phenomena often seem mysterious to us, because we cannot “see” them. What if some other animal species could? “Seeing” quantum correlations between pairs of electrons might be precisely the way certain birds navigate from North-South. 

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Mystery solved: ‘Sailing stones’ of Death Valley seen in action for the first time

moving stones

Racetrack Playa is home to an enduring Death Valley mystery. Littered across the surface of this dry lake, also called a “playa,” are hundreds of rocks — some weighing as much as 320 kilograms (700 pounds) — that seem to have been dragged across the ground, leaving synchronized trails that can stretch for hundreds of meters.

What powerful force could be moving them? Researchers have investigated this question since the 1940s, but no one has seen the process in action — until now. In a paper published in the journal PLOS ONE on Aug. 27, a team led by Scripps Institution of Oceanography, UC San Diego, paleobiologist Richard Norris reports on first-hand observations of the phenomenon.

Sailing_StonesBecause the stones can sit for a decade or more without moving, the researchers did not originally expect to see motion in person. Instead, they decided to monitor the rocks remotely by installing a high-resolution weather station capable of measuring gusts to one-second intervals and fitting 15 rocks with custom-built, motion-activated GPS units. (The National Park Service would not let them use native rocks, so they brought in similar rocks from an outside source.) The experiment was set up in winter 2011 with permission of the Park Service. Then — in what Ralph Lorenz of the Applied Physics Laboratory at the Johns Hopkins University, one of the paper’s authors, suspected would be “the most boring experiment ever” — they waited for something to happen.

But in December 2013, Norris and co-author and cousin Jim Norris arrived in Death Valley to discover that the playa was covered with a pond of water seven centimeters (three inches) deep. Shortly after, the rocks began moving. “Science sometimes has an element of luck,” Richard Norris said. “We expected to wait five or ten years without anything moving, but only two years into the project, we just happened to be there at the right time to see it happen in person.”

Their observations show that moving the rocks requires a rare combination of events. First, the playa fills with water, which must be deep enough to form floating ice during cold winter nights but shallow enough to expose the rocks. As nighttime temperatures plummet, the pond freezes to form thin sheets of “windowpane” ice, which must be thin enough to move freely but thick enough to maintain strength. On sunny days, the ice begins to melt and break up into large floating panels, which light winds drive across the playa, pushing rocks in front of them and leaving trails in the soft mud below the surface. Via Mystery solved: ‘Sailing stones’ of Death Valley seen in action for the first time

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What would life be like with just two (or four) dimensions?

What would life be like with just two (or four) dimensions?

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One would normally assume that massive bird nests would house massive birds. These nests are so big that one wonders if they could house dinosaurs…

They are built, in actuality, by some of the dinosaurs smallest descendents: Social Weaver Birds live in Namibia. They look rather like sparrows, and are about the size of sparrows. But somehow or other, they seem to have got into their bird-brains the necessity to build BIG, that is, REALLY BIG nests. Indeed, they build the largest nests of any bird on Earth.

Built on acacia trees, or atop telephone poles, or electric pylons, or any other tall structure conveniently far from the snake-infested ground, the nests range to 8 by 2 meters, and could weigh a ton. Each nest provides residence to tens to hundreds of birds, and can be reused as long as the nest lasts, perhaps a thousand years. The nests are, actually, less nest than an apartment complex constructed by insulation material of bird woven weeds, twigs, and grasses: inner rooms within the structures retain warm in the cold desert nights, and the outside rooms are relatively cool compared to the desert heat. Via Facebook.

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Scotland’s ‘space whisky’ will return to Earth next month


A vial of malt whisky from Scotland’s Ardbeg Distillery was launched to the International Space Station in October 2011 along with some particles of charred oak. A team from US-based space research organisation NanoRacks said it was an experiment to see how the two interacted in almost zero gravity conditions. The whisky has been orbiting the Earth’s atmosphere for 1,045 days so far, and is expected to land in Kazakhstan on 12 September. According to the BBC, it was launched by a Soyuz rocket from Baikonur in Kazakhstan, and an identical bottle of whisky has been kept at the distillery as a control. Once the space whisky returns, it will be compared with the Earth whisky to see what changes have occurred.

Ardbeg’s director of distilling and whisky creation, Bill Lumsden, told the BBC:

“This is one small step for man but one giant leap for whisky. The team hopes to uncover how flavours develop in different gravitational conditions – findings which could revolutionise the whisky-making process. We hope to shine new light on the effect of gravity on the maturation process but who knows where it will lead us? It could be to infinity and beyond.” Via Scotland’s ‘space whisky’ will return to Earth next month

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What’s going on at SciFoo this year?

Thanks to Deskarati’s friend George Ford for pointing out this interesting blog by Dominic Cummings. – Deskarati


Dominic recalls his experience at this years SciFoo Camp conference and lists some of the scenarios being discussed:

1) Extinct species are soon going to be brought back to life and the same technology will be used to modify existing species to help prevent them going extinct.

2) CRISPR  – a new gene editing technology – will be used to cure diseases and ‘enhance’ human performance but may also enable garage bio-hackers to make other species extinct.

3) With the launch of satellites in 2017/18, we may find signs of life by 2020 among the ~1011 exoplanets we now know exist just in our own galaxy though it will probably take 20-30 years, but the search will also soon get crowdsourced in a way schools can join in.

4) There is a reasonable chance we will have found many of the genes for IQ within a decade via BGI’s project, and the rich may use this information for embryo selection.

5) ‘Artificial neural networks’ are already outperforming humans on various pattern-recognition problems and will continue to advance rapidly.

6) Automation will push issues like a negative income tax onto the political agenda as millions lose their jobs to automation.

7) Autonomous drones will be used for assassinations in Europe and America shortly.

8) Read Neil Gershenfeld’s book ‘FAB’ if you haven’t and are interested in science education / 3D printing / computer science (or at least watch his TED talks).

9) Scientists are desperate to influence policy and politics but do not know how.

Read Dominic’s blog post here.

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You Can Now Access All Of Richard Feynman’s Physics Lectures For Free

The lectures of Nobel Prize winning physicist Richard Feynman were legendary. Footage of these lectures does exist, but they are most famously preserved in The Feynman Lectures. The complete online edition of The Feynman Lectures on Physics has been made available in HTML 5 through a collaboration between Caltech (where Feyman first delivered these talks, in the early 1960s) and The Feynman Lectures Website. The online edition is “high quality up-to-date copy of Feynman’s legendary lectures,” and, thanks to the implementation of scalable vector graphics, “has been designed for ease of reading on devices of any size or shape; text, figures and equations can all be zoomed without degradation.”

Volume I deals mainly with mechanics, radiation and heat; Volume II with electromagnetism and matter; and Volume III with quantum mechanics. Via You Can Now Access All Of Richard Feynman’s Physics Lectures For Free.

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Measurement at Big Bang conditions confirms lithium problem

The field of astrophysics has a stubborn problem and it’s called lithium. The quantities of lithium predicted to have resulted from the Big Bang are not actually present in stars. But the calculations are correct – a fact which has now been confirmed for the first time in experiments conducted at the underground laboratory in the Gran Sasso mountain in Italy. As part of an international team, researchers from the Helmholtz-Zentrum Dresden-Rossendorf (HZDR) studied how much lithium forms under Big Bang conditions. The results were published in Physical Review Letters.

Lithium, aside from hydrogen and helium, is one of the three elements that are created before the first stars form. These three elements were – according to the theory – already created early on, through what is known as “primordial nucleosynthesis.” That means that when the universe was only a few minutes old, neutrons and protons merged to form the nuclei of the these elements. At the Laboratory for Underground Nuclear Astrophysics (LUNA), the nucleosynthesis of lithium has now been reproduced by an international team of scientists. Michael Anders, who earned his doctorate in the last year at TU Dresden and HZDR on this very topic, took a leading role on the team. Within the framework of a project that was funded by the German Research Foundation, he was supervised by Dr. Daniel Bemmerer, group leader at HZDR.

In the Italian underground laboratory, the scientists fired helium nuclei at heavy hydrogen (known as deuterium) in order to reach energies similar to those just after the Big Bang. The idea was to measure how much lithium forms under similar conditions to those during the early stages of the universe. The result of the experiment: the data confirmed the theoretical predictions, which are incompatible with the observed lithium concentrations found in the universe. Via Measurement at Big Bang conditions confirms lithium problem.

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You have a bacterial ‘aura’ that follows you around


Auras belong in the realm of pseudoscience, but microbiologists may have just discovered an element of truth in the concept. Scientists have found a microbial ‘aura’ of unique and identifiable communities of bacteria living on people’s skin and in their homes. These communities follow people whereever they go and leave traces that can be used almost like a fingerprint to determine a person’s movements. The US Department of Energy’s Argonne National Laboratory and the University of Chicago conducted the research as part of the Home Microbiome Project. The results were published in Science this week.

Seven families, including 18 people, gave swab samples of themselves and their homes every day for six weeks. Scientists conducted DNA analysis of these samples to build up an idea of the diversity of each individual’s microbe community. The researchers found that they could accurately predict which sample came from which home using the microbial ‘fingerprint’.

Comparing the surfaces of old and new homes, scientists found that the microbes settled into a new location within one day of occupancy by a new family. They also found that individuals who had increased physical contact, such as partners, had similar microbes. The scientists found they could determine the comings and goings of individuals living in the same house through the conspicuous absence in their microbial ‘aura’. Via You have a bacterial ‘aura’ that follows you around

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This amazing starry sky is a cave full of glowworms in New Zealand

NASA’s Astronomy Picture of the Day features an amazing photo by Phill Round. It looks like a frame from a Spielberg movie—an humanoid figure appearing at the base of a mountain, with the unknown starry sky of an alien world behind it. In reality, it’s a man getting into New Zealand’s Hollow Hill Cave.

From NASA: Captured in this long exposure, the New Zealand glowworms scattered across the cave ceiling give it the inviting and open appearance of a clear, dark night sky filled with stars. Unsuspecting insects fooled into flying too far upwards get trapped in sticky snares the glowworms create and hang down to catch food. Via This amazing starry sky is a cave full of glowworms in New Zealand.

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Your Brain On Coffee

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US researching implants that’ll help your body and mind heal itself

America’s mad science division is at it again, this time imagining a future where your body won’t need (as much) medicine to stay healthy, simply by using the resources it already has. Put simply, a person’s peripheral nervous system runs the internal organs and summons the troops to fight off infections and repair injuries. DARPA’s just received $78.9 million of funding to look into harnessing this system to develop a miniscule implant that’d not only make people healthier and less prone to disease, but could also be used to treat mental health complaints like post traumatic stress disorder in the future.

DARPA’s plan is to build implants no thicker than a nerve fiber that can then be implanted into people’s bodies. Once there, the devices would monitor the status of your nervous system, organs and overall health, keeping the system regulated by triggering responses through electrical impulses. In a way, it’s a bit like building a pacemaker for your central nervous system, except one that’s capable of helping people live with complaints like arthritis and other inflammatory diseases.

According to neural engineer Dr. Douglas Weber, the eventual goal is to turn the body into a “closed-loop system,” that continually assesses itself, ensuring that as soon as any sickness is detected in an organ, the body can quickly deal with it. The upside is that patients won’t need to take medicines (which can have adverse side-affects) because they’ll rely more upon their super-charged immune systems to deal with problems. Of course, even for DARPA, this is a big ask, since current neuromodulation implants are huge and require complex surgery to install, and we doubt that the technology will shrink to nerve-fiber sizes in just five years. That said, we’ll be first in the queue if this ever becomes available Via US researching implants that’ll help your body and mind heal itself.

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Renewable energy now makes up 22% of the world’s power


“In 2013, renewable power capacity expanded at its fastest pace to date,” said the Paris-based International Energy Agency (IEA) of the results of its latest market report. According to the report, wind, solar, and other clean, renewable energy sources continued to grow rapidly, reaching almost 22 percent of the total energy sources around the world, compared to the 21 percent in 2012 and the 18 percent in 2007.

“Globally, renewable electricity generation is now on par with that of natural gas, which remained relatively stable in 2013,” says the report. “Investment in new renewable power capacity topped USD 250 billion globally in 2013 and is likely to remain at high levels.”

Meanwhile, says Brian Merchant at Motherboard, 14 percent of the US is now powered by renewable energy sources, according to the results of another recent report run by the American Energy Information Administration. The research also indicated that biofuels for transport and renewable heat energy continue to grow, but not at the rate of renewable electricity.

“The news isn’t all rosy, however,” says Merchant. “The IEA also downgraded its forecast for renewables through 2020, because many governments are dropping their support for incentives – right at the time when wind and solar are becoming cost-competitive with fossil fuels.” Via Renewable energy now makes up 22% of the world’s power

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What Character Was Removed from the Alphabet?

ampersandJohnson & Johnson, Barnes & Noble, Dolce & Gabbana: the ampersand today is used primarily in business names, but that small character was once the 27th part of the alphabet. Where did it come from though? The origin of its name is almost as bizarre as the name itself.

The shape of the character (&) predates the word ampersand by more than 1,500 years. In the first century, Roman scribes wrote in cursive, so when they wrote the Latin word et which means “and” they linked the e and t. Over time the combined letters came to signify the word “and” in English as well. Certain versions of the ampersand, like that in the font Caslon, clearly reveal the origin of the shape.

The word “ampersand” came many years later when “&” was actually part of the English alphabet. In the early 1800s, school children reciting their ABCs concluded the alphabet with the &. It would have been confusing to say “X, Y, Z, and.” Rather, the students said, “and per se and.” “Per se” means “by itself,” so the students were essentially saying, “X, Y, Z, and by itself and.” Over time, “and per se and” was slurred together into the word we use today: ampersand. When a word comes about from a mistaken pronunciation, it’s called a mondegreen.

(The ampersand is also used in an unusual configuration where it appears as “&c” and means etc. The ampersand does double work as the e and t.) Edited from How ampersand came from a misunderstanding

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On this day in 1789 William Herschel discovered Saturn’s sixth-largest moon, Enceladus. The moon’s richly textured surface implies that Enceladus has been tectonically active in (geologically) recent times. Geyser-like jets of water vapor shoot into space from its south pole. Indirect evidence of a large subsurface ocean of water suggests that Enceladus could harbor extraterrestrial life.


In Greek mythology Enceladus was one of the Gigantes (Giants), who according to Hesiod, were the offspring of Gaia, born from the blood that fell when Uranus (Sky) and was castrated by their son Cronus. The Giants fought Zeus and the other Olympian gods in the Gigantomachy, their epic battle for control of the cosmos. A Giant named Enceladus, fighting Athena, is attested in art as early as an Attic Black-figure pot dating from the second quarter of the sixth century BC. In literature, references to the Giant occur as early as the plays of the fifth century BC Greek tragedian Euripides, where, for example, in Euripides’ Ion the chorus describes seeing on the late sixth century Temple of Apollo at Delphi, Athena “brandishing her gorgon shield against Enceladus”.

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‘Gut Reaction’ – Part 2

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When did Primates first appear?

After an ‘interesting’ discussing last night I have tried to find the answer to the question ‘When did primates first appear?’ After reading wiki and a couple of other articles the following seems to encompass the latest perceived understanding. There is a bit here for all sides of the debate: – Deskarati


Many people take an understandably human-centered view of primate evolution, focusing on the bipedal, large-brained hominids that populated the jungles of Africa a few million years ago. But the fact is that primates as a whole–a category of megafauna mammals that includes not only humans and hominids, but monkeys, apes, lemurs, baboons and tarsiers–have a deep evolutionary history that stretches as far back as the age of dinosaurs.



The first mammal that palaeontologists have identified as possessing primate-like characteristics was Purgatorius, a tiny, mouse-sized creature of the late Cretaceous period (just before the K/T Impact Event that rendered the dinosaurs extinct). Although it looked more like a tree shrew than a monkey or ape, Purgatorius had a very primate-like set of teeth, and it (or a close relative) may have spawned the more familiar primates of the Cenozoic Era. (Genetic sequencing studies suggest that the earliest primate ancestor may have lived a whopping 20 million years before Purgatorius, but as yet there’s no fossil evidence for this mysterious beast.)



Recently, scientists have touted the equally mouse-like Archicebus, which lived 10 million years after Purgatorius, as the first true primate, and the anatomic evidence in support of this hypothesis is even stronger. What’s confusing about this is that the Asian Archicebus seems to have lived around the same time as the North American and Eurasian Plesiadapis, a much bigger, two-foot-long, tree-dwelling, lemur-like primate with a rodent-like head. The teeth of Plesiadapis displayed the early adaptations necessary for an omnivorous diet–a key trait that allowed its descendants tens of millions of years down the line to diversify away from trees and toward the open grasslands. Via Evolution – The Story of Prehistoric Primates.

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Schrödinger’s cat caught on quantum film

Schrödinger’s cat is the poster child for quantum weirdness. Now it has been immortalised in a portrait created by one of the theory’s strangest consequences: quantum entanglement. These images were generated using a cat stencil and entangled photons. The really spooky part is that the photons used to generate the image never interacted with the stencil, while the photons that illuminated the stencil were never seen by the camera.

When two separate particles are entangled, measurements of their physical properties are correlated, and they effectively share a single quantum state. Gabriela Barreto Lemos at the Austrian Academy of Sciences in Vienna and her colleagues used this quantum connection between particles to make these images of a cat without directly photographing it. To do it, the researchers created yellow and red pairs of entangled photons. The yellow photons were fired at the cat stencil, while the red photons were sent to the camera. Thanks to their entanglement, the red photons formed the image of the cat because of the quantum link to their yellow twins.

The silicon stencil was transparent to red light and the camera could only detect red light. This demonstrates that the technique can image objects that are invisible to the detected photons. Via Schrödinger’s cat caught on quantum film

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Astronaut Chris Hadfield on space oddities

Fans of UNSW Science and ScienceAlert got to pose a series of questions to youtube’s most famous astronaut Chris Hadfield. Watch the interview with Veritasium’s Derek Muller at the exclusive Space Oddity event at Sydney’s Powerhouse Museum – the annual ScienceAlert event celebrating all things science.

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