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A very neat visual proof for the formula of the first n square numbers.

Correction: as pointed out by @othermaterial, the right-hand side of the formula should have variables n instead of k.

The Boatyard at Saint Mammes by Alfred Sisley

Size: 38.8x56 cm

The Pork Butcher by Camille Pissarro

Size: 66x54 cm Medium: oil on canvas

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Archaeologists Discover Unknown Fortress Walls, Byzantine Gold Coin

Two unknown fortress walls and three unknown fortress towers as well as a 14th century Byzantine gold coin have been discovered by archaeologists during the 2016 excavations of the major medieval fortress of Rusocastro in today’s Southeast Bulgaria.

The Rusocastro Fortress is best known for the Battle of Rusocastro in 1332 AD. It was the last big military victory of the medieval Bulgarian Empire before it was conquered by the invading Ottoman Turks at the end of the 14th century.

It was also the last major battle of the seven-century-long Bulgarian-Byzantine Wars for domination of the Balkan Peninsula (lasting from the 7th until the 14th century), which ended when, weakened by their hostilities against one another, among other factors, Bulgaria and Byzantium were both conquered by the Ottoman Turkish invaders at the end of the 14th and the beginning of the 15th century. Read more.

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2017 January 14

Stardust in the Perseus Molecular Cloud Image Credit & Copyright: Lorand Fenyes

Explanation: Clouds of stardust drift through this deep skyscape. The cosmic scene spans nearly 2 degrees across the Perseus molecular cloud some 850 light-years away. A triangle of dusty nebulae reflecting light from embedded stars is captured in the telescopic field of view. With a characteristic bluish color reflection nebula NGC 1333 is at left, vdB13 at bottom right, and rare yellowish reflection nebula vdB12 lies at the top. Stars are forming in the Perseus molecular cloud, though most are obscured at visible wavelengths by the pervasive dust. Still, hints of contrasting red emission from Herbig-Haro objects, the jets and shocked glowing gas emanating from recently formed stars, are evident in NGC 1333. At the estimated distance of the molecular cloud, legs of the triangle formed by the reflection nebulae would be about 20 light-years long.

∞ Source: apod.nasa.gov/apod/ap170114.html

First signs of weird quantum property of empty space?

A team led by Roberto Mignani from INAF Milan (Italy) and from the University of Zielona Gora (Poland), used ESO’s Very Large Telescope (VLT) at the Paranal Observatory in Chile to observe the neutron star RX J1856.5-3754, about 400 light-years from Earth [1].

Despite being amongst the closest neutron stars, its extreme dimness meant the astronomers could only observe the star with visible light using the FORS2 instrument on the VLT, at the limits of current telescope technology.

Neutron stars are the very dense remnant cores of massive stars – at least 10 times more massive than our Sun – that have exploded as supernovae at the ends of their lives. They also have extreme magnetic fields, billions of times stronger than that of the Sun, that permeate their outer surface and surroundings.

These fields are so strong that they even affect the properties of the empty space around the star. Normally a vacuum is thought of as completely empty, and light can travel through it without being changed. But in quantum electrodynamics (QED), the quantum theory describing the interaction between photons and charged particles such as electrons, space is full of virtual particles that appear and vanish all the time. Very strong magnetic fields can modify this space so that it affects the polarisation of light passing through it.

Mignani explains: “According to QED, a highly magnetised vacuum behaves as a prism for the propagation of light, an effect known as vacuum birefringence.”

Among the many predictions of QED, however, vacuum birefringence so far lacked a direct experimental demonstration. Attempts to detect it in the laboratory have not yet succeeded in the 80 years since it was predicted in a paper by Werner Heisenberg (of uncertainty principle fame) and Hans Heinrich Euler.

“This effect can be detected only in the presence of enormously strong magnetic fields, such as those around neutron stars. This shows, once more, that neutron stars are invaluable laboratories in which to study the fundamental laws of nature.” says Roberto Turolla (University of Padua, Italy).

After careful analysis of the VLT data, Mignani and his team detected linear polarisation – at a significant degree of around 16% – that they say is likely due to the boosting effect of vacuum birefringence occurring in the area of empty space surrounding RX J1856.5-3754 [2].

Vincenzo Testa (INAF, Rome, Italy) comments: “This is the faintest object for which polarisation has ever been measured. It required one of the largest and most efficient telescopes in the world, the VLT, and accurate data analysis techniques to enhance the signal from such a faint star.”

“The high linear polarisation that we measured with the VLT can’t be easily explained by our models unless the vacuum birefringence effects predicted by QED are included,” adds Mignani.

“This VLT study is the very first observational support for predictions of these kinds of QED effects arising in extremely strong magnetic fields,” remarks Silvia Zane (UCL/MSSL, UK).

Mignani is excited about further improvements to this area of study that could come about with more advanced telescopes: “Polarisation measurements with the next generation of telescopes, such as ESO’s European Extremely Large Telescope, could play a crucial role in testing QED predictions of vacuum birefringence effects around many more neutron stars.”

“This measurement, made for the first time now in visible light, also paves the way to similar measurements to be carried out at X-ray wavelengths,” adds Kinwah Wu (UCL/MSSL, UK).

This research was presented in the paper entitled “Evidence for vacuum birefringence from the first optical polarimetry measurement of the isolated neutron star RX J1856.5?3754”, by R. Mignani et al., to appear in Monthly Notices of the Royal Astronomical Society.

European Southern Observatory

Saint-Sauves-d'Auvergne via Armand Guillaumin

Anahita and Ishtar: Connections to the Planet Venus

Anahita was a goddess associated with water, fertility, wisdom, warfare, and eventually the planet Venus. During the Achaemenid dynasty in Persia, she became incorporated into the Zoroastrian religion as a Yazata, a type of minor divinity. Her association with warfare and the planet Venus was not very prominent before the Achaemenid Period, leading some to conclude that her cult and persona may have become influenced by the goddess Ishtar. In becoming associated with Ishtar, she may have taken on the characteristics of a Venus god/Venus goddess, a type of god which appears to occur across cultures associated with the planet Venus.  

Read more…

Ancient Buddha statue emerges in E. China reservoir

Archaeologists have started an underwater detection project after villagers in eastern China’s Jiangxi Province found the head of a Buddha statue emerging from the surface of a local reservoir.

The head was spotted at Hongmen Reservoir, Nancheng County in the city of Fuzhou, at the end of last year when a hydropower gate renovation project lowered water levels in the reservoir by more than 10 meters.

Judging from the head design, the statue was carved during the Ming Dynasty (1368-1644), said Xu Changqing, head of the provincial research institute of archaeology.

He said that the researchers had also found rectangular holes carved on the cliff, obvious marks of architecture, which meant that a temple could have existed there. Read more.