Lovecraft's mathematical horrors

Sometimes we can find on the web something of interesting, like the following review of the 4D Man.
We can read on Wikipedia:

Brilliant but irresponsible scientist Tony Nelson (James Congdon) develops an amplifier that allows any object to achieve a 4th dimensional (4D) state. While in this state that object can pass freely through any other object.

Reading these words I immediatly think to Howard Philips Lovecraft and his Cthulhu Mythos, in particular to Dream in the Witch House. In this short story Walter Gilman, a student of mathematics, lives in the house of Keziah Mason, one of the Salem's witches. In the story there are some mathematically interesting quotes:

She had told Judge Hathorne of lines and curves that could be made to point out directions leading through the walls of space to other spaces beyond (...)

We can argue the Lovecraft's use for his purpouse of the non-euclidean geometry, in particular in the following quotation:

[Gilman] wanted to be in the building where some circumstance had more or less suddenly given a mediocre old woman of the Seventeenth Century an insight into mathematical depths perhaps beyond the utmost modern delvings of Planck, Heisenberg, Einstein, and de Sitter.

or in the following point, in which HPL seems refer to Riemann's hypotesys:

He was getting an intuitive knack for solving Riemannian equations, and astonished Professor Upham by his comprehension of fourth-dimensional and other problems (...)

Indeed Gilman was studying

non-Euclidean calculus and quantum physics

Illustration by Greg Nemec

And Walter, dreaming, has experienced the high dimensional space of the limitless abysses:

abysses whose material and gravitational properties, and whose relation to his own entity, he could not even begin to explain. He did not walk or climb, fly or swim, crawl or wriggle; yet always experienced a mode of motion partly voluntary and partly involuntary. Of his own condition he could not well judge, for sight of his arms, legs, and torso seemed always cut off by some odd disarrangement of perspective; (...)

Durign his travel in the fourth-dimension, Gilman seen

risms, labyrinths, clusters of cubes and planes, and Cyclopean buildings

that are characteristic in lovecraftian literature.
Another non-euclidean reference is in The Call of Cthulhu⁽¹⁾:

He said that the geometry of the dream-place he saw was abnormal, non-Euclidean, and loathsomely redolent of spheres and dimensions apart from ours.

And Cthulhu itself is a fourth dimensional creature. Cthulhu was one of the Great Old Ones: these creatures

(...) were not composed altogether of flesh and blood. They had shape (...) but that shape was not made of matter.

We can imagine Cthulhu in our world like the projection of a dodecaplex in a three dimensional space, for example:

News from the OPERA

Today, at 15:30 at Physics Department in Milano, Italy, Luca Stanco, one of the 15 OPERA's collaboration who didn't sign the preprint, discussed in a brief presentation (about half an hour, without quests) the OPERA's results. In conclusion we have a lot of interesting informations. He described the experiments, starting from the production of neutrinos' beams and arriving to the detection in Italy, under Gran Sasso mountain. He briefly described the measure of the distance and the GPS system.
The most interesting part of the presentation is the production of neutrinos' beams⁽¹⁾. First of all reasearchers need to produce one proton bench in PS (is a little synchrotron), so they send the bench in SPS, a much greater synchrotron than PS. In order to fill SPS are needed 11 PS benches, but researchers decided to inject in SPS 5 beams (each one with a time length of about 10.4 μs) and after a time range of about 50 ms they inject others 5 benches. So, if we observ with attention the neutrino's signal, we see 5 peaks, a remember of the protons benches that origined the signal. In this process there is one of the criticism: it is necessary to be secure that the proton's probability density function and the neutrino's probability density function are equals. Another important point to clarify is the time of flight⁽²⁾ or the presence of some effects dued by day/night or seasons.
But the really news arrived in the end of the presentation:

OPERA collaboration decided this morning to postpone the submission of paper of about one month

I lost the first of the two motivation, but the second is simple: CNGS is preparing new benches spaced at 500 ns. So OPERA could have a really first opportunity to test their data.

Probably not

A group velocity faster than $c$ does not mean that photons or neutrinos are moving faster thsn the speed of light.

This is the conclusion of Fast light, fast neutrinos? by Kevin Cahill⁽¹²⁾. He start his briefly analisys from some experimental observations of superluminal group velocity. In these experiments researchers measure a speed of light faster and slower than $c$ in vacuum. The first observation was occured in 1982⁽¹⁾, but an interesting collection of work in this subject is in Bigelow⁽⁷⁾ and Gehring⁽¹¹⁾. Experimentally when some pulses journey into a highly dispersive media occur some exotic effects. One of these is the observation of a negative group velocity, that coincides with a superluminal speed.
In Bigelow's and Gehring's works wasn't a really theoretical explenation. For example Bigelow proposed the following explaination:

(...) as the combination of different absorption cross sections and lifetimes for Cr³⁺ ions at either mirror or inversion sites within the BeAl₂O₄ crystal lattice. The superluminal wave propagation is produced by a narrow “antihole” [612 Hz half width at half maximum (HWHM)] in the absorption spectrum of Cr³⁺ ions at the mirror sites of the alexandrite crystal lattice, and the slow light originates from an even narrower hole (8.4 Hz) in the absorption spectrum of Cr³⁺ ions at the inversion sites.

They also considered

(...) the influence of ions both at the inversion sites and at the mirror sites. In addition, the absorption cross sections are assumed to be different at different wavelengths.

The arrows indicate the locations of ion sites that have mirror or inversion symmetry. On the right, the corresponding energy-level diagrams for Cr³⁺ ions at the different sites are shown.

Tempest: another great timelapse

Some days ago Nasa published the following incredible photo:

It is an infrared mosaic produced using Hubble's shots and represent the Universe observed by the space telescope. But also from Earth we can observe some spectacular images, like the stars in the sky or the Milky Way. Thursday we see a greattimelapse from Jared Brandon and today I propose you another great timelapse, realized by Randy Halverson (via Universe Today):

I think it could represent the perfect fusion between Earth and Sky, like in this shots from the slideshow of the video:

Thanks also to Annarita Ruberto, who shared the video in Italy.

Milky Way in timelapse

Writing a card about Milky Way for Italian Olympiad Astronomy syllabus, I search for some video in timelapse about our galaxy, and I find some interesting videos and a great artist, or photographer, as you like. The photographer was cited on Daily Mail and Photo Blog on msbc.com (and other sites in the web), and this is his great photo (source):

Tommy Eliassen (facebook, 1X) is the photographer, and he is very talented.
But this is simple the introduction to the timelapse video of today, Mt Ruapehu Timelapse by Jared Brandon:

The name of our galaxy comes from greek mythology. Indeed Zeus put on Hera's chest his son Heracles. And the hero started to suck the divine milk in order to became immortal. But Hera waked up (she was spleeping) and she pushed Heracles away. In that moment a splash of milk from the breasts of the goddess became the Milky Way:

The origin of the Milky Way by Jacopo Tintoretto

The mathematics in the 2011 Nobel Prize in Chemistry

The Nobel Prize in Chemistry 2011 is assigned to Daniel Shechtman

for the discovery of quasicrystals

The paper of the discover, written with Blech, Gratias and Cahn, starting with the following worlds:

We report herein the existence of a metallic solid which diffracts electrons like a single crystal but has point group symmetry $m \bar{35}$ (icosahedral) which is inconsistent with lattice translations.⁽²⁾

The lattice translations are, indeed, most important tools in order to classify crystals. Indeed in 1992 the definition of crystals given by the International Union of Crystallography was:

A crystal is a substance in which the constituent atoms, molecules, or ions are packed in a regularly ordered, repeating three-dimensional pattern.

So the discover of Shechtman and collegues was very important: they introduce a new class of crystals, named quasicrystals by Levine and Steinhardt some weeks later⁽³⁾, and a new way to view crystals.
In particular Shechtman, studying Al with 10–14% Mn, and collegues observed that

The symmetries of the crystals dictate that several icosahedra in a unit cell havedifferent orientations and allow them to be distorted (...)⁽²⁾

And when they observe crystal using lattice translations:

crystals cannot and do not exhibit the icosahedral point group symmetry.⁽²⁾

They also oserve that the formation of the icosahedral phase is a transition phase of the first order, because the two phases (the other is translational) coexist for a while during translation⁽²⁾.

Italian Wikipedia and the fight for neutrality

We are Italians. We are wikipedians. And we are neutral. And now our neutrality is in danger cause by an italian law. You can read here the communication.
And this is an e-mail from Wikimedia Foundation:

The Wikimedia Foundation first heard about this a few hours ago: we don't have a lot of details yet. Jay is gathering information and working on a statement now.

It seems obvious though that the proposed law would hurt freedom of expression in Italy, and therefore it's entirely reasonable for the Italian Wikipedians to oppose it. The Wikimedia Foundation will support their position.

The question of whether blocking access to Wikipedia is the best possible way to draw people's attention to this issue is of course open for debate and reasonable people can disagree. My understanding is that the decision was taken via a good community process. Regardless, what's done is done, for the moment.

Super-Nobel in Physics 2011

The first observation of a supernova is dated 1572 by Tycho Brahe, but the hystorically most important supernova's observation is the Galilei's observation in 1604:

The supernova of 1604 caused even more excitement than Tycho's because its appearance happened to coincide with a so-called Great Conjunction or close approach of Jupiter, Mars and Saturn.⁽¹⁾

The Galilei's discover was revolutionary for one important reason:

Galileo's observations and those made elsewhere in Italy and in Northern Europe indicated that it was beyond the Moon, in the region where the new star of 1572 had appeared. The appearance of a new body outside the Earth-Moon system had challenged the traditional belief, embodied in Aristotle's Cosmology, that the material of planets was unalterable and that nothing new could occur in the heavens.⁽¹⁾

About the new star

Galileo states that [it] was initially small but grew rapidly in size such as to appear bigger than all the stars, and all planets with the exception of Venus.⁽¹⁾

We can confrount the observation with modern definitions:

Novae are the result of explosions on the surface of faint white dwarfs, caused by matter falling on their surfaces from the atmosphere of larger binary companions. A supernova is also a star that suddenly increases dramatically in brightness, then slowly dims again, eventually fading from view, but it is much brighter, about ten thousand times more than a nova.⁽¹⁾

These dramatical events became soon a good tools in order to observe the expansion of the universe:

Type Ia supernovae are empirical tools whose precision and intrinsic brightness make them sensitive probes of the cosmological expansion.⁽⁵⁾

And observing a series of supernovae the team of Brian Schmidt (1967) and Adam Riess (1969) in 1998⁽³⁾ and the team of Saul Perlmutter (1959) in 1999⁽⁴⁾ found an important consmological observation: Universe is accelerating!

Video abstract: The hyperring of adèle classes

We have encountered Alain Connes when I write the brief post about the Riemann hypothesis. Now he explain in the following video abstract his paper The hyperring of adèle classes (arXiv) written with Caterina Consani: