Maths in Europe: Seven cosmic messengers

Let us suppose we travel from Earth to the furthest observable point in the universe. We have seven satellites on our spacecraft, used to keep communications between us and the Earth. Let’s suppose that the speed of the satellites coincides with that of light, or in any case equal to a speed whose difference with c is negligible, while the speed of the spacecraft is $v = 2 / 3c$. The satellite, once it reaches Earth orbit, transmits the information we have loaded into its memory, then heads back to us to collect the new information. Meanwhile, within 24 hours of each other, we launch all the satellites.
The time each probe takes will be given by the formula \[t = \frac{y_1+y_0}{c}\] where $y_0$ is the distance traveled on the outward journey (or if you prefer the relative position of the spacecraft respect to the Earth at the time the first probe was launched), $y_1$ the distance of the return (or the position of the spacecraft when the first probe returns) and c is the speed of the probe.
(continue on Mathematics in Europe)

Great number

The Large Numbers hypothesis asserts that all the large dimensionless numbers occurring in Nature are connected with the present epoch, expressed in atomic units, and thus vary with time. It requires that the gravitational constant G shall vary, and also that there shall be continuous creation of matter. The consistent following out of the hypothesis leads to the possibility of only two cosmological models. One of them, which occurs if one assumes that the continuous creation is a multiplication of existing matter, is Einstein’s cylindrical closed Universe. The other, which occurs if one assumes the continuous creation takes place uniformly through the whole of space, involves an approximately flat Minkowski space with a point of origin where the Big Bang occurred.
Dirac, P. A. M. (1974). Cosmological models and the large numbers hypothesis. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 338(1615), 439-446. doi:10.1098/rspa.1974.0095

Beneficio

Evaluating Beneficio is by no means trivial. The narrative is all concentrated around a woman in search of herself, remembering her missing grandmother.
There is not only this, however. The protagonist's journey takes her to Beneficio, a valley near the Spanish village of Orgiva where there is a community that lives in contact with nature in self-built tents, tepees and shelters.
In this environment the woman begins to reflect on her life and then passes, without any solution of continuity, to the universe and the divine, mixing fantastic, almost religious ideas, with the great scientific questions still unanswered. All within a valley surrounded by large mountains, wild and peaceful.
The narrative itself fits the theme: the story is diluted and rarefied, the pages with the minimum number of vignettes (rarely more than three or four), while the drawings now look like travel sketches, at other times particularly detailed.
Overall, both from a narrative and an aesthetic point of view, Beneficio by Michał Kalicki and Krzysztof Gawronkiewicz is almost a land version of Daisuke Igarashi's Children of the sea.

Supermassive web hole

With the help of ESO’s Very Large Telescope (VLT), astronomers have found six galaxies lying around a supermassive black hole when the Universe was less than a billion years old. This is the first time such a close grouping has been seen so soon after the Big Bang and the finding helps us better understand how supermassive black holes, one of which exists at the centre of our Milky Way, formed and grew to their enormous sizes so quickly. It supports the theory that black holes can grow rapidly within large, web-like structures which contain plenty of gas to fuel them.
The location of the supermassive black hole is in the Sextans' constellation.
Sextans is a small and dark constellation straddling the celestial equator and located near Leo. Introduced in 1687 by Johannes Hevelius, thanks to its equatorial position, the Sextant is visible from most of the Earth's surface.
The main stars are not particularly bright, but with a particularly clean sky it is possible to identify them even with the naked eye, in particular Alpha Sextantis, a blue-white giant with a magnitude of 4.48, and 35 Sextantis, an orange double star, the whose main star has a magnitude of 5.79. Also noteworthy there are the white Gamma Sextantis (magnitude 5.07) and the blue Beta Sextantis (magnitude 5.08).
(via ESO)

John Barrow: Some Generalities About Generality


John D. Barrow - via commons
On 1 December 2014 I had the pleasure of attending a lecture by John David Barrow at the "Enriques" Department of Mathematics in Milano. Very kind person, when I approached him to be able to shake his hand and take a picture of him, he granted me both honors with great simplicity. Unfortunately that photo has now been lost among smartphone changes, perhaps kept in some hard disk stored somewhere, nor did I publish it on one of my social networks, but I still wanted to pay homage to it by offering you the abstract of an article from 2015, the fifth chapter of the book The Philosophy of Cosmology (arXiv):
We survey a variety of cosmological problems where the issue of generality has arisen. This is aimed at providing a wider context for many claims and deductions made when philosophers of science choose cosmological problems for investigation. We show how simple counting arguments can be used to characterise parts of the general solution of Einstein's equations when various matter fields are present and with different spatial topologies. Applications are described to the problem of singularities, static cosmological models, cosmic no hair theorems, the late-time isotropisation of cosmological models, and the number of parameters needed to describe a general astronomical universe.

The flying Batman

Comics' authors, and more generally those who write about fiction (but not only them), are the modern Scheherazade of One Thousand and One Nights. This comparison is very fitting for Detective Comics #1027 which celebrates at the same time #27, where Bob Kane and Bill Finger's Batman made his debut, and the 1001th issue of the magazine dedicated to the Caped Crusader, so you understand the initial comparison.
I'm not here, though, to write you why Detective Comics's 1001 releases with Batman (if you want to, follow note(1)), but to seize the opportunity and talk about Batman's physics.

Robot stories

The comic transposition of Isaac Asimov's I, robot created by Raul Cuadrado is reminiscent of the first flash animations of a decade ago, a bit like the style of Carlos Meglia, famous in particular for Cybersix. Made on a horizontal rather than vertical page structure reminiscent of newspaper strip stories, the comic book I, robot is a quick and intelligent reading, with a slightly retro style thanks to the duotone, true to Asimov's spirit.

The obscure Planet Nine

Planet Nine is an hypothetical plante in Our Souls System. Its existence is inferred by the orbital data of a group of extreme trans-Neptunian objects, that seemed influenced by the presence of an undiscovered planet, or something else. Recently Amir Siraj and Abraham Loeb proposed a new hypothesys: Planet Nine could be a little black hole, about five times more massive than Earth with the dimension of an orange:
Planet Nine has been proposed to potentially be a black hole in the outer solar system. We investigate the accretion flares that would result from impacts of small Oort cloud objects, and find that the upcoming LSST observing program will be able to either rule out or confirm Planet Nine as a black hole within a year. We also find that LSST could rule out or confirm the existence of trapped planet-mass black holes out to the edge of the Oort cloud, indirectly probing the dark matter fraction in subsolar mass black holes and potentially improving upon current limits by orders of magnitude.
Siraj, A., & Loeb, A. (2020). Searching for Black Holes in the Outer Solar System with LSST. ApJL 898 L4 arXiv:2005.12280. doi:10.3847/2041-8213/aba119 (arXiv).

The distance from the Moon

The method currently used to evaluate the distance from the Moon dates back to 1962, when a team from MIT (Massachusetts Institute of Technology) in collaboration with soviet astronomers from the Crimean Astrophysical Observatory carried out an experiment to measure the round-trip time of a laser pulse reflected on the surface of the Moon. The evolution of this experiment was completed thanks to the Apollo missions of 1969, when the astronauts placed reflective mirrors on the lunar surface in order to improve the accuracy of the measurement. Lasers traveling to the Moon involve multiple structures and are part of the Lunar Laser Ranging.
The distance measurement from this project is 384402 km with an error of 1.1 millimeters(1), which in terms of light time corresponds to just under 1.3 seconds.
The pre-laser method is also inspired by the same principle: in 1957 the US Naval Research Laboratory sent 2 μs radar pulses from a radio antenna with a diameter of about 15 meters. After the echo produced by the waves on the surface of the Moon, the experiment detected the return signal and measured the delay time, from which to derive the distance from our satellite. Unfortunately, this experiment was subject to an excessively high error with respect to the signal and therefore the result produced was not considered reliable(2).
The experiment was repeated the following year, in 1958, by the Royal Radar Establishment in Great Britain. In that case, radar pulses of 5 μs were sent with a maximum power of 2 megawatts and a frequency of 260 pulses per second(3).

Human: the man of the future

500,000 years and more in the future. Disused satellites and space debris orbit around the Earth. Among these there is a structure that resembles a space station. Suddenly a module detaches and crashes onto the planet. After the explosion, we follow an animal that, from the top of a cliff, spreads its wings and flies to the impact site. From the relatively distant readers' point of view, the flying shadow could be a pterodactyl and the Earth we see, in reality, that of prehistory: even the vegetation and the gigantism of the environment would seem to suggest it. Instead, when we get closer to the impact site, the figure becomes more defined: it is a kind of monkey with wings.
The guides in the exploration of this regressed world of the future are Diego Agrimbau and Lucas Varela and they use a robot, Alpha, as their guide. His job is to assist the terrestrial scientist Robert who, together with his wife June, devised a complex plan to repopulate the Earth with homo sapiens. Robert, in fact, predicting the fate of extinction of human beings, has decided to freeze himself and his wife while waiting for the planet to recover from the ecological disasters left on its surface by the passage of the human race.

Rocks from space


via commons
Our solar system is crossed by a lot of rocks like comets and meteorites. Following the panspermia hypotesis, these cosmic objects could be at the origin of life-as-we-know. And two paper recently published seems confirmed it.
Comet 21P/Giacomini-Zinner belongs to the cometary family of Jupiter, with an orbital period of about 6.6 years. Discovered on the 20th decembre 1900 by Michel Giacobini, it could be the origin of the Draconids meteor shower. In July 2005 a japanese team of astronomers decided to observe 21P using the Comics instrument (Cooled Mid-Infrared Camera and Spectrometer) mounted on the Subaru telescope. Now they have concluded the examination of data, detecting an unidentified infrared emission, as well as thermal emissions generated by the silicate and carbon grains, which is probably due to complex organic molecules.
Ootsubo, T., Kawakita, H., Shinnaka, Y., Watanabe, J. I., & Honda, M. (2020). Unidentified infrared emission features in mid-infrared spectrum of comet 21P/Giacobini-Zinner. Icarus, 338, 113450. doi:10.1016/j.icarus.2019.113450
In the meanwhile another japanese team studied a couple of meteorites falled on Earth: Nwa 801, recovered in 2001 in Morocco, and Murchison, fallen in Australia in 1969.
Also in these cases the results are very interesting: the team, indeed, find some sugars essential for life: ribose and other biotic sugars, including arabinose and xylose. In particular the ribose is an essential component of ribonucleic acid, commonly known as Rna, a molecule of fundamental importance for life. This nucleic acid, in fact, performs the delicate function of copying the genetic instructions contained in the DNA molecule (deoxyribonucleic acid) to deliver them to the molecular factories inside the cell, called ribosomes, where proteins are synthesized.
Furukawa, Y., Chikaraishi, Y., Ohkouchi, N., Ogawa, N. O., Glavin, D. P., Dworkin, J. P., ... & Nakamura, T. (2019). Extraterrestrial ribose and other sugars in primitive meteorites. Proceedings of the National Academy of Sciences, 116(49), 24440-24445. doi:10.1073/pnas.1907169116

A laser particle accelerator

Particle accelerators are usually associated with large national facilities. Because photons are able to impart momentum to electrons, there are also efforts to develop laser-based particle accelerators. Sapra et al. developed an integrated particle accelerator using photonic inverse design methods to optimize the interaction between the light and the electrons. They show that an additional kick of around 0.9 kilo–electron volts (keV) can be given to a bunch of 80-keV electrons along just 30 micrometers of a specially designed channel. Such miniaturized dielectric laser accelerators could open up particle physics to a number of scientific disciplines.
Sapra, N. V., Yang, K. Y., Vercruysse, D., Leedle, K. J., Black, D. S., England, R. J., ... & Byer, R. L. (2020). On-chip integrated laser-driven particle accelerator. Science, 367(6473), 79-83. doi:10.1126/science.aay5734

The action of UV-C against covid19

The research about the action of ultraviolet radiation against covid19 arrived at an interesting conclusion: the team, leaded by Istituto Nazionale di Astrofisica and Università Statale di Milano and with the collaboration of Istituto nazionale dei tumori and Irccs, has provided the first experimental data about the high germicidal power of ultraviolet rays against Sars-Cov-2.
Andrea Bianco, head of the astronomers' team, says to MediaINAF (Google Translate):
We have seen very distinct behaviors. At the lowest concentration, we had to wait six days for the virus to replicate and infect cells without being subjected to UV-C illumination. In the intermediate concentration, which we took as a reference, already with the lowest dose of irradiation, after 24 hours we had a reduction of a factor greater than 1000. Waiting longer, we saw that the virus no longer grows back, that is, it is no longer able to replicate itself: it is said that it has been completely inhibited. While in the highest concentration, at the lowest dose of irradiation, at the beginning there is a fairly significant decrease in the amount of active virus but after it goes back up, which means that the virus has been inactivated but the concentration is so high that it is able to restart (because it has not been completely inhibited). When we gave him the second dose - 16.7 mJ / cm2 - it was seen that it is sufficient to completely inhibit him : even after 72 hours he is unable to "regain his strength". In this high concentration of the virus, therefore, this aspect emerged: at low doses I can have a significant decrease in the active virus but he is still able to infect the cells, so after a certain time he restarts with his activity.
But:
Going from Uv-A to Uv-C the danger for man increases, in the sense that Uv-C radiation causes mutations, therefore increases the probability of having skin cancers considerably. So much so that, by law, the maximum dose of Uv-C that one can take daily is very low. Uv-B and Uv-A are much less so, so much so that we tan, protecting ourselves with creams to avoid the risk of cancer and skin rashes. The risk is there but with much less probability.
Bianco, A., Biasin, M., Pareschi, G., Cavalleri, A., Cavatorta, C., Fenizia, C., ... & Saulle, I. (2020). UV-C irradiation is highly effective in inactivating and inhibiting SARS-CoV-2 replication. medRxiv. doi:10.1101/2020.06.05.20123463
The potential virucidal effects of UV-C irradiation on SARS-CoV-2 were experimentally evaluated for different illumination doses and virus concentrations (1000, 5, 0.05 MOI). Both virus inactivation and replication inhibition were investigated as a function of these parameters. At a virus density comparable to that observed in SARS-CoV-2 infection, an UV-C dose of just 3.7 mJ/cm2 was sufficient to achieve a 3-log inactivation, and complete inhibition of all viral concentrations was observed with 16.9 mJ/cm2. These results could explain the epidemiological trends of COVID-19 and are important for the development of novel sterilizing methods to contain SARS-CoV-2 infection.
Nicastro, F., Sironi, G., Antonello, E., Bianco, A., Biasin, M., Brucato, J. R., ... & Trabattoni, D. (2020). Modulation of COVID-19 Epidemiology by UV-B and-A Photons from the Sun. medRxiv. doi:10.1101/2020.06.03.20121392
It is well known that 200-290 nm ultraviolet photons (hereinafter UV-C radiation) photo-chemically interacts with DNA and RNA and are endowed with germicidal properties that are also effective on viruses. Fortunately, Solar UV-C photons of this wavelength are filtered out by the Ozone layer of the upper Atmosphere, at around 35 km. Softer UV photons from the Sun with wavelengths in the range 290-320 nm (UV-B) and 320-400 nm (UV-A), however, do reach the Earth s surface. The effect of these photons on Single- and Double-Stranded RNA/DNA viruses and the possible role they play on the seasonality of epidemics, are nevertheless little studied and highly debated in alternative or complementarity to other environmental causes. Notably though, the effects of both direct and indirect radiation from the Sun needs to be considered in order to completely explain the effects of UV radiations in life processes (with e.g. the UV virucidal effect enhanced in combination to the concomitant process of water droplets depletion because of Solar heat). Herein we present a number of concurring circumstantial evidence suggesting that the evolution and strength of the recent Severe Acute Respiratory Syndrome (SARS-Cov-2) pandemics, might be have been modulated by the intensity of UV-B and UV-A Solar radiation hitting different regions of Earth during the diffusion of the outbreak between January and May 2020. Out findings, if confirmed by more in depth data analysis and modeling of the epidemics, which includes Solar modulation, could help in designing the social behaviors to be adopted depending on season and environmental conditions.

Where planets born

T Tauri stars are a class of variable stars that are less than about ten million years old. This class is named after the prototype, T Tauri, a young star in the Taurus star-forming region discovered in October 1852 by John Russell Hind. They are found near molecular clouds and identified by their optical variability and strong chromospheric lines. T Tauri stars are pre-main-sequence. In photo you can see 21 T Tauri stars with their protoplanetary disks, rotating circumstellar disks of dense gas and dust. This is probably the beginning of a solar system formation.
Garufi, A., Avenhaus, H., Pérez, S., Quanz, S. P., van Holstein, R. G., Bertrang, G. M., ... & Zurlo, A. (2020). Disks Around T Tauri Stars with SPHERE (DARTTS-S)-II. Twenty-one new polarimetric images of young stellar disks. Astronomy & Astrophysics, 633, A82. doi:10.1051/0004-6361/201936946

A journey to Proxima Centauri


Proxima Centauri is a red dwarf located approximately 4.2 light years from us, in the area of ​​sky covered by the Centaur constellation. Thanks to ESO's telescopes, in particular to the HARPS spectrograph, and using the Doppler (or radial velocity) method, in 2016 it was anounced the discovery of a planet around this star, Proxima Centauri b.
Given the proximity, one might think that the world of comics has devoted much attention in recent years to the star and its planet. In fact, to have a comic set around this star, you have to wait until the second half of 2018 when Image Comics publishes the six-issue miniseries Proxima Centauri by Farel Dalrymple.
The work, subsequently collected in volume in January 2019, is halfway between science fiction and fantasy. The main character is Sherwood Breadcoat, a teenage magician trapped on an artificial spheroid called Proxima Centauri, evidently put in orbit around the homonymous star. Of course, this information is not very clear, but overall the whole Dalrymple comic is rather lack of information, closed in a hermetic narration with an open ending that allows the author keep some subplots open, like the relationship between Sherwood and the scientist, that sometimes seems help the teen, other times usi it for his purposes; or as one of Sherwood's opponents, which is actually a sort of virtual, but also physical manifestation of a character hidden somewhere on the spheroid and who seems to be a videogame player, given that he explicitly states that he wants to repeat the vlash with Sherwood, although it ended badly more than once.
In all this, although science would seem to play a fundamental role, at least according to some lines of Breadcoat, a character who believes only in science and magic (?), it is a simple narrative accessory, a way to not deepen the technology used or to hide all the magical aspects of the story, only apparently sci-fi.
In any case, Dalrymple's comic is good to remember that, quite recently, a team of Italian astronomers, studying the data coming from Proxima Centauri with more accuracy, has supposed the existence of a second planet around the star, roughly six times more massive than Earth. We will see if it will be confirmed or not.

The other side of the matter

We know that exist a particular type of matter: the antimatter. Antimatter is composed by antiparticles. An antiparticle has the same mass as the corresponding particle but has opposite charge. And luckily for us antimatter is substantialy absent from our universe: indeed the interaction between matter and antimatter leads to the annihilation process, with the disappearance of particle and antiparticle and energy production. So, if in the universe there were the same amount of matter and antimatter, it would be filled exclusively with radiation. For this reason it is particularly interesting understand where this asymmetry originates: we know that would be a symmetry violation in some place and time of the universe, and the T2K experiment in Japan tested neutrinos' oscillations, in particular the oscillation from muonic to electronic neutrino. The results of ten years of data say that 90 neutrinos and only 15 antineutrinos were caught oscillating from muonic to electronic: different numbers mean violated symmetry.
The most interesting detail is that the experimental result doesn't exclude an interesting idea about an anti-universe that exists at the other side of the Big Bang.
Abe, K., Akutsu, R., Ali, A., Alt, C., Andreopoulos, C., Anthony, L., ... & Ashida, Y. (2020). Constraint on the Matter-Antimatter Symmetry-Violating Phase in Neutrino Oscillations. Nature volume 580, pages 339–344. doi:10.1038/s41586-020-2177-0
Boyle, L., Finn, K., & Turok, N. (2018). C P T-Symmetric Universe. Physical review letters, 121(25), 251301. doi:10.1103/PhysRevLett.121.251301

Sun in High-Res

A team of researchers from the University of Central Lancashire and NASA's Marshall Space Flight Center published images of the Sun in unprecedented resolution. Obtained with NASA's high resolution Coronal Imager, used incandescent plasma filaments never seen before:

Using ultraviolet radiation against SARS-CoV-2


Alessio Zanuta
Astrophisicts of Brera's Astronmical Observatory in Milano are collaborating with researchers at Milano University are developing and testing ultraviolet devices for air disinfection and inactivation of the SARS-CoV-2 virus. The italian science magazine, Media INAF, has interviewed Alessio Zanuta. Here there is the english tranlsation. In the post I extracted an interesting quote:
(...) we are developing new ideas for fighting the virus in terms of disinfection
First of all by conducting targeted studies to understand how it behaves and which are in weak points of this virus if subjected to radiation. We speak above all of ultraviolet rays, and we wonder if they are effective in inactivating it, at what wavelengths, how long exposure it takes, and what doses. While there is a large literature on how Uv rays - especially the most energetic ones (the so-called Uv-C rays) - have effective sanitizing effects also on viruses, currently specific information on the doses necessary to specifically annihilate the Sars-Cov-2 virus is lacking responsible for the current pandemic. This bibliography information is missing right now, either because the virus is new, or because the similarities with other types of viruses are labile. After collecting all the necessary data, we aim to develop devices useful for disinfection. Furthermore, the idea that even less energetic rays, those emitted by the Sun and which are not absorbed by the atmosphere, can have a disinfectant effect, with important epidemiological consequences and with interesting information to manage the so-called "Phase 2" in return from the lockdown. In the summer, there could be a drop in infections, also thanks to greater illumination by the Sun.

The road to reality

The discussion around what we know about the universe is in continuous development. If we take the infographic below, for example, we are faced with three possible scenarios: an accelerated expanding universe that will conclude is run in a big rip, in which the universe eventually turns completely black; a universe in which expansion is in balance with gravity, but nevertheless destined to make the skies of planets black and starless; a universe where expansion is blocked and reversed to a big crunch.

Source: visual.ly

Black hole simulation

This graphic shows the computer simulation of a black hole from start to finish. Plasma is falling slowly toward the black hole in a (at the upper left). The plasma has a magnetic field, shown by the white lines. It picks up speed as it falls toward the hole in b (at the upper right), c (lower left) and d (lower right). However, the rotating black hole twists up space itself (and the magnetic field lines) and ejects electromagnetic power along the north and south poles above the black hole. The red and white color shows the immense electromagnetic power output, which eventually will pick up particles and form squirting jets. This simulation was conducted using supercomputers at Japan's National Institute for Fusion Science.
source: archive.org

Maths in Europe: John Conway

Card Colm Mulcahy, an irish mathematician and John Conway's friend, on 11 april 2020 published on twitter the news of the death of Conway. His source was a close associate of his and confirmed by the family.
I written a little post in his honour on Maths in Europe, a ahort article about the free will theorem.
The theorem was proposed by Conway with Simon Kochen, inspired by the question about the interpretation of quantum mechanics. The statement is:
If the choice of directions in which to perform spin 1 experiments is not afunction of the information accessible to the experimenters, then the responsesof the particles are equally not functions of the information accessible to them.
(continue to read)

Breaking comets


Comet Atlas, portrait by Tim Connolly
First of all I start from Atlas, a new comet that is coming here! It will arrive at the end of May, passing only 0.25 AU from the sun. It could be a good opportunity for amateurs to observe a new object in the sky, but there is a not so reassuring news:
New data from astronomers around the world show that the once-promising comet is beginning to fade.
- via spaceweather.com
This is not the only bad news: the first insterstellar comet, 2I/Borisov, that it goes away from the Sun with a speed of about 17 km/s (it will reach a speed of 32 m/s), seems to have lost a piece of the core (ATel #13611, ATel #13613).

Road to Mercury: flyby with Earth

A flyby is close passage of a space probe, at high speed, near a planet or other celestial object. It can be used to speed up or slow down the space probe.
The first successful planetary flyby ever made was performed the 14th December 1962 by the Mariner 2 NASA spacecraft with the planet Venus, but it was with the Mariner 10 mission, thanks to an intuition of the italian Mathematician Giuseppe Colombo in 1970, that we use now the flyby as orbital correction maneuver. Indeed, the professor from Paduan was invited from the JPL to participate in a conference about the Mariner 10 directed to Mercury. When he observed the spacecraft computed orbit, he noted that the Mariner 10 would have an orbital period around the sun twice the Mercury year. Hence, he suggested to carfully calibrate the first passage over Mercury in such a way that the spacecraft would have exactly the delta velocity from the planet to re-encounter Mercury at the next revolution. His suggestion was fully accepted and, thanks to him, Mercury 10 (llaunched in the 1973 on its way to Venus) had its first flyby with Mercury on 5th February 1974, and a second a third flyby on 21th September 1974, and also a third on 16th March 1975. The change in trajectory found by Giuseppe Colombo allowed to greatly increase the scientific return of the mission, as well as the scientific knowledge of the planet Mercury.
(...)
On the early morning of the 10th of April, there will be the possibility, hopefully, to observe the crossing on the sky of BepiColombo spacecraft crossing the sky from East to West. The closest approach is foreseen at 04.25 UTC with a minimum distance of 12.677 km from the Earth's surface.
If you want to compute your own plot for your location by inserting latitude and longitude here: https://bepicolombo.iaps.inaf.it.

source: esa

Abel Prize 2020: Furstenberg and Margulis

The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2020 to Hillel Furstenberg (left in the photo), Hebrew University of Jerusalem, Israel​ and Gregory Margulis (right in the photo), Yale University, New Haven, CT, USA,
for pioneering the use of methods from probability and dynamics in group theory, number theory and combinatorics.

Hillel Furstenberg and Gregory Margulis invented random walk techniques to investigate mathematical objects such as groups and graphs, and in so doing introduced probabilistic methods to solve many open problems in group theory, number theory, combinatorics and graph theory. A random walk is a path consisting of a succession of random steps, and the study of random walks is a central branch of probability theory.
The works of Furstenberg and Margulis have demonstrated the effectiveness of crossing boundaries between separate mathematical disciplines and brought down the traditional wall between pure and applied mathematics
says Hans Munthe-Kaas, chair of the Abel committee. He continues:
Furstenberg and Margulis stunned the mathematical world by their ingenious use of probabilistic methods and random walks to solve deep problems in diverse areas of mathematics. This has opened up a wealth of new results, such as the existence of long arithmetic progressions of prime numbers, understanding the structure of lattices in Lie groups, and the construction of expander graphs with applications to communication technology and computer science, to mention a few.

Due to the corona pandemic there will not be a physical Laureate ceremony on May 19 this year. The honoring of the Abel Prize Laureates will be announced later.
press release

Dyson sphere

A heartfelt tribute to Freeman Dyson
(...) Dyson is too modest.
Richard Carrigan(8)
The search for extraterrestrial life has, as I already written, some illustrious founding fathers: Enrico Fermi and his paradox; Giuseppe Cocconi and Philip Morrison and their 1959 proposal to use radio astronomy to search for extraterrestrial signals of intelligent origin(1); Frank Drake with his famous equation, and therefore with the Ozma project(2), so called for the queen of the imaginary land of Oz, a very distant place, difficult to reach and populated by exotic beings, a kind of proto-SETI, project that Drake helped to found and launch.
Another important contribution to the quest of intelligent signal in the universe come from Freeman Dyson(3, 8):
If extraterrestrial intelligent beings exist and have reached a high level of technical development, one by-product of their energy metabolism is likely to be the large-scale conversion of starlight into far-infrared radiation. It is proposed that a search for sources of infrared radiation should accompany the recently initiated search for interstellar radio communications.(3)
Dyson, taking our solar system as a model, observed how the mass of Jupiter, if distributed with spherical symmetry on a double orbit compared to that of the Earth, would have been 2 tons per square meter thick:
A shell of this thickness could be made comfortably habitable, and could contain all the machinery required for exploiting the solar radiation falling onto it from the inside(3)