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.

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- 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.

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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.

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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.

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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.

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press release

Dyson sphere

A heartfelt tribute to Freeman Dyson

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(...) 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⁾

Carl Ludwig Siegel: number thoery, pig and nazional socialism

via Lang, S. (1994). Mordell's review, Siegel's letter to Mordell, diophantine geometry, and 20th century mathematics. Mitteilungen der Deutschen Mathematiker-Vereinigung, 2(4), 20-31.

This is the letter that the german mathematician Carl Ludwig Siegel wrote to Louis Mordell about the book Diophantine geometry by Serge Lang. Here I proposed you an extract in which we can read Siegel approach to mathematics and also his political position about nazism:

When I first saw [Lang's Diophantine geometry], about a year ago, I was disgusted with the way in which my own contributions to the subject had been disfigured and made unintelligible. My feeling is very well expressed when you mention Rip van Winkle!
The whole style of the author contradicts the sense for simplicity and honesty which we admire in the works of the masters in number theory - Lagrange, Gauss, or on a smaller scale, Hardy, Landau. Just now Lang has published another book on algebraic numbers which, in my opinion, is still worse than the former one. I see a pig broken into a beautiful garden and rooting up all flowers and trees.
Unfortunately there are many "fellow-travellers" who have already disgraced a large part of algebra and function theory; however, until now, number theory had not been touched. These people remind me of the impudent behaviour of the national socialists who sang: "Wir werden weiter marschieren, bis alles in Scherben zerfällt!"
I am afraid that mathematics will perish before the end of this century if the present trend for senseless abstraction - as I call it: theory of the empty set - cannot be blocked up.

The poet and the pendulum

Looking upward, I surveyed the ceiling of my prison. It was some thirty or forty feet overhead, and constructed much as the side walls. In one of its panels a very singular figure riveted my whole attention. It was the painted figure of Time as he is commonly represented, save that, in lieu of a scythe, he held what, at a casual glance, I supposed to be the pictured image of a huge pendulum, such as we see on antique clocks. There was something, however, in the appearance of this machine which caused me to regard it more attentively. While I gazed directly upward at it, (for its position was immediately over my own,) I fancied that I saw it in motion. In an instant afterward the fancy was confirmed. Its sweep was brief, and of course slow. I watched it for some minutes, somewhat in fear, but more in wonder.

- from The pit and the pendulum by Edgar Allan Poe

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After the abandonment of Tarja Turunen, the Nightwish engaged Anette Olzon as a female voice for five years, from 2007 to 2012. Again the separation it was not the best, but the fact is that Anette, despite the apparent sympathy, certainly did not enter the hearts of the fans, evidently still loving Turunen. His place was then taken by the dutch Floor Jansen, who turned out to be a worthy substitute for Turunen, but in the meantime Olzon sang one of Tuomas Holopainen's most interesting and inspired songs, evidently inspired by Edgar Allan Poe and to his mystical story The pit and the pendulum:

Gerbert's satanic signs

In the history of numbers, Gerbert of Aurillac, better known as Sylvester II, the 139th Pope of the Catholic Church, takes on a curious role.
He was an eclectic character: enthusiast about science and mathematics, it is handed down that he was the introducer of the Arabic numbers in Europe:
Gerbert was a figure of utmost importance as a religious, politician and scientist, who could not be ignored by his successors to the papal throne. He was considered the greatest intellectual exponent of the 10th century and one of the most important of the Middle Ages, a multifaceted and profound connoisseur of the arts of trivium and quadrivium. Thanks to his contact with the most advanced Islamic culture, Gerbert introduced in Europe the use of the clock, of a siren running on water vapor, and was the inventor of complicated musical and astronomical instruments. He used these inventions in Reims for teaching in the cathedral school. For example, Gerbert had built a complex system of celestial spheres designed to calculate the distances between the planets and, again in astronomy, asked in a letter of 984 to Lupito of Barcelona for the translation of an Arabic astronomy treaty, the Sententiae Astrolabii. Always in Reims he had a hydraulic organ built that excelled on all the previously known instruments, in which the air had to be pumped manually, and that in the sixteenth century was still visible in Ravenna. In the field of mathematics, the introduction of Arabic numerals in Europe has long been attributed to Gerbert, a merit of difficult attribution: surely the young aquitan knew them at the Hatto's school in Vich, but nothing authorizes us to think that he then made them know in the old continent. Certainly, Gerbert had the great merit of contributing to the studies on the astrolabe and of reintroducing the abacus in Europe, of which, according to an ancient chronicle, he would have learned the use by the Arabs.
The Arabic numbers were then considered demonic signs, so it should not be surprising that Pope Innocent X, in 1648, decided to resume the body with the aim of finding out if there was any trace of these sings on his predecessor. The exhumation was thus narrated by Cesare Rasponi:

When we dug under the portico, the body of Sylvester II was found intact, lying in a marble sepulcher at a depth of twelve palms. He was dressed in pontifical ornaments, his arms crossed over his chest, his head covered by the sacred tiara; the pastoral cross still hung from his neck and the ring finger of his right hand carried the papal ring. But in a moment that body dissolved in the air, which still remained impregnated with the sweet perfumes placed in the urn; nothing else remained but the silver cross and the pastoral ring.

The Arabic numbers derive from the Indian Brahmi symbols probably dating back to 300 BC and were spread mainly by the Arab mathematicians al-Khwārizmī and al-Kindi. Despite the meritorious work of introduction of Gerbert, it was only with Leonardo Fibonacci that, at the turn of the 1200s, the Arabic numbers were adopted in Europe in a systematic and widespread manner.