Field of Science

A mathematical theory of communication

A mathematical theory of communication is a paper by Claude Shannon published in two part in July and October 1948. The paper posed the basis for the modern information theory and the basi elements of communication:
  • An information source that produces a message
  • A transmitter that operates on the message to create a signal which can be sent through a channel
  • A channel, which is the medium over which the signal, carrying the information that composes the message, is sent
  • A receiver, which transforms the signal back into the message intended for delivery
  • A destination, which can be a person or a machine, for whom or which the message is intended


Shannon, C. (1948). A Mathematical Theory of Communication Bell System Technical Journal, 27 (3), 379-423 DOI: 10.1002/j.1538-7305.1948.tb01338.x (pdf)
Shannon, C. (1948). A Mathematical Theory of Communication Bell System Technical Journal, 27 (4), 623-656 DOI: 10.1002/j.1538-7305.1948.tb00917.x (pdf)

The Marvel Universe as a real social network


Cover of the first number of Marvel Team-Up, comic book dedicated to the collaborations between Marvel heroes
We investigate the structure of the Marvel Universe collaboration network, where two Marvel characters are considered linked if they jointly appear in the same Marvel comic book. We show that this network is clearly not a random network, and that it has most, but not all, characteristics of "real-life" collaboration networks, such as movie actors or scientific collaboration networks. The study of this artificial universe that tries to look like a real one, helps to understand that there are underlying principles that make real-life networks have definite characteristics.
R. Alberich, J. Miro-Julia, & F. Rossello (2002). Marvel Universe looks almost like a real social network arXiv arXiv: cond-mat/0202174v1

Postcards from Pluto

The New Horizons mission has provided a lot of observations about Pluto, the farthermost known celestial object in our Solar System. Thanks to these observations, astronomers can now describe some interesting Pluto's characteristics.
The Pluto system is surprisingly complex, comprising six objects that orbit their common center of mass in approximately a single plane and in nearly circular orbits. (...)
All four of Pluto's small moons are highly elongated objects with surprisingly high surface reflectances (albedos) suggestive of a water-ice surface composition. Kerberos appears to have a double-lobed shape, possibly formed by the merger of two smaller bodies. Crater counts for Nix and Hydra imply surface ages of at least 4 billion years. Nix and Hydra have mostly neutral (i.e., gray) colors, but an apparent crater on Nix's surface is redder than the rest of the surface; this finding suggests either that the impacting body had a different composition or that material with a different composition was excavated from below Nix's surface. All four small moons have rotational periods much shorter than their orbital periods, and their rotational poles are clustered nearly orthogonal to the direction of the common rotational poles of Pluto and Charon.

A prize for a theorem

Pierre de Fermat was born in 1601 in Beaumont-de-Lomagne in southwestern France. He was not even a mathematician; he was a civil servant who devoted himself to mathematics as a hobby. He was regarded as one of the most gifted self-taught mathematicians who ever lived.
I think that this quotation from The girl who played with fire by Stieg Larson, the second novel from the series Millennium, was the perfect introduction to a post about the Fermat's Last Theorem and Andrew Wiles, who proofed it in 1993. And he awarded the Abel Prize just some days ago.
Simply a joke?

Pierre de Fermat by Bernarda Bryson
Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos ejusdem nominis fas est dividere: cujus rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.(1)
This is what Pierre de Fermat wrote in the margin of Arithmetica by Diofanto and it establish the impossibility to find solutions in the field of natural numbers for the diophantine equation(2) that generalizes the Pythagorean theorem: \[a^n + b^n = c^n\] Following the Pythagorean theorem, for $n = 2$ the Fermat's equation has solutions in the field of natural numbers, called Pythagorean triples. For $n$ greater than 2 the story, instead, becomes more complicated, so that the same Fermat, while writing what follows, never provided a full demonstration, but only for the special case of $n = 4$:
I have discovered a truly marvelous proof of this theorem, which can't be contained in the too narrow page margin.

Ludolph van Ceulen: in searching of pi

One of the most important mathematicians for $\pi$, was Ludolph van Ceulen, German mathematician born 28 January 1540 in Hildesheim. His father, Johannes Van Ceulen, was a small trader who could not afford advanced education for a son who showed some interest in mathematics. The main difficulty for Ludolph studies was the Latin, the language in which they were written the basic texts as well as the more recent ones in mathematics and science at the time. And Latin was a subject to be advanced studies.
Another fundamental challenge was the particular historical period in which Ludolph lived. At that time, in fact, life for Protestants was rather complicated: the Spanish Inquisition was, in fact, powerful enough to extend his long hands even in Germany. The Van Ceulen's, as Protestants, were forced, like many in the same conditions, to migrate to the most welcoming Netherlands of Prince William of Orange.
On the other hand Ludolph himself was a traveler: immediately after his father's death became a little travel first in the region of Livonia (Latvia and Estonia in our age), then to Antwerp to visit his brother Gert and then to Delft in the Netherlands where he settled for a time, since there was born one of his five daughter on May 4th, 1578.
His wife, Mariken Jansen, died in 1590, but Ludolph remarriage on June 17th of that year with Adriana Simondochter, widow of Bartholomew Cloot, accounting and math teacher, with whom he had generated eight children, for a total of 13 mouths to feed. The two families, Cloot and Van Ceulen, were in a close relations of friendship, so it's pretty obvious to imagine that the marriage between Ludolph and Adriana was the best solution to avoid losing a strong relationship.

The tabulating machine

Herman Hollerith, an American inventor, was born on the 29th February 1860. His most famous invention was the electromechanical tabulation of data:
At the urging of John Shaw Billings, Hollerith developed a mechanism using electrical connections to trigger a counter, recording information. A key idea was that data could be encoded by the locations of holes in a card. Hollerith determined that data punched in specified locations on a card, in the now-familiar rows and columns, could be counted or sorted mechanically. A description of this system, An Electric Tabulating System (1889), was submitted by Hollerith to Columbia University as his doctoral thesis, and is reprinted in Randell's book.
In the patent of his invention, we can read:
The herein-described method of compiling statistics, which consists in recording separate statistical items pertaining to the individual by holes or combinations of holes punched in sheets of electrically non-conducting material, and bearing a specific relation to each other and to a standard, and then counting or tallying such statistical items separately or in combination by means of mechanical counters operated by electro-magnets the circuits through which are controlled by the perforated sheets, substantially as and for the purpose set forth.
In 1896 Hollerith founded The Tabulating Machine Company, that in 1911, with four others company, became the Computing-Tabulating-Recording Company, renamed International Business Machines (IBM) in 1924.

Save research in Italy

About three weeks ago, Nature published a letter by Giorgio Parisi and signed by 69 italian scientists about the state of the research in Italy. This is the text:
We call for the European Union to push governments into keeping their research funding above subsistence level. This will ensure that scientists from across Europe can compete for Horizon 2020 research funding, not just those from the United Kingdom, Germany and Scandinavia.
Europe's research money is divided between the European Commission and national governments. The commission funds large, transnational collaborative networks in mostly applied areas of research, and the governments support small-scale, bottom-up science and their own strategic research programmes.
Some member states are not keeping their part of the bargain. Italy, for example, seriously neglects its research base. The Italian National Research Council has not overseen basic research for decades, being itself starved of resources. University funding has dwindled to a bare minimum. The ministerial initiative known as PRIN (Research Projects of National Interest) has been defunct since 2012, apart from a few limited programmes for young researchers.
This year's PRIN allocation of a euro92-million (US$100-million) funding call to cover all research areas is too little, too late. Compare this with the annual French National Research Agency's allocation of up to euro1 billion, or with Italy's euro900-million annual contribution to the EU Seventh Framework Programme that ran in 2007–13. That resulted in a net annual loss of euro300 million for Italian science.
To prevent distorted development in research among EU countries, national policies must be coherent and guarantee a balanced use of resources.
You can sign the petition on change.org.