Field of Science

Snowden and the debate on surveillance versus privacy

In June 2013, NSA contractor Edward Snowden met with journalists Glenn Greenwald and Ewen Macaskill and film-maker Laura Poitras in Hong Kong. The whistleblower gave them documents which proved the existence of a massive scale surveillance system that allows the American NSA and other intelligence and security agencies to gather information on citizens without judicial supervision. While in the USA and in Germany the major media outlets reported extensively on the issue, in Italy there hasn't been a proper public debate on privacy and surveillance, as - except for the work of handful of journalists – the media chose not to cover the implications of such revelations. On the other hand, politics is quick to use the fight against terrorism to push for reforms that might limit people's privacy, a fundamental human right that is currently under attack all over the world. Without a proper balance between surveillance and privacy, the freedom of citizens is at risk. Without a proper public debate, it is hard to understand what is at stake. For the first time in Italy, such debate will take place including the voices of the people who made the information public: Edward Snowden, the whistleblower who revealed the scope of the NSA surveillance practices, will be joining the conversation, as well as the independent film-maker Laura Poitras. Poitras recently won an Academy Award for the documentary Citizenfour, where she shows the meetings between the whistleblower and the journalists, and a Pulitzer prize for her journalistic work on the story. The human rights implications will be explored by Ben Wizner (ACLU), Snowden's lawyer, and Andrea Menapace, who directs the newly-born Italian Coalition for Civil Rights and Freedoms. Organised in association with Italian Coalition for Civil Rights and Freedoms (CILD) and American Civil Liberties Union (ACLU) Speakers: Edward Snowden (via Skype) Laura Poitras (via Skype) Ben Wizner (ACLU) Andrea Menapace (CILD) Simon Davies (Privacy International) Introduction: Patrizio Gonnella (CILD) Moderator: Fabio Chiusi Con: Fabio Chiusi (journalist and author), Simon Davies (founder Privacy International), Patrizio Gonnella (president CILD), Andrea Menapace (director CILD), Laura Poitras (documentary film-maker (via Skype)), Edward Snowden (whistleblower (via Skype)), Ben Wizner (ACLU), Ben Wizner

Cassini ovals

#HappyEaster from @ulaulaman with #math

via commons
A Cassini oval is a quartic plane curve defined as the set (or locus) of points in the plane such that the product of the distances to two fixed points is constant. This may be contrasted to an ellipse, for which the sum of the distances is constant, rather than the product. Cassini ovals are the special case of polynomial lemniscates when the polynomial used has degree 2.
Cassini ovals are named after the astronomer Giovanni Domenico Cassini who studied them in 1680. Other names include Cassinian ovals, Cassinian curves and ovals of Cassini.
Read also: MathWorld, McTutor

Louis Nirenberg, the geometry and the Abel Prize

http://t.co/rTEYZLbVDZ by @ulaulaman about #AbelPrize #LouisNirenberg
Great news: John Nash and Louis Nirenberg win the Abel Prize for 2015:
The Norwegian Academy of Sciences and Letters has decided to award the Abel Prize for 2015 to the American mathematicians John F. Nash Jr. and Louis Nirenberg “for striking and seminal contributions to the theory of nonlinear partial differential equations and its applications to geometric analysis.” The President of the Academy, Kirsti Strøm Bull, announced the new laureates today 25 March. They will receive the Abel Prize from His Majesty King Harald at a ceremony in Oslo on 19 May.
While Nash is known for his contribution to game theory with Nash equilibria, Nirenberg is
considered one of the outstanding analysts of the twentieth century. He has made fundamental contributions to linear and nonlinear partial differential equations and their application to complex analysis and geometry.
His first result was the completion of the solution of a problem in differential geometry, starting from the 1916 work of Weyl (read On the work of Louis Nirenberg by Simon Donaldson, pdf).
The statement is very simple: an abstract Riemannian metric on the 2-sphere with positive curvature can be realised by an isometric embedding in $R^3$.
In 1994 he received the Steele Prize by the American Mathematical Society. In that occasion, the Society writes (via MacTutor) a good summary of his activity:
Nirenberg is a master of the art and science of obtaining and applying a priori estimates in all fields of analysis. A minor such gem is the useful set of Garliardo-Nirenberg inequalities. A high point is his joint research with [Shmuel] Agmon and [Avron] Douglis on a priori estimates for general linear elliptic systems, one of the most widely quoted results in analysis. Another is his fundamental paper with Fritz John on functions of bounded mean oscillation which was crucial for the later work of [Charles] Fefferman on this function space. Nirenberg has been the centre of many major developments. His theorem with his student, Newlander, on almost complex structures has become a classic. In a paper building on earlier estimates of [Alberto] Calderón and [Antoni] Zygmund, he and [Joseph] Kohn introduced the notion of a pseudo-differential operator which helped to generate an enormous amount of later work. His research with [François] Trèves was an important contribution to the solvability of general linear PDEs. Some other highlights are his research on the regularity of free boundary problems with [David] Kinderlehrer and [Joel] Spuck, existence of smooth solutions of equations of Monge-Ampère type with [Luis] Caffarelli and Spuck, and singular sets for the Navier-Stokes equations with Caffarelli and [Robert] Kohn. His study of symmetric solutions of non-linear elliptic equations using moving plane methods with [Basilis] Gidas and [Wei Ming] Ni and later with [Henri] Berestycki, is an ingenious application of the maximum principle.
I hope that you can appreciate the list of collaboration performed by Nirenberg: indeed he is one of the most collaborative mathematician in the word. In particular for this reason I'm really happy for the award to Nirenberg.
Read also: Interview with Louis Nirenberg (pdf)

Pi day: Zilienski, Wallis and the square

http://t.co/SopVLuLJHM by @ulaulaman #piday
A good pi day to all readers! I hope that the following post, that I cannot review after the first writing, could be interesting to all!
The technique used by the ancient Greek for their geometric constructions was called "ruler and compass". In this way you can build a lot of regular polygons, for example, but there are three problems that are impossible unless you use different techniques: the angle trisection, doubling the cube, squaring the circle.
In particular for the squaring, it is easy to calculate the relation between the radius $r$ of the circke and the side $l$ of the square with the same area of the starting circle: \[L = \sqrt {\pi} r \] Now, since $\pi$ is a transcendental number, the formula above is the simplest representation of the impossibility of squaring the circle using ruler and compass: with these devices you can treat rational and irrational numbers, such as $\sqrt{2}$ (in this case simply draw a square of side 1).
So, using these two tools it is possible to obtain an approximate construction and, therefore, a corresponding approximate value for $\pi$: during the XX century there are produced a lot of approximations, for example by CD Olds (1963), Martin Gardner (1966), Benjamin Bold (1982). They are all variations of the geometric construction discovered by Srinivasa Ramanujan in 1913, that approached $\pi$ with the fraction \[\frac{355}{113} = 3.1415929203539823008 \dots\] right up to the sixth decimal place.
In 1914, Ramanujan discovered a more accurate approximation (to eight decimal places), always using ruler and compass: \[\left (9^2 + \frac{19}{22}^2 \right)^{1/4} = \sqrt[4]{\frac{2143}{22}} = 3.1415926525826461252 \dots\]

Riemann zeta function's fractal

#arXiv #abstract on #zetafunction and #fractals

via imgur
The quadratic Mandelbrot set has been referred to as the most complex and beautiful object in mathematics and the Riemann Zeta function takes the prize for the most complicated and enigmatic function. Here we elucidate the spectrum of Mandelbrot and Julia sets of Zeta, to unearth the geography of its chaotic and fractal diversities, combining these two extremes into one intrepid journey into the deepest abyss of complex function space.
Fractal Geography of the Riemann Zeta Function by Chris King

Rock, paper, scissors, lizard, Spock

http://t.co/a0l4FP6ftF Goodbye #LeonardNimoy, #Spock from #StarTrek
One popular five-weapon expansion is "rock-paper-scissors-lizard-Spock", invented by Sam Kass and Karen Bryla, which adds "Spock" and "lizard" to the standard three choices. "Spock" is signified with the Star Trek Vulcan salute, while "lizard" is shown by forming the hand into a sock-puppet-like mouth. Spock smashes scissors and vaporizes rock; he is poisoned by lizard and disproven by paper. Lizard poisons Spock and eats paper; it is crushed by rock and decapitated by scissors. This variant was mentioned in a 2005 article of The Times and was later the subject of an episode of the American sitcom The Big Bang Theory in 2008.
The majority of such proposed generalizations are isomorphic to a simple game of modulo arithmetic, where half the differences are wins for player one. For instance, rock-paper-scissors-Spock-lizard (note the different order of the last two moves) may be modeled as a game in which each player picks a number from one to five. Subtract the number chosen by player two from the number chosen by player one, and then take the remainder modulo 5 of the result. Player one is the victor if the difference is one or three, and player two is the victor if the difference is two or four. If the difference is zero, the game is a tie.
Alternatively, the rankings in rock-paper-scissors-Spock-lizard may be modeled by a comparison of the parity of the two choices. If it is the same (two odd-numbered moves or two even-numbered ones) then the lower number wins, while if they are different (one odd and one even) the higher wins. Using this algorithm, additional moves can easily be added two at a time while keeping the game balanced:
  • Declare a move N+1 (where N is the original total of moves) that beats all existing odd-numbered moves and loses to the others (for example, the rock (#1), scissors (#3), and lizard (#5) could fall into the German well (#6), while the paper (#2) covers it and Spock (#4) manipulates it).
  • Declare another move N+2 with the reverse property (such as a plant (#7) that grows through the paper (#2), poisons Spock (#4), and grows through the well (#6), while being damaged by the rock (#1), scissor (#3), and lizard(#5)).
(via en.wiki)

The dark side of the moon

#moon #astronomy #NASA #video #PinkFloyd

The first photo of the lunar far side taken by the Soviet spacecraft Luna 3 on Oct. 7, 1959 - via Universe Today