Understanding Shakespeare

Understanding Shakespeare / Approaches: "The goal of this approach was to provide an overview of the entire play by showing its text through a collection of the most frequently used words for each character. A scene is represented by a block of text and scaled relatively according to its number of words. Characters are ordered by appearance from left to right throughout the play. The major character’s speeches are highlighted to illustrate their amounts of spoken words as compared to the rest of the play."

Hubble astronomers capture deepest view yet of night sky

Hubble astronomers capture deepest view yet of night sky | Science | guardian.co.uk: "Piecing together 10 years of Hubble space telescope images, astronomers on Tuesday unveiled the deepest view yet of a small sliver of the night sky, revealing a kaleidoscope of galaxies and other celestial objects.

The Hubble eXtreme Deep Field, or XDF, adds another 5,500 galaxies to Hubble's 2003 and 2004 view into a tiny patch of the farthest universe.

Hubble returned to the same target more than 50 times over the past decade, racking up an additional 2m seconds of exposure time. The most distant objects found date back to about 500m years after the universe's formation some 13.7bn years ago.

The early universe was a violent place, filled with colliding and merging galaxies that radiate in bright blue light, a telltale sign of new star formation.

The Hubble portrait also shows brilliantly shining spiral galaxies and older red fuzzy galaxies whose star-formation days are over.

More than 2,000 images of the same field, taken by Hubble's Advanced Camera for Surveys and its near-infrared Wide Field Camera 3, were combined to form the XDF.

'XDF is the deepest image of the sky ever obtained,' astronomer Garth Illingworth, with the University of California at Santa Cruz, said in a statement. 'It allows us to explore further back in time than ever before.'"

Michael Perkins: Visualizing Hamlet

Michael Perkins: Visualizing Hamlet: "A TextArc is a visual representation of a text. In a TextArc analysis, the full text of a work is drawn in a tiny, one pixel tall line in two concentric spirals. Each distinct word is also drawn in a readable font at a location that is the average of all the actual word locations. Each of the readable words is then attached to the tiny words that occur in the text by lines.  This provides a graphical representation of the word's distribution in the text. "

'Warp drive' may be more feasible than thought

'Warp drive' may be more feasible than thought, scientists say | Fox News: "A warp drive to achieve faster-than-light travel — a concept popularized in television's Star Trek — may not be as unrealistic as once thought, scientists say.

A warp drive would manipulate space-time itself to move a starship, taking advantage of a loophole in the laws of physics that prevent anything from moving faster than light. A concept for a real-life warp drive was suggested in 1994 by Mexican physicist Miguel Alcubierre, however subsequent calculations found that such a device would require prohibitive amounts of energy.

Now physicists say that adjustments can be made to the proposed warp drive that would enable it to run on significantly less energy, potentially brining the idea back from the realm of science fiction into science.

'There is hope,' Harold 'Sonny' White of NASA's Johnson Space Center said here Friday (Sept. 14) at the 100 Year Starship Symposium, a meeting to discuss the challenges of interstellar spaceflight."

Planes write out pi over the skies of San Francisco Bay Area

Planes write out pi over the skies of San Francisco Bay Area | Crave - CNET: "Many denizens of the San Francisco Bay Area and Silicon Valley noticed a long series of cloudy numbers in the skies around noon on Wednesday, September 12. No, their coffee wasn't spiked with hallucinogens. The ephemeral event, known as Pi in the Sky, utilized five aircraft with dot-matrix skywriting technology to write out a thousand numbers of the beloved mathematical constant pi (3.14159..) at a 10,000-foot altitude. If that wasn't impressive enough, the numerals of pi written in the sky each stood nearly a quarter-mile tall, stretched for a 100-mile loop, and undoubtedly caused mass inspiration and confusion all at once."

ABC Proof Could Be Mathematical Jackpot - ScienceNOW

ABC Proof Could Be Mathematical Jackpot - ScienceNOW: "You can't always solve a mathematical problem by reducing it to something you've already solved. Sometimes, you need to invent an entirely new field of mathematics. Last month, Shinichi Mochizuki of Kyoto University in Japan announced that a new field he's been developing for several years—which he calls Inter-universal Teichmüller theory—has proved a famous conjecture in number theory known as the 'abc conjecture.' But the abc conjecture is only the beginning: If Mochizuki's theory proves correct, it will settle a raft of open problems in number theory and other branches of math."

Ivars Peterson's MathTrek - The Amazing ABC Conjecture

Ivars Peterson's MathTrek - The Amazing ABC Conjecture: "In number theory, straightforward, reasonable questions are remarkably easy to ask, yet many of these questions are surprisingly difficult or even impossible to answer.

Fermat's last theorem, for instance, involves an equation of the form x^n + y^n = z^n. More than 300 years ago, Pierre de Fermat (1601-1665) conjectured that the equation has no solution if x, y, and z are all positive integers and n is a whole number greater than 2. Andrew J. Wiles of Princeton University finally proved Fermat's conjecture in 1994.

In order to prove the theorem, Wiles had to draw on and extend several ideas at the core of modern mathematics. In particular, he tackled the Shimura-Taniyama-Weil conjecture, which provides links between the branches of mathematics known as algebraic geometry and complex analysis.

That conjecture dates back to 1955, when it was published in Japanese as a research problem by the late Yutaka Taniyama. Goro Shimura of Princeton and Andre Weil of the Institute for Advanced Study provided key insights in formulating the conjecture, which proposes a special kind of equivalence between the mathematics of objects called elliptic curves and the mathematics of certain motions in space.

The equation of Fermat's last theorem is one example of a type known as a Diophantine equation -- an algebraic expression of several variables whose solutions are required to be rational numbers (either whole numbers or fractions, which are ratios of whole numbers). These equations are named for the mathematician Diophantus of Alexandria, who discussed such problems in his book Arithmetica.

In fact, it was in the margin of a page of a Latin translation of Arithmetica that Fermat first set down the proposition that came to be known as Fermat's last theorem. He had studied the book closely, making marginal notes in his copy. After Fermat's death, his son published a new edition of Arithmetica that included the notes in an appendix.

Interestingly, the Wiles proof of Fermat's last theorem was a by-product of his deep inroads into proving the Shimura-Taniyama-Weil conjecture. Now, the Wiles effort could help point the way to a general theory of three-variable Diophantine equations. Historically, mathematicians have always had to state and solve such problems on a case-by-case basis. An overarching theory would represent a tremendous advance."

Mathematician Claims Proof of Connection between Prime Numbers

Mathematician Claims Proof of Connection between Prime Numbers | LiveScience: "A Japanese mathematician claims to have the proof for the ABC conjecture, a statement about the relationship between prime numbers that has been called the most important unsolved problem in number theory.

If Shinichi Mochizuki's 500-page proof stands up to scrutiny, mathematicians say it will represent one of the most astounding achievements of mathematics of the twenty-first century. The proof will also have ramifications all over mathematics, and even in the real-world field of data encryption."