Archive for the ‘Mathamatics’ Category

Mathemusician Vi Hart Explains Space-Time with a Music Box and a Möbius Strip | Brain Pickings   Leave a comment

Mathemusician Vi Hart Explains Space-Time with a Music Box and a Möbius Strip

by Maria Popova

“The fabric of the universe via backwards Bach.

If mathemusician Vi Hart — who for the past three years has been bringing whimsy to math with her mind-bending, playful, and illuminating stop-motion musical doodles — isn’t already your hero, she should be, and likely will be. (Cue in the GRAMMYs newly announced search for great music teachers.) In her latest gem, Hart uses music notation, a Möbius strip, and backwards Bach to explain space-time:

Music has two recognizable dimensions — one is time, and the other is pitch-space. … There [are] a few things to notice about written music: Firstly, that it is not music — you can’t listen to this. … It’s not music — it’s music notation, and you can only interpret it into the beautiful music it represents.

Also see Hart on the science of sound, frequency and pitch, and her blend of Victorian literature and higher mathematics to explain multiple dimensions.

For a decidedly less whimsical but enormously illuminating deeper dive, see these 7 essential books on time and watch Michio Kaku’s BBC documentary on the subject, then learn how to listen to music.”

via Mathemusician Vi Hart Explains Space-Time with a Music Box and a Möbius Strip | Brain Pickings.

AN : Just as the author , Maria Popova , writes of mathemusician Vi Hart  : “If mathemusician Vi Hart — ….- isn’t already your hero, she should be, and likely will . “….so you would be enamoured with the effervesent writings and curations of Maria through her site “ ” . Absolutely a gem  of ideas, innovation and thought leadership !

Posted February 11, 2013 by arnoneumann in Mathamatics, music

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Lost and Found: The Secrets of Archimedes reveals texts from the ancient world discovered by conserving and imaging The Archimedes Palimpsest   Leave a comment

“Discoveries in The Archimedes Palimpsest

Archimedes, in his treatise The Method of Mechanical Theorems, works with the concept of absolute infinity, and this Palimpsest contains the only surviving copy of this important treatise. He claims that two different sets of lines are equal in multitude, even though it is clearly understood that they are infinite. This approach is remarkably similar to 16th- and 17th-century works leading to the invention of the calculus.

Also found only in the Palimpsest is Archimedes’ Stomachion.  It is the earliest existing western treatise concerning combinatorics. It is thought that Archimedes was trying to discover how many ways you could recombine 14 fixed pieces and still make a perfect square. The answer is high and counterintuitive at 17,152 combinations. Combinatorics is critical in modern computing.

In addition to Archimedes’ works, six other erased books of history and philosophy were discovered. Twenty pages of the Palimpsest were created from the erased texts of ten pages from a manuscript containing speeches by Hyperides, an Athenian orator from the golden age of Greek democracy. Twenty-eight pages were from the erased text of 14 pages containing a Commentary on the Categories of the ancient Greek philosopher Aristotle. Aristotle’s Categories is a fundamental text to western philosophy. This commentary survives nowhere else.

When the Palimpsest was imaged at SSRL, the name of the scribe that erased Archimedes’ writings was discovered on the first page of the Palimpsest. His name was Johannes Myronas, and he finished transcribing the prayers on April 14, 1229, in Jerusalem.

via Lost and Found: The Secrets of Archimedes, opening at the Walters Oct. 16, 2011, reveals texts from the ancient world discovered by conserving and imaging The Archimedes Palimpsest.

AN : an arduous task and facinating story and exhibit at The Walters Art Museum in Balimore Maryland,USA. Innovation that goes back to Archimedes time (0212 BC ) and 1229 AD and 1998 AD :

“Archimedes lived in the Greek city of Syracuse in the third century B.C. He was a brilliant mathematician, physicist, inventor, engineer and astronomer. In 10th-century Constantinople (present day Istanbul), an anonymous scribe copied the Archimedes treatise in the original Greek onto parchment. In the 13th century, a monk erased the Archimedes text, cut the pages along the center fold, rotated the leaves 90 degrees and folded them in half. The parchment was then recycled, together with the parchment of other books, to create a Greek Orthodox prayer book. This process is called palimpsesting; the result of the process is a palimpsest.

On Oct. 28, 1998, The Archimedes Palimpsest was purchased at Christie’s by an anonymous collector for two million dollars. It is considered by many to be the most important scientific manuscript ever sold at auction because it contains Archimedes’ erased texts.

“The collector deposited the Palimpsest at the Walters for conservation, imaging, study and exhibition in 1999, but many thought that nothing more could be recovered from this book. It was in horrible condition, having suffered a thousand years of weather, travel and abuse,” said Archimedes Project Director and Walters Curator of Manuscripts and Rare Books Will Noel. “Detailed detective work and the serendipitous discovery of important documents and photographs allowed us to reconstruct what happened to the Palimpsest in the 20th century, when it was subject to appalling treatment and overpainted with forgeries. A team of devoted scholars using the latest imaging technology was able to reveal and decipher the original text.”

Before imaging could begin, the manuscript had to be stabilized. Conserving the manuscript took 12 years, including four years just to take the book apart due to the fragile nature of parchment damaged by mold and a spine covered in modern synthetic glue.

“I documented everything and saved all of the tiny pieces from the book, including paint chips, parchment fragments and thread, and put them into sleeves so we knew what pages they came from,” said Abigail Quandt, Walters senior conservator of manuscripts and rare books. “I stabilized the flaking ink on the parchment using a gelatin solution, made innumerable repairs with Japanese paper and reattached separated folios.”

In 2000, a team began recovering the erased texts. They used imaging techniques that rely on the processing of different wavelengths of infrared, visible and ultraviolet light in a technique called multispectral imaging. By employing different processing techniques, including Principal Components Analysis, text was exposed that had not been seen in a thousand years.

By 2004, about 80% of the manuscript had been imaged. The most difficult pages left were covered with a layer of grime or 20th-century painted forgeries. These leaves were brought to the Stanford Synchrotron Radiation Lightsource (SSRL), one of the most advanced light laboratories in the world, where a tiny but powerful x-ray beam scanned the leaves. The x-rays detected and recorded where beams bounced off iron atoms, and since the ink of the Palimpsest’s under text is written with iron, the writing on the page could be mapped. This enabled scholars to read large sections of previously hidden text.”

Posted December 14, 2012 by arnoneumann in History, Mathamatics

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