An anonymous reader shares a report: According to the Ancient Greek philosopher Pythagoras, 'consonance' -- a pleasant-sounding combination of notes -- is produced by special relationships between simple numbers such as 3 and 4. More recently, scholars have tried to find psychological explanations, but these 'integer ratios' are still credited with making a chord sound beautiful, and deviation from them is thought to make music 'dissonant,' unpleasant sounding.

But researchers from the University of Cambridge, Princeton and the Max Planck Institute for Empirical Aesthetics, have now discovered two key ways in which Pythagoras was wrong. Their study, published in Nature Communications, shows that in normal listening contexts, we do not actually prefer chords to be perfectly in these mathematical ratios. "We prefer slight amounts of deviation. We like a little imperfection because this gives life to the sounds, and that is attractive to us," said co-author, Dr Peter Harrison, from Cambridge's Faculty of Music and Director of its Centre for Music and Science.

The researchers also found that the role played by these mathematical relationships disappears when you consider certain musical instruments that are less familiar to Western musicians, audiences and scholars. These instruments tend to be bells, gongs, types of xylophones and other kinds of pitched percussion instruments. In particular, they studied the 'bonang,' an instrument from the Javanese gamelan built from a collection of small gongs.

Mark Tyson reports via Tom's Hardware: A commercial smartphone or Linux computer can be used to crack RSA-2048 encryption, according to a prominent research scientist. Dr Ed Gerck is preparing a research paper with the details but couldn't hold off from bragging about his incredible quantum computing achievement (if true) on his LinkedIn profile. Let us be clear: the claims seem spurious, but it should be recognized that the world isn't ready for an off-the-shelf system that can crack RSA-2048, as major firms, organizations, and governments haven't yet transitioned to encryption tech that is secured for the post-quantum era.

In his social media post, Gerck states that a humble device like a smartphone can crack the strongest RSA encryption keys in use today due to a mathematical technique that "has been hidden for about 2,500 years -- since Pythagoras." He went on to make clear that no cryogenics or special materials were used in the RSA-2048 key-cracking feat. BankInfoSecurity reached out to Gerck in search of some more detailed information about his claimed RSA-2048 breakthrough and in the hope of some evidence that what is claimed is possible and practical. Gerck shared an abstract of his upcoming paper. This appears to show that instead of using Shor's algorithm to crack the keys, a system based on quantum mechanics was used, and it can run on a smartphone or PC.

In some ways, it is good that the claimed breakthrough doesn't claim to use Shor's algorithm. Alan Woodward, a professor of computer science at the University of Surrey, told BankInfoSecurity that no quantum computer in existence has enough gates to implement Shor's algorithm and break RSA-2048. So at least this part of Gerck's explanation checks out. However, the abstract of Gerck's paper looks like it is "all theory proving various conjectures - and those proofs are definitely in question," according to Woodward. The BankInfoSecurity report on Gerck's "QC Algorithms: Faster Calculation of Prime Numbers" paper quotes other skeptics, most of whom are waiting for more information and proofs before they organize a standing ovation for Gerck.

According to a new book entitled "Megalith," which was released on June 21 to coincide with summer solstice, ancient humans who designed Stonehenge followed Pythagoras' theorem 2,000 years before his birth, around 2500 B.C. The theorem states that the square of the hypotenuse is equal to the sum of the other two squares on the triangle. TechTimes reports: [The theorem] was developed by ancient Greek mathematician Pythagoras, who was born in 570 B.C. However, Stonehenge was assembled 2,000 years before his birth, around 2500 B.C. This theory suggests that these ancient humans were smarter than what people give them credit for. In order to use Pythagoras' theorem, they had to be really skilled at geometry.

"We think these people didn't have scientific minds but first and foremost they were astronomers and cosmologists," John Matineau, the editor of the book, told the Telegraph. "They were studying long and difficult to understand cycles and they knew about these when they started planning sites like Stonehenge."

dryriver shares a report from the BBC: Celebrated inventor and physicist Nikola Tesla swore by toe exercises -- every night, he'd repeatedly "squish" his toes, 100 times for each foot, according to the author Marc J Seifer. While it's not entirely clear exactly what that exercise involved, Tesla claimed it helped to stimulate his brain cells. The most prolific mathematician of the 20th Century, Paul Erdos, preferred a different kind of stimulant: amphetamine, which he used to fuel 20-hour number benders. When a friend bet him $500 that he couldn't stop for a month, he won but complained "You've set mathematics back a month." Newton, meanwhile, bragged about the benefits of celibacy. When he died in 1727, he had transformed our understanding of the natural world forever and left behind 10 million words of notes; he was also, by all accounts, still a virgin (Tesla was also celibate, though he later claimed he fell in love with a pigeon). It's common knowledge that sleep is good for your brain -- and Einstein took this advice more seriously than most. He reportedly slept for at least 10 hours per day -- nearly one and a half times as much as the average American today (6.8 hours). But can you really slumber your way to a sharper mind? Many of the world's most brilliant scientific minds were also fantastically weird. From Pythagoras' outright ban on beans to Benjamin Franklin's naked "air baths," the path to greatness is paved with some truly peculiar habits.

An anonymous reader writes "The tallest building in the United States is set to become a soaring vertical solar farm, as Pythagoras Solar just launched a project to emblazon the building's glass façade with transparent photovoltaic panels. The new windows, dubbed high power density photovoltaic glass units, are a clever hybrid technology that lays a typical monocrystalline silicon solar cell horizontally between two layers of glass to form an individual tile. An internal plastic reflective prism directs angled sunlight onto the solar cells but allows diffuse daylight and horizontal light through. The high-profile project will begin on the south side of the 56th floor and could grow up to 2 MW in size — which is comparable to a 10-acre field of solar panels."

brothke writes "Imagine for a moment what his novels would read like if Dan Brown got his facts correct. The challenge Brown and similar authors face is to write a novel that is both compelling and faithful to the facts. In Tetraktys, author Ari Juels is able to weave an interesting and readable story, and stay faithful to the facts. While Brown seemingly lacks the scientific and academic background needed to write such fiction, Juels has a Ph.D. in computer science from Berkeley and is currently the Chief Scientist and director at RSA Laboratories, the research division of RSA Security." Read below for the rest of Ben's review.

54mc writes "The BBC reports that Dr. James Anderson, of the University of Reading, has finally conquered the problem of dividing by zero. His new number, which he calls "nullity" solves the 1200 year old problem that niether Newton nor Pythagoras could solve, the problem of zero to the zero power. Story features video (Real Player only) of Dr. Anderson explaining the "simple" concept."

David Halprin writes with a review of a new (and mighty odd sounding) mathematics book: "In my humble opinion, we have an unjustified polemic in the world of mathematics, yet again. My background is tertiary level mathematics and concomitant research in specialised areas, so when a friend e-mailed me the link to this book, I was so excited after reading the author's hype, that I ordered a pre-publication copy. My expectations have not been met, unfortunately, hence my analysis precipitated this review." Read on for Halprin's idiosyncractic take on Norman John Wildberger's Divine Proportions: Rational Trigonometry to Universal Geometry.

danila (Danila Medvedev) writes "'Gnothi seauton' was the precept inscribed in gold letter upon the temple of the Oracle of Delphi. The authorship of this famous maxim was ascribed to every great Greek philosopher, from Pythagoras to Socrates. According to Juvenal, this precept descended from heaven. It is immensely strange, then, that most people, including you, my dear reader, never really make the effort to 'know thyself.' The number of misconceptions, superstitions and myths that we spread about ourselves is indeed astonishing. Fortunately for you, someone else has already taken the time to understand you and present the results in entertaining, easily digestible, but at the same time scientifically rigorous format. Let me introduce Mapping the Mind by Rita Carter, an illustrated user manual to the software that runs inside our skulls -- the human mind." Read on for the rest of Medvedev's review.

An anonymous reader writes "The unknown Newton -- The genius who gave us three laws of motion wrote even more about the Apocalypse and the Whore of Babylon. Eventually, all of his work -- about 10 million words -- will be on the Web. Quote from the article: 'Yet if we go by sheer word count, physics was only one of Newton's intellectual priorities. He devoted more time to what we would now regard as non-scientific topics such as theology and alchemy, writing treatise after treatise on early church history and biblical prophecy.' An interesting note on Pythagoras and religion too. Should we consider ourselves 'Natural Philosphers' instead of Scientists?" Neal Stephenson fans may find this article a nice adjunct to Quicksilver.

Chris Cowell-Shah writes "If David Foster Wallace can't explain infinity to us, nobody can. At least, that's what I told myself while anxiously waiting for his Everything and More: A Compact History of Infinity. The book promised to be an intellectual history of the mathematical concept of infinity, with heavy doses of history, math, and philosophy. And while it proves heavy going at times, I'm pleased to say that it delivers admirably on this promise." Read on for Cowell-Shah's lengthy review of Everything and More.

raceBannon writes "The book surprised and fascinated me. I thought it was going to be solely about the Golden Ratio. Mario Livio does cover the topic but along the way he throws in some mathematical history and even touches on the idea that math may not be a universal concept spread across the galaxy." Read on for the rest of raceBannon's review.

Internet Ninja asks: "After only doing mathematics in high school level and in my first year of University, I've suddenly developed an interest in mathematics. Since that was now almost 10 years ago I'm a little rusty. Anything past pythagoras is a little tough for me :) but I know I could get back up to speed quickly. I could probably steal my daughters math textbooks and start reading but I'm wondering if there is a better way. I considered a part-time University paper at US$495 each and you need to do two as bridging courses in order to even start on undergraduate courses. A bit pricey when you have a home and family to look after as well. Another option was a night courses but I'm kept pretty busy with work. Does anyone have any advice or good resources?"

cybrpnk2 writes: "The story is one of epic proportions: Boy genius gets PhD from Cal Tech at age 20, is the youngest recipient ever of the MacArthur Foundation Genius Grant, writes the Mathematica simulation software used by millions of people, makes millions of dollars in the process, becomes enticed by the seductive lure of the Game of Life, and goes into a decade of seclusion to discover the secrets of the universe. You can catch up on the resulting speculation and hype here. The years of anticipation and publication delays came to an end Tuesday, May 14, 2002 with Stephan Wolfram's release of his opus, A New Kind of Science." Read on for cybrpnk2's review of Wolfram's much-heralded work.