Imagine a one-celled organism the size of a mango. It's not science fiction, but fact: scientists have cataloged dozens of giant one-celled creatures, around 4 inches (10 centimeters), in the deep abysses of the world's oceans. But recent exploration of the Mariana Trench has uncovered the deepest record yet of the one-celled behemoths, known as xenophyophores.
Xenophyophores are the largest known single cells, and have been found in great abundance on the sea floor. But given their fragility and deep-water lives, they are incredibly difficult to study and much of their natural history remains mysterious to scientists.
"As one of very few taxa found exclusively in the deep sea, the xenophyophores are emblematic of what the deep sea offers. They are fascinating giants that are highly adapted to extreme conditions but at the same time are very fragile and poorly studied," explains Lisa Levin, director of the Scripps Center for Marine Biodiversity and Conservation. "These and many other structurally important organisms in the deep sea need our stewardship as human activities move to deeper waters."
March 14 is Pi Day, 3-14! Daniel Tammet painted this picture of how he sees the first 20 digits of pi. He set the European record for memorizing and reciting digits in 2004.
In Daniel Tammet's mind, three is a dotted green crescent moon shape, one is a sort of white sunburst and four is a blue boomerang. Every number has a distinct color and shape, making the number pi, which begins with 3.14, unfold like a beautiful poem.
For math enthusiasts around the world, March 14 (3-14) is Pi Day, honoring the number pi, which is the ratio of circumference to diameter of a circle. On Thursday, Tammet is promoting France's first Pi Day celebration at the Palace of Discovery science museum in Paris.
Tammet's relationship to this number is special: At age 25, he recited 22,514 digits of pi from memory in 2004, scoring the European record. For an audience at the Museum of the History of Science in Oxford, he said these numbers aloud for 5 hours and 9 minutes. Some people cried -- not out of boredom, but from sheer emotion from his passionate delivery.
"What my brain was doing was inventing a meaning, like a story," Tammet said. "What I did was make a poem or a novel out of pi, and took those colors and those emotions and used them to perceive patterns, or at least to perceive patterns in my mind that were memorable, that were meaningful to me."
Many people around the world have been interested enough in this number, or in memorization itself, to see how many digits they can bank. Pi has infinitely many digits with no discernible pattern, yet it mathematically explains the shape of all circles. This makes memorizing it a difficult, yet somehow meaningful, challenge. Serious pi memorizers such as Tammet have become fascinating subjects of study for scientists, too. They bring up fundamental questions about innate ability vs. learned skills. Are the brains of people with superior memory somehow different? Or can anyone learn thousands of random digits?
Superior memorizers, according to the research of K. Anders Ericsson, professor of psychology at Florida State University, have three special skills. They use knowledge and patterns that they already know to encode information in their long-term memory. They associate that information with retrieval cues, so that they can trigger the information again. They also get faster at all this by becoming better at encoding and retrieval through intense practice and effort.
This theory appears to explain Chao Lu, who set the current world record for pi recitation at 67,890 digits in 2005, at age 23. Creating associated meanings in numbers played a big part of that. He used mnemonics relating to the sounds of numbers as well as the shapes or meanings of particular digits and images, according to a 2009 study by Ericsson and colleagues.
Strangely, if presented with one number at a time, at one digit per second, Lu's recall is no better than the average person's, Ercisson and colleagues found. With that rate of presentation of numbers, he is forced to rehearse numbers in his head just like everyone else, Ericsson said.
But with large blocks of numbers, it's a different story. Lu and a previous pi-memorizing record holder, Hideaki Tomoyori, who recited 40,000 digits of pi, have said they linked words or images to groups of two, three or four numbers. Then they created stories connecting them. Tomoyori practiced daily, spending between 9,000 and 10,000 hours total memorizing before his recitation.
A rare case was Rajan Mahadevan, who set a record at 31,811 digits of pi and did not report using any mnemonics. When tested by researchers, it appeared he sequentially memorized numbers in blocks of 10. While some argued that Mahadevan may have an innate ability to memorize, Ericsson and colleagues found in their experiments with Mahadevan that he learned his unusual methods for memorizing numerical patterns after a thousand hours of practice.
New results of a numerical search for periodic orbits of three equal masses moving in a plane under the influence of Newtonian gravity, with zero angular momentum have been found. A topological method is used to classify periodic three-body orbits into families, which fall into four classes, with all three previously known families belonging to one class. The classes are defined by the orbits geometric and algebraic symmetries. In each class the researchers present a few orbits initial conditions, 15 in all; 13 of these correspond to distinct orbits.
A multimedia feature published this week in the New York Times, “Pushing Science’s Limits in Sign Language Lexicon,” outlines efforts in the United States and Europe to develop sign language versions of specialized terms used in science, technology, engineering and mathematics
Calculations show that the weight of large support structures can be dramatically reduced if their design consists of patterns that are the same at large scales as at the tiniest scales.
Earlier this month, on a nice day, Felix Baumgartner jumped from 39,045 meters, or 24.26 miles, above the Earth from a capsule lifted by a 334-foot-tall helium filled balloon (twice the height of Nelson’s column and 2.5 times the diameter of the Hindenberg). Wolfram|Alpha tells us the jump was equivalent to a fall from 4.4 Mount Everests stacked on top of each other, or falling 93% of the length of a marathon. At 24.26 miles above the Earth, the atmosphere is very thin and cold, only about -14 degrees Fahrenheit on average. The temperature, unlike air pressure, does not change linearly with altitude at such heights. As Wolfram|Alpha shows us, it rises and falls depending on factors such as the decreased density of air with rising altitude, but also the absorption of UV light by the ozone layer.
Remember the first time you saw a Möbius strip (the ring-shaped surface with only one side) and it felt like your world had been turned upside down? The hexaflexagon tends to have a similar effect. Only more so. In this video Vi Hart presents the topologically fascinating hexaflexagon. First discovered in the 1930s by a daydreaming student named Arthur H. Stone, flexagons have attracted the curiosity of great scientists for decades, including Stone's friend and physicist Richard Feynman. Here, Vi Hart introduces the folding, pinching, rotating, multifaceted geometric oddity with her signature brand of rapid-fire wit and exposition. She even shows you how to make your own.
A pair of mathematicians -- one from Indiana University and the other from Sichuan University in China -- have proposed a unified theory of dark matter and dark energy that alters Einstein's equations describing the fundamentals of gravity.
Shouhong Wang, a professor in the IU College of Arts and Sciences' Department of Mathematics, and Tian Ma, a professor at Sichuan University, suggest the law of energy and momentum conservation in spacetime is valid only when normal matter, dark matter and dark energy are all taken into account. For normal matter alone, energy and momentum are no longer conserved, they argue.
While still employing the metric of curved spacetime that Einstein used in his field equations, the researchers argue the presence of dark matter and dark energy -- which scientists believe accounts for at least 95 percent of the universe -- requires a new set of gravitational field equations that take into account a new type of energy caused by the non-uniform distribution of matter in the universe. This new energy can be both positive and negative, and the total over spacetime is conserved, Wang said.
Using existing programming tools, writing high-performance image processing code requires sacrificing readability, portability, and modularity. This is a consequence of conflating what computations define the algorithm, with decisions about storage and the order of computation. These latter two are the schedule, including choices of tiling, fusion, recomputation vs. storage, vectorization, and parallelism.
The Halide team proposes a representation for feed-forward imaging pipelines that separates the algorithm from its schedule, enabling high-performance without sacrificing code clarity. This decoupling simplifies the algorithm specification: images and intermediate buffers become functions over an infinite integer domain, with no explicit storage or boundary conditions. Imaging pipelines are compositions of functions. Programmers separately specify scheduling strategies for the various functions composing the algorithm, which allows them to efficiently explore different optimizations without changing the algorithmic code.
The power of this representation can be demonstrated by expressing a range of image processing applications in an embedded domain-specific language called "Halide", and compiling them for ARM, x86, and GPUs. Our compiler targets SIMD units, multiple cores, and complex memory hierarchies. This system can handle algorithms such as a camera raw pipeline, the bilateral grid, fast local Laplacian filtering, and image segmentation. The algorithms expressed in the Halide language are both shorter and faster than state-of-the-art implementations.
In 1949 the mathematician D. R. Kaprekar from Devlali, India, devised a process now known as Kaprekar's operation. First choose a four digit number where the digits are not all the same (that is not 1111, 2222,...). Then rearrange the digits to get the largest and smallest numbers these digits can make. Finally, subtract the smallest number from the largest to get a new number, and carry on repeating the operation for each new number.
Fractals are split in to parts of geometric shapes, patterns and scaling. These fractals are designed using Apophysis, Photoshop and Paintshop Pro. Enjoy these unforgettable 3D fractals -- you will remember them for a long time.
The Golden Ratio can be illustrated within special dimensions of Sprials, Triangles and Rectangles where the ratio of the length of the short side to the long side is .618, was noted by ancient Greek architects as the most visually pleasing rectangle and its dimensions were used to construct buildings such as the Parthenon.
The Golden Ratio has also been used extensively in classical paintings where it was believed to produce the most visually pleasing figures. The ratio also appears all over nature, such as the number of petals on some flowers, biological forms like the nautilus shell, mollusks, animal antlers, leaves, human proportions, galaxy spirals, and the relations between harmonious tones in music.
Dive down deep into the infinite world of fractals. An epic journey across the Mandelbrot set, exploring many different embedded Julia sets. This video can be watched fullscreen in 720p HD. Designed and rendered using FractalNet, a distributed fractal renderer.
STATS FOR THIS VIDEO: Total iterations: 104,066 billion. Average iterations per frame: 6.69 billion. Render time: 14 days 13 hours 6 minutes. Average render time per frame: 1 minute 21 seconds. Average rendering rate: 82.8 million iterations/second. Deepest zoom: 400 billion times magnification (2.5E-12 view width).
An origami fractal made out of nearly 50,000 business cards is the first physical representation of the Mosely Snowflake three-dimensional fractal in the world. The sculpture was put together by more than 300 students and volunteers at the University of Southern California.
"Our community has brought this object into being for the first time,” said Catherine Quinlan, Dean of USC Libraries. “Before this project, this beautiful and enigmatic fractal existed only digitally and in the imaginations of mathematicians and artists.”
In mathematics, there's a little more to the concept of the fractal than the psychedelic computer-generated imagery with which we're all familiar. According to mathematician and "father of fractal geometry," Benoit Mandelbrot, a fractal is "a set for which the Hausdorff Besicovich dimension strictly exceeds the topological dimension."
Mandelbrot's definition is a little like ancient parchment: very difficult to illuminate without committing vandalism, in this case to the subtlety and complexity of the idea. What's crucial is a property of the fractal that, actually, the computer visuals are rather adept at visualizing: their self-similarity at different scales. Get close up and what you'll see will strongly resemble the whole. The same is true of 3D fractals, physically manifest or otherwise.
The Mosely Snowflake fractal was discovered in 2006 by engineer and origami practitioner Jeannine Mosely, whose construction of the Menger Sponge fractal that same year (also out of business cards ... 66,000 of them) received widespread attention. The Menger Sponge was the first 3D fractal to be discovered, by Karl Menger in 1926.
If fractals had DNA, the Menger Sponge and the Mosely Snowflake would share an awful lot, but where the Menger Sponge is built from, and results in, cube shapes, the Mosely Snowflake generates broadly-hexagonal snowflake-like forms.
The quest by a group of math geeks to create a three-dimensional analogue for the mesmerizing Mandelbrot fractal has ended in success.
They call it the Mandelbulb. The 3-D renderings were generated by applying an iterative algorithm to a sphere. The same calculation is applied over and over to the sphere’s points in three dimensions. In spirit, that’s similar to how the original 2-D Mandelbrot set generates its infinite and self-repeating complexity.
The following images are worth a look. Each photo is a zoom on one of these Mandelbulbs. Daniel White, the amateur fractal image maker who coordinated the Mandelbulb effort, admits this creation isn’t exactly the Mandelbrot in 3-D. It’s mesmerizing and beautiful, but as he notes, only some versions of their original formula generate the kind of detail and complexity they are looking for. Their original equation doesn’t work very well unless you take it beyond the 2nd power. The picture above, White says, doesn’t have the level of detail that should be there.
“That means the biggest secret is still under wraps, open to anyone who has the inclination, and appreciation for how cool this thing would look,” White wrote on his website.
On January 25th at 23:30:26 UTC, the largest known prime number, 257,885,161-1, was discovered on Great Internet Mersenne Prime Search (GIMPS) volunteer Curtis Cooper's computer. The new prime number, 2 multiplied by itself 57,885,161 times, less one, has 17,425,170 digits. With 360,000 CPUs peaking at 150 trillion calculations per second, 17th-year GIMPS is the longest continuously-running global "grassroots supercomputing" project in Internet history.
Dr. Cooper is a professor at the University of Central Missouri. This is the third record prime for Dr. Cooper and his University. Their first record prime was discovered in 2005, eclipsed by their second record in 2006. Computers at UCLA broke that record in 2008 with a 12,978,189 digit prime number. UCLA held the record until University of Central Missouri reclaimed the world record with this discovery. The new primality proof took 39 days of non-stop computing on one of the university's PCs. Dr. Cooper and the University of Central Missouri are the largest individual contributors to the project. The discovery is eligible for a $3,000 GIMPS research discovery award.
To prove there were no errors in the prime discovery process, the new prime was independently verified using different programs running on different hardware. Serge Batalov ran Ernst Mayer's MLucas software on a 32-core server in 6 days (resource donated by Novarti] IT group) to verify the new prime. Jerry Hallett verified the prime using the CUDALucas software running on a NVidia GPU in 3.6 days. Finally, Dr. Jeff Gilchrist verified the find using the GIMPS software on an Intel i7 CPU in 4.5 days and the CUDALucas program on a NVidia GTX 560 Ti in 7.7 days.
GIMPS software was developed by founder, George Woltman, in Orlando, Florida. Scott Kurowski, in San Diego, California, wrote and maintains the PrimeNet system that coordinates all the GIMPS clients. Volunteers have a chance to earn research discovery awards of $3,000 or $50,000 if their computer discovers a new Mersenne prime. GIMPS' next major goal is to win the $150,000 award administered by the Electronic Frontier Foundation offered for finding a 100 million digit prime number.
Nasa's Voyager spacecraft have enthralled everyone with their exploits at the edge of the Solar System, but their launch in 1977 was only possible because of some clever maths and the persistence of a PhD student who worked out how to slingshot probes into deep space.
On the 3 October, 1942, the nose cone of an early V2 test rocket soared high above the north German coast before falling back to a crash-landing in the Baltic Sea. For the first time in history, an object built by humans had crossed the invisible Karman line, which marks the edge of space. Astonishingly, within 70 years - just one human lifespan - we'd hurled another spacecraft right to the edge of the Solar System. Today, 35 years after leaving Earth, Voyager 1 is 18.4 billion km (11.4 billion miles) from Earth and about to cross over the boundary marking the extent of the Sun's influence, where the solar wind meets interstellar space. Sometime in the next five years, it will likely break through this so called "bowshock" and head out into the galaxy beyond. Its twin, Voyager 2, having flown past all the outer giant planets, should pass over into interstellar not long after.
Going back in time, in 1957, as Sputnik 1 became the first engineered object to orbit our home planet, mission planners started to look towards other worlds to propel their probes. At that time, Nasa couldn't guarantee a spacecraft for more than a few months of operational life, and so the outer planets were considered out of reach. That was until a 25-year-old mathematics graduate called Michael Minovitch came along in 1961. Excited by UCLA's new IBM 7090 computer, the fastest on Earth at the time, Minovitch decided to take on the hardest problem in celestial mechanics: the "three body problem". Astronomers had been pondering the three-body problem for at least 300 years, ever since they'd started plotting the path that comets took as they fell through the inner Solar System towards the Sun. Undeterred by the fact that some of the finest minds in history, including Isaac Newton hadn't solved the three-body problem, Minovitch became focused on cracking it. He intended to use the IBM 7090 computer to home in on a solution using a method of iteration.
Using a solution to the three-body problem, a single mission, launching from Earth in 1977, could sling a spacecraft past all four planets within 12 years. Such an opportunity would not present itself again for another 176 years. With further lobbying from Minovitch and high level intervention from Maxwell Hunter, who advised the president on US space policy, Nasa eventually embraced Minovitch's slingshot propulsion and Flandro's idea for a "grand tour" of the planets.
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.
The ABC conjecture, proposed independently by the mathematicians David Masser and Joseph Oesterle in 1985 but not proven by them, involves the concept of square-free numbers, or numbers that cannot be divided by the square of any number. (A square number is the product of some integer with itself).
Mochizuki, a mathematician at Kyoto University, has proved extremely deep theorems in the past, lending credence to his claim that he has the proof for ABC.
The most difficult known Sudoku puzzle has 'Richter scale' rating of 3.6, according to a new mathematical description of puzzle hardness. But there could be harder puzzles out there. Sudoku puzzles are generally classified as easy, medium or hard with puzzles having more starting clues generally but not always easier to solve. But quantifying the difficulty mathematically is hard.
Now Ercsey-Ravasz and Toroczkai say they've worked out a way to do it using algorithmic complexity theory. They point out that it's easy to design an algorithm that solves Sudoku by testing every combination of digits to find the one that works. That kind of brute force solution guarantees you an answer but not very quickly. Instead, algorithm designers look for cleverer ways of finding solutions that exploit the structure and constraints of the problem. These algorithms and their behaviour are are more complex but they get an answer more quickly. The central point of Ercsey-Ravasz and Toroczkai argument is that because an algorithm reflects the structure of the problem, its behaviour--the twists and turns that it follows through state space--is a good measure of the difficulty of the problem.
Methods for super-resolution (SR) can be broadly classified into two families of methods: (i) The classical multi-image super-resolution (combining images obtained at subpixel misalignments), and (ii) Example-Based super-resolution (learning correspondence between low and high resolution image patches from a database). This approach here is based on the observation that patches in a natural image tend to redundantly recur many times inside the image, both within the same scale, as well as across different scales. Recurrence of patches within the same image scale (at subpixel misalignments) gives rise to the classical super-resolution, whereas recurrence of patches across different scales of the same image gives rise to example-based super-resolution. The approach taken here attempts to recover at each pixel its best possible resolution increase based on its patch redundancy within and across scales.
In words: (capital) Psi equals the integral of e raised to the quantity of i over h-bar multiplied by the integral of R over 16 pi G minus F squared plus psi bar i D psi minus lambda phi psi bar psi plus the absolute value of D psi squared minus V phi.
'It seems like Nature has some secret that lets it make complicated stuff in an effortless way,' Stephen Wolfram recently told an audience at Oxford University’s Mathematical Institute. In his talk, Wolfram, the scientist behind Mathematica and Wolfram Alpha, explored how advances in computation could benefit mathematics.
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