Fields medallist: How Rubik's cube inspired new maths - opinion - 13 August 2014 - New Scientist

Fields medallist: How Rubik's cube inspired new maths - opinion - 13 August 2014 - New Scientist

Physicists eye neural fly data, find formula for Zipf's law

Physicists eye neural fly data, find formula for Zipf's law: ...George Zipf... found that if you rank words in a language in order of their popularity, a strange pattern emerges: The most popular word is used twice as often as the second most popular, and three times as much as the third-ranked word, and so on. This same rank vs. frequency rule was also found to apply to many other social systems...

"We showed mathematically that the system becomes Zipfian when you're recording the activity of many units, such as neurons, and all of the units are responding to the same variable," Nemenman says. "The fact that Zipf's law will occur in a system with just 40 or 50 such units shows that biological units are in some sense special – they must be adapted to the outside world."

Seeker, Doer, Giver, Ponderer - NYTimes.com

Seeker, Doer, Giver, Ponderer - NYTimes.com: James H. Simons... His passion... is basic research — the risky, freewheeling type. He recently financed new telescopes in the Chilean Andes that will look for faint ripples of light from the Big Bang, the theorized birth of the universe.

The afternoon of the interview, he planned to speak to Stanford physicists eager to detect the axion, a ghostly particle thought to permeate the cosmos but long stuck in theoretical limbo.

Quantum theory reveals puzzling pattern in how people respond to some surveys

Quantum theory reveals puzzling pattern in how people respond to some surveys: The survey changed the order in which these questions were asked between respondents and, as expected, there were question-order effects found. When respondents were asked about Clinton first, 49 percent said that both Clinton and Gore were trustworthy. But when respondents were asked about Gore first, 56 percent said that both were trustworthy.

The pattern that quantum theory predicted – and that the researchers found – was that the number of people who switch from "yes-yes" to "no-no" when the question order is reversed must be offset by the number of people who switch in the opposite direction...

The researchers called this phenomenon "quantum question equality." They found it in every one of the surveys studied.

Mathematician unleashes 'a wave of new results' in geometric analysis

Mathematician unleashes 'a wave of new results' in geometric analysis: "If you drive into a parking garage and go up a level, that spiral ramp is part of a helicoid," he says. "And one of the things we were able to show was that every embedded minimal surface could be built out of these things. So the minimal surface either looks like a nice flat thing where the area is bounded, or it looks exactly like one of these double spiral staircases..."

They have been able to prove, he says, that of the infinite number of singularities that could possibly affect a surface through this curvature flow, only two types are stable enough to survive in reality. "If you were to wiggle your surface ever so slightly, in fact only two are stable of the infinitely many that are possible," Minicozzi says. "So if you are trying to understand [mean curvature flow] and you have to deal with all of these cases, it's much better to have to deal with two cases than an infinite number."

A Beautiful Mind: Brain Injury Turns Man Into Math Genius�

A Beautiful Mind: Brain Injury Turns Man Into Math Genius�: Padgett recalls being knocked out for a split second and seeing a bright flash of light...

Soon after the attack... he noticed that everything looked different. He describes his vision as "discrete picture frames with a line connecting them, but still at real speed." If you think of vision as the brain taking pictures all the time and smoothing them into a video, it's as though Padgett sees the frames without the smoothing. In addition, "everything has a pixilated look," he said.

Carbon, Avogadro's Constant and the Importance of the Number 12 | MIT Technology Review

Carbon, Avogadro's Constant and the Importance of the Number 12 | MIT Technology Review: He says that a practical solution is to choose a number that is divisible by 12 so that a whole number of carbon-12 atoms are equal to the mass of a gram, at least to a first approximation...

His idea is to define Avogadro’s constant in terms of a number of hexagonal sheets of graphite piled on top of each other to form a hexagonal prism...

He suggests that if this number—the number of layers and the number of atoms along each hexagonal edge—was equal to 51,150,060, then the total would be 602,214,158,510,196,804,982,800 atoms.

Impossible Cookware and Other Triumphs of the Penrose Tile - Issue 13: Symmetry - Nautilus

Impossible Cookware and Other Triumphs of the Penrose Tile - Issue 13: Symmetry - Nautilus: One of the curious aspects of aperiodic division of the plane is that information about positioning is somehow communicated across great distances—a Penrose tile placed in one position prevents the placement of other pieces hundreds (and thousands and millions) of tiles away. “Somehow a local constraint imposes a global constraint,” says Harriss. “You impose that at no scale will these tiles give you something that is periodic..."

It turns out crystals don’t always form atom-by-atom. “In very complex intermetallic compounds, the units are huge. It’s not local,” says Shechtman. When large chunks of crystal form at once, rather than through gradual atom accretion, atoms that are far apart can affect one another’s position, exactly as do Penrose tiles.

Video: New Shape Born From Rubber Bands | Science/AAAS | News

Video: New Shape Born From Rubber Bands | Science/AAAS | News: In an attempt to create a spring that replicates the light-bending properties of cuttlefish ink sacs, a team of researchers suspended two rubber strips of different lengths. Connecting the bottoms of the two strips to a cup of water, the shorter band stretched to the same length as the longer one. After gluing the two stretched strips together, the researchers gradually drained the water from the cup. As the bands retracted and twisted from the reduced strain, the researchers were shocked to see a hemihelix with multiple perversions form...

Game of primes ends as mathematics gets too difficult - physics-math - 23 April 2014 - New Scientist

Game of primes ends as mathematics gets too difficult - physics-math - 23 April 2014 - New Scientist:
The twin prime conjecture posits that there are an infinite number of pairs of primes separated by two, such as 3 and 5. In May 2013, Yitang Zhang at the University of New Hampshire in Durham made the first major progress by proving that there are an infinite number of prime pairs separated by at most 70 million.

Since then, researchers have been advancing his methods to find prime pairs separated by smaller intervals...

In a few weeks they had reduced the gap to just under 5 million, and today it stands at 246. In theory, the methods used could find gaps as small as six, but the researchers say they have reached a point of diminishing returns.

A Mathematical Proof That The Universe Could Have Formed Spontaneously From Nothing — The Physics arXiv Blog — Medium

A Mathematical Proof That The Universe Could Have Formed Spontaneously From Nothing — The Physics arXiv Blog — Medium: The new proof is based on a special set of solutions to a mathematical entity known as the Wheeler-DeWitt equation...

In each of these cases, they find a solution in which the bubble can expand exponentially and thereby reach a size in which a universe can form—a Big Bang...

Prime number enigma could be solved by simple networks - physics-math - 03 March 2014 - New Scientist

Prime number enigma could be solved by simple networks - physics-math - 03 March 2014 - New Scientist:

To investigate, Marián Boguñá of the University of Barcelona, Spain, and his colleagues turned the numbers from 2 to 1 billion into a network by linking composites to their prime building blocks. They also devised a way to generate similar networks using other simple rules to link the numbers, and wondered if they could get these networks to reproduce the pattern of links between primes and composites.

Their rules depend on probabilities, so the generated networks are different each time. On average, the researchers found that the webs are very close to the real network of primes and composites...

After 400 years, mathematicians find a new class of solid shapes

After 400 years, mathematicians find a new class of solid shapes: During the imagined bulging process, even one that involves replacing the bulge with multiple hexagons, as Craven points out, there will be formation of internal angles. These angles formed between lines of the same faces – referred to as dihedral angle discrepancies – means that, according to Schein and Gayed, the shape is no longer a polyhedron. Instead they claimed to have found a way of making those angles zero, which makes all the faces flat, and what is left is a true convex polyhedron...

First light-bending calculator designed with metamaterials - physics-math - 09 January 2014 - New Scientist

First light-bending calculator designed with metamaterials - physics-math - 09 January 2014 - New Scientist: The metamaterial computer works because light waves can draw mathematical curves in space, akin to a graph. In calculus, differentiation describes the slope of that curve at various points, while integration gives the area under the curve.

The team's metamaterial block can perform these calculations by modifying the light wave's profile. For example, if you shine a light wave describing a parabola (which corresponds to the equation y = x2) into a metamaterial that computes differentiation, it will come out the other side looking like a straight line described by y = 2x.siu

Mathematical study of photosynthesis clears the path to developing new super-crops

Mathematical study of photosynthesis clears the path to developing new super-crops: Around three per cent of all plants use an advanced form of photosynthesis, which allows them to capture more carbon dioxide, use less water, and grow more rapidly. Overall this makes them over 50% more efficient than plants that use the less efficient form.

Physicists Discover Geometry Underlying Particle Physics | Simons Foundation

Physicists Discover Geometry Underlying Particle Physics | Simons Foundation: The amplituhedron looks like an intricate, multifaceted jewel in higher dimensions. Encoded in its volume are the most basic features of reality that can be calculated, “scattering amplitudes,” which represent the likelihood that a certain set of particles will turn into certain other particles upon colliding.

Rota's Conjecture: Researcher solves 40-year-old math problem

Rota's Conjecture: Researcher solves 40-year-old math problem: Rota's Conjecture relates to a specialised area of mathematics known as matroid theory, a modern form of geometry, which Geoff specialises in.
Rather than focusing on distance and angles, matroid theory investigates properties of structures which don't change under projection—for example, whether or not three points are always on a line, or four points are on a plane.
The theory investigates geometric structures that can be completely different from those in our world, and Rota's Conjecture is a way of using mathematics to recognise these alternative structures.

How to Build a Time Cloak with Mirrors | MIT Technology Review

How to Build a Time Cloak with Mirrors | MIT Technology Review:  His idea is to use one set of mirrors to divert light through an extra distance before it reaches the clock and another set of mirrors that diverts light through a similar distance after it has hit the clock.

This extra distance essentially slows down the lights before it hits the clock. After it has been reflected, the light can be speeded up by avoiding the diversion so that it does not travel the extra distance.

Math Advances Raise the Prospect of an Internet Security Crisis | MIT Technology Review

Math Advances Raise the Prospect of an Internet Security Crisis | MIT Technology Review: “Our conclusion is there is a small but definite chance that RSA and classic Diffie-Hellman will not be usable for encryption purposes in four to five years..."

 ...it is possible that algorithms able to solve the discrete logarithm problem quickly could exist...

...French academic Antoine Joux published two papers that suggest such an algorithm could be found before long...

When fluid dynamics mimic quantum mechanics | KurzweilAI

When fluid dynamics mimic quantum mechanics | KurzweilAI: In the experiments reported in PRE, the researchers mounted a shallow tray with a circular depression in it on a vibrating stand. They filled the tray with a silicone oil and began vibrating it at a rate just below that required to produce surface waves.

They then dropped a single droplet of the same oil into the bath. The droplet bounced up and down, producing waves that pushed it along the surface.

The waves generated by the bouncing droplet reflected off the corral walls, confining the droplet within the circle and interfering with each other to create complicated patterns. As the droplet bounced off the waves, its motion appeared to be entirely random, but over time, it proved to favor certain regions of the bath over others...

The statistical description of the droplet’s location is analogous to that of an electron confined to a circular quantum corral and has a similar, wavelike form.