Were the succession of stars endless, then the background of the sky would present us a uniform luminosity, like that displayed by the Galaxy - since there could be absolutely no point, in all that background, at which would not exist a star. The only mode, therefore, in which, under such a state of affairs, we could comprehend the voids, which our telescopes find in innumerable directions, would be by supposing the distance of the invisible background so immense that no ray from it has yet been able to reach us at all.
Suitable Fit
In 1966, Austrian mathematician Leo Moser asked a pleasingly practical question: If a corridor is 1 meter wide, what’s the largest sofa one could squeeze around a corner? That was 46 years ago, and it’s still an open question. In 1968 Britain’s John Michael Hammersley showed that a sofa shaped somewhat like a telephone receiver could make the turn even if its area were more than 2 square meters (above). In 1992 Joseph Gerver improved this a bit further, but the world’s tenants await a definitive solution. Similar problems concern moving ladders and pianos. Perhaps what we need are wider corridors.
Benham’s Top
Shuttles Come Nose-to-Nose
NASA's space shuttles Endeavour and Atlantis switched locations today at Kennedy Space Center in Florida, and in the process came "nose-to-nose" for the last time in front of Orbiter Processing Facility 3.
Endeavour was moved from Orbiter Processing Facility 2 to the Vehicle Assembly Building where it will be housed temporarily until its targeted departure from Kennedy atop the Shuttle Carrier Aircraft in mid-September. After a stop at the Los Angeles International Airport, Endeavour will move in mid-October to the California Science Center for permanent public display.
Now in the processing facility after leaving the Vehicle Assembly Building, shuttle Atlantis will undergo preparations for its move to the Kennedy Space Center Visitor Complex in November, with a grand opening planned for July 2013.
From Pedro A. Pisa in Scripta Mathematica, September 1954 — this identity:
1234 + 2484 + 3674 = 1254 + 2444 + 3694
… remains valid when the digits in each term are permuted in the same way:
1234 + 2484 + 3674 = 1254 + 2444 + 3694
1243 + 2448 + 3647 = 1245 + 2444 + 3649
1324 + 2844 + 3764 = 1524 + 2444 + 3964
1342 + 2844 + 3746 = 1542 + 2444 + 3946
1423 + 2448 + 3467 = 1425 + 2444 + 3469
1432 + 2484 + 3476 = 1452 + 2444 + 3496
2134 + 4284 + 6374 = 2154 + 4244 + 6394
2143 + 4248 + 6347 = 2145 + 4244 + 6349
2314 + 4824 + 6734 = 2514 + 4424 + 6934
2341 + 4842 + 6743 = 2541 + 4442 + 6943
2413 + 4428 + 6437 = 2415 + 4424 + 6439
2431 + 4482 + 6473 = 2451 + 4442 + 6493
3124 + 8244 + 7364 = 5124 + 4244 + 9364
3142 + 8244 + 7346 = 5142 + 4244 + 9346
3214 + 8424 + 7634 = 5214 + 4424 + 9634
3241 + 8442 + 7643 = 5241 + 4442 + 9643
3412 + 8424 + 7436 = 5412 + 4424 + 9436
3421 + 8442 + 7463 = 5421 + 4442 + 9463
4123 + 4248 + 4367 = 4125 + 4244 + 4369
4132 + 4284 + 4376 = 4152 + 4244 + 4396
4213 + 4428 + 4637 = 4215 + 4424 + 4639
4231 + 4482 + 4673 = 4251 + 4442 + 4693
4312 + 4824 + 4736 = 4512 + 4424 + 4936
4321 + 4842 + 4763 = 4521 + 4442 + 4963
And everything above holds true if each term is squared.
Probability
Imagine two concentric roulette wheels, each divided into 100 sectors. Choose 50 sectors at random on each wheel, paint them black, and paint the rest white. Prove that we can now position the wheels so that at least 50 of the aligned sectors match.
Ans:
Follow a sector on the inner wheel through a complete revolution: That sector will find exactly 50 matches. The same is true for each of the 100 sectors on the wheel; altogether, as the wheel turns through 100 positions, there will be 100 × 50 = 5,000 matches. This means that the average number of matches per position is 50, so there must be at least one position with 50 matches.
The Hustle and Bustle of Our Solar System
This diagram illustrates the differences between orbits of a typical near-Earth asteroid (blue) and a potentially hazardous asteroid, or PHA (orange). PHAs are a subset of the near-Earth asteroids (NEAs) and have the closest orbits to Earth's orbit, coming within 5 million miles (about 8 million kilometers). They also are large enough to survive passage through Earth's atmosphere and cause damage on a regional, or greater, scale.
Our yellow sun sits at the center of the crowd, while the orbits of the planets Mercury, Venus and Mars are shown in grey. Earth's orbit stands out in green between Venus and Mars. As the diagram indicates, the PHAs tend to have more Earth-like orbits than the rest of the NEAs. The asteroid orbits are simulations of what a typical object's path around the sun might look like.
The dots in the background are based on data from NASA's NEOWISE, the asteroid-hunting portion of the Wide-field Infrared Survey Explorer (WISE) mission, which scanned the whole sky twice in infrared light before entering hibernation mode in 2011. The blue and orange dots represent a simulation of the population of near-Earth asteroids and PHAs, respectively, which are larger than 330 feet (100 meters).
NEOWISE has provided the best overall look at the PHA population yet, refining estimates of their numbers, sizes, types of orbits and potential hazards. The NEOWISE team estimates that about 20 to 30 percent of the PHAs thought to exist have actually been discovered as may 2012, the date of this image.
Image Credit: NASA/JPL-Caltech
Exploring the Quantum World
Researchers at JPL and Caltech have developed an instrument for exploring the cosmos and the quantum world.
This new type of amplifier boosts electrical signals and can be used for everything from studying stars, galaxies and black holes to exploring the quantum world and developing quantum computers. An amplifier is a device that increases the strength of a weak signal.
One of the key features of the new amplifier is that it incorporates superconductors--materials that allow an electric current to flow with zero resistance when lowered to certain temperatures. For their amplifier, the researchers are using titanium nitride and niobium titanium nitride, which have just the right properties to allow the pump signal to amplify the weak signal.
Although the amplifier has a host of potential applications, the reason the researchers built the device was to help them study the universe. The team built the instrument to boost microwave signals, but the new design can be used to build amplifiers that help astronomers observe in a wide range of wavelengths, from radio waves to X-rays.
The Higgs boson made simple
So what's the Higgs boson, and why are people spending billions of
dollars to find that god-danged subatomic particle? I've rounded up a
variety of resources aimed at showing you why the hunt for the Higgs is a
big deal.
First, a little context: The Higgs particle, and its associated field, were hypothesized back in the 1960s by British physicist Peter Higgs and others to fill a weird gap in the Standard Model, one of physics' most successful theories. The model as it stood had no mechanism to explain why some particles are massless (such as the photon, which is the quantum bit for light and other types of electromagnetic radiation), while other particles have varying degrees of mass (such as the W and Z bosons, which play a part in the weak nuclear force). By rights, all particles should be without mass and zipping around freely.
The Higgs mechanism sets up a field that interacts with particles to endow them with mass, and the Higgs boson is the particle associated with that field — just as photons are associated with an electromagnetic field. For more than four decades, physicists have assumed that the Higgs field existed, but found no experimental evidence for it. It requires a super-powerful particle smasher such as the Large Hadron Collider to produce energies high enough to knock a Higgs boson into existence under controlled conditions.
But the heavy particles created in a collider exist for just an instant before they decay into lighter particles. The LHC's physicists have been looking for particular patterns in the spray of particles that match what they'd expect to see from the decay of the Higgs boson. They've collected data for roughly a quadrillion proton-on-proton collisions, and on Wednesday they'll announce the status of the Higgs search based on those conclusions.
The teams at the LHC's ATLAS and CMS detectors are likely to say they're pretty sure they see a new type of particle with Higgs-like characteristics, but will need more time to nail down those characteristics completely. If that's the case, physicists can then go on to find out if the Higgs mechanism works exactly the way they expected it to, or whether there are unexpected twists. Some of the theories about how the universe is put together are pretty far-out — for example, suggesting that there are several dimensions in space that we can't perceive directly, or that there are huge troops of subatomic particles that we haven't yet discovered. Following the tracks left behind by the Higgs could reveal whether there's any truth to those theories.
Analogies, please!
For decades, experts have been trying to come up with analogies to illustrate how the Higgs mechanism works. One of the best-known was proposed in 1993 by David Miller, a physicist at University College London. Imagine looking down from a balcony in a ballroom, watching a cocktail party below. When just plain folks try to go from one end of the room to the other, they can walk through easily, with no resistance from the party crowd. But when a celebrity like Justin Bieber shows up, other partygoers press around him so tightly that he can hardly move ... and once he moves, the crowd moves with him in such a way that the whole group is harder to stop.
The partygoers are like Higgs bosons, the just plain folks are like massless particles, and Bieber is like a massive Z boson.
The Guardian's Ian Sample demonstrates a variant of this analogy in a 4.5-minute video: Imagine a tray with ping-pong balls scattered on it. The balls roll freely around the empty tray. But then, if you spread a layer of sugar over the tray, the balls sitting on the piled-up sugar don't roll so easily. The grains of sugar introduce a kind of inertial "drag," and that's the kind of effect that the Higgs field supposedly has on particles with mass.
In a 60-second shot of science written for Symmetry magazine, Howard Haber of the University of California at Santa Cruz uses a livelier comparison to a high-speed bullet plowing through a vat of molasses.
What good is it?
Particle physicists try to avoid forecasting the applications of an experimental advance before the actual advance is confirmed, but in the past, advances on a par with the discovery of the Higgs boson have had lots of beneficial applications, and some that are more questionable. The rise of nuclear power and nuclear weaponry is a prime example of that double-edged sword.
The discovery of antimatter is what made medical PET scanning possible, and antimatter propulsion could eventually play a part in interstellar travel, just like on "Star Trek." Particle accelerators have opened the way to medical treatments such as proton eye therapy — as well as advances in materials science, thanks to neutron scattering.
It's
conceivable that the discoveries made at the Large Hadron Collider will
eventually point to new sources of energy, Michio Kaku, a physicist at
City College of New York, told me during a discussion of the LHC's promise and peril.
And if the discovery of the Higgs leads to fresh insights into the
fabric of the universe, it's conceivable that we could take advantage of
the as-yet-unknown weave of that fabric for communication or
transportation. Who knows? Maybe this is how "Star Trek" gets its start.
Courtesy : http://cosmiclog.msnbc.msn.com/_news/2012/07/03/12547980-the-higgs-boson-made-simple?lite
First, a little context: The Higgs particle, and its associated field, were hypothesized back in the 1960s by British physicist Peter Higgs and others to fill a weird gap in the Standard Model, one of physics' most successful theories. The model as it stood had no mechanism to explain why some particles are massless (such as the photon, which is the quantum bit for light and other types of electromagnetic radiation), while other particles have varying degrees of mass (such as the W and Z bosons, which play a part in the weak nuclear force). By rights, all particles should be without mass and zipping around freely.
The Higgs mechanism sets up a field that interacts with particles to endow them with mass, and the Higgs boson is the particle associated with that field — just as photons are associated with an electromagnetic field. For more than four decades, physicists have assumed that the Higgs field existed, but found no experimental evidence for it. It requires a super-powerful particle smasher such as the Large Hadron Collider to produce energies high enough to knock a Higgs boson into existence under controlled conditions.
But the heavy particles created in a collider exist for just an instant before they decay into lighter particles. The LHC's physicists have been looking for particular patterns in the spray of particles that match what they'd expect to see from the decay of the Higgs boson. They've collected data for roughly a quadrillion proton-on-proton collisions, and on Wednesday they'll announce the status of the Higgs search based on those conclusions.
The teams at the LHC's ATLAS and CMS detectors are likely to say they're pretty sure they see a new type of particle with Higgs-like characteristics, but will need more time to nail down those characteristics completely. If that's the case, physicists can then go on to find out if the Higgs mechanism works exactly the way they expected it to, or whether there are unexpected twists. Some of the theories about how the universe is put together are pretty far-out — for example, suggesting that there are several dimensions in space that we can't perceive directly, or that there are huge troops of subatomic particles that we haven't yet discovered. Following the tracks left behind by the Higgs could reveal whether there's any truth to those theories.
Analogies, please!
For decades, experts have been trying to come up with analogies to illustrate how the Higgs mechanism works. One of the best-known was proposed in 1993 by David Miller, a physicist at University College London. Imagine looking down from a balcony in a ballroom, watching a cocktail party below. When just plain folks try to go from one end of the room to the other, they can walk through easily, with no resistance from the party crowd. But when a celebrity like Justin Bieber shows up, other partygoers press around him so tightly that he can hardly move ... and once he moves, the crowd moves with him in such a way that the whole group is harder to stop.
The partygoers are like Higgs bosons, the just plain folks are like massless particles, and Bieber is like a massive Z boson.
The Guardian's Ian Sample demonstrates a variant of this analogy in a 4.5-minute video: Imagine a tray with ping-pong balls scattered on it. The balls roll freely around the empty tray. But then, if you spread a layer of sugar over the tray, the balls sitting on the piled-up sugar don't roll so easily. The grains of sugar introduce a kind of inertial "drag," and that's the kind of effect that the Higgs field supposedly has on particles with mass.
In a 60-second shot of science written for Symmetry magazine, Howard Haber of the University of California at Santa Cruz uses a livelier comparison to a high-speed bullet plowing through a vat of molasses.
What good is it?
Particle physicists try to avoid forecasting the applications of an experimental advance before the actual advance is confirmed, but in the past, advances on a par with the discovery of the Higgs boson have had lots of beneficial applications, and some that are more questionable. The rise of nuclear power and nuclear weaponry is a prime example of that double-edged sword.
The discovery of antimatter is what made medical PET scanning possible, and antimatter propulsion could eventually play a part in interstellar travel, just like on "Star Trek." Particle accelerators have opened the way to medical treatments such as proton eye therapy — as well as advances in materials science, thanks to neutron scattering.
Courtesy : http://cosmiclog.msnbc.msn.com/_news/2012/07/03/12547980-the-higgs-boson-made-simple?lite
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