We’ve all had the experience—over and over all the time. You go down to the street to wait for the bus (the train, the subway, the boat); you know that buses come roughly every 10 minutes, so you expect to wait about 5 minutes (arriving, on average, in the middle of the between-buses interval). But in fact, we all know that almost always you have to wait longer than that! Is this an illusion we’ve developed over the centuries because we believe in the “persistence of bad luck,” or is it, perhaps, something real?
It is, in fact, a real phenomenon, and this result can even be proved mathematically. Because you arrived after the last bus has left, your overall waiting time is, on average, longer than half the average
interval of 10 minutes.
An intuitive way of seeing this is to draw the timeline, with short and long intervals—their average is indeed 10 minutes long, but by randomness some of them will be longer and some will be shorter than the stated average.
Your appearance at the bus stop is also a random event, and this event is more likely to take place during a long interval
between two buses than during a short one!
By Rebecca Boyle
When NASA announced in May that its celebrated planet-finding telescope Kepler was broken, astronomers and journalists started collectively mourning. The Kepler space telescope had found 2,740 possible exoplanets since its launch in March 2009, and it was so successful that NASA approved funding for it through 2016, with hopes that many years of discoveries would follow.
And Kepler managers finally announced last week that they are giving up trying to reactivate the telescope’s busted gyroscopic wheels, which stabilize it for staring at possible planet-harboring stars.
But that doesn’t mean the telescope’s days of discovery are over. NASA is soliciting ideas for using Kepler in its hobbled form — something for which there’s plenty of precedent.
Kepler was designed to stare at bright stars to look for blips in their brightness that could indicate planets passing in front of them, a technique called photometry. It was built with four gyroscopic reaction wheels — one for each axis of movement, and one spare — that spin to correct for the solar wind and keep Kepler precisely pointed at those bright stars. One wheel stopped working more than a year ago, and astronomers started wondering what Kepler could do should another wheel fail.
When that happened, in May, scientists initially worried Kepler would move around too jerkily for any precision photometry. But, while it won’t be able to find Earth-sized planets around sun-like stars, tests this summer showed it may still be up for other tasks, including looking for bigger planets.
“Everybody is excited; they’re thinking, ‘Hey, we have a telescope in space, what can we do with it?’” said Steve Howell, Kepler project scientist at NASA’s Ames Research Center. “And you can do a lot with it.”
On April 17 of this year, a relatively unknown Chinese-born mathematician in his fifties—who since coming to the U.S. had to work odd jobs, including at a sandwich shop, before joining the faculty of the University of New Hampshire—announced a discovery that shocked the world of mathematics. Yitang (“Tom”) Zhang just solved one of the most persistent mysteries in the theory of numbers—of the kind that the famous British mathematician G. H. Hardy had described as being “at present beyond the resources of mathematics.”*
Ever since the Greek mathematician Euclid of Alexandria proved 2,300 years ago that there are infinitely many prime numbers, mathematicians have been intrigued by the existence of twin primes, a pair of prime numbers that differ by two—such as 11 and 13; 17 and 19; 29 and 31; and 41 and 43. Other than the first pair of prime numbers, 2 and 3, which are adjacent to each other, all further pairs of primes must be separated by at least one number because even numbers greater than two cannot be primes (since they are divisible by 2).
Mathematicians have wanted to learn about the behavior of pairs of primes, in particular pairs separated by one number, such as the twin primes in the examples above. Their hunt even has a name, the “twin prime conjecture,” which asks: are there an infinity of twin primes?
The thing about crossing into uncharted territory is that you may not know when, exactly, you have crossed into it. No one needs to tell that to the Voyager 1 spacecraft, which is currently at the center of a controversy about where the solar system ends and interstellar space begins.
Today, a press release from the American Geophysical Union initially stated Voyager had left our solar system. Two hours later, though, they issued a correction calling Voyager’s current location a “new region of space,” which is considerably less flashy (but equally scientifically valuable). The NASA Jet Propulsion Laboratory, which oversees the spacecraft, weighed in with a press release saying that no, in fact Voyager was still in the solar system.
So why the controversy? What is the debate about the boundary of the solar system? And what is this “new region” of which the scientists speak?
By Amy Shira Teitel
The year was 1962. The Cuban Missile Crisis was at its peak, and it had been only days since President Kennedy learned that the Soviet Union was establishing missile sites in Cuba. The U.S. Air Force was on DEFCON-2. American and Soviet military forces were an order away from launching a nuclear attack.
But on Saturday, October 27, it wasn’t a military general or political leader who nearly upended that delicate world balance and set off World War III. It was the aurora borealis.
Amy Shira Teitel is a freelance space writer whose work appears regularly on Discovery News Space and Motherboard among many others. She blogs about the history of spaceflight at Vintage Space, and tweets at @astVintageSpace.
This month marked the 55th anniversary of the first living being launched into orbit. It wasn’t a simple fruit fly or bean sprout, but a stray dog from the streets of Moscow.
As the first space traveler, Laika was a hero of her time, extensively trained and outfitted in a custom-designed space suit. But even on those early missions, the Soviet Union was establishing a pattern in its space flights: missions were designed to stay one step ahead of the Americans, often at the cost of quality and safety—and sometimes fudged for good measure.
Preceding Laika’s flight on Sputnik 2 was the first Sputnik, the more famous one, which scored a significant psychological coup for the Soviet Union. The 184-pound beeping satellite shot fear into the hearts of Americans and began a decade of Soviet leadership in space that challenged the United States’ position as the world’s technological superpower. But Sputnik was an innocuous satellite, far simpler than the sophisticated payloads the Soviets had been developing. Speed had trumped sophistication in the quest to launch before the Americans.
Soviet leader Nikita Khrushchev felt the power of Sputnik just like the Americans did. He was so pleased with the satellite’s success that the day after its launch—October 5, 1957—he met with the Soviet space program’s Chief Designer Sergei Korolev to plan the next launch. Khrushchev wanted another satellite on an astounding timetable: November 7 that year marked the 40th anniversary of the Great October Socialist Revolution and Khrushchev wanted another satellite to mark the occasion with something grand. So Korolev suggested they launch a dog.
Andrew Grant is an associate editor at DISCOVER. His latest feature, “William Borucki: Planet Hunter,” appears in the December issue of the magazine.
Last night Major League Baseball announced the winners of the Cy Young Award, given to the year’s best pitchers in the American and National leagues. The National League victor was New York Mets pitcher R.A. Dickey. That he won the award is remarkable, and not just because he is a relatively ancient 38 years old or because he plays for the perennial punch line Mets. Dickey is the first Cy Young winner whose repertoire consists primarily of the knuckleball, a baffling pitch whose intricacies scientists are only now beginning to understand.
Most pitchers, including the other Cy Young finalists, try to overwhelm hitters with a combination of speed and movement. They throw the ball hard—the average major league fastball zooms in at around 91 miles per hour—and generate spin (up to 50 rotations a second) that makes the ball break, or deviate from a straight-line trajectory. Dickey does neither of those things. Rather than cock his arm back and fire, he pushes the ball like a dart so that it floats toward the plate between 55 and 80 mph. The ball barely spins at all—perhaps a quarter- or half-turn before reaching the hitter.
Amir D. Aczel writes often about physics and cosmology. His book about the discovery of the Higgs boson, Present at the Creation: Discovering the Higgs Boson, is published in paperback by Broadway Books in November 2012.
If somebody told you that there are angels floating in space, observing our world and forming their impressions of our everyday reality, you would think that this person is nuts—a religious fanatic with an active imagination, and certainly not a scientist. Scientists, as we all know, are rational beings who believe only in what nature reveals to us through experimentation and observation, coupled with theory that is never divorced from the physical measurements they make. The link between the two remains tightly regulated through the strict rules of the scientific method.
So how do you explain the bizarre fact that, for about five years now, some of the world’s most prominent physicists have been describing a scenario—which they seem to truly believe may be real—in which, instead of the Biblical angels, space is permeated by disembodied brains?
These compact, conscious observers, called “Boltzmann brains,” cruise the vastness of intergalactic space, and beyond it, to the infinite “multiverse” that some scientists believe exists outside the reaches of the universe we observe through our telescopes and satellites. Their consciousness makes the Boltzmann brains recreate our reality. They imagine life such as the one you and I believe we are experiencing here on Earth, to the point that these brains in space may think that they are living on a planet like ours, that they may even be us. Some recent physics papers and commentaries have even explored the possible limits on the number of Boltzmann brains in the universe as compared with “real” brains, in an effort to estimate the probability that we are real rather than Boltzmann entities.
Ethan Siegel is a theoretical astrophysicist living in Portland, Oregon, who specializes in cosmology. He has been writing about the Universe for everyone since 2008, and can’t wait for the launch of the James Webb Space Telescope. A different version of this post appeared on his blog, Starts With a Bang.
“It is by going down into the abyss that we recover the treasures of life. Where you stumble, there lies your treasure.” –Joseph Campbell
One of the bravest things that was ever done with the Hubble Space Telescope was to find a patch of sky with absolutely nothing in it—no bright stars, no nebulae, and no known galaxies—and observe it. Not just for a few minutes, or an hour, or even for a day. But orbit-after-orbit, for a huge amount of time, staring off into the nothingness of empty space, recording image after image of pure darkness.
What would we find, out beyond the limits of what we could see? Something? Nothing? After a total of more than 11 days of observing this tiny area of the sky, this is what we found:
The Hubble Ultra Deep Field—the deepest view ever of the Universe, was the result. With all those orbits spent observing what appears to be a blank patch of sky, what we were really doing was probing the far-distant Universe, seeing beyond what any human eye—even one aided by a telescope—could ever hope to see. It took literally hundreds of thousands of seconds of observations across four separate color filters to produce these results.
What you’re seeing—in practically every point or smear of light—is an individual galaxy. The result gave us the information that a very large number of galaxies exist in a minuscule region of the sky: around 10,000 in the tiny volume surveyed by the Hubble Ultra Deep Field image, below.
Image credit: NASA, ESA, S. Beckwith (STScI) and the HUDF Team
By extrapolating these results over the entire sky (which is some 10 million times larger), we were able to figure out—at minimum—that there were at least 100 billion galaxies in the entire Universe. I even made a video about it.
But that’s not the end of the story; not by a long shot. You see, there might be at least 100 billion galaxies, based on what we’ve observed, but there might be more. Galaxies that are too dim to observe with “only” 11 days of Hubble data. Galaxies that are redshifted too far for even Hubble’s farthest infrared filter to pick up. Galaxies that might appear, if only we had the patience to look for longer.
So that’s exactly what we did, looking for a total of 23 days over the last decade—more than twice as long as the Ultra-Deep Field—in an even smaller region of space. (There are over 1,000 observing proposals submitted to Hubble every cycle, so getting that much time, even spread over a decade, is remarkable.) Ladies and Gentlemen, may I present to you the Hubble Extreme Deep Field!
Amir D. Aczel (amirdaczel.com) writes about mathematics and physics and has published 18 books, numerous newspaper and magazine articles, as well as professional research papers.
A Higgs candidate event from the ATLAS detector of the LHC.
Courtesy of CERN
What made me fall in love with theoretical physics many years ago (in 1972, when I first met Werner Heisenberg) was its stunningly powerful relationship—far beyond any reasonable expectation—with pure mathematics. Many great minds have pondered this mysteriously deep connection between something as abstract as mathematics, based on theorems and proofs that seem to have little to do with anything “real,” and the physical universe around us. In addition to Heisenberg, who brilliantly applied abstract matrix theory to quantum physics, Roger Penrose has explored the deep relation between the two fields—and also, to a degree, between them and the human mind—in his book The Road to Reality.
And in 1960, the renowned quantum physicist and Nobel Laureate Eugene Wigner of Princeton wrote a fascinating article that tried to address the mysterious nature of this surprising relationship. Wigner marveled at the sheer mystery of why mathematics works so well in situations where there seems to be no obvious reason why it does. And yet, it works.