Birthday problem In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are 366 possible birthdays, including February 29). However, 99.9% probability is reached with just 70 people, and 50% probability with 23 people. These conclusions include the assumption that each day of the year (except February 29) is equally probable for a birthday. The history of the problem is obscure, but W. The mathematics behind this problem led to a well-known cryptographic attack called the birthday attack, which uses this probabilistic model to reduce the complexity of cracking a hash function. A graph showing the computed probability of at least two people sharing a birthday amongst a certain number of people. Understanding the problem distinct possible combinations of pairing. and .
Human observation of dark energy may shorten the life span of the universe Could humanity's observation of dark energy have shortened the life span of the universe? The answer is "yes" according to the author of a new scientific paper that has recently come to light. Featured in the latest edition of New Scientist magazine, the subscriber-only story, "Has observing the universe hastened its end?", discusses the paper and its claims. Now, before I go further, I must point out that this work has not yet appeared in any peer-reviewed journal. Their official paper, titled "The Late Time Behavior of False Vacuum Decay: Possible Implications for Cosmology and Metastable Inflating States," is far from grandiose. To understand the potential implications of the calculations in the paper, one must start at the beginning—the Big Bang, and even before. This idea was challenged in the late 1990's by the discovery of dark energy. How does this relate to the work in the research article? How could something like this possibly happen?
Earth's True Shape Revealed for 1st Time After two years in orbit, the European Space Agency’s (ESA) Gravity field and steady-state Ocean Circulation Explorer (GOCE) is nearing the end of its planned life span in February, producing the most accurate map ever of the so-called geoid -- an Earth-encompassing spirit level and global reference surface. An unused supply of xeon fuel will allow the mission to be extended until at least the end of 2012. Markedly different from a simple sphere or ellipsoid, the geoid is the mathematically 'true' shape of Earth. It represents a motionless global ocean but takes into account the effects of the Earth’s rotation, weight difference resulting from the position of mountains and ocean trenches, and uneven mass distribution and density variations in the planet’s interior. The resulting small variations in the Earth’s gravitational field feature on the geoid as ‘bulbs’ and ‘dips’ in an idealized ‘ocean’ surface. The Daily Galaxy via ESA
The 5 Scientific Experiments Most Likely to End the World Let's face it, we really trust science. In fact, studies suggest that the vast majority of people will murder another human being, if a guy in a lab coat tells them it's OK. But surely in their insatiable curiosity and desire to put knowledge above all things, science would never, say, inadvertently set off a chain of events that lead to some sort of disaster that ended the world. Right? Well, here's five experiments that may prove us wrong. Recreating the Big Bang Scientists are kind of pissed that they weren't around when the Big Bang happened. The solution, science says, is to make it happen again. God, 1. What Could Possibly Go Wrong? Well, first imagine an apocalyptic nuclear holocaust. So, Basically It's Like... Imagine you have a huge tanker truck parked outside a children's hospital. How Long Have We Got? Meet the Large Hadron Collider. This is not only the largest particle accelerator ever built, it's the largest anything ever built. Risk Level: 3 The Quantum Zeno Effect Risk Level: 5
Your beliefs about intelligence affect your beliefs about learning Your beliefs about intelligence really matter. Learning is a lifelong process. Kids go to school to be exposed to new topics ranging from history to math to science. Adults need to pick up new knowledge to understand world events and to succeed at new tasks at work. Sometimes, of course, the things we learn are fairly easy to pick up. Many people watching the political events unfold in North Africa and the Middle East in 2011 may not have known much about the governments of countries like Tunisia and Egypt before protests brought down those governments. Other information is harder to pick up. How does the difficulty of learning about something affect your beliefs about how much you can learn about it? This question was explored by David Miele, Bridgid Finn, and Daniel Molden in a paper in the March, 2011 issue of Psychological Science . They were interested in the role of people's beliefs about intelligence on learning. This result is quite important.
thermodynamics - Cooling a cup of coffee with help of a spoon Stirring will win, hands down, every time. This is why physicists need to talk to chemists once in a while. As Georg correctly remarks, the latent heat of vaporization of water is enormous - but he's wrong about waving the spoon; stirring is the champion here. Why? It's similar to stirring iced tea. This kind of thing has a lot of applications to laboratory and industrial chemical processes, surface catalysis, petroleum cracking, yadda yadda. If you want an even faster way to cool a cup of coffee, here's a tip from my Granddad Parker: forget the spoon and saucer your coffee. Spiders Fleeing Floods Build Mosquito Buffet in Trees Photo: Russell Watkins / DFID When heavy rains caused rivers to overflow and flood parts of Pakistan last year, it set into motion a surprisingly complex chain of events that scientists are only now beginning to understand -- and which may have ultimately saved countless human lives. As waters began to rise, thousands of spiders sought refuge in tall trees, cluttering the leaves and branches with their webs in a manner reminiscent of cotton-candy. That, of course, is just the beginning of the story. >> WATCH SLIDESHOW: 10 of the World's Weirdest Spiders In the heavily flooded region of Sindh, Pakistan, these spider-web laden trees seems to have been quite effective at catching insects. Unfortunately, the trees themselves didn't benefit from being host to the spider's buffet. From New Scientist : Although slowly killing the trees, the phenomenon is seemingly helping the local population.
I, For One, Welcome Our New Computer Overlords Last night, IBM’s Watson computer won the final round of the three-day Man V. Machine Jeopardy! competition. At the beginning of the show, the humans were fierce, proving that they could buzz in faster than Watson, even though the machine knew the answer. Both human competitors, Ken Jennings and Brad Rutter, got it correct as well. Rutter: $21,600Jennings: $24,000Watson: $77,147 But although Watson won the competition, humans still prevailed. On Jeopardy! In this video from IBM, project researchers describe how a computer system like Watson could be capable of reading an unlimited number of documents, understanding the information and completely retaining it. Financial companies could use a computer like Watson to read and analyze news reports, market reports, trade publications, world events, blogs — you name it — and extract meaningful information for investors or business owners. I think Watson is agreat achievement of our time.
6 Terrifying Ways Crows Are Way Smarter Than You Think Mankind has a long and checkered past with crows and ravens: They have been feared as symbols of death, because they're all black and scary, revered as creators of the world because, well, it was either them or the seagulls, and worshiped as trickster gods, because of their baffling intelligence. Intelligent enough, in fact, for us to start worrying ... #6. They Can Remember Your Face Next time you see a group of crows, look closely. OK, so the scientists weren't just playing out horror movie fantasies -- they were testing whether the crows could recognize human faces or not. In case you think they were just telling each other "get the guy with the mask," they weren't: The test was repeated with multiple people wearing multiple masks, and without fail, the crows left the masked men who hadn't messed with them alone, but went murder-crazy on the mask that had been worn while messing with them. "Wow. Oh, and also none of the scientists were ever seen again. #5. #4. One.
News ::: Columbia Engineers Prove Graphene is Strongest Material July 21, 2008 Columbia Engineers Prove Graphene is the Strongest Material Research scientists at Columbia University’s Fu Foundation School of Engineering and Applied Science have achieved a breakthrough by proving that the carbon material graphene is the strongest material ever measured. Graphene holds great promise for the development of nano-scale devices and equipment. It consists of a single layer of graphite atoms arranged in a hexagonal lattice, similar to a honeycomb. As a two-dimensional material, every atom is exposed to the surface. Until now, graphene’s estimated strength, elasticity and breaking point were based on complex computer modeling theories. “Our team sidestepped the size issue by creating samples small enough to be defect-free,” said Columbia Professor Jeffrey Kysar. The studies were conducted by postdoctoral researcher Changgu Lee and graduate student Xiaoding Wei, in the research groups of mechanical engineering professors Kysar and James Hone.
Caveman: An Interview with Michel Siffre In 1962, a French speleologist named Michel Siffre spent two months living in total isolation in a subterranean cave, without access to clock, calendar, or sun. Sleeping and eating only when his body told him to, his goal was to discover how the natural rhythms of human life would be affected by living “beyond time.” Over the next decade, Siffre organized over a dozen other underground time isolation experiments, before he himself returned to a cave in Texas in 1972 for a six-month spell. Michel Siffre's tent in Midnight Cave, Texas, glows with incandescent lights. In 1962, you were just twenty-three years old. You have to understand, I was a geologist by training. Instead of studying caves, you ended up studying time. Yes, I invented a simple scientific protocol. Siffre's cave-appropriate reading: Plato. During your first stay underground, temperatures were below freezing, and humidity was ninety-eight percent. There was a very large perturbation in my sense of time. What did you find?