CARLOS Tiger without Time

Henri Poincare (1854-1912) was one of the most eminent French mathematicians of the past two centuries.

One of Poincare’s best-known problems is what is today called the Poincare conjecture.

The poincare conjecture is considered so important that the clay Mathematics Institute named it one of the seven millennium prize problems will be awarded $1 million.

The Poincare conjecture falls within the realm of topology.

This branch of mathematics focuses, roughly speaking, on the issue of whether one body can be deformed into a different body through pulling, squashing or rotating, without tearing or gluing pieces together.

A ball, an egg, and a flowerpot are, topologically speaking, equivalent bodies, since any of them can be deformed into any of others without performing any of the “illegal” actions.

A ball and a coffee cup, on the other hand, are not equivalent, since the cup has a handle, which could not have been formed out of the ball without poking a hole through it.
The ball, egg, and a flowerpot are said to be “simply connected” as opposed to the cup, a bagel, or a pretzel.

Poincare sought to investigate such issues not by geometric means but through algebra, thus becoming the originator of “algebraic topology.”

In 1904 he asked whether all bodies that do not have a handle are equivalent to spheres. In two dimensions this questions this question refers to the surfaces of eggs, coffee cups, and flowerpots and can be answered yes. (Surfaces like the leather skin of a football or the crust of a bagel are two-dimensional objects floating in three-dimensional space)

For three-dimensional surfaces in four-dimensional space the answer is not quite clear. While Poincare was inclined to believe that the answer was yes, he was not able to provide a proof.

Several Mathematicians were able to prove the equivalent of Poincare’s conjecture for all bodies of dimension greater than four. This is because higher-dimensional spaces provide more elbowroom so mathematicians find it simpler to prove the Poincare conjecture.

But, for three-dimensional surfaces in four-dimensional space –remember: The surface of a four-dimensional object is a three-dimensional object. Poincare’s conjecture remained as elusive as ever.

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Carlos Tiger without Time

How the twin primes to cause the error in the processor Pentium Intel?
Whitin the group of integers, prime numbers are in a way thought of as atoms, since all integers can be expressed as a product of prime numbers (for example, 30=2x3x5), just as molecules are made up of separate atoms.

The theory of prime numbers continues to be shrouded in mystery and still holds many secrets.

Taking the first 100 numbers we count 25 primes; between 1001 and 1100 there are only 16; and between the numbers 100,001 and 100100 there are a mere six.

Prime numbers become increasingly sparse. In other words, the average distance between two consecutive primes becomes increasingly large.

Around the turn of the 19th century, the Frenchman Adrien-Marie Legendre and the German Carl Friedrich Gauss studied the distribution of primes. Based on their investigations they conjectured the space between a prime P and the next bigger prime would on average, be as big as the natural logarithm of P.

Sometimes the gaps are much larger, sometimes much smaller. There are even arbitrarily long intervals in which no primes occur whatsoever. The smallest gap. On the other hand, are two, since there is at least one even number between any two primes.

Primes that are separated from each other by a gap of only two –for instance, 11 and 13, or 197 and 199- are called twin primes.

There are also prime cousins, which are primes separated from each other by four nonprime numbers. Primes that are separated from each other by six nonprime numbers are called, sexy primes.

Much less is known about twin primes than about regular primes. What is certain is that they are fairly rare.

Among the first million integers there are only 8169 twin prime pairs. The largest twin primes so far discovered have over 50,000 digits. But much is unknown.

Nobody knows whether an infinite number of twin prime pairs exist, or whether after one particular twin prime pair there are no larger ones.

Working on the theory of twin primes, Thomas Nicely from Virginia, in the 1990s. He was running through all integers up to 4 quadrillion.

The algorithm required the computation of the banal expression X times (1/X). But to his shock, when inserting certain numbers into this formula, he received not the value 1 but an incorrect result.

On October 30, 1994, his computer consistently produced erroneous results when calculating the above equation with numbers ranging between 824,633,702,418 and 824,633,702,449. Through his research on twin primes, Thomas Nicely had hit on the notorious Pentium bug.

The error in the processor cost Intel, the manufacturer, and $500 million in compensations.

See you later
Carlos Tiger without Time

Combining western scientific knowledge with eastern spiritual wisdom, Deepak Chopra has developed his own unique form of complementary, mind-body medicine.

Chopra said:
“I grew up with the myths, the stories, and the history of Siddhartha the prince, who then became Gautama the monk, who then became Buddha the enlightened being. My father passed away six years ago, and then shortly after that, my mother did, too.

I was immersing the ashes of my father in the ganges up in the north of India, which is very rich in Buddhist lore. I thought, well, I’m the next in line for the experience of death.

In the time Siddhartha lived, India was a place where everyday reality was en meshed in mythology, and it is so even today. People very easily move back and forth, both in their imagination and their behavior, between reality and the world of mythical beings.

The meaning “ENLIGHTENED ONE” is that your real self is not a person, that there is no such thing as a separate self, that a person doesn’t really exist. What we call a person is a transient behavior of the total universe, and when you get to the consciousness that is behind all the intelligent activity of the whole universe. So enlightened here means transcendence to that level of existence where the personal self becomes the universal self.

I don’t consider myself Buddhist because I don’t think Buddha himself believed in ideology or dogma.

Buddha says when you look deep enough into your enemy; you will see that he is yourself. But what Jesus calls sin; Buddha calls ignorance, lack of awareness.

The God question is also very different. In the Judeo-Christian tradition, God created the universe, whereas in the Buddhist tradition, God, or the intelligence that is at the source of creation, is not some outside intelligence but is inherent in the consciousness that conceives, governs, and becomes the universe.

I think spirituality is a domain of awareness where we all experience our universality and where we experience universal truth. It has very little to do with religious dogma, ideology, or even self-righteous morality.

* Summarized and adapted of Time, June 2007

Note:

Place number 42   United States : 77.9 years

 * New York Post, September 13, 2007 

THE last time Irene Pepperberg saw Alex she said goodnight as usual. “You be good,” said Alex. “I love you.” “I love you, too.” “You’ll be in tomorrow?” “Yes, I’ll be in tomorrow.” But Alex (his name supposedly an acronym of Avian Learning Experiment) died in his cage that night, bringing to an end a life spent learning complex tasks that, it had been originally thought, only primates could master.

In science as in most fields of endeavour, it is important to have the right tool for the job. Early studies of linguistic ability in apes concluded it was virtually non-existent. But researchers had made the elementary error of trying to teach their anthropoid subjects to speak. Chimpanzee vocal cords are simply not up to this—and it was not until someone had the idea of teaching chimps sign language that any progress was made.

Even then, the researchers remained human-centric. Their assumption was that chimps might be able to understand and use human sign language because they are humanity’s nearest living relatives. It took a brilliant insight to turn this human-centricity on its head and look at the capabilities of a species only distantly related to humanity, but which can, nevertheless, speak the words people speak: a parrot.

The insight in question came to Dr Pepperberg, then a 28-year-old theoretical chemist, in 1977. To follow it up, she bought a one-year-old African Grey parrot at random from a pet shop. Thus began one of the best-known double acts in the field of animal-behaviour science.

Dr Pepperberg and Alex last shared a common ancestor more than 300m years ago. But Alex, unlike any chimpanzee (with whom Dr Pepperberg’s most recent common ancestor lived a mere 4m years ago), learned to speak words easily. The question was, was Alex merely parroting Dr Pepperberg? Or would that pejorative term have to be redefined? Do parrots actually understand what they are saying?
Bird brained
Dr Pepperberg’s reason for suspecting that they might—and thus her second reason for picking a parrot—was that in the mid-1970s evolutionary explanations for behaviour were coming back into vogue.

A British researcher called Nicholas Humphrey had proposed that intelligence evolves in response to the social environment rather than the natural one. The more complex the society an animal lives in, the more wits it needs to prosper.
The reason why primates are intelligent, according to Dr Humphrey, is that they generally live in groups. And, just as group living promotes intelligence, so intelligence allows larger groups to function, providing a spur for the evolution of yet more intelligence. If Dr Humphrey is right, only social animals can be intelligent—and so far he has been borne out.

Flocks of, say, starlings or herds of wildebeest do not count as real societies. They are just protective agglomerations in which individuals do not have complex social relations with each other.

But parrots such as Alex live in societies in the wild, in the way that monkeys and apes do, and thus Dr Pepperberg reasoned, Alex might have evolved advanced cognitive abilities. Also like primates, parrots live long enough to make the time-consuming process of learning worthwhile.

Combined with his ability to speak (or at least “vocalise”) words, Alex looked a promising experimental subject.
And so it proved. Using a training technique now employed on children with learning difficulties, in which two adults handle and discuss an object, sometimes making deliberate mistakes, Dr Pepperberg and her collaborators at the University of Arizona began teaching Alex how to describe things, how to make his desires known and even how to ask questions.

By the end, said Dr Pepperberg, Alex had the intelligence of a five-year-old child and had not reached his full potential. He had a vocabulary of 150 words. He knew the names of 50 objects and could, in addition, describe their colours, shapes and the materials they were made from.He could answer questions about objects’ properties, even when he had not seen that particular combination of properties before. He could ask for things—and would reject a proffered item and ask again if it was not what he wanted. He understood, and could discuss, the concepts of “bigger”, “smaller”, “same” and “different”. And he could count up to six, including the number zero (and was grappling with the concept of “seven” when he died). He even knew when and how to apologise if he annoyed Dr Pepperberg or her collaborators.
And the fact that there were a lot of collaborators, even strangers, involved in the project was crucial. Researchers in this area live in perpetual fear of the “Clever Hans” effect. This is named after a horse that seemed to count, but was actually reacting to unconscious cues from his trainer. Alex would talk to and perform for anyone, not just Dr Pepperberg.
There are still a few researchers who think Alex’s skills were the result of rote learning rather than abstract thought. Alex, though, convinced most in the field that birds as well as mammals can evolve complex and sophisticated cognition, and communicate the results to others. A shame, then, that he is now, in the words of Monty Python, an ex-parrot.

Wednesday, September 19, 2007
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Scientists doubt that the supposed meteorite strike that sickened some 200 residents of Peru over the weekend actually involved anything from space.
Based on reports of fumes emanating from the crater, some scientists actually suspect that the event could have been some kind of geyser-like explosion rather than a meteorite impact.
“Statistically, it’s far more likely to have come from below than from above,” said Don Yeomans, head of the Near Earth Object Program at NASA’S Jet Propulsion Laboratory in Pasadena, California.

The noxious fumes that have supposedly sickened curious locals who went to examine the crater would seem to indicate hydrothermal activity, such as a local gas explosion, because “meteorites don’t give off odors,” Yeomans told SPACE.com.

Skepticism warranted
Several times in recent history, reports of meteorite impacts have turned out to be untrue after scientific examination. Doubt in the scientific community was as rampant Wednesday as the speculations out of Peru.
Details surrounding the incident are also increasing experts’ skepticism.

“Many of the reported features of the crater (“boiling water,” sulphurous fumes, etc.) point to a geological mechanism of the crater formation,” wrote Benny Peiser, a social anthropologist at Liverpool John Moores University in England, in a daily newsletter that catalogues research and media coverage of space rock impacts and other threats to humanity.

“I would not be surprised if, after careful analysis,” he added, “the alleged meteorite impact reveals itself to be just another ‘meteorwrong.'”

It’s not impossible that the crater was left by a meteorite, Yeomans said, but if so, then the impact object most likely was small, based on the size of the crater.

It would also probably have been a metal meteorite, because those are the only kind of small meteorites that don’t burn up as they plummet through Earth’s atmosphere, he added. Small stony meteorites rarely make it to the surface.

A couple features of the event reports suggest there was a space rock involved, said geophysicist Larry Grossman of the University of Chicago.

The bright streak of light and loud bangs seen and heard by locals are consistent with a meteor streaking through Earth’s atmosphere, he said. Most meteors do burn up, never becoming meteorites (which is what they’re called if they reach the surface).

Because no one actually saw anything impact at the crater site, it’s hard to say whether a space rock was involved because they are often deceptive as to where they will land.

Many times, people swear a meteor landed nearby when in fact it was so far away that it dipped below the local horizon but never actually struck the ground.

“Sometimes these things land hundreds of thousands of miles away from where [people] think they will land,” Grossman said.
Investigation needed Pictures of the crater show that the hole in the ground appears fresh, Grossman said, and the debris strewn around it is consistent with a meteorite impact but also could have been caused by digging.

And there are no previous reports of noxious fumes emanating from meteorite remnants or their craters, he said.
“If the noxious fumes came from the hole, it wasn’t because the meteorite fell there,” Grossman said, saying they would like have come from something already in the ground.

Grossman said that to determine whether the crater was made by a meteorite, the water in the hole must be pumped out and any large chunks of rock at the bottom should be examined to see if they are consistent with meteoritic composition.
Peruvian geologists are on their way to examine the crater, according to news reports.

LIMA, Peru – A fiery meteorite crashed into southern Peru over the weekend, experts confirmed on Wednesday. But they were still puzzling over claims that it gave off fumes that sickened 200 people.

Witnesses told reporters that a fiery ball fell from the sky and smashed into the desolate Andean plain near the Bolivian border Saturday morning.
Jose Mechare, a scientist with Peru’s Geological, Mining and Metallurgical Institute, said a geologist had confirmed that it was a “rocky meteorite,” based on the fragments analyzed.

He said water in the meteorite’s muddy crater boiled for maybe 10 minutes from the heat and could have given off a vapor that sickened people, and scientists were taking water samples.
“We are not completely certain that there was no contamination,” Mechare said.

Jorge Lopez, director of the health department in the state where the meteorite crashed, told The Associated Press on Tuesday that 200 people suffered headaches, nausea and respiratory problems caused by “toxic” fumes emanating from the crater, which is some 65 feet wide and 15 feet deep.
But a team of doctors sent to the isolated site, 3 1/2 hours travel from the state capital of Puno, said they found no evidence the meteorite had sickened people, the Lima newspaper El Comercio reported Wednesday.

Modesto Montoya, a member of the team, was quoted as saying doctors also had found no sign of radioactive contamination among families living nearby, but had taken blood samples from 19 people to be sure.
He said fear may have provoked psychosomatic ailments.

“When a meteorite falls, it produces horrid sounds when it makes contact with the atmosphere,” he told the paper. “It is as if a giant rock is being sanded. Those sounds could have frightened them.”
Justina Limache, 74, told El Comercio that when she heard the thunderous roar from the sky, she abandoned her flock of alpacas and ran to her small home with her 8-year-old granddaughter. She said that after the meteorite struck, small rocks rained down on the roof of her house for several minutes and she feared the house was going to collapse.
Meteor expert Ursula Marvin said that if people were sickened, “it wouldn’t be the meteorite itself, but the dust it raises.”

A meteorite “wouldn’t get much gas out of the Earth,” said Marvin, who has studied the objects since 1961 at the Smithsonian Astrophysical Observatory in Cambridge, Mass. “It’s a very superficial thing.

By Monte Hayes
The Associated Press
Updated: 4:45 p.m. ET Sept 19, 2007

The West says that it is perplexed by Russia’s “aggressive” behavior of late, and suggests that Moscow is desirous to regain its past superpower status, and even a little empire. But if cashing in on oil is imperialism, how do we explain the following U.S. moves:

10. Scrapping the Anti-Ballistic Missile Treaty – In December 2001, three months after 9/11, U.S. President George W. Bush told Russian President Vladimir Putin that the U.S. was pulling out of the 1972 ABM Treaty, a Cold War-era document that specifically forbade the development and deployment of anti-missile defense systems. The treaty ensured that signatory nations adhere to the mutually assured destruction (MAD) concept – if you destroy us we will destroy you formula. Yes, it was certainly MAD, but it kept the peace for 30 years. Former Defense Secretary Donald Rumsfeld attempted to reassure Moscow that the decision was nothing personal. “It [the treaty] failed to recognize that the Soviet Union is gone and that Russia is, of course, not our enemy.” Putin called the move “a mistake.”

9. “Mission Accomplished” – On March 20, 2003, the United States – without a mandate from the United Nations, and against the heated objections of France, Germany and Russia – invaded Iraq on the pretext that the secular Baathist state of Saddam Hussein had weapons of mass destruction and was a proud sponsor of terrorism. Both accusations were proven wrong. Former UN Secretary-General Kofi Annan told the BBC in an interview that the attack was a violation of international law. “From our point of view and the UN Charter point of view, it [the war] was illegal.”

8. Pentagon Spending Spree – The United States, which just put the finishing touches on a $583 billion dollar shopping trip for 2008, accounts for about half of global expenditures (or the next 14 nations). However, as Robert Higgs of the Independent Institute argues, “the trillion-dollar defense budget is already here.” Higgs calculated that U.S. military-related spending in 2006 was actually $934.9 billion if we figure in Homeland Security ($69.1bln), the Dept. of Energy, which oversees nuclear weapons ($16.6 bln) and the Dept. of Veterans Affairs ($69.8 bln), as well as other juicy pork chops. In May, the Democrat-controlled House and Senate approved almost $95 billion for the ongoing wars in Afghanistan and Iraq through September (Go Dems!). Meanwhile, “aggressive” Russia, with a 48 percent increase in military spending since 1996, still spends ‘just’ $85 billion annually on military expenditures.

7. NATO XXL – As Dan Simpson, a retired U.S. diplomat argued in the Pittsburgh Post-Gazette, “The United States and other NATO members have taken some actions along the way to lull the Russians into acquiescence as NATO expanded to include the former Warsaw Pact nations… The argument was that these countries wanted to join NATO and that their membership posed no threat to Russia. That line prevailed as NATO membership grew to include also Estonia, Latvia and Lithuania, former republics of the Soviet Union. Now the Russians see the same argument being advanced for Georgia and Ukraine. That’s getting close to home.”

6. New Military Bloopers – As the Pakistani government of Gen. Pervez Musharraf struggles to contain the fallout of an 8-day battle against militants at the Lal Masjid (Red Mosque), a U.S. official turned up the heat by telling CNN that if the U.S. “had actionable targets, anywhere in the world,” including Pakistan, then “we would pursue those targets.” Meanwhile, talk about a possible attack on Iran, a nation that ranked on America’s axis of evil hit parade, continues.

5. Think-Tank Saber Rattling – Keir A. Lieber and Daryl G. Press write an article in the prestigious U.S. journal Foreign Affairs entitled “Nuclear Primacy” (March/April 2006), which argues, in a nutshell, that “It will probably soon be possible for the United States to destroy the long-range nuclear arsenals of Russia or China with a first strike.” Is this the sort of article that America should be supporting if it wants Russia to believe that elements of the proposed U.S. missile defense system in Poland and… oops! Don’t want to spoil the plot! Anyways, Moscow ‘responds’ with very accurate penmanship one year later as it test-fires its new RS-24 ballistic missile that it said could “overcome any potential missile defense systems developed by foreign countries.”

4. Cheney Comfort – One month after the above love letter hit newsstands, Vice President Dick Cheney, during a trip to Vilnius, Lithuania, assuaged Moscow’s fears by reiterating, once again: “Russia has nothing to fear and everything to gain” by ‘democratic activity’ on her borders.

3. Gates’ Gated Community – In early 2007, Pentagon chief Robert Gates urged viligance when he warned, “We don’t know what’s going to develop in places like Russia and China, in North Korea, in Iran and elsewhere.” Was this a simple case of mistaken identity by a former White House Russian analyst? Whatever the case, it certainly helped to provoke Putin’s heated Munich speech in February, where he admonished the world’s “one master, one sovereign.”

2. EU Culpability – As the War on Terror continues, Europe is losing its Snow White innocence. As the German magazine Der Spiegel reported, “On July 19, 2002, a Gulfstream business jet took off from Frankfurt am Main bound for Amman, Jordan. The flight received an AFTM exempt [pilot code for ‘extreme situation’], although it carried neither patients nor politicians. Instead, the jet was carrying a CIA team that took a Mauritanian terrorism suspect… to Guantanamo.” Der Spiegel reported that this “camouflaging of an illegal kidnapping as a rescue flight” was not an isolated event: There were 390 such takeoffs and landings in Germany between 2002 and 2006. And considering Eastern European hotels, it’s just too scary to consider those secret terrorist prisons that allegedly exist in Poland and Romania.

1. Don’t Worry, These anti-Missile Missiles won’t Hurt You, Really – Washington is now incredulous, shocked, mortified that Moscow has the nerve to suggest that there could be less than good intentions involved in the construction of an anti-missile defense system in Poland and the Czech Republic, even though there are no bad-guy technologies on the horizon that such a system could intercept. Go figure!

By Robert Bridge