Mathematicians Find New Solutions To An Ancient Puzzle

ScienceDaily (Mar. 18, 2008) — Many people find complex math puzzling, including some mathematicians. Recently, mathematician Daniel J. Madden and retired physicist, Lee W. Jacobi, found solutions to a puzzle that has been around for centuries.

Jacobi and Madden have found a way to generate an infinite number of solutions for a puzzle known as 'Euler's Equation of degree four.'

The equation is part of a branch of mathematics called number theory. Number theory deals with the properties of numbers and the way they relate to each other. It is filled with problems that can be likened to numerical puzzles.

"It's like a puzzle: can you find four fourth powers that add up to another fourth power" Trying to answer that question is difficult because it is highly unlikely that someone would sit down and accidentally stumble upon something like that," said Madden, an associate professor of mathematics at The University of Arizona in Tucson.

Equations are puzzles that need certain solutions "plugged into them" in order to create a statement that obeys the rules of logic.

For example, think of the equation x + 2 = 4. Plugging "3" into the equation doesn't work, but if x = 2, then the equation is correct.

In the mathematical puzzle that Jacobi and Madden worked on, the problem was finding variables that satisfy a Diophantine equation of order four. These equations are so named because they were first studied by the ancient Greek mathematician Diophantus, known as 'the father of algebra.'

In its most simple version, the puzzle they were trying to solve is the equation: (a)(to the fourth power) + (b)(to the fourth power) + (c)(to the fourth power) + (d)(to the fourth power) = (a + b + c + d)(to the fourth power)

That equation, expressed mathematically, is: a⁴ + b⁴ +c⁴ +d⁴ = (a + b + c + d)⁴.

Madden and Jacobi found a way to find the numbers to substitute, or plug in, for the a's, b's, c's and d's in the equation. All the solutions they have found so far are very large numbers.

In 1772, Euler, one of the greatest mathematicians of all time, hypothesized that to satisfy equations with higher powers, there would need to be as many variables as that power. For example, a fourth order equation would need four different variables, like the equation above.

Euler's hypothesis was disproved in 1987 by a Harvard graduate student named Noam Elkies. He found a case where only three variables were needed. Elkies solved the equation: (a)(to the fourth power) + (b)(to the fourth power) + (c)(to the fourth power) = e(to the fourth power), which shows only three variables are needed to create a variable that is a fourth power.

Inspired by the accomplishments of the 22-year-old graduate student, Jacobi began working on mathematics as a hobby after he retired from the defense industry in 1989.

Fortunately, this was not the first time he had dealt with Diophantine equations. He was familiar with them because they are commonly used in physics for calculations relating to string theory.

Jacobi started searching for new solutions to the puzzle using methods he found in some number theory texts and academic papers.

He used those resources and Mathematica, a computer program used for mathematical manipulations.

Jacobi initially found a solution for which each of the variables was 200 digits long. This solution was different from the other 88 previously known solutions to this puzzle, so he knew he had found something important.

Jacobi then showed the results to Madden. But Jacobi initially miscopied a variable from his Mathematica computer program, and so the results he showed Madden were incorrect.

"The solution was wrong, but in an interesting way. It was close enough to make me want to see where the error occurred," Madden said.

When they discovered that the solution was invalid only because of Jacobi's transcription error, they began collaborating to find more solutions.

Madden and Jacobi used elliptic curves to generate new solutions. Each solution contains a seed for creating more solutions, which is much more efficient than previous methods used.

In the past, people found new solutions by using computers to analyze huge amounts of data. That required a lot of computing time and power as the magnitude of the numbers soared.

Now people can generate as many solutions as they wish. There are an infinite number of solutions to this problem, and Madden and Jacobi have found a way to find them all.

"Modern number theory allowed me to see with more clarity the implications of his (Jacobi's) calculations," Madden said.

"It was a nice collaboration," Jacobi said. "I have learned a certain amount of new things about number theory; how to think in terms of number theory, although sometimes I can be stubbornly algebraic."

The article, ""On a⁴ + b⁴ +c⁴ +d⁴ = (a + b + c + d)⁴" is published in the March issue of The American Mathematical Monthly.

Infringement!

By PETER LAURIA of the New York Post

Artist managers are girding for battle with their music overlords over when their clients are going to see some of the dough negotiated last year in copyright-infringement settlements with a host of Web sites.

Universal Music, Warner Music and EMI - either collectively or individually - settled claims with Napster, Kazaa and Bolt.com. Napster alone had to cough up $270 million.

The fourth major label, SonyBMG, was not part of the suit because Napster was owned by BMG parent company Bertelsmann.

All four struck separate deals with YouTube that included revenue participation.

A contingent of prominent artist managers claims that little to none of that money has trickled down to their clients. They are now considering legal action.

"Artist managers and lawyers have been wondering for months when their artists will see money from the copyright settlements and how it will be accounted for," said lawyer John Branca, who has represented Korn, Don Henley, and The Rolling Stones, among others.

"Some of them are even talking about filing lawsuits if they don't get paid soon."

Record label sources said corporate bosses are still deciding on how best to split the money. In determining the payout, they said not every artist is owed money and it must be calculated with regard to the level of copyright infringement for each artist.

What's more, these sources said that after the labels recouped their legal expenses, there wasn't much left to pass along to the artists.

But a source on the artists' side said that is an argument heard all too often in the music business.

Getting money out of the major labels is never easy, but given the industry's downward financial spiral it is exponentially more difficult now, the source said.

"The record labels are experts at transferring money around and putting the onus on artists managers to find it."

Irving Azoff, the legendary talent manager for The Eagles and Jewel, among others, echoed that sentiment.

"They will play hide and seek, but eventually will be forced to pay something," Azoff said. "The record companies have even tried to credit unrecouped accounts. It's never easy for an artist to get paid their fair share."

Reps for the three labels dispute the notion that they are withholding settlement money.

A spokeswoman for EMI said the label has started the process of "sharing proceeds from the Napster and Kazaa settlements with artists and writers whose work was infringed upon."

Warner Music's representative said the label "is sharing the Napster settlement with its recording artists and songwriters and at this stage nearly all settlement monies have been disbursed."

A Universal Music spokesman said the label's policy "is to share its portion of various settlements with its artists, regardless of whether their contracts require it."

Is there another planet in the solar system?

Found at Bad Astronomy.

Could there be another planet lurking in the dark, frigid outskirts of the solar system?

This isn’t as silly as it seems at first. No, I’m not talking Nibiru or any of that other nonsense (and it is nonsense), I’m talking about an actual planet, Earth-sized or so, that could be orbiting the Sun well beyond Pluto Neptune.

Why would we think there might be one out there?

We see some stars in the midst of forming planets. The stars are surrounded by thick disks of material, and in some we can actually see gaps in the disk, dark rings like the gaps in Saturn’s rings, that we think are due to forming planets gobbling up material in the ring. You’d think the disk would fade away with distance form the star, like our air gets thinner with altitude. But some disks appear to have sharp outer edges. This can be caused by a planet orbiting outside the disk; its gravity sweeps up the material and over time cleans up everything farther out. In one disk, this sharp boundary indicates a planet 200 AU out (an AU is the distance of the Earth to the Sun, about 150 million kilometers or 93 million miles).

Neptune orbits at 30 AU from the Sun, so 200 AU is a long way out. Could a planet like that have formed in our solar system? Maybe. Thing is, while our proto-planetary disk has been gone for billions of years, we do have lots of objects out past Neptune: the Trans-Neptunian Objects (they have lots of names, including Kuiper Belt Objects). These are basically giant balls of ice, some hundreds of miles across. As a group they form a puffy disk of objects stretching from Neptune’s orbit outward… but they seem to abruptly stop past about 50 AU out from the Sun. That’s called the Kuiper Cliff, the cause of which is unknown. Incidentally, it’s not because they’re too faint to see (that is, they’re there but we can’t spot them); at that distance we should have spotted lots of them by now.

Not only that, but a lot of these objects have orbits that are tilted more and are more elliptical than you’d expect if they just formed a long time ago and were left alone. Theyir orbits don’t bring them in very close — they tend to stay outside of Neptune’s orbit — but again, this is something that needs to be explained.

Could it be that there is another massive planet orbiting the Sun, way out there, which has swept up the objects gravitationally, creating the Kuiper Cliff and tossing the iceballs into tilted, oval orbits?

A newly released paper shows that may very well be the case. A team of scientists ran a whole mess of simulations, and found that a small planet (in this case, around half the size of the Earth) could have formed inside Neptune’s orbit (where there was plenty of material in the early solar system), gotten tossed into a bigger orbit by Neptune, and then knocked around the orbits of the iceballs, distorting their orbits and creating the Kuiper Cliff.

This idea is not new, but this new research is a provocative indicator of such a planet’s likelihood of existence. I’m not saying it’s out there, but it’s worth looking for. In fact, I’ve been saying that since about 1998 or so, when I worked on Hubble and was involved with a project that found a truncated disk around another star. I even worked with another astronomer on the team to investigate whether the robotic telescopes used to look for Near Earth Asteroids could spot such a planet.

It’s not all that easy. It wouldn’t be too faint to see, necessarily, but it’s a big sky. At that distance, the planet would move slowly, and the orbital motion would be hard to distinguish given the procedures used by NEA searches. We tried to convince some of them to modify their software to look for Planet X (yes, why not, though now it would be Planet IX), but we were met with mixed success. The fact that no one has discovered this planet shows you that this is still hard to do.

But maybe, just maybe, with this new research we’ll get people looking more seriously. It’s amazing to me that we can understand so much about galaxies and hugely distant objects, but find that there may be surprises waiting for us in our own back yard.

Fortune Cookies Help Cops Nab Suspect

(03-07) 19:35 PST Tulsa, Okla. (AP) --

Two fortune cookies helped Tulsa police make an arrest after a pair of break-ins Chinese restaurants. Terrence Middleton, 30, was booked Friday on charges of second-degree burglary and attempted second-degree burglary after police responded to a burglar alarm to find him with more than $20 in coins and the cookies in his pockets, Officer Leland Ashley said.

Middleton was being held on $15,000 bond.

Ashley said police were able to link Middleton to the Asian Express that was robbed because he had possession of the same type of fortune cookies that were at the restaurant.

The alarm went off at the Asian Express about 14 minutes after one sounded at the Chinese Chef Restaurant down the street Thursday night, Ashley said.

When officers arrived, both restaurants had their front doors broken. At the second restaurant, the cash register had been pulled open.

Minutes later, officers stopped Middleton, who was walking down the street, and he dropped various coins and a prison identification card, Ashley said.

Ashley said it appeared there was nothing stolen from the first restaurant, and all that was missing from the second restaurant was $20 in change — and the fortune cookies.

AP Probe Finds Drugs in Drinking Water

By JEFF DONN, MARTHA MENDOZA and JUSTIN PRITCHARD
Associated Press Writers

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A vast array of pharmaceuticals (AP) -- including antibiotics, anti-convulsants, mood stabilizers and sex hormones - have been found in the drinking water supplies of at least 41 million Americans, an Associated Press investigation shows.

To be sure, the concentrations of these pharmaceuticals are tiny, measured in quantities of parts per billion or trillion, far below the levels of a medical dose. Also, utilities insist their water is safe.

But the presence of so many prescription drugs - and over-the-counter medicines like acetaminophen and ibuprofen - in so much of our drinking water is heightening worries among scientists of long-term consequences to human health.

In the course of a five-month inquiry, the AP discovered that drugs have been detected in the drinking water supplies of 24 major metropolitan areas - from Southern California to Northern New Jersey, from Detroit to Louisville, Ky.

Water providers rarely disclose results of pharmaceutical screenings, unless pressed, the AP found. For example, the head of a group representing major California suppliers said the public "doesn't know how to interpret the information" and might be unduly alarmed.

How do the drugs get into the water?

People take pills. Their bodies absorb some of the medication, but the rest of it passes through and is flushed down the toilet. The wastewater is treated before it is discharged into reservoirs, rivers or lakes. Then, some of the water is cleansed again at drinking water treatment plants and piped to consumers. But most treatments do not remove all drug residue.

And while researchers do not yet understand the exact risks from decades of persistent exposure to random combinations of low levels of pharmaceuticals, recent studies - which have gone virtually unnoticed by the general public - have found alarming effects on human cells and wildlife.

"We recognize it is a growing concern and we're taking it very seriously," said Benjamin H. Grumbles, assistant administrator for water at the U.S. Environmental Protection Agency.

Members of the AP National Investigative Team reviewed hundreds of scientific reports, analyzed federal drinking water databases, visited environmental study sites and treatment plants and interviewed more than 230 officials, academics and scientists. They also surveyed the nation's 50 largest cities and a dozen other major water providers, as well as smaller community water providers in all 50 states.

Here are some of the key test results obtained by the AP:

-Officials in Philadelphia said testing there discovered 56 pharmaceuticals or byproducts in treated drinking water, including medicines for pain, infection, high cholesterol, asthma, epilepsy, mental illness and heart problems. Sixty-three pharmaceuticals or byproducts were found in the city's watersheds.

-Anti-epileptic and anti-anxiety medications were detected in a portion of the treated drinking water for 18.5 million people in Southern California.

-Researchers at the U.S. Geological Survey analyzed a Passaic Valley Water Commission drinking water treatment plant, which serves 850,000 people in Northern New Jersey, and found a metabolized angina medicine and the mood-stabilizing carbamazepine in drinking water.

-A sex hormone was detected in San Francisco's drinking water.

-The drinking water for Washington, D.C., and surrounding areas tested positive for six pharmaceuticals.

-Three medications, including an antibiotic, were found in drinking water supplied to Tucson, Ariz.

The situation is undoubtedly worse than suggested by the positive test results in the major population centers documented by the AP.

The federal government doesn't require any testing and hasn't set safety limits for drugs in water. Of the 62 major water providers contacted, the drinking water for only 28 was tested. Among the 34 that haven't: Houston, Chicago, Miami, Baltimore, Phoenix, Boston and New York City's Department of Environmental Protection, which delivers water to 9 million people.

Some providers screen only for one or two pharmaceuticals, leaving open the possibility that others are present.

The AP's investigation also indicates that watersheds, the natural sources of most of the nation's water supply, also are contaminated. Tests were conducted in the watersheds of 35 of the 62 major providers surveyed by the AP, and pharmaceuticals were detected in 28.

Yet officials in six of those 28 metropolitan areas said they did not go on to test their drinking water - Fairfax, Va.; Montgomery County in Maryland; Omaha, Neb.; Oklahoma City; Santa Clara, Calif., and New York City.

The New York state health department and the USGS tested the source of the city's water, upstate. They found trace concentrations of heart medicine, infection fighters, estrogen, anti-convulsants, a mood stabilizer and a tranquilizer.

City water officials declined repeated requests for an interview. In a statement, they insisted that "New York City's drinking water continues to meet all federal and state regulations regarding drinking water quality in the watershed and the distribution system" - regulations that do not address trace pharmaceuticals.

In several cases, officials at municipal or regional water providers told the AP that pharmaceuticals had not been detected, but the AP obtained the results of tests conducted by independent researchers that showed otherwise. For example, water department officials in New Orleans said their water had not been tested for pharmaceuticals, but a Tulane University researcher and his students have published a study that found the pain reliever naproxen, the sex hormone estrone and the anti-cholesterol drug byproduct clofibric acid in treated drinking water.

Of the 28 major metropolitan areas where tests were performed on drinking water supplies, only Albuquerque; Austin, Texas; and Virginia Beach, Va.; said tests were negative. The drinking water in Dallas has been tested, but officials are awaiting results. Arlington, Texas, acknowledged that traces of a pharmaceutical were detected in its drinking water but cited post-9/11 security concerns in refusing to identify the drug.

The AP also contacted 52 small water providers - one in each state, and two each in Missouri and Texas - that serve communities with populations around 25,000. All but one said their drinking water had not been screened for pharmaceuticals; officials in Emporia, Kan., refused to answer AP's questions, also citing post-9/11 issues.

Rural consumers who draw water from their own wells aren't in the clear either, experts say.

The Stroud Water Research Center, in Avondale, Pa., has measured water samples from New York City's upstate watershed for caffeine, a common contaminant that scientists often look for as a possible signal for the presence of other pharmaceuticals. Though more caffeine was detected at suburban sites, researcher Anthony Aufdenkampe was struck by the relatively high levels even in less populated areas.

He suspects it escapes from failed septic tanks, maybe with other drugs. "Septic systems are essentially small treatment plants that are essentially unmanaged and therefore tend to fail," Aufdenkampe said.

Even users of bottled water and home filtration systems don't necessarily avoid exposure. Bottlers, some of which simply repackage tap water, do not typically treat or test for pharmaceuticals, according to the industry's main trade group. The same goes for the makers of home filtration systems.

Contamination is not confined to the United States. More than 100 different pharmaceuticals have been detected in lakes, rivers, reservoirs and streams throughout the world. Studies have detected pharmaceuticals in waters throughout Asia, Australia, Canada and Europe - even in Swiss lakes and the North Sea.

For example, in Canada, a study of 20 Ontario drinking water treatment plants by a national research institute found nine different drugs in water samples. Japanese health officials in December called for human health impact studies after detecting prescription drugs in drinking water at seven different sites.

In the United States, the problem isn't confined to surface waters. Pharmaceuticals also permeate aquifers deep underground, source of 40 percent of the nation's water supply. Federal scientists who drew water in 24 states from aquifers near contaminant sources such as landfills and animal feed lots found minuscule levels of hormones, antibiotics and other drugs.

Perhaps it's because Americans have been taking drugs - and flushing them unmetabolized or unused - in growing amounts. Over the past five years, the number of U.S. prescriptions rose 12 percent to a record 3.7 billion, while nonprescription drug purchases held steady around 3.3 billion, according to IMS Health and The Nielsen Co.

"People think that if they take a medication, their body absorbs it and it disappears, but of course that's not the case," said EPA scientist Christian Daughton, one of the first to draw attention to the issue of pharmaceuticals in water in the United States.

Some drugs, including widely used cholesterol fighters, tranquilizers and anti-epileptic medications, resist modern drinking water and wastewater treatment processes. Plus, the EPA says there are no sewage treatment systems specifically engineered to remove pharmaceuticals.

One technology, reverse osmosis, removes virtually all pharmaceutical contaminants but is very expensive for large-scale use and leaves several gallons of polluted water for every one that is made drinkable.

Another issue: There's evidence that adding chlorine, a common process in conventional drinking water treatment plants, makes some pharmaceuticals more toxic.

Human waste isn't the only source of contamination. Cattle, for example, are given ear implants that provide a slow release of trenbolone, an anabolic steroid used by some bodybuilders, which causes cattle to bulk up. But not all the trenbolone circulating in a steer is metabolized. A German study showed 10 percent of the steroid passed right through the animals.

Water sampled downstream of a Nebraska feedlot had steroid levels four times as high as the water taken upstream. Male fathead minnows living in that downstream area had low testosterone levels and small heads.

Other veterinary drugs also play a role. Pets are now treated for arthritis, cancer, heart disease, diabetes, allergies, dementia, and even obesity - sometimes with the same drugs as humans. The inflation-adjusted value of veterinary drugs rose by 8 percent, to $5.2 billion, over the past five years, according to an analysis of data from the Animal Health Institute.

Ask the pharmaceutical industry whether the contamination of water supplies is a problem, and officials will tell you no. "Based on what we now know, I would say we find there's little or no risk from pharmaceuticals in the environment to human health," said microbiologist Thomas White, a consultant for the Pharmaceutical Research and Manufacturers of America.

But at a conference last summer, Mary Buzby - director of environmental technology for drug maker Merck & Co. Inc. - said: "There's no doubt about it, pharmaceuticals are being detected in the environment and there is genuine concern that these compounds, in the small concentrations that they're at, could be causing impacts to human health or to aquatic organisms."

Recent laboratory research has found that small amounts of medication have affected human embryonic kidney cells, human blood cells and human breast cancer cells. The cancer cells proliferated too quickly; the kidney cells grew too slowly; and the blood cells showed biological activity associated with inflammation.

Also, pharmaceuticals in waterways are damaging wildlife across the nation and around the globe, research shows. Notably, male fish are being feminized, creating egg yolk proteins, a process usually restricted to females. Pharmaceuticals also are affecting sentinel species at the foundation of the pyramid of life - such as earth worms in the wild and zooplankton in the laboratory, studies show.

Some scientists stress that the research is extremely limited, and there are too many unknowns. They say, though, that the documented health problems in wildlife are disconcerting.

"It brings a question to people's minds that if the fish were affected ... might there be a potential problem for humans?" EPA research biologist Vickie Wilson told the AP. "It could be that the fish are just exquisitely sensitive because of their physiology or something. We haven't gotten far enough along."

With limited research funds, said Shane Snyder, research and development project manager at the Southern Nevada Water Authority, a greater emphasis should be put on studying the effects of drugs in water.

"I think it's a shame that so much money is going into monitoring to figure out if these things are out there, and so little is being spent on human health," said Snyder. "They need to just accept that these things are everywhere - every chemical and pharmaceutical could be there. It's time for the EPA to step up to the plate and make a statement about the need to study effects, both human and environmental."

To the degree that the EPA is focused on the issue, it appears to be looking at detection. Grumbles acknowledged that just late last year the agency developed three new methods to "detect and quantify pharmaceuticals" in wastewater. "We realize that we have a limited amount of data on the concentrations," he said. "We're going to be able to learn a lot more."

While Grumbles said the EPA had analyzed 287 pharmaceuticals for possible inclusion on a draft list of candidates for regulation under the Safe Drinking Water Act, he said only one, nitroglycerin, was on the list. Nitroglycerin can be used as a drug for heart problems, but the key reason it's being considered is its widespread use in making explosives.

So much is unknown. Many independent scientists are skeptical that trace concentrations will ultimately prove to be harmful to humans. Confidence about human safety is based largely on studies that poison lab animals with much higher amounts.

There's growing concern in the scientific community, meanwhile, that certain drugs - or combinations of drugs - may harm humans over decades because water, unlike most specific foods, is consumed in sizable amounts every day.

Our bodies may shrug off a relatively big one-time dose, yet suffer from a smaller amount delivered continuously over a half century, perhaps subtly stirring allergies or nerve damage. Pregnant women, the elderly and the very ill might be more sensitive.

Many concerns about chronic low-level exposure focus on certain drug classes: chemotherapy that can act as a powerful poison; hormones that can hamper reproduction or development; medicines for depression and epilepsy that can damage the brain or change behavior; antibiotics that can allow human germs to mutate into more dangerous forms; pain relievers and blood-pressure diuretics.

For several decades, federal environmental officials and nonprofit watchdog environmental groups have focused on regulated contaminants - pesticides, lead, PCBs - which are present in higher concentrations and clearly pose a health risk.

However, some experts say medications may pose a unique danger because, unlike most pollutants, they were crafted to act on the human body.

"These are chemicals that are designed to have very specific effects at very low concentrations. That's what pharmaceuticals do. So when they get out to the environment, it should not be a shock to people that they have effects," says zoologist John Sumpter at Brunel University in London, who has studied trace hormones, heart medicine and other drugs.

And while drugs are tested to be safe for humans, the timeframe is usually over a matter of months, not a lifetime. Pharmaceuticals also can produce side effects and interact with other drugs at normal medical doses. That's why - aside from therapeutic doses of fluoride injected into potable water supplies - pharmaceuticals are prescribed to people who need them, not delivered to everyone in their drinking water.

"We know we are being exposed to other people's drugs through our drinking water, and that can't be good," says Dr. David Carpenter, who directs the Institute for Health and the Environment of the State University of New York at Albany.

The $2 Trillion Nightmare

By BOB HERBERT

New York Times

We’ve been hearing a lot about “Saturday Night Live” and the fun it has been having with the presidential race. But hardly a whisper has been heard about a Congressional hearing in Washington last week on a topic that could have been drawn, in all its tragic monstrosity, from the theater of the absurd.

The war in Iraq will ultimately cost U.S. taxpayers not hundreds of billions of dollars, but an astonishing $2 trillion, and perhaps more. There has been very little in the way of public conversation, even in the presidential campaigns, about the consequences of these costs, which are like a cancer inside the American economy.

On Thursday, the Joint Economic Committee, chaired by Senator Chuck Schumer, conducted a public examination of the costs of the war. The witnesses included the Nobel Prize-winning economist, Joseph Stiglitz (who believes the overall costs of the war — not just the cost to taxpayers — will reach $3 trillion), and Robert Hormats, vice chairman of Goldman Sachs International.

Both men talked about large opportunities lost because of the money poured into the war. “For a fraction of the cost of this war,” said Mr. Stiglitz, “we could have put Social Security on a sound footing for the next half-century or more.”

Mr. Hormats mentioned Social Security and Medicare, saying that both could have been put “on a more sustainable basis.” And he cited the committee’s own calculations from last fall that showed that the money spent on the war each day is enough to enroll an additional 58,000 children in Head Start for a year, or make a year of college affordable for 160,000 low-income students through Pell Grants, or pay the annual salaries of nearly 11,000 additional border patrol agents or 14,000 more police officers.

What we’re getting instead is the stuff of nightmares. Mr. Stiglitz, a professor at Columbia, has been working with a colleague at Harvard, Linda Bilmes, to document, among other things, some of the less obvious costs of the war. These include the obligation to provide health care and disability benefits for returning veterans. Those costs will be with us for decades.

Mr. Stiglitz noted that nearly 40 percent of the 700,000 troops from the first gulf war, which lasted just a month, have become eligible for disability benefits. The current war is approaching five years in duration.

“Imagine then,” said Mr. Stiglitz, “what a war — that will almost surely involve more than 2 million troops and will almost surely last more than six or seven years — will cost. Already we are seeing large numbers of returning veterans showing up at V.A. hospitals for treatment, large numbers applying for disability and large numbers with severe psychological problems.”

The Bush administration has tried its best to conceal the horrendous costs of the war. It has bypassed the normal budgetary process, financing the war almost entirely through “emergency” appropriations that get far less scrutiny.

Even the most basic wartime information is difficult to come by. Mr. Stiglitz, who has written a new book with Ms. Bilmes called “The Three Trillion Dollar War,” said they had to go to veterans’ groups, who in turn had to resort to the Freedom of Information Act, just to find out how many Americans had been injured in Iraq.

Mr. Stiglitz and Mr. Hormats both addressed the foolhardiness of waging war at the same time that the government is cutting taxes and sharply increasing non-war-related expenditures.

Mr. Hormats told the committee:

“Normally, when America goes to war, nonessential spending programs are reduced to make room in the budget for the higher costs of the war. Individual programs that benefit specific constituencies are sacrificed for the common good ... And taxes have never been cut during a major American war. For example, President Eisenhower adamantly resisted pressure from Senate Republicans for a tax cut during the Korean War.”

Said Mr. Stiglitz: “Because the administration actually cut taxes as we went to war, when we were already running huge deficits, this war has, effectively, been entirely financed by deficits. The national debt has increased by some $2.5 trillion since the beginning of the war, and of this, almost $1 trillion is due directly to the war itself ... By 2017, we estimate that the national debt will have increased, just because of the war, by some $2 trillion.”

Some former presidents — Washington, Franklin Roosevelt, Truman, Eisenhower — were quoted at the hearing on the need for accountability and shared sacrifice during wartime. But this is the 21st century. That ancient rhetoric can hardly be expected to compete for media attention, even in a time of war, with the giddy fun of S.N.L.

It’s a new era.

Black Fungus Found in Chernobyl Eats Harmful Radiation

Found at Foxnews

Fungi could eat dangerous radiation to survive, an unexpected finding that could one day help feed astronauts in space — at least those willing to eat a crawling fungus.

The research began with the discovery of black fungus growing on the walls of the damaged, highly radioactive Chernobyl nuclear reactor and collected by robots.

The fungus was rich with melanin, the same pigment that gives human skin its color, protecting the skin from solar and ultraviolet radiation. Melanin is found in many, if not most, fungal species.

"The fungal kingdom comprises more species than any other plant or animal kingdom," said researcher Arturo Casadevall, an immunologist at Albert Einstein College of Medicine in New York.

Nuclear and other high-energy reactions give off ionizing radiation — dangerous rays and particles that can damage genes and thus cause mutations, and eventually cancer.

"Just as the pigment chlorophyll converts sunlight into chemical energy that allows green plants to live and grow," so might melanin help fungi make use of ionizing radiation, said nuclear medicine specialist Ekaterina Dadachova at the Albert Einstein College of Medicine.

The scientists experimented on three species of fungi. They consistently found that ionizing radiation significantly boosted the growth of fungi that contained melanin.

"In general we think of radiation as something bad or harmful. Here we have a situation where these fungi appear to benefit, which is unexpected," Casadevall told LiveScience.

For example, the researchers exposed two kinds of fungi — one that naturally contained melanin (Wangiella dermatitidis) and another that scientists induced to make the pigment (Crytococcus neoformans) — to levels of ionizing radiation about 500 times higher than normal, the doses one might see at high altitudes where atmospheric shielding from cosmic rays is lessened.

Both species grew significantly faster, as detailed in the May 23 issue of the journal PLoS ONE.

The researchers stressed these findings do not mean fungi can eat radioactive matter and somehow cleanse it. Rather, the fungi can simply harness the energy that radioactive materials give off.

The ability of fungi to live off ionizing radiation could prove useful to people.

"Since ionizing radiation is prevalent in outer space, astronauts might be able to rely on fungi as an inexhaustible food source on long missions or for colonizing other planets," Dadachova said.

Casadevall also noted that the melanin in fungi is no different chemically from the melanin in human skin.

"It's pure speculation — but not outside the realm of possibility — that melanin could be providing energy to skin cells," he said. "While it wouldn't be enough energy to fuel a run on the beach, maybe it could help you to open an eyelid."