There's a new Sage in mathematics

Need to solve a calculus problem, model a galaxy, map a 12-dimensional object, or calculate rainfall patterns under global warming? Until now you'd have to spend hundreds or even thousands of dollars on a commercial software program like Matlab, Maple, Mathematica, or Magma.

But now your problem can be solved for free, using an open-source tool called Sage that recently won first prize in the scientific software division of Les Trophées du Libre.

William Stein, associate professor of mathematics and lead developer of the tool, worked with over a hundred mathematicians to combine user-friendly and powerful number-crunching with new features such as collaborative online worksheets.

My question is, with the state of American math education, will anyone know how to use it?

A new way to beat the stock market

Do you remember the first time you heard the sure-fire advice to "buy low and sell high"?

Well, researchers at the University of Warwick discovered a way to detect precisely when ordered patterns form in everything from plasma in the solar wind and fusion reactors, to crowds of people, to flocks of birds. And the technique can be used to find unusual patterns in stock market prices.

They analyzed when complex systems move suddenly from chaos to order using an information technology tool called mutual information that can detect patterns and correlations from a very small set of points, as few as ten within a large system. Their analysis had one-fourth the error rate of traditional statistical methods.

I guess all stock market traders have to do now is buy chaos and sell order.

A new solution to support Moore's Law

Moore's Law, formulated by Intel co-founder Gordon E. Moore in 1965, says the number of transistors on an integrated circuit doubles approximately every two years. For more than half a century the law has held.

But engineers do not see conventional computers being able to support Moore's Law much longer. So it was exciting news when researchers at the Foundation for Fundamental Research on Matter controlled the spin of a single electron using only electric fields, clearing the way to make a super-fast quantum computer, in which an electron's spin can exist in both its states simultaneously.

Hmm, kind of sounds like a Presidential campaign.

Using math to avoid the Christmas traffic jam

Have you ever been stuck in bumper-to-bumper traffic and then with no apparent reason the traffic just starts moving again at 60 mph? A team of mathematicians from the Universities of Exeter, Bristol and Budapest published the reason why in the journal Proceedings of the Royal Society.

Something as simple as a slow truck moving into a different lane on a busy highway - defined as more than 25 vehicles per mile, or one every 200 feet - can cause a ripple effect called a backward traveling wave.

University of Exeter Dr. Gábor Orosz said, "When you tap your brake, the traffic may come to a full stand-still several miles behind you. It really matters how hard you brake - a slight braking from a driver who has identified a problem early will allow the traffic flow to remain smooth. Heavier braking, usually caused by a driver reacting late to a problem, can affect traffic flow for many miles."

Just great. Now we can ruin hundreds of people's day just by braking too late on the highway.

Monkey math

Not good at math? Monkeys might actually do it better: a new study shows that monkeys can perform mental addition in a manner remarkably similar to college students.

Monkeys and college students took the same test - one that showed possible totals for the number of dots on a computer screen. The average response time for both monkeys and humans was about one second; the college students were correct 94 percent of the time and the monkeys 76 percent.

The findings point to ancient origins of math in humanity and our distant relatives. The researchers did say that monkeys will not pass college math tests anytime soon, although 76 percent probably will do it for most math classes.

The mathematics of square dancing

The Montessori method calls for students to use all their senses and their bodies to learn math. Sounds good if you're in Kindergarten.

But Math Professor David Schmitz of North Central College in Napierville, IL teaches a class called the Mathematics of Square Dancing, where students learn group theory, permutations, and other math concepts by moving their bodies. North Central now even sports a square dancing club, called the Square Roots.

To quote Professor Schmitz, "It's math in motion: you're walking through mathematics and would have no idea you're working with concepts that most college math majors don't study until their fourth year," adding that dancing is like "solving a Rubik's Cube."

Maybe there is hope after all for the U.S., currently in the bottom 20% among industrialized nations in math performance: we do have one million square dancers.

The errors of excellence

Life is often random. But not always so. Warren Buffett, day traders, and math PhD quantitative financial analysts have all made millions even billions by acting on the fact that not all variation is noise.

In an article published in Nature Magazine, researchers Evren Turner and Michael Brainard believe that errors made by high-performance athletes, musicians, and even CEOs vary not because of noise or uncontrolled variables but due to an attempt to learn and further improve performance by trial and error. To reach their conclusion they analyzed errors in adult bengalese finch birdsong, even that which was previously perfectly sung.

Here's my conclusion: perfection is a goal never reached perhaps because it is impossible to define.

Infinity

Mathematicians often use the concept of infinity. But real life applications abound. For example, each of our lives may be considered infinite as one never knows birth or death, just what comes in between.

Which shows that infinity is one of those things that makes the brain hurt. Zeno's infinity paradox has inspired countless (see?) philosophers. The idea of adding up infinitely many infinitesimally small amounts to make something is the basis of calculus. In the stock market short sellers have a theoretically infinite loss potential.

German mathematician Georg Cantor proved that there are different orders of infinity: some infinities are larger than others. There are more real numbers, for example, than counting numbers, even though there is an infinite number of each.

Einstein proposed that the universe is infinite in three dimensions, and finite in four, somewhat following the math of Gabriel's Horn, which is infinite in surface area and finite in volume, making it possible to fill but not to wash.

Is your head hurting yet?

Glowing in the dark

Scientists play cat and mouse in two related stories.

First, South Korean scientists cloned cats with a gene that produces a red fluorescent protein that makes them glow in the dark when exposed to ultraviolet rays. The experiment may help people with certain genetic disorders.

In another experiment, Japanese scientists found and turned off the gene that causes a mouse's fear of cats, removing through genetic engineering the nasal cells that mice use to detect cat odor. Thus a mouse's fear is genetic and not learned behavior.

It's just a matter of time - and studies - when we'll find out if both cats and mice fear people that glow in the dark.

Simple voting math not so simple in Ohio

A team organized to study Ohio election integrity picked locks to access memory cards and used hand-held devices to plug false vote counts into machines. At boards of election, it introduced malignant software into servers.

The team found it easy to corrupt election equipment and software made by several companies, including Elections Systems and Software; Premier Election Solutions, formerly Diebold; and Hart InterCivic.

Now Ohio Secretary of State Jennifer Brunner wants to replace all Ohio voting machines and use optical scanners that read ballots voters have filled in by hand.

This all brings to mind Florida's 2000 Secretary of State Katherine Harris. The next thing you know Jennifer Brunner will be running for Congress, using the voting machines she conveniently installed. At least they won'

Brain teasers

A cowboy rides into town on Friday, stays two consecutive days, and leaves on Friday. How could that be?

That's a typical interview question asked by cool companies that seek creative thinkers. The best candidates don't score points for the right answer, just for the right approach, kind of like new math.

Google Labs even had its own aptitude test, called GLAT. My favorite question on that test was, "what was the most beautiful math question ever derived?"

So what is the deal with the cowboy? If Friday is a day of the week, for which our thinking is reinforced by the fact that the cowboy stayed two consecutive days, the question seems impossible. So our assumption that Friday is a day of the week could be wrong. For example, Friday could be the name of the cowboy's horse.

Companies have come a long way from, "tell me about your last job." But they still ask you to work on Friday.

Ticket price math

I could never understand why there are ticket scalpers. What ever happened to the free market? Why don't stadiums, theaters, and concert halls just charge what people will pay?

As usual the market will determine the final selling price but here's the real question: If someone's going to pay $1,000 for a ticket to go see Hannah Montana that originally cost $100, should that extra $900 go to a scalper - or to Miley Cyrus? I know what Miley Cyrus would say!

Other models are available. Priceline has an opaque pricing system; eBay's auction is more transparent. But neither is a fluid bid-and-ask system that would maximize the efficiency of the transaction over time. Airlines have revenue optimization down. American Airlines for example generates an extra $1 billion in annual incremental revenue from manipulating ticket prices.

But will they take you to see Hannah Montana?

The search for beauty

The most beautiful woman, man, science breakthrough, literature, and so on usually merits a prize:
Miss America, Mr. Universe, the Nobel prize, the Pulitzer prize.

The men and women are easy, just ask People Magazine: J Lo, Angelina, Brad Pitt, Tom Cruise. Science breakthrough? That's pretty easy too: Einstein's Theory of Relativity and the discovery of DNA would be high on anyone's list. Most beautiful poem? Shall I compare thee to a summer's day?

What do musicians say when asked for the most beautiful piece of music ever written? My informal survey says Schubert's Cello Quintet in C gets the prize.

And how about Google candidates when asked for the most beautiful math equation ever derived? e to the i pi equals minus 1 comes to mind. Just think: you put together an imaginary number and two transcendental numbers and get minus 1 as the result. This is at least as cool as Pythagoras. Just beautiful.

They're back: Led Zeppelin, who almost wasn't

There's a lot of math and science in music. Even with Led Zeppelin. The only band to have every one of its albums hit the US Billboard Top Ten, Led Zeppelin has sold over 300 million albums. Last night they played London's The O2, in a performance like oxygen to their fans.

Remember that echo on Zeppelin I and II that came before, and not after, the music? Zep guitarist Jimmy Page says he invented the technique, contradicting others who say the echo is the result of someone accidentally leaving the recording tapes in a hot car.

So who came up with the name Led Zeppelin? You can thank Keith Moon, then drummer for the Who, who said Page's erstwhile name for his group, The New Yardbirds, would go over, not like a lead balloon, but like a lead Zeppelin. Page removed the "a" from "lead" and the rest is history.

Although it almost wasn't. In high school, Jimmy Page was interested in science and almost took a job as a Lab Assistant. Now that would have been a rocking lab.

We're all optimists when we first determine who we like

According to a Harvard Business School study led by Michael Norton, people optimistically interpret ambiguous information and assume they will get along. As we learn more, our thinking is less forgiving.

The research examined the differences in opinions before and after dates arranged online. Before the date, when participants knew less, prospective dates were rated between 6 and 10 on a 10-point scale, and no one scored below 3. After the date, average scores were lower, and ones weren't uncommon.

Norton says that "people are so motivated to find somebody they like that they read things into the profiles." When a man writes that he loves the opera, his would-be mate imagines dressing to the nines to see the Met but when she learns more, she discovers "opera" refers to singing in the shower. "Once you see one dissimilarity, everything you learn afterward gets colored by that," Norton says.

I'm waiting for the next study on couples to see if instead of communicating better they worked hard to maintain ambiguity.

The stats say moderate drinking may be good for you

Are you a moderate drinker, consuming on average just over one drink a day?

You have a 15 percent greater chance of developing colon cancer and if you're a woman, a 13 percent greater chance of developing breast cancer.

But the good news is, that's a loss of under 12,000 lives per year. Moderate drinking saves 30,000 lives a year simply by reducing the number of fatal heart attacks.

Of course it's a new numbers ball game if you become an alcoholic. To improve your odds, stick to wine: according to a Danish study wine drinkers have a statistically lower risk of drinking to excess.

How a nuclear weapon works

Back in July 1945 the U.S. detonated the first nuclear explosion in New Mexico.

Here's how it works: when a slow moving neutron hits a Uranium 235 nucleus a funny thing happens: the nucleus accepts the neutron and then becomes unstable, breaking into two or more different nuclei and emitting on average two and a half more neutrons, that can then enter more Uranium 235 nuclei. This behavior was first observed in 1938; it took just seven years to make the bomb.

Hmmm, 1945. Sixty-two years ago. No computers. No Internet. No cell phones. With all this new technology I would have thought everyone, including the Iranians, would have figured it out by now.

Maybe for once it's a good thing the world is more stupid today.

Not good math news

A recent study of 30 industrialized nations found that fifteen year old Americans do not have math knowledge or the ability to apply it.

The most recent Program for International Student Assessment, or PISA for short, showed only four countries: Italy, Greece, Turkey, and Mexico, faring worse than the US in math. In fact, the US math scores were worse than those of some countries considered non-industrialized, such as Estonia and Slovenia. The US's score is worse than it was the last time the test was administered, in 2003.

The top countries? Finland, Canada, Japan, and New Zealand.

Alas, the worst news may be about reading. The US test results were thrown out - because of errors in the reading exams introduced by the North Carolina firm that printed them.

Is it all about geometry?

Garrett Lisi likes to surf and snowboard, which is what he does when not giving lectures at places like the International Loop Quantum Gravity Seminar on the Theory of Everything.

Lisi, who has a PhD in Physics from the University of California, San Diego, has been getting a lot of press for his proposal that uses E8, a 248-dimension Lie Group, originally researched by Norwegian mathematician Marius Sophus Lie in 1887, to explain all the known forces of the universe in a GUT or grand unification theory.

Some think the results of Lisi's work may be equivalent to that of string theory. Others just want to string him up: one string theorist called Lisi a crackpot. But Lisi can take comfort in riding this wave: at least to date no one has called him a lousy surfer.

Transportation: what's safe, energy, efficient, and cheap? You may be surprised.

Travelers, like companies, like a good ROI - return on investment. When deciding between traveling by car, train, or plane, it turns out trains - and Amtrak in particular - have distinct advantages over alternatives when considering safety, efficiency, and pollution.

Using deaths per billion passenger miles, Amtrak ranks with airplanes as 13 times safer than autos. Getting more than twice as many passenger miles per gallon than planes, Amtrak also beats out cars with fewer than five passengers. And Amtrak is the eco-friendliest, spewing out 82% less pollution than planes, and 70% less than cars.

But Amtrak takes a little longer, 8% longer between New York and Boston, for example, and costs a little more: 25 cents per passenger mile vs. 19 for planes and between 18 and 36 for cars.

Government subsidizes planes 16 times more than it does Amtrak; autos 32 times more. That works out to $1 billion for Amtrak, $16 billion for the airlines, and $32 billion for cars. Like travelers, maybe the government should better familiarize itself with the concept of ROI.

Nitpicking numbers

Republican Presidential hopeful Rudy Giuliani has been using statistics incorrectly. To quote the New York Times, certain of his statements are "incomplete, exaggerated or just plain wrong."

Giuliani says this is nitpicking.

Politicians don't have a lock on misusing numbers. Consider Musician Kate Bush. When singing Pi on her album Aerial, she got the 54th digit wrong.

So what's worse: misquoting Pi or underestimating the U.K.'s prostate cancer survival rate by over 30 percentage points?

Numbers: love 'em or leave 'em. Or, as Guiliani would say, nitpick 'em.

Do you know the secret to stock options?

The stock market has been on a crazy ride recently. First it was 10% down, then in two days made its biggest advance in five years. It can make one dizzier than an astronaut on a daily commute to space.

Some folks don't want the actual ride; they only want to benefit if the market - or a particular stock - reaches and passes a certain price. They pay for the option to buy or sell at a particular price within a certain amount of time.

The Black-Scholes formula revolutionized the pricing of options. First published in 1973, it is now widely used on Wall Street. But it has its limitations: assumptions include no transaction costs, risk-free lending, no dividends, and measuring volatility as a constant.

Alas these assumptions mean that Black-Scholes is at best an approximation to reality. And its misapplication may not only spell disaster for investors. With the current situation in sub-prime mortgage debt and real estate devaluation, maybe a better name might be black holes.

Pioneering mathematician Gene Golub dies

The study of algorithms in continuous mathematics is called numerical analysis, used in virtually everything from building stability to stock picking to weather prediction.

But one couldn't predict that numerical analysis pioneer Gene Golub, a Turing Award nominee and numerical analysis guru, would succumb to leukemia at the age of 75 only three days after diagnosis.

Golub was the inventor of the SVD algorithm, commonly used in search engines and signal processing. SVD, which stands for singular value decomposition and works with matrices, has so many applications that many mathematicians consider it the Swiss Army knife of numerical analysis.

Mathematical algorithms? Practical applications? The Swiss Army knife? Maybe the government should be looking more into those types of weapons.

Losing money? You have good company.

In 1720 calculus inventor Isaac Newton lost a fortune in a stock market crash that he had personally predicted. Mark Twain lost a fortune investing in an automatic typesetting machine. Dozens of entertainers and sports stars have at some point filed bankruptcy, including Randy Quaid, Jerry Lewis, Grace Jones, Kim Bassinger, Walt Disney, and Mickey Rooney, who did it twice.

These are not stupid people. But the list doesn't include the 50% of Americans who file bankruptcy because of medical bills.

McKinsey & Co. estimates that by 2015 consumers will be paying $420 billion for medical expenses out of their pockets, not including insurance premiums.

Maybe it's time for us to learn from Isaac Newton by doing some calculus to get us out of this mess.

Giving thanks and gifts

With the Internet Black Friday is no longer the busiest shopping day of the year. The distinction goes to the Saturday before Christmas - and to Cyber Monday, the Monday after Thanksgiving.

If you're in an office with Internet access, chances are better than half - 54.5% - that you'll be shopping at work today. With good reason of course: 72.2% of retailers plan a Cyber Monday promotion.

Some say higher gas prices may put a damper on gift giving this year. In a Consumer Federation of America survey, 38 percent of respondents said the cost of gasoline and home heating fuel would cause them to either somewhat or greatly decrease their holiday spending, up from 32 percent in 2006.

But with all the hot air retailers provide to promote their specials, and consumers' fingers doing the shopping online, gas may not be in such great demand anyway.

Order from chaos

Psychologist George Miller found 2.5 bits to be an approximate limit for a certain type of channel capacity. In Watership Down, Richard Adams coined the term "hrair," referring to a maximum countable number, which for rabbits was four. IT guru Ed Yourdon defined hrair for a computer programmer at between five and nine.

Each of these experts attempts to quantify the optimal number of relationships.

The best explanation of why most humans have two or three children may lie in what Physicist Mitchell Feigenbaum discovered: chaotic behavior tends to occur when a certain parameter, called the first Feigenbaum constant, is approximately four and two-thirds, about the average human family size.

Could it be that the optimal number of relationships occurs when chaos is maximized? How could we ever make order out of that?

Thanksgiving numbers

In 1863 President Lincoln made Thanksgiving a national holiday celebrated on the last Thursday in November. FDR modified the date to the fourth Thursday in November, to leave more time for shopping.

Mention Thanksgiving, and like the 1621 Pilgrims, we think of food. Americans made 7.2 billion pounds of turkey, 690 million pounds of cranberries, 1.6 billion pounds of sweet potatoes, 1 billion pounds of pumpkins, and 294 million pounds of tart cherries. On second thought, it could be we need that extra time for digestion.

The magic number for safety is 165 degrees - both turkey and stuffing - although some food experts say 170 degrees is best for thigh meat. And global warming might be helpful this time of year, if unusually warm days help save the economy by encouraging more shoppers to venture out and open their wallets. It makes one wonder who the turkeys really are.

The arms race in animals: can we learn something?

Scientists discovered the fossil of what they believe was an 8-foot sea scorpion that lived 390 million years ago.

Simon Braddy, a paleontologist from the University of Bristol, said that many fossils have been discovered of monster millipedes, super-sized scorpions, colossal cockroaches and jumbo dragonflies. But nothing as big as this sea scorpion.

According to Prof. Jeorg W. Schneider, a paleontologist at Freiberg Mining Academy in southeastern Germany, these scorpions were dominant for millions of years because they didn't have natural enemies. Eventually they were wiped out by large fish with jaws and teeth.

Being the biggest and having the most armor does keep a species dominant. The U.S. has recently been concerned with a new arms race with China and possibly Japan. But maybe we should change our approach and start looking out for ways to cope with large fish with jaws and teeth.

Two trillion dollars is a catchy number

Banks make money by taking in deposits and lending them out at higher rates than it pays. They don't lend it all out - what they keep is called the capital ratio and it is typically around 10 percent of what they have lent.

For example, say a bank has $1,000 in outstanding loans. It keeps 10% or $100 in cash. That's $100 it won't lend because to do so would put its capital ratio below 10%.

Now say just 1% of the $1,000 in outstanding loans go bad, which is $10 of bad loans. The bank has to pay the $10 out of cash since the loan has to be repaid by someone. Now the bank only has $90 in cash; the maximum amount it can lend is $900. But it has $990 left in outstanding loans. Ooops, the capital ratio just went down to 9.1%.

The bank would need to reduce its lending another $90 to get back to a 10% capital ratio. That's a total reduction of $100 in lending: $10 for the bad loan and $90 to keep the 10% capital ratio.

The bottom line? A bank needs to reduce its loan balance by $10 for every $1 in losses.

Goldman's chief U.S. economist estimates that because of sub-prime mortgage losses, lending may be reduced by as much as $2 trillion, 7% of US non-financial debt, raising the likelihood of recession.

Now there’s a depressing thought.

Literacy, is it just reading?

The National Endowment for the Arts says Americans are reading less. Here are the numbers:

Half of 18 to 24 year olds never read a book for pleasure. Americans 15 to 24 spend an average of 7 to 10 minutes a day on voluntary reading, 60% less than the average American. Reading scores for 17 year olds have dropped.

Given that 58% of middle and high school students listen to music, watch TV, or use other media, some say literacy is more than reading: a better definition would include multimedia. But the NEA says the downturn in reading trends correlates "to fewer job opportunities, lost wages, higher incarceration rates and less participation in civic and community life, including voting and volunteering." Just what we need to compete effectively with China.

In life, one person can make all the difference in the world. With reading, the same may be said of a book: Reading scores for 9-year-olds are at an all-time high. Call it the Harry Potter effect: JK Rowling just may be saving Western civilization as we know it.