Discovery

Mother Nature may be the world’s greatest mathematician.

Bonni Kealy saw that firsthand in how tiger bush will grow in patterns found throughout other parts of nature, like the spots on a cat.

“Math isn’t just about equations,” Kealy said. “It’s beautiful and natural. You see it around you every day.”

Indeed, mathematicians often tease out the numerical underpinnings of seemingly random phenomena, discerning patterns in everything from the coats of felines to algae-filled water, Kealy said. In effect, two dissimilar things are interacting in predictable ways, and a mathematician can describe how.

Kealy, 29, and her advisor David Wollkind started to create a new modeling equation for the spread of tiger bush, a plant unique to arid and semi-arid areas, by mining the past, Kealy said.

They used existing pattern formulas as a foundation for their work, but the earlier models worked only on sloped land. Kealy and Wollkind’s model works on flat land, a more common habitat for tiger bush. It focuses on how water spreads over the soil surface and interacts with plants as vegetation expires.

Kealy and Wollkind refined their formula and presented it at the Joint Mathematics Meetings earlier this year in Boston. They received so many invitations to speak at the conference that they had to turn down a few opportunities.

“The work has kind of taken on a life of its own and grown,” Kealy said. “The Joint Mathematics Meetings is kind of the Big Kahuna of math research, so we are getting some recognition.”

The work also has practical implications beyond the simple beauty of math. The equation has joined an ongoing discussion on stopping desertification, the expansion of desert landscapes.

“The big picture is to help understand this vegetation in arid climates and prevent any further desertification,” she said. “That and to show that when math works, it’s really cool.”

According to the International Fund for Agricultural Development, one-fourth of the earth is already desertified. An additional 12 million hectares are lost each year to soil degradation. This equates to losses of $42 billion in income from agriculture and other lost infrastructure.

Kealy thinks her and Wollkind’s equation can help, but she still sees room for improvement. She hopes to adjust the equation for new variables, like how water moves below the soil surface.

“This whole thing seems a little surreal,” Kealy said. “You can’t beat the chance to see your own math in action.”

 

It’s the worst of times to be in the Red Sox Nation and among the best of times for those who relish baseball’s marriage of probability, improbability and dazzling statistical detail.

One week after the premiere of Moneyball, a movie in which baseball stats play an improbable starring role, the Boston Red Sox concluded a late-season swan dive with a similarly improbable last-minute loss to the Baltimore Orioles.

It has Craig Parks’ gears spinning. Of course you’re thinking, hmm, as a WSU psychologist, he must be wondering what went through the Sox players’ minds as they choked so spectacularly. But no, as a fan of both statistical analysis and baseball, he sees several numbers wonders, including those in the race for the National League batting title and another batting title of a century ago.

His thoughts:

The Red Sox are the first team ever to blow a nine-game lead in September but the Braves came close—they were up 8.5 games on the Cardinals when September started.

An even cooler stat thing that almost happened: With two games left to play, the difference between the #1 and #2 batting averages in the NL was .00006. New York Met Jose Reyes broke away from Milwaukee’s Ryan Braun over the last two games and won the batting title outright, but there was serious discussion about what to do if they had maintained that degree of closeness.

Technically one guy would have had a higher average, but it was unclear whether Major League Baseball wanted to go to that degree of fineness to determine the batting champ.  Or whether it was even legitimate to do so, as that difference is pretty much uninterpretable.  Maybe they would have declared a tie, but the situation has never come up in baseball history, so there’s no precedent to appeal to.

Which calls to mind the 1910 batting title.

With two games left in the season, Ty Cobb is hitting .385, Nap Lajoie is hitting .377.  League-wide, everyone hates Cobb, including many of his Tigers teammates, and loves Lajoie.  Cobb sits out the last two games, but Lajoie plays his final two, a doubleheader against the Browns (now Orioles).  Browns catcher-manager Jack O’Connor positions his third baseman back on the outfield grass every time Lajoie comes to bat, which means if Lajoie lays down a bunt, there’s no way the third baseman can get to it in time.  Lajoie reaches base eight times across the two games—five times on bunts—though the last bunt is scored as an error, so he officially goes seven for eight.  This raises his average to .384.  So he misses the batting title, but just barely.  Cobb wins it.  (By the way, the O’Connor manager was fired afterwards.)

Cut to 1981.  A baseball researcher discovers that, in 1910, a box score for the Tigers was counted twice in the official calculation of Cobb’s average.  Cobb had gone two for three in that game.  Subtract out that phantom game, and his average falls to .383.  Now Lajoie is the batting champ.

But, if we’re going to start adjusting hit totals, you can argue that Lajoie’s last two games should be thrown out, since it was clear the Browns were giving hits to Lajoie.  In fact, there is some evidence the Browns tried to bribe the official scorer to change that last at-bat from an error to a hit.  Do that, and Lajoie’s average resets to .377, and Cobb is clearly the batting champ.  Also, the 1910 American League president reviewed and certified Cobb’s average, so some people question whether it’s appropriate to retroactively change it, despite the apparent error.  Others wonder whether there would be this much scrutiny if the player in question was someone other than Cobb, who was indeed a nasty, vicious man.

 

The USDA’s Economic Research Service released the latest series of state fact sheets today, based on the 2007 Census of Agriculture. As the son and grandson of  farmers, I’m always curious about the state of ag in our state, particularly for small farms. A few items caught my attention as I browsed Washington State’s stats.

The first surprise was the shrinking size of farms. Conventional wisdom tells me that farms are consolidating and growing larger, but the average farm size went from 426 acres in 2002 to 381 acres in 2007. The percent of very small farms (1-99 acres) grew, while the percentage of farms with 500 or more acres decreased.

The average age of farmers continues to climb. In 2007, farmers averaged 57 years old, up from 55 in 2002 and 53 in 1997.

Another fact jumped out: only 45.9 percent list farming as their primary occupation, down from 58.5 percent in 2002. 

A significant change was the number of women listed as principal farm operators. That number jumped from 5,632 in 2002 to 8,090 in 2007.

There are a lot of other stats to look at on the fact sheet. What do the numbers mean? Do they accurately reflect the state of agriculture in Washington? Are there longer term trends that are shifting, from farm size to ownership to gender to ongoing rural poverty?

Links

Washington State Fact Sheet (USDA/Economic Research Service)

USDA/Economic Research Service home page