Imagining Numbers: a recommendation

OK, you are desperate to read a good math book, but you don’t want to do any heavy duty math. You are in luck. Barry Mazur meditates on imagination, art, and mathematics in his charming Imagining Numbers (particularly the square root of minus fifteen).

As he says in the preface:

This book began as a letter to my friend Michel Chaouli. The two of us had been musing about whether or not one could “feel” the workings of the imagination in its various labors.

The only math background you need is knowing how to multiply and recalling from high school algebra that X is the unknown quantity.

From the back cover of the book:

Barry Mazur invites lovers of poetry to make a leap into mathematics. Through discussions of the role of the imagination and imagery in both poetry and mathematics. Mazur reviews the writings of the early mathematical explorers and reveals the bafflement of these Renaissance thinkers faced with imaginary numbers. Then he shows us, step-by-step, how to begin imagining these strange mathematical objects ourselves.

Published in: on May 31, 2006 at 1:44 pm  Leave a Comment  

Gamma: a recommendation

Julian Havil’s Gamma: exploring Euler’s constant is a charming mathematics book filled with interesting results on every page. A good calculus course will prepare you for most of the material.

One of the things I particularly like about the book is that at the end he presents a very elegant and accessible account of the Prime Number Theorem and the Riemann Hypothesis. On top of that he gives the necessary background in complex function theory required for the Riemann Hypothesis in an appendix. I have never seen a better brief.

So if you looking for a really good math book on summer vacation, and you like playing with numbers, then check this one out.

Published in: on May 31, 2006 at 12:48 pm  Leave a Comment  

Some late night sports

Wow. It is almost 4 in the morning. Tempus fugit.

My impressions from yesterday have to do with sports. I don’t think that is all bad.

England beat Hungary 3-1 in a friendly match tune up before the World Cup. The match was nil nil at the half. England scored two goals in the first five minutes of the second period. That made it academic the rest of the way out.

The press has fixated on Rooney’s broken foot, but I say that England has a honey of a football team and is a threat to go all the way in the World Cup.

Meanwhile, in Chicago, the Cubs beat the Reds for the second day in a row. After the Cubs not winning a game last week, I am stoked about a two game winning streak this week for my beloved Cubs.

Published in: on May 31, 2006 at 2:52 am  Leave a Comment  

New Treasury Secretary

Henry Paulson will succeed John Snow as Treasury Secretary. The change is meaningless.

The Treasury Secretary has no clout within the Bush Administration. The Secretary must promote politically motivated economic policies originating from the White House, and otherwise keep out of the way.

As has been reported and discussed, those economic policies include tax cuts for the wealthy, big government spending to support special business interests and privileged classes, and slashing programs that benefit low and middle income workers.

Continue to keep both eyes and both hands on your wallet.

Published in: on May 30, 2006 at 10:43 am  Comments (4)  

No museum pieces

When I was a sophomore in college I took an art course. I already knew from painful experience in my previous school art classes I had no talent for it. I may have done it because my roommate that year was an art major.

I didn’t do very well, but it was a welcome break from the other courses, such as math, I was taking. I never missed a class, and I worked hard on my final project, which I recall was a tile print of some sort. I forget the lingo you call it by. The most embarrassing experience was the week we had to draw a model. My drawing was a stick woman with no clothes on.

I got a B in the course, so I was happy about that. It ruined my perfect 4.0 grade point average I maintained at the time. For some perverse reason I remain glad I took the course.

In the immortal words of Tom Cruise in Risky Business–sometimes, you just have to say what the fuck.

Published in: on May 28, 2006 at 7:47 am  Comments (2)  

Out on the town, or not

One of the nice things about living in downtown Chicago is that if you want to go out on the town, you are already in town. The option is always comfortably there.

However, I am home watching the Heat/Pistons game tonight. I don’t like to go out on Saturday nights anymore as I once did. I sometimes like being joyously alone.

Published in: on May 27, 2006 at 7:09 pm  Leave a Comment  

I forgot

Super spook General Hayden has been confirmed as the new CIA Director. The Senate rolled over as was to be expected. I found it truly touching during the hearings when Hayden was asked whether he had the wherewithal to speak the truth to power. One should always remember that when speaking the truth to power, power often already knows the truth and does not care. Such is the case with the Bush Administration.

On a brighter note, it has been fun watching Speaker Hastert take on President Bush over the raid and theft of documents from a Congressional office. President Bush had to intervene when ace law enforcement official Attorney General Gonzales failed to blow away the opposition. The documents are supposed to be sealed for forty five days. That is like closing the barn door after the horse has galloped merrily down the road and out of sight.

Finally, Lay and Skilling were found guilty on all charges. Their stupidity defense kind of backfired. Remember the old Steve Martin comedy routine. “When you are in court and none of your defenses are working, just look the judge straight in the eye and say, I forgot.”

Have a good weekend and don’t forget to boogie.

Published in: on May 26, 2006 at 11:52 am  Leave a Comment  

Some questions concerning Capital volume 1

I have been preoccupied with questions about Karl Marx’s Capital volume 1. One question seems frivolous, but I think it has merit. Where should one place Capital on the bookshelf?

I have seen it in the philosophy, economics, and the politics sections of the large bookstores. I prefer to think of it as a book of politics. Marx presents a guide to thinking about working class exploitation, one he hoped would aid in overthrowing the capitalist regime of his time.

There are other elementary questions that may appear frivolous, but I think have merit.

Who are the proletariat today? The cook at the local restaurant earning $14,000 per annum is definitely in. The factory worker earning $40,000 per annum is in. The computer programmer who knows the current hot technology and earns $180,000 per annum may or may not be in. The CEO earning $10,000,000 per annum definitely is not in even though he works for wages.

Who are the capitalists today? The person who owns 10 shares of Coca Cola stock doesn’t appear to be much of a capitalist. The person who owns 1,000,000 shares of Coca Cola stock seems a likely candidate for capitalist even though he takes no active part in running the company and his stake is small compared to all shares outstanding.

What is the status of the notion of surplus value given the current state of economic knowledge? How does it translate into modern parlance? These are important questions if one wants to use Capital as a guide to political action.

Whether frivolous or not, these are questions Marx asked and answered. He is dead though. That leaves us to answer the questions without his help. To further complicate matters, the world has changed since his time. Capital does not offer much in the way of practical advice in organizing a modern state and economy. That may sound like heresy to some, but the notion of “from each according to his ability and to each according to his needs” has never been easy to resolve when it comes to cases.

Even though I read Capital a few months ago, I will be reading it again this summer. I have too many unanswered questions.

Published in: on May 26, 2006 at 9:48 am  Leave a Comment  


I took the lead in my fantasy baseball league the third week of the season. My team is far ahead of the second place team. All my players are having good years and many are having all star years.

I had reservations about playing this year. It takes a bit of work each day if you want to win. With the Cubs playing abysmally, I am glad I did. The season is already over for the Cubs, but not for me.

And isn’t that what fantasy is all about? We all like to believe we have a shot at doing well and with some luck winning something.

Published in: on May 26, 2006 at 9:23 am  Leave a Comment  

At the Moment

A summer-like day. Partly overcast, warm, and humid.

Thoughts about the past and future don’t count for much at midday. Only the moment matters. Time to pack a book, a notebook, and a pen in a canvas bag, and go out for lunch. After that, find a place to write for a spell.

I admit my failure as a writer, yet I cannot see beyond doing it for one more day.

Last year, I took a quiz on the Internet that predicted how long I would live given my life style and health habits. It predicted I should be dead. Now, I’m one year older, and with my cold lingering on far too long I wonder just how close I am from being gone.

Certainty is a very interesting question. I am almost certain that I will live in and for the moment this afternoon. But who can really say?

These days when I am relaxed at my work don’t happen very often. I must take advantage of them.

Published in: on May 25, 2006 at 10:30 am  Leave a Comment  

Teaching Alternative Global Financial Games

I began reading Robert Rubin’s In an Uncertain World last night. I’ve been meaning to read it for two years. It has me thinking about global financial games and how they are taught.

Rubin devotes the first chapter to the Mexican financial crisis of 94-95 when he first became Secretary of the Treasury. Those familiar with the crisis won’t learn much new in the way of details about what happened. I pressed on into the second chapter.

In the second chapter, Rubin explains what he did when he first joined the Goldman Sachs arbitrage department when he was 28 years old. He played the mergers and acquisitions arbitrage game. He does a reasonably good job of explaining arbitrage in general and M&A arbitrage in particular.

I taught myself how to play the M&A arbitrage game back in the Nineties. I was involved in several acquisitions at the company where I worked during the Eighties and Nineties. My curiosity was aroused by how acquisitions were chosen and how the deals got done. But most of all, I wanted to know how one makes money off of the business deals. By the way, I never did any insider trading. That’s illegal and you can go to jail for a long time unless you can afford very expensive legal counsel.

I’ve played the M&A arbitrage game for my own account for the past seven years. I have reasonably sophisticated models that help me decide whether to bet or stay on the sidelines. The models are plugged into the latest financial data of companies around the world. I lose money most of the time, yet when I win, I make pretty good money for a guy goofing around on his computer.

I haven’t bet on anything for almost a year. Maybe, I have become risk averse in my old age.

The global capital game seems to tap into some sort of primal gambling instinct in many of us. As has been said many times before, it is not the money but the desire to win—the desire to beat one’s opponents and the system—that drives a player to the game.

Schools teach the global financial game at an early age. Students participate in fantasy stock market leagues where the players get play money and compete to see who can accumulate the most money over a given period of time. Schools have used this method to teach the elements of the stock market to students since I was a schoolboy. Thus are certain values subtly taught us in our youth.

One can imagine another kind of global financial game used for teaching purposes. The students would be the leaders of a rich country. The object of the game would be to see how much they, as a rich country, could improve the living standards of a destitute country. The team that helps the destitute country the most wins the game.

It would seem the alternative game could teach a different and important set of values.

Published in: on May 25, 2006 at 8:45 am  Leave a Comment  

Coming soon: a bridge too far

The storming of the Congressional office of Rep. William Jefferson by FBI agents has angered Republican Congressional leadership. Even they claim that the Executive has exceeded its powers and violated Constitutional separation of powers. The vast majority of Constitutional scholars have claimed this for some time.

The raid on a Democrat creates issues of partisan politics that the Republicans don’t need before Congressional elections and would surely like to avoid.

Attorney General Gonzales claims it was necessary to move his criminal investigation along. History refutes his assertion. No Attorney General has ever raided the United States Congress. The raid smacks of police state tactics; Republican Congressional leaders know it.

The Bush Administration does not care. That will eventually land them in bigger trouble than they expect. They will abuse their powers again during the remainder of President Bush’s term. At some point they will go too far. Congress will be left with no choice but to begin impeachment proceedings.

It has been well documented, by insiders and outsiders, that President Bush does not possess the mental acuity to deal with complex and ambiguous issues. Most likely he suffers from adult attention deficit disorder. He must rely on the advice of those whose goal is to weaken the Constitutional authority of Congress and the Supreme Court. His inability to analyze even the simplest cases, such as the raid on Congress, indicates the severity of the problem.

Instead of surrounding himself with advisors who could render his weaknesses more tolerable, he has surrounded himself with those who prey upon his weaknesses and prejudices. This creates the conditions for the perfect storm. An ineffective President teamed with a ruthless group of advisors making the ultimate power grab. They will not resist the temptation to spy on political opponents. They will eventually be caught in the act.

The Bush Administration does not practice prudence. It will eventually be their undoing. President Bush will be impeached and removed from office.

Published in: on May 24, 2006 at 4:54 am  Comments (2)  

A Cold

I have a cold. I’m watching X-Files reruns in the middle of the night. I thought I had kicked that habit.

I’m sure things will work out for the best all the same.

Published in: on May 24, 2006 at 1:46 am  Leave a Comment  

Doing the Deal in Iraq

Joshua Holland has a nice article in Alternet, The Great Iraq Oil Grab.

For those who don’t understand how multi-national corporations in the resource, engineering, construction, and finance businesses work their magic in resource rich countries, the article presents a great primer in how things get done.

The so called development of Iraq fits what is by now a classic model for exploiting a resource rich country to the maximum. One suspects the Iraqi people will not benefit from Iraq’s wealth after one looks at the history of how these deals have been made in other countries around the world and who has ultimately benefited. Highly lucrative deals for multi-national corporations have already been cut with the Iraqi government. The multi-national corporations who come into poor countries to develop the resources of the country receive the major benefits.

We regrettably have had to fight an expensive and bloody war in Iraq to pave the way to riches for the powerful few. Don’t you just hate it when that happens?

I’m not saying blood for oil. Nobody wants to fight when they can plunder at will without violence, or at least on a small or invisible scale. Sometimes it just doesn’t work out that way.

Published in: on May 22, 2006 at 12:40 pm  Leave a Comment  

Cubs Chances – 2006 Edition

As you know, we do it at State Street so you don’t have to.

Now that the season has passed the quarter way mark, what are the Cubs chances of righting the ship and making the playoffs?

I ran a 25 trial Monte Carlo simulation on the Cubs remaining 119 games. The Cubs winning percentage stands at .419. The Cincinnati Reds stand at .568 and would get the Wild Card spot if the season ended today. So I used a p-value of .419 for the Bernoulli trials and assumed that the Cubs needed to win enough games for a .568 winning percentage.

In 25 trials the Cubs did not finish over .500 once let alone achieve a .568 winning percentage.

If you are betting the Cubs to win the World Series, you better be asking for some seriously long odds. I see the Cubs have fallen to 50-1 to win the World Series in the betting futures. Those odds may not be good enough to take the bet.

Published in: on May 22, 2006 at 9:26 am  Leave a Comment  

Cubs vs. White Sox – day three

The Cubs lost to the White Sox 7-0 yesterday. The game was highlighted by a second inning bench clearing brawl, which I won’t describe.

I am headed back out to Sox Park this afternoon to cheer for the Cubs. It appears it will take a miracle for the Cubs to win, but stranger things have happened.

Published in: on May 21, 2006 at 8:16 am  Leave a Comment  

Reality and Honesty

The stock market took a tumble this past week. One wonders if the market is predicting dire things to come, or is, itself, catching up to reality.

The Bush Administration has been touting a 3.8% increase in wages over the past year. However, when Secretary of the Treasury Snow was questioned before Congress, he admitted the numbers were not adjusted for inflation. When one undertakes that standard adjustment for all economic numbers involving prices, all of the gains in wages disappear. The misinformation coming from the White House manages to be both patently and absurdly false and dishonest.

Another piece of dishonesty coming from the Bush Administration is that tax cuts have spurred investment. However, when you exclude housing investment, you find that business investment has stagnated.

Thus, we come around to the basic fact that the economy has grown because of consumer spending. This consumer spending has been fueled by the housing sector through a combination of low interest rates and personal, public, and international debt at unsustainable levels.

Honest folks who study and comment on these things, be they socialist or conservative or somewhere in between, all agree on the basic numbers and facts. Naturally, predictions and prescriptions vary, but the facts are seldom in dispute.

That is unless it comes from the Bush Administration, all of whom appear to be ignorant or dishonest or both.

Oh, did I just say the unspeakable? I called people who tell lies liars.

Published in: on May 21, 2006 at 6:09 am  Leave a Comment  

Cubs vs. White Sox

I’m going to the Cubs/White Sox game at Sox park today. It’s always great at the ballpark. However, I’m a Cubs fan, the Cubs stink, and the White Sox are playing very well. I’d be deliriously happy if the Cubs got their act together today, but I’m not counting on it.

What are you going to do? That’s baseball, and there is no crying in baseball.

Published in: on May 20, 2006 at 6:10 am  Leave a Comment  

On Debunking

I have been reading Confessions of an Economic Hit Man by John Perkins. The book has lived up to the hype and its bestseller status. I quote from the back cover of the book.

“Economic hit men,” John Perkins writes, “are highly paid professionals who cheat countries around the globe out of trillions of dollars. Their tools include fraudulent financial reports, rigged elections, payoffs, extortion, sex, and murder. They play a game as old as Empire but one that has taken on terrifying dimensions during this time of globalization.”

John Perkins should know—as an economic hit man for an international consulting firm, he convinced developing countries to accept enormous loans and to funnel that money to U.S. corporations. The American government and international aid agencies then requested their “pound of flesh,” including access to natural resources, military cooperation, and political support.

Confessions of an Economic Hit Man is the story of one man’s experiences inside the intrigue, greed, corruption, and little-known government and corporate activities that America has been involved in since World War II, and which have dire consequences for the future of democracy and the world.

The book is one of those stories that presents the difference between myth and reality when it comes to topics economical such as international development. First, there is a theory. Second, there is how the deeds actually get done. Theory and action often do not coincide.

Debunking myths and illustrating the difference between myth and reality have their claims to scientific methodology along with other scientific methodological tools. Regardless of where one’s economic and political sentiments lie, it never hurts to be clear how things actually get done.

We are never free from economic prejudices, which often coincide with our economic self interest. This seems a mundane and indisputable fact, although many try to forget it. Reading the economic news with an orthodox economics textbook by one’s side proves instructive. Trying to explain events on the basis of the orthodoxy is often no easy chore.

One reason why this is the case is because government is persuaded to intervene on the side of one privileged and favored economic interest. That is not to say that this is a bad thing. Despite what some people say there are such things as public goods that government should supply. The burden of paying for these public goods does not fall upon everyone equally.

The economic actor who bellies up to the public trough will often explain his need in glowing ideological terms that also happen to coincide with the public good. That is why the request should always be measured against the ideology to see if they match. For instance, Conservatives have been highly successful in convincing the media, policy makers, and the public that they are merely proposing free market ideas when they are doing no such thing. The truth is that they have been using government to achieve favored economic outcomes for certain groups at the public expense, and in many cases an increase in the size of government.

Keynes may have been right when he claimed the hard headed business man who eschews economics may, all the same, be influenced by the ideas some long dead economist. Adam Smith and Karl Marx were the two most influential economists in history. They arguably are the least read also. That leaves one wondering exactly what economic dogma rolls around in the mind of the busy business person.

The motives of business people vacillate between the egoistic and the altruistic. John Perkins points that out in his case. One can always rationalize one’s actions no matter what damage they cause others. That is another reason why it is important to not only listen to the ideology coming from mouths, but also to look at the actions of the bodies espousing the ideology.

Fortunately, sorting through myth and reality is a scientific endeavor that one does not have to be a specialist to do. In fact, in a democracy the citizen is expected to reason herself to conclusions about what is myth and what is reality. Not to do so is to give up the status of sovereign ruler.

Professional economists have lamented the woeful state of economic literacy in the United States. Maybe, the goal of economic literacy should be to arm the citizen with the basic tools to debunk economic myths, and not merely at the expense of keeping certain privileged myths unquestioned and in place. We all have our opinions on the way the world ought to be. Explaining why things often do not turn out that way is a valuable activity too.

Three cheers for debunking.

Published in: on May 19, 2006 at 10:27 am  Comments (2)  

Just a hired hand getting his just reward

Tyler Cowen, economist and co-author of the interesting and valuable econ blog Marginal Revolution, takes a contrarian position on CEO compensation in his NYT article, A Contrarian Look at Whether U.S. Chief Executives Are Overpaid. He cites a paper recently published by economists Xavier Gabaix and Augustin Landier.

Their core argument is simple. If we look at recent history, compensation for executives has risen with the market capitalization of the largest companies. For instance, from 1980 to 2003, the average value of the top 500 companies rose by a factor of six. Two commonly used indexes of chief executive compensation show close to a proportional sixfold matching increase (the correlation coefficients are 0.93 and 0.97, respectively; 1.0 would be a perfect match).

Cowen does not discuss what has happened to the average worker’s compensation during this same time period. Without looking it up, I’d bet that it did not rise by a factor of six.

One theory says that CEOs are merely hired hands increasing shareholder value for their shareholders. If compensation is dependent on shareholder value, doesn’t that apply to the other workers also?

Published in: on May 18, 2006 at 10:24 am  Comments (1)  

The Conservative Nanny State

Yesterday’s great find on the Internet was The Conservative Nanny State by Dean Baker of The Center for Economic and Policy Research. The book is free and available in PDF and HTML formats.

In his new book, economist Dean Baker debunks the myth that conservatives favor the market over government intervention. In fact, conservatives rely on a range of “nanny state” policies that ensure the rich get richer while leaving most Americans worse off. It’s time for the rules to change. Sound economic policy should harness the market in ways that produce desirable social outcomes – decent wages, good jobs and affordable health care.

Conservatives are every much in favor of big government as those on the left. Where they differ is on who gets the benefit. Conservatives favor the rich. Those on the left favor the middle and lower income classes.

One needn’t go farther than reading the brutal facts and numbers in today’s NYT piece, House Pass’s a $2.7 Trillion Spending Plan by Edmund L. Andrews, for a graphic illustration of the point.

Published in: on May 18, 2006 at 9:32 am  Comments (1)  

Meanwhile, down at the border

Alex Tabarrok at Marginal Revolution is soliciting signatures from economists to a letter to President Bush on the immigration issue. The letter states that immigration has provided modest yet net benefit to Americans. He already has signatures from prominent economists on the left and right. That’s the good news.

Meanwhile, in Washington D. C., the President and Congress want to build a hi-tech virtual wall along the border. Round up the usual suspects: large defense contractors. Here they are as reported in the NYT.

Lockheed Martin, Raytheon and Northrop Grumman, three of the largest, are among the companies that said they would submit bids within two weeks for a multibillion-dollar federal contract to build what the administration calls a “virtual fence” along the nation’s land borders.

These technologies have been tried with varying degrees of success and abject failure around the world. The oversight for this spending will come from Homeland Security, the agency we have grown to love and respect.

This once again indicates the complete failure of governance coming from Washington D. C. Instead of tackling the difficult economic issues that would benefit both American and Mexican workers, the government will buy some expensive gee whiz technology, and retire for cocktails with their favorite lobbyist and contractor.

Everyone’s conscience is assuaged. And at least a few people continue to grow rich.

One is left wondering where the real border lies in this country.

Published in: on May 18, 2006 at 8:06 am  Leave a Comment  

Platitudes and profound truth

The other day, I was reading a review of John Kenneth Galbraith’s work written by some economist, but I’ll be darned if I remember who. He was not much impressed with Galbraith’s work. He claimed that part of it was merely mouthing some Marxist platitude.

Let’s see. Everything Marx wrote was a platitude. Everything contained in an orthodox economic textbook is profound scientific truth.

Galbraith was fond of saying that one could approach economic truth by discovering where the vested economic interests lie.

That does not seem a controversial way of explaining events. Or am I mouthing another Marxist platitude?

Published in: on May 17, 2006 at 12:21 pm  Comments (4)  

The savvy executive and the immigration issue

Let’s stalk the immigration issue in its native habitat to see what we find. That might prove a workable methodology.

The issue has been framed as the United States being threatened and challenged by alien hordes come to sack the Republic. Throw in a dash of terrorism for seasoning. Bake until well overheated. Bring in the National Guard. Then serve while hot.

Agreements such as NAFTA were supposed to bring economic prosperity for all living in North America. The two richest countries have stayed that way. The poorest has stayed that way too. Although agreements such as NAFTA are called free trade agreements, they are designed to fix market outcomes in favor of one privileged party. That privileged party is not the North American worker.

When in doubt, playing the blame game is sometimes useful. Much has been written about Mexico’s need to reform its economy. The incentives work against it. The opportunistic Mexican politician can do very well by catering to the needs of United States business interests without getting into all the messy details of economic reform. Besides, there is a dangerous trend toward leftist and populist reform south of the border. Nobody wants to open that can of worms in Mexico.

Doing business in China and other less developed countries is not as easy as it sounds. Producing over there carries more risk than in the United States. The smart or lucky executive who has found a ready pool of low wage labor in the United States has to think twice about going overseas when he can execute the same business model close to the elegant and rich suburb in which he resides.

You don’t see a lot of top CEOs weighing in on the immigration issue—either pro or con. The savvy CEO is more than willing to sit on the sidelines until the “secure the borders” hysteria subsides. Actually, the CEO can’t lose, for he will get low wage labor either from Mexico or from a severely chastened pool of American workers who will work for the same low wage.

When the smoke clears the battlefield and all the wounded are decently shot, the North American worker will be the loser. The immigration debate has been framed to guarantee precisely that outcome.

Published in: on May 17, 2006 at 9:44 am  Comments (1)  

It could have been me

I was strolling home from McDonald’s early in the AM last night when I witnessed a mugging and robbery on State Street just a few blocks from where I live. Once I recognized what was going on, I rushed to the victim’s aid. He lost his money and cell phone, but the two guys who assaulted him left him his wallet. Nice guys.

I called 911 and checked his head for blood of which there was none. Two squad cars arrived on the scene within 60 seconds since this is a well patrolled part of town. They checked my ID and whisked away the victim in their squad car after that.

I was lucky. If he had not been walking along State Stree at the same time as me, then his fate would have been mine.

I’m home tonight at a decent hour.

Published in: on May 16, 2006 at 11:12 pm  Comments (2)