Tuesday, April 26, 2011

Marge Anovarra

Marge Anovarra

By Bobby Neal Winters
“Hey, Doc,” I heard the voice from across the restaurant. I thought the voice was familiar, but as I looked up from my barbecue ribs to the direction whence it came, I didn’t recognize it.  I must have looked confused because I heard the voice again, and this time I saw who was speaking.
“Hey, don’t you recognize me?” the woman in her mid-thirties said.  “I must have really gotten old.”
It is always so cute to hear 35-year-olds say that.  But after subtracting a minor amount of gray from her hair and an inch or two of width from her face, I did know her. 
One of the great joys that a teacher has is keeping in contact with former students.  Not all of them, you understand, but certain ones do bring us a great deal of joy.  Such is the case with my former student Marge Anovarra.
Marge was not a math major.  She was a Communication major from Krebs, Oklahoma. She was a proud Italian and a proud Okie.  Pride isn’t rare in either of those races, but it is rare to see the Italian and the Okie combined.  The reason it is combined in her case is the same reason that she chose to come to my university: mining.
It is little known that there has been coal mining in both Southeastern Kansas and Eastern Oklahoma. The Italians immigrated to both places to take part in that.  Marge came to my university because it allowed her to take part in her Italian cultural it a place that was not home but like home and not terribly far from home.  And, as one might expect, after she finished her university degree, she moved back home.
She now practices her talents as a journalist and free-lance writer throughout the region and is successful.
She first caught my attention in class when I was calling roll on the first day.  With a name like Anovarra, I assumed she was a local and started joking with her.  I told her that we would learn more about her during class when we started talking about confidence intervals and the margin of error.  The class laughed, but afterwards she approached me an explained in very serious tones.
I was informed that her last name had been changed when her ancestors came to this country.  The folks who’d registered them had been in a hurry and when her great grandfather was asked his last name, he’d stuttered.
Thus the last name preserved that error from that time onward.
When we did get to margin of error, Marge—and that was her first name, not Margaret—did like it.  She liked the entire practical turn of statistics.  It’s based on the idea that even if you can’t know something for sure that shouldn’t keep you from trying your best.
The concept of margin of error first occurs in the calculation of confidence intervals of the mean.  The idea is that you want to know the average of some number associated to a group of objects, such as the average shoe size of everyone on our campus.  This is not information that our admissions people ask for, so if we really want to know this, we would either
1) phone everyone on campus and ask, “What’s your shoe size?” and listen to approximately 7000 phones slam in our ears, or
2) take a sample and use the sample to find an estimate.
The latter course is simpler and less expensive.  The idea is that a random sample of a group—a population being the technical term—models that group.  The average on that sample should be close to the average of the whole group.  There are ways this could go badly wrong.  You could choose only to sample from the men’s basketball team who would have larger feet than the typical folks on campus; or you could choose to sample only the female gymnasts, who would tend to be smaller than typical. But the idea is that a randomly chosen sample will, for the most part, yield an average closer to that of the group.
It needs to be noted that the average of the sample will tend to be close to the average of the population, but it will almost certainly be wrong.  It is for this reason that statisticians give themselves some leeway: the Margin of Error.
So you start with the average of the sample and you know that you are wrong.  Your average might be too big, so you subtract the margin of error from the sample average; your average might be too small, you add the margin of error to the average of the sample.  After all this, you still might be wrong, but the probability that you are correct is called the level of confidence.
You calculate the margin of error with this level of confidence in mind.  So estimating the average shoe size of campus won’t give you a single number.  It will give you an interval of numbers and you still have a small chance of being wrong.
That appealed to Marge’s practical nature, and it all came back to me in a flash, a microscopic fraction of the time it has taken me to relate it to the reader.
“Marge,” I said, not disguising the joy I felt in seeing her after an interval of 15 or 20 years. (I have to leave myself a margin of error you understand.) I invited her to join our table when we were sampling not only ribs but brisket and pulled port.
“It’s great to see you,” I said after she placed her order.  “I understand you are a journalist now.”
“That’s right,” she said. “I write for a few papers and do some freelance work.  Right now I am working on a piece for the Morning Ritual.  The Morning Ritual is the house publication of a health food company that encourages the consumption of bran.  The company is a sole proprietorship, owned by a militant vegan.”
After she ordered burnt ends, she then went on to explain that she’d been approached to do an expose of the barbeque restaurants in the region.  The editor had approached her with shocking news.
“Almost half of the barbecue places in the region serve road kill,” he’d said in serious tones.
The research she’d done in preparation for her article didn’t bear that out.  Out of a sample of 143 restaurateurs, 51 of them said that they had served road kill.  She’d done the calculation and that had only worked out to 35.7 percent.
“That seems awfully high, but it’s not close to half,” she said.  “I remember you teaching about margin of error, but I’ve forgotten how to apply it here.”
My family looked strangely at their plates.
I, on the other hand, took out my pen and did a little figuring on the napkin. Then I called the waiter over to borrow a calculator.  I figured that the margin of error was 7.8 percent.  This meant that the fraction of restaurants serving road kill was between 27.9 and 43.5 percent with 95 percent confidence.
“What might’ve happened,” I said, “was that someone looked only at that upper part of the estimate and rounded it to 44 and from there it’s not so hard to say almost half.” 
This isn’t a very ethical way to present that particular data, but looking at the other end of the confidence interval is awfully disturbing too. It is saying that over one-fourth of the barbecue restaurants serve road-kill.
“Where was this survey taken?” I asked.
“It was at a barbecue festival,” she said. “But I see where you are going.  I will do a little more digging to find the particulars.  Thanks.”
She then finished up her burnt ends and excused herself. I gave her my business card with my e-mail address on it as she left, asking her to keep me filled in. It was a week before I got an e-mail from her.
It turns out that it wasn’t clear these people were restaurant owners at all. They were simply people that attended a barbecue festival catering to people who cooked wild game.  The survey was administered at a workshop entitled “Using a dark sauce to cover tire tracks.”
“That kind of explains it,” she wrote. “I wasn’t able to use the data, but digging to get to the bottom opened up a whole new subculture that I was able to write about.”

Thursday, April 21, 2011

Custer’s Last Stand

Custer’s Last Stand

By Bobby Neal Winters
We are told that a prophet is not without honor except in his own home town.  And it’s true that those of us who know us best have the most trouble believing that we might know anything ourselves.  This is especially true, in my opinion, when you practice mathematics.  I think this is because that it can be so technical that non-professionals can’t tell what is relatively easy from what is hard because they don’t understand either.
At times it has been important to me to convince my kinfolks that I do know something about mathematics.  This is made difficult for me because I am not very good with arithmetic.  If you ask me to add up a column of figures, I do like everyone else and reach for a calculator.  Add to this the fact that my expertise is in the topology of non-compact three-manifolds which is something that doesn’t just naturally come up in conversation after Thanksgiving dinner.
I have learned a tiny bit of statistics by teaching it over the years and that has provided an opportunity to help at least one of my kinfolks recently.  That kinsman was my cousin Custer.
Custer is the grandson of my Aunt Vidalia.  He was her special pet when he was growing up and she spoiled him rotten.  His parents spoiled him rotten as well.  They are fun to spoil, but sooner or later there is a price to pay, and Custer has had a problem that in some circles is referred to as failure to launch. 
That is to say that they can’t get him to move out of the house; he just hangs around and obsesses on Bigfoot all day. 
The reason for this has to do with work.  It’s not that he can’t get a job.  He’s had lots of jobs.  Vidalia has lots of friends who have either given him jobs or found jobs for him.  It’s keeping the job that’s the problem.  Some of the elders in the family have been of the opinion that if he spent half as much time working as Vidalia’s friends have in finding work for him that he would be president of Standard Oil by now, but I believe in giving everyone a chance.
His latest job had been at the Sucker-Rod Museum. According to its brochure, it was the home of the world’s largest pile of sucker-rods.  For those of you who didn’t grow up in the oil field, a sucker-rod is a cylindrical piece of metal.  They are about an inch in diameter and about 30 feet long.  None of this is important to what comes next, but I didn’t want you to be worried about not knowing that.
The job had been given to him by one of Vidalia’s friends who is big in the oil field.  He’d set up the Sucker-Rod Museum and had needed someone sit at the reception desk, invite the visitors to sign the book, and to keep track of the number of folks who visited.  Previously this job had been given to a retired old-field worker who was confined to a wheel chair.  The job had opened up when the old fellow had died at the age of 92.
The fellow had taken the job seriously and had kept an immaculate set of records.  I know this because I’d seen them as a part of a project I’d done for Custer.
Not long after getting the job, Custer had e-mailed me with a project he was working on.  He had the records that his predecessor had collected and wondered if there were ways of predicting the number of visitors to the Museum on a given day.
Now, I get nervous when people start using that word “predict.”  We can make statements about trends over time given certain assumptions, but we can’t actually be prophets.  People want magic, however, and sometimes it’s hard not to get sucked in.
I answered his e-mail and told him to send me a copy of his records and I would see what I could do.
The Museum is opened 6 days a week, Tuesday through Sunday, 52 weeks a year.  It’s closed on Christmas and Easter, so that usually works out to being open 310 days a year.  The last year that I had full data on, it had 300 visitors.  This was an average of 0.97 visitors a day.  The other years were off from this slightly but not by much.
The idea of having an average of 0.97 visitors can be somewhat comical, as we try to imagine what 0.97 of a person is.  Would these be old oil-field workers missing a few fingers or a hand?  Maybe that’s not so comical.  Anyway, that is not how averages work, of course.  That this means is that some days several people would come in and some days nobody would be there.  While on any given day, it is not necessarily predictably what will happen, one can sometimes say something about the distribution.  By this I mean to say that there will be a certain fraction of the days when no one will come in, there will be a certain fraction of the days with one person will come in, a certain fraction when two will come in, and so forth.
Often situations like this will follow the Poisson Distribution, which is also known as the Law of Rare Events.  This is kind of misleading because the Law of Rare Events can also model very busy places like restaurants and barbershops.  The word rare is a reference to on any given day the probably of a particular person going to a particular restaurant might be small.  The distribution depends upon the average number of visits per day, such as the 0.97 for the Sucker-Rod Museum.
I examined all the data he sent me, and it turned out that the pattern fit the Poisson Distribution very nicely. I sent him a report saying that on 38 percent of the days there would be no visitors, on 37 percent of the days there would be one visitor, on eighteen percent there would be two visitors, on six percent there would be three, and on one percent there would be four.
I swear that is all that I told him.
A few weeks later I got a hot call from Custer’s father, in whose basement Custer is living, telling me that I’d gotten Custer fired.
“What?” I asked, hurt and confused.
“He said that you’d done some math and he used it and was fired because he used it.”
After saying that I didn’t see how what I told him could get him fired, I said that I was sorry that he’d lost his job, then I hung up, and made a few phone calls.  After talking to several people, the following picture emerged.
Custer observed that 93 percent of the days there would be two or fewer visitors.  He then deduced—correctly—that only on seven percent of the days were there more than visitors.  He then developed the habit of closing the museum after the second visitor left deducing—incorrectly—that where was only a seven percent chance that anyone else would come.
Over the course of time there were complaints from people who showed up to the museum wanting to see the world’s largest pile of sucker-rods only to find the museum closed.
My final call was to my Aunt Vidalia.  Who explained how it came to an end.
“Custer has always been a big fan of Sasquatch.  It all came crashing down on the weekend of the Bigfoot Festival in Honobia, Oklahoma,” she pronounced Honobia as Hoe-nubby just as its inhabitants do.  “He’d taken that weekend off without telling his boss.  He was afraid he wouldn’t get paid if he told him.  Then the boss came by.  Well, he just didn’t understand.”
I commiserated a bit with Vidalia over this before I said good-bye.
Custer made quite a few mistakes here.  The non-mathematical ones I leave to you.  The mathematical ones are a bit subtle and don’t have anything to do with the Poisson Distribution which I’d done correctly.
Custer’s problem was his assumption that if he left after the third visitor there was only a seven percent chance that there would be another one.  It turns out that if you’ve already had three visitors, then there is about a thirty percent chance of having more visitors.  This is because already knowing that you have had three visitors changes the initial assumptions of the problem. 
It’s called conditional probability and it catches a lot of people by surprise.  The one thing that is not a surprise is that Custer is out of work, and the family is blaming it on me.

Thursday, April 14, 2011

Keeping track of the factors

Keeping track of the factors

By Bobby Neal Winters
You may recall my having told you about a person named Wilma B. Even in a piece entitled “Uncountable Candy.”  Wilma is the president of the United Methodist Women in the First United Methodist Church in Kimberly, Kansas.
By the way, don’t look for Kimberly, Kansas on any map because it has so far avoided the attention of any cartographer.  It was christened Kimberly after Kimberley, North Cape, South Africa, a place where diamonds were discovered.  It’s in Kansas, there were never any diamonds discovered there, and the folks who named it left out the last “e” because it didn’t look to them like it was actually needed.  They are a parsimonious lot in Kimberly.
In my mind, the name fits, however, because the people there are such jewels. Wilma is one of those jewels and personifies the spirit of the place better than anyone else I know.
The parsimony of Kimberly is a result of its location in what in many ways is still a frontier.  As one looks west from Kimberly, except for the occasional town and small city, one sees a gradual thinning of population, a great emptiness. One gets the feeling there is no one around to help, and one learns not to count on help.  This argues against waste.  It argues against change.
Wilma is a product of this environment and one of its best exemplars. One of her characteristics is that she finds a way to do something and then falls into the trap that it is the only way or the best way. Such was the case during her church’s Vacation Bible School a few years ago.
It had been her church’s custom to give the children different gifts on each day of the week: on Monday they would receive crayons; on Tuesday coloring books; on Wednesday scissors; on Thursday glue; and on Friday they would receive glitter.
Looking at the list, there is a certain logic in it.  I can envision a reality in which there would’ve been reasons associated with giving the gifts in this precise order.  Indeed, I’ve been shown the curriculum the church used to use and there were needs for particular items on particular days.  Due to the realities of the publishing industry, they’ve been forced to switch to a particular curriculum in which the children having their own scissors earlier in the week would be handy.
As with so many things that come my way by virtue of having a wide circle of acquaintances, I do not know exactly how everything occurred, and, what is more, I don’t want to know.  I have been told there was an energetic discussion in which one of the Vacation Bible School teachers informed Wilma that there were a lot of different ways to do this.  Wilma disagreed with that—energetically—and words were exchanged.
Let me emphasize that I knew nothing, and I mean nothing, of this when Wilma approached me. I am a friend of Wilma’s, and being Wilma’s friend has a certain amount of overhead associated with it.
We had met at an event—I don’t remember which one—in which donuts and coffee were being served.  Before I had time to notice, she had laid out the situation involving giving out the gifts in a very neutral way and then proceeded cagily.
“How many ways are there of doing that?” she asked.  “Would it take too long for you to figure that out?”
I had no idea I was being asked a controversial question.
“It wouldn’t take long at all,” I said. “There are 120 ways to do it.”
She seemed somewhat surprised with the rapidity of my answer.
“How did you figure that out so quickly?” she asked.  “I am not sure I trust an answer that you can get so quickly.”
“Oh,” I said, “this is something that I teach almost every semester.  When you make an ordered list of five items there are five factorial ways of putting those items in order.  Five factorial is equal to 120.”
She was beginning to look a little grim.
“I am not sure what you are saying,” she said. “Five factorial?”
“That’s right,” I said. “Five factorial is five times four times three times two times one.  That is equal to 120.”
“Okay,” she said, “I understand that five times four times three times two times one is equal to 120, but why is that the number of ways of putting five things in order.”
I’d just finished my donut and had a napkin in my hand that was no longer serving a purpose, so it was at that point I pulled my pen from my pocket and drew a diagram on the aforementioned napkin that looked something like this.   

“For the sake of time,” I began, as I showed the napkin to her, “I’ve decided to consider the case only for the first three days.  I am sure that this will be enough for you to see the pattern.”
We mathematicians are optimistic creatures and have confidence that in following a pattern three times is enough for anyone to get it.  As with most optimists, we are constantly disappointed.  Nevertheless, she nodded her head that she was willing to buy into the proposition.
“On the first day, there are three choices: crayons, books, and scissors.”
She nodded, so I continued.
“Suppose that we choose crayons as our first choice.  This leaves only books and scissors to choose from.”
Again she nodded.
“Then suppose on the second day we choose books.  This leaves scissors as the only thing left to choose on the third day.  That path along the top in my graph represents that particular series of choices.”
She nodded again.
“Noticed that this graph I’ve drawn branches.”
Again there was a nod.
“This is because there are choices to be made. On the first day there are three alternatives, on the second day there are two, and on the third day there is only one choice.  Notice that we each sequence of choices corresponds to one of the paths in the graph.  The number of paths can be obtained by multiplying three by two by one.  If we go the whole week, it is the same principle.”
She wasn’t looking too happy, but this isn’t too unusual in people I explain math to, so I am used to it, but she was still listening to me.  That, I am not used to.
“You call this ‘factorial’?” she asked.
“Yes,” I said.  “You may have seen it written out as an exclamation mark.”  I turned over the napkin and wrote it out.
“See, they get quite big,” I said.  “That takes a lot of people by surprise.”
“Yes, it does,” she said.
I didn’t learn until later the story behind it all.

Monday, April 4, 2011

The porcelain pig problem

The porcelain pig problem

By Bobby Neal Winters
Ever since learning about Marcus Nathaniel Release, the mathematically talented twelve-year-old cousin of a friend of mine, I enquire about his progress.  Talent in a particular area is one thing, but success is a mixture of factors.  If a talent is to be used, it has to be developed to be sure, but there is even more. One cannot allow talent to be an excuse for poor behavior.
As you may recall, Mark had estimated the size of the large family next door with the use of a paintball gun.  Rather than in receiving a punishment, this had resulted in the mother of that large family inviting Mark over to play with her children.  I wasn’t sure whether that was sending the young man the right message, but, as I don’t even know the family, that is none of my business. And if I’d brought it up, you can be sure I would’ve been told so.
I do make inquiries about him through my friend because, among other reasons, I’d like to see him as a student at my university one day.
“How is Marcus?” I asked.  “Has he painted any more of his neighbors?”
My friend, who’d just taken a bite of a doughnut, took a napkin to wipe the corners of his mouth.  He then smiled a little, in a mysterious sort of way.
“No,” he said. “At least none who weren’t also shooting paint at him at the same time.  He’s become good friends with that family next door.  The mom has sort of taken him in as another son.  You know how it is with large families; there is always room for one more.  He eats supper with them about half the time and he’s even started going to Sunday School with them.”
I nodded.  Having grown up in a similar locale, I am familiar with the culture and none of this sounded strange, though I did notice a bit of a mischievous smile playing at the corner of my friend’s lips, so I remarked upon it.
“You’re smiling,” I said. “Is there something funny?”
“Funny?” he said, smiling even more broadly. “To me and you, maybe.  To those involved, it was deadly serious.”

In the Ozarks, there is a high value put on the native, homespun crafts.  The crafts are everywhere.  There are numerous local festivals.  There are theme parks.  And, as religion is one of the principal conduits of culture in the region, crafts are integrated into church activities. 
The church to which Mark’s neighbors belong is rural, but, in spite of that, has a large congregation.  It is big enough so that they can support an impressive physical plant that includes a gymnasium.  Every year they open their gym to local artisans so that they can display their wares, sell a few, and donate some of the proceeds to support of a local ministry for the poor. 
This year Mark and his parents attended this event as guests of their neighbors.  One might think that this sort of event wouldn’t hold a lot of interest for a rambunctious young man like Mark, and one would be correct, but the organizers are aware of this so the couple the event with a barbecue and games.
Most of the crafts exhibited are woodworking and sewing; things which are not necessarily very delicate.  One of the exhibitors by the name of Peter Paulson, however, does ceramics.  He’s known for his porcelain pigs.  He calls them his porcelain porkers.
At one point during the narrative, my friend paused and said, “Peter Paulson is pretty persnickety about his porcine pottery.”
Some people.
Paulson numbers his creations.  There are little index numbers on each that are hidden in obscure spots.  Each particular series is numbered consecutively from 1 to the highest number than he makes.  He is a true artist in the sense that he continues making his art until the spirit leaves him.  The pigs are each roughly the size of a baking potato, and he presents them partaking in various activities not usually associated with pigs such as riding bicycles, playing cards, and—somewhat disturbingly—eating bacon. 
They are surprisingly delicate.  They can be held in the palm of your hand, but you wouldn’t want to drop one even from a short distance.  Paulson had a whole series on display at this particular event.
It happened on a Saturday afternoon.  The men of the church had spent the morning smoking meat for the barbecue.  It had been very sunny.  The children had been playing outside and the women had been exploring the crafts.  Then, as so often happens in the spring, it clouded up and began to rain. The children who had been enjoying themselves a great deal in the out-of-doors were forced inside by the rain.
They say that a butterfly flapping its wings in China can cause a hurricane in the Caribbean. We are told that for the want of a nail a horse was lost.  That is all well understood.  How much more well understood is the combination of rambunctious, over-stimulated boys, gymnasiums, and basketballs. 
Someone at the church had left the basketballs out in a huge trash can on wheels.  One of the boys—somehow ignoring the craft booths set up on the basketball court—took one of the balls and launched it from half court toward one of the goals.
The ball ricocheted off the rim and landed directly in Peter Paulson’s booth.  The table fell with a thud, crushing every single porcelain porker on it.  There was nothing larger than a postage stamp left of the porcelain pigs.
It was a mess.
As the pieces of porcelain pig were swept up, Peter Paulson, the pastor, and the holder of the insurance policy had a discussion. The insurance company would pay.  The pigs were valued at $50 apiece.  The question was: how many were there.  The answer was: Peter didn’t know.  He knew how many he’d sold, but he didn’t know how many he’d brought.
“It was an entire series,” he said.  “It could’ve been 150 or it could’ve been 500.  I just don’t know.”
“Well,” the pastor said, “I know how we will find out.  We will make these boys put the pigs back together.  The punishment will fit the crime.”
The people standing there looked at the bucket of porcelain crumbs and at the group of boys between the ages of eight and 14.  When they looked back at the pastor, they had a look in their eyes, but it wasn’t belief.
Then a small voice with a country accent spoke up. It was Mark.
“Preacher,” he said. “We don’t have to do all that if you just need a general idea.”
“Son, I know you…” the preacher began, but he was interrupted by the mother of Mark’s neighbors.
“Listen to what he says,” she said gently.
“Okay,” the pastor said.  “Go ahead.”
Mark then looked serious.
“If you just need a general idea,” Mark said, “I can tell, but I have to look through the pieces.”
“Well,” the pastor said, “you can do that while we are thinking.”
Mark and the rest of the boys went to the bucket containing the porcelain fragments.  They each dug out a handful, pour them out on a table, and began looking through them. It took about twenty minutes, mainly because the boys would occasionally start tossing pottery fragments at each other.
At the end, Mark wrinkled up his nose in thought, and then stood up and walked over to the pastor.
“There were 160 give or take 10,” he said.
Peter Paulson got a hard look on his face.
“We just decided that to say there were 500,” he said.  “So thank you for your trouble young man.”
Paulson was trying to take the attention away from Mark, but Mark wouldn’t let him.
“But that cain’t be right,” he said.  “The error cain’t be that big.”
At this point, the insurance man was showing some interest.
“You know,” he said, “we probably could just pay an expert to weigh the fragments, but the cost of that would have to be deducted from your insurance settlement.”
Paulson then got a funny look on his face.
“You know, now that I think about it, there were about 160 pigs.”

My friend was grinning from ear to ear when he finished the story.
“What I’d like to know,” he said, “is how the boy knew how many there were just be looking at a few serial numbers.”
“I think that he used something that we call the German Tank Problem,” I said.  “Back during World War II, the Allies wanted to know how many tanks the Germans were producing, so that used this formula.”
I wrote it on a napkin for him.  It was: N=m(1+1/k)-1.
“The N is the estimated number of tanks, k is the total number of captured serial numbers, and m is the largest serial number.  You can get a rough estimate of the area by dividing N by k. My guess is that Mark and his friends found fifteen serial numbers and the largest of the numbers was 150.  Mark knew there couldn’t have been 500 because the margin of error isn’t that big.”
I was curious about something.
“So, how was Mark rewarded for this?” I asked.
“He was spanked,” my friend said without hesitation.  “He was the boy that shot the basketball to begin with.”

Friday, April 1, 2011

Chasing the dollar

I wrote this a number of years ago and it had never found its way to this blog.

Chasing the dollar

By Bobby Neal Winters

Before I begin this story, I have to make it absolutely clear that my Aunt Vidalia was always a good Baptist. By this I mean to say that she loved God, loved her neighbor, and took care of those in need.

On the other hand, she never let anything as abstract as the Church Covenant get in the way of her taking a couple of trips to Vegas per year and availing herself of the facilities while she was there.

Vegas and Aunt Vidalia were made for each other. In Vegas, you have a city built in a desert with grand edifices creating a beautiful illusion. With Aunt Vidalia, there was a tall hairdo, fake cherry-sucker red finger nails, and enough costume jewelry to have a yard sale.

The difference between Vegas and Aunt Vidalia is that if bulldozers were to push down Vegas there would only be desert underneath, while there is a very real person at the heart of Aunt Vidalia.

Vidalia’s husband died some years back and after a period of grieving, she took up with a man called “Bum.” This is a case where the name Bum is deceiving. Bum is short for bumpkin and is a name that was stuck on him when he first entered the army out of the deep Oklahoma backwoods. Bum took to the military like a duck takes to water and retired as a Lieutenant Colonel, and with the name Bum glued to him all through is career.

Bum retired early so that he could spend time with his wife and this turned out to be a good thing because after about ten years she passed away. He’d love her and this had left him lonely.

He met Aunt Vidalia and immediately recognized her as a person of worth in spite of the surface accoutrements that others might’ve taken as signs of shallowness. While she was in many ways the opposite of his late wife, who was reserved and understated in her choice of clothing, he discovered that Vidalia had the same inner strength in her that had enabled him to rise from an Okie in the backwoods to the rank of Lieutenant Colonel.

Little did he realize that this commonality they share would lead to a loss of domestic tranquility.

The occasion of this loss of tranquility was a party in the nicer part of Shawnee, Oklahoma. There would be those who’d deny that such a place exists, yet “nicer’ is a relative term and I will stand by it. Bum had been invited to this party by an old high school friend of his who’d gone into the oil business and made good of it.

It was one of those parties where liquor flowed rather freely. I don’t want to leave the impression that anyone was incapacitated in a noticeable way, but there came a stage of the party when many of those present were not in total possession of their better judgment.

It is at this point that a new character enters the picture. He was the son of the party’s host and I will refer to him as Jack. Jack was a graduate student who was majoring in math and was visiting his parents over the weekend.

My Aunt Vidalia is a friendly sort and struck up a conversation with him.

“What are you learning in school?” she asked. “Is it all just faster ways to multiply and divide?”

“I’m studying Game Theory,” he said.

By this time there were other people listening in on the conversation.

“Game theory,” Aunt Vidalia asked, ‘what’s that?”

“It’s just what it sounds like,” he said. “We study games.”

Aunt Vidalia was skeptical. She’d grown up poor and had to work all the time so she didn’t see much use in that.

“Studying games?” she asked. “What good is that?”

“Let me show you,” he said as he reached in his pocket and pulling out a dollar. “I can sell this dollar and make money on it. I’ll auction it off to the highest bidder. The only thing different from a regular auction is that both the highest bidder and the second highest bidder pay. Who will start the bidding at one penny?”

Aunt Vidalia likes games and the notion of getting a dollar for a penny was more than she could pass up.

“I’ll bid a penny for that,” she said.

Unfortunately for her, that sounded like a good idea to other folks at the party too. There were bids of 2 cents, 3 cents, and a nickel in quick succession.

Aunt Vidalia chimed in at 10 cents and again at a quarter.

Had she been paying closer attention, she would have noticed that people where dropping out of the bidding. She didn’t notice until she bid 50 cents that she and Bum were the only folks left bidding.

The slower pace of bidding gave her time to think. She would only be making 50 cents now if she got the dollar, but if she came in second she would lose 50 cents. If only Bum would drop out she would be all right.

“Fifty-one cents,” Bum said. He smiled and took another sip of the scotch and soda he’d been working on.

Clearly Bum was having a good time, but she wanted the dollar now. She looked him square in the eye.

“Ninety-nine cents,” she said and took a swallow of the Bloody Mary in her hand. She thought that she’d get her dollar, make a penny for her trouble, and Bum would get stuck holding the bag.

Now it was Bum’s turn to look her in the eye.

“One dollar,” he said.

If looks could kill, he would have dropped dead, but they can’t so he didn’t.

Bum and Vidalia were so busy looking at each other, they didn’t see the look on Jack’s face or anybody else’s. Jack was grinning like a possum, and everyone else was as well. If Aunt Vidalia had seen the way Jack was smiling, she might have smile herself and let laughter end the game.

As it was, she didn’t.

“One-dollar and fifty cents,” she said without batting an eye.

“Are you crazy?” Bum asked. “You are paying a dollar and fifty cents for a dollar?”

“No,” she said, “I’m paying 50 cents to stick you for a dollar.”

He paused just long enough to internalize that.

“Two dollars,” he said.

They fifty-cented back and forth until Bum bid $10.50. Then Aunt Vidalia remembered she only had 10 dollars in her purse.

“You can have the damn thing,” she said.

Bum gave Jack the ten-fifty, Aunt Vidalia gave him ten, and Jack gratefully accepted and handed the dollar to Bum. Bum offered it to Aunt Vidalia, and she told him where to go.

“I think it’s time to go home,” Bum said. So they did.

In silence.

It’s been about a week now, and they haven’t spoke again. I hope it all turns out all right.