Tuesday, March 29, 2011

Robbery at the Craft Round-up

By Bobby Neal Winters

The pleasures of small-town life are manifold and one of them is our annual fall festival with its associated Craft Round-up. The fall festival is an occasion to wander amongst the various mobile food establishments sampling funnel cakes, bratwurst, sweet potato fries, curly fries, buffalo burgers, steak sandwiches, and other means of putting Lipitor to a test of its abilities.

For those who can pry themselves away from the culinary sensations, there are the booths of the Craft Round-up where the artists and artisans of the region can display their wares and occasionally set something.

I attend every year, mainly for the bratwurst, but I fill in the time it takes to digest by visiting the craft booths. One such booth caught my attention. There was a banner above the booth that declared the owners to be “The Old Shavers.”

There booth featured carvings of wizened old men with corn-cob pipes and bashed in hats who were holding jugs of moonshine. There were also sweet looking grandmotherly women in bonnets and aprons among the carvings and an ample number of loose-skinned old hound dogs.

I have a number of friends who are quite fond of such things, so I saw this as an opportunity to do a little early Christmas shopping. The items were priced reasonably for such things but strangely. Rather than being priced a round figure, they sported prices like $5.01 and $10.03.

I picked out the bust of a wise-looking Native American woman which was priced at $25.07 and presented it for checkout.

“That’ll be twenty-five dollars and ten cents,” the venerable gentleman said.

“I beg your pardon,” I said, “but I am confused. It’s marked twenty-five dollars and seven cents. I don’t mind the three cents extra, but why the extra.”

The venerable gentleman looked very serious.

“It’s marked $25.07 because that’s what it cost,” he said. “I round everything up to the nearest dime because I don’t use pennies or nickels. It’s against my religion.”

I was experiencing the dual reactions of flabbergasted-ness and curiosity.

“Pennies and nickels are against your religion?” I tried to keep rude inflections out of my voice. “Why?”

“Lincoln and Jefferson where evil so I will not traffic in their images.”

I had just laid down a twenty-dollar bill, a five-dollar bill, and a dime.

“Oh,” I said, picking up the five. “I’ll just take this back then because I wouldn’t want to offend you.”

“That’s all right,” he said, retrieving the five from me. “It’s okay if it is on paper.”

I collected my purchase and wander off shaking my head slowly from side-to-side in confusion. Soon I had put the strange incident behind me comforting myself with a root beer float over at the Methodist church.

It was there that Suzanna Doughcoup our local homicide detective found me and took a place by me at the table.

“Sue,” I said, spooning the root beer coated vanilla ice-cream into my mouth, “to what do I owe the pleasure.”

She looked rather stern and attempted to look more so at the sound of the word “pleasure.”

“I am afraid that I take no pleasure in larceny,” she said.

“Larceny?” I echoed stupidly. “I thought murder was your specialty.”

Her visage brightened somewhat at the mention of murder.

“Yes, it is,” she said. “But unfortunately there is not enough murder in this town to justify a full-time homicide detective so I have to spend my time on less important matters like taking care of thieves.”

I took a sip of the ice cream flavored root beer and pursued the conversation further.

“So who are the thieves?”

She looked at my Indian-head bust and nodded toward it.

“I see you’ve met them,” she said.

“Oh,” I said, “you mean the Old Shavers?”

“Yes,” she said. “You see how wily they are. They price their items off the round numbers and then round everything up to the nearest dime. That is misleading and I think that’s stealing. There is no telling how much that adds up to over the course of a day. You’re a mathematician, so I thought I’d come to you to get an estimate. You know how little things add up.”

As a matter of fact, I’d been thinking about it. I went over to the church ladies and fetched a napkin and a pen along with a piece of cherry pie.

“Well,” I said, beginning the calculation with a flurry of the pen, “we can figure that every person is overcharged between zero and nine cents, inclusive, and that this amount is uniformly distributed.”

Sue’s face was as blank and hard as an empty chalkboard, so I continued.

“That means, on the average, each transaction over charges the customer by four-point-five cents. The discrete version of the uniform distribution has an easy formula for variance which in this case works out to thirty-three divided by four.”

I find that by the time I get to the word “variance” in any statistical discussion the eyes of those listening have glazed. Sue was no exception to this, but, I do admit, it was harder to tell.

Sensing the indifference to the beautiful details of the calculation, I began summarizing.

“To make a long story short, if we assume there are 1000 transactions, we can calculate the margin of error to be about two cents with 95 percent confidence.”

Sue paused and thought for a minute.

“What does all that mean?” she asked.

I paused myself so as to phrase my response in the most useful manner possible. Then I began.

“They cheat each person out of an average of four-point-five cents. If they have 1000 customers, that means they have cheated their customers out of a total of $45, but there is a margin of error of about $20 which means they have cheated people of between $25 and $65, and I can be 95 percent sure of that.”

Then Sue did something I have seen her do only rarely. She smiled.

“You can be my expert witness then. I think that I will take this to the DA.”

Before I could say anything else, she disappeared. I thought that I would do the same, so I strolled from the church lawn down the street, following the smell of funnel cakes and hoping against hope that I could elude the formidable Detective Doughcoup for the remainder of the day.

My hopes were for naught because less than an hour later she found me three quarters of the way through a funnel cake and praying for a quick death after a day of over-eating.

Her normally stoic expression betrayed disappointment.

“What’s the matter?” I asked, trying to sound as interested as my heartburn would let me.

“The DA won’t prosecute,” she said. “I found him down by the ribbon-sliced fried potatoes. He said that everyone who bought anything there had the choice to buy it or not, and that nobody was making them. He also said the Old Shavers could just raise their prices up to a round number if they wanted to, anyway. But lastly, he said the margin of error was too high.”

I nodded, feigning to share Sue’s disappointment.

“Well,” I said, “you might be comforted to know that there are professional criminals who do penny-shaving. The sometimes infiltrate banks or places that to a lot of computer transactions. They set the computer to always round down instead of rounding fairly so they are stealing money beyond the second decimal place.”

“Really?” Sue asked, seeming curious.

“Yes. They steal, on the average twenty-five ten-thousandths of a cent with every transaction. If you figure this is done for a million transactions that adds up to about $2500 and you can calculate the margin of error to be about $50 with a 99 percent level of confidence. So you are only going to be off about fifty bucks on way or the other.”

She still looked disappointed.

“That’s not going to help me now,” she said.

“I tell you what,” I said, rubbing my sternum. “If it makes you feel better, you can prosecute every food vender in this festival for murder after I die of heartburn.”

That made her smile again.

Monday, March 21, 2011

Mark N. Release

Mark N. Release

By Bobby N Winters

I am known among my friends to be of a mathematical bent, and they like to share the mathematical experiences they have with me. Most often this is in the form of forwarded mathematical e-mails with videos or puzzles or puzzles within the videos. Some of the time, however, it is of a more personal nature. Such an instance came recently when a friend of mine brought a story to me over coffee.

“You mathematicians,” he said, “can just turn up anywhere. There is no rhyme nor reason.”

“I am not going to disagree with you,” I replied, but, being cautious I added, “but what exactly do you mean?”

“Geography, socio-economic factors,” he said, “it doesn't matter you just turn up. That mathematical mind just pops up anywhere.”

“That's right,” I nodded. “The gift is just imposed on some of us capriciously.”

I didn't like the way he curled up one of his nostrils when I said gift, but I let it slide. I was curious as to why he'd started on this line so I thought I would encourage him.

“Why are you bringing this up at this particular time?”

“Well,” he drawled out, “it is because of one of my cousin's kids back home.”

My friend is from Arkansas. As a native Oklahoman, I like Arkies. We Okies like them in general because they are a group we can consider to be less sophisticated than ourselves; they reciprocate this. I like them in particular since we seem to share many of the same experiences and attitudes. He began a tale about his cousin.

This cousin was from the Release branch of his family who lived in the Ozarks of North Central Arkansas. If you've not been there, you may need to be told that the region is beautiful. There are many “hills and hollers” that simply invite you to drive through and enjoy their natural beauty. Many parts are so isolated and untouched that they might remind you of the old Wild Kingdom television series. You expect to run into Marlin Perkins and his assistant Jim on an expedition of some sort.

My friend's cousin has a family, and it is his twelve-year-old son Marcus Nathaniel who has been gifted with the mathematical gene, as it were. The family lives on the old farmstead where they have a few cattle, a few hogs, and a few more dogs than absolutely warranted. They get their water from a well; they do have electricity, but don't have natural gas. None of this is necessary to understand the mathematics that follows, but it does give you an ideal of the caprice of the mathematics gods, as it were.

The Releases don't have TV. Being rural, there is no cable and they have not yet opted for a satellite dish. They entertain themselves in more traditional way. Young Mark is fond of hunting and fishing as young men have done in that region for many generations, but he's added one more element to it: paint-ball.

Paint-ball, as odd as it may seem, marks a point of entrance for us to observe a bit of our young man's mathematical behavior. The occasion of this particular bit of mathematics was the arrival of some new neighbors.

This is a part of the world where not many people come and go. Actually, these days there are more going than coming, so it was a particular interest when a new family moved in next door. Here I used the phrase “next door” which I now realize might be a bit misleading. Next door in that part of the world can mean that you are only separated by a fence, but it can also mean you are separated by a fence and a wooded area and a creek and distance of about a quarter of a mile. In this case, it was the latter.

The family moved in and Mark's mom, as is the custom in that area, took them over a pie. When she went over she determined that the family was blessed with a large number of children. They were so active that she couldn't tell how many that there were.

Mark was overjoyed when he heard the news because there would be new kids to play with. He was less thrilled to learn that the the parents were fairly strict and didn't let the kids play with strangers and it might be a while before the Releases didn't qualify as strangers.

This annoyed Mark and helped set up the incident that follows which began, really, when he overheard his parents talking.

“It's a shame them being so stuck-up,” his father said. “It'd be good for Mark to have some more kids to play with.”

“Well,” his mother said, “they are really religious and there very careful with their kids. I can't blame them none. These days you just don't know. And it's not like their kids are hard up for playmates. They've got more than I can count.”

Overhearing this, Mark took it as a challenge. He loaded up his paint-ball gun and hiked through the woods, forded the creek and hid himself in the underbrush. And he waited.

Soon a group of children emerged in the back of the house within his sight and began to play. He waited until they were all occupied in their game before he took aim and began squeezing off rounds. Before his was done, he'd stained six of the children neon yellow. He then beat a hasty retreat back into the woods and across the creek, losing the larger of the children who were following him.

He put his paint-ball equipment away and waited until the next day, whereupon he repeated this process with blue paint-balls. At that time, he stained five of the children, two of whom he'd marked before. He could tell because the paint is really hard to get out and some of them were green afterwards instead of blue.

This time when he got home, there was a car in the front yard and a strange woman with an angry sort of look on her face in the kitchen. It was not nearly so angry a look as that on his mother's face. She looked directly at the paint-ball gun in his hand.

“All right, Mister,” his mother said, “what in the world have you been up to?”

He looked at them both and spoke matter-of-factly.

“They have about fifteen kids, give or take about 4.”

“What?” his mother asked confusedly.

“They have about fifteen kids give or take,” he repeated. “I caint tell you exactly because they move around so much and they look so much alike being kin and all, but there's about fifteen of them.”

The strange woman's visage changed from stern to amused.

“We've been blessed with twelve children,” she said with a smile. “Is that was this was all about?”

“Yep,” Mark said crisply. “Even if you won't let me play with 'em, I can still count 'em.”

My friend end the narrative with a smile on his face.

“After that,” he said, “little Mark got to play with the neighbor kids next door whenever he wanted to. I don't know if the mom decided that Mark was okay or it was a case of keep your friends close and keep your enemies closer, but they've been getting along well. What I don't know is how the kid estimated the number.”

“Well,” I said, sipping my coffee, “I can't be for sure, but I think he may have been using the Mark-and-Recapture method. This is a way field biologists estimate numbers. You may have seen nature shows where they capture animals and put tags on their ears. It makes for great TV. What you don't see is they come back later and capture some more. If they recapture animals which have been tagged they can then estimate how big the population is. If you want to know the formula...”

My friend stopped me before I could continue.

“I am sure that is fascinating,” he said, “but I've got somewhere I need to be.”


“I don't know,” he said, “but there's got to be somewhere.”

Since he didn't want to know, I will simply share it with you. If M is the number captured and marked the first time and C is the number captured the second and if R is the number captured the second time that had been marked the first time, then the estimated size of the population is N=MC/R.

As Mark had painted six the first time, five the second, and two of them twice this works out to fifteen. There is also a more complicated formula for the standard deviation and Mark figure that the true number would be within on standard deviation of the mean.

Wednesday, March 16, 2011

Doodling in math class

V. Hart does some pretty good stuff.