Thursday, June 30, 2011

Too much pair of dice

Too much pair of dice

By Bobby Neal Winters

Custer walked across the parking lot toward the tall building.  The sun was setting and the lights on the side of the building were beginning to be more visible in the darkness.  The colored lights, red, blue, and green, alternately flashed and shot up the side of the building.

Unknown to Custer, one hovering above his right shoulder and one above his left, were entities. 

 Those of a certain bent might call them spirits, others might refer to one as an angel and the other as a devil, and those of a more secular stripe might refer to them as manifestations of Custer’s bicameral mind.  We will call them Poindexter and Jezebel and refer to them as entities, allowing the reader to interpret things as the reader might wish.

The closer the trio approached the tall building, the more Poindexter became concerned.

“That sure is an expensive building,” he said.  “I wonder how they can afford that.”

Jezebel, for her part, was delighted.  She had a natural aura about her and it pulsed in harmony with the lights of the building.

“Just like you to think about money,” she said dismissively.  “They’ve designed everything so that it will be more fun!” With that she shot off into the distance, circling around a couple of pretty girls who were much too immodestly attired in Poindexter’s opinion.  She then shot up, circled the neon sign on the front of the building that read “Casino”  twice, and shot back down to her position above Custer’s shoulder.

Though Poindexter as an entity surely had no need of glasses, those who had seen flashes of him often remembered him as having horned-rimmed glasses.  Has they had such a flash now, they would’ve seen him with those glasses slid down toward the end of his nose.

“You know,” he said with as much seriousness as he could muster, and he was capable of mustering seriousness by the truckload, “if you lose the first and last letters of casino what you have left spells ‘a sin.’ Maybe you ought to think about that.”

Jezebel, who’d only also been seen in flashes, would’ve subconsciously reminded Custer of a twenty-year-old version of his Grandma Vidalia.  This might have bothered Custer a great deal had he been paying attention during his college psychology class, but he wasn’t because he was distract by a real twenty-year-old girl who subconsciously reminded him of his Grandma Vidalia.
In any case, Jezebel simultaneously shook her head and rolled her eyes upward.

“Whatever!” she said, making that last syllable last about ten seconds.

Unaware in any real sense of either of the entities around him, Custer flowed along with the growing stream of humanity around him until they left the growing darkness of the outside world and enter into the interior of the casino with its artificial stars dazzling him with their brilliance.

Once inside, Jezebel flitted around with delight.  She buzzed past all of the slot machines with their whirling numbers, flew under dice as they themselves rolled along the tables, and orbited around the roulette wheels as they turned.

Poindexter, in stark constrast, grew more and more stern. As Jezebel hovered above a waitress who was exposing altogether too much cleavage both above and below and drew more of Custer’s attention, Poindexter prepared for one last stand: he would use pure mathematical reason.

Poindexter reached into Custer’s mind and stimulated a memory of one of Custer’s math class.  This wasn’t too difficult because Custer’s math professor looked much like the way people remembered Poindexter looking.

Hovering above Custer’s right shoulder, Poindexter said the words, but in Custer’s head he remembered his professor saying them.

“The first thing you must know,” the words came out dead and dull, “is that a casino is in the business to  make money, not to be fair.  Whatever the game, the casino will always have an edge.”
Custer was dazzled by the spectacle about him, but never the less he echoed the words.

“Have and edge.”

“The games are arranged so that the house will win, on the average, just a little more than half of the time. Let us denote this edge by the Greek letter epsilon.”

Jezebel’s attention had settled upon Poindexter’s efforts.

“Epsilon,” she laughed. “You think that you are going to convince him with an epsilon.”
Poindexter looked daggers at her but continued.

“Epsilon must be chosen carefully,” he said.  “If the edge is too much, then the gambler’s will not get enough positive feedback from winning, but if it is set too small the casino will not make enough money to pay it’s expenses.”
“Expenses,” Custer mouthed subconsciously.

“The casino,” Poindexter continued his lecture, “is able to take advantage of the Central Limit Theorem.  With a large enough number of gamblers, the casino can assure itself a profit even if it has allowed itself only a small edge.

“For the sake of argument, assume that a casino has 1000 patrons during the course of a day and that each of these patrons gambles $20, stopping when they have gambled with it all, not necessarily lost it, just gambled with it.”

“Just gambled with it,” muttered Custer. His eyes were fixed upon another patron of the casino who was wearing cowboy boots and hat and cutt-off jeans he imagined as just one thread away from being a skirt.

Poindexter husbanded his strength and Jezebel circled the young lady’s halter-top.

“Also assume each gambler gambles at least 30 times and that the edge, epsilon, is equal to 0.05, that is to say, five percent.”

“Epsilon,” Jezebel rolled her eyes again.

“At the end of the day,” Poindexter/professor was triumphant, “the casino will have won $2000 dollars give or take $15.  At the same time the average gambler will have lost $2, which isn’t much, but, what is more, 290 of those 1000 gamblers will come out ahead.  Some of them might come out way ahead, and you can be sure that they will be put in the spotlight.”

Poindexter could see that Custer was thinking on his own now and listened to Custer’s subconscious.

“Only lost $2.  In the spotlight.”  

Custer smiled.  This was bad, Poindexter thought.

“But don’t you see?” Poindexter was panicking. “If you gamble long enough, you will inevitably lose yourself.  And you in particular won’t be able to gamble with discipline.  You will just gamble your money until it is all gone, and even if you do win, you will just gamble until that’s gone!”

“Gamble ‘til it’s gone!” This time Custer shouted.

This caught the attention of a waitress in a very tight t-shirt who gave him a complimentary drink.  Custer then walked over to a roulette table, plopped a twenty down.

“Red!” he shouted.

Jezebel, who was all aglow, flittered over to Poindexter’s side.

“Buy you a drink?” she asked.

“Make it a double,” he said.

Tuesday, June 28, 2011

A square deal

A square deal

By Bobby Neal Winters
Jim looked at his daughter, Kristin, who was down on the floor working on her homework.
“What ya doing there, Sweetie?” he asked.  
The girl was lying on her tummy with the book spread before her and the TV blaring in front of her.  She craned her neck back towards her father and smiled.
“Geometry,” she said. “Wanna help?”
At the word geometry, Jim made a face.
“I can’t say I can help you much with geometry,” he said. “I could always figure it out and always thought I understood it, but I never seemed to get it to suit the teacher. ”
He’d always enjoyed doing his math homework, but whenever he turned it in, it always came back painted red.  He’d leave out the T in his ledger proof or something like that.  After a while, he’d just given up on pleasing the teacher.  There was plenty of work to do out on the ranch and he didn’t get graded on it except by the cattle, and they wound up on somebody’s grill, so that didn’t matter.
“I do remember a joke though,” he said.  “Wanna hear it?”
She looked like she wasn’t too sure, but he went ahead anyway.
“It’s about an Indian chief named Pythagoras,” he said.  “He had three wives.  One was big and fat and sat on a hippopotamus hide. The other two sat an the other hides.  He said that the squaw on the hippopotamus was the sum of the squaws on the other two hides.”
That got the attention of his wife who’d been in the kitchen.
“Don’t go telling her stuff like that, or you will get her into trouble,” came a rather stern feminine voice from the other kitchen.
Jim smiled at his daughter. She smiled back and turned back to her books.
“I have to go out to work on the fence,” Jim said. “You help your maw. ”
With that the girl brightened somewhat and began to get up.
“Can I come too?” she asked.
“Nope,” Jim said. “You stay hear and work on your lessons and help your maw.  You don’t want to be out today no how.”
His wife came quietly to his side and whispered to him.
“You know,” she said, “she’s not going to be wanting to be around you forever.  Before long she’s going to get interested in boys and you won’t see her unless she has her hand out for a twenty-dollar bill.”  Having finished, she quietly stepped back into the kitchen.
Jim screwed his mouth around a second or two as he thought.
“Come on, Punkin,” he said. “I just remembered a job I have for you.”
With that, Jim headed to the mud room, as it was called, and pulled on his boots.  Then he pulled on his jacket and hat.  Thus prepared he stepped outside and was greeted by a northerly breeze.  His daughter was there at his side.  
He faced the breeze and scowled.  His own father had always said on days like this that there wasn’t anything between them and the north pole but a barb-wire fence and a couple of jack rabbits.  He didn’t know about the jack rabbits, but there was going to be another barb-wire fence before it was over.
He climbed into his truck, his daughter hopping in to ride shotgun. He cranked the engine to life and headed down the dirt road.  He’d purchased some more land a few miles away and he’d putting some improvements in on it.  He’d rented a dozer and dug a couple of ponds for his cattle to drink from and now he was in the process of fencing it off.
“Well,” he said as he pulled off to the side of the road, “here we are.”
They extracted themselves from the truck and slammed the doors.
“What are we going to do, Daddy?” Kristin asked.
“We are going to so some practical geometry,” he said.
She looked confused.
“Building fence,” he clarified.
They began extracting the things they needed from the pickup’s bed and setting it up on the ground. The tools included three log chains of differing lengths, two piece of re-bar, and a mallet.
“You see,” he said pointing to the fence that ran parallel to the road. “I already have it fenced in.  What I want to do now is to run a fence along the middle so I can have my cattle graze one side while the other side rests.  I want the fence along the middle to be at an exact right angle.”
“Is that what the log chains are for?” Kristin asked.
He smiled.  She was a sharp one, she was.
“That’s right,” he said. “The short one is three yards long, the middle one is four yards, and the long one is five yards.”
He handed her one end of the short chain while he took the other.
“Let’s run this along the fence that’s already there.”
They walked over and lay it along the ground underneath the fence.  Once it was stretched out, he hammered re-bar through the last link on each end and into the ground, leaving about four inches sticking up.
“Run and get me that middle-sized piece,” he said.
Kristin gamely ran over and picked up the piece of change that was four yards long and carried it back over.  Jim saw it was heavy, but as she didn’t ask for help, he didn’t give it.
Before he could say anything else, she ran over and drug the 5-yard piece back. Only someone who’d known him as long as his wife had would’ve been able to see the smile on his lips, and she wasn’t there.
“Okay,” he said, “you put the last link in that piece over the re-bar on your side”--he pointed--”and I’ll do the same with mine.  But first we need to crawl over to the other side of the fence.”
After they’d crawled on their bellies to the other side, they did as he said, and then he took the free end of her chain.
“I am going to walk these taut,” he said, “and you make sure the other ends don’t come loose.”
He then walked into the field until the chains were tight and laid them all out on the ground.
“Come here,” he said, gesturing to her.  “That’s a right angle.  I am gone to put in my first fence post where the 4-yard chain meets the 5-yard chain.  Since you can crawl under the fence better than your old daddy, run and get me my diggers and then start handing fence posts over.”
They then went to work, but as the business of digging and setting posts goes more slowly than the carrying thereof, Kristin soon finished and took to drawing in the dirt in a place where the grass was worn through.
After a while, Jim began to feel hunger pains and noticed that the sun was getting low.
“So, Kristin,” he said, putting his post-hole diggers aside, “do you reckon your momma’s got us some supper ready yet?”
Kristin, who’d been rather intent on whatever she’d been drawing in the dirt, had to forcibly extract herself from what she was doing.
“I guess so,” she said. “But, before we go, can we try something?”
“Sure, Sweetie,” he said.  “What do you want to do?”
“Do you have a tape-measure?” she asked.
He nodded.
“It’s in the back of the truck,” he said.
Before he could ask why, she’d already crawled under the fence, fetched the tape measure, and brought it back.
“Hold that end at the corner post,” she said.  She handed him the free end of the tape measure.  She then walked down the fence that was parallel to the road.
“Three yards, four yards, five yards,” she counted.  The she took a ribbon from her hair and tied it to the fence.
“Okay,” she said, “stay where you are.”
Jim was a bit confused, but like any proud father spending time with his daughter, he indulged her.  Kristin, for her part, walked to the other fence and began counting out loud again.
“Six yards, eight yard, ten yards, twelve yards,” she said.  As she uttered her last words, she found herself exactly by a fence post.  “Okay, Daddy, you come her and hold the spool.”
“What do you want me to do with this end?” he asked.  This was getting complicated.
“Leave it there,” she said. “We’ll switch placed.”
After they swapped, she began walking toward the piece of ribbon she’d tied to the fence earlier.
“If I am right,” she said, “that will read exactly thirteen yards when I get to the ribbon. I want you to check for me.”
It didn’t seem likely to Jim that she would walk five yards down the fence and it would only pull out one more yard of tape, but he kept it to himself.  Kids have to try things.  
He watched the tape come out.  It was too fast to read, but then she stopped.
“What does it say, Daddy?”
He looked and uttered a profanity.
“Well, I’ll be John Brown,” he said. “It’s dead on thirteen yards. How did you do that?”
She smiled a smile that warmed his heart.
“It worked with 3, 4, and 5, so I wondered if it worked for any other numbers, so I figured it out on the ground.”  She indicated the place in the ground where she’d been scratching.  There were equations there that read: a=n2-m2, b=2nm, and c=n2+m2.
“You can do that for about as many numbers as you want,” she said. “What do you think, Daddy?”
“I think that me and your momma’s gonna have a long talk after supper.”

Thursday, June 23, 2011

Summing it up

Summing it up

By Bobby Neal Winters
Being a mathematician is a special thing.  We mathematicians have been touched by God--touched at least--but it’s not without its cost.  Part of that cost is being set apart as a separate branch of humanity, considered somewhat strange by one’s fellow man.  Another is spending a large part of your life distracted by one problem or another.
This was the case with me the other day as I was coming home from a neighboring state.  I was set apart because I was driving alone, but mainly I was distracted by a problem.  The maddening thing is that now I can’t even remember what the problem was.  This is another one of those things which sets us apart from humanity, a certain forgetfulness in the simple matters of living.
In any case, I was distracted for some extended interval of time, and, as happens so often when we go off on these little mental vacations, the rest of the world keeps going on around us.  In this particular instance, my car kept finding its way along the road, but it didn’t keep going along the right road.  I missed a turn.  When I shook off my distraction, I was off the main highway and in the heart of what we in these parts, in homage to Ned Beatty, refer to as banjo country.
I came to a place where the road widened slightly and to the right side there was an unpainted wooden building with a sign above the door that read “Groceries.”  There was also a sign that said “Cold Pop.”  As it was a warmish day and as I had been riding along with the windows rolled down, the idea of a cold pop appealed to me.
I stepped out of the car onto the gravel and walked to the store.  I couldn’t tell whether the store had ever been painted, but the door, which looked to have been a later addition, had been green at one time. It was a wooden frame with rusted screen wire held to it in a rather haphazard fashion by tacks. When I opened it, it screeched so loudly that the bell above it seemed superfluous.
This was all misleading, however, because when I got inside everything seemed new.  And as I reread that last sentence, I realize it is misleading because it wasn’t new, it was old, but looked new.  The pop machine was an antique, an expertly restored antique, but an antique none the less.  I looked inside and it had been filled with nostalgia brands of soda pop which aren’t available anymore along with currently popular brands in classic packaging.  Before I could extract the pop which and lured me into the store in the first place, I was betrayed by the mathematician in me and became distracted by the rest of the place.
The food shelves had been restored in a fashion similar to the pop machine and were stocked with products in old-style containers.  My eyes ran along them and were drawn immediately to the coffee which was in old-fashioned cans.  I have sorely missed the metal cans that coffee was sold in not so long ago.  My first thought was I wanted to buy some.  My second thought was that in these fancy, classic cans that it would be very expensive.  My third thought was that it wouldn’t hurt to simply see what the price was.
My fourth thought was complete astonishment.  The cans were fairly small but their price was a fraction of what I usually pay.  It don’t remember exactly because the price is not important, but let’s say it was $1.22 for a size I usually pay $5 for.  I must have said “Wow” to myself or something because I heard a voice from the direction of the counter.
“Kin I hep ya, Mister?”
It was an old fellow who was clearly in costume.  He wore a crumpled old felt hat and had a corncob pipe jammed between the jaw teeth on the right side of his mouth.
“Uh...yeah,” I stuttered, “are these prices real?” I asked.
“Yup,” came the answer.
“Is there any limit on the number of cans I can buy?” I asked again, not daring to hope.
“Nope,” was the single syllable reply.
I began to load up my arms.  I don’t know how I managed it, but I got thirteen cans total and, forgetting about the soda pop I’d come in for completely, toted them up to the front.
I sat them down on the counter and he eyed them.
“Thirteen?” he asked.
“Thirteen,” I confirmed.
It was then I noticed that he had several cans in front of him containing different objects.  From two of these he removed numbered disks: one red disk with $1 on it, two green disks each with 10 on them, and two blue disks each with 1 on them.  He laid these out in a row in front of himself and to the right.
He then reached into a can and extracted some black objects that looked like carved scarab beetles.  He laid them out into two rows: one six scarabs long and the other seven, making a total of thirteen.
What happened next happened with a speed that only comes as a result of practice.  I will try my best to explain it to you.  One of the rows of scarab beetles was one longer than the other.  He removed the extra scarab from it and set it my his row of disks.  He then picked up an entire row of scarabs and put them back into their can.
Then he took more of the colored disks from cans and laid out exactly twice as many of each of the different kinds as he had before.
Then he laid out the remaining six scarabs, left over from the first round, into two columns.  Actually, a better way to describe it would be to say he put them into three rows of two.  This was so that he would not have to do any mental activity at all; he just laid out the scarabs mechanically.  As there wasn’t an extra one left over this time, he didn’t set it by the row of disks, but he did take one of the columns and put it back in the scarab can.
He then took numbered disks and doubled the number he’d put down in the previous round, and, as before, laid out his scarabs.  This time there was one row of two and one left over which he put by his pile and put one of the remaining two back in the scarab can.
I could see this process was going to soon stop so I watched carefully.  He doubled the numbered disks one last time and put the lone remaining scarab down next to it pro forma.
Then he put away the numbered disks from the rows without scarabs, counted the remaining ones, and said, “Ya owe me fifteen dollars and eighty-six cents.”
I did a little mental guestimation--as I am lousy at arithmetic--decided it was a fair price in any case, took out the money, and paid the man.
I carried the coffee back out the the car, loaded it and myself up, and drove off.  On the way home, again distracted by what I had seen, it came upon me what the old coot had done.  It is know as the Russian Peasant Algorithm or Egyptian Arithmetic, depending upon whether you are trying to impress Russian peasants or Ancient Egyptians.  
It is a mechanical process which will literally produce the number of objects needed.  In societies that had not yet discovered a way to represent numbers that makes arithmetic convenient, a process such as this one would be quite valuable.  
Lets consider how one could multiply seventeen by thirteen. It is much more fun to do with tokens, of course, but in writing it is more convenient to do it as follows:
13 *
208 *

Note I’ve used * in place of the scarabs.  The sum of the starred number is 221 which is the product of seventeen and thirteen.
Those of a mathematical bent will, of course, be led to think of binary numbers. One should be aware that the Egyptians where doing this when all the silicon chips in our computers were still sand.
When I ran through all of the cheap coffee I bought that day, I made my way back over to the neighboring state and tried to find that dilapidated old store, but I wasn’t able to.

Monday, June 6, 2011

Decision time

Decision time

By Bobby Neal Winters

An old friend of mine rolled into town the other day and we headed over to one of the local upscale coffee shops to get a designer coffee.  There are a lot more decisions involved in getting coffee now than there were in the days of old.  I’ve subverted the system by simply getting the same thing every time.  It is a beverage I like to call “coffee.”  The barista knows what I want when I asked for it, and  I can then put cream and sugar into it--or not as the availability dictates.
My friend is cut from a different bolt of cloth, and he explores permutations making decisions according to what he’s tried before and giving preference to the new and different over the old.
“I like to try new things,” he told me after putting his lips to his latest concoction.  When he sat down his cup, he was left with a whipped-cream mustache that he wiped away with a napkin.
“I am glad,” I said, sipping at my tried and true, no-nonsense coffee. “You can explore for the rest of us.”
My friend, who has been in the business world since graduation, looked sort of wistful.
“You know,” he said, “I sometimes wish that I had the sort of freedom to explore new ideas in my work that you guys do at the university.  In business, most of our decisions are determined by policy and there is not much incentive for exploration.”
He’d caught my attention when he said this, because I teach hypothesis testing as a part of my Elementary Statistics course, and I am always looking for real-life examples.  
Hypothesis Testing deals with creating schemes to make decisions.  The hypotheses that the students are given are quantitative statements that are either true or false but which, by their nature, you can’t ever be certain. You can’t know whether its true or false but you  set a procedure to decide whether or not to treat the statement as true or false.
I explained all of this to my friend while contemplating the possibility of a second cup of coffee and maybe a muffin to go along with it.  I was hoping to be able to get my friend’s opinion of whether the sort of examples I use have any sort of connection with reality.  He’d opened his mouth and was about to say something when I heard a voice coming over my shoulder.
“Yes-sir-ee, sometimes decisions are hard.”
The voice had a pronounced Texas; the word “decision” was pronounce DEE-cis-zhun. The voice was attached to a person whose appearance wouldn’t lead one to expect anything else.  From the wrinkles in his face, I  judged his age to be anywhere from 70 to 170. He wore a new, clean cowboy hat made out of straw, a spotless white shirt, and what I took to be a brand new pair of blue jeans.  In Texas, Oklahoma, and similar places, there is a subculture in which such an outfit will work for church, doing serious business, or, apparently, getting a designer coffee.  How he’d made it to this part of Kansas, I couldn’t guess.
I was going to just smile and ignore him, but I guess he caught my friend’s interest.
“So you’ve made some hard decisions?” he asked.
“Well,” the old man drawled, “I guess I have.  I guess that anyone who’s lived as long as I have would’ve made some hard decisions, some good, some bad.  I ain’t never had a class on it though.  I was just thinking about the first time I ever rode in an airplane.  It was almost the last.”
Usually, I am a good listener, but I couldn’t see where this connected and I was more interested in listening to what my friend had to say than whatever this rustic, old fellow had to say, so I attempted you re-engage my previous conversation. I turned to my friend, looked him in the eye and spoke.
“You were saying...”
My friend’s attention had been captured, however.
“Oh, I wasn’t going to say anything important,” he said. “Just some business stuff.  Let’s listen to what this gentleman has to say.”
So we listened.

I’d been following the wheat harvest from west Texas up though western Oklahoma, Kansas, and Nebraska.  I’d gotten tired of all logging all of those miles back to visit this girl I was trying to spark back home, so I thought that I’d want to learn to fly one of those airplanes.
But I figured I wanted to ride in one first before I flew it.  It just sort of made sense to me.  So I was talking about it with a fellow by the name of Jack “Hot Shot” Burns.  Jack was a good old boy.  He’d spent some time out west fighting forest fires in the mountains.  He’d fly his plane out over the fire, drop a big load of water, and put it out.  
It’d kind of got to him though.  He was as fearless as any pilot that ever was, except when it came to fire.  When I was talking to him, I lit up a cigarette, and he about come unglued.  I had to stamp it out right away and put my lighter out of sight.
Anyway, Jack and me and Floyd Jumper was talking over beer and I said that I wanted to learn to fly, but I figured I’d better go up in a plane first.  And they said it was a good idea.
Floyd had been a parachute jumper in the Army and he and Jack had a thing going where they’d take people up and teach them how to jump.
“I don’t want to learn how to jump,” I said. “Just how to fly.”
They said that they wouldn’t make me jump, but, as they were doing that all the time anyway, it would be easy to take me up.  So we finished our beers, went out to the airstrip, and took off.
Now, you fellows probably are used to those airports like they have in Kansas City or Tulsa.  This wasn’t like that.  It was an airstrip out in the west Texas plains.  There wasn’t anything but wheat or grass or cattle as far as the eye could see.  We got into his airplane which was barely big enough for the three of us, I tell you.  
I could see that it would be a good plane to parachute jump from because I wanted out of it from the minute I got in.  Jack sat in the pilot seat of course; he had Floyd sit in the back; and he had me sit up in the seat usually reserved for the co-pilot so that I could see better what flying was like.
Then we look off.  
It was something.  After we climbed to about 10,000 feet, I got over the pure terror of being up in the air without anything but a thin piece of tin between me and eternity and I got to thinking that maybe I would like to fly one of these machines, so I started looking over the console.
There were a lot of gauges, nobs, and lights on the dashboard and it struck me that it would be a lot to keep up with, but I figured that was something you’d be able to learn.  It all looked good to me but I saw a red light on, so I figured I’d ask a question.
“Jack,” I said. “What does this light mean that says ‘FIRE WARNING.’”
Jack didn’t answer.  He just got a crazy look in his face and went berserk.  I’ve  never seen a man so panicked.  He tried to climb out of the plane over me, and when I turned him back, he opened the door on his side of the plane and just stepped out.  No parachute, no nothing. Jack was gone.
Floyd hopped into the front seat and closed the pilot’s door.  He then leaned over and looked at the light.  He called me a name I can’t say in front of polite people like yourselves.  Then he tapped the light.
“That says ‘TIRE WARNING.’”  And he called me the name again.
I couldn’t see that this was my fault because Jack had made a poor decision.  I don’t know about you, but it is going to take more than one person’s word to get me out of an airplane without a parachute.
There was a period of awkward silence when Floyd appeared to be doing a lot of thinking.  I couldn’t take much of that so I asked a question.
“So, I guess you’ll be landing the plane now so we can tell them about poor old Jack.”
Floyd looked at me pretty serious then.  
“I don’t guess we can do that,” he said.  “You see, I don’t know how to fly a plane either.”
Since then, I’ve heard stories about folks being in situations similar to ours and having people on the radio talk them down.  We hadn’t heard of any of that, and we didn’t think about it because the radio in the airplane didn’t actually work.
Floyd finally got figured out whatever he was thinking about, and he turned to me.
“Fella,” he said, “I don’t know how to fly, but I do know how to jump and I can teach you.  Usually, we have some classes on the ground first, but now there’s not time.  You can either learn or crash with the plane, but I am jumping before we get too much farther from the airstrip.”
Now you’d be surprised how fast you can learn when you have to.  He talked me through all of the procedures, and then we were ready.
“We’ll jump at the same time,” he said.  “You count to ten and pull.  When I see you are okay, then I will pull.”
Jumping out of an airplane is hard even when you know it’s going to crash, but I did it.  And I counted to ten. I actually screamed my numbers.  Then I pulled and that parachute opened with a jerk.
Floyd looked, saw that I was okay, and even gave a little nod.  Then he pulled his rip cord.
And nothing happened.
Again, being it’s such polite company, I won’t tell what I saw next, but I will say I won’t ever forget it.

“So I guess the moral to this story,” he said with a grin, “is that when the stakes are high unless you’ve got pretty good you’d better stand pat.  Jack didn’t follow that rule.  If there is another moral, it’s that sometimes you can make the best decision possible and still wind up flat. That’s what Floyd found out.”
My friend was totally intrigued.
“What did you find out?” he asked.
“Nothing beats luck,” the old-timer said. “I went to the place where poor Floyd landed and found oil.  That was the first of many wells.  I am a billionaire today.”
Then he left. I looked at my friend and shook my head.
“The decision I have to make is whether to believe a single word he said.”
I heard another voice.  This time it was the barista.
“I’d believe him if I was you,” she said, holding something in her hand. “He just tipped he with a Canadian Maple Leaf.”