I have to go through a four-way stop on my way to the cemetery where I run every day. It continually amazes me how many times 3 or 4 cars arrive at the stop signs at practically the same time. We all hesitate then creep forward, hit the gas and suddenly the brake, stop and then start again until someone has had enough and just goes. Did you know that these types of situations are known as Canadian Standoffs? In a Canadian Standoff, everyone tries to be polite and not take advantage of anyone else. This is usually how things play out at my four-way stop. My guess is most of the yahoos who live around me are being courteous because they are driving without insurance and don’t want to clip another car while on their journey to their favorite haberdashery.
The other day I successfully made my way through the intersection and to the cemetery. I was running my laps and listening to Athena’s band (you will be learning a lot more about her in future posts) when, for reasons I will get to in a minute, I thought of John Nash. I am pretty sure you all know who he is, even if you don’t recognize his name. He is the subject of the book and the subsequent movie, A Beautiful Mind. I recently bought the book, so I decided to immediately move it to the top of my reading list. I just finished it a few minutes ago, it is terrific; at least as good as the movie (and the movie was exceptional).
I
thought of Nash because I am working on a series of essays whose
topic is game theory, the area of research that garnered Nash his
Nobel Prize. That volume, one that can wait a bit longer to be
written, is about tennis; this one is about three people with loaded
guns and bad intentions.
We all know what a duel is, but do you have any idea what a truel is? All you have to do is add another person to a duel, and you have a truel, a special version of which is popularly known as a Mexican Standoff. Scenes showing three people all pointing guns at each other show up a lot in movies, especially old Westerns. My favorite, though, has to be the standoff shown near the end of Reservoir Dogs. If you ever find yourself making a film and need to create a little tension, all you have to do is give three people guns, set them out in a triangular pattern, give them all reasons to want to shoot each other, and let them have at it.
Author’s note: I have some friends from Mexico, and they all tell me the term Mexican Standoff is perfectly acceptable; no offense meant and none perceived. I have dug a little deeper into this topic and I am not so sure that it is satisfactory; there appears to be some evidence that it has racist overtones. I am not surprised by that at all, are you? Meanwhile, other sources seem to think the phrase originated in Mexico and is absolutely fine. I prefer to err on the side of caution, it doesn’t cost us anything to veer slightly so we don’t unintentionally insult our friends to the south. The best I can do is offer the alternative of a “Three Person Standoff” or a “Three Person Impasse.” I am going to hold my breath while I wait to see if those phrases catch on.
So, here is the totally implausible situation I want to consider. Imagine that Natalie Portman, my favorite actor, Danica Patrick, my favorite retired racecar driver, and Athena, the woman whose band I mentioned earlier, are fighting over which one of them gets to go to lunch with me. Go ahead and scroll up to the first page of this essay and look again at the title. You will now completely understand why I used the word “unlikely” instead of something like “certain” or “unavoidable.”
I proposed several different types of contests the women could participate in to settle this dispute. A slew of emails went back and forth between me and their respective camps. How about a checkers tournament? No. Footrace, perhaps a 10k? No. Corndog eating contest? Out of the question. This went on for quite some time until someone, I can’t quite remember who, suggested a truel using low impact paintball guns. After more lengthy negotiations (you know: time, place, brand of equipment, etc.), everyone agreed.
Let’s
assume that Natalie is the worst shot out of the bunch, she can only
hit her target one out of every three attempts. Danica appears to be
much better, she connects with the target (human or not) two out of
three times. Both of them have a big problem with Athena, I have no
idea how or why, but she never misses; her success rate is 100%.
Of course, I try to talk to them again and again, but the three of them are not willing to compromise and share me. I finally grudgingly accepted their decision. Ultimately, who can blame them?
When it became clear that none of them were going to listen to me (imagine that, a fellow human being not listening to me!) I let them have at it with the following stipulation: Natalie (33%), by virtue of the fact that she is the worst shot, gets to shoot first; then Danica (67%) if she is not clipped by some green paint, and then Athena (100%) if she is lucky enough to avoid a slight boo-boo. Each woman shoots in turn, and the paintballs keep flying until only one hungry woman is standing.
Now, finally, we get to the interesting game theory aspect of this problematic situation. I know, you might have thought that the real problem is that I am totally delusional, but that is neither very interesting or game-theoretical. The simple question is this: What should Natalie do? She gets first shot, and she better make it count. She wants to eat lunch with me, and if she gets splattered with paint, that is not going to happen. Take some time and give this some thought.
What did you come up with? Did you have Natalie shoot at Athena with her little plastic gun? If so, you got it totally wrong. For those of you who thought she should aim at Danica, you are equally off base. Believe it or not, it can be demonstrated mathematically that Natalie’s best bet for a meal at Red Lobster or Olive Garden with me is to shoot into the air, to intentionally miss both Danica and Athena. My my my, we have reached the point where our intuition miserably fails us. Many of the posts to follow are about the faulty nature of human intuition, I tend to write a lot about that fascinating subject.
So, what is going on here? Well, remember that immediately after Natalie takes a shot (and misses) Danica gets to shoot. Who is Danica going to aim at? Not Natalie, she knows Natalie is not her biggest threat; she is going to shoot at Athena because Athena never misses. What if Danica misses and Athena gets to shoot next? Natalie must certainly also consider this scenario. Athena is not going to take aim at Natalie because Danica is clearly the better shot. Either way, by shooting into the air, Natalie has turned a truel into a duel. Now she has only one person instead of two to deal with. Consequently, she now has the first shot in a duel, not the first shot in a truel. Due to her less than stellar marksmanship, it is the best she can hope for.
As for me, I bet there is a good chance I will starve to death while waiting for this highly unlikely truel to take place. You know, scheduling conflicts and such will make it challenging to get the three of them together. I think it might be in my best interest to get a bag or two of pretzels and a couple jars of peanut butter to tide me over while I nearly burst with anticipation over which of these women might be the lucky winner.
“Detective,
this way.” The uniformed officer guided Detective John Gibbons
through the back door and toward the kitchen.
“You were the first on the scene?”
The
young officer nodded his head.
“Don’t
worry son, this won’t always be so hard. The more of these you see,
the easier they get. Just try to keep your nerves in check. Deep
breaths will help more than you can imagine.”
Once
again, the patrolman nodded.
“Through
this door, sir.”
Gibbons
pushed on the swinging door and was immediately struck by the amount
of destruction. There were spent Nerf darts everywhere, perhaps
hundreds of them. Some of the projectiles were still stuck to the
garments of those unlucky enough to be eating when the shooting
started.
The
patrolman pointed toward an elderly couple sitting at a table, their
plates still neatly positioned in front of them.
“I
believe they saw the whole thing. I asked them to stay right there,
I knew you would want to talk to them first.”
Gibbons
nodded his approval.
“If
you haven’t already, start a canvas both east and west of the
entrance. Got it?”
“Yes,
sir. I am on it.”
Detective
Gibbons made his way to the old couple huddled together at a small
table near the restrooms. He took a seat across from them.
“Folks,
my name is John Gibbons, I am a detective with the Iroquois County
Police Department. I am so sorry this happened to you.”
The
couple shook their heads. The old man attempted to force a smile.
“My name is Fred Sampson, and this is my wife, Claire.”
“Mrs.
Sampson, I know this must have been quite a shock. Tell me, how are
you doing?”
“Oh, it was scary, but you don’t have to worry about me, I am doing good.”
Mr.
Sampson rolled his eyes as he clasped his wife’s wrist. “Now
Claire, you know that you are doing well, not good. Let’s try to
remain civilized in the face of all this nonsense.”
“What?”
“Dear, when someone asks you how you are doing, you should respond that you are doing well, not good. If they simply ask how you are, it is fine to say you are good, but if they ask how you are doing, you must respond that you are fine.”
“Oh,
good grief. Well then, I am not doing very well at all. How’s
that?”
“That
is fine.” Mr. Sampson turned toward Detective Gibbons. “How may
we help you?”
“Can
you tell me exactly what happened?”
“We came here to get the fish dinner, Fred has always loved fish. Haven’t you, dear?”
“Oh yes, I have always loved fish. As I have gotten older, I find I am a little more picky about how it is prepared but, yes, I do indeed love fish. I especially love fish that isn’t too fishy, if you know what I mean.”
“I
see, go on.”
“Well,
we were about to start dessert…”
“You
were starting your dessert, I still had some broccoli to finish.”
“Of course, dear.” She looked the detective directly in the eyes. “I have always been a faster eater than my husband.”
“Oh
yes, she has. I have always worried that someday she was going to
choke.”
“Oh, that’s ridiculous. I may eat fast, but you are the one who takes big bites. If one of us is going to choke, it is going to be you.”
“Oh,
I wholeheartedly disagree with that. I am the one who took a course
on The Heimlich Maneuver.”
“Of course you did, you took it so that you would know how to jab yourself in the tummy when an entire broccoli stock tries to make its way down your gullet.”
The
detective pretended to be writing in his notepad. In reality, he was
drawing a crude picture of himself with his head in a bear trap. The
caption read Misery is temporary. “Please continue.”
“So, I looked up from my Key Lime Pie, and that is when I saw him. He was sitting way over there.” She pointed across the room near the entrance. “He got up…”
“Wait,”
her husband said. “How do you know it was a he?”
She
let out a little sigh. “Well, I guess I don’t. I just assumed.”
“Now
dear, you know what happens when you assume, you make a donkey out of
you and a donkey out of me.”
“Fred, I am telling the story, so let me tell it. I am sure you will get a turn.”
“OK,”
Detective Gibbons said, “what do you mean you couldn’t tell if it
was a male or a female?”
“Hair,
lots and lots of hair.”
“Hair?”
“Oh my yes, panda bears have lots of hair.”
“Honey,
the word bear is redundant.”
“Huh?”
“It
is like a tuna fish sandwich. Tuna is enough, you don’t need to add
the word fish.”
The detective looked them both over closely. “Wait, you’re saying that this was a panda who did this to you?”
“Of
course.”
“Yes, it was.” They both looked at each other with a sense of disbelief, they couldn’t understand why the detective was questioning their account.
“Well
now, isn’t that something? Where exactly was this panda of yours
sitting?”
“Over
there, way on the other side of the restaurant.”
The
detective stood up and gathered himself.
“Can I have your attention, please? My name is Detective Gibbons. How many of you saw a person in a panda suit?”
All
the people in the restaurant remained silent.
As
Gibbons stood there dumbfounded, a man in a coonskin cap started
walking over toward him.
“That
twernt no one in a panda suit, that were a true to life panda what
done this.”
“Excuse
me?”
“You
heard me, it was sitting right over yonder. All of a sudden it got
up and it started a firin’ some newfangled weapon. I don’t know what
it was, the make or nothin’.”
“Show
me exactly where this panda was sitting.”
As they moved across the restaurant, a waiter appeared from behind a set of swinging doors. He sheepishly approached the walking men.
“I’m
sorry, I have been watching you from the kitchen. I was the panda’s
waiter.”
He pointed to a table, and then all three men walked toward it.
“He
was sitting right here. I was reluctant to come out and talk to you
because I still can’t quite believe what I saw. I have been trying
to collect myself in the kitchen. I am still trying to convince
myself that I really saw what I think I saw.”
“All
right, let me get your statements in turn. You sir, what is your
name?”
The
waiter tried to spit it out. He finally came up with something that
sounded like Robby.
“OK, Robby come with me. If the rest of you will please be patient, we have more officers on the way. I promise you we will get you out of here as soon as we can.”
They found themselves at a well-lit booth in a now empty part of the restaurant.
“Robby,
tell me exactly what happened here.”
“OK, this panda walks in. He does not wait to be seated. He comes directly to this table, carefully places his briefcase on the tabletop, and then takes a seat.”
“This
is the panda’s briefcase?”
“It
sure is.”
“OK,
so this is where he was seated…”
“Yes, it is,” Robby said. “He took the seat facing that wall, the one with the restrooms.”
“Go
on.”
After he sat down, he took a large manila folder out of his briefcase and placed it right here, on the left side of his table.”
“Where
is the folder now?”
“I
have no idea.”
The detective stepped back to get an overview of the table. The more he studied it, the more confused he became. He noted that the briefcase was sitting on the edge of the table opposite of where the bear (or the person in a bear suit) was seated. It appeared to be meticulously placed, the side of the case parallel to the edge of the table. Equally as odd, the ends of the case looked like they were the same distance from the opposite table edge.
“Robby,
did you touch anything on this table?”
“No,
sir.”
“Think,
take your time. Are you absolutely sure?”
“The
only thing I did was place a drink and a sandwich on the table.
After that, I did not touch the table again.”
“OK,
good.”
“Are
you done with me detective, I really need to sit down.”
“Just
one more question and then we are done. Why are you so sure that
this was a real panda and not a person in a really good panda suit?”
“The
smell. Even its breath smelled like wet bamboo.”
“OK
Robby, go take a break. Don’t leave yet, I may need you later.”
“Sure.”
The detective walked back toward the Sampsons. They were having a conversation with the man in the cap. As Gibbons arrived, Mrs. Sampson was squeezing the end of her nose with her left arm.
“Can
each of you tell me how you know that this was not just a person in a
panda suit?”
As
if on cue, Mrs. Sampson started swinging her right arm back and forth
over her face.
“Smell,”
she said.
“Smell.
It smelled like bamboo and dirt.”
“That
thing smelled like wet bamboo.”
“It
really did stink. It stunk up the whole restaurant.”
“That
were one true smellrod.”
“I
thought I was in the Papasan section of a Pier One store after a
flood,” said Mrs. Sampson.
“Now dear, I think those are made of rattan, not bamboo,” replied Mr. Sampson. He looked over the group, stuck out his chest a little, and said: “It is a fairly common misconception.”
Mrs.
Sampson stood still for a few seconds. She was staring off into the
distance, her hands on her hips and her lips pursed.
In one graceful motion, Mrs. Sampson turned and started walking back to her table. She motioned for Mr. Sampson to follow her. When they arrived, she picked up the Key Lime Pie and slowly pushed the plate into the face of her husband.
“It is not a Boston Creme Pie, but it is close enough,” she said as she picked up her purse and walked toward the exit.
Mr. Sampson picked up a napkin and started to wipe the pie from his face. “40 years,” he said to no one in particular. “For 40 years, I have been putting up with her.”
The
man in the coonskin cap grabbed a handful of napkins and started to
help clear the pie from the man’s ears and neck. He grabbed the old
man by the shoulders. “Why you put up with that? Why you let her
do that to you?”
“Ah, her daddy has money. When I married her, I thought he would be dead in a few years. Here I am all these decades later and he is still dying from the same heart attack.”
“I
tell ya bubba, that is rough.”
“Well, if I had known he had the DNA of a Galapagos Tortoise, I would have moved along to the next young damsel rather quickly.”
“Sounds
like you still should.”
“Ah,
my friend, life sure would be easier if we each had a crystal ball
and the instructions on how to use it.”
Detective Gibbons was smiling, touched that these two people who, under normal circumstances, wouldn’t bother to say hello to each other were bonding because they seemed to have something in common, even though he wasn’t quite sure what that something was. As he was thinking about this new Odd Couple, he was struck with a flash of inspiration. At that moment, Detective Gibbons had an idea. Like most of his best ones, it seemed to flash from out of nowhere.
“Excuse
me, gentleman,” he said as he quickly walked toward the
restaurant’s entrance. He grabbed the arm of the first uniformed
officer he saw.
“Look,
I need you to call in Carlson. Get him here ASAP.”
“Which
Carlson sir, the linguist or the new guy, the one who works on
electronic data patterns?”
“My
mistake, I didn’t know we had a new guy. Get me Alphonso Carlson,
the linguist.”
“Yes, sir.”
Gibbons
walked back inside. He took a look at all the patrons being attended
to by the county and city police officers who had responded to the
initial call of “shots fired.” He got himself a glass of water
and then made his way to the shooter’s table. He was about to start
his examination of the briefcase when Sergeant Wilson tapped him on
the shoulder.
“Detective,
I just talked to Carlson.”
“That
was quick. Is he on his way?”
“No.”
“No?”
“He’s not coming. He said he has seen dozens of these panda cases, and they all play out the same.”
“You’re
kidding me?”
“No.
He said you are to look through the panda’s papers. In there you
will find your answer.”
Gibbons
rubbed his chin. How did Carlson know he had papers?
“Did
Carlson happen to say anything else?”
“Yes
sir, he did, something a little odd. He said that superfluous commas
can be a wonderful, interesting, or dangerous thing.”
Gibbons took a long drink of water. “Thank you, Sergeant. That will be all.”
Gibbons
studied the table as he pulled out a pair of latex gloves from his
pocket. The briefcase was already open, the shooter must have left
it unlatched when the manila folder was removed. Where is that
folder? Gibbons glanced under the table and then reached inside the
briefcase and pulled the papers out. He carefully placed the contents
in a small pile on an adjacent desk.
He started going through the stack. The first page was a flyer celebrating the virtues of the weekly special at Billie’s Taco Emporium. In the upper left corner was a picture of a trout (or is that a salmon?) on a unicycle. Through an oversized megaphone, he was extolling the virtues of their “Fishy McFish Face Tacos.” It took only one more piece of paper for the detective to find what he was looking for. He found a scanned page from what appeared to be an encyclopedia or an old dictionary. This is what was circled in red ink:
PANDA
– Large mammal native to China. Eats, shoots and leaves.
Gibbons
shook his head and tried his best to suppress a smile. It was still
early, his Saturday night hadn’t been completely ruined. He decided
he was going to call his wife and ask her if she was up for a late
dinner and an even later movie.
*****
Do you know any members of The Grammar Police? If you look at a person, their membership is not apparent, they are all undercover. None of them wear Grammar Squad badges or walk around sporting bandoleers filled with red ink pens.
I am not a member. Never have been, never will be. I view membership as the equivalent of an old man sitting on his front porch yelling at the kids to get off his lawn. The problem is, no matter what you do, the trespasser’s ranks grow exponentially while the size of the lawn stays the same. It is not a battle worth fighting.
The fact is language changes in ways that can not be predicted. New words pop into existence, old ones go away or get repurposed, and meanings and usage are constantly in a state of flux. Simply stated: languages evolve. And as you might have guessed, the digital age that we find ourselves living in has rapidly accelerated the rate of change. Have you happened to look at any text exchanges between teenagers recently? Is that even English? Apparently, it is, the kids seem to have no problem understanding each other.
I always shake my head when I hear someone say they are going to start a campaign to get people to use proper grammar in their emails and texts (yes, it does come up from time to time). That ship has disappeared over the horizon. I guess you can start dog paddling if you want, but I guarantee you Michael Phelps has no chance, how good do you really think your odds are?
As you might have guessed, this essay is about commas, those confusing little squiggles that give pause to most writers. Should I put one here? Does that comma belong there? Does this sentence require a comma, or is a (Gasp!) semicolon more appropriate?
Why
commas? What is so important about them? Well, I think the poor
folks who were trying to eat a quiet dinner would agree that a
misplaced comma can create some problems.
They
needed this:
PANDA
– Large mammal native to China. Eats shoots and leaves.
They
got this:
PANDA
– Large mammal native to China. Eats, shoots and leaves.
It
is a small difference that totally changes the meaning of the
sentence. Sure, you might be thinking, it is a convenient prop if
you are looking to tell an elaborate story about a fictional panda,
but do commas really play that important a role here, in the real
world? For better or worse, they certainly do. Here are two
examples.
Do you own a gun? Do you have an opinion on our Second Amendment right to bear arms? (Note that I passed up the opportunity for a cheap joke about “arming bears.” It is hurting me inside, but I am going to let it go and move on.) Lots of legal scholars certainly do. Their arguments, though, are based on a single comma within the text of the amendment itself. Some believe that it changes the meaning of the following important sentence, others not so much.
“A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.”
Numerous lawsuits have been filed based on this interesting comma, the one highlighted between “State” and “the”. In fact, if you hear of a Second Amendment lawsuit being filed, there is an excellent chance the lawyers will be arguing about that single comma. One of my old professors once told me that language was never meant for communication. The older I get, the more I realize what he was talking about.
This leads me to an important point, the purpose of punctuation itself. It is there to help us clarify our intentions. The things we write are of little value if our anticipated audience has difficulty interpreting our intended message. Think about this: Have you ever received a message (probably a text) that did nothing more than confuse you? I know I have. I have gotten texts that leave me struggling as I tried to figure out the intended meaning. On more than one occasion, I have given up and texted back a series of question marks. Language, and the grammatical rules that go along with it, does us no good if it is not common to both the sender and the receiver. This might be one reason the younger generation has so radically changed the English language through texting. If their parents can not decipher the messages, all the better. For the kids, change is good, rapid change is better.
There
is one particular type of comma that has created lots of debate (yes,
some people sit around and fight about stuff like this). That would
be the serial comma, aka the Harvard comma or the Oxford comma.
Consider the following sentence:
I
bought Propel, Diet Dr Pepper, Diet Coke and some beer.
Now
this one:
I
bought Propel, Diet Dr Pepper, Diet Coke, and some beer.
Do
you see the difference between the two sentences? That little
squiggle between “Coke and “and” is the serial comma. People
tend to have strong opinions about whether or not to use them.
Serious advocates, armed with grammatical rules and historical
precedent, can be found on either side.
The
questionable comma from the Second Amendment may or may not be a
serial comma, hence the confusion. Most people view the inclusion of
a serial comma as a stylistic choice. I think we all now know that
the issue runs a little deeper than that.
At some point in my education, I was given a sheet of paper by a thesis adviser. It listed a few common grammatical mistakes, ones we were to avoid at all costs. It also stated that we were never, ever, under any circumstances, to use any type of qualifier for the word unique. Unique meant unique, not “mostly” unique or “pretty” unique. The last thing on the list was an explanation of The Harvard Comma with a list of reasons why we were always to use them. The handout, oddly enough, did not mention the Second Amendment.
Now
that we have a little more experience with serial commas, we can move
on to the next point. The second example of a comma causing big
trouble involves a lawsuit filed by a group of disgruntled truckers
in Maine. Take a close look at the following text, a little snippet
taken from the Maine law that describes what type of work does not
allow for overtime pay.
The canning, processing, preserving, freezing, drying, marketing, storing, packing for shipment or distribution of:
(1) Agricultural produce; (2) Meat and fish products; and (3) Perishable foods.
The drivers won their suit because there was no serial comma between “packing for shipment” and “or distribution of.” The drivers did the distribution, but they did not do the packing. The judge found that the law, as written, was ambiguous. I don’t know much about judicial decisions or The United States Court Of Appeals for the First Circuit, but I submit the first sentence in the decision, written by Judge David J. Barron, is an instant classic. Barron wrote: For want of a comma, we have this case.
Barron goes on to explain that if a serial comma would have been placed after “shipment,” the law would have been clear. I must admit that the distinction is subtle, but the drivers won their case because they didn’t pack anything, all they did was distribute. As a fan of the mighty serial comma (known to me as The Harvard Comma (all caps please)), I am going to take a little time to bask in its glory. I have long argued that by using it, writers can lessen the risk of being ambiguous.
This essay is near the end, I have introduced a couple interesting ideas about commas, and I find myself ready for a well-earned pause before I attempt to tie everything together. I just took a long drink from one of those Diet Dr. Peppers I mentioned earlier. That did the trick, just one or two more small details, and then we are done.
Do
you think that the serial comma is useful? Are you now an advocate
for its use? I know people who insist they always be used and others
who loathe their appearance in printed text. Do you think we will
ever come together and declare a standard for the use or abandonment
of the serial comma? I doubt it. Even if the proper grammatical
authorities (there really are such people) offer a proclamation of
standardization, I doubt it will be followed. The folks on the other
side will not go down easy. They will fight, fight, fight, and fight
some more ( :-) ).
I will leave you with one final thought. Do you have an opinion of Mr. Sampson, the old guy from the restaurant? Is he the kind of person you would want to hang around with? I think I would rather sit home alone than hang out with that guy. As for his wife, what do you think poor Mrs. Sampson did for a living? I am not quite sure, but I can guarantee you it did not involve the written word. If it had, Mr. Sampson never would have made it to retirement.
NOTES:
The
Maine court case can be found here: United
States Court of Appeals for
the First Circuit, O’Connor
v. Oakhurst Dairy, case
number
No. 16-1901.
The panda joke has been around a long time but was popularized by a tiny British grammar book that became a bestseller. Eats, Shoots & Leaves by Lynne Truss is a fantastic book. It is interesting to read through the differences in our grammar and that of British English. It is one of my favorites.
HUMANS AS CYLINDERS: A FEW THOUGHTS ON CHIA PETS & PIGEONHOLES or (alternate title) MY MATHEMATICAL TAKE ON A VERY HAIRY SITUATION
A year or two ago, my buddy Mobe and I were, no doubt, engaging in sophisticated repartee when he casually dropped an innocent comment into the conversation. As I recall, we were enjoying a snifter of brandy with our foie gras and caviar when Mobe told me that he was pretty sure he was turning into a Chia Pet. He was near the point, he said, where he was going to get his back hair braided just to change things up a bit.
Nearly everyone who knows me instantly realizes that most of the previous paragraph is total nonsense. I have never had brandy, foie gras, or caviar, and I had to do a Google search to confirm what a snifter is. So, maybe (just maybe), Mobe and I were sitting in some dive bar drinking beer and eating burritos when he brought up this Chia Pet business. Listening to Mobe talk about his increasingly shaggy person got me thinking about how hairy human bodies are or can possibly be. As I thought more about it, I realized that the trusty cylinder, a standard geometric shape known for perplexing students with its volume formula, can be utilized to help us explore this topic. So I ordered another beer, took a bite of my burrito, and decided to turn Mobe into a cylinder.
Can you imagine what this cylinder business could possibly be about? Has it occurred to you that anyone would ever have occasion to think of human beings in terms of cylinders? Did you ever wake up and think: You know what, today seems like a great day to mathematically model human beings as cylinders? That is one of the great things about being ever curious, thinking logically, and utilizing the scientific method; you just never know when such opportunities might present themselves.
Now it is time to get to work and turn Mobe into a cylinder. Actually, I want to model all human beings as cylinders. Why? I want to answer an improbable question, one that Mobe inadvertently reminded me of during our profound (cough, cough) philosophical discussion. The problem is: Are there two human beings alive that have the same exact number of hairs on their bodies? Take a few minutes and give that some thought. Now consider this: We don’t have to count the hairs on anyone’s body to answer the question. You might want to think about how that might work before you read on. After all these years, I still find the answer as surprising as it is fascinating.
This might seem like a tough problem; at the very least, it is an unusual one. I decided to write an essay about it because it allows me to introduce the concept of pigeonholing. Pigeonholing is a simple, yet robust, tool commonplace throughout science and mathematics.
A pigeonhole is just that, a little cubbyhole that you can place something in. Of course, it got its name from the fact that pigeons like to pick cozy little places to nest in. We, on the other hand, are going to take the idea of pigeonholes and co-opt it. We are going to use the concept theoretically and, instead of pigeons, files, or rubber bands, we are going to place cylindrical humans into our little niches.
So, instead of dwelling on Mobe’s inherent hairiness, let’s think of how hairy a human being can possibly be. To do this, let’s make a theoretical human and turn him (or her) into a cylinder. We can start with the assertion that there is no human 100 inches around. Admittedly, there are some big dudes out there, but I have never come across one that big. How about someone 100 inches tall? None of them running around either.
Consequently,
as you might have guessed, we now have a cylinder 100 inches tall by
100 inches around. We have 10,000 square inches of surface area.
Keep in mind that there is no actual human being that can come close
to that size. As you will soon realize, we are overestimating for a
very good reason.
Now that we have our cylinder, we can address hair density. Do you think that a person could have 10,000 hairs per square inch on their skin? I am certain that even Mobe can’t approach that figure. Clearly, that is a density that no human can ever hope (is hope the right word?) to attain. As for a Sasquatch or Chewbacca, they are (unfortunately) beyond the scope of this topic.
If we do some simple math, we find that we have a surface area of 10,000 square inches with a maximum hair density of 10,000 hairs per square inch, which gives us a total of 100,000,000 hairs for our theoretical most hairy human possible. Remember, we have modeled this person by vastly overestimating all the variables. There is no real person with close to this number of hairs, we are just trying to err on the side of caution. Any idea yet why we are doing this?
This is where the Pigeonhole Principle comes in. Let’s imagine an enormous hotel. This hotel has a long corridor with door after door after door. Each numbered door corresponds to its own room. Next, we line up every person now living and count the hairs on their body. When we get done with the first person, we arrive at a number and then give them a key and send them off to the room number that corresponds with the number of hairs on their bodies.
You should quickly be realizing what is going to happen. What is the Earth’s population? Last time I checked, it was a lot more than 100,000,000. Since the number of people alive today is far greater than the number of hairs a human can possibly have, we know there have to be two people with exactly the same number of hairs. At some point, two people will get the key to the same room. We need not count the hairs on anyone’s body to know this.
I
love this little problem. It demonstrates the power of simple
concepts such as pigeonholing. Also, it lets us know that a tiny bit
of math and a little thought can take us a long, long way.
