Piper Pandora Pennington threw her backpack on the faded red seat of the booth and slid in beside it. She crossed her arms and stared at the old man sitting across from her. He didn’t lookup. His nose was buried in a notebook full of mathematical scribbles.
“Well…are you going to talk to me or are
you going to sit there like a big lump of doofus?”
Buford Lister slowly lifted up his
head. “Lump of doofus? Is that what all the 12-year-old girls are
saying this week? Is that the trendy
language? Is that the name of a new hit
song by some teenybopper that you just can’t stop listening to?”
“I have been listening to The Ramones
and Daniel Johnston. And for your
information, I don’t spend a lot of time talking to 12-year-old girls.”
“No,
you spend your time bothering people who have better things to do than being insulted
by a self-proclaimed tween math prodigy.”
“I’m not self-proclaimed, and you know
it. I am 100% certified and recognized.”
Buford Lister tried his best to reclaim
the smile that wanted to overtake his face.
She was right, and she knew it.
P-cubed. P to the 3. Present (and hopefully) future math genius.
“Well, did you find anything? I am guessing that you pointed your massive brain at the problem I gave you. So…”
P-cubed reached into her backpack for
her notebook. She lifted it up and made
sure Buford Lister got a good look at it.
“See this,” she said. “I am not
some kind of fossil, I don’t need to write things down just so I can remember
them.”
“I see.”
He wanted to tell her to wait; that time would get her just as it gets
everyone else. He decided to keep quiet,
she would find that out on her own soon enough.
“You know, Socrates didn’t want anyone
to write anything down. I mean, you guys
are about the same age, right?”
He took a long drink of water, wiped his
mouth with a napkin, and shook his head.
“I can tell you what you found, nothing.
You got a big zero.”
He turned his notebook to a blank page
and held it up in the air.
“Ladies and gentlemen, the contributions
of Piper Pandora Pennington, 12-year-old math genius, to the 10,958 problem,
are summarized for your reading pleasure on the following page.”
He waved his hand over the blank page as
Piper gave him the look, the one that combined sarcasm, raw intelligence, amusement,
and the confidence only a girl like Piper could muster. After all, she was too young to realize that
there were lots of people smarter than her, and maybe even better looking than
her. She just hadn’t met them yet.
“Well, duh? Where’s your big medal? You have done just as much on this problem as I have.”
Buford Lister tried his best to keep a
straight face as he put the notebook down.
“You, young lady, are a very hard case.”
*****
Some time ago, I stumbled upon a strange
math problem. It is straightforward and
yet appears to be unsolvable. Do I have
your attention? Thought so.
A Brazilian mathematician named Injer Taneja wrote a paper called “Crazy Sequential Representation,” available for free on the internet. In this paper, he took every whole number from 0 to 11,111 and did something fun and unusual with them. It is easier to show you what he did than try to explain it. Check this out:
10,934 = (12+3+4) x (567+8)+9 10,934 = (9+8x7x65-4) x 3-2+1
Do you see it? He used the numbers 1 thru 9 in ascending and
descending order, along with a few mathematical operators to create 10,934. Here are a few more examples:
So, you can use addition, subtraction,
multiplication, and division along with exponents (what he calls potentiation).
Feel free to put brackets wherever you like, just make sure the numbers are in
order. The task is simple; create the
target number by that process. What
could be easier?
*****
Piper went into a deep think, Buford
Lister thought he could see a little steam rising out the top of her head. She was trying to work through something. He sat back and let her go.
She finally spoke. “I set up a Raspberry Pi cluster, and I wrote
the code. It has been running 24 hours a
day. You know what I found, so I don’t
have to tell you.”
“No, you don’t have to tell me. Wasted
attempts aside, what do you think about this problem?”
12-year-old math geniuses can sometimes
go off the rails, Buford Lister hadn’t seen any indication of that yet from her,
but he was continually probing. There
are few things worse than a bored genius with vast amounts of computer and math
knowledge.
“Primes are the building blocks, I am
not sure why we would expect the numbers 1 thru 9 to serve the same purpose. I am still thinking about it.”
“It is a tough problem. I think that maybe there are some big
implications, too.”
“Well…duh!”
“By the way, did your little sister help
you with the cluster and the coding?”
“Double duh! Susie does all that kind of stuff with me. You should know that by now.”
*****
On page 158 of Taneja’s paper is
something curious. Take a look at this:
10,958 = still not available 10,958 = (9+8x7x65+4) x 3-2+1
Still not available? Taneja has a solution for every natural number from 0 to 11,111, except for 10,958 ascending. Not only that, most numbers have multiple solutions. I find this very strange, I am a bit disturbed by it. This shouldn’t be.
Other mathematicians have hopped aboard
this train; I have heard rumors that all the numbers up to 30,000 have been
solved both ascending and descending…except for 10,958.
*****
Buford Lister started to talk, Piper
held up her hand; her universal sign to keep quiet because she was about to
monologue. Buford Lister obliged.
“It could be that 10,958 is the first in
an infinite list of numbers that cannot be solved by this method. That is one possibility. It doesn’t make any sense at all that 10,958
is the only number that can’t be. I have
been thinking a lot about it, and there is nothing special about 10,958.”
“Except that it hasn’t been solved in an
ascending fashion.”
“Yeah, and I don’t think there is an
answer. My code is good, and I know lots
of others have been running programs for a long time. If there were an answer, someone would have
found it a long time ago.”
“I think that is right. So, what are you going to do now? Keep running your code? Try to come up with a better algorithm? Give up?”
Piper sat in silence as Rinny, the
granddaughter of the owners, approached the table.
“The usual for you, Piper?” Piper nodded.
“And you, sir? Need a refill of
your Diet Coke? How about that water?”
“Tell your grandparents that I am going
to have to find a new diner unless they get a liquor license. I would much prefer a beer to this
concoction.”
“Well, for one thing, it is 9:00 in the
morning, for another thing, you have been coming in here for decades and
telling me and my mom and my grandparents the same thing every day. So, I’ll get right on that for you.”
“Thank you. Much appreciated.”
“Give me your glass! Piper, I’ll be right back with your root beer
float.”
Piper nodded her approval and went right
back to her monologue.
“If there are an infinite amount of
numbers that cannot be constructed, then I would think that there should be
more of them this early on in the sequence.
This is all very strange. The
only thing exceptional or unusual about 10,958 is the fact that it can’t be solved. I don’t know what to think about this.”
“So…one of the reasons I gave you this
problem is that it is unlike all the other things you have been doing. It is one thing to open up a calculus book
and instantly understand everything in it.
When I was younger than you are now, I used to do that, I would get
these thick books, and when I read them, it was like I had written them. All that knowledge seemed second nature to
me. It was something I had already
known, I just hadn’t realized that I already knew it. You…I know you know exactly what I mean.”
Piper nodded.
“Now you are out over your skis. This problem is strange, unusual, and really
simple. Maybe, just maybe, it speaks to
something deeper about the nature of numbers and the nature of mathematics
itself. I just don’t know exactly what
that is yet.”
Piper nodded her approval as Rinny
approached with her root beer float. She
sat in silence as she attacked it with a spoon and a straw.
Buford Lister took out a pen from his
backpack and opened his notebook. He jotted
down a couple equations as he waited for Piper to eat.
Piper put the straw back in the glass
and made a fluttering motion with her left hand. “You know, I did solve it, but I had to use concatenation. I also solved it with a square root.”
“Not allowed. Even so, what is so special about 10,958 that
you had to use techniques not needed for all the other numbers?”
“I know.
I know. I know. I was just playing around with the code, I
wanted to see what would happen.”
“Well, I highly encourage that type of
behavior.” He wanted to egg her on a
little. “I didn’t know you were that
advanced as a coder.”
“Duh…what you don’t know could fill a
warehouse!”
*****
One of the great things about this
problem is that anyone can work on it.
Phones all have calculator apps, notebook paper is cheap, and computer
screens are readily available, so all you have to do is pick a method and start
concentrating. Feel free to have it;
mathematical immortality awaits the person who can solve 10,958 ascending. Good luck, you are going to need it.
You’ve got to be kidding me. How does a human being run that fast for that long? That’s not possible, is it? Buford Lister (personal communication)
Years ago,
one of my brothers, J, was coaching a high school tennis team. They weren’t necessarily
perennial contenders for the league championship. It wasn’t the coach’s fault; this area is not
a hotbed of athletic talent. If you
could get enough players to come out for the team that was considered a
victory. The high school banquet was
coming up, and J told me that he didn’t know what to say during his speech. The
team only won 2 matches, an improvement from only a single victory the year
before. I told him to tell the parents that the varsity doubled its win total,
and if that trend continues, they will be undefeated state champions in 25
years. Of course, I was assuming that the win totals would go up arithmetically,
not exponentially.
He told the
joke, got a big laugh, and then everyone went about their business. I was reminded of that story when I heard
what Eliud Kipchoge of Kenya did. He ran
an unprecedentedly fast time in a marathon, specific circumstances aside. That speedy performance got me thinking about
records, whether they be the win-loss of high school tennis teams or the time
it takes to run a certain distance.
So, what
exactly did I mean by wins going up arithmetically or exponentially? Take a
look at the following figures consisting of a scatterplot with an added
trendline. If these fabricated win
totals are arithmetic in nature, then the team can count on one additional win
per year. On the other hand, if we
consider exponential growth, that elusive state championship will come a lot sooner. Such is the power of an exponent as opposed
to a plus sign.
Let’s say he
started coaching in 1990 and won one match; the exponential growth curve
illustrates that by 1995, the team will win 32.
An arithmetic progression would give a paltry total of 6 wins in that
same time frame.
Now that we
have the introductory stuff behind us, we can get to Kipchoge’s fantastic feat
(which, by the way, he accomplished with his feet). A sub-2-hour marathon? Unbelievable.
I am truly astonished. I have run
6 of them, and I can’t imagine a person keeping up that kind of pace for 26.2
miles. Exactly how fast was he running? He averaged 4:34 per mile for the
entire race. Yes, you read that
correctly.
This essay
isn’t about Kipchoge; his time speaks for itself. I am not sure I have much expert analysis to offer
other than “Wow, that is a fast time.” This post is a mathematical one about
linear regression and the slippery nature of extrapolation. No worries, the
math is simple even though the ideas are big.
The
following figure illustrates the best times in the world for the marathon from
1909 to 2019. Notice how well the data
points cluster around the trendline. In
this instance, the trendline (the line of best fit) is also known as the
regression line.
I dug into
the record for the marathon, both official and unofficial. For various reasons,
Kipchoge’s time will not be recognized as a world record. That doesn’t mean he
was riding a motorized scooter, he did run the distance and finished at the
stated time. His time won’t be considered because he had pacers surrounding him,
support cars, and a laser projection on the road ahead of him to show his pace. This wasn’t staged as a footrace against
other humans, he was only racing the clock.
For me, that does not diminish the accomplishment at all, no matter the
circumstances, he ran a marathon in under 2 hours.
The
scatterplot is set up to show the correlation between the passage of years with
the lowering of marathon times. The
relationship is strong; see the R2 value in the upper right of the
figure? That means that over 93% of the
variability found in the marathon times can be explained simply by the march of
time. As the years go by, the times go
down at a predictable rate; that is what the model is telling us.
You will
also notice an equation in the corner of the figure. If we plug in some numbers, we can make some
predictions. The equation gives a time
of 2:28:07.2 for 1930, the actual record time then was 2:30:57.6. Really close.
The model provides a time of 2:21:14.4 for 1950 versus the real record
time of 2:20:42.2. As mathematical
models go, this one is good; the R2 value of 0.932 is about as decent
as it gets when using real-world data.
Now we get
to the curious part, we have created a reliable mathematical model of the
progression of record marathon times.
You know what we need to do, right?
We need to extrapolate out into the future to see what times we can
expect the best runners in the world to be posting. A few quick calculations give us a fantastic time
of 1:29:12 in 2100 and an even more ridiculous time of 55:17.4 in 2200. I don’t think so.
Our model
does not consider the physical limits of bone and tendons, the ability of a
human to metabolize oxygen, or anything else of that nature. Even though the model is sound, it can’t be
used to predict what is going to happen far down the road.
Linear
regression, as a mathematical tool, is indispensable to modern statistics. I have done thousands of regressions, and I
am always learning something interesting when I enter some data and click that particular
button. The trick is to know when the
model is telling us something useful and to have the training to realize when
there are gaps in our assumptions. There
is a reason scientists spend so much time in school. In graduate school, I was often told that
nature is a lot smarter than we are. If
we want to extract information, we have to be subtle; the object of our
interest is exceptionally obstinate. As
a general rule: the more careful you are, the better.
Of course,
I have a story about linear regression; I will end this essay with it. The method was discovered by the German mathematician
Carl Friedrich Gauss, often
referred to as the Prince of Mathematicians. Gauss was one of the greatest thinkers who have
ever lived.
My story begins sometime in the late 1700s. Gauss is doing Gauss stuff, hanging out, and
being a general genius. He had linear
regression all worked out, along with the least-squares method essential to the
process. Gauss didn’t think much of his
discovery, he viewed the math as trivial.
I know what he meant; a long time ago, I took a deep dive into
regression in a stats class I was taking.
The math is elementary, even though it leads to one of the most potent
modern statistical tools we have.
Gauss moved on to the dozens of other
great discoveries he is credited with.
He was a mathematical machine, a child prodigy who more than lived up to
all the expectations. He was so busy
publishing important work in other areas that he never bothered to let the
world know about his discovery of linear regression. We all know what happened, right?
In 1805, along came Adrien-Marie Legendre,
a top French mathematician. He got Gauss’
attention when he published a paper called “New Methods for Determination of the Orbits
of Comets.” You guessed it; in
that paper, he outlined the least-squares method of linear regression. It was on.
In science or mathematics, there are few things juicier than a full-on priority
dispute.
Gauss wasn’t too impressed with Legendre, he wasn’t going to let the Frenchman have any credit for an idea that Gauss claimed he had years ago. Gauss published a paper in 1809 on the topic of planetary orbits; it included a mention of Legendre’s work, it also has a passage about how late Legendre was to the party. Gauss claimed he had been using the method for over 15 years.
Priority disputes like this one are
sprinkled throughout the history of science and mathematics. The most famous probably being the discovery
of calculus. Isaac Newton and Gottfried Wilhelm Leibniz, along with their supporters, had a significant
tussle over that issue. The fact that
such a dispute is taking place is an indication that the idea is important. No one bothers to fight over the uninspired
stuff. Linear regression, even though based
on simple math, is inspired. I have
often wondered why Gauss didn’t immediately see this.
So, what did Gauss do? Did he ultimately give Legendre credit? Not
even a little. Gauss was not willing to
bend, he refused Legendre even the slightest accommodation. It might surprise you to learn that most
historians side with Gauss on this issue.
His notebooks show that he had discovered this idea long before Legendre. Curious, isn’t it? Almost always, the person who publishes first
gets all the fame and glory. Today,
Gauss receives the bulk of the credit for the discovery; if you look hard, you
can find Legendre’s name in the footnotes.
I was introduced to linear regression later in life, I came across it in a Ph.D. level statistics course. Today, I hear of elementary school kids who are getting exposed to this technique. They can undoubtedly understand the math, it is that simple. Also, computers can do all the grunt work now. I just hope their teachers are up to the task. I don’t want to see a blue ribbon given to the kid who’s science fair project claims that in 2057, we can expect someone to average a 4-minute mile for the marathon.
I
have a nephew named Corndog. Recently, I was telling a story about
him to a friend of mine. He stopped me mid-sentence: “Wait, your
brother named his son Corndog?” Uh, no; his real name is not
Corndog but he is known far and wide by that moniker.
Corndog is my oldest nephew. Before he was born I was trying to decide what I was going to call him. Calling him Connor, his real name, was out of the question. So, I floated a couple different names. I first thought of the nickname “Con-man,” not bad; certainly serviceable if not inspired. Next, I came up with “Con-dog,” not exceedingly clever; I would classify it in the same group with Con-man. Then something interesting happened, the expectant mother caught wind of “Con-dog.” She said the name was totally unacceptable because it sounded too much like Corndog. In an instant, a nickname was born.
A few years later, Corndog got a brother. I considered calling him Sheepdog or Hot Dog but I settled on Z, in retrospect I believe that was the right choice. He definitely looks and acts like a Z. I have given it some thought and I think Z is the coolest letter in the alphabet. G? No way. M? No chance. I’m confident in my choice.
This
essay is about a problem I gave Corndog when he was 7. We were at a
surprise birthday party for his mom when I called him over and told
him I had a little puzzle for him. I asked him to assume he had a
piece of paper that could be folded in half 50 times; if he were to
do this how big would the lump of paper be? You can either envision
a magic piece of paper that can be folded that many times or you can
just imagine adding a sheet of paper to represent the first fold,
then two more to represent the second fold, four for the third, and
so on. If you think about it for a bit you will see it is the same
difference.
For
many years I have been asking people this question and the typical
answer is always a couple inches, a few feet, or maybe a little
taller. I think the most anyone has ever gone is about 10 feet. So,
how thick do you think the stack would be? Go ahead and think about
it for a bit. The answer will surprise you.
A typical sheet of paper is about 0.1 mm thick (0.0000001 km). You’re right, that is not very thick. The thing is, if you had a special sheet of paper that could be folded 50 times you would create an unimaginably large stack. How large? Well, if you take a sheet of paper 0.0000001 km thick and fold it 50 times you end up with a stack reaching 112,589,990.7 km. For some perspective, the moon is less than 400,000 km away. The sun is about 150,000,000 km away, more or less. Wow, 50 folds of a sheet of printer paper get us way past the moon; good grief, it nearly reaches to the sun.
This little question is another one of those “huh, really?” problems that I love. Once again, our feeble human intuition has miserably failed us. I would hate to leave us all feeling bad about ourselves so I have decided to end this essay on a high note. I think we are all going to smile when you read the following short quote from the 7-year-old version of Corndog. When I told him that if he folded a piece of paper 50 times the resulting thickness would just about reach the sun he responded in the only way the coolest 7-year-old alive possibly could. He looked at me excitedly with big, wide eyes and said: “Let’s do it!” Corndog, my man, you are preaching to the choir.
To understand and be understood is to be free. Daniel Johnston
I did something highly unusual the other day, something I had never done before. Did I beat a Grandmaster at chess? No, I am secretly a checkers guy; chess was never my game. Did I solve an open math problem, somehow stumbling upon a clever solution that will make me an immortal? Nope, I didn’t do that either. The odds of that ever happening are growing increasingly slim as the years roll by. No, my “achievement” was slightly more pedestrian; I bought an onion. As always, there is a story about why I ordered an onion and how I got it home.
I don’t cook, or bake, or spend much time at all in my kitchen. I am single, I have never been married, and there is nearly a 100% chance things are going to remain that way. Any single person can tell you it is very difficult to cook for one. I have tried it in the past, and the results were disastrous. I ended up throwing lots of food out, and I hate doing that. I decided decades ago that bringing something home to eat was the cheapest and most efficient way to get it done. Of course, I also eat out as long as I am not too tired to leave my couch. I hate to admit this, but last night, exhausted from a long day, I had beer and animal crackers for dinner.
As you might imagine, I do not like grocery shopping. I do it occasionally, it is always nice to have food in the house. Also, I have been known to make myself a random tuna sandwich, or I might microwave a frozen meal. You know, nothing complicated.
I was happy to learn that Walmart now has people who will do my grocery shopping for me. I sit at home and click what I want and when I want to get it. Is this service the greatest thing ever? Sure, why not. I love it. I use it a lot. I still don’t like having to carry all that stuff in by myself, and putting it all away isn’t a lot of fun, but I am not quite sure how to solve that problem.
Not too long ago, I submitted a big order for groceries to Walmart. I was motivated by my purchase of a George Foreman Grill; the promise of the occasional grilled hamburger didn’t sound too bad. As I was clicking through all the stuff I wanted, I thought that it would be great if I got an onion to put on the hamburgers that were shortly going to start pouring out of my new grill. So, for the first time ever, I bought an onion. Of course, things couldn’t be quite that simple, could they?
I pulled into Walmart at my allotted time and found a spot. The app on my phone prompted me to input the parking space I was in. I tapped the number three and sat back and relaxed. Before I knew it, a young man with a large cart came up to my window. He verified my identity and then loaded most of the groceries into the bed of my truck. He came back around to my window, handed me a couple bags of chips and an onion, then had me sign a handheld device with my finger, no stylus necessary. Thinking we were done, I started my truck. Turns out, we were not quite finished. The young man struck a pose, not quite a buffalo stance, not something from Madonna’s Vogue video, but something a little different. He looked at me, smiled, and said: “Today, we are going to play a little game.”
Intrigued, I said “OK” and awaited my instructions. He pointed to his name tag. “See this?” I spied a Where’s Waldo sticker affixed to a piece of plastic. “Yes.” I started chuckling, and then I started laughing. I was alone in the truck; there were no kids in there, it was just me and my phone (along with some Fritos and an onion).
“I have hidden one of those stickers somewhere in your food. It is your task to find it.”
At this point, I was laughing out loud. First of all, I thought it was funny that he thought a man my age would be interested in such a game. Second of all, I was deeply impressed with his insight into human nature.
He went on to explain to me that if I was able to find the sticker, I was to call the number listed in an email receipt they were going to send me. I said “OK” and drove off down the road, smiling and chuckling the whole way home.
I pulled into my drive and started to carry everything into the house. I had to make a bunch of trips, lots of Diet Dr. Pepper; 24-pack cases of cans, 16 and 20 oz bottles, plus all the bags. I got them to the kitchen counter, and then my task began.
I carefully examined every item before I put it away. Fritos – check, Frozen meatloaf with mashed potatoes – check, cans of tuna – check, no Waldo there either.
I looked over every item I had purchased, and I could not find Waldo. I took all the groceries out of the cupboards and looked at them again. No Waldo. I went back to my truck and looked in the bed and the cabin (the sticker could have fallen off, right?). No Waldo. I followed my path from the drive to the house. No Waldo.
Where’s Waldo? I mean Where Is Waldo, where could he be? I had no idea. I looked over every item again as I put them back, one by one, into the cupboards. No Waldo. It was only then that I noticed the six-pack of 20oz Diet Dr. Pepper bottles that were on my kitchen counter. In stealth mode, I slowly approached them, using all my ninja skills (of which I have none) to make sure I got the drop on the bottles. I grabbed the plastic carrier and then rotated the first bottle around its axis. No Waldo. Then the second, the third, the fourth…wait…Yes, It’s Waldo! Victory, it appears, is more precious when you have to work for it.
That dude at Walmart had placed Waldo on a bottle of pop and then rotated the bottle so that I wouldn’t see it. Pure genius. I bow to the Walmart employee and his Where’s Waldo sticker game.
Basking in glory, I called my buddy Les to tell him about this bizarre experience. His response: “Who’s Waldo?” Wait, who is Waldo? You’ve got to be kidding me? Les had never heard of the Where’s Waldo books! I was a bit shocked. We grew up in the same town, went to the same schools, and even though he is 6 years younger than me, we had similar experiences growing up here in this part of the world.
So, the question now becomes: How is it possible that Les had never heard of the Where’s Waldo books? My first thought was to see how many of those books are in print. It turns out, that is not an easy question to answer. I did find out that the books were originally based in the UK and were called “Where’s Wally.” That was before the Where’s Waldo franchise took over the world, except (apparently) this little section of The United States. A little more research led me to guess that there are over 30,000,000 Where’s Waldo books in print.
*****
Buford Lister took off his glasses and started to rub his eyes. This new allergy medicine was supposed to take care of this itching. Man, what is going on? He examined the bottle containing his new prescription and then tossed it into a desk drawer. These things are worthless. “Alexa, why are my eyes itchy? I am taking medicine that is supposed to fix this mess.”
Sorry, I don’t know that.
“You know, I think one day soon you are going to know, and you are going to answer me with an appropriate response. Alexa, do you hear me?”
I am here. I listen when I hear the wake word.
He put his glasses back on and immediately noticed a flashing red light coming from a tray on the bottom right of his computer screen. Hmmm, company this early. I wonder what this is about? He clicked on the icon, and a picture of a disheveled man, a standing skeleton, appeared on the security camera screen. He was moving about wildly as he tried over and over to press the doorbell. How was I not given a heads up about this? He got up and made his way to his gun cabinet. He took out a pistol and stuck it in the waistband of his pants.
*****
With the Walmart episode behind me, the last couple of weeks have been normal, just like most of those that came before. The sun came up, stayed a while, and then disappeared, only to return the next morning (take that David Hume! Chalk up another temporary victory for inductive reasoning). I saw people rushing about, too preoccupied to use their turn signals as they sped off to who knows where. Kids got on the school bus in the morning and were dropped off later in the day. Something was different though, the world that everyone was moving through was a little dimmer; well, maybe more than a little. I, too, was oblivious to the creeping darkness until I accidentally stumbled onto something extraordinary.
The interesting part of that day, the accidentally stumbling day, began as I sat on my porch and watched a guy zoom down the road on a speeding motorcycle. He was texting, no helmet, on a four-lane road. What dedication, I thought. Off he goes to save the life of a child, maybe even a future president. I would have thought that a pediatric surgeon would take better care than that, but I am not a medical doctor, so I really can’t be sure. I mean, it couldn’t have just been a random doofus risking his life and the lives of others for no apparent reason, right?
Just as I trusted that the sun would come up, I also had a pretty good idea that my truck would start when I turned the ignition key. It did (That is two victories for induction as David Hume remains totally unimpressed). I went about my business about as normal as possible until I saw something about the death of a singer-songwriter on the internet. An influential and famous one at that (or so they said). I read a little about him and started to get confused. I read more about him and became really confused. If this man was my generation’s Bob Dylan, then how is it possible that I had never heard of him? I kept reading… I saw with my own eyes, on my computer screen (the very screen I am looking at now) the words used to describe him. The word genius appeared over and over. Tortured was also an adjective that materialized in nearly every account. Severe mental illness was a phrase that showed up a lot. I read a few stories about him, and then I decided to give this man the ultimate test, I went to The New York Times website to see if they granted him an obituary. Did they ever.
In many ways, the overall impact of a public life can be discerned by how much space The Times gives an individual for their obituary. I wrote about this in my Beef Stroganoff essay, the one about the brilliant rocket scientist, Yvonne Brill (it will be posted here at a later date). In the headline, The Times noted that this man, this mysterious singer-songwriter, had drawn comparisons to William Blake, a long-dead Englishman who is a towering figure in the history of poetry. William Blake‽ You’ve got to be kidding me! I became even more confused, how did this person evade me all these years? A mystery was upon me, I had to do more research.
*****
Once he double-checked to make sure he was locked and loaded, Buford Lister opened the door.
“I did it. I did it. Look, I did it!” The excited man grabbed Buford Lister by the shoulders and started shaking him as best he could. “I got it. Right here in this notebook. It’s in there. Ya gotta look, it’s in there!”
He let go of his brother, sat an old backpack down on the ground, and started to reach in. Buford Lister drew his pistol.
“Festus, I’ll get it. Step away from the backpack. I’ll get it, OK? Just take a few steps back and relax.”
Festus looked his brother in the eye. “Jealous, all the time jealous. I knew you were going to try to steal my proof. You were always too dense to understand my ideas. Well, I learned my lesson a long time ago with you.” Festus pulled a thin lead pipe out of his belt loop and started swinging. Down, across, and then down again, catching nothing but air.
Buford Lister backed away, disappointed in himself that he didn’t see the pipe. He wasn’t going to shoot his brother…unless he really had to. He kept his pistol aimed at Festus, grabbed the backpack, and shut the door. Once he was sure the door was secure, he went into an adjacent room and pressed a button at the base of a Mozart bust. A section of one of the bookcases slowly rotated, revealing a metal briefcase. He pressed his thumbs on top of the scanner, dialed in the combination, and popped the case. The phone was right where he left it, nestled in its little cubbyhole. He grabbed it and pressed the triangular taupe button. A few seconds passed…
“Festus is here. He is on my porch, swinging a lead pipe. Now, I can go out and shoot him or you can do your job and come get him.”
His head dropped as he listened to the terse response.
“Another thing, how could you people not tell me that he was coming my way. Last I heard about him he was on the other side of the country. It is not that hard to let me know that he is in my area. I don’t understand what is up with you people. The older I get, the sloppier you guys are.”
His eyes drew into a squint as he grasped the phone tighter.
“Fine, I’ll do your job for you and call the police.”
*****
I recently discovered Billie Eilish, a singer-songwriter who is on the cusp of taking over the world. I think that young woman is a genius, I feel it when I listen to her music. There is a special spark there, a big and unusually bright one. I am looking forward to what comes next for her. I’ll tell you a little secret, I am fairly certain she has access to The Book.
I have written a lot about The Book and Paul Erdos, the great Hungarian mathematician who often talked about its importance. Many of my future posts will include stories about him. For now, I need to let everyone know that The Book contains all the most elegant mathematical formulas and proofs that do, or will ever, exist. Straight from the mind of The Supreme Fascist (what Erdos called God) to The Book. I wrote my own book about The Book, I will be posting chapters from it soon. As my story goes, I got to see it once; only one time for a brief instant, but that glance changed my life. I wrote about the pages I saw and my spirited attempt to get another look between those elusive covers. I discovered that The Book is not just filled with mathematics, there are lots of different chapters in there. I am certain that writers, along with extraordinary scientists, and artists, and many others, get to peek in there occasionally. I got a glimpse (and got a collection of essays out of it), I am sure Billie Eilish is going to become very familiar with its layout, and I know for certain that Daniel Johnston, the subject of this essay, was reading from its pages on a routine basis.
I just learned that a man named Daniel Johnston existed, and I am truly sad that he is gone. More importantly, I am very unhappy that I live in a world that so undervalues genius that it took his death for me to become familiar with his work. There is no excuse. Where’s Waldo books are one thing, a living genius whose work touches me at my deepest level of existence is quite another. I would be mad, but I don’t know where to direct the anger, I simply don’t know who to be mad at.
*****
The paramedics gave way to the police. Festus was still waving the pipe in wild fashion. He was screaming gibberish, at least that is what the police thought.
“Poincare! Stand back, or I’ll brain the lot of you. I solved it. You hear me, I got it. That’s right. You are all looking at a genius.”
“Sir, please drop the pipe.”
“Drop it, don’t make us shoot.”
“Drop it now!”
Buford Lister appeared from the side of the house. “Please, everyone relax. Put down your weapons.” He turned toward his brother. “Festus, put down the pipe.”
“I’m not putting this down. You come any closer to me, I’ll brain you. You know I’ll do it. Stand back. Get away from me.”
“OK, Festus. Look, just let these men take you to a hospital, they all just want to help you. They just want to give you medicine that will calm you down.”
“Yeah, you mean the medicine that turns me into a zombie, the stuff that makes me forget my math. I can’t think right when I take that stuff. I’m not going to live that way.”
“Look, Festus, they just want to help.”
Festus threw the pipe at his brother; as soon as it left his hand the officers rushed him. They quickly cuffed him and put him in an ambulance. All the while, Festus was screaming: “I used Ricci Flow to solve Poincare. Poincare! Let me go, you have no idea what you are doing. I am a millionaire, let me go! I have to go get the check. I’m going to be on the cover of The New York Times!”
Buford Lister took a big gulp of air as he let his brother’s words seep in. Oh man, could he have done it? This is going to be bad. He quickly went through the possible scenarios, none of them good. There wasn’t a single possibility that had a decent outcome.
A paramedic approached and patiently waited until Buford Lister looked up at him.
“Sir, you are Buford Lister, correct?”
“Yes.”
“And this is your brother?”
“Yes, Festus is my brother.”
“If I may, do you have a list of the medications he is supposed to be on?”
“No, I don’t. He has been away for a long time. I have no idea what he has been prescribed, and I have no idea who his primary care doctor is now.”
“Ok, thank you, sir. We will be transporting him to Iroquois General.”
“All right.”
As Buford Lister sat on his front steps, Detective John Gibbons approached and took a seat next to him.
“Buford Lister, good to see you. It has been a while. I’ll tell you, what a mess.”
“You might say that,” he said as he leaned over and shook hands with the detective.
“Why weren’t we given a heads up that your brother was in town?”
“No idea, they didn’t even tell me. I saw Festus on my home monitoring system, that is the first I knew of it.”
“Well, it has been a long time, and those old boys down in D.C. must have things that are a higher priority now than you and your brother.”
“Sounds about right. A policeman’s value can go up as they age but that of a mathematician…it doesn’t quite work that way.”
“What was that name Festus was screaming? Any idea what that was all about?”
“He seems to think that he has solved The Poincare Conjecture, it’s awfully complicated to even explain. All you need to know is that it is one of those million-dollar Millenial Prize Problems.”
“It’s that big a deal?”
“Well, it was to the guy who solved it over ten years ago. Apparently, Festus hasn’t been keeping up with the academic journals or the nightly news.”
“So, even…”
“Even if he did solve it, there is no reward for coming in second, no matter how clever the proof.”
“Do you think he did it? Could he really have solved the problem?”
“The thing is, most of the best math is done by the young folks, as mathematicians age they lose it. And I’ll tell you one thing; the drop off is a cliff, not a stairwell. One day you wake up and realize your best years are behind you, and there isn’t anything you can do about it. It’s all over, and no one bothered to say goodbye.”
“So, basically no chance?”
“A slim one. When Festus was young, he was a math prodigy. You know that. He was destined to solve things like Poincare, I thought he had a chance to become one of the greatest mathematicians who ever lived and then…”
“Yeah, I remember. I was there, I worked on that case.”
“We all remember that case. The whole town remembers that case. Not much you can do when the forces that constantly torture a genius overtake the factors working to keep him sane and normal.”
“Yes, sir. Your brother is a cautionary tale for being born too smart.”
Buford Lister remained silent. He knew when someone was fishing, trying to get him to tell his own story, the story of a promising career flushed in a couple seconds by a stupid mistake. He had heard through the grapevine that one of his old colleagues, a European physicist, was writing a book about what people were calling The Lister Affair. He looked up at Gibbons and asked him for a ride to the hospital. They rode together in silence.
*****
I am truly at a loss for words; my discovery of Daniel Johnston has thrown me, I am a little tilted. All I can do is finish telling the story of my introduction to the tortured genius that was one of our greatest living songwriters, a man who managed to evade me for my (and his) entire life.
After I read the obituary in The Times, I did another search for Daniel Johnston to see what I could find. I stumbled upon a tweet from the actor and director Judd Apatow, a short message with a link to a video:
So sad to hear of the death of the great Daniel Johnston. Here is a beautiful performance of his which makes me cry every time.
Ninjas, I had a vague sense of ninjas. I didn’t see them, I was too captivated by my computer screen. I couldn’t believe what I was seeing and hearing. I don’t ever recall coming in contact with such honesty and lack of pretense. Did you catch those first two lines?
Don’t want to be free of hope And I’m at the end of my rope
I was hooked. I didn’t need to hear any more to know I was listening to a genius. The first line got my attention, a pure masterclass in phrasing. And then the rest of the song just poured it on, more and more lyrical brilliance just gushing out of him. The singing? Did you believe him when he told you he was at the end of his rope? Sincerity, fragility, and truth coming out of (what I soon learned to be) a loveless and tortured soul; that was what I saw and heard. I couldn’t believe what I was experiencing. He was wearing clothes, but he might as well have been naked, it was the same difference. This broken man was totally exposed in a way that you have to see and hear to believe. I had never seen anything like it.
It’s so tough just to be alive When I feel like the living dead
Then more ninjas. The rest of the horde entered through my back door, near the kitchen. Or maybe they crawled in through the kitchen window. I am not sure of the method, but I am sure of the point of entry. They made their way up the stairs. My security system did not detect them. I didn’t see them, I could only sense them. Ninjas, with all their stealth and skill. Ethereal assassins, blades sharp and drawn; I never had a chance.
I’m giving it up so plain I’m living my life in vain And where am I going to
Baffled and confused, I sat quietly as Daniel Johnston struggled to read the lyrics to his own song, words he had written so long ago. I considered my options, I had none.
I’ve got to really try Try so hard to get by And where am I going to
The masked entities surrounded me, the quarters were close; swords unsheathed and at the ready. I was overmatched and overcome. I was defeated.
Stunned, I sat for some time in silent contemplation. I played the video again to confirm what I thought I saw, and then I did something I normally don’t do; I scrolled through the comments to see if people had similar reactions. I found I was not alone; not only were there a lot of people who had just discovered him but there were many people having the same visceral reaction to him that I had. Perhaps my favorite comment was from a man named Dave Bonawits, he wrote: wow. I just had an unexpected meltdown watching this.
I write these essays with the goal of introducing my readers to topics I find interesting. I like to think that somehow (after I am long gone) these posts will leave behind a record of what it was like to be me as I traveled through space and time among my fellow human beings. Know this: The reason I get up in the morning is that, even though I know the odds are low, there is a chance I might be introduced to someone like Daniel Johnston. I am gobsmacked.
There are lots of YouTube videos out there featuring this man and his music as well as an award-winning documentary about his life called The Devil and Daniel Johnston. I think it is worth learning more about a man who turned down a multi-record deal with Electra Records because he was convinced that the band Metallica, a member of that label, was in league with the devil. Your time will be well spent hearing the stories about how a young man became famous for recording music with a cheap boombox and then giving the cassettes away. Go ahead, take a deep dive, go down the Daniel Johnston rabbit hole, and see what you can find. I am still down there and I must say that what I am finding is astonishing.
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.
