A Mathematical Monster

The Mathematician slowly turned to see if Alexa was toying with him. Was it really time to get up already? He was having a lucid dream about Danica Patrick. They were eating lunch at a picturesque sidewalk café when he was rudely interrupted.

“Alexa, good morning. Thank you for waking me up at the exact moment Danica was about to tell me some sort of secret. She waved me closer to her and was about to whisper in my ear when…”

“Sorry, I’m not sure about that.”

“Yeah, you and me both.“

The Mathematician slowly sat up. His feet found his slippers, and he trudged into the bathroom for his morning ritual. He looked closely at himself in the mirror. Have I aged a day or perhaps more? He pressed his fingers against the skin near his eyes and moved in closer. I guess a day is about right, don’t look much different than I did yesterday.

At that moment, a ghoul appeared in the upper right corner of the mirror. Its countenance was that of a determined and poised demon bent on havoc. It shook its head in disappointment when The Mathematician did not react.
The ghoul came through the mirror and took a more or less human form. It tapped its cane on the bathroom sink and looked The Mathematician directly in the eye.

“I know you have many questions, but I do not care to address those at this time. All you need to know is that my colleagues and I have come to an understanding. Unfortunately, our decision impacts you in a most severe way.“

The Mathematician shook his head and turned toward the shower. “Do your worst. I have been dealing with specters like you for a long time. You don’t scare me.”

When The Mathematician pulled back the shower curtain, the ghoul was in the tub, pretending to wash his face with a bar of soap.

“Well, you are the first of your kind I have ever seen who could manipulate material objects like that. What are you, exactly?”

“Oh, I assure you, you have never come across anything like me. I am what you would call a higher-level apparition. Entities of my ilk only reveal ourselves for momentous occasions.”

“What is so special about this visit?”

“Ah, I am afraid that I have an unwelcome message for you. It has been determined, not without thoughtful debate, that the human race has one month to resolve The Riemann Hypothesis or else.”

“Or else what?”

“We are going to take your home for our own. You and all those like you will be tossed into history’s garbage bin. There won’t be any evidence any of you ever existed.”

“What? What are you talking about?”

“Resolution or extermination,” said the figure as it glided back to the sink.

“Wait…”

With that, the ghoul retreated back into the mirror. The Mathematician, confused and disoriented, reached for the sink to balance himself. He was reeling as he lost his bearings and fell, his ear cut by the sink corner. He collected himself and tried to stand. He made it to his knees before his energy gave out, and he landed back on the floor. He pulled a piece of toilet paper out of the garbage can and pressed it against his bleeding ear. He sat silently, his brain working hard to try to figure out what just happened.

The Riemann Hypothesis? Well…that was unexpected. The most brilliant people in the world have been trying to resolve that problem for what, 150 years or so. It can’t be done in a month, probably can’t be done at all.
The Mathematician thought back to when his brain was nimble, and the possibilities were near limitless. He still had a box of all his failed attempts to prove the Riemann problem. He kept a hard drive, somewhere, documenting all his elusive tries at a counterexample.

As he struggled to get up, he called out, “Alexa, what just happened in here?”

“Sorry, I couldn’t understand.”

“I know. I don’t understand either.”

He walked back to the bedroom and sat down on the bed. He grabbed his phone and immediately noticed the messages and the calls. As he scrolled through the texts, he quickly realized he wasn’t the only person to get a strange visit. Friends and colleagues from around the world were texting similar experiences, all dealing with an apparition and a request concerning The Riemann Hypothesis.

He turned his phone ringer on and immediately got a call.

“Hello.”

“Yeah, me too.”

“I don’t understand any of this.”

“OK, what time? Send me the link, and I’ll jump on. I don’t have to tell you, but if this is real, we are in an awful situation.”

The Mathematician set the phone down on the bed and leaned back.  I wonder if I go back to sleep will things be different?  Can I wake up to a different day? Will the ghoul choose not to appear?  Is there a different reality, maybe of the parallel variety, waiting for me if I go back to sleep?  He considered the possibilities and then got back up.

Later that morning, an online meeting was held with many of the top mathematicians in the world. All of them had been visited by the mysterious entity, and the warning was consistent, resolve Riemann or go extinct. For reasons not entirely clear, everyone intruded upon by the apparition took the threat seriously. As for the others, the non-mathematical types who were not paid a visit, not so much. No one believed the mathematical community when press releases were issued and pleas made through various media outlets. The mathematicians needed help, and all they got was ridicule. I suppose it is reasonable to understand why no one took them at their word. After all, the story does seem a little far-fetched, especially for those with a scientific mindset.

Of course, there were people worldwide already working on The Riemann Hypothesis. They were of no help. No one had a clever or novel approach to the problem. Even so, many tens of thousands were put to work to prove the veracity of the conjecture. It was the opinion of the vast majority that the hypothesis was indeed true. The problem was coming up with a logical, mathematical proof.

Thousands of mathematicians were tasked with trying to find a counterexample. They coded the Riemann Zeta Function and used as much computer power as they could muster in search of a result of zero where it should not be. No one was optimistic such an answer would be found.
Only a few days had passed when the mathematical community pleaded with world leaders to find the threatening ghoul and kill it. Some of the best minds in existence thought this was our only chance. The problem is too elusive for a rigorous proof, and finding a counterexample could take decades if one even exists. They were met with silence, then skepticism, then outrage.

“You would have me believe this ridiculous tale from a group of liberals?” The television announcer smirked into the camera as a third-rate mathematician sat across from him.

“Believe what you will, but I was also visited by the demon. I received that same message the others did. Either resolve it or face extermination.”

“Right, of course, you did.”

“If I may, what is the mathematical community’s angle here? If you think this is a big lie, why exactly are we lying? I know that the only thing you and people at your network can think about is money so let me ask you, how are we making money from this supposed lie?”

“Money has been pouring into math departments the world over, sent by delusional people that believe such an outrageous thing can be true. There was no demon, there is no demon, and one month from now, the sun will come up as it has every day since the creation of the sun and earth.”

“Well, the horror of all this is that you will not know if we are right. You, along with the rest of us, will simply die. It will be hard for you to understand why you are dead if you are dead. It will also be difficult to know that you are dead when you are dead.”

“If this is so important, why aren’t you working day and night on the problem? Why are you sitting smugly across from me with your little bow tie and dark glasses? Shouldn’t you be in your office scribbling away?”

“Math, especially this kind of math, is a young man’s game. I cannot offer any help or guidance. I, like many mathematicians, do not have a clue how to solve the problem. It is well beyond my diminished capacity.”

“Explain it to us. Tell us about this Reimann Hypothesis.”

“Well, I imagine if the problem could be understood by a person like you, its answer wouldn’t be valuable enough to the power that wants to destroy us. It is entirely possible that the enemy does not have the answer and needs it for some reason. Threatening us, apparently, is their best bet to achieve a mathematical resolution.”

“That doesn’t make any sense.”

“None of this does.”

Exactly one month after the demon’s arrival, the sun came up, and people the world over shook their heads and mocked the disgraced mathematical community. Clearly a case of mass hysteria, some said. Others wondered why such a cruel prank would be played on innocent populations.

As the sun started to set, people began to disappear. Those still alive did not believe what was happening on the other side of the world. They laughed. Most were smug. Some prayed. The majority of the mathematicians were resigned to their fate. They had done all they could do, they worked as hard as they could, they gave maximum effort. There is nothing else they could have done. In the end, it was of little consolation.

 

A Small (not TALL) Tale about a Chicken

I remember reading about the story I am about to tell you.  I can’t quite remember when or where I first came across the adventures of this exceptional chicken, but I never forgot her.  She has to be one of the most extraordinary chickens that ever was.

The story began a long time ago; I am not sure exactly when.  The students at Harvard College were accepting nominations for class president.  As always, ambitious young people threw their hats in the ring.  After all, what looks better on a resume than being president of your class at a place like Harvard?

A few students were thoughtful about the process; perhaps overthinking a bit.  One night, I imagine after a few cocktails, they looked over the rule book that governs how one runs for class president.  These clever, enterprising individuals found a couple interesting things.  First, nothing states that a candidate for president of any Harvard class must be a student at Harvard.  Obviously, an oversight to be exploited.  And second, nothing in the book says that a candidate needs to be human.  And there you have it.

A group of exceptional students, ones apparently with a light course load,  set out to create a bit of chaos.  They quickly found a “psychic chicken” and nominated her for class president.  Of course, the chicken won in a landslide.  One failed candidate, i.e., a human Harvard student who lost to the chicken, got his father, a Wall Street lawyer, to raise a big ruckus.  Lawsuits flew across the campus in an attempt to throw out the election results.  As far as I can tell, the “psychic chicken” did not see any of this coming.

I wish I had a resolution to this story.  I have been searching for this incident, and I can’t find any proof that it ever happened.  I was reasonably sure that I read about this in Harvard Magazine, a publication sent to my mailbox every month.  I went online and searched the back catalog.  Much to my disappointment, the phrase “psychic chicken” did not appear.  I also did a more considerable search of the entire internet, and I could not find it.  It won’t surprise you to learn that Google Scholar also came up empty.    I am at a loss.  I am confident I read about it, and the reporting was accurate.  This story did not come from The Harvard Lampoon.

As it stands, if you come across a story with a chicken, psychic or not, winning an election for class president at any university, not just Harvard, please let me know.  I have long wondered what became of the gifted and ambitious Harvard chicken.  It would be nice to see if she had any kindred spirits out there.  You know, chickens with fire in their bellies who, like many politicians, longed to be in the arena.

That is One Strange Bunny Hole

Over ten years ago, I wrote an essay called Breakfast at Tiffany’s.  The other day I decided to take a look at it.  I wanted to edit it so that I could include it in this blog.  The best-laid plans…

On the first page, I referenced the “food service industry.”  Grammarly, my best nonsentient writing friend, tagged it and requested that I correct the spelling of “food service.”  What?  The mighty program wanted me to combine the words to form a one-word “foodservice.”  I don’t know about you, but that doesn’t look right to me.  Faced with this dilemma, I had no choice; I dove headfirst down a “food service” bunny hole.  This is what I found.

Some people think that food service and foodservice are interchangeable.  They mean the same thing, and any person can choose either one and be correct.  Yeah, some people think that.  Others believe that someone, an unknown linguistic provocateur, introduced the combined word years ago in a corporate context.  Then, for reasons unknown, the new word stuck.  Some think this was done on purpose, while others view it as a simple mistake that caught on.

Other linguistic sleuths believe that the two words have distinct meanings.  Food service applies only to those involved in the preparation and serving of food.  At the same time, foodservice pertains to the industry as a whole.  And yes, the only reason I am writing about this is that I woke up in the middle of the night, and I can’t get back to sleep.  Sure, this discussion is slightly interesting, at least I guess that it is.

I found English majors and professors of all types chiming in on this topic.  The arguments are not as spirited as those relating to grammar, but they are pretty good.  Many people say that foodservice simply does not look right.  Others say it is okay and should be used when talking about the industry in general and not the person who brings you your cheeseburger.

Now, finally, I can get to something I find fascinating.  Have you ever heard of the Google NGram Viewer?  You can query Google’s vast collection of books to find the popularity of words through time.  Take a look at the following “food service” versus “foodservice” graph.

 

 

The word foodservice started to take off in the 1970s.  It became more and more popular until the late 1990s.  Oddly enough,  food service constantly has remained more popular than its counterpart.  This indicates that the people arguing for foodservice as a word applying to the industry as a whole are correct.  Someone came up with it in the 1960s, and the distinction gained traction.

I highly recommend that you visit the Google NGram Viewer and play around with it.  I certainly have.  You can answer many of those questions that have been plaguing you for decades.  For example, have you ever wondered who is more prevalent in literature; Albert Einstein, Sherlock Holmes, or Frankenstein?  I went to the viewer and created this graph.

 

 

I believe my work here is done.  Now that I know Frankenstein is in the lead I might be able to finally get some sleep.

 

 

 

 

 

 

The Unknown Opponent

This is a post about playing tennis against an opponent you have never seen play.  This is a fairly common occurrence if you are a tournament player or play tennis socially on a ladder.  What are you supposed to do when you want to defeat such an opponent?  I have a few suggestions.

The first thing I would recommend is to hit the ball down the middle of the court during warmups.  You will quickly find out if your opponent prefers to hit a backhand or forehand.  If they continually gravitate to one shot over the other, you have gained valuable information before the match starts.  And you can trust me, they won’t hit the ball on their weaker side if they have a choice.  Your opponent will not be practicing their weaker shots in warmups; they will go with their preferred shot.

The next thing you should do is look at the grips they are using.  If your opponent has a full western grip on the forehand side, you now know that they are susceptible to low balls on that side.  And how about the backhand?  Do they have any hitches in that stroke that you could exploit?

Where is your opponent standing with respect to the baseline?  Are they far behind it, implying that they are a passive, counter-punching type of player.  If they are half volleying their groundstrokes as they hug the baseline, you can bet they are more aggressive.  This is more valuable information that you can attain before the match starts.

What about your opponent’s footwork?  Are they taking those extra, small steps good players take to adequately address the ball?  Are they lunging at the ball?  Do they seem to be off-balance as they recover from hitting a shot?

How are they at the net?  Do they only want a couple volleys, and then they are done?  Many players who camp out at the baseline act like they are irritated to come to the net during warmups.  Pay particular attention to their overheads.  Are they letting the ball bounce?  Do they seem tentative in any way?  Are they hitting the shot crisp and clean?  If the shot seems weak, you can easily exploit it when play starts.

When it comes time to serve, take note of where the player stands when returning your serve.  Are they way behind the baseline, or are they hugging it?  Their position will give you some clues as to how they are going to play.

When you are returning their serve, pay attention to their toss.  Is it consistent, or is it flying all over the place?  Is it a high toss?  If their toss is not consistent, there is a chance you will have trouble reading their serve.  You can’t know where the player will hit it if they have no idea where it is going.

If the player is a good one, try to see if they are telegraphing the type of serve they will hit by the kind of toss they are using.  A topspin serve might have a different toss than a slice serve.  A player has to be very accomplished to use the same toss for the different types of serves they are capable of hitting.  Unless you are playing a very good player, you can usually spot a thing or two that will help you out once play starts.

After warmups are done, a racket is spun, or a coin is tossed to determine who has the option of serving first.  I always decline; I want to return.  Your best chance to break serve might be the first game.  Perhaps your opponent is not fully warmed up, or their nerves haven’t settled yet.  If given a choice of sides, I always choose the side that is least affected by the sun.  I want my opponent, in that first game, to have every possible disadvantage.  If there is a chance the sun will come into play, I want the other player to have to deal with it as soon as the match starts.  This is especially true if they are not wearing a hat and sunglasses.

These are just a few suggestions.  You can do a lot more if you really want to get to know your opponent before the match starts.  I have it on good authority that you can get an advantage in any match you play if you mow the lawn in your tennis shoes.  Seriously, it works.  During warmups, simply hit the first couple of balls high into the fence behind your opponent.  After the second ball lands, profusely apologize to them and explain that you have been playing exclusively on grass for the last few months, and your timing is severely off.  You will be inside the other player’s head for the duration of the match.

Finally, everyone reading this post needs to get their hands on the most remarkable tennis book I have ever read.  That book is Winning Ugly by Brad Gilbert.  Reading it will give you insight into how the author reached number 4 in the world with no real discernable weapon other than his enormous tennis brain.  And I would certainly rather win ugly than lose elegantly.  After you read his book, you will too.

 

We’re Going to State!

My niece, Haley, is a freshman in high school.  She is a tennis player.  She is the first girl in the history of her school to win the sectional tournament.  The fantastic thing is that she beat every opponent 6-0, 6-0.  She was never in danger of dropping a single game.

Haley made the state tournament.  Again, she is the first freshman in her school’s history to do so.  In her first-round match, Haley plays the defending state champion.  Can she win?  Can he beat the state champion?  Yes, she can.  This post is not about Haley’s attempt to win a state championship as a freshman; not really.  This post is about expectations.

Haley’s high school has five state titles in ‘20-’21 alone.  That is five titles in various sports in a single calendar year, and, of course, the year is not over.  That is mighty good.  Back when I was in high school, the prospect of a state title was never mentioned for any sport.  The thought of a league title mainly was out of the question.  During my four years of high school, our football team did not win a game.  Some people claim that we won one, but I don’t remember us winning any at all.

At Haley’s school, the student-athletes are expected to make the honor roll and compete for state championships.  Not all schools expect such things from their students.  Mine certainly didn’t.  I know this much; it is easier to excel when surrounded by people with high expectations.  Especially when those expectations are for you and everyone else in their sphere of influence.  That makes all the difference.  Trust me, I do know a little about this topic.

When I was young, about 12 or 13, I decided that the way people used baseball statistics was deeply flawed.  I was especially dubious of ERA (earned run average) for relief pitchers and batting average for hitters.  I knew there was a better way to rank success or failure for the players, so I set out to fix it.  I came up with numerous equations to better address the value of a given player.  Of course, when I showed all my work to my coaches and teachers, they all sighed a big sigh and more or less told me I was wasting my time.  Such is the fate of a person being taught by people who strived to only be mediocre.  And I must say, a middling existence as a teacher or mentor was well out of their range.

I often say that the thing I needed more than anything else when I was a kid is the 50-year-old version of me.  That guy had a handle on lots of different things.  Had he been around, today I might be considered the father of modern-day sports analytics.  That is not a joke.  Instead, I am just a dude sitting at a keyboard.

The fifty-year-old version of me would have immediately taken the 12-year-old kid and put him on intellectual steroids. That youngster would have been encouraged until the ideas became fully realized.  A nudge here, an introduction to a statistics professor there, you get the idea.  The older version of me knew what proper expectations were.  The 12-year-old kid didn’t know anything about anything, and more importantly, neither did his coaches and teachers.

Haley has a much better situation.  Obviously, right?  I talked to her and her brother about Harvard ever since they were big enough to listen.  I still tell them stories today about that one place where expectations need not be explicitly stated; they are implied.  No matter what else may happen in your life, it is understood that you have an obligation to become the best version of yourself possible.  And while you are at it, making the world a better place is considered an everyday goal.

Haley’s life at this point is much different than mine was.  When I was a kid, I had a few uncles who ended up drinking themselves to death.  Sure, a couple of the others were hard-working family men who were always nice to me.  Even though I enjoyed being around them, I am not sure there was any inspiration for me to be found.  Those men, either drunk or sober, certainly did not have any expectations for me.  And I’ll say this with great confidence, I know it never occurred to my parents that any of their kids would get a degree (or two) from Harvard.  It was out of the question.  After all, my mom was a coal miner’s daughter, and both sides of my family came from the hills of West Virginia.  I recently did some work and found out something interesting on my dad’s side of the family.  Not only was my dad the first person to graduate from high school, but he was also the first person in the family tree to even attend high school.

Haley has it much better than I did; that is a simple statement of fact.  And that is the way it should be, right?  Uneducated “sons of the soil” have been transformed into competent (and excellent) teachers and coaches who can actually help her instead of hindering her athletic and intellectual development.

My point is a simple one.  I was discouraged by a bunch of people who passed themselves off as authority figures. I now know these people had no idea what they were talking about.  On the other hand, Haley gets to compete for a state championship as a freshman in high school.  She will have every opportunity to attend a first-rate university and pursue her tennis career and any academic course of study that she wants to.  The expectation level was raised for her.  Perhaps more importantly, she isn’t being taught and coached by ignorant “sons of the soil,” as I was.  If they ever call and ask, I can assure the people at Harvard that I have done my best to meet my obligations as a graduate.  I’ll just tell them that my niece is going to the state tennis tournament as a freshman; they will infer the rest.

 

 

 

 

Colin Powell

I have long admired Colin Powell. I always wanted him to run for President of the United States. I wasn’t too concerned about his stance on specific issues; I knew he was a measured, intelligent man of great integrity, and that was enough for me. I was surprised and saddened to hear that he has passed away due to complications from Covid-19.

In June of 1993, Powell gave the keynote commencement speech at Harvard’s graduation ceremony. I don’t remember much about his address; I do remember the number of people who stood with their backs to him as he talked. The protesters held on to pink balloons to protest the military’s “Don’t ask, Don’t Tell” policy. The protesters did not shout him down; they let him speak. They got their message across without ruining the proceedings for everyone else. All the graduates and their guests appreciated that.

This post is not about Powell’s speech or the protesters. As I sat in my folding chair, in my academic regalia, surrounded by people getting all types of different degrees, I looked over the people on the dais. Many were there to get honorary degrees; some were there to speak. I saw General Powell talking to a woman sitting to his right. The next time I looked up, they were still talking. So it went during the entire ceremony. It took me a few moments to figure out who that woman was. I looked down at my program and realized who the mystery woman was. She was there to get a well-deserved honorary doctorate.

One thing that I love about Harvard is that it brings together people of such varying backgrounds. I never would have imagined that Colin Powell and this mystery woman would be able to hold a conversation and enjoy each other’s company for hours. It surprised me.

After I thought about it for a bit, I realized they would have lots to talk about. After all, we all like to eat, don’t we? Who is the mystery woman? I found a picture of them together at the graduation ceremony. Get ready to smile as you take a look at two buddies, General Colin Powell and Julia Child, taking in the festivities.

As I recall, they both looked like that every time I glanced up at the stage. June 10th, 1993, was quite a day. I will never forget watching the two of them interact during the ceremony. I hope they were swapping recipes; at least in my mind, that is precisely what they were doing.

 

Watching Tennis

Why would anyone care about how I watch a tennis match? That is an excellent question. That is about all I can say. I have no idea what the answer is. Of course, I hope that others might gain some insight into the game by reading about how I watch tennis matches on TV.

First of all, I rarely watch the ball. My head is not going back and forth like it is on a swivel. When the match starts, I am focused on one player; can you guess which one? Am I watching the server or the returner?

When the match starts, my eyes are fixed on the person returning serve. I want to know if the returner has a good sense of where the serve is going. I have watched matches where the returner leans the wrong way on nearly every serve. This implies that they are being fooled by something in their opponent’s service motion or toss. I have also seen matches where the returner can anticipate the direction of every serve.

A lot can be learned by watching the returner. After the return of serve goes over the net, I follow the feet of the returner. I am looking to see how light the player is on their feet. I am also looking to see if there is anything unusual in the player’s grips. Is there a lot of movement necessary for the player to change grips from forehand to backhand? This is important because the ball travels so fast in today’s game that many skilled players can take advantage of their opponent’s extreme grips. If you can make your opponent rush, you have an advantage. Roger Federer is the best I have ever seen at taking time away from his opponent. If a player can do this, they are at a decided advantage.

The next thing I look for in the returner is their ability to change direction quickly. There are lots of players on both tours that do not like to move forward. Coming to the net is not something that many modern players enjoy doing. Nearly all players camp out at the baseline in the modern game. That said, I spend lots of time analyzing the player’s movement from left to right. That first step is crucial when changing directions. It also can give insight into how well the player is anticipating their opponent’s shot selection.

One of my favorite tennis players of all time is Miloslav Mecir. He was a pro’s pro. He got up to number 4 in the world before a back injury necessitated his retirement at 26. He was an elegant player who never defeated an opponent by hitting them off the court. He used his brains and ability to place the ball wherever he wanted to win Olympic gold in 1988. He reached at least the semifinals of all 4 grand slam tournaments. He was light on his feet, and he was the best I have ever seen at getting pulled off the court and recovering. He was exceptionally quick. He was so much fun to watch; in fact, I believe that he was the most-watched player by other professionals. He could win tennis matches with his head alone.

After I watch the returner, I will move on to the server. Suppose the returner is having trouble determining the direction of the serve. In that case, I will try to figure out what the server is doing to create all the ruckus. I will watch closely to see if I can figure out where the serve is going to go. Of course, the angle isn’t the best, but I can usually see a thing or two. There is only so much to be learned if I can not see with the eyes of the returner, a view TV broadcasts do not show.

The same goes for a returner who is not fooled. I will try to figure out if the server is telegraphing their serve. The best story of a server letting their opponent know where the serve was going was told by Andre Agassi. He let the world know that Boris Becker, one of the greatest servers who ever lived, let Agassi know where the serve was going by unconsciously sticking out his tongue to the left or right. As you can guess, the direction of the tongue foretold the direction of the serve. Amazing, isn’t it? After I heard that, I was surprised that Becker’s camp never noticed what Becker was doing with his tongue.

What comes next? That is easy; I want to know how comfortable each player is with changing direction with their groundstrokes. I have noticed that the lesser ranked players have more trouble taking a cross-court shot and going down the line with the ball. And if they go down the line, especially on the backhand side, the shot is not near the sideline. They leave the ball in a place where it can easily be reached by their opponent. The top players tend to punish the ball with their down-the-line shots. They are much more assertive with their stroke and a lot more confident in the thought process behind it. Lesser ranked players create angles for their opponent to exploit when their down-the-line shots do not penetrate the court as much as they had hoped.

I will focus only on one player when the ball is in play, for example, during a long rally. I am watching their feet. Are they getting in the proper position to strike the ball? Are they taking that one extra step instead of lunging at the ball? Some professional players, especially the taller ones, have difficulty getting their feet to do what they want. Intelligent opponents take advantage of this.

The last thing I want to know is if either player is running around their backhand. In the men’s game, most players do. There are a couple of things I am looking at when this happens. Is the player simply running around their backhand to protect it because it is such a weak shot (Steve Johnson, I am looking at you), or are they hitting good, penetrating forehands. With most male players, the big forehand (and the crushing serve) got them on the pro tour.

One final thought on running around the backhand. In my estimation, the ability to hit the forehand “inside in” instead of “inside out” is a difference-maker. For a player to hit “inside in,” which is down the line instead of cross-court, indicates a very high skill level. Not all professional players attempt such shots, especially the lower-ranked ones.

I will be writing more about tennis, especially the mathematical, Game Theory approach to the game. I am also working on an essay about how to size up an opponent you have never played. Lots of tennis stuff coming shortly, including a piece about my niece, a freshman in high school who just qualified for the state tennis tournament.

Even More Collatz

You know, the reason we have so much trouble trying to prove The Collatz Conjecture suggests to me that it might not be true.
Buford Lister, personal communication

How many posts can I write based on something as simple as The Collatz Conjecture?  Apparently, at least one more.  If you are unfamiliar with it, all you have to do is take any positive integer you want and if it is even, divide it by two.  If it is odd, multiply it by three and then add one.  In 1937, Lothar Collatz, a man who haunts my dreams, conjectured that any positive integer you can think of will meander its way back to one when you apply that rudimentary algorithm.  It is a very simply stated problem.  As I sit here today, no one knows how to prove the conjecture, and no one has found a counterexample.

People have often asked me if there is a prize for proving The Collatz Conjecture.  Until recently, the answer was no; all you could hope for is mathematical immortality.  I was surprised to hear that Bakuage, a Japanese web services company, has offered 120,000,000 Yen to anyone who can prove the “truth” of the conjecture.  To me, that means that a counterexample will get you the prize of about 1.1 million U.S. dollars.

I know that people worldwide are committing computer power to find any elusive number that defies Collatz.  Now that there is money on the table, it wouldn’t surprise me if a counterexample is found relatively soon, that is, if one exists.

 

Three Lists

People like to rank things.  Who are the top ten basketball players who ever lived?  Which rock group is the greatest?  Or how about the greatest pitcher or the best soccer player?  You get the picture.  This post is about three of my personal lists: my favorite actor, comedian, and drummer.

I just finished watching HBO’s The Wire for the third time, and it still holds up; it did not fall from my number one all-time ranking for television dramas.  Why number one? Excellent writing, stellar production, and the acting of the great Michael K. Williams.  Not only is Williams my favorite actor, but he also made Omar Little into one of the greatest characters in the history of television dramas.  With all due respect to Tony Soprano and Walter White, I would argue the Omar Little is number one on the most interesting and most nuanced list of fictional characters.

Every great show starts with excellent writing.  Without that, it doesn’t matter how accomplished the cast is; the show is doomed.  Conversely, a great actor can take the script and transcend the words on the page.  That is what Micheal K. Williams did with Omar.  He brought a sensibility to the character that elevated the written word to extraordinary levels.  He was also brilliant as Albert “Chalky” White on Board Empire, another of my all-time favorite shows.

Now we move on to my next list, favorite comedian.  This one is easy; Norm Macdonald always makes me laugh.  He can tell the same joke over and over, and I will laugh.  I can watch his appearance on Conan with Courtney Thorne-Smith five times a day and laugh so hard that I cry each time I click on the YouTube link.  And don’t get me started on his “moth joke,” will the laughter never end?

Macdonald had a role in one of my favorite shows.  He played Pigeon in Mike Tyson Mysteries, a hilarious show that ran from 2014-2020 on Adult Swim.  In case you haven’t seen it (and I am nearly 100% sure you haven’t),  the show consisted of Mike Tyson driving around in a van solving mysteries.  His “mystery team” consisted of his adopted daughter (an Asian woman left on his doorstep), a ghost, and a drunken, lustful, depraved, and sarcastic pigeon played by Macdonald.  I don’t recall them solving many mysteries; the show usually ended in chaos with unresolved cliffhangers.  I laughed my way through 70 episodes.  I am still sad that the show was canceled.

I recently wrote about the great Charlie Watts, my favorite drummer.  There is nothing more I can say about him.  He was as brilliant a musician as Williams was an actor or Macdonald a comedian.

It didn’t dawn on me until I sat down to write.  I was working on separate posts about Williams and his role as Omar in The Wire and Macdonald’s appearance with Courtney Thorne-Smith, a short video I consider to be the funniest thing I have ever seen.  It hit me when I cycled through a couple of my open Word documents.  I mean, really?  All three?  All so close together?

I consider the early death of Mozart to be the greatest cosmic ripoff in history.  He was only 35 when he was taken, and he was ready to fly.  He would have moved music into untold magical and unexpected directions.  Sure, Charlie Watts got to live a full life, but Wiliams and Macdonald were taken far too soon.  Whenever an artist is taken prematurely, I think of Mozart.  I think about how the world instantly became a lesser place when he passed.  Today, I feel bad for all of us; the world is a little less fascinating, a little less brilliant, than it was a few short days ago.  And that makes me more than a little sad.

An Unusual Unit of Measurement

About 35 years ago, I went for a run in Boston.  Sure, I ran a lot back then, but this day was special.  I started at my Somerville apartment, made my way to Harvard’s campus, turned left, and ran along the Charles River until I arrived at MIT.  There is a bridge there that spans the Charles and connects to Boston.  It is officially known as the Harvard Bridge.  Unofficially, well, that is a different story.

My run that day was a long one.  I ran through downtown Boston to the ocean and then made my way back up the river, turned right at Harvard, and then back home.  I ran for 15 miles or so.

I am writing about that day because of what I saw on the sidewalk of the Harvard Bridge.  As I ran across the bridge toward Boston, I kept noticing spray-painted messages on the sidewalk.

…10 SMOOTS…20 SMOOTS…30 SMOOTS…

When I reached the end I saw this:

It was clear to me that the bridge had been measured in an unusual unit.  I had a pretty good idea what happened but confirming my suspicion wasn’t easy in the mid-1980s.  The computer was of little value as Google was a distant dream.  I had to bide my time.

I eventually found out that the Harvard Bridge had been set upon in 1958 by a group of MIT fraternity boys.  Of course, they positioned Oliver R. Smoot, MIT class of 1962, on the ground and measured the bridge in 5’7″ increments.  I had guessed that something like this happened.  What I didn’t know is that the Harvard Bridge is known to locals as the Smoots Bridge.

It is my understanding that even the police use the Smoot unit to identify coordinates on the bridge.   The Smoot has become so accepted that a large grant was awarded to replace lights on the bridge under the condition that they are placed at Smoot-friendly units, not those standardized things that the code called for.  And, yes, the grant was accepted, and the lights are a Smoot or two apart.

If you feel inspired, you can go to Google Calculator and get any distance you want converted to Smoots.  If you need to know how many Smoots it is from Cleveland, Ohio to Cleveland, Mississippi, have at it.  The Smoot has become an accepted unit (cough, cough), at least in some places.

Of course, this is nothing more than a fun little tale.  MIT still makes a big deal out of the Smoot unit, as well they should.  Students at MIT repaint the numbers twice a year to make sure the sacred markings are preserved.  Oliver R. Smoot returns to campus for parades and celebrations.  The aspect of this story that makes me shake my head is not the bridge itself; it is the career of Oliver R. Smoot.  He went on to become chairman of the American National Standards Institute’s Board of Directors.  Those people concern themselves with standardized units of measure.  Smoot is unique in history as the only person to enforce the good practice of standardized units of measure while also being one himself.  And that is truly remarkable.