Random Thoughts from a Nonlinear Mind

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.

A Special Kind of Consciousness

Come on, what have you got to lose?  The first stick is free.  Here, take it… Trust me, it is going to change your life.  You are going to love it.  One day you will thank me. Go on, go on…
A short conversation (that I happened to overhear) between a sketchy University Professor and a young, naïve mathematics graduate student.

I went to a 7^th rate school when I was an undergrad.  I used to tell people that it was a 5^th rate university until I started giving it some thought.  Right now, I am still inclined to provide the school with the benefit of the doubt.  Deep down, though, I know it is a 9^th rate institution…at best.

One of the hallmarks of a 9^th rate university is the faculty.  Schools like mine didn’t go out of their way to recruit recent Ivy League PhDs.  If my recollection is correct, if you had a pulse, they gave you a job.  And you didn’t necessarily have to be sober; sobriety, even during class, was nowhere to be found in the job description.  People think I am exaggerating, but I can assure you I am not.

I don’t understand why the university still exists.  There is nothing extraordinary about it; the entire campus could easily be folded into other large state schools in the surrounding area.  The students wouldn’t miss a beat.  Why such a strong attitude toward one of my alma maters?  Lots of reasons.  I choose the following story as an exemplar.

I had a philosophy professor explain consciousness to me back in the early 1980s.  I will never forget when he held up a piece of chalk and asked me what type of consciousness it had.  I didn’t think he had any evidence that chalk was self-aware, so I replied that the piece of chalk wasn’t capable of consciousness; therefore, it had none.  He immediately corrected me.  “No, no.  Chalk has chalk consciousness.  And you, by virtue of being human, have human consciousness.”  I thanked him, paid my tuition bill, and immediately registered for any classes he was offering the next session.  After all, where else was I going to get such insight?

Little did I know that one day in the far distant future, I would be writing an essay about chalk.  Thankfully, this post is not about chalk consciousness.  I haven’t gone that far off the rails yet.  Keep coming back, though; I might get there.

The type of chalk I am writing about is mathematical chalk.  Did you have any idea that there exists a brand of chalk that mathematicians claim is incapable of producing a false proof?  Did you know that the mathematical community was in crisis a few years ago when the manufacturer of this magic chalk went out of business?  And finally, would it surprise you to know that a handful of mathematicians went gangster and tried to buy up all available product so that they could sell at inflated street-level prices?

Those things did happen (sure, mathematicians are not prone to go full gangster, but you get my drift).  The chalk is Hagoromo, made by a Japanese company that, apparently, sold its soul to the mathematical gods.  If you happen to know a mathematician, ask them about Hagoromo chalk.  They might be willing to admit that they were a few sticks away from a Fields Medal when the vagaries of the Japanese economy conspired against them.

What an unusual and interesting topic.  There really was a thing called Hagoromo chalk, and top-flight mathematicians loved it.  There was a bit of a crisis when the company that made it went out of business.  And yes, if you search for that special brand of chalk, you will find it.  A Korean company came to the rescue of the mathematical community.  They bought the formula and are now producing a faithful re-creation of the greatest chalk in mathematical history.  Mathematicians have stopped hoarding and have returned to their daily responsibilities unhindered.  Between you and me, those people have an unnatural affinity for that chalk.  But then again…

Epilogue

I am not surprised that mathematicians have a favorite brand of chalk.  Back in my archaeology days, I used a Marshalltown trowel.  Why Marshalltown?  Because every archaeologist in the western hemisphere used Marshalltown.  It would not occur to anyone to use another brand.  It often came up that every archaeology student must purchase a Marshalltown trowel or go without.  Other brands were never considered.  Archaeologists loved their trowels so much, became so attached to them, that they would keep them until they were nothing more than a nub.  I knew many people who holstered their favorite Marahalltown long after it stopped resembling a useful digging implement.  It was a sort of badge of honor to have a trowel that wasn’t a trowel anymore.

I sat through a short lecture on the merits of the Marshalltown trowel.  My advisor at Harvard made it abundantly clear to me that trowels to an archaeologist were like bows to a violinist.  Mine, the one I used my entire career, is hanging up in my living room, next to my pith helmet and my obligatory Indiana Jones fedora.

Since I started this post, I have been thinking.  I wonder if there exists a magical fiction keyboard that only produces great stories.  I’ll make sure to let everyone know what I find.

 

 

A Tale of Two (Make that Three) Drummers

“Please, if you would be so kind.  I want to ask you a bit of an unusual question.  Why do you bother to get up in the morning after all you have seen and experienced?  I have known many people who have simply given up after seeing what their lives had become.  They are playing out the string, doing next to nothing as they wait for The Great Escape.  You, though, are different.  You seem as eager as ever to attack the world.  Why is that?”

Buford Lister paused.  He then took off the bandana that was wrapped around his head and slowly unwrapped it.  I must say that I was a bit confused by his actions.  I had no idea what was going on until he took the white, faded bandana and wiped the tears from his eyes.

“Scientists often say that language fails them when they try to discuss deep topics.  The people working in quantum physics are particularly guilty of this.  I believe that there are other realms of experience that can also be classified as equally problematic.  To be left speechless, to know that there is no formal way to express yourself, to know that no words exist to properly relate your experience, those are the situations I live for.  Of course, you can never know when you will be faced with such a dilemma.  These experiences come out of the ether to taunt us every once in a great while.  You are young, so maybe you have never experienced such a thing.  I have only come face to face with such emotions a couple times in my life.  That is the only reason I get up.  I know there is a chance I will be set upon by something beautiful, something unexplainable, perhaps sublime.  Even at my advanced age, I know I can be fundamentally changed by something I never considered.  That is why I get up.”

Buford Lister (this excerpt was taken from an unpublished interview by students from the Cultural Studies Department at Reederstock University four years ago).

*****

I have a favorite drummer, do you?  I have long thought that Charlie Watts was the perfect drummer for The Rolling Stones.  Along with Bill Wyman on bass, they formed the backbone for one of the greatest rock and roll bands we have ever seen.  They both played just enough to keep the beat and let the other members of the band shine.

Who was cooler than Watts?  Name someone, anyone, and I will take the side of Charlie, and you can argue the other side.  I will be happy to stand for Charlie, a man I always saw as a reluctant rock star.  He had a style and substance that is unusual for a rock and roll drummer; he played his instrument in an understated fashion, he kept time so the others could ascend to their musical heights.  He was the best.

I was surprised to hear that Charlie Watts passed on the other day.  I knew he was sick and that he would miss the Stones’ upcoming tour, but I, like most people, had no idea how sick he was.

Many of you might not know that Watts was a jazz musician at heart.  It seems pretty clear to me that he loved jazz more than rock and roll.  He formed jazz bands, and he would take them on tour.  My impression of him is that he was more at home playing jazz.  He was one of those rare people who mastered his instrument, and jazz might have challenged him a bit more than rock.  I am sure he found it more interesting.  What a fascinating man; I am sad that he is gone.

*****

Author’s Note:  Some years ago, I wrote a book of essays called The Athena Chapters.  The identity of Athena remains shrouded in mystery, and I will take the secret of her identity to my grave.  The night that I met her, I went to see another band, a group of traveling minstrels that were my favorite musical group for a long, long time.  She changed all of that.  The reasons for that band’s demotion are complicated and due entirely to her.  I guess I can’t listen to them anymore unless it is in terms of Athena, and I don’t like that.  I don’t need to be reminded of her; I have enough crap to deal with on a daily basis.

I include this lengthy “Author’s Note” because the driving force of the band that used to be my favorite was their bass player and drummer, my second favorite combo behind Watts and Wyman.  The two guys in the unnamed band were sublime.  One night, after a concert, I cornered the bass player and told him exactly what I thought of him.  As I remember, he wouldn’t let go of my hand.  He was genuinely happy with what I had to say.  He was immensely appreciative, and I sensed him getting emotional as I went on about his playing.  I remember him telling me that his bass coach told him that if he played correctly, no one would know that he played at all.  That was the essence of his sound.  He and the drummer were a perfect match.  Just like Watts and Wyman, they were born to play together.  As I turned to leave, one of the roadies rang up the drummer to tell him what I had said.  It was an excellent night.  I left feeling good about myself, after all, I had done a good deed, and I had been entirely truthful.

*****

For the last year or so, I have been following the drum battle between Dave Grohl, a 50ish white man living in Los Angeles, and Nandi Bushell, a mixed-race 11-year-old girl from England.  Of course, you should know who Grohl is, he is one of the most famous musicians alive.  He is a two-time inductee into The Rock and Roll Hall of Fame, once as a member of the seminal band Nirvana and again as the leader of Foo Fighters.  I have always admired Grohl; I have long thought he is one of the most interesting musicians alive.

As for Nandi, she is a badass rock star.  I still can’t believe what I have seen from that young lady.  This I know, Nandi and Grohl, by virtue of their unusual and unexpected relationship, have managed to spread love and joy across the world for the last year or so.  That is not hyperbole; search around on the internet if you are skeptical.

Their story has been well documented; even The New York Times did a piece on the relationship between the two unlikely rock stars.  Nandi, then 10, made a video challenging her hero, the mighty Dave Grohl, to a drum-off.  I urge you to search out the clips.  They offer nothing other than pure joy.  I am not sure I have ever seen anything like it.  She bashed the kit into oblivion, all the while keeping time like the human metronome that she is. Grohl never stood a chance.  Of course, he was forced to concede defeat.

A few days ago, I was surprised to see clips of a Foo Fighters concert showing up on YouTube.  They played at the LA Forum, and they ended the show with an appearance by a special guest.  Guess who showed up to blow the doors off the arena.  Go ahead, guess before you click the link.  Just a word of warning, some people might find a couple of words questionable, so I would consider the following clip NSFW.

 

 

I have long been a fan of Dave Grohl; I now declare myself a lifelong fan of Nandi Bushell.  She couldn’t have picked a better mentor.  I look forward with great interest to see what the future holds for both of them.  I must say, I am struck by the timing of this.  Shortly after my favorite drummer passes away, his replacement comes out of the ether in the form of a girl 70 years younger than him.  Truly astonishing.

In my more sentimental moments, I think that their relationship offers hope to all of us.  The world would be a better place if everyone could feel what I do when watching that clip.  And yes, I only wish I had the words to express what I truly feel.

Epilogue

I have written extensively about the hope my colleagues and I had for the burgeoning internet when I was at Harvard University in the 80s and early 90s.  Up until now, I have only commented on what a cesspool the entire enterprise has become.  As you know, you can easily find any form of hate and intolerance you want with just a few clicks.  I can’t help but think that the drum-off between Dave and Nandi was what we all had in mind when we thought about the possibilities for the internet.  The interaction between those two highlights the original promise of the internet.  Perhaps more importantly, it gives me real hope for the future.

Some News About The Collatz Conjecture

As many of you know, I spend a fair amount of time writing about and researching The Collatz Conjecture.  I have a computer running 24/7 whose only purpose is to find a counterexample to this insanely complex yet straightforward problem.  For those of you unfamiliar with the conjecture, it couldn’t be more simple.  Take any positive integer; if it is even, divide it by 2.  If it is odd, multiply it by 3 and then add 1.  In 1937, Lothar Collatz proposed that any positive integer subjected to this process would end up at 1.

No one has proven this conjecture, and young mathematicians are strongly encouraged not to work on it.  Many people believe the mathematics required to solve it has not yet been discovered.  It really is a curious, impenetrable problem.

I have written about the surprising progress the great mathematician Terry Tao made a couple of years ago on this topic.  He proved that the conjecture is true for nearly all numbers; if there are counterexamples, they are rare.  It truly is an astonishing piece of work.

This short post is about the loop that the numbers make at the end of the sequence.  If a number reaches 1, what happens next?  By rule, it turns into a 4, which turns into a 2, which becomes a 1.   And then, of course, the infinite 4-2-1 loop continues.

I came across a video the other day on the Veritasium channel.  They do outstanding work over there; we all should subscribe.  Watching the video, you will learn that the collective “we” has tested every number up through 2 raised to the 68^th power.  They all return to 1 via the 4-2-1 loop.  What came next shocked and discouraged me.  Mathematicians have concluded that if a loop other than 4-2-1 does exist, it must be larger than 186,000,000,000 numbers long.  Huh?  Well, all right then.

After playing that section of the video multiple times just to make sure I heard correctly, I decided that I am still going to build my own Raspberry Pi “Super Computer” to attack this problem.  If a novel loop is calculated, I doubt I will ever be able to spot it.  There is a chance, though, that I could still discover that elusive counterexample, and that would be very cool.  After all, mathematical immortality awaits the person who finds one of those vast numbers (if any really do exist).

NOTES:

I once heard someone explain what mathematical immortality really is.  He said that if you are a mathematical immortal, that means that one day (probably 500 years or so from now), a student will look up your name to include it in a research paper that only their professor will read.  Not bad, not bad at all…

Hayes

I have a few thoughts on getting older. I know, I know…we all are aging. Time and entropy have a stranglehold on life on Earth. I am concerned with what happens when the order turns to disarray and the imperceptible daily changes accelerate. I am interested when we look in the mirror and ask, “Who is that, and when did this happen?”

I knew an undergraduate student at Harvard named April. She was 19 when I met her. April was so pretty that she wore glasses she didn’t need. She told me she wore them to get some peace. Without them, she was constantly hit on by all shapes and sorts of humans. I saw her once without her glasses. I can still see her face. I must say, I understood her dilemma.

One day I asked April what she wanted to do when she got out of school. She immediately answered, “Chief Justice of the Supreme Court.” The thing about Harvard is you take people seriously when they say something like that. At my first Harvard graduation, Barack Obama was in the group to my right. I didn’t know him, I don’t ever recall meeting him, and my dad still can’t find the DVD he took of the ceremony. There is a good chance the future president shows up somewhere in the footage.

The people I knew there all had big, realistic ambitions. “Hey dude, what equation is going to be on your tombstone?” They would also ask how many inches The New York Times would dedicate to your obituary. You know, simple stuff like that.

I think at some point, most of the people there thought they were the next Einstein. Many of them had never met anyone as bright as they were until they arrived on campus. A small percentage looked around and said, “OK, I guess I have a chance. I don’t see any space aliens roaming around.” For others…their experience was totally different.

I heard a story about Bill Gates. I can’t remember where or when I heard it, but it goes like this. Gates was the most brilliant mathematician he knew when he arrived on campus. He was clearly smarter than anyone who took classes with him or attempted to teach him. After his arrival, it didn’t take him long to realize that he was the 7th or 8th best mathematician on the floor of his dorm. Don’t shed any tears for him; his life worked out just fine. His foundation is working hard to change the world, and it is succeeding.

Lately, I have been spending some time catching up with some people from my past. I have a few reasons for this, and, at this point, I will keep those motives to myself. Unfortunately, what I have found has generally been disheartening and disturbing.

So many of my cohorts and old friends have simply given up. Those dreams of the younger versions of themselves died a slow, painful death. They have fallen into a routine, and that is that. They are heading to retirement with as much enthusiasm and energy as they can muster. The bright, ambitious young people that I knew are nothing but figments, long-forgotten apparitions.

Their lives have been nothing but one compromise after another. They settled mainly because they were too tired to fight. The realization that they weren’t going to do anything extraordinary with their lives was a slow burn more than an unwelcome flash of insight. This is the way of the world. Nothing unusual here.

For reasons that aren’t entirely clear to me, I have not set my mace down. My armor remains polished. I will admit that the chainmail has sections with broken linkage, but it is still effective. While I know it is unlikely to be accurate, I keep telling people that I am delusional enough to think that my best days, my good old days, might still be ahead of me.

This brings me to a man I graduated high school with, a person I have not seen in 40 years. I found him online and sent him an email. I discovered that he is about to set out on an incredible adventure. He is selling all his stuff and moving nearly halfway around the world. I have always called him Hayes. I keep a top-secret list of my all-time favorite people, and yes, he is certainly included.

One day when we were in high school, Hayes mentioned his grandfather to me. I can’t remember the circumstance of how grandpa came up, but I never forgot what Hayes told me about him. “My grandfather lived until he died,” was all that Hayes said. In my mind, that meant that gramps disregarded all the doctors. He also didn’t listen to his relatives and friends. He woke up each morning and got the most out of that day; he damned the torpedoes and moved forward along the path he alone chose. I never met Hayes’ grandfather, but I have always admired him. It sure looks like Hayes inherited his spirit. Three cheers and a tiger for Hayes and his grandpa. I am inspired by their example, as we all should be.

In the last five years, I have twice faced down the maniacal entity that is death. I am not encouraged by what I saw. I am going to fight off the inevitable as long as I can. And, yes, at this point, I am growing increasingly concerned about the natural order of life on this planet. I have a lot of work to do, and I need more time to get it done. Know this, I am not going down without an epic battle; I am confident that inspiration from a man I never knew will steel my resolve. Just like Hayes’ grandfather, I have every intention to live until I die.

Epilogue: The story of Sang Ho Baek

A few months ago, a tragic story involving a 20-year-old pitcher on George Mason University’s baseball team made national news. Sang Ho Baek had elbow surgery and died from resulting complications. A traveling blood clot killed him. This circumstance is precisely what happened to me 5 years ago. I fell while running and shattered my elbow. Shortly after the surgery, I found myself in a field on my knees, having difficulty breathing. The clot had traveled to my heart and got shredded into dozens of clots that filled my lungs. I have no idea why I was spared while Sang Ho Baek was taken from us. I was lucky; he was not.

Of course, as the vagaries of luck would have it, the clots returned last year. This time they cut off 90% of the pathways to my lungs. Once again, I was fortunate to survive. Can they come back again? My doctors say no; the medication I am taking leaves them a virtual zero percent chance of returning. The issue I am facing is residual damage. I will have to wait a while longer to get that all sorted out.

Sang Ho Baek had a limitless future. I feel the need to honor him and all others taken far too soon. I still get a kick out of waking up every morning, and I vow to try my best to make every day count. My contribution to humanity is still to be made, and I am confident I will make it by tapping the keys on my keyboard. I may be misinformed, but by leaving behind a record of what it was like to be me, I hope to offer deeper insight to others about their lives and their place in the universe. After all, to do less would dishonor the memory of those who were never given a chance at a full, productive life.