Quin Houff is Causing Problems!

Quin Houff is Causing Problems!

This is a short post about the relationship between practice times and average green flag speeds for drivers in The NASCAR Cup Series.  The question is: Do practice times translate to the race?  Can you predict how fast a car will be during the race based on 10 lap practice averages?  And finally, if there appears to be a correlation, is it statistically valid?

On March 1, 2020, the Auto Club 400 was held in Fontana, California.  30 cars took at least 10 practice laps, below is a Stem and Leaf Plot of those speeds.

163  6
164
165
166
167
168
169  8
170
170  6
171  04
171  55
172  1244
172   788
173  11
176  556677888999
174  1
174
175  3

At the very top of the plot (representing the slowest speed) is Quin Houff at 163.6 mph.  Below is a Box Plot of the same data.  Notice the circle way off to the left.  Once again, our friend Quin Houff insists on being apart from the group.  What does that mean?  He was slow, very slow, problematically slow, and, most importantly, statistically slow. More on that in a bit…

 

 

Now that the preliminaries are out of the way, we can get to it.  Perhaps the easiest and, coincidentally, the most powerful way to see if practice times translate to race speed is through linear regression.  The figure below shows the relationship between 10 lap practice speed and average green flag race speed.  The data shows that about 82% of the average green flag race speed can be explained as a function of 10 lap practice speed.  Not bad, not bad at all.  This analysis suggests that there is a pretty strong predictive relationship between practice speeds and how fast a driver’s car will be in the race.

 

 

As you study the above figure, can you guess who the blue diamond in the lower left-hand corner represents?  You guessed it, our good friend Quin Houff.  I included the Stem and Leaf Plot and the Box Plot earlier for a specific reason.  Both figures suggest that Houff’s data should be eliminated from the study because he was so much slower than all the other drivers.  This is a common practice in Exploratory Data Analysis, the area of statistics I was trained in.  So, in that spirit, I have included another regression analysis.  This one ignores Houff and his statistically irrelevant car.

 

 

I have to admit, this surprised me.  When Houff’s times are eliminated, the explanatory value of the model goes way down.  Now the 10 lap practice averages only explain about 57% of the variability found in the green flag speeds.  Very curious.

So, where do we stand?  Are 10 lap practice averages predictive of race performance?  Clearly, more data is needed, data from lots more races.  Once all that is gathered up, the numbers would have to be broken down by type of track.  My guess is that the relationship would not be the same for short tracks and superspeedways, nor would there necessarily be a correlation between flat tracks and those with high banks.  And, of course, we would have to break the data down by the type of package being run by NASCAR at the time.

In this post, I didn’t intend to answer any big questions, I only wanted to offer a path toward better understanding.  It would be quite a job to gather all the necessary information and do a suitable study.  But, adequately armed, I do believe a useful answer to the question could be achieved.  I know some people who would be very interested in that information…for recreational purposes only.  :-)

 

NOTES:

On October 18, 2019, I published an essay called 1:59:40.2.  That post has more information about linear regression and how it can be used.  I also write about the discovery of regression analysis and the fight for who deserved credit for developing one of the most powerful statistical tools known.

If you are unfamiliar with Stem and Leaf Plots, I talk about them in my post from 2/21/20 entitled An Average Tennis Essay.

 

The Athena Chapters: Chapter Zero

Random Thoughts from a Nonlinear Mind, Volume 2: The Athena Chapters, Chapter Zero:
The Zeroth Chapter of this Book

 

“Excuse me, isn’t that supposed to be a negative one (-1) in line 16?”
Phillip “The Yeti” Frank

 

*****

 

An anxious and fresh-faced Buford Lister sat at the center of the head table.  The rows of seats before him formed an asymmetrical pattern, skewing sharply to his left.  He looked at the nameplate in front of his chair to double-check he was sitting in the right place.  Sure enough, it said, “Buford Lister” in faded black marker.

Buford Lister rolled his head around and back.  The big clock on the sidewall read 12:12. OK, talk starts in 18 minutes.  He was an East Coast boy on his first trip out west, the unfamiliar surroundings putting him slightly on edge.  He couldn’t sleep on the overnight flight, so he read a biography of Einstein that The Plumber had given him.  Now son, it is always good to learn more about the giants upon whose shoulders you are standing.  Never a morning person, the time change, coupled with the lack of sleep, wasn’t doing him any favors.

The hall was already about half full, quickly filling with the sounds of footsteps and idle chatter.  The glances consistently came Buford Lister’s way, they were the looks that young people like him get at places like this;  stares of intense jealousy, some of constrained hatred, and a few of admiration.  This, after all, was not just a talk.  It was a coronation.

The heavyweights, the established scientists, came sauntering in at their own pace; that is what silverbacks do.  Buford Lister watched the procession, it was a who’s who of all-star academics, mostly balding white males.  Even though it was loosely organized, he recognized it as The March of The Gatekeepers.

He was only slightly nervous even though he had never given a presentation like this before.  It’s not that he was unprepared; he had been over the paper a thousand times, his academic advisers tearing it apart and then building it back up.  Subtle, nuanced questions asked and answered in the same spirit they were given.  No worries, the problem was solved.

The buzz in the hall was growing.  Buford Lister ran his routine down in his head one last time.  Always start off with a joke.  Always.  He had memorized the entire presentation, all except for the funny.  He glanced down at the yellow legal pad in front of him as he let out a giant yawn.  This is exactly what he had written in his notes (by that I mean what follows is a verbatim account of what appeared in his own handwriting):

Once upon a time, there was this horse.  Now, let me tell you this was no ordinary horse.  No siree, what we have here is a mathematical horse.  This horse actually knew arithmetic.  He could add and subtract with ease.  Impressive?  You bet.  Algebra, you ask?  No problem what…so…ever.  Heck, this animal could even prove The Pythagorean Theorem in unusual and unexpected ways.  This was one heck of a horse!  But let me tell you… if you tried…and people did…if you tried to teach this horse analytic geometry, he would get up on his hind legs and scream bloody murder.  Oh, the tales that have been told about this animal.  He would kick and violently thrust his head from side to side at the first mention of anything, and I mean anything, to do with analytic geometry.

Well, ladies and gentlemen, the moral of the story is simply this.  [Pregnant Pause] You can’t put Descartes before the horse.

[…wait for uncontrollable applause and laughter to die down…then get to work]

 

*****

 

Why am I starting this volume with a Chapter Zero?  That is an excellent question.  I will try to give you an answer, at least a preliminary one, in this chapter.  You will have to wait until you get to the end of the last essay for the full explanation.  At least I hope that by the time any reader works their way through the entire book, they will look back at this essay and have a good idea of why I decided to add a Chapter Zero after I had finished writing several chapters.  I certainly didn’t plan it this way, that is just the way things worked out.

 

*****

 

It was 12:32 when Sandy “The Plumber” Wilkins stood up to introduce his protege, his latest pride and joy.  The Plumber had been awarded a Fields Medal (a very big deal for mathematicians) twenty years ago to the day of this conference.  He hadn’t disappointed.  He had done major, innovative work since then; perhaps most importantly, he was currently mentoring a young genius named Buford Lister.  This was to be a crowning achievement for both of them.  The Plumber was a special guy, he wasn’t a person who was jealous of his students who were smarter than him (lots of people in his position are), he simply nudged them and then got out of their way.  He was a man who understood that his place in history wouldn’t be evaluated based only on his accomplishments, it would be measured by the contributions to humanity made by his students.  He rarely talked about him, but he greatly admired a British physicist named Fowler.  That guy had mentored many future Noble Laureates as well as dozens of prominent scientists.  That, The Plumber always thought, was a meaningful legacy.

The Plumber was not a blue blood, he wasn’t the offspring of academic royalty.  Any advantages he got while growing up were those that he had earned himself.  When he was young, The Plumber worked in the family business during the summers, hence the nickname.  Some privileged students at Harvard had started calling him The Plumber when he was an undergrad.  He embraced the name, he was proud of the fact he wasn’t where he was because he was born to a rich daddy.  He always had trouble understanding why the other guys thought they were better than him simply because of who their parents were.  He found that curious, more than a little weird.  If he was at Harvard, it had to be based on ability alone, his family didn’t know anyone able to pull any strings on his behalf.  Why would anyone look down on a person like that?

Whenever his house or the houses of his friends needed plumbing work, he would gladly do it, but he spent most of his time being one of the most famous mathematicians in the world.  After this short talk, he knew that Buford Lister was going to happily share his newfound fame with him.

The Plumber waited for the applause to subside, and then he got to it.  He told the audience that no one, not even him, was able to solve the problem they all were going to hear about today.  He gave a short history of the famous people who had tried and failed to unmask this cosmic mystery.  The rise in intensity during the build-up was palpable.  He reminded the audience that many brilliant people in that very room had worked on this problem and had failed.  Some made a little progress, but ultimately they all came up against it; that stout, impenetrable, mathematical wall.  The Plumber was fond of saying that people ran out of talent right at the moment they needed it most.  All, that is, except one.

The introduction was brief; the applause that followed was loud, too loud to be just polite.  Buford Lister began his short talk (no one had any idea how short) about the problem and how he came to his solution.  He started off by telling the audience that Sandy often spoke of things that were “well known.”  Something “well known” was an assumption about the nature of the universe that was, apparently,  generally accepted as legitimate and valid.

Buford Lister began to move around the podium.  He didn’t need the mic, he became so energized that the boom in his voice meant that the people standing in the back would have no trouble hearing him.  Besides, the mathematics sloppily written on the blackboard spoke louder than he ever could.  He got so excited as the energy in the room started to rise that he forgot to tell the joke.

 

*****

 

Sometimes people view daily occurrences as trivial, routine events that actually turn out to have a deep, essential meaning.  I think that happens more than we all realize.  There are probably things in your own day to day life that you view as unimportant, which really are profound if you took the time (as if you have the time) to think about it.  This certainly is true in my case.  Much of this book can be understood in terms of things once viewed as trivial that turned out to be of critical importance.  Here is a fine example…

Over a decade ago, a lifelong friend of mine named Mobe (you will hear much more about him later) innocently handed me a CD he had purchased a few weeks earlier.  He hadn’t bought any new music in a long time, but he was compelled to get this particular disc.  He had heard one of the songs on the radio and liked it a lot.   As it turned out, uh, I kind of liked it, too.

I am not the type of person who dabbles in things.  When I get interested in something, I tend to do my due diligence.  I learn as much as I can about the topic, be it dark matter, string theory, British Literature, or a punk band who made a CD that I thought was really good.  As you might imagine, I bought everything this group had done.  I still have that pile of CDs in my house.  I ripped the music for my portable devices, and I (sigh, sigh, sigh) started going to their concerts.  I had no idea that by handing me that CD, Mobe was putting me on a life-changing path.  How was I to know that around ten years down the road, I would walk into the dingiest concert venue imaginable as one person and walk out as another?  How could I even imagine that hearing that music would start a chain of events that ultimately would change me in a most fundamental way?  The easy answer is that I couldn’t.

This Chapter Zero nonsense is, at least on the surface,  about heat and the way it is measured.  Slightly underneath the surface, within the subtext, is an in-depth discussion about how seemingly trivial things can change lives.  I am the first to admit that Athena generated quite a bit of heat the night I met her, but, inexplicably, this essay is not explicitly about the night we met.  The thing is, this essay is a little different than those to follow.  The subsequent essays detail what happened to me when she introduced herself; this one is a bit more mysterious in structure and content.

 

*****

 

The young and suddenly energetic Buford Lister was feeling it, Mathematical Mojo emanating out of every pore.   As he started his presentation, he actually began strutting (Ladies and gentlemen, I am proud to introduce to you The Mathematical Mick Jagger).

“I always wondered what that meant…for something to be well known.  At first, I suspected that someone, maybe decades ago, had run the proof and confirmed the mathematics of whatever argument it was that Sandy was talking about on a given day.  Then I reached that critical point in the life of any scientist; I had an intense realization that just because something was in a textbook didn’t mean that is was right, true, or even meaningful on anything other than a superficial level.  I realized that nearly everything I believed, at least the important things, I believed simply because someone told me the ideas represented an accurate reflection of reality.  This, of course, is standard fare for all non-scientists in the world.  I don’t know anyone out there in the real world who knows anything worth knowing that they weren’t told is true by someone passing themselves off as an authority figure.  Self-perpetuating nonsense, generation after generation; no one questioning the validity of the ideas, everyone just wanting to fit in.  I decided that day to break free of socially constructed knowledge; at that very moment, I made the decision to reduce all my knowledge to mathematics.  We are here today so that I can talk about what I found.”

Buford Lister went on to tell the audience that the conjecture had been confirmed.  The proof was to be found in the lines of mathematics.  Buford Lister declined to go through the proof, that would have taken way too long.  “The proof has been vetted.  It is correct.”

 

*****

 

In 1931 something very interesting and more than a little strange happened.  OK, I am sure lots of noteworthy things happened in 1931, but I am speaking of one thing in particular.  During that year, a British physicist named Sir Ralph Howard Fowler (Sir Ralph to you and me) came up with an intriguing insight.  His discovery created a problem concerning the standardized numbering systems that scientists like to use.  Sir Ralph discovered an essential relationship between thermal systems that appeared so trivial to those who came before him that they thought it not worth mentioning.

I am not going to talk about the exact nature of the discovery.  It is irrelevant.  And besides, if I did nearly everyone reading this would stop and move on to the next thing on their list of things to read.  If you want to know more then you can Google the Zeroth Law of Thermodynamics, trust me, you can learn all you ever wanted to know.  I am interested in just a couple things when it comes to this Zeroth Law.  The first thing is what it is.

The Zeroth Law says something like this:  If A = B and B = C, then A = C.  Well, duh!  That is what everyone thought before Fowler came along.  Could anything be more obvious?  All the scientists working on thermal systems passed this little nugget over when it came to naming and numbering the universal laws of thermodynamics.  Originally there were three of them called, believe it or not: The First Law of Thermodynamics, The Second Law of Thermodynamics, and The Third Law of Thermodynamics.  After the three laws had been documented, Fowler came along and said something like, “Uh, excuse me but there is a problem.”  And there was.

It seems that trivial little relationship between A, B, and C is critically important when it comes to deriving the mathematics of the previously mentioned three laws.  Also, it is fundamentally important if you want a mathematical definition of temperature that can relate the concept of heat to what a person sees when they read a thermometer.   This created a bit of a problem.  There were already three laws in place, and the one that everyone passed over, the trivial one that everyone ignored, turned out to be fundamental to the whole enterprise.  With Fowler’s insight, that little relationship instantly became the most fundamental law of thermodynamics.

The problem then became one of what to do.  Science has some very specific rules when it comes to naming things.  Scientists spend a lot of time and energy putting things into different categories, it is a big part of what many of them do.  Physicists have a particular problem when it comes to naming and categorizing things like laws.  The most important one always comes first, that is just the way it is.  The problem here is that the three laws already in existence were very well established.  Everyone knew them by those names and numbers.  Fowler came up with just about the only solution possible, he named his insight Law Zero.  With one publication, the world was introduced to The Zeroth Law of Thermodynamics.  I remember scratching my head when I first was introduced to the Zeroth Law decades ago.  I knew there had to be a story behind it, and sure enough, there is.  I think it is a fascinating one.

 

*****

 

Out of nowhere, it happened, the beginning of Buford Lister’s waking nightmare.  A huge man in a Grateful Dead tee shirt stood up.  He wasn’t from a major university, it wasn’t even clear that he had an academic appointment anywhere.  No one on the podium seemed to recognize him, and this was a guy you wouldn’t forget.  The man, nearly seven feet tall with shocking white hair down to his waist and a beard to match, rose and said the infamous words that ruined more than a couple reputations and destroyed the promising career of Buford Lister.  “Excuse me, isn’t that supposed to be a negative one in line 16?”  It was quite the spectacle to witness him wildly gesticulate as he made the sign of a -1 in the air with his right index finger.

Buford Lister laughed, as did the entire audience.  The hall held 1500, every seat was taken, and the people standing along the back wall added another couple hundred to the total.  Over the laughter, another voice from way off to the left said, “Yes, I see it.  That should be a -1, not a 1.”

Buford Lister felt a rush of anxiety as he put his head down to look over his copy of the paper, the same paper he had read thousands of times.  It can’t be…no…it can’t be.  He, along with everyone else there, knew that a mistake on page one would negate the entire proof.  Time seemed to stop as he considered what was going to happen if that tiny number 1 was really supposed to be a -1.  He looked the first page over hard, looked over at The Plumber, looked back at the stranger, and then said: “I have no idea how this happened, it appears you are correct.”

The Plumber, one of the experts who had vetted the paper, dropped his head into his hands as people began to walk out.  The other people at the head table started mumbling to themselves as they got up to leave.  All left their seats except for one, Buford Lister sat paralyzed in his chair, his eyes glued to lines one through sixteen.  This can’t be happening.  How can this be?  How did this happen?

Author’s Note (you will occasionally get these throughout this volume): Rarely does an entire career, an entire life, get derailed in a singular moment like this.  Most times, things like this are the result of slow, smoldering implosions.  Buford Lister knew there would be no second chances, he had embarrassed the people who believed in him most.  He instantly realized that things would never be the same.  He was right, at that very moment (blah, blah, blah negative one, negative one) life as he had known it was over.

 

*****

 

I love the tale of The Zeroth Law of Thermodynamics.  It is not the science that won my affection, it is the story behind the law’s discovery and how it got its name.  Fowler’s brilliant insight created some pretty cool problems, don’t you think?  My little flash, while much more elusive and undoubtedly not brilliant, has also created its own set of issues.   I will leave it to each and every individual reading this book to reach their own conclusions on the matter.  All I know is I was standing against a wall in a dive bar drinking a beer (and, I might add – minding my own damn business) when I saw a chick; that constitutes the simple beginning of my story.  The moment she introduced herself things, and by that, I mean each and every one of them, were permanently and fundamentally altered.

How about a Breaking Bad style flash-forward?  If you are anything like the people who read this book before it was published, there is a very good chance that, at some point as you are reading along, you are going to view this collection of essays as some kind of bizarre and tragic love story.  Do me a favor, if you ever feel like you are reading a book that is simply about a hopeless guy’s attempt to get a pathetic lunch date from a beautiful punk rocker chick I want you to refer back to this chapter.  The Zeroth Chapter of this book, like every other chapter, is included for a specific purpose.  The major reason I am including this essay is because I think there is much more to my story than an empty stomach and an intense attraction.

My situation, even though it also lead to the inclusion of a number zero, is unlike Sir Ralph’s in many ways.  He had rock-solid mathematics and logic to back up his claims.  He actually convinced all the other scientists that there needed to be a Zeroth Law of Thermodynamics.  Can you imagine?  That is a huge deal.  I, on the other hand, have no such proof to offer as evidence of my dramatic and mind-numbing discovery.  All I can do is try to string sentences together in a somewhat meaningful way.  By doing this, I hope to convince Athena that something magical happened on the night we met.  The invitations to join me on my quest have already been sent.  No RSVP required.

 

*****

 

Scientists are a tough bunch.  Forgiveness is not something in their vocabulary.  One mistake, especially one like this, and you are done.  No one will ever recommend you for a job, that is if they even give you your degree and send you on your way.  After episodes like this, lots of places hand the poor slob a master’s degree and tell him not to let the door hit his butt on the way out.  At least that is what they usually did back in the day that Buford Lister made his grand mistake.

Like everyone else, he was given only one chance to lose his reputation.  Once it was gone, there was no getting it back.  There was no appeals process, no redemption; the only viable option was oblivion.  Go now and live out your life in total obscurity, that was The Plumber’s implied message as he sent Buford Lister on his way.  The two of them never spoke again.

As best as anyone could figure, this is what happened: copies had been sent out across the country by a student on work-study, mimeographed copies.  The paper was 84 pages of dense formulas, that meant that just a few copies were sent out in the mail.  The people who got their copies made mimeographs of their own.  And on and on and on.  By the time the bulk of the people got their copies, they were reading a faded version of the original.  The Yeti had picked up a near-pristine copy from a table outside the lecture hall.  Apparently, so did the other guy who quickly caught the simple mistake.  Not many smudges on their prints, marks that people might assume are a minus sign and such.

As for The Plumber and Buford Lister, well…they both wanted the paper to be correct; so much so that they simply missed it.  In their defense, the first page was basic background information; it consisted of high school algebra.  A departmental secretary had typed out those pages, and maybe she made a mistake.  A smudge here got interpreted as a minus sign there.  That is just a guess.  The fact is, no one really knows.

The sections in the paper that were really important, the stuff that constituted a breakthrough, were logically tight.  The passages that were going to make history had been vetted and were correct.  The problem was that the sections that were going to alter the foundation of the natural, the physical, and the social sciences all needed that number on line sixteen to be a negative one, not a positive one.

 

*****

 

The next essay you are going to read is one very special to me.  I started writing it the night I met Athena.  I was in a haze the entire time.  It has been many years since then, and I am the first to admit that my vision is still cloudy.

Chapters One through Fourteen are much different than this one.  You will see how I changed my mind over and over as I thought about what meeting Athena ultimately means to me.  Each chapter is a snapshot of what I was thinking at the time.  Each reveals my struggle to figure out why she has had such a tremendous impact on me.  I came up with a bunch of ideas, you will read about them.  I guess the best way to put it is to say that you are going to learn about my struggle to make sense of the most important night of my life.

 

*****

 

The lecture hall where The Lister Affair took place had been completely renovated decades ago.   The blackboards were all gone, replaced by whiteboards and projection screens.  A small, circular vent that lecturers had used to hide chalk was gone, in its place was mounted a panel to relay the remote control wishes of the wizard du jour. 

The changes, though, weren’t quite enough.  To those sensitive to these types of things, that space still reeked of doom and confusion.  The demons brought to life so long ago were still in their prime, lurking in the ceiling corners and in the aisles where they patiently waited their opportunity to pounce.

Those ethereal creatures cared very little that the coast was unusually cold on the big day, the day of another coming-out party of a young superstar.   A guest lecturer, a young assistant professor from a major Midwest university, was invited to give a talk about his latest research project.  Scientists from all around the world were there.

The old man sat in the back of the lecture hall and fidgeted in his chair.  These things make me so damn uncomfortable.  He knew that the audience members were going to be watching him as much as they would be The Hotshot, the latest in a long line of prodigies to strut through the gates of the university.  Nothing he could do about that.

The Hotshot started with the flash of insight that got him on the right path.  He looked directly at the old man and said, “Sir, I was reading through one of your papers for what must have been the 100th time when I paused to take a sip of my warm beer.  I nearly choked because I could feel something, an ambiguous flash.  I didn’t quite know what it was, but I had a sense that it was important.  I went for a walk.  After I finished, I jumped in the shower, and it was right when the water hit me that I realized the answer to this dilemma.  I understood why the path that you took was the wrong one.  I knew I had to zig where you had zagged.”

The old man thought back to when he was as young and arrogant as The Hotshot.  He remembered the sleepless nights, the little flashes of insight, and the occasional big ones.  His mind wandered; he didn’t have to listen to this; he knew his own research better than The Hotshot did.  Hell, he knew that little shit’s research better than the little shit himself did.  He had been through it again and again, looking for that one small mistake, the one oversight that would lead him to throw the manuscript in the garbage.  He never found it.

He watched as The Hotshot droned on and on about how uninspired all the attempts to work out the problem were until he, a divine gift from the cosmos, was sent to grace humanity with his special kind of genius.  It is a simple fact of human nature that sometimes the only way a person can feel better about themselves is by making other people feel worse.  The Hotshot was already feeling good, but he was taking more than a little joy (schadenfreude, right?) in the demise of the old man.

The math was becoming tighter the longer The Hotshot went on.  The old man wondered how he could have missed it, how he did not see the solution.  I was so close, I was right there time and time again.  All of it, every last hour of work…meaningless.  He tugged on his long gray beard and wondered what kind of prize he would get for living a wasted life.  Deep down, he knew he would get what everyone else in his circumstance gets, nothing more than an empty plate of remorse.

Author’s Note: There are rare times when atheists pray.  It is not what you think.  It is usually not when they are in dire straights, and they believe they are about to die.  No, the times that nonbelievers desperately appeal to a higher authority are times like these.

This is what he did: The old man closed his eyes and hoped and wished that someone from the back of the room would stand up and say, “Shouldn’t that be a negative one in line such and such?”  His prayer, while totally sincere, went unanswered.

After the bows and the obligatory curtain calls, the old man limped his way up to The Hotshot; there were so many things he wanted to tell him, none of it relevant right at that moment.  He cleared his throat and extended his hand. “You, young man, have solved a problem I have spent a lifetime trying to solve.  Thank you.”   A quick glance away, and Buford Lister was off.  Thunderous applause (you wouldn’t believe how loud) followed him out.  It never occurred to Buford Lister, the man whose face was often mistaken for a tattered road map, that the applause was for him.

 

The Athena Chapters: Preface & Introduction

Random Thoughts from a Nonlinear Mind, Volume 2: The Athena Chapters Preface

 

Do you have any idea what a Preface is as opposed to an Introduction?  I have read thousands of books, and I must admit that I was not clear on the distinction, so I hit my favorite search engine (Google) and got to work.  For the last few hours, I have been doing some research, and I have learned a few interesting things about the difference between a Preface and an Introduction.  Apparently, in the Preface, I am supposed to tell you how the book came about and why you should read it.  At least, that is what most everyone knowledgeable about these types of things seems to agree on.  I am going to start there.

It is really very simple, I wrote this book because I was compelled to.  Over five years ago, I went to a punk rock concert that changed my life.  There I met a woman I am calling Athena.  I still shake my head whenever I think of her.  Every night (and I mean every single night) I wake up at 3 or 4 in the morning and stare at the ceiling.  I keep asking myself the same question over and over: “OK genius, what was that all about?” My answer varies depending on my mood that day.

As it turns out, the day after I met her, I decided to make it my mission to see if I could get this incredible lady to go to lunch with me.  That is pretty much it.  Deep down, I wanted to see if my head would pop off the next time I saw her.  Of course, there is much more to the story than that, the chapters in this volume give the details.

I started writing these essays because a singer in a punk band changed my life with one evening of conversation.  The transformation was instantaneous, it took me no time to realize that something highly unusual was happening to me.  As it turned out, meeting her was the most fascinating, life-altering experience I have ever had.   That, briefly, is how this book came about.  She said, “I’m Athena,” and I went home and gazed at my blinking computer screen for years.  Nothing unusual about that, is there?

The next thing a Preface is supposed to do is give the potential reader a reason to keep turning the pages.  So, why should you read this book?  I do have a couple reasons.

I have gotten in the habit of asking people to go home and write about their significant others.  I tell them I will patiently sit while I wait for them to give me a rough draft.  Of course, being the nice guy that I am, I let them know I would be more than happy to edit anything they come up with.  I usually ask them to do this after they launch into intense criticism of me for wasting my valuable time by writing this book.  By asking them to write, I am trying to get them to understand how difficult a thing it is to do.  Go ahead, give it a try.  Start typing and try to come up with something interesting to say about your husband, wife, or partner.  Make it something intriguing enough that you would be willing to share it with the world.  While you are at it, make it unique.  Try your best to come up with something exciting and unexpected; tell us all something we do not know.

If you give that last paragraph a little thought, you will see that it is nearly impossible to do something like that.  At least no one has taken me up on my challenge.  Not a single person has come up with anything at all to say.  Not a single one.

So, why should you read this book?  For starters, this collection of essays is not about my wife or the mother of my children.   I have never been married, and I have no kids.  This collection of essays is simply about what happened to me when I met a chick with a guitar.

How many women have ever inspired a book to be written after a single meeting with them?  We all know the answer, right?  Not many.  How about people in general?  How many people in the history of the written word have ever inspired a person who met them one time to sit down and spend years in front of a keyboard?  My guess is that number is not very large either.

The fact that someone, especially me, wrote a book about their experience of meeting a person once is reason enough to give the first couple chapters a read.  If you find them interesting, and I hope you will, then the rest of the book should go down smoothly.

 

Random Thoughts from a Nonlinear Mind, Volume 2: The Athena Chapters Introduction

 

This collection of essays is about a dude that went to a rock show and met a chick.  I have done quite a bit of research on the topic of people meeting each other at concerts, and it appears I am obligated to refer to all such individuals as dudes and chicks.  I can’t just say that a man met a woman at a show and go from there.  Apparently, I am obligated to adjust my seat, kick off my vans, and pull my pork pie hat down real low before I can tell the story of what happened when a dude met a chick unlike anyone he has ever known.

The only other thing you need to know before you tackle the next three chapters (huh, three?) is that in the spring of 2011, a rip in the space-time fabric of the universe was detected in a dive bar located somewhere in the Midwest.  At that moment, the dude, ever so sensitive to the quantum structure of reality, became unstuck in time.  The chick, ever so cool, bounced.  What follows is simply an elaborate attempt by the dude to get the chick to meet him for lunch.  No kidding.

That is the original introduction that I wrote over two years ago.  Initially, I wrote three essays about the woman I am calling Athena (not her real name).  Things quickly got out of hand as the ideas for new chapters just kept coming and coming.  In about two years, I wrote all the following essays about meeting Athena.  Well, to be honest, this volume is not really about her; each essay is about what happened to me after she introduced herself.

Clearly, this situation is the most remarkable and extraordinary thing that has ever happened to me.  I really hope that remains true, I don’t know if I could stand anything more unusual than the stories you are about to read.

I hope you experience a sense of kinship while seeing me vacillate between patience and frustration; I hope you are compelled as I write of my battle between hope and hopelessness; I hope you can feel at least a little sympathy as I struggle within myself between “give her some more time” and “I don’t have time for this.” I hope you find yourself rooting for me to get my elusive lunch date with a woman who totally stunned me with two little words.  As you are about to find out, she said, “I’m Athena,” and I was forever changed.

“Write drunk, edit sober.”

“Write drunk, edit sober.”
Ernest Hemingway never said this.

“If you are going to do a Mathematical Deep Think, it is best that you be sober…and around 22 years old.”
Buford Lister (personal communication)

I am not that big a fan of Ernest Hemingway or his writing.  That said, there are a couple of quotes attributed to him that keep coming up in my day to day life.  The first is the title of this post.  There is no evidence that he ever said it or that he endorsed such a thing.  Apparently, he wrote in the early morning when he was stone sober.  As for the second quote, well… let’s say that string of letters is just as problematic.  We can start with a little quiz.

Who was it who said the following?

“There is nothing to writing. All you do is sit down at a typewriter and bleed.” 

Most people that I know attribute that quote to Hemingway, the problem is that it is not apparent that it belongs to him.  I did some searching, and it appears that many people said similar things, but it is not clear if Hemingway ever said it at all.  So, who should we attribute the quote to?

Red Smith was one of the finest sports columnists we have ever seen.  He was so good that he was awarded a Pulitzer Prize for commentary in 1976.  When asked how difficult it was to churn out a daily column, Smith replied that is wasn’t hard at all.  He said:

“You simply sit down at the typewriter, open your veins, and bleed.” 

That might be the origin of the quote.  I guess people attributed it to Hemingway because it sounds like something he should have said.  It’s always about what makes for the best story, right?

Paul Gallico, the author of The Poseidon Adventure, a movie I just watched the other day, wrote this in 1946:

It is only when you open your veins and bleed onto the page a little that you establish contact with your reader.

Smith’s quote is probably a few years older than Gallico’s.  I guess it really doesn’t matter who we attribute the quote to, it is the sentiment that is important.  So, what exactly does it mean to sit down at a keyboard and bleed?  I have a few thoughts on that.

In my recent past, I have come across many young people who want to be writers.  I always tell them the same thing. “If you want to be a writer, you have to know how to write.  More importantly, you need to have something to say.” As for the bleeding part, I let them in on that a little later.  If they prove that they are serious, that they really are willing to sit down at a keyboard for hours a day, I tell them that every writer must decide how much of themselves they are willing to reveal to their readers.  If they are ready to totally expose their inner being, then they are on the cusp of opening a vein over their keyboard.

Sitting down and bleeding means (at least to me) that you are writing with such depth and feeling that the reader can’t help but be impacted by the words.  Such a thing is much easier for musicians, all they have to do is switch to a minor key, and they can evoke emotion.  It is not nearly that easy for a writer, there aren’t any special keys to press on our keyboards that can instantly conjure a specific mood.  It is much harder than that.

If you sit down at a computer with the express intention of exposing your inner being to the world at large, then you are bound to bleed.  The bloodletting can be barely noticeable, or you may need to keep a supply of reasonably priced keyboards in your closet.  That is the decision any serious writer needs to make.

There is one aspect of this topic that I find fascinating, I am curious about what compels a person to do such a thing.   The implicit question is: How can a writer possibly be inspired to such an extent that they feel it is necessary to sit and bleed.  For me, that is the interesting part.

Sitting at a keyboard and bleeding is not an everyday occurrence.  Nor is it reasonable to expect such a thing from a writer.  It seems unnatural and unnecessary; after all, most of today’s best selling authors write uninteresting genre fiction.  The only bleeding they do will be the result of things like paper cuts.

Typing and bleeding is a very tough thing to do, I know…I have done it.  I do not think you have seen it yet in these posts, but that is about to change.  I will be posting one or two chapters a week from a book I wrote over the course of many years called Random Thoughts From A Nonlinear Mind, Volume 2: The Athena Chapters.  That fancy little tale is about…well,  you’ll find out soon enough.

 

 

 

An Average Tennis Essay

An Average Tennis Essay

This post is about Rahul and his tired right arm.  One night, not long ago, he couldn’t sleep.  At around 5:00 a.m., he got up and decided to head down to the tennis courts to hit some serves.  He got all his electronic equipment together (speed gun, camera, etc.) and fired up his 1959 Ford Edsel.  He hit 88 serves before his arm started to hurt.

So, that is our setup.  We have 88 data points to work with.  All we have to do is find the average speed of the serves he hit, and then we are done.  I can tell you that the average was 95.8 mph.  Thank you for dropping by my blog.  Stop back in a couple days for another exciting and informative post!

Wait…you know that I wouldn’t be writing about the average speed of tennis serves unless I had something interesting to say.  Take a look at this Stem and Leaf Plot:

               8   44455
               8   666677
               8   8888999999
               9  0000000000111111
               9  2222223
               9   4
               9
               9   88999
              10  0000111111
              10  2222223333333
              10   44445555
              10   6677
              10   888

I imagine most people have seen these before.  It is my understanding that most kids in elementary school get exposed to this handy tool.  Between you and me, I didn’t see these until I took a Ph.D. course in statistics.  This type of display wasn’t invented until the 1970s, and it took time for their use to become widely adopted.

For those of you new to this type of figure, they are pretty simple to explain.  If you look at the top line of the plot, you see “8  44455.”  The 8 is the stem, and 44455 forms the leaf.  This means that the serve speeds were 84,84,84,85,85.  Do you see how that works?  That is about all there is to it.  The bottom line reads “10  888.”  This means that Rahul hit three serves at 108 mph.

A Stem and Leaf Plot is a very nice way to visualize a data set.  Making a picture or some type of image is always helpful when dealing with large batches of numbers.  The visual representation of data is a hallmark of Exploratory Data Analysis, an approach to statistics that I heavily endorse.  After all, it is much easier to study a picture than it is a large table or string of numbers.

Whenever I am tasked with analyzing data, I first turn to the Stem and Leaf Plot.  Look at the plot carefully, and you will see why.  I said earlier that the average speed of Rahul’s serves was 95.8 mph.  Do you see the two peaks on the plot?  Are there any serves that were hit 95 or 96 mph?  The answer is no; he didn’t hit any serves that speed, so how can an average of 95.8 be representative of the data?  The short answer is it isn’t, the longer answer is coming up.

Any data set with two peaks, like this one, must be broken into two separate batches.  Instead of averaging the speed of Rahul’s serves, we need to look more closely at the data to see what might be going on.  It is apparent to me that Rahul was practicing both his first and second serve.  The first serves were the speedy ones.  The slower serves were his second serves; in those instances, he was more concerned with spin than speed.

Here is the proper Stem and Leaf Plot for the second serves.  The data has only one peak, and the average speed is now 89.13 mph.  This makes more sense, doesn’t it?  Just by looking at the plot, I would guess that the average should be around 90 mph.

               8   44455
               8   666677
               8   8888999999
               9  0000000000111111
               9  2222223
               9   4

As for the first serves, this is what we end up with.  The average speed works out to 102.7 mph.  That seems about right when looking at the plot.

               9   88999
              10  0000111111
              10  2222223333333
              10   44445555
              10   6677
              10   888

Once again, calculating averages is not as simple and straightforward as it seems it should be. If you ever need to find the average of a set of numbers, I suggest you first make a Stem and Leaf Plot.  That way, you will know if it is proper to treat the numbers as a set or if they need to be broken apart.

One last thought, I know Rahul, and there is no way he hits any of his serves that hard.  My guess is the entire data set is in kph, not mph, but that is a story for another post.

How About Some Tennis Math?

How About Some Tennis Math?

I have been thinking a lot about probability, especially the probabilistic nature of tennis. Why have I been on a probability kick lately? It certainly is a tricky and slippery subject, perhaps the hardest I have ever studied, and I guess I am just trying to keep on top of my game. Hey, you never know when a Golem or a Centaur might show up at my door with a life or death riddle based somehow on probability theory. I guess I just want to be prepared for any contingency.
tt
To begin, I will assume that everyone has a rudimentary knowledge of the game of tennis. I hope you all realize that the server has an advantage, especially as the players get better. As a general rule, this is more true for men than for women, particularly in the professional ranks. The server starts every point, and they know where the serve is going while the receiver has a minimal window of time to figure out the trajectory of the ball. With that in mind, let’s imagine the following scenario. A server wins 60% of their service points against a particular opponent. That means that the returner wins 40% of those points. We can ask and answer a series of questions based only on this information. Let’s get to it. For reasons that will become clear later, we will begin with a game that is already at deuce.

We will start our analysis with a player that wins 60% of all their service points against a random player. Once the game reaches deuce, the probability that the server will win the next two points is .6 x .6 = .36. That means that the server will win the next two points a little over 1/3 of the time, 36% to be exact. What about the receiver winning the next two points to break serve? That would be .4 x .4 = .16. So, 16% of the time the receiver will break serve by winning two points in a row. What is left? The only other possibility is a return to deuce. There are a couple ways we can figure this. We know that all possibilities have to add up to 1 so we can simply solve the following equation:

1- .36 – .16 = .48.

Therefore, 48% of the time the service game will return to deuce. The other way to arrive at that figure is with the following:

.6 x .4 + .4 x .6 = .48.

If you take a minute to study that short equation, you will quickly realize why it makes sense.
tt

Now, this gets a little tricky. With the game at deuce, what is the probability that the server will eventually win the service game? Well, they can win by winning the first two points after the first deuce, which they do at a rate of 36%. The other thing that can happen is that the game can return to deuce, which will happen 48% of the time before the server goes on to win. Therefore we end up with this equation: P = .36 +.48P. Solving for p gives an answer of .692. We now know that the server will win 69.2% of all of their service games against this opponent once the score has reached deuce.
rr
Notice that this player has a 60% rate of winning individual service points but ends up with a 69.2% success rate when it comes to holding their serve during a service game that has reached deuce. That is pretty interesting, maybe even a little unexpected.
dd
We can now break down other probabilities based on how this player does against other opponents. The first category considered is 50% of service points won. Anything less, i.e., a success rate of less than 50%, and this type of analysis is not very useful. I think we can all agree that the player’s time is better spent on improving their serve than it is doing math. For all other players that are somewhat proficient at serving, the results are as follows.

 

50% of points won on serve
Server will win the next 2 points 25% of the time.
Returner will win the next 2 points 25% of the time.
Game returns to deuce 50% of the time. Server wins 50% of service games that have reached deuce.

 

60% of points won on serve

Server will win the next 2 points 36% of the time.

Returner will win the next 2 points 16% of the time.

Game returns to deuce 48% of the time. Server wins 69% of service games that have reached deuce.

 

67% of points won on serve

Server will win the next 2 points 44.9% of the time.

Returner will win the next 2 points 10.9% of the time.

Game returns to deuce 44.2% of the time. Server wins 80.5% of service games that have reached deuce.

 

70% of points won on serve

Server will win the next 2 points 49% of the time.

Returner will win the next 2 points 9% of the time.

Game returns to deuce 42% of the time. Server wins 84.5% of service games that have reached deuce.

 

75% of points won on serve

Server will win the next 2 points 56.3% of the time.

Returner will win the next 2 points 6.3% of the time.

The game returns to deuce 37.4% of the time. Server wins 89.9% of service games that have reached deuce.

 

80% of points won on serve

Server will win the next 2 points 64% of the time.

Returner will win the next 2 points 4% of the time.

Game returns to deuce 32% of the time. Server wins 94.1% of service games that have reached deuce.

 

90% of points won on serve

Server will win the next 2 points 81% of the time.

Returner will win the next 2 points 1% of the time.

Game returns to deuce 18% of the time. Server wins 98.7% of service games that have reached deuce.

 

So, why did we start our analysis with a game that was already at deuce? That is an interesting question. We began there because the math gets a little out of hand if we start at the beginning of a player’s service game. I guess I was just trying to get everyone loose and nimble. Now that we have done our warm-up and taken off our old school polyester tops, it is time to really get down to business. Don’t worry; if the math makes your head spin, you can move on to the table. There is no crime in that.
ss
The probability that a tennis player holds serve (P) is equal to the probability that he holds at love (P @ love) plus the probability that they hold at 15 (P @ 15) plus the probability they hold at 30 (P @ 30) plus the probability they hold when the game goes to deuce or multiple deuces (P @ D(s)). Got it? That makes perfect sense, doesn’t it?

Now consider the following:

The probability that the player holds at love = p4

The probability that the player holds at 15 = 4p4 (1-p)

The probability that the player holds at 30 = 10p4 (1-p)

The probability that the player holds in a game that goes to deuce is much more complicated. The equation looks like this:

20p^{3}\left ( 1-p \right )^{3}D\; where\; D=\frac{P^{2}}{1-2p\left ( 1-p \right )}

When the algebra is worked out, we end up with this equation:

\frac{20p^{5}\left (1-p \right )^{3}}{1-2p\left ( 1-p \right )}

Whew, that was a bit of work. The good news is that we can now determine how often a given player will hold serve based on the percentage of time they will win a service point. The following table contains relevant data for select service point percentages. As you can see, it also includes lots of other information. The mathematics behind the rest of the table becomes a little mind-bending, so I have decided not to add them here. You will just have to trust that the assumptions are logically based on the probability (P) that a given player will win a single service point. The rest of the table is built on that mathematical base. You will also note that I have also included the expected outcome of various matches between players serving at different rates of success.

 

serve pts hold serve tiebreak tiebreak set adv set 3 set match 5 set match
PLAYER A 80.00% 97.80% 52.10% 52.80% 54.80% 54.20% 55.20%
PLAYER B 79.00% 97.40% 47.90% 47.20% 45.20% 45.80% 44.80%
serve pts hold serve tiebreak tiebreak set adv set 3 set match 5 set match
PLAYER A 80.00% 97.80% 59.80% 63.90% 71.00% 70.30% 74.70%
PLAYER B 75.00% 94.90% 40.20% 36.10% 29.00% 29.70% 25.30%
serve pts hold serve tiebreak tiebreak set adv set 3 set match 5 set match
PLAYER A 75.00% 94.90% 51.90% 52.90% 54.00% 54.40% 55.50%
PLAYER B 74.00% 94.10% 48.10% 47.10% 46.00% 45.60% 44.50%
serve pts hold serve tiebreak tiebreak set adv set 3 set match 5 set match
PLAYER A 74.00% 94.10% 51.80% 53.00% 53.90% 54.40% 55.50%
PLAYER B 73.00% 93.20% 48.20% 47.00% 46.10% 45.60% 44.50%
serve pts hold serve tiebreak tiebreak set adv set 3 set match 5 set match
PLAYER A 70.00% 90.10% 51.70% 53.10% 53.70% 54.70% 55.80%
PLAYER B 69.00% 88.80% 48.30% 46.90% 46.30% 45.30% 44.20%
serve pts hold serve tiebreak tiebreak set adv set 3 set match 5 set match
PLAYER A 70.00% 90.10% 55.20% 59.40% 60.80% 63.90% 67.20%
PLAYER B 67.00% 86.10% 44.80% 40.60% 39.20% 36.10% 32.80%
serve pts hold serve tiebreak tiebreak set adv set 3 set match 5 set match
PLAYER A 70.00% 90.10% 58.50% 65.60% 67.50% 72.60% 77.30%
PLAYER B 65.00% 83.00% 41.50% 34.40% 32.50% 27.40% 22.70%
serve pts hold serve tiebreak tiebreak set adv set 3 set match 5 set match
PLAYER A 70.00% 90.10% 66.30% 79.50% 81.40% 89.10% 93.80%
PLAYER B 60.00% 73.60% 33.70% 20.50% 18.60% 10.90% 6.20%
serve pts hold serve tiebreak tiebreak set adv set 3 set match 5 set match
PLAYER A 67.00% 86.10% 53.40% 56.50% 57.20% 59.70% 62.00%
PLAYER B 65.00% 83.00% 46.60% 43.50% 42.80% 40.30% 38.00%
serve pts hold serve tiebreak tiebreak set adv set 3 set match 5 set match
PLAYER A 65.00% 83.00% 51.70% 53.30% 53.60% 54.90% 56.20%
PLAYER B 64.00% 81.30% 48.30% 46.70% 46.40% 45.10% 43.80%
serve pts hold serve tiebreak tiebreak set adv set 3 set match 5 set match
PLAYER A 65.00% 83.00% 58.20% 66.30% 67.40% 73.70% 78.50%
PLAYER B 60.00% 73.60% 41.80% 33.70% 32.60% 26.30% 21.50%
serve pts hold serve tiebreak tiebreak set adv set 3 set match 5 set match
PLAYER A 62.00% 77.60% 51.60% 53.40% 53.60% 55.10% 56.30%
PLAYER B 61.00% 75.60% 48.40% 46.60% 46.40% 44.90% 43.70%

Take some time to study this table.  You will find that a 1% advantage in service points won translates into a much bigger chance of winning sets and matches.  The table is quite interesting and informative.  I will be posting many more essays on this topic in the future.  Stay tuned…

 

An Average Post…(harmonic, that is)

An Average Post…(harmonic, that is)

Sometimes I sits and thinks…and sometimes I just sits…
A.A.Milne

Sometimes I sits and thinks…and sometimes I sits and thinks about thinking…
Buford Lister, personal communication

I remember reading somewhere a long time ago, that what made humans unique in the animal world is that we can think about thinking.  Not only do we think, but we can take the process to the next level and analyze the thinking itself.  This is simply a guess, but I don’t believe any of the pets I have had during my life were capable of such a feat.  Actually, I am not sure that most…well, you get the idea.

Over the decades, I have thought a lot about how thinking about thinking works.  Back in the 80s, I tried, again and again, to sneak into a great course at Harvard.  It was called Thinking about Thinking, and it was taught by Alan Dershowitz, the famous lawyer, Robert Noczik, one of the leading philosophers from the last century, and Stephen Jay Gould, the evolutionary biologist who has influenced me in more ways than I would care to admit. There you have it, three superstar professors from different departments coming together to dazzle a bunch of impressionable minds.   The course was designed to show the students how different ways of thinking lead to different approaches to how we view the world and our place in it.  At least, that is how I looked at it.

That course was highly popular, and it was near impossible to get anywhere near the classroom.  When I was there, the course was taught in the Science Center, a building that resembles an old Polariod camera on its side.  There were guards checking registration slips at each entrance.  If you were a registered student and happened to forget your slip, you were out of luck, you missed that day’s class.  I often thought of trying to crawl through the heating ducts to get in there.  After a few minutes, I thought about my thinking and reconsidered, I thought better not to try it.

One day, I was sitting in the small cafe right inside the main entrance to the Science Center. Who do you think sat down near me?  It was the three professors.  I had no choice; I had to eavesdrop on their conversation.  I fell into a bit of a pattern, I made sure I arrived at the cafe around the same time on the days when the class was meeting.  I got to hear lots of conversations.  I can only recall one topic, it was the same topic the three of them talked about every week.  They talked about baseball, baseball, and then more baseball.

Why all this stuff about thinking about thinking, also known as meta-thinking?  Easy, we are going to talk about how to take averages, really simple averages.  How about this one: if Sally has 40 apples and Billy has 20 apples, what is the average number of apples that the kids have?  If I am writing a post about such a thing, you should immediately start doing some meta-thinking, right?  If it really was so straightforward, why would I be writing about it?  And that is a very good point, and of course, it is true.  I wouldn’t be writing about averages if I didn’t have something a little unusual and surprising to say about them.

The average of a and b are calculated in this familiar way:\large \frac{a+b}{2}

So, if Sally has 40 apples and Billy has 20 apples, the average number of apples = 30.  No problem.  The answer is simple and straightforward.  Now consider this:

Joe’s car gets 40 miles per gallon, and Steve’s gets 30 miles per gallon.  What are the average miles per gallon of the two vehicles?

\large \frac{30+40}{2}\neq 35\: MPG

And, no surprise, that answer is wrong.  Why? Let’s suppose that both Joe and Steve drive for 120 miles.  Joe would use 3 gallons of gas, and Steve would use 4 gallons.  Now, we can add everything up.  A total of 7 gallons of gas was used to travel 240 miles.  Therefore, the average is 34.28, and that is the correct answer.  34.28 is the harmonic mean or harmonic average, it is quite different from the simple averages we are used to calculating.

This is the equation for harmonic averages:

\large \left (\frac{\frac{1}{a}+\frac{1}{b}}{2} \right )^{-1}

That equation can be reduced to the following:

\large \frac{2}{\frac{1}{a}+\frac{1}{b}}

The important thing to think about is that you want to get a common denominator, not a common numerator.  That creates a lot of confusion when it comes to computing harmonic averages.

So, where do we now stand?  We all now know that some averages are more simple to compute than others.  As always, the trick is to know when to use a harmonic average instead of a simple one.  I will be posting more about this topic in the future.  Simple averages and harmonic averages are not alone in their “average” universe, check back in and you will see what I “mean.”

 

 

 

 

The Package

The Package

This is a piece of Flash Fiction.  The topic: A person arrives home to find a package on their doorstep.

Simeon Langdon felt an unnaturally cold chill as he unbuckled his radiation suit and removed his propulsion pack.  Damn, the hairs on my arms are standing on end.  Why are they doing that?  What is going on with me?  He touched the proper sequence of buttons on the control panel, and the pad lifted him to his apartment.

He instantly saw the package as the platform rotated and then locked into place.  Huh, I don’t remember ordering anything.  I wonder what it could be…  He picked up the box and opened his door.  He set it down, injected himself with an aqua fluid, and went to the mandatory decontamination chamber.  He tried to relax as the toxins were slowly removed from his body.

After about 20 minutes, he made his way out of the chamber and examined the box.  He found perfectly symmetrical block letters on all six sides.

BROCKTON LANGDON
256 JOHNSTON COMPLEX
TUSCON, REPUBLIC OF ARIZONA
(TO BE DELIVERED ON FRIDAY, AUGUST THIRTEENTH IN THE YEAR 2652)

 Simeon took a deep breath, followed by a long pause.  Brockton was his grandfather, and he had been dead for at least 50 years.  How is this possible? I didn’t live at this address, there wasn’t a Republic of Arizona when he was alive, how and why did I get this package?  He closely examined the box and the material used to seal it.  No return address, no other clues, nothing.

Simeon cautiously opened the package.  He jumped back as an orb floated up out of the box and settled near the ceiling.    A flash of energy engulfed the room, and then a hologram of his grandfather appeared.  Not the grandfather he knew, not the aged, mysterious figure who showed no emotion and kept to himself.  The hologram seemed to be the 20-year-old version of a man he barely recognized.

Out of the eyes of the hologram came a shot of laser light targeting the data port in Simeon’s left shoulder.  He was overwhelmed by the encoded information, all ones and zeros, the binary language of computers.  Simeon heard the words the data stream was speaking to him, but he couldn’t understand how and why.

“The Langdon family is directly descended from the beings who seeded this planet with life billions of years ago.  The DNA animating this planet is ours.  It was me, in consultation with The Superiors, who set the wheels in motion all those years ago to destroy much of the life on Earth.  It is now your job to eliminate what is left of it in North America.  Your cousins will take care of the rest.  You will initially fight and struggle within yourself, but you will do your ancestor’s bidding.  Moreover, after you fully understand, you will want to do it, you will be compelled to do it.  The orb will deliver the devices, all you have to do is deploy them.  You will know where to go, what to do, and when to do it.”

The hologram disappeared into the orb, and then the orb disappeared into Simeon.  It felt warm and energizing.  He smiled as he basked in the epiphany that revealed his life’s true purpose.  As it was, gentleness and compassion never were words in his lexicon.  He now felt emboldened, fully realized, complete.  He put his head down and started to analyze the Orb-driven algorithms running through his matrix, his concentration only momentarily broken by the faint screams of “HELP!” coming from the kidnapped women he had locked in his bedroom closet.

02.02.2020

02.02.2020

The First Rule of Palindrome Club: Name no one, man.
The Second Rule of Palindrome Club: See above.
Anonymous (personal communication)

Today is February 2, 2020.  Any idea what makes this day so special? Well, I just watched The Australian Open men’s final.  Novak Djokovic won…again.  It is just a matter of time before he and Raphael Nadal both pass Roger Federer for the most Grand Slam titles.  Can you still be the GOAT if you are third on that list?  I doubt it.

Today is also Groundhog Day.  I hear that Phil is about 50% correct with his shadowy predictions.  By the way, how do they tell if he really saw his shadow?  Does The Old Farmer’s Almanac offer instructions or some kind of insight into groundhog vision?

In a few hours, I hear that the Super Bowl will be televised.  I haven’t watched a football game since the Browns packed up and left Cleveland for Baltimore.  For me, that was the end.  Football no longer warrants any of my time or attention.

So, what is special about 02.02.2020?  I am sure that you have already figured it out.  That series of numbers form a palindrome.  Notice that is doesn’t matter what order you put the day or month in, you still are golden.  It is also a palindrome in ISO format.

Here are a few more interesting points about 02.02.2020.  That day is the 33rd day of the year (a palindrome), and there are 333 (a palindrome) days left in the year.  This particular confluence of circumstances will never happen again.

In a somewhat shocking and surprising (though totally predictable) turn of events, I am going to tell you something about mathematical palindromes that I find astonishing.  If I told you that any positive integer can be written as the sum of three palindrome numbers, would you believe me?  As incredible as it sounds, it is true.

Usually, I would go through the basics of the argument and then give a couple examples.  I can’t do that this time, the paper this idea is based on contains 40 pages of dense mathematics.  A number of algorithms are required to solve for any and every case.  In total, everything is quite complicated.  Instead, I suggest you click on this link.

On the website, you will find that all the math has been coded.  Just type in any number you can think of and the special numbers that form it will appear.

I have just one final thought as I get ready to head to the gym.  A person from Finland who deals in soap (a saippuakuppinippukauppias) has to be losing their mind today.

A Most Curious Text

A Most Curious Text

I have a bunch of relatives that live down South.  Many of them live in M i crooked letter crooked letter i crooked letter crooked letter i humpback humpback i. At least that is how I was taught to spell Mississippi by my cousin Christy when she was around 5 years old.

Christy’s sister Tammy is one of those Mississippians.  When she was young, she lived in Ohio, then moved to Mississippi.  She went to college in Georgia and…wait…what’s that?  Did I hear someone say “fascinating, tell me more :sarcmark: ” (If you don’t recognize that little squiggle, check out my post from 1/14/20 ).

Well, I am going through Tammy’s history because I am trying to figure out where and when she learned French.  Have I heard her speak French? No.  Did she write me an email in French? She didn’t do that either.  So, what evidence do I have that she knows French?  I offer the following text she sent after she read the last post, the one about the mathematical exploits of her uncle.

 

 

Do you notice anything about her text?  Anything unusual at all?  I did.  It appears to be written by a French person or someone who knows how the French like to punctuate their sentences.  See the extra space between “that” and the question mark?  That is the giveaway.  It is one of those things that strikes Americans as unusual.  It just doesn’t look right.

Speaking of punctuation that does not sit well, I have a friend who insists on punctuating her texts in the British style.  Any and all quotation marks are inside of all punctuation.  She does this even though I am reasonably sure she has not been further east than Ohio.  It is just one of those things.  That said, I do believe that Tammy’s text is unique in my experience, I can not recall ever getting a message with French punctuation.

So, I had to do some research to get to the bottom of this.  It didn’t take me long to discover that autocorrect has been known to add an extra space before punctuation.  In fact, I read that many people have noticed this and are not fans of this quirk.  I have never been a fan of autocorrect, it sometimes has a mind of its own and that intelligence doesn’t necessarily mesh with mine.

There is another possibility, the predictive text function that shows up when texting.  If you choose a word from the available selections, the program puts a space after it.  It requires a little extra work to get rid of it, and I stand with those who can’t be bothered by such nonsense.

This is the end of this short post about a text Tammy sent me.  Do I think that she knows French, or is the extra space a function of her texting app?  The fiction writer in me wants to believe that she is a spy, planted here by the French government at a very young age for some nefarious purpose.  The scientist in me…well, who cares what that guy thinks, the spy theory makes for a much better story.