Random Thoughts from a Nonlinear Mind

King of the Comma Splice

What is the most crucial factor if a person wishes to become a productive and successful writer?  Discipline? The fortitude to read lots and lots of books?  Education in the way of words?  Plenty of interesting and unusual life experiences? While all those things are important, I think there is another answer to the question.  Look no further than a competent and thoughtful editor.  Writing without an editor is very difficult, I know; I have never had one.  I have always had to edit everything myself.  That is, until recently…

I bought the Grammarly program a year or so ago.  It is fantastic.  It picks up many of the things I might miss while tapping away at the keys.  I will never write without it.  I wish I had it years ago; it would have made my life a lot easier.

Grammarly is a sophisticated program.  It asks for the style of writing you are striving for and then adjusts its comments accordingly.  And without it, I would never have known that I am the undisputed King of the Comma Splice.  After I finish the first draft of anything I am writing, and I tend to write very sloppy first drafts, I stop to read all of Grammarly’s suggestions.  The number one issue is always the comma splice.

A comma splice is a misuse of the comma.  The standard definition is that two independent clauses are improperly joined by a comma.  An independent clause is a group of words that can stand alone as their own sentence.  Here is an example:

Koala bears are not actually bears, they are marsupials.

I took this directly from the Grammarly website.  Of course, as soon as I typed it, my Grammarly program flagged it as a comma splice.  I like this example because I don’t see much wrong with the sentence.  It is the type of sentence I tend to write in first or second drafts.  The issue is that there is a consensus that the comma is not appropriate to use in this situation.  Grammarly always suggests that I replace it with a semicolon or split the sentence in two.

Here is another example from a couple of paragraphs ago:

I wish I had it years ago; it would have made my life a lot easier.

As soon as I typed that sentence, it was flagged.  The message was polite, more polite than my mental response.  Yes, of course, it is a comma splice.  Isn’t every sentence I write a comma splice?  As you can see, I chose a semicolon over splitting the sentence in two.  Nothing more than personal preference, nothing else to see here.  Let’s move along.

So, I have made it pretty clear that I know how to write with comma splices, and I also know how to edit my writing and fix them.  The title of this post says it all.  What you don’t know is that there is a Queen of the Comma Splice, and she writes far more of them than I could hope for.  The thing is, she leaves them in.  She does not take them out or massage her sentences in any meaningful way.  What is the big deal?  Well, millions of young people read her books, and she has tremendous influence over them.  Ostensibly, they are learning how to write while they are reading.  Her name is JK Rowling.  If you have been living on the moon, she wrote the Harry Potter books.

As I was researching the comma splice, I came across a bunch of angry and concerned English teachers. They have strong feelings about Rowling’s writing.  They are very upset at all the comma splices that can be found in her books.  Apparently, they number in the thousands.  I have never read her books, so I can’t speak to what may or may not be in there.  Other people, though, have gone through the texts and counted the comma splices.  I guess she really likes them.  I must admit I find it curious that she uses them.  I find it even more curious that her editor does not insist the sentences be changed.

There are instances where comma splices can be used to significant effect.  You can use such sentences to create specific moods if you are so inclined.  I think the type of mood being implied by a comma splice will get 10 different answers from 10 different writers.  I think most writers would just insert a semicolon and move on to the next paragraph.

In this post, we have learned that I am the King of the Comma Splice. Still, I must bend the knee to the undisputed Queen, the prolific and wealthy creator of Harry Potter and the world he inhabits.  It really is curious, isn’t it?  Maybe one day, she will ask to write a guest post on my blog explaining her position. We all know that is not going to happen, she will never make such an offer.  And yes, that last sentence is a comma splice.  I just can’t help myself.

 

 

Roman, Arabic, and…Cistercian?

 

We’ve all seen Roman Numerals.  For some reason, I was taught those letters at some point in grade school.  The odd thing is, none of my teachers ever taught me to add or subtract in that format.  How about multiplication or division?  If you ever tried it, you know that Roman Numerals do not lend themselves to such tasks.

The number system we use is typically called the Arabic System.  It includes a zero, and we can manipulate the numbers with ease. I’ll bet that it has never occurred to anyone reading this essay to try to do any math with Roman Numerals.  We can all agree that the approach we use is far superior.

During the Middle Ages, the Arabic System competed with Roman Numerals for dominance.  Roman Numerals are fine if you are writing dates or numbering the pages in a preface; other than that, they have little utility.

 

*****

 

Piper Pandora Pennington descended her attic room’s steps and landed outside the bedroom of her six-year-old sister, Susie.  She took a quick peek inside before she determined her next course of action.  She quickly decided that she needed to get to the kitchen for a bottled water and an apple before tackling the strange site in her sister’s room.

One quick trip later, Piper landed back at her sister’s door.

“Permission to enter, please.”

“Pi!.” Susie picked up Melvin, the stuffed octopus, and moved him side to side in a fit of excitement.

“Melvin, should we let Pi in?”

A muffled, poorly disguised voice said, “Sure, that sounds fine.”

At that moment, Dogzilla started a wrestling match with Pi’s left foot.  Before she could stop him, Dogzilla had removed her sock and was doing his best to eat it.

“Hey, stop that.  Dogzilla…No!”

He ignored her and kept at the sock.  He paused when Susie tapped her blackboard with a piece of chalk and announced, “Attention!  Attention!  Class come to order!”

Dogzilla, as if on cue, dropped the sock and sat down on the floor beside Melvin.  Piper found a place on the floor and waited with anticipation.

“Ok, class.  Today we will learn about a numbering system, and it’s not Roman Numerals or the Arabic one.   It is something different, and it is very cool.”

Piper got curious.  She knew nothing about another number system; she had never thought about it.  As she pondered this mystery, it occurred to her that Susie was capable of acting twenty years older than she actually was at times.  Most times, she was simply a six-year-old girl, but this was not one of them.

 

*****

 

During the Middle Ages, there was another, competing number system; a system few have ever heard of.  I just recently learned of its existence; it never came up when I was getting a graduate degree in the history of science at Harvard.  Nor did it turn up in any history of mathematics classes I have taken since I left Cambridge.  I was surprised when I recently came across The Cistercian System.  It is a bit odd and just as useless as Roman Numerals when it comes to manipulating numbers, but it has its charms.

 

*****

 

Susie took her piece of Hagoromo chalk and started drawing on the board.  Piper and Melvin sat at strict attention as Dogzilla sprinted to attack Susie’s foot.

“Ouch!  Dogzilla, stop it.  We can play in a little bit, but first, you need to hear this.”

Piper grabbed the furball and held him as Susie regained her composure.  Susie turned and drew a beautiful figure.

“That class…is 5863.”

Piper turned her head slightly to the left. “Really, little sis? I have never seen that before.”

“Yep, I saw it on a video, and I knew I better tell everyone.”

“Can you write out some more numbers?”

“Sure can Piper-o.”

Susie turned fully around in an attempt to disguise the drawing until it was done.  After a few moments, she turned and struck a pose.

“Ta-dah!”

“What is that one?” said Piper as she narrowed her eyes and concentrated.

“Mmmm…1234.”

“You mean one thousand two hundred and thirty-four?”

“Yep.”

As Piper studied the drawing,  she heard a buzz coming from the black box on Susie’s wall.  Karen, the girl’s stepmother, had hit the call button on the Raspberry Pi controlled intercom and said, “Susie, are you there?”

“Yep!”

“Susie, Mama Rose, and Papa Joey say they need your help with something.  They want you to go over there right now.”

Susie, feigning surprise, hit a dramatic pose, leaned in, pressed the button on the wall, and said, “Yep.”

Susie grabbed Melvin and ran into Piper’s arms. “Gotta go, sister-o.”

Piper kissed the top of her head and sent her on her way.  As she watched Susie and Melvin bound down the stairs, Pi was ambushed by Dogzilla, who was hiding under a dresser.  Piper picked him up and took the furball to her room, where they both were going to research this strange and mysterious Cistercian Number System.

 

*****

 

Who were The Cistercians?  You have probably heard of the Benedictine Monks; they are a well-known order of the Catholic Church.  The Cistercians are an offshoot of the Benedictines.  Basically, they thought that the Benedictines partied too much.  They weren’t quite aesthetic enough, or sufficiently fundamentalist, for the Cistercian’s tastes.  There are very few of them to be found nowadays, but they are not extinct.  Of course, they left behind this interesting and obscure numbering system.  Not a bad legacy.

 

*****

 

Piper placed Dogzilla on the floor.  She took a few chew toys off her desk and tossed them across the room.  She almost smiled as she watched Dogzilla attack the bone and rope.

“Alright, let’s get to work,” she said to no one.

She typed “Cistercian Numbering System” into Google and sat back as the results quickly populated her screen.

“Hmmm, I’ll be.  See that, Dogzilla?  There is such a thing.  Who knew?”

She looked at Dogzilla rolling on the floor with the rope, oblivious to the conversation she was trying to have with him.

“Well, I can see you are not going to be of much help.”

She read all there was to read about the numbering system.  Within about 30 seconds, she had a complete understanding of how it works.  It took her another second to dismiss the system as useless for her needs.  Still, she took a little more time to look at the construction of the numbers.  Really cool.

 

*****

 

The Cistercian System is best learned by studying examples of the numbers.  It is unnecessary to get into the mechanics of how the system works; there is not much to be discovered from that.  For instance, the system will not allow any number larger than 9999.  Like the Roman System, it makes no sense to try to add or subtract Cistercian Numbers.  About the only thing they are suitable for is numbering pages and writing dates.

I decided to write a post about these numbers because I was surprised to learn about them.  I don’t know how they have spent all this time eluding me.  I spent many years studying medieval science and mathematics, and I don’t understand how I missed this number system.  It doesn’t make any sense.

I will end this post with a few more examples of numbers written in Cistercian form.  Why?  Piper Pandora Pennington and her sister, Susie, are right.  These numbers look really cool.

                                    

     4892        5555         8321          6751

 

 

 

A Few of my Favorite Things

I have often written of my love for The Simpsons.  I still faithfully watch the television show, having never missed an episode.  The latest offering, aired just a few days ago, is one of my favorites.  This short post is about why I liked that 22 minutes more than most.

I usually try to avoid trailers of The Simpsons.  I don’t read the little blurbs about what the future episodes are supposed to be about; I like to be surprised.  Last Sunday, though, I was caught off guard when I found out that night’s program was not airing at its regular time of 8:00 PM.  Instead, my sources were telling me it was coming on at 9:00 PM.  Quite unusual.

Armed with this knowledge, I decided to try to find out why Fox fiddled with the time slot.  Was this a special episode?  Was the content a little more adult than usual?  As it turns out, the show was moved so that Fox could premiere a new show at The Simpsons’ normal time.

As I was researching the time change, I came across the description of The Simpsons’ episode being aired at 9:00 instead of 8:00.  When I saw that one of the guest stars was Bob Balaban, I took particular interest.  Balaban is one of the actors who shows up in Wes Anderson’s films.

Anderson tends to use the same cast of actors in his films.  Balaban is one of them.  People such as Jeff Goldbloom and Bill Murray are counted among the others.  I found it noteworthy that Balaban was guest-starring on The Simpsons.  I wondered what that was about.

Not long ago, Family Guy did a parody of Wes Anderson for part of its show.  Peter and the gang moved through an Anderson inspired space, speaking in an Anderson-esque way.  I was hoping that Balaban’s appearance meant that The Simpsons were going to do something similar.  I was not disappointed.

Near the end of the show, Homer and Marge were tasked with finding the childhood home of Jeff Albertson, aka Comic Book Guy.  Jeff had retreated to his family’s estate, leaving behind his wife and comic book shop.  When they arrived, the Wes Anderson parody/homage began.  It was well done.  I was surprised and pleased to see it.

I was most happy to know that the people working on The Simpsons have a high opinion of Anderson’s work.  After all, they never would have made that episode if the producers and writers didn’t find his work worthy.

2020 is over; I know everyone hopes that the new year brings better times for us all.  I have always seen January 1^st as just another day, not a time to turn over a new leaf or to resolve to do this or that.  The 3^rd of June is as good as any other day for such things.  I will say this, the episode of The Simpsons I just saw was better than anything I experienced in 2020.  Perhaps that episode will foreshadow better things for 2021.  If our lives were novels, and I was writing the stories, that might be something I would conjure up…and if wishes were horses, beggars would ride.

 

The Worst People in the World

I really, really hate those guys.
Buford Lister, personal communication

I have a list of the worst people I have ever known; it is not a written list.  I have it committed to memory; I will never forget who they are.  I don’t dwell on it, but I use it as inspiration for many of the things I write.  A few of those people could not help themselves; they simply didn’t know better.  Some of them were victims of circumstance; others were too self-centered to think of anyone other than themselves.  One of the people was a mean-spirited drunk, and he was always drunk.  Oddly, most of them are (or were) near Youngstown, Ohio.

This isn’t a post about those people; I don’t know what purpose such an essay would serve.  It is enough to see that they show up in one form or another in the stories I write.

This post is about a group of people, a loosely connected consortium, who share a love for one math problem.  These people are known as The Trisectors, and count yourself lucky if you have never met one.  They are often referred to as cranks, crackpots, and naïve ignoramuses.  And those remarks are among the kinder things said about them.

The story begins in 1837.  Pierre Wantzel, a French mathematician, published a complicated proof showing that the trisection of an arbitrary angle with just an unmarked straightedge and a compass is not possible.  No matter how hard you try or how smart you think you are, all attempts are doomed to spectacular failure.  Of course, The Trisectors ignore this nasty little fact.

This trisection problem dates back to ancient Greek mathematics.  You may have even heard about it in school.  Uninformed math teachers often tell their students that no one has ever been smart enough to trisect an arbitrary angle.  Ignorant of Wantzel’s proof, they send some unlucky students down a path of despair.  Not only is it impossible, but it is a tremendous waste of everyone’s time to make any attempt at all.  There is nothing to be gleaned from failed trisections.

Think of it this way, if I were to send you off with the task of finding two even numbers, any two, that when added together give you an odd number, what would you do?  Would you spend decades trying to find the elusive answer?  Perhaps you would realize what a terrific waste of time the question is, and you would quickly move on to something else.

What if I asked you to think really hard about finding a power of 2 that is evenly divisible by 3?  It is not possible; there is no such number.  In very simplified terms, this is why the type of trisection we are talking about is impossible.

Underwood Dudley, a mathematician with a great name, collects as many of these attempts at trisection that he can find.  He has written a book about The Trisectors, including advice about what to do when you run across one.  The book is called Mathematical Cranks, and I hope he is writing part two as I write this post.  The world deserves nothing less.  By the way, the best advice seems to be to run as fast as you can in any direction when confronted by a Trisector.

It has been a while since I have come across a true Trisector.  They are probably laying in wait, polishing up their “proofs,” binding them in leather, preparing for the opportunity to spring them on me.  The next time I meet one, I will tell them that what they are trying to do is impossible.  After they argue for a bit, I will tell them about Wantzel’s proof.  The bottom line is, if they want any chance for their “proof” to be considered, they must first find a mistake in Wantzel’s work.  Try as they might, they won’t find one.

So, we have a mathematical proof that it can’t be done, but that does not stop The Trisectors.  They waste vast amounts of time writing and then rewriting their “proofs.”  It is an embarrassment.  One thing they are fond of doing is sending their indecipherable work to math departments all over the world.  After all, who else could possibly recognize their genius?

I will end this post on a positive note.  I hope everyone smiles when they hear what math departments do with the goofy, impossible “proofs” they receive on a weekly basis.   Let’s say that Fred Gorman sends in a 150 page “proof” of his brilliant trisection to the math department at Reederstock University in Iroquois County.  A couple of days later, Laszlo Crump sends in a “proof” of his brilliant approach to the trisection problem.  Now that the stage is set, consider the following letters that the department secretary sends out a few days later…

Dear Mr. Gorman,

Thank you for your proof.  As our department does not have anyone expert enough to vet your mathematics, we would like to put you in touch with an expert in your field.  Laszlo Crump can be reached at…

Dear Mr. Crump,

Thank you for your proof.  As our department does not have anyone expert enough to vet your mathematics, we would like to put you in touch with an expert in your field.  Fred Gorman can be reached at…

Odds are that both men will report back to the math department that the other guy is crazy and talked nothing but nonsense.  What is certain is that as long as Underwood Dudley is alive, he will be receiving recycled, unintelligible “proofs” from naïve ignoramuses.  The Trisectors and their band of slack-jawed yokels are going to die hard.

 

A Problem with a Goat and a Rope

I heard some news the other day.  A man named Ingo Ullisch, a German mathematician, has solved The Tethered Goat Problem.  Does that mark a significant achievement in the advancement of science?  Probably not, but Ullisch did some excellent work.

The problem seems pretty straightforward.  You are presented with a goat that is tethered to a fence post on the edge of an enclosed circular space.  In this case, the grazing area is precisely 1 acre.  The question is: How long a rope do you need such that the goat can graze on exactly ½ of the available land?  I have included a figure below.

Download (PDF, 125KB)

Oddly enough, I had never heard of this problem.  I decided to sit down to see if I could solve it.  I used analytic geometry to come up with my answer.  It didn’t take me long, I got the answer on my 6^th attempt of informed estimation.  Of course, there is a problem; my answer is considered an approximation; it is simply not good enough for the Mathematical Gods.  They tend to be sticklers for precision.

Ullisch used Complex Analysis to get his answer.  He has imaginary numbers floating around his equations in an “imaginative” way.  This strategy leads him to what mathematicians call a Closed-Form solution to the problem.  Now The Gods are happy, and life can get back to normal.

That is about it for this little problem.  I will say this, without a computer and a piece of software written to do analytic geometry, I would never have attempted to find a solution.  After all, The Collatz Conjecture is still out there, mocking me and everyone else who has heard of it.

 

 

The Art of the Eavesdrop, Part Two

 

Something extraordinary happened to me the other day.  I decided to write a  post to let everyone know exactly what happened.  It was confusing; I remain astonished.

My story begins at The Red Cat Café, one of Iroquois County’s finer dining establishments.  I was sitting alone in a corner booth.  I was wearing my homemade headphones, Mozart blasting through the wires leading to my ears.  I had in front of me a draft of a novel I am trying to finish.  I guess it was the tenth draft of this project.  I remember thinking that I might be getting to the point where the novel was not getting any better; it was simply becoming slightly different.  For me, that is the hardest thing about writing, knowing when a novel is done, knowing when the draft I am working on should be the finished product.

I was deep into a sentence.  It didn’t sound right to me; there was something about the cadence that seemed off.  When that happens, the best thing to do is rewrite it and get on with your life.  Almost always, that means that I chop it up; one long sentence becomes two or three smaller ones.  I was busy trying to make such a decision when I felt someone walk toward my table.  When I looked up, I saw a figure sitting across from me.

“Hello.”

“Man, can’t you see I am busy.  As you know, this work is important.”

“Trust me; I know its value.”

“Then why are you disturbing me?  Some might think you a bit rude.”

“I suppose, but we need to talk.  I have a request.”

“I don’t do requests.  You know that.”

“I understand.  I am asking you to set a meeting.  That is all.  I will make my intentions known to the other party.”

“The other party?  Are you serious?  Your level of respect is about ten rungs below where it should be.”

“Are you going to do it or not?”

“If I do set this meeting, I want you to know I am doing it only out of morbid curiosity.  I am not in the business of doing you any favors.  You are becoming more of an annoyance than anything else.”

“Not much I can do about that.”

“You are correct.  You ready to meet right now?”

“I was hoping you would say that.”

Have you ever been in a situation where you can predict precisely what is going to happen?  Perhaps a couple of your friends come together.  You know what the conversation will be about based on their personalities.  You might even be able to predict the sentences.  How about if two people come together as a couple, and you know the relationship will be a slow-motion train wreck?  Ever seen that?  I knew exactly what was going to happen, but I set the meeting anyway.

The next day I was back at The Red Cat; this time, I had my computer out on the table.  I had decided that the novel I was working on, which was creating more problems for me than it was going to solve, needed to be put away for a while.  That is another common strategy.  I always try to let projects sit before they near publication.  I am in no hurry.

One moment I was alone; the next, I was joined by Buford Lister.  Once again, he sat across from me.  He looked disheveled and disoriented.  If I didn’t know better, I would think he had been up all night working on some project or working on the beginning of an epic bender.

“Is he coming?  Did you set the meeting?”

“Set it yourself.  You are a powerful man.  You have lots of money; I am sure you could buy a meeting if you really wanted one.”

“You know I can’t do that.  He would never, ever take a call from me.  That is just the nature of reality.”

“Your reality, mine is much different.  I would have thought you would know that.”

The old man became more and more agitated as he reached into his green backpack, removed a large can of beer, and started to drink.

“Sir, excuse me Sir, but you can’t drink that here.  What made you think you can bring your own beer into this restaurant when we sell it.”

The server looked the old man over, her disgust growing stronger with each passing second.

“Young lady, just put the corkage fee on my tab.”

“What’s that?”

“Ahhh, go ask a manager.  I don’t have time for this nonsense.”

“Miss, Buford Lister here is referring to the special relationship he has with The Red Cat.  I haven’t seen you before, so I know you must be new.  When did you start?”

“I have only been here for a few days.”

“Just go have a chat with a manager; they will explain what you need to do.  And if I may, we are expecting a guest.  You will recognize him by his pork pie hat and checkerboard Vans.”

“What is a pork pie hat?”

“OK, just keep a lookout for the shoes.”

As she walked away, I could see Ryan-Tyler N. Mason approach.  I quickly moved to an adjacent table to give the two men some privacy.  I didn’t want to hear this; I was too embarrassed for Buford Lister to listen to what was about to happen.  I did, though, record it.

BL: Good to see you.  I am glad you agreed to see me.

The transcript reveals around 30 seconds of uncomfortable silence.

RTNM: So, what do you want?

BL: I wanted to talk to you; I need to speak with you about a couple things.

RTNM: I am listening.

BL: I want a do-over.  I want to do the whole thing again, but I want to do it right.

RTNM: Good luck with that.

BL: Please, I am not one to beg, but I will beg if you make me.  You have it in your power to…

RTNM: Unbelievable.  Truly astonishing.  What makes you think I can do this?  Not that I would, but what makes you think I have that kind of power?  You are surprisingly clueless.

BL: I am certainly not clueless; I am desperate.

I remained silent.  At this point in their conversation, I had predicted the content and their individual word choice with 100% accuracy.  I ordered a celebration size beer, room temperature, and settled in.

RTNM: Are you, the great Buford Lister, telling me that you have regrets?  Are you trying to say that you want me to make you young again so you can be famous for being a world-class mathematician instead of a ridiculous poker player? Good luck.

BL: I know you can do it.  I am humbly asking for some help.

RTNM:  Perhaps you are looking to change your personal history.  Would you like to go back in time and lock a particular gun cabinet, thereby saving the life of your young wife?

BL: Please, help me.

RTNM: You don’t get it.  The only reason you are of interest to anyone is because of the things that eat at you every day of your life.  It is your tragic and conflicted nature that allows you to live.  If you were a happy person who had lived a fulfilling life, no one would care.

BL: That is not true.

RTNM: It most certainly is.

At this point, I was ready to go home.  My beer was empty, and I was becoming embarrassed for both of them.  I decided to intervene.

THE WRITER:  All right, enough of this nonsense.  You both are confused and ignorant.  I will try to enlighten you.  Sit back and listen.  There is a person called the author.  That is usually one person, but it doesn’t have to be; people do collaborate.  After that, there is someone called the implied author.  You can read my books, but you don’t ever really learn anything about me.  You only learn what the implied author allows you to know.  Then, of course, is the pen name, the nom de plume, the writers’ quintessential mask.   You, Buford Lister, while you may be asking a legitimate question, are asking the wrong person.  Your salvation is not to be found in Ryan-Tyler N. Mason, nor is it to be found in me.

RTNM: How is that a legitimate question?  He is asking to be made young again.  He wants his story changed.  He wants a second chance.  No one gets a do-over simply because they ask for it.

THE WRITER: Possibly.  As for you, your problem is specific to people in your line of work.  You have no clue how easily you can be replaced.  You might walk out that door and be mauled by a bear, the one who just made its way out of the woods and is walking down the middle of Main Street.  If some type of tragedy were to befall you, life here, in this universe, would go on seamlessly.  No one would even take a second to mourn your passing.  I can’t think of a single person that would care.

RTNM: Well, I don’t…

THE WRITER: You don’t what?  You don’t agree with my analysis of the value of your life?  Tell me, what exactly are you going to do about it? I’ll sit right here while you do your worst.  Go ahead, I am waiting. C’mon, conjure up something good.

RTNM: I am trying, but I can’t think of anything. I’ve got nothing, nothing at all.

“Oh, my gawd!  Look, it’s a bear!”

The patrons turned to look out toward Main Street.  Sure enough, there he was, a young adult brown bear walking down the middle of the street like he owned it. Within moments, groups of townspeople came running out of the buildings to hurl objects at the critter.  Batteries, stones, cans of food, whatever they had.  The bear picked up speed, rounded a corner, and was gone.

“Someone should call the police.”

“In all my life, I have never seen a bear in this town.”

“Well, now, I have seen it all. A bear walking down Main Street.”

The people in the café were in no mood to settle down and go back to their meals.  After all, they had just experienced something highly unusual.  Even though the authorities knew that young adult male black bears were coming in from Pennsylvania, they didn’t necessarily want that fact to become common knowledge.  The bears were not aggressive, and if left alone, they wouldn’t pose any problem.

THE WRITER: Well, you should probably head on out there to make sure that bear is safe.  We wouldn’t want any of the locals to hurt him, would we?

RTNM: You have got to be kidding me.

BL: I’ll go.

THE WRITER: You will do no such thing.  Listen closely, Buford Lister; in your life, you have been through the pit of Hell and back.  You have had several terrible things happen to you.  At this point, having you get attacked by a bear would be gratuitous.  It would be totally unnecessary, it would serve no purpose, and it would tend to make people very angry.

BL: Why’s that?

THE WRITER: People like happy endings.  They do not want to see a man suffer most of his life only to endure more pain at the end.  People live off hope.  Human beings believe in redemption.  They have to; without the belief in a brighter future, many would give up.  They would die long before they are dead.  So, you, Buford Lister, can remain seated.  You, Ryan-Tyler N. Mason, can go check on the bear.  Take a good look around, see if anyone will tell you which direction he went.  We really want to keep that bear safe.

RTNM: Sure.

As he left, I turned my attention back to Buford Lister.  I took a good look at him.  He was getting old, his body had started betraying him years ago, but I knew that wasn’t his biggest concern.  Any mathematician will tell you that their most productive years come when they are young.  The phrase “aging mathematician” is never used in a positive context.  An old mathematician like Buford Lister can spend a lot of time lamenting their declining mental abilities.  That is simply the way of the world.

BL: What’s going to happen to him, to RTNM?

THE WRITER: I don’t care.  I’m sure he will search for the bear.  Maybe he will find it, and perhaps he won’t.  It really does not matter.  These stories are about you and your more or less tragic life.  More catastrophic at the beginning, I think, than at the end, but that remains to be seen.  I can not predict the future.

BL: So, there is nothing you are willing to do for me?

THE WRITER: You still don’t get it; there is nothing I can do for you.  Think about it this way, use a simple rule- “I can’t do something for you that I couldn’t do for myself.”  Think about that before you approach me in the future.

It is time to go, that unwelcome intruder, that nasty interloper, has just shown up, and I am in no mood to deal with more nonsense today.  Do us all a favor, when you come across an Omniscient Narrator, run for the hills.  Those things have no respect for anyone’s privacy.

 

The Art of the Eavesdrop, Part One

There once was a famous course taught at Harvard University by three very well-known professors.  The course was called Thinking About Thinking, and the professors were Stephen Jay Gould, Alan Dershowitz, and Robert Nozick.  The course was taught at The Science Center, a building outside Harvard Yard that looks like an old-fashioned Polaroid camera placed on its side.  Way back when, during the time I was wandering around the campus, there was a café on the first floor.  Our story begins in that café.

One day I was sitting in the café, drinking a large diet coke and minding my own business, when the three professors sat down at a table right next to me.  What was I supposed to do?  They were grabbing a bite to eat before their class started, and I was sitting within easy earshot.  Of course, I settled in and listened.  I didn’t make it too obvious; I just made sure my internal audio antenna was pointed in their direction.

The next week I went back to see if they would appear again.  They did, and, once again, I was sitting right beside them.  This went on for much of the semester.  None of the discussions were scientific, legal, or philosophical in nature; they were all about baseball.  What else were they going to discuss?  They had to save the good stuff, the thinking about thinking stuff, for the classroom, right?

Author’s Note:  The following story is true.  I happened to witness the whole thing.  Once again, I was sitting alone in a booth at The Red Cat Café (minding my own business, as usual) when Buford Lister and Piper Pandora Pennington sat down beside me.  I was wearing a pair of homebuilt over-ears headphones that not only were noise-canceling but, at the flip of a switch, transformed into spy speakers.  I don’t really want to explain why I built such a device; it is not central to our story, but I will say the headphones acted much better than any hearing aid you might get from a doctor.  Oh yeah, they also have Bluetooth recording capabilities.  As I already stated, you don’t need any details.

Buford Lister looked the young girl over.  He checked off each part of her uniform.  White Daniel Johnston “Hi, How Are You?” t-shirt.  Check.  Black yoga pants at least a size too small. Check.  Checkerboard Vans, no socks. Check.  Old school Oakley sunglasses with built-in mp3 player.  Check.  Black backpack nearly as large as she is.  Check.  Ratty, black Bad Brains hat turned backward.  Check.

“All right, young lady. What’s up today?”

She sat silently.  I could hear the ruffling of some papers.  I wasn’t at a booth where I could see them.  I could only listen to what was going on.

“Well, if you don’t have anything to say, I might as well head home and take a nap.”

“I just read that mathematicians might be totally replaced by computers.  Pretty soon, computers are going to be able to do proofs.”

“And your question is…”

“Duh! I don’t have a question.  That was just an observation.”

“Yes.  A very interesting one.  I have thought for a long time that computers are eventually going to replace almost everyone.  That is just part of the deal.”

“I didn’t make any deal.”

“No, but one was implied when your presence graced the world.  You didn’t have a choice; it is just part of the human experience.”

“What am I supposed to do?  Do I stop studying math and take a deep dive into programming the computers that are going to take over?”

“I want to tell you a little story.  We are going way back in time for this one.  I have memories of watching the original Star Trek TV series many, many decades ago.  What caught my attention about that show was that they rarely mentioned money.  It soon dawned on me that those on the ship were not doing a job for pay; they weren’t working to accumulate wealth.  There was something else going on.  One day it dawned on me; they were working to improve themselves.  That was the point of their existence.  They wanted to make themselves better, thereby making those around them better.  That was the point. “

“And your point is?”

“My point is an important one.  Those fictional characters offer an example for all of us.  We should all try to make the world a better place.  It seems to me that the easiest way we can do that is by learning as much as we can and then applying that knowledge in the best way we see fit.  The hope is that by improving ourselves, we can elevate everyone.”

“Yeah, playing poker is an honorable way to spend one’s time, isn’t it?”

“My story is not an average story.  It does not apply due to lots of different circumstances.”

“You mean like the ones in this book?”

“I haven’t read it.  I know exactly what happened.  I don’t need to read some outsider’s account of my life.  I lived it.”

“Well, duh!  I guess your life has been a bit unusual, but that still doesn’t explain why you waste so much time playing poker.”

“Luckily, I don’t have to explain myself to you.”

“I guess not, but it would be OK if you did.”

“Unfortunately, we are not evolved enough as a species as the people in Star Trek were.  My grandfather used to say to me, ‘People say money isn’t everything but just you try living without it.’ Of course, he was right.”

“What did your grandfather do for a living?”

“Coal miner.  He had a hard life.  He would be happy to know you don’t have such struggles with money.”

“Yeah, yeah.  My dead mother left me a lot of money.  Would he be happy about that?  Would he be happy about how I got to be rich?”

“OK, listen.  The point I am making is that the answer to every question in the world is the same.  I don’t care what the question is; ask any question you like.  The answer is always money.  Money will usually be the direct answer, and sometimes it will be the indirect answer.  Look close, and you will find it.”

“So that is why you play poker, money?”

“That is the only reason I play.  I am very, very good at it.  I make lots of money.  Dump trucks full of money.”

“Ptttfff…you just said…”

“I said that we as a species are not yet evolved enough to give money up.  And I’ll tell you one thing – for me, money is freedom.  It gives me the free time to work on my math problems, to meet with you, to do all the other things I want.”

“So, you are not wasting time by playing poker?”

“Oh, I am certainly wasting time.  I can’t think of any other place that is a bigger waste than sitting at a poker table.  Unfortunately, I need to do it.”

“I don’t get it.”

“Look, physicians make a difference every day.  Most people in the medical field do.  Their life’s work is an accumulation of all the good they do throughout their careers.  Every night they can go home knowing that they made the world a better place.  If you choose to be a physician, that is the kind of life you will lead.”

“Why would I do that?  They are going to be replaced by computers, just like everyone else.”

“I think that is correct.  Geneticists will take over for the family doctors, and then the computers will replace the geneticists.  Surgeons will lose out to the robots, and on and on we go.”

“So, what am I supposed to do?”

“The good news is that hopefully, this will free us all up to live in a society more like the one on Star Trek.  Maybe we can all work to improve ourselves instead of wasting time working to accumulate wealth.  I certainly won’t live to see it, and you might not either, but I hope that we eventually get there.”

“Uhhh…”

“I can help guide you; I can nudge you, I can point you in different directions.  I can steer you away from dangerous bunny holes like The Collatz Conjecture. Still, I can’t know what ultimately inspires you.  I can only throw darts and hope that something sticks.”

“I’m a dartboard?”

“You are a twelve-year-old genius that I am hoping does not decide to lead a life of destruction.  I know how angry you are, and I have seen what anger can do to a person.”

“People are so stupid…”

“I understand that.  If only everyone were as smart as you…”

“Then, the world would be a very different place.”

“Yes, it would.  Unfortunately, you are special.  And as such, you have an obligation to make a contribution to humanity.”

“I don’t owe anything.”
“So you say.  My hope is that as you get older, your attitude will change.  Maybe you will end up at Harvard in a few years.  There you will be surrounded by people who feel that responsibility and they just might rub off on you.”

“Pfffttt…”

“You are young, rich, brilliant, beautiful beyond words, and white—most people living in the world today experience things much differently than you do.  For them, this is a very different planet.  Even in this country, most people live paycheck to paycheck.  Their struggle is real.”

“Yeah…well…”

“Tell me…how many poor people do you know?”

“I see them all the time; they are always around the library.”

“You mean, the homeless.”

“Yes.”

“And how many of those people do you know?  How many have you sat down with and had a nice talk?”

“Well, duh!  None, and you know it.”

“You need to understand the world is a different place for different people.  Your view is from a privileged space.  You need to understand your obligation to those homeless people, to the poor people struggling to feed their families. I hate to tell you this, but you certainly do have a duty to all those people.”

“Yeah, what if I play poker instead.  What if I am a gastropod, like you?”

Author’s Note:  All that followed was laughter.  Buford Lister thought it was pretty funny that little Pi has called him a gastropod.  He was confused about why she used that particular word.  How did she know that calling someone a gastropod was his go-to playful insult?  If he had read The Lister Affair, he would have had his answer.  The term was referenced throughout the book.  There was even a section about the trouble a group of mathematicians had trying to get an exact translation of gastropod into their native tongues.  The discussion broke down into a drunken brawl.  The story was included in the book because a man named Ichabod Won Torino had a chair smashed over his back.  As the chair hit him, he had a flash of insight into an obscure Set Theory problem he had been working on for years.  Ichabod screamed, “Eureka,” the brawl stopped, and everyone sat as Ichabod started writing on the blackboard.  Estimates have it that several hundred papers resulted from those scribbles.  The conference went down in history as The Gastropod Meeting. The obscure area Ichabod Won Torino became famous for studying is now known as Gastropod Theory.

“You, young lady, should be very grateful that I like you.  I wouldn’t let just anyone call me a gastropod.”

The recording, at this point, is a bit hard to understand.  As I played it over and over, I almost think I heard a snort and a giggle from a twelve-year-old girl.  I know I must be mistaken; Piper Pandora Pennington does not snort or giggle in public.  The only confirmed cases of such things happen when she is with her sister, Susie.  When she is with her, it is at times hard for her to stop smiling.  The face she shows the world is a very different one, and I don’t blame her at all.  She is under the impression that there is an inverse relationship between intelligence and happiness.  I think the issue isn’t yet settled, but she has research to back up her position.

So, I guess there wasn’t a whole lot to be learned from their interaction—no deep insights into humanity or anything like that.  I will mention that as they parted, Pi told Buford Lister that she was off to the library to spend the next couple of days working on The Collatz Conjecture.  All I heard on the recording was a “Pfffttt!,” followed by what sounded like a backpack zipper.  I casually, cooly, and silently watched them leave.

 

 

I am going to tell you a story.  It is not a long tale; it will only take a couple hundred words.  The setting is Harvard’s campus, probably in the mid to late 80s.  It is hard for me to remember exactly when this happened, but I will never forget what happened.

It was summer; most people do not know that summer classes at Harvard are open admissions.  People come from all over the world to study for a couple months.  High school kids also show up, really smart ones.  The youngsters have to apply; there is a rigorous process they go through before their parents are allowed to fork over a basket of cash.  At least, that is the way it used to be.  It has been so long since I have been there that they may have moved the campus to San Diego.  Doubtful, but you get my point.

I was taking a seminar in The History of Science Department.  I can’t remember exactly what; it was probably something relating to medieval science, either that or the course topic was the PreSocratic philosophers.

There were 7 or 8 students in the seminar.  One particular person of interest was a man in his mid -20s.  He was from Germany, and his English wasn’t the best.  I guessed he probably read the language much better than he understood or spoke it.  That is not uncommon with academic types.

As the semester went on, the young man appeared to be getting nervous.  I thought that I would be nervous too if I were taking a Harvard seminar in a language other than my native tongue.

One day, as always happened in these types of classes, someone asked the professor about the paper we were to write for our grade.  There were never any exams in these classes.  We wrote and then wrote some more.  The question was always pretty much the same, “How long should our paper be?”

I knew John Emery Murdoch, the professor of the seminar.  I took 5 or 6 classes with him.  He was one of the most passionate people I have ever met.  He loved his job.  He was a scholar’s scholar.  I could tell that there was no place he would rather be than in a classroom talking about the history and philosophy of science.  His response to that question was always the same…

“Well, brevity is the soul of wit, but also, I am brief; therefore, I am obscure, so somewhere between 4 and 40 pages.”

After he said his standard line, he did something extraordinary, something totally unnecessary, and something exceptionally kind. He looked over at the German student and said, “You can write your paper in German.” I thought the young man was going to cry.

“Really?”

“Sure, I can read it. It is not a problem.”

“Thank you!”

If someone were to ever ask me if I have seen the weight of the world magically lift off a person’s shoulders, I would reply that I have indeed seen it.  I will then tell them the story I just told you. I will tell them about the kindness shown to a German student by the late, great Professor John Emery Murdoch.

 

The Corndog Conjecture

I have written extensively on The Collatz Conjecture, that seemingly simple yet deceptively difficult problem conjured up by Lothar Collatz in 1937.  Simply put, take a positive whole number; if it is odd, multiply it by three and add one.  If it is even, then divide it by two.  Collatz suggested that any number you can think of, even one a million digits long, will work its way back to one.  Lots of serious mathematicians have worked on this problem; I would say that any professional mathematician has at least taken some time to think about it, and no one knows if the conjecture is true or false.

I was shocked when, about a year ago, I came across a paper by the great UCLA mathematician Terrance Tao.  His paper, while not proving the conjecture, shows that the conjecture is true for almost all numbers, and if there are numbers that don’t fit the pattern, then those numbers are very rare.

Tao’s paper is remarkable.  He readily admits that his approach will not lead to a proof, but it represents the best work done on the conjecture.  I think few would argue that Tao’s work is the greatest advancement ever seen on the problem.

A year or so ago, I had a couple of my nephews over.  We went upstairs to the computer/math/science lab I built for them.  While we were there, I asked Corndog to play around with the variables in the Collatz Conjecture.  Instead of 3n+1, what would happen if it were 5n+1, or even 7n+1?  Well, he opened up Scratch and changed 3 to 4.  He hit the green flag and let the program run.  Here are the results:

5
21
85
341
1365
5461
21845
87381
349525
1398101
5592405
22369621
89478485
357913941
1431655765
5726623061
22906492245
91625968981
366503875925
1466015503701
5864062014805
23456248059221
93824992236885
375299968947541
1501199875790165
6004799503160661
24019198012642644
12009599006321322
6004799503160661
24019198012642644
12009599006321322
6004799503160661
24019198012642644
12009599006321322
6004799503160661
24019198012642644
12009599006321322
6004799503160661
24019198012642644
12009599006321322

As you might have noticed, the output cycles between three truly large numbers.  Interesting…that is a pretty good find for a first run.

As the day went on, Z kept working in an arcade we are building, and Corndog experimented with different numbers in his Collatz code. I must let everyone know that I put a special lab notebook on one of the desks.  In that book, we were to put any and all notes about the experiments we were running or the robots we were building with our Raspberry Pi computers.  I wish Corndog had used it.  Why?  He put in a number, let the program run, and then watched some ninja videos on his phone.  After a substantial period of time, he glanced over at the monitor and said, “Hey, it is back where it started!”  And it was.

The iterations had produced an outrageously large number and then returned to the starting point.  Which number was that?  I have no idea.  Corndog didn’t write it down, and I was sure I would not forget it when he told me what it was.  You guessed it, I forgot, and Corndog has no idea what the mystery number is.

You would think that wouldn’t be much of a problem, right?  Simple experimentation should get us back to that number.  It should, but it hasn’t.  I spent some time trying to find it, and I can’t.  It appears to have disappeared into the ether along with Corndog’s mysterious code.

I decided to write about this fiasco because it reminded me of a story from my graduate school days.  Way back then, and I mean way back, we all used notebooks to scribble in when we sat in class.  There were no decks of beautiful slides.  There were no whiteboards; if the professor didn’t have chalk, we were all out of luck.

All those decades ago, I was famous for writing everything the professor said down in my book.  Even if it was a tangential story, I would include it because I found that the story would help me remember the stuff that would appear on the test.  It all formed one big link for me.  When I had lots of stuff to memorize, and trust me, I often had lots of stuff to memorize, this method worked well.

As the story goes, one day, I was sitting in a Ph.D. level evolutionary biology class. The professor, a very bright man indeed, started talking about…well, I can’t remember.  And when he said, “And this would make for an important paper.  It wouldn’t be hard to write, either.  All the research has been done; it just needs to be synthesized.”  I knew he was right.  This is perfect for my buddy Scott and me.  We could probably have a rough draft together in a weekend.  Note, I said, “I thought,” and not, “I wrote.”

You guessed it, Scott and I talked about the paper a few days later, but neither of us could remember the topic.  We went to the professor, and he rubbed his chin and said, “I can’t remember; it is gone.”  And it was gone.  We had all forgotten the subject of this paper that would have gotten us all fantastic prizes, wonderful gifts, and dates with European supermodels.  I checked my notebook, and there wasn’t a mention of it.  And so it goes…

It is fairly apparent that I write a lot.  I am always getting ideas; back in the good old days when I was able to run, I would think out entire chapters during a single run.  Almost all of The Athena Chapters were written this way.  Now that I can’t run, the ideas trickle in whenever they want.  They are not anxious to be discovered; they tend toward the shy side.

That said, I still try to keep a pen and paper with me at all times.  I also have been known to email myself with whatever brilliant idea pops up when I am in line to get a hamburger.

As unbelievable as it may sound, I just got an idea for a chapter in a novel I am writing.  I have a yellow pad beside me; in the middle of the page, I just wrote: “Sasquatch McGuine meets the cops at the cafe.  He tells them he is working on an app, a special app, a Sasquatch detecting app.”  I didn’t write this next part because I believe it is understood: “hilarity ensues…”  Not only that, I just figured out Sasquatch has a wife named Gertrude, I think she might be a member of Congress, or maybe she just lost her reelection bid. Or maybe, just maybe, she falls down a Collatz Conjecture bunny hole, never to be seen again.

 

 

 

 

5863

You can’t spell gravity without gravy.
Homer Simpson

I decided to pick a number at random and research it.  5863 was the lucky winner.  Is there anything special about this number, or is it just a number? Let’s find out.

I quickly found that metanumbers.com has a lot of information about 5863.  Everything you would ever want to know, and a lot more.  Does any of that information make the number special?  No, the same information can be displayed for any other number you might wish to search.

I did find one interesting table, and it had nothing to do with 5863 specifically.  The table shows how the number translates into other bases. There is, of course, Base 2 (1011011100111), Base 6 (43051), and so on.  The last line of the table caught my attention.  It never occurred to me that anyone would, or could, translate a number into Base 36.  I have never seen such a thing before.  Just so you know, 5863 in Base 36 is “4iv.” I doubt that will ever come up in conversation, but if it does…

After I saw the Base 36 row in the table, I wondered why it was there.  After a bit of time, it dawned on me that we have 10 fingers and 26 letters in our alphabet.  Ha!  There you have it.  That is why we have a base 36 available if we ever need it.  As for me, I guess I could use it in a story about Piper Pandora Pennington.  I am sure she knew about Base 36 long before I did.

During my research, I came across a play written by Rudi Stroebel called “5863.” The title refers to a prison number assigned to an incarcerated man.  The playwright said that the number 5863 was chosen randomly, even though that might not be the case.  It is not that I don’t believe him; it’s just that I know secret messages can easily be encoded in things like the titles of plays and headings of posts.  Just as you can’t spell gravity without gravy, sometimes a random number is just that, and sometimes it isn’t.  Just as there is nothing profound in Homer’s little quip, sometimes a random number is just that, and sometimes it isn’t.  And sometimes a short post is just that, no hidden messages implied, and sometimes it isn’t.