More Wisdom from Cliff Stoll

More Wisdom from Cliff Stoll

As often happens, I write on a particular topic and then find something else to add a few days or weeks later.  Well, it happened again with Cliff Stoll.  I had seen his TED Talk, but I had forgotten a few critical statements he made near the beginning.  This is what he said:

The first time you do something, it’s science.  The second time, it’s engineering.  A third time, it’s just being a technician.

Cliff was explaining why he wasn’t going to talk about things that happened in the distant past.  He took this position despite the fact most people probably showed up to hear him talk about his days running down KGB computer hackers.  But, as the story goes, he had been there and done that.  After all, he is a scientist.  The curious (and scientists are the most curious of all) are always in the market for the novel.

I decided to write about those short statements mainly because I ran into Buford Lister the other day.  I was at The Red Cat Café thinking about what Cliff had said.  I knew I needed to write something about it, but I didn’t quite know what.  That is when the following happened…

I should have known better, but I guess I wasn’t thinking straight.  Of course, he would be there; where else would he be on a Tuesday morning.  I shouldn’t have been surprised when I looked up and saw him approach my table, his crooked smile more of a snarl.

“Mind if I sit down?”

I let out a big sigh. “Whatever you please, just don’t start your usual ranting.  I have told you hundreds of times before that I can’t help you.”

“All right, all right.  I just wanted to see what you are up to.  You appeared to be deep in thought, and I suspect it had something to do with me.”

“Typical.  You are not the central focus of my existence.  I don’t spend all my time thinking about your life’s arc.”

“Sure you do, most of it anyway.”

I took out my notebook and showed Buford Lister the short quote from Cliff Stoll’s TED Talk.  He almost started to smile as he read it.

“Yeah, that’s a nice insight.  Unfortunately, your friend there didn’t go far enough.”

“What are you talking about?”

“What he didn’t say, and what I am positive that he knows, is that when you do something more than three times, when you do it over and over until you get old and tired…”

“Ugh… I know exactly what you are going to say.”

“Of course, you do.  How do you think I know it?”

“It wasn’t the appropriate time or place for him to say what you are thinking.  He is a nice fellow; he wouldn’t want to insult the audience or make them feel bad in any way.  His talk was meant to be uplifting, not some sort of nihilistic Buford-Lister-inspired fiasco.”

“The fact remains, more than three times, and you are nothing more than a trained monkey, a mindless drone living out its days at the carpet store.”

“Not everyone has your mindset, you know.”

“Well, that is a mighty good thing, don’t you think?”

“Of course, it is.”

I sat back and watched Buford Lister hand the server his personal celebration size stein.  She gave him a half-smile as she glanced at the clock.  I could tell she wanted to say that he should at least wait until noon.  I was glad she bit her lip.  It was just as likely that Buford Lister was in the middle of a three-day bender, and I didn’t want to hear about it.

We sat in silence for a while.  I took a long hard look at him; he wasn’t aging particularly well.  I wasn’t going to tell him, but he had the look of a man who had been doing the work of a mindless drone for decades.  The bright eyes of a child prodigy (and he certainly was a mathematical Mozart) had faded into those of a beaten-down monkey.  Sure, he had become perhaps the world’s most accomplished poker player, but it was all mindless repetition.  He hadn’t experienced anything new or gained any real insight in decades.  And he knew that playing poker was the worst profession in the world, the greatest possible waste of a person’s time and talent, and that is precisely why he chose to play.  It wasn’t possible to make the world a better place by sitting at a poker table, which conveniently made it impossible to fail at a former child prodigy’s life purpose.

Buford Lister gave the server a thumbs up as she sat the giant stein down on the table.  He made sure not to make eye contact with me until he finished his beer.  It didn’t take long.  Of course, he immediately ordered another.

Was he trying to make me feel sorry for him?  There was a vacant look in his eyes, one of a man defeated by decades of the universe’s uncaring stance.  Still, though, there was a glimmer of humanity (slight as it might be).  If you look closely, you can usually tell if someone has given up.  I was reasonably sure he hadn’t, even though I couldn’t quite figure out why.

Between you and me, his life has been an abject lesson in grotesque spirit-crushing.  He knew his luck hadn’t been the best and that he had done a few things worthy of regret.  He also learned at an early age that the universe was indifferent to his plight.  As I watched him chug his beer, I found myself hoping that it would never dawn on him that he had wasted his life.  I hope that he somehow forgets that he was born with the ability to take the genius of Mozart and translate it into inexplicable mathematical insight.  My wish is that the alcohol dims the pain enough for him to get through the day.  After all, that is the best I can do for him.

 

 

Kellen

Kellen

The morning was spent on his usual routine, hair.  There…it finally looks perfect.  He got the desired look, the one of a douche-bag, the kind that drives the young (and sometimes not so young) women crazy.

Kellen climbed into his beater RV, not a Corvette or a Mustang.  Sure, he could have just as easily chosen a dump truck but this sick son of a bitch, ever a slave to self-amusement, had to get an RV right out of a third-rate camping advertisement.

He put in a cassette of Rudy Vallee music (jerk) and headed down the road, feeling good, feeling full of himself; (and why not?) he was a stone-cold pimp wannabe on his way to raise some hell.

There, there, my, my…what have we here?  He pulled the RV into a parking lot, lowered the driver’s window, and took a quick look at her (possible victim?…maybe). No, intended victim.  After a second or two, he knew all he needed to know.  He closed the window, shut his eyes, and sent himself into a psychic trance.  It was Remote Viewing time.  There she is in front of the mirror earlier today…yes, yes.  Finish your breakfast, think about what you are going to do at work today.  Perfect, deliciously perfect.

 Kellen, a dry land Aquaman, was able to call on the birds and the turtles and such to do his bidding.  Such is the luck of the draw.

Bright sun, so bright.  That is good, lots of glare, lots and lots of glare.  She won’t have very good vision in this sun.  Sure, her hat will help her a little, but it won’t be enough, not nearly.

He knew where she was going; that wasn’t an issue.  The problem was trying to convince a pretty little bird to off himself just so Kellen could get his jollies.  As he got older and his reputation grew, he found it harder to get the avians to do his bidding.  They always did what he wanted in the end, but it took more and more of his energy to control their little minds.

Keep going…yes, open the door.  Now little bird, now.  The window shook as an object dive-bombed the bookstore in a disgusting act of coercion.

Startled, yes, she is shaken. “Oh my, poor little bird. Oh no, you’re badly hurt.  No, you’re….”

Kellen smiled to himself as he watched her get a dustpan.  That will inspire her.  Instead of just drinking whiskey tonight, she will drink whiskey and write.

And write she did.  It took her months to get the cadence and the word order just right, but she eventually nailed her poem about a dead little bird.  Would she thank Kellen if she knew what he did?  No, I think she is a lot like me; if she knew what happened, her hatred of Reverse Vampires would be as deep-seated as mine.  I don’t like those idiots one little bit.

 

 

Cliff Stoll

Cliff Stoll

To a mathematician, I’m a pretty good physicist… To a physicist, I’m a fairly good computer maven. To real computer jocks, they know me as somebody who’s a good writer. To people who know how to write … I’m a really good mathematician!

Cliff Stoll
Wired.com 12/18/19

 

Cliff Stoll sells Klein Bottles (more on that in a bit).  Sure, he has done a lot more than that in his time.  Go ahead and Google him.  Do yourself a favor and watch a few of the Numberphile videos that pop up.   You will not come across a more interesting person than Cliff Stoll.

Cliff Stoll jumps in the air when he gets excited, and man, is he excitable.  Years back, he gave a TED talk, a very good one.  Seek it out.  Try to count how many times he jumps in the air while imparting his particular type of wisdom.

There are so many different ways I can address this incredible man in an essay.  He is a Ph.D. astronomer; his work in that field could take up an entire essay.  How about the story of him and the KGB computer hackers he caught in the mid-’80s?  Well, a lot has been written about that ordeal.  At that point, during the birth of the internet, no one knew what a computer hacker was.  Even still, Stoll caught them, and they were brought to justice.

I mentioned Klein Bottles in the first paragraph.  Ever seen one?  Have any idea what they are?  Pictured are some examples taken from www.kleinbottle.com, the site that Stoll owns.  Simply put, a Klien Bottle is a 3D representation of a four-dimensional, non-orientable, one-sided object of zero volume.  Simply put, that is…

 

 

Of course, its 2D counterpart is the ubiquitous Mobius Strip.  Below is an example.  That object has only one side.  Don’t believe me; cut one out and draw a line down the middle.  If it is two-sided, the line will never end where it began, right?  Draw a line and see what happens.

 

 

Klein Bottles have always fascinated me (and yes, they are composed of two Mobius strips).  I have one sitting on a shelf in my library.  There aren’t a lot of things more remarkable than Klein Bottles.  Oddly, though, this short essay is not about Klein Bottles and Stoll’s long fascination with them.  This essay is about something else entirely.

I was talking to my niece the other day.  She was telling me about the essays she has to write for school.  I told her about a class I took some time ago on the topic of essay writing.  I told her that I like to bury the lede and put my thesis statements at the bottom of page 17.  Being the good uncle that I am, I did not advise her to do the same.  I am not sure that eighth-grade English teachers or standardized test graders would be amused at such a tactic.  She readily agreed.

So, this essay is a bit unusual for me.  I put the thesis statement, the real point of the essay, in the epigraph, right there at the beginning.  As a reminder, here is the quote from Stoll once again:

To a mathematician, I’m a pretty good physicist… To a physicist, I’m a fairly good computer maven. To real computer jocks, they know me as somebody who’s a good writer. To people who know how to write … I’m a really good mathematician!

What is the big deal about this?  Well, it is something I have known to be true for decades.  I know that if you are an archaeologist who understands statistics, you are considered to be a brilliant scientist even though to a Professor of Statistics, you might be seen as pedestrian.  That is the way of the world.  I shook my head in agreement the first time I came across Stoll’s quote.  You have no idea how true it is.  In my experience, I have found this to be the way of the world, academic and otherwise.

I think that mathematicians, in general, view the mathematics of physicists as sloppy at best.  That is unless you are Edward Whitten, the only physicist to be awarded the Fields Medal, one of the highest honors mathematics has to offer.  And suppose you are a physicist who is an absolute whiz with computers. In that case, it is easy to be considered a computer genius until real computer people show up.

And on and on and on it goes.  One person’s genius is another’s dullard.  When I read what Cliff Stoll said, I was glad to learn that my insight is more widespread than I thought it might be.  I was happy to know that I wasn’t the only person who noticed this.  After all, one person’s leap is another’s baby step, and in the land of the blind, a one-eyed person is an exalted leader.  And on and on and on it goes.

 

 

Air Effects

Air Effects: a second-person account of an individual who picks up an almost empty can of air freshener.

 

You are in your upstairs library; you appear to be reading Proust.  Your thoughts, though, are not on the text.  Let’s begin there.

Things seem normal until you put down a half-eaten madeleine and pick up a can of Febreze (old book smell can sometimes be overwhelming). Then…well, then things get stilted and awkward.  As you slowly squeeze the nozzle, you can see each of the individual droplets as they slowly exit the cylinder.  You not only smell them, but you can also feel each unique sphere.  Preoccupied with childlike innocence and amazement, you do not notice that the walls are beginning to lean in.  Even worse, the heat suddenly radiating from your chest overwhelms you.

Are you having a stroke?  Probably not; you seem healthy enough.  Maybe you fell in love, and that is what this is all about.  Ahhhh yes…love is powerful enough to warp matter and slow the flow of time.  Didn’t you read that somewhere?  What was straight and simple becomes slanted, geometrically unstable.  Do you really need me to tell you that you are in love?

You must listen to me:  Time and space are part of the same thing; separate them out at your own risk.  The fact that everything is in slow motion and the walls are warping is no coincidence.  The warmth in your chest?  Good luck, you are going to need it.

You…you and your logical mind, is all this too much for you?  What, you think you are some sort of Vulcan, Spock incarnate?  Look around you; the walls are closing in; they are bending at strange and severe angles.  Do you even realize it is also getting darker?  Open your damn eyes; it is getting darker.

It is totally dark now, not regular dark but intense black light dark.  It is pervasive (how unusual); the light seems to be piercing you, invading your essence.  You feel it…you don’t like it…not even a little.

The smell, that’s it!  It is the smell!  The scent of the Febreze reminds you of what Chris was wearing the night you met.  Unfortunately, your deep insight isn’t helping matters.  The walls are so close that you can reach out and touch all four, five, six, seven (what…seven walls?).  You wonder how this is possible.  There were only four walls here a few minutes ago, weren’t there?

You realize the scent that is ostensibly responsible for this fiasco is dissipating.  In your troubled mind, this means that Chris is also fading away.  People like you love metaphor; in a certain sense, you live by it.  Do you even realize the can is still in your left hand?  You do?  Then squeeze the trigger.  What?  Is it empty?  Oh no…

You have just experienced something rare, an unimaginable event at the intersection of your understanding of space and of time.  The Fifth Dimension, the one of pure love and joy, opened up (ever so briefly) around you.  What now?  What of you?  I know exactly what you are going to do next, you are going to buy more Febreeze.

 

 

 

 

 

 

 

 

 

The Inuit

The Inuit

Sergio the Eskimo, that is what everyone called him.  No one meant anything mean by it, it was just that his real name was way too hard to pronounce.

No one knew his back story (no one ever cared enough to ask).  The other tenants in his apartment complex would see him around and say “hi” and that was about it.  To them, he was just another guy living in the building.

No one saw him get up at dawn every day to go down to the beach for his workouts.  No one knew he would sprint and sprint and then sprint some more until he threw up on the sand.  No one knew he would come home and meditate for hours and then go back to the beach long after the sun went down.

He never had to explain that he didn’t have to work because the people back home all pitched in to send him to the mainland.  (He was as invisible as a man in plain sight could be.)

One day Sergio posted a notice on the community bulletin board.

RACE AGAINST SERGIO.

All comers welcome.  150 meters.

This is your chance to race against the fastest Inuit sprinter ever.

One week from today at noon.

The big day came and Sergio walked down to the beach to see a couple dozen people at the start line.  They all did their stretches.  Sergio took off his shirt, an old Sergio Tacchini tennis warm-up top, and put it in his duffel bag.

The race began and all 25 people took off.  Sergio crossed the finish line in 19th place.  He looked stunned as he walked back to his apartment.  He sat for a long time before he was able to compose the following e-mail:

Dearest Elders,
The Americans in San Diego are damn fast runners.  I am sorry that you gave me all your money and sent me here for the greater glory of our people.  I will not be making anyone’s Olympic Team.  I am sorry.  I will come back home soon.

The elders were confused.  Sergio was the fastest runner any of them had ever seen.  Most said that he set the earth on fire with each stride.  They didn’t know what to make of the message.  They quickly called for a council meeting.

A few days later Sergio wrote the council again to tell them that he would be heading home.  He said that he was deeply sorry that he wasted the council’s time and wasted his people’s money.  The elders waited at the train station to greet Biisaiyowaq with a large banner made in his honor.  He never got off the train.

Back in San Diego a policeman came across a canvas bag on a bridge.  There wasn’t much in it, nothing to identify who it belonged to or where it came from.  He had no idea that it belonged to the pride of an Inuit village, a man some called Sergio.

 

Mona’s Song

I posted a video I put together of a song by The WRB Project.  Give this one a listen.  Justin wrote it for his late sister.  I really like it, it is powerful.

As always, videos are shot with a budget of zero.  We use the best equipment we can scrounge up.  The point is simply to get the music of The WRB Project heard.  Fortunately, these videos have been getting thousands of views.  I am happy that the music is finding an audience.  I hope you enjoy the song.

 

Nonplussed

Nonplussed

Aside from all the racial and cultural epithets that are being hurled with more and more frequency, there is a particular word that I genuinely do not like.  It constantly confuses me; its use makes me stumble and bumble even though I am very familiar with it.  I’ve seen it written and heard it spoken numerous times.  Each time this happens, I furrow my brow and wish the author or speaker had chosen another word.

I vowed a long time ago to never use this word in my own writing.  Why?  I simply do not like it.  Words should not create confusion and ambiguity unless that is the intent of the writer.  And I must say that this word always leaves me dazed; I guess you could say that when I read it or hear it, I am nonplussed.

Author’s Note: Yes, I realize that I promised never to use “that word” in my writing, but I have thought about it and have no choice.  I can’t write about “nonplussed” without typing “nonplussed.”  And for those of you who think that is ironic, don’t get me started.  That is a topic for a distant day.

I have been researching this tricky word, and I have found that I am not alone in my dislike for it.  Let’s be generous and just say that its definition seems to be evolving.  In fact, I think that about half the people who use it believe that it means the opposite of what it actually does.  Like I said, its use leaves me confused.

That said, let’s see if we can get to the “root” of the problem.

Author’s Note:  So, an attempt to get to the “root” of the problem?  Of course, I must mean the Latin roots of the word.  I also dislike writing about Latin.  I mean, those people had a different word for everything.  Sure, some of it is pretty close but…

Non and plus in Latin translates to “no more.”  And the way I see it, it is that negative prefix, the non in nonplussed, that is responsible for all the confusion.  Can you think of another word for confused that has a negative prefix?  A negative prefix implies that the person in question is not confused.  See how confusing this is?  You shouldn’t be wondering why I have banned this word from my vocabulary.  If you are, read on.

Historically,  nonplussed meant confused or bewildered to the point you can not speak.  Simple enough, but, once again, we have the negative prefix problem.  Non implies you are not confused; at least it should, right?

In popular use, nonplussed means unfazed, not bothered, or even unimpressed. See all the “un” prefixes?  It seems to me that the popular usage makes more sense.

The big problem is the “non” prefix.  That negative prefix implies that if a person is nonplussed, they are not “plussed,” which means they are unfazed. As Charlie Brown says, Good Grief.  In popular use, the word means something akin to the opposite of its historical definition.  And yes, I am nonplussed.

I am all for the evolution of language.  It is going to happen no matter what any of us do to stop the changes.  My gripe is that words shouldn’t suddenly mean the opposite of what they historically have meant.  If I could somehow fix this problem, that would be really sick.  I mean, people would view me as a bad dude, right?  They might even call me the goat.  Or maybe they all would be too nonplussed to care. Sigh…

 

 

 

It’s a Beautiful Day for Baseball!

It’s a Beautiful Day for Baseball!

I just heard that the great Joe Tait died.  The news was not unexpected; he was old and had several health problems.  Still…

This I know, Joe’s voice was the theme music of my youth.

It was Joe who would let me know that “The Cavs are going right to left on your radio dial” when I tuned in to listen to my team lose again and again.

It was Joe who made me jump out of my seat when “Cleamons got a rebound!” (one of the greatest moments in Cavs history).  It was Joe who made me feel like I was at the old Richfield Coliseum instead of in my bedroom.  He was the best radio announcer I have ever heard.  And yes, I know that every team in the NBA thinks that their announcer is the best, but Cleveland was right; no one was better than Joe.

Joe Tait was the radio voice of the Cleveland Cavaliers.  He also did radio and TV for the Cleveland Indians.  I can remember sneaking a radio to school so that I could listen to his opening day call.  Even if it was 30 degrees and snowing, which it often was in April, you can bet that the broadcast began with “It’s a beautiful day for baseball.”

Even at a young age, I knew that Joe Tait had mastered his craft, but it took a high school basketball game for me to truly appreciate his skill.  Joe would travel around Ohio and sit in with the local announcers for select games.  He usually came to my hometown once a year.  One day, I happened to turn on the radio just as a game was starting.  You guessed it, Tait was sitting in.  As the game went on, I was wondering what was happening.  The game sounded like any other.  The local guys were doing all the talking.  No Joe, not a peep.

Halftime arrived, and I could hear Joe’s canned voice doing a commercial for a local pizza joint.  The other two guys analyzed the first half, and then something extraordinary happened.  As the second half started, the local guys turned off their mics, and Joe Tait took over.  I soon realized he had spent the first half learning all the players and their numbers and sizing up each team’s offensive and defensive schemes.  He spent the second half announcing the game just as he would if the Cavs played the Bulls.  A 5’6” point guard became Mark Price and a 6’2” center transformed into Brad Daugherty.  It was unbelievable; Tait flawlessly announced the second half without hesitation, without a single stumble or a fumble.  He was sublime, and I was awed.

It wasn’t until I heard that second-half call that I truly appreciated Joe Tait.  I still think about what he did that night.  Know this: The kids were not wearing their names on the back of their jerseys; there was only a number.  Tait knew every one of them.  That man was smooth.

I read that Joe wanted to be a writer, that he wanted to paint pictures with his printed words on a page.  As an announcer, he did much more than that.  He spent decades making people believe they were at the sporting event instead of sitting in their living room.  I always smiled when told the Cavs were starting the game on the right side of my radio dial and moving to the left.   And no, I never wondered why the opposite wasn’t true.  I merely suspended disbelief, leaned back, and let Joe Tait take me courtside.

How many nights did I fall asleep after Joe said, “Have a GOOD night, everybody!” following another Cleveland loss?  Too many to count.

Not many of us will be able to say that no one ever lived who was better at their job than we were at ours.  This I know:  No one was better than Joe Tait.  He was the best.

Truth Machine

Truth Machine

I am a boxing fan.  There is something about two people standing face to face in a ring that is pure and primal.  And yes, sometimes I think the sport should be outlawed.  But then I watch a little UFC, and I realize boxing is tame in comparison.  I find mixed martial arts to be barbaric; I am not a devotee of that type of violence.  When a man or woman is down, where is the sport in jumping on them and pummeling them until you are yanked off by a stripped interpreter of an ill-conceived rulebook?  I think that it says something about human nature that UFC has become far more popular than boxing.

Boxing is known by all its fans as “The Sweet Science.”  Watching two skilled fighters is like seeing a chess match played out with jabs and crosses and bobs and weaves.  While the science aspect of boxing is sweet and underappreciated in today’s climate, it is another aspect of boxing that interests me today.

There is a famous quote about sports not developing character but revealing it.  It is generally attributed to basketball coach John Wooden or sportswriter H.H. Broun.   I always found that sentiment interesting.  I think it is true, that character is revealed and not built, especially when it comes to boxing.  Set any two people in the ring, and you can learn a lot about them in those three-minute rounds.

That quickly brings us to former heavyweight champion Joe Frazier.  His three matches with Muhammed Ali are classics.  Each man tried their best to rip the heart out of the other man’s body.  I just rewatched Ali – Frazier I, on today, the 50th anniversary of the fight.  And yes, on that day Joe Frazier was something else; he was transcendent and sublime.

Larry Merchant, a boxing commentator on HBO’s telecasts for decades wrote what is perhaps the greatest lede in sports journalism history.  This appeared in the March 9, 1971 edition of The New York Post:

Muhammad Ali fought a truth machine last night, and the truth that emerged was painfully clear. The arrogance and hubris that made Ali a great champion made him a former champion.

You can’t con Joe Frazier for 15 rounds. Joe Frazier comes at you too honestly, too openly. He lets you find out what you have inside you. It is going to take an honest man made of stern stuff to beat him. Ali was not honest enough last night.

Joe Frazier the truth machine. Can you imagine imagery more profound than that?  Larry Merchant just turned 90, and I hope he is still proud of that lede.  Stripped of all pretense, Frazier came at his opponent with no trickery, no hubris; he simply marched forward, baiting his opponent to stop him.  He wasn’t interested in showmanship or style; he was on a mission to break the spirit of the man opposite him in the ring.  Frazier’s opponents learned deeply held secrets about themselves when they stood across from him.  Frazier exposed his opponents to the world.  Had they worked hard enough to withstand him?  Did they have the fortitude to stand face to face with him for 12 or 15 rounds?  Were they willing to take his punishment?

That night Frazier was relentless.  He gave no quarter.  His march was forward, his character revealed.  He was a great fighter, a true champion.  He kept asking Ali how deep his well was.  With every left hook, he was asking Ali to see if he could dig a little deeper.

How many of us get to do battle with a truth machine in our lives?  I wouldn’t think many of us do.  At least not one as on point as Frazier.  Our revelations come in different ways.  It is easy to fool ourselves into thinking that we are titans when we are never asked to prove it.  We can’t know how deep the well goes unless we are asked to reach deep down by our own nemesis, our own version of a truth machine.

Of course, we all do face a Truth Machine.  It is Time, that undefeated fabric of the universe.  The difference is, a person could hope to defeat Frazier, which Ali did the next two times they fought.  None of us can say the same about the ticking clock.

Some pundits argue that neither fighter was quite the same after that fight.  They say that the back and forth, the exchange of punishment, took something fundamental from both men.  I believe that is true; I also believe that on that day, fifty long years ago, Muhammed Ali fought a Truth Machine. Larry Merchant had the insight to know that we all can learn something profound from those 15 epic rounds.  I know I did.

Subtle is as Subtle does, the Strange but True Story of 13 over 27

Subtle is as Subtle does, the Strange but True Story of 13 over 27

I have studied lots of different subjects.  The most slippery is easy to identify. It is probability theory.  Problems in this branch of statistics trip up experts (and me) all the time.  There are lots of stories of famous scholars who have gone down in flames when presented with what seem to be straightforward questions about the probability of this or that.  This essay is about one such problem.

Let’s imagine that I met a high school classmate at a reunion.  When I saw him, I said, “Hey, I hear you have a son; I saw something about him in the paper.” He replied that he has two children, and the oldest is indeed a boy.  Now the simple question is:  What is the probability that the other child is also a boy?

Well, what are the possibilities?  He could have a boy (B) and a girl (G) or a boy (B) and a boy (B).  Therefore the probability that both children are boys is 1/2, which is 50%.  Take a look at the following table:

BB
BG
GB
GG

Since we know that the first child is a boy, we can eliminate the GB and GG rows.  That leaves only two possibilities, BB and BG.

That little scenario is easy to figure out.  Of course, it can’t all be that easy, right?  Are you ready?  Do you hear The Twilight Zone music in the background?  What if the guy had told me that he has two children, but he didn’t tell me whether the boy was the oldest or the youngest?  What then are the odds that the other child is a boy?

Author’s Note:  There are points in some of my essays where the reader’s head might explode.  This is just a “heads up.” The following might be one of them.

Let’s go back to our table.

BB
BG
GB
GG

The only possibility that can be eliminated is GG.  Therefore (do you see it?), the probability that both children are boys is one in three, or 33.3%.  Very strange.  Most everyone’s intuition tells them that the probability should be 1/2, that it is a fifty-fifty proposition.  When the question is carefully considered, the correct answer is the counterintuitive one.

Probability is subtle; finding the correct answer always depends on meticulously considering all available information.  That said, I almost hate to continue.  I hope some young student isn’t reading this and immediately decides not to study statistics.  Don’t do that!  When you develop some mastery over the material, probability theory goes from the counterintuitive to the sublime.  It can teach you a lot about how human brains evolved, it can give deep insight into the nature of the mathematical world that we live in…and it can be a lot of fun.

Author’s Note:  I will be posting many more essays on probability.  Consider this one a bit of a warm-up.  Now that the blood is flowing, things are about to get even stranger.  Keep in mind how awful human intuition is when it comes to this branch of statistics, and you will be fine.  Remember, it’s not you; almost all of us have terrible mathematical intuition.

Our story continues…

I ran into another guy I went to school with.  He was always a bit eccentric, and it appears nothing has changed.  I said, “I hear you have two children.”  He immediately replied, “Why yes, I do.  In fact, one is a boy born on a Tuesday.”  With that, he turned and danced across the room and out the door.

You guessed it.  Now we need to find the odds that the other child is a boy.  How subtle can this problem get?  The fact that the boy was born on a Tuesday does change the problem, and it certainly impacts the answer.  Think about that for a moment.  How can it matter at all on what day the boy was born?  Let’s find out…

There are 196 possibilities.  We get 49 due to the older or younger siblings being born on any of the 7 ways of the week.  If you don’t believe me, create a matrix of days of the week with possible births.  Such a table is shown below:

So, if you were to create a matrix with every option, you would end up with:

49BB
49BG
49GB
49GG

Out of the 196 possibilities, we can isolate all of those that have a boy born on a Tuesday.  There are 27 cases we can look at that meet this criterion (13 BB, 7 BG, and 7 GB).  The 13 BB scenarios are shown below.  Therefore the odds of two boys is 13/27.  13/27?  48.1%?  Really?  Yes, really.  Study the table below and it will become clear.  It is important to note the overlap on Tuesday / Tuesday (TUTU); we don’t count it twice, giving us 13 instead of 14.

 

 

The probability bunny hole is a deep one.  The more I study the subject, the more interested I become in the limits of human intuition, especially the mathematical type.  It appears we have very little instinct when it comes to numbers, and I don’t think that should surprise anyone.  I have a hard time figuring out when insight into subtle probability problems would have been beneficial during our evolutionary history.  I don’t see when it ever would have been influential on a genetic level.

Not too bad for an introduction to conditional probability theory.  Fairly tame by comparison.  Trust me, things are about to get weird.  Come along for the ride, it is a bit bumpy (seat belt required), but the destination is worth the trip.