Random Thoughts from a Nonlinear Mind

This is a piece of Flash Fiction.  The topic: a second-person account of an individual who picks up an almost empty can of air freshener.

 

Air Effects

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) and then…well, then things get stilted and awkward. As you slowly squeeze the nozzle, you can see each individual droplet as it slowly exits 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 begins to overwhelm 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 plum 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?  That is probably part of the same deal, at least you better hope so.

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 blacklight 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’ apartment used to smell like. 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 initiated this fiasco is dissipating. In your troubled mind, this means that Chris is also fading away. Even though you do not know it, people like you are wedded to metaphor; in a certain sense, you live by it and for it. Do you even realize the can is still in your left hand? You do? Then squeeze the trigger. Try again…press harder. What? It is empty? Oh no…

You have just seen and experienced something rare, an unimaginable (almost inconceivable) moment in space and in time. The Fifth Dimension, the one reputed to be of hope and ecstasy, opened up (ever so briefly) around you. What are you supposed to do now? I know precisely what you are going to do next, you are going to buy more Febreeze.

 

 

 

 

 

 

An Existential Threat

Two things happened in the last couple of days that have required me to spend hours in front of my computer.  First, Harvard Magazine sent me a digital copy of my monthly subscription.  Second, Harvard played Yale in football on Saturday.  Decades from now, people will be writing about that game, not for who won or lost, but for what happened at halftime.

In the latest edition of Harvard Magazine, there is an article about a debate going on at Harvard concerning divestment.  Lots of faculty and students want the university to sell all the stock in the endowment that has anything to do with fossil fuels.  Not only that, they want Harvard to sell any holdings in companies that contribute directly to climate change.  The employees, alumni, and students asking for divestment do not feel that Harvard should profit from the destruction of the earth.  That last sentence seems commonsensical, doesn’t it?  It is also entirely nonsensical that I had to write it.

It is hard to imagine that anyone at a place like Harvard would argue against this position, but of course, the administration is taking a hard line.  Money still rules, maybe more so at Harvard than other universities.   In the article, professors and students offered up their arguments for and against divestment, I found one to be quite powerful.

Charlie Conroy, a professor of astronomy at Harvard, published the following statement.  It is taken in its entirety from Debating Divestment in the Faculty of Arts and Sciences, an excellent article written by John S. Rosenberg dated 11/5/19 for Harvard Magazine. 

I am an astronomer. I spend most of my time collecting data and running computer models to understand the origin of our Galaxy. But today I speak to you as a deeply concerned member of our community.

I have grown up with the reality of what we once called global warming: rising temperatures, melting glaciers, species extinctions, destabilizing weather patterns. The consequences for humans have also been in plain view: increased occurrence of famine, droughts, and diseases, and, on the horizon, a refugee crisis unparalleled in human history. And yet, like many people I became numb to the increasingly urgent calls for action. I was busy and preoccupied with issues closer to home: raising a family, conducting research, securing tenure. I focused on small acts—recycling, commuting with public transit, eating locally grown food. What more could I do? I am after all only one person.

That thinking was wrong.

As members of the Harvard faculty we have a powerful platform to effect change. This means that we also have a responsibility to use that power in extraordinary times. And these are extraordinary times.  

As I speak California is burning. UC Santa Cruz, where I used to teach, has been subjected to forced blackouts resulting in canceled classes. Fire-related evacuations are now a routine part of life for many communities. This is the new normal. In recognition of the climate crisis, the University of California system is divesting its $13-billion endowment and its $70-billion pension fund from fossil fuels. 

The ice sheets on West Antarctica and Greenland together hold enough water to raise global sea level by 13 meters. Destabilization of these ice sheets could result in sea level rise of 2 meters by the end of this century and 6 meters by the end of the following century. With 6 meters of sea-level rise significant portions of the Harvard campus will be underwater. As will all of MIT, Fenway, and the South End. Globally the situation will be much worse: 600 million people live at an elevation within 10 meters of sea level.

We in rich countries may be able to mitigate the worst effects of climate change, though the costs may be staggering. Maybe. Maybe not. But island nations, poor countries in South Asia and elsewhere, will not have the option of buying their way out of disaster. 

The predicted short-term consequences of climate change from major organizations such as the IPCC [Intergovernmental Panel on Climate Change] tend to be conservative. We see evidence of this every year as new reports indicate the pace of change is accelerating faster than predicted. The global climate is a complex system with multiple non-linear feedback cycles that are poorly understood. The near future could easily turn out to be much more extreme than current models predict—during the Pliocene Epoch the levels of CO₂ in the atmosphere were comparable to today’s levels. During that time the Earth was 3^° C warmer and global sea levels were 10-20 meters higher.

There is currently five times more fossil fuel in proven reserves than can be burnt if we are to stay within the 2^°C warming scenario advocated by the UN Paris Agreement. Avoiding catastrophic changes to our world will therefore require leaving huge reserves of fossil fuel in the ground. And yet, the fossil-fuel industry continues to devote vast sums of money and resources to identifying new reserves. Despite its profession of support for the Paris Agreement, ExxonMobil has not changed its position since this agreement was signed. In 2015 ExxonMobil projected that by 2040 fossil fuels would supply over 75 percent of the world’s energy needs. In its latest projections from this year, that number has actually risen to 80 percent.   

It is simply unrealistic to expect the fossil-fuel industry to willingly walk away from so much money in the ground. As our colleague Naomi Oreskes has demonstrated through extensive scholarship, the fossil-fuel industry has for decades engaged in deliberate doubt-mongering on the topic of climate change. This includes explicit undermining of public policy and indirect undermining of attempts to move to alternative energies. In light of these facts, the idea of working in collaboration with the fossil-fuel industry is dangerously naïve and counterproductive.

These extraordinary times require big ideas and bold leadership.  

The scale of the problem is so enormous that many ideas must be pursued simultaneously. We should commit to a carbon-free campus on a rapid timescale. We should incentivize reduced air travel and the use of a robust public transit system. We should encourage significant new academic and research ventures. We should engage with our community beyond Harvard. And we should divest from the fossil-fuel industry.

There are multiple reasons to support divestment. There are arguments from history and from economics that my colleagues will discuss. My perspective is this: the degree of action and change required to avoid the worst-case scenarios is far larger than anything we could hope to accomplish on our own, even as teachers and researchers. Every one of us could commit 100 percent of our time and resources to combating climate change, but that would fall far short of what is needed. This is where divestment comes in. It is an opportunity, perhaps our best opportunity, to catalyze action and change far beyond these walls. 

Imagine I came here to announce that a civilization-destroying asteroid is heading toward Earth. Would we wait to act until the probability of disaster is 100 percent? No. Would we wait to act until the impact was days or weeks away? No. Climate change is that asteroid. Its impact will be felt not instantaneously but over years, decades, and centuries. As scientists we have an obligation not only to identify and study the asteroid, but to act upon the clear and present danger it represents, and to join our colleagues in other disciplines in urging responsible action.

Harvard is in a position to lead on this issue. We have a responsibility to do so. Now is the time to act.

Conroy’s points are well taken.  I mentioned that he is a young professor, and I think that is important to remember.  Older people tend to be more concerned about money than the type of world their grandchildren are going to inherit.  That is simply a fact.  As I look around, I see little evidence to the contrary.  How many people do you know who are cutting back on fuel consumption in an attempt to better the lives of their grandchildren?  With that settled, we get to the football game between Harvard and Yale.

Who won the game?  Who cares?  The only important point is that the second half of the game was delayed by about an hour.  Why?  Student, faculty, and alumni protestors from both schools took to the field and sat in protest of older generations’ refusal to take climate change seriously.  The young people are correct, the old folks running things have given little indication that they care at all about what is happening to earth’s climate.  The battle is up to people like 16-year-old Swede Greta Thunburg.  She is an activist on an inspired mission to get the people in power to take action on climate change.  Ms. Thunberg is the closest thing to a superhero that we have.  I will be watching her career through the coming decades with great interest.

How bad is the situation? What are people like Greta Thunberg up against? I often tell people that if New York City is underwater, the people in the Midwest will laugh at them and say: “See…that is what you get.  God’s vengeance and so forth and blah, blah, blah…”  Even then, the threat won’t be taken seriously.  It is quite curious, but I don’t see many older people lamenting the amount of government debt they are leaving their grandchildren.  And they certainly don’t care about a figurative asteroid approaching the earth.  I guess that asteroid is moving a bit too slowly for them to bother.  As for the debt, I think it is a bit too abstract for most people to wrap their heads around.  I am not sure what excuse the politicians have, it appears that they simply do not care.

As for the science behind the warming of the globe, I took a course in Climate Change a long time ago.  The threat is real, the science is solid, the math is inspired.  In recent years it has become clear that the earth is warming at a rate much faster than predicted by the worst-case scenarios.  The professor who taught the course was optimistic that the human race would come to its senses and tackle the problem head-on.  I chuckled to myself when I heard that.  I was not optimistic then, and I feel even more pessimistic about the future now.  We may be at the point where we need a Hail Mary type technological solution that will scrub the earth’s atmosphere.  I have no idea how that would work, neither does anyone else.  I wish us all luck.

One final thought: I read somewhere that there is only one group of people in the world who do not believe in the science of Climate Change.  It should not be too hard to guess that there are old, angry, white members of the Republican Party in the United States.  Why don’t these people believe in science?  It gets a bit complicated, but religion is the main culprit.  Have you ever talked to an evangelical about Climate Change?  The reaction of most of them to the topic is that it is a liberal conspiracy.  There is no such thing as Climate Change because God gave us all that coal, oil, and natural gas.  Why would God give it to us if we weren’t supposed to use it?  Simple, isn’t it?  There is another group of evangelicals, one slightly more sophisticated (I will never type a bigger oxymoron than sophisticated evangelical).  They believe that Climate Change is real, but they think that it is part of God’s plan for the earth and its inhabitants.  Apparently, God wants the planet to warm for reasons that are far beyond simple human understanding.  In any event, neither group has any interest in doing anything about the problem, that would be far too inconvenient.

I will be writing more about this topic in a future post entitled The Science Wars.  This regrettable episode in intellectual history was running at full tilt when I was at Harvard during the mid-80s to early 90s.  The perpetrators set the scholarly foundation for the rejection of science we are seeing in our society today.  Unfortunately, no one knew just how high the stakes were.

 

 

 

 

This is a piece of Flash Fiction.  The topic: A teenage girl gets a letter from George Mason University.

 

Professor Bob

Rosemary bounced through the door, simultaneously kicking off her vans and throwing her backpack against the couch. She didn’t notice that her giant chapstick fell out and rolled under the big, puffy chair her dad used to sit in before he crossed over.

“Rosemary, you have a letter on the table.”

“Mom, geez, you know I hate being called Rosemary! Gah…why do you have to call me that?  Everybody calls me Rosie, you know that.”

“Rosemary is your name.  It was good enough for your grandma, and it is good enough for you.”

“Well…duh!”

Mom put down the parsley she was chopping up to garnish the evening meal and walked over to the dining room table.

“I noticed it was from a university, but I didn’t pay much attention. Which one is it now?  What school is trying to steal my little girl.”

Rosie tried to remain calm; this was bad, really bad. “George Mason mom, well actually it is not officially called George Mason mom, it is just George Mason. I think I’ll go upstairs and research this school. Do I have a little time before dinner?”

“Yes, but first, exactly where is this George Mason University located?  I don’t know how many times I have told you that you aren’t going to school far away from home.”

Rosie pursed her lips as her back muscles tightened.  “It is in Fairfax, Virginia, all right ` It is just outside of D.C.  Guh, do I have some time before we eat or not?”

“A little time is all.  Dinner will be ready in a few minutes.”

Rosie ran upstairs to the computer room – buttons pressed, switches flipped, levers pulled…and (most importantly) the door locked. Rosie concentrated her gaze at the correct spot as her right eye was scanned.  She then reached between two bookcases and touched the wall in the specified pattern to open the portal. The cylindrical staging platform opened up and began glowing steady neon green.  Rosie put on her helmet, adjusted her goggles, took a deep breath, and headed in.

Total silence.  That was always the thing that bothered her most.  It was eerie.  She stood for a few seconds as wispy particles appeared seemingly out of nowhere to form the bust of a figure, a very familiar one.

“Rosemary, good…you got the letter. I wasn’t sure the teleportation had worked properly.”

“Well…duh.  Of course, I got the letter. If I hadn’t gotten it, we wouldn’t be talking now, would we?  What is going on?”

The conjured figure, a sage-like older man (you would never believe how old!) winced as he told her that perdition was upon them. “Rosie, they got out, they escaped. My last experiment went very, very wrong. You and I both know where they are going. I sent out a communique to all the others, they have all checked in and are on their way. You understand exactly what I am saying, right?”

“Uh-huh.  And I also know this must be really bad if you couldn’t just send a message directly to me.  I don’t want to ask, but why did you have to zap a letter into the mailbox?  What’s that all about?”

The old man saw the look in her eyes. He didn’t want to tell her that they were totally compromised, that a data hack and a simple case of blackmail had exposed nearly everything.   “Now listen Rosie, stay right where you are. You are not to leave your house, and even if they show up on your front porch, you are not to engage them. Do you understand me? That is an order. If they come, you are to initiate a complete lockdown of the premises.  If they somehow get through, you are to get your mom and immediately come to the portal, OK?” He looked at her and knew it had been a mistake to warn her, he should have just sent someone to collect her.  Had he been thinking clearly, there are a lot of things he would have done differently.

Rosie stood at the portal, her hands on her hips.  She leaned slightly to the left and shook her head slowly back and forth.

“Rosie, please listen, there isn’t much time…” Rosie cut him off and skipped away from the portal. She was about to get her battery packs and ammunition when her mom’s voice came through on the communication panel.  “Rosie, there is a group of people on the porch asking for you. What is going on, are these new friends of yours?  I certainly didn’t make enough food to feed all those people.”

Rosie looked out a window and saw the group milling around on the front porch and driveway.  “Hey mom, can you come up here for a minute?”

“What is going on?  Is something wrong?”

“Of course not, I just need your opinion on an outfit.  I am trying to impress one of the boys out there.  He is a new kid, and all the girls like him.”

As mom walked through the door, Rosie quickly wrapped her arms around her, lifted her up, and pushed her into the mechanism.  Risking psychosis by getting into the portal unprepared was better than staying and facing the mob.  Easy choice.  As soon as mom was locked in and protected, Rosie did one of those teenage girl waves and then went to the closet for her duffle bag full of ammo.  She threw it on the table and then quickly moved across the room to open a hidden compartment to reveal a silver case, one full of weapons.  She got all the arms locked and loaded, gave her mom a quick glance, and initiated the transport sequence.  You’ll make it.  No worries.  As her mom phased out of existence, she holstered her weapons and headed downstairs.

Author’s note: If you do a little research, you will find that there is a famous professor at George Mason University who is trying to create life in the laboratory.  Sister, you don’t know the half of it.

 

 

 

 

My Favorite President: A Note on The Pythagorean Theorem

Many years ago I had a buddy named Mariah, she was a high school senior working part-time at a restaurant I used to hang out at.  One day she approached me to tell me about a paper she needed to write for both her Government and English classes.  The topic was a President of the United States, to be assigned at random by the teachers.  I immediately said, “Yes!” and started a discussion with anyone who happened by the bar where I was sitting.  The question of the day became: Who is your all-time favorite President?  The surprising thing is that most everyone had an immediate answer.    

As I recall, Mariah was hoping to get assigned George Washington or Theodore Roosevelt, but she ended up with JFK.  That turned out OK because I think she learned a few things, and she completed the assignment on time and to the satisfaction of both of her teachers.  Sadly, I didn’t get to help her as much as I wanted because she had no internet and I couldn’t get my hands on any drafts.  Believe me, I tried, but every time I saw her, she didn’t have her backpack with her, so no draft of her paper was to be found.

So, do you have a favorite President?  I sure do, and isn’t it curious that I can write about him within the context of The Pythagorean Theorem.  It certainly is mysterious unless you know that one of our former presidents actually came up with a smart and original proof of The Pythagorean Theorem.  You had no idea, did you?  Trust me, most people don’t.

Before we get to a discussion of James Garfield, I need to take a detour, a pretty big one.  I am going to tell you a little about how I write these essays and, in particular, what happened when I started to write this one.

There are many different ways that individual writers approach their craft.  I have heard from many sources that Kurt Vonnegut, my favorite novelist, would write three pages of perfect prose in the morning and call it a day.  No editing or revision of any kind required.  If I tried to do that, I would still be on page one of essay one.  I simply could not do it, I am not capable of writing that way.

There is another popular approach to writing called the “scattershot method.”  That is exactly how I write.  When utilizing the scattershot method, you write whatever comes to mind, you don’t worry at all about grammar, spelling, or punctuation.  It is all about ideas and concepts.  When I write, I just try to get the thoughts down on paper as quickly as possible.  There will be plenty of time to clean things up later, right?

Well, guess what?  I have in front of me a sheet of printer paper that contains an outline for this chapter.  I got the idea for this essay as I was finishing up one about an interesting algebra problem I stumbled upon.  The mechanics of that problem (which will appear in a future post) reminded me of The Pythagorean Theorem.  That inspired to write something about the most famous theorem in math, which made me think of the paper Mariah had to write.  Get it?  It all came together in a flash, so I grabbed a piece of paper and wrote down an outline so that I wouldn’t forget what I wanted to write about.  Sigh, much more on that coming up.

Here is a word for word account of what I wrote.  I am reading it off the original sheet of paper.

My Favorite President

-Mariah

-Cohen & Newton

-T.R. & Gould

-Garfield & P.T. proof

I include this because I have a huge problem.  I understand exactly what everything on there means except for the “Cohen & Newton” segment.  Good grief, I know who they are; Cohen is I. Bernard Cohen, the founder of the History of Science department at Harvard University, and Newton is, of course, Issac Newton, arguably the greatest scientist who has or ever will live.  The thing is, I have no idea why I wrote their names down.  I do not know what I am supposed to say about them, I haven’t a clue as to how either man relates to this essay.  I find that a little perplexing.

This is simply more evidence of a disturbing trend, one that I realized a few years ago.  One night some time ago, I was reading an article on a topic relating to evolutionary biology.  I came across an interesting discussion concerning the biological concept of species.  As this was research I was unfamiliar with, I made copious notes in the margin of the paper and went to bed.  The next morning I woke up and decided to quiz myself on what I had read the night before.  I knew there were three major themes that the author had written about.  The big problem is that I could not remember anything about the article.  I couldn’t remember who wrote it or what it was about.  Yikes, that is not good.  I have talked to many other people about this, and they all say that things like that happen to them from time to time, so it is nothing to worry about.  I will say this, I don’t find it reassuring that many of my friends might be losing their minds right along with me.  Seriously though, I hope they are right, and these gaps in memory are not a big deal.  One thing is sure, time, in all its undefeated glory, will eventually chime in with the correct answer.

The fourth line of my infamous sheet of paper reads “T.R. & Gould.”  I know exactly what that means, and I can tell you a little bit about that now.  That line is about President Theodore Roosevelt and Stephen Jay Gould, the greatest science essayist who has ever lived.  Chapter 14 in Gould’s “Bully for Brontosaurus: Reflections in Natural History” is entitled “Red Wings in the Sunset.”  It is a neat little essay about Roosevelt’s accomplishments, not as a politician, but as a scientist.  Bet you didn’t know that Roosevelt published an important scientific article, did you?  Well, he most certainly did.

After he left office, Roosevelt wrote a paper on coloration in birds and mammals.  It was published in the Bulletin of the American Museum of Natural History in 1911.  The technical details of the article are not important, the point here is that Roosevelt was, at heart, a scientist – ever curious about the world and all its inhabitants.  Can you imagine?  A former president sat down and wrote over 100 pages about how and why certain animals are colored the way they are.  Such a thing could have easily gotten Roosevelt my vote as my favorite president, but as it stands now, he is a close second.  Who knows, he may move up to the top spot one day.  I am sure his decedents will be sending me fruit baskets with the intention of influencing me.

Now we can get to my favorite president, James Garfield.  Garfield was college-educated, he got his degree in mathematics from Williams College.  As you are about to see, he put the degree to good use, and that is what makes him my favorite President.

A few years before he became President Garfield, Congressman Garfield came up with a unique proof of The Pythagorean Theorem.  The theorem, the most famous in mathematics, states that for any right triangle, the square of side “a” plus the square of side “b” will equal the square of the hypotenuse, known as side “c.”  That special relationship has been known for centuries, but Garfield was inspired to find his own proof for why the relationship holds.  He did it in a way no one had ever thought of.  He proved that a² + b² = c² by taking an inspired look at the area of a trapezoid.  

Here is the trapezoid President Garfield used for his proof.  It is broken into three right triangles.  I love this proof because it is algebraic, you won’t find any geometry in his argument.  That makes for an intelligent, and unusual, little proof.

The first thing Garfield did was find the area of the trapezoid.  That is easily done in the following way.

 

 

Next Garfield, in an ingenious leap, decided to find the areas of the three right triangles.  The equations are as follows.

He then took the sum of the areas of the individual triangles as follows.

Since the two areas have to be the same, Garfield simply set the equations equal to each other.

Multiplying each side by 2 gives:

Subtract 2ab from each side:

Simply astonishing.  I have to admit that I have a secret ambition (not so secret now) relating to this topic.  I want to come up with the worst, most clumsy proof of the theorem that could possibly exist.  I want it to be Rube Goldberg-esque, the foulest string of mathematics imaginable, yet I want the proof to be correct.  This is the only reasonable hope I have as it appears all the good ones are taken.  There are hundreds of beautiful and thoughtful proofs that can easily be found online.  President Garfield certainly did his part in that regard.  I very much admire his simple, elegant proof.

 

 

 

 

  

 

                       

 

 

             

Bonus Eruptus!

Let me begin by letting everyone know that I love The Simpsons.  The show is now in year 31, and I still look forward to each week’s episode.  I will admit that a few years in the middle of the run were pretty lean, but the show is experiencing a renaissance.  The Simpsons are back on solid footing.

Some of you may remember when Dr. Nick introduced us to Bonus Eruptus.  It was episode 21 of season 7.  The episode is entitled 22 Short Stories about Springfield, and that is exactly what transpires, 22 vignettes about the characters populating Homer’s hometown.  I think it is very clever and I have always wanted them to do more episodes like that one.  This particular episode, one of my favorites, first aired on 4/14/96.  Wow, the show has been around a long time, hasn’t it?  I will gladly take another 30 years.

During that stellar episode, Dr. Nick defined Bonus Eruptus as “a terrible condition where the skeleton tries to leap out of the mouth and escape the body.”  Apparently, Grandpa Simpson had this condition, at least that was the diagnosis of the esteemed Dr. Nick Riviera.  I want to take a closer look at the mathematics behind this ostensibly severe condition.  Why?  I think that we might be able to learn a thing or two about probability theory and the inherent problems that come along with mass medical testing.

Please indulge me for a moment.  Let’s all pretend that we live in Springfield USA and that Bonus Eruptus is a legitimate concern.  I know I wouldn’t want my skeleton to try to take its leave of me.

Imagine that Mayor Quimby, in a transparent attempt to get reelected, offers free, yet mandatory, testing to all the inhabitants of Springfield.  Since I have no idea how many people live there, let’s say that 10,000,000 people are living in the greater Springfield area.  I know that is more of a Capital City number but just play along, OK?  Of those, let’s say that 50,000 of them have the dreaded Bonus Eruptus.

Now let’s imagine that Bonus Eruptus is caused by a virus, one easily detectable by a simple test.  Like all tests, though, it is not perfect.  Some people who have the virus will test negative, and a certain percentage of the people who are negative will, in fact, test positive.  Imagine that the false-positive result rate is 2%.  Also, the poor people who have the virus will test positive only 95% of the time. So, the simple question is:  If someone actually tests positive, e.g., Bumblebee Man or Jeff Albertson (extra points if you know who that is), what is the probability that they actually have the terrible disease?  Think about that a while before you go on.  As you might already have guessed, the answer is not nearly as straightforward as you might think.  After all, why else would I be writing about it?

So, here we go.  Of the 50,000 people who have the virus, only 47,500 of them will actually test positive.

50,000 x .95 = 47,500

We know that 9,950,000 total people do not have it.

10,000,000 – 50,000 = 9,950,000

Of the people who do not have the virus, there will be 199,000 who will test positive anyway (the false positives).

9,950,000 x .02 = 199,000

So now, we can do some simple addition and see we come up with a total of 246,500 people who will test positive for Bonus Eruptus.

47,500 + 199,000 = 246,500

Of those, we know that only 47,500 will actually have it.  So if you test positive for the virus, there is only a 19.3% chance that you actually have Bonus Eruptus!. D’oh!

47,500 / 246,500 = 19.3%

Isn’t that interesting?  Without walking through the math, there is no way that a 19.3% chance would even seem to be a possibility.

It is time for me to go.  I have to prepare for this week’s show.  I hear that Homer is going to do something stupid, and Marge is going to get upset.  I am about to burst with excitement.

Where is my Dollar?

This is an essay about counting. Simple counting, you know, like the kind that the puppet vampire on Sesame Street does. You remember “The Count,” right? One, Two, Three, Four, blah, blah, blah, blah.  I just did a little research, and I discovered his full name is Count Von Count.  Who knew?

I have sat through a lot of lectures in my life, so many that I couldn’t begin to count (get it?).  This may sound surprising, but one of the best lectures I ever attended was about the proper way to count.  This was in a graduate statistics class.  This seemingly straightforward process is a lot more complicated than you might imagine.

To set the stage, I must tell you that in what feels like a previous lifetime, I was an archaeologist.  I worked in The Bahamas at the Island of first contact, the one made famous by Christopher Columbus and his crew.  For those of you who do not remember, the name of the Island is San Salvador, and it is beautiful.

There are numerous ways we could begin our journey into the strange world of simple counting. We could quickly start with a discussion of how easy it seems to be to count, say, artifacts excavated from an archaeological site. If you do not “dig” that we could talk about how scientists count the number of genes in the human genome.  Instead, and by explicit design, we will start with a fictitious handyman.  This man works at a non-existent motel located in a town that you will not find on any map. His story is much more fascinating and informative than anything else I might dream up.

The story begins like this: there was a man named Ichabod who worked at a campground as a general laborer. Ichabod spent most of his time doing odd jobs, usually something different every day.  On a random Friday, the 13^th three men came in needing a cabin. The manager took their information, charged them $60, and sent them on their way. A few hours after they left, the manager realized he made an error and called Ichabod into his office. He told Ichabod that he had mistakenly overcharged the three guys at campsite number 234 by $5 and gave Ichabod the money to hand over to them.

Ichabod worked his way down a winding dirt road to cabin number 234 with 5 one-dollar bills in his pocket. As he approached their camp, he realized that he had no way to divide the $5 evenly by three. He thought that there would be no harm in just giving each of the three guys one dollar and pocketing the extra two dollars for himself. That is precisely what he did.

A few hours later, Ichabod was bored, his work for the evening was done, and there were no pressing emergencies. He decided that he wanted to figure out why the three guys got a discount. He quickly found out that they had a AAA coupon for $5 off for one night’s stay. Something didn’t seem quite right, so Ichabod got the manager’s calculator and multiplied $19 by three. After Ichabod gave them each a dollar back, that is what each of them paid. He came up with $57. He then looked in his pocket and found the two dollars he decided to keep for himself. He multiplied 19 by three again and once again came up with 57. He added the two in his pocket to get $59. Wait a minute, he thought, they initially paid $60.

Ichabod mulled this over for a few more minutes. Let’s see, each guy ended up paying $19 for the campsite. The three of them together paid $57. I kept two. Ichabod had a perplexed and slightly angry look on his face when he looked up at the stars and yelled: “Where is my dollar?”

Do not bother racking your brain just yet. The answer will be as curious at the end of this essay as it is right now. The point to consider at this juncture is simply the slippery nature of straightforward counting. And yes, the Twilight Zone feel of the end of the last paragraph was put there on purpose.

One of the little known aspects of science is the serious thought that scientists have to put into the seemingly artless process of counting. Counting should be straightforward, shouldn’t it?  It should be easy regardless of whether you have kids learning sums or if you have archaeologists counting projectile points. Unfortunately, this is not the case. Simple counting is anything but.

Consider the dilemma of the archaeologist studying regional settlement patterns.  This form of archaeology had become more commonplace in recent decades.  When studying regional settlement patterns, archaeologists do not look at a single site, they consider the relationship between all the sites in a given area. Typically, the scientist would be interested in the differences in the artifacts found at the various locations. Different artifacts found at a particular site would imply different uses for that site, and this is what studying non-site level archaeology is all about. How exactly to do this, though? Simple counts are virtually useless because Site A may have twice as many projectile points as Site B, but maybe the site itself is 10 times as large. The naive investigator might think that Site A was an area where the use of projectile points was much more important than it actually was.

What to do then? There are nearly as many strategies employed as there are archaeologists to do the counting. Many people find percentages to be very powerful.  If projectile points are found to be 85% of the total number of artifacts found at Site A, then this is a very important observation, especially if Site B has three times as many projectile points, but they only represent 2% of the total excavated from that site.

Some archaeologists prefer to work with volumes. They weigh the artifacts and then calculate volumes with respect to all other excavated material. You can even consider the weight of individual types of artifacts vis-à-vis the total amount of dirt dug up. This can lead to percentages or even ratios. The point being that simple counts are almost always deceptive and are rarely useful.

Animal bones, including those of humans, present more issues. A simple, yet potent technique, called Minimum Number of Individuals, or MNI, is often used. If you find 15 sheep vertebra at your site, they may have come from 15 sheep. That is not a whole lot of help. But what happens if you are studying mass burials in the U.S. Southwest and you discover 35 human vertebrae, 8 finger bones, 22 foot bones, and 5 right clavicles? The minimum number of individuals required to explain that group of artifacts is 5. Why 5? Because humans have only one right clavicle each. That might prove to be something worth knowing.

The types of issues we have been talking about are fundamental and might even be surprising to someone who thinks only of Indiana Jones whenever archaeology is mentioned. Once the archaeologist decides how they want to count, the problem with counting is just beginning. Then issues of a statistical nature raise their ugly heads.

It might well be the case that some aspects of the size, e.g., length, of the projectile points that have been excavated are diagnostic. In other words, they can tell us something vital if we are smart enough to tease the information out of the material. You might think that it would be a good idea to get an average length of the points so that you could compare this number with a similar amount from other sites. Let’s see if we can illustrate just how tricky that is.

Determining the average length of points could not, on the face of it, be more simple. Just add all the individual lengths up and then divide by the total number of points to get an average. No calculus involved here. The problem is that it might very well be the case that you will end up with an average size that is not representative of anything in existence. What if you found 6 points 1 centimeter in length and 5 that were 4 centimeters in length? You will calculate an average projectile point length of around 2.5 centimeters. This 2.5-centimeter long point does not exist, you did not find even one that is that length. It should be clear that this is a terrible idea.

The solution to the averaging problem is to split the points up into two separate “batches” of numbers that will be considered separately.  It is pretty obvious that the larger points were used for different purposes than the smaller ones. Reviewed independently, two distinct averages can be calculated that will prove very informative when compared to comparable data from other sites.

This essay has been about simple counting. I am sure that you now appreciate how much care goes into adding, subtracting, multiplying, and dividing. Truth be known, we have only scratched the surface of what is an important scientific issue. This topic becomes even more outrageous when advanced statistical techniques are employed. This is true for all scientists, not just archaeologists.

I am sure that there are many clever ways to end an essay of this nature. Ridiculous puns about counting ways to make mistakes come readily to mind. Or I could remind you to count yourself lucky that you do not have to think deeply about such nonsense. You and I both know, though, that I must end with a simple, elegant, yet slightly disturbing question. Tell me, exactly where is Ichabod’s dollar?

 

 

Negative One Twelfth

There is a perfect epigraph for this essay, but I advise you not to use it. It is too on point.  If you think about it, I am sure you can come up with something.
Buford Lister (personal communication)

I have been reminiscing about my time at Harvard University. I admit that for someone who does not like looking back, that is a bit unusual. There is a good reason, though. We will get to that in due time.

As for my experience there, I found that place to be full of the smartest and the hardest working people I have ever known. Nearly all of them had big ideas and the ambition to go along with them. The people I knew cared deeply about making the world a better place. Without question, the time I spent there was the best in my life.

I was “Pahking my cah in Hahvahd Yahd” before the internet took off. The Web was in its infancy; AOL, Prodigy, and CompuServe were all years off. There were only a few sites I could visit with my home built computer (the one with no hard drive and a nine-inch mono screen). There was lots of excitement, though, about how the internet was going to give voice to people who historically did not have one. My colleagues, friends, and associates at Harvard imagined discussions amongst people who would never meet in real life. They envisioned an exchange of ideas that, otherwise, would never have been possible. The hope was that these people from diverse backgrounds would realize they were basically the same, that their similarities outweigh the differences in geography or ideology. There was a kind of magic in the air. There was real hope that democracy would substantially benefit from a thoughtful and nuanced exchange of ideas from people of different backgrounds.

Did you make it through that last paragraph without shaking your head and saying, “Yeah, right!” to yourself?  Did you throw up on your shoes? I almost did while writing it because we all know what ended up happening. Nearly every thread I have ever seen on any web page I have ever visited devolved into a racial hate fest within a couple posts. One insult after another hurled by the cowards who hide behind the anonymity that their user names afford them. It really is disappointing; instead of rational and informed discussion, I see lots of intolerance and bullying.

This is the main reason I do not have a social media presence. I have had my fill of hate and, as you know, there is lots and lots of it out there. Trolls, by nature, are always looking to take a negative stance, regardless if they understand the topic or not. I simply do not need it.

So, why THAT introduction? The title (Negative One Twelfth) implies that this might be a math essay, even though I am the first to admit it is curious that the number is spelled out. The other way (-  ) seems like it would be cleaner, doesn’t it?  Well, this is a math essay. As usual, I am going to bury the lede by taking off on a seemingly irrelevant mathematical tangent. 

Let’s start by doing some straightforward calculations and see if we can eventually make our way back to the introduction. Unfortunately (and I do mean UNFORTUNATELY), by the end of this essay, my reasoning will become clear.

We are going to start here: What is: 1-1+1-1+1-1+1…? We will call this SUM_1.

[That little string of addition and subtraction has its own particular name. In 1703 Guido Grandi, an Italian scholar, did some interesting work on this problem. As the years went on, other mathematicians started to refer to the problem as Grandi’s Series. Lots of hard and thoughtful work has been done on that simple string of 1s.]

So, do you have an answer? Let’s do what any good, curious mathematician would do; let’s play around with the series and see what we get.
SUM₁ = (1-1)+(1-1)+(1-1)+(1-1)… = 0. Fair enough, right?
BUT:
SUM₁ = 1+(-1+1)+(-1+1)+(-1+1) … = 1. Now something interesting is happening.
If we solve the series one way, we get 0. If we move our parentheses around, we get 1. So, if you like, we can split the difference:

Angry yet?  Probably not, my guess is you are more confused than angry.  I can understand why you might not be convinced that SUM₁ does equal (it does, perhaps we should look for some better evidence).

Let’s tackle the problem using a different methodology. Consider the following series:

Any guesses where that sequence is going?  One way we can solve this problem is by looking at partial sums. We can do that like this:

Do you see what is happening? We are taking the first term, then the sum of the first two terms, then the sum of the first three terms, etc. Our partial solutions are approaching 2, which is the correct answer to the sequence. There is another way (among many) we can solve this problem, and we need to take a look at it.

We can treat the partial sums we just found as a new series, i.e., 1, 1.5, 1.75, 1.875, 1.9375… Now we can take the average of the partial sums in the following way:

We get: 1, 1.25, 1.42, 1.53, 1.61,…

As before, the sequence is moving toward 2. This method, the averaging of the partial solutions, is simply one other way of getting to the correct answer. Got it? Don’t worry if it takes a bit of time to let it sink in. It is a somewhat unusual concept.

Why did I bother bringing this up? Because we can use the same logic to solve SUM₁.

SUM₁ = 1-1+1-1+1-1+1…

First we get the partial sums: 1, 1-1=0, 1-1+1=1, 1-1+1-1=0, 1-1+1-1+1=1, 1-1+1-1+1=0…

We end up with: 1,0, 1, 0, 1, 0… This does not help much, all we are getting is alternating 1s and 0s. But, as you are about to see, something interesting happens when we average the partial sums. Take a look at this:

Using this method, we find that the sequence is approaching . The further we go out, the closer we will get to . It has taken a bit of time, but most of you should be convinced that SUM₁ =.  If you are still skeptical, I suggest a Google search. The Wiki page on Grandi’s Series is full of useful information.

Here is our next problem, we will now tackle SUM_2.

SUM₂ = 1-2+3-4+5-6…

This next step is totally legitimate. We are not breaking any mathematical rules. We are simply going to add SUM₂ to itself.

     

That sequence should be familiar, it is SUM₁.  Now we can easily solve SUM₂.

I am the first to admit that you should be fairly astonished at this point. I know I am.

Now I am going to let you in on a little secret, one that mathematicians and physicists (and me) have known about for a long time. It is a bit of information that makes people very angry. Here we go:

I know, trust me, I know. I came across this little nugget some time ago while taking a course on Number Theory. It didn’t make sense then, and it does not appear to make any sense now, but it is important to note that this result pops up in physics quite a bit. You can find it in String Theory and something called The Casimir Effect (I know a young man who got his Ph.D. in physics from MIT, his dissertation: The Casimir Effect). So yes, if you keep adding numbers forever, you get a negative fraction. Here is the proof:

Easy enough.

Even easier.

 

So, we now know that 1+2+3+4+5+6+7+8… = Negative One Twelfth. I will admit, the result is slightly counterintuitive. Maybe a little more than “slightly.” Bizarre might be a more appropriate word. I wish everyone reading this the best of luck. It might be helpful to keep in mind that physicists have provided experimental evidence that this solution is correct. Simply astonishing.

I always write these essays intending to use the most straightforward methods possible to introduce the readers to things that I find unusual and fascinating. This Negative One-Twelfth nonsense is undoubtedly a worthy topic. As always, I hope that anyone coming across this essay will become interested enough to do further research. There are lots of blanks to fill in, and a computer search will provide any and all answers you might want. This topic, as you might have guessed, has a fascinating history. Take a look around the internet, you will learn about (among other things) convergent and divergent series, Cesaro Summation, and Abel’s quote that Buford Lister thought was too obvious. If you are genuinely inspired, you will become familiar with the concept of analytic continuation. If you can’t sleep at night because this result hurts your brain, you will be introduced to Leonhard Euler and Bernhard Riemann (true geniuses) and their Zeta Function, a methodology that will also get you to Negative One Twelfth.

I guess it is time to close out this essay. I still owe you an explanation for the introduction. I started the piece the way I did because there are numerous threads out there on this very topic. In general, math and science discussion boards are respectful and informative places where intelligent people discuss the issues of the day. Three Cheers and a Tiger from and for all those Harvard people from so many years ago. Well, you can guess where I am going, right? Discussions concerning this topic get people so riled up that they do little more than fling insults at everyone, including the professors who are trying to explain why Negative One Twelfth is a perfectly respectable (and reasonable) answer to SUM₃.

Words such as “stupid” and “moron” are hurled at Ph.D.s by people who have no idea what they are talking about. This is discouraging and totally unacceptable. This problem is elusive; there are instances where Negative One Twelfth is the correct answer, and there might be other instances where it is not appropriate at all. As usual, nature (with all her subtly and nuance) will chime in and let us know when and where to use it.

My final point is that people interested in a problem such as this one are precisely the people who should know better than to head straight to the sewer when they are presented with something they do not understand. Lashing out at people who know more than you about a math or science issue serves no purpose (HACK, HACK, CLIMATE CHANGE, COUGH, COUGH). The internet certainly has given voice to people who otherwise would not be heard, and I am sometimes left wondering just who is benefiting.

 

 

1 = .999…

Q. How many mathematicians does it take to screw in a light bulb?
A. .999…

One of my hobbies is Number Theory. I have a bunch of DVD courses on the topic as well as quite a few books. Consequently, I have always had a secret ambition to write an entire essay consisting of nothing but equations. Mathematics can be so much more beautiful and concise than the words we all struggle to string together.  As the language of nature, mathematics has an elegance that far surpasses anything I can try to tap out on my keyboard. So, what do you say; let’s find out if 1 does indeed = .999…

You know what “.999…” means, right? It is a repeating decimal, that means that the 9s just keep going and going; they never, ever stop. So what am I talking about when I say that 1 = .999…?  Well, why don’t we take a look at some simple math?  I can easily prove to you that 1 and .999…are the same number.

 Could the math be any simpler? Interesting, isn’t it? Take a look at this:

So, are you becoming a believer?  The thing about mathematical proofs is that they do as advertised, they prove things.  Finally, this proof also gets us there but in a slightly different way.

Phil, from Phil’s Slight Oversight fame, read this when he was a college student.  He brought it to one of his professors to see if I was doing some sort of magician’s trick just to fool him.  His professor told Phil that it is true, 1 does, in fact, equal .999… Phil then asked him if that is so, can he write .999… instead of 1 on a test when it comes up?  “Of course,” he replied, “but I wouldn’t do it in any class other than this one.”  

Years ago, a high school student named Tayler also read this.  She brought it to the attention of her high school math teacher, who immediately told her that I didn’t know what I was talking about.  She told Tayler that the idea was nonsense after she spent a few minutes consulting her calculator. Such is life in Iroquois County. 

This short post is a prelude to a longer one that is coming next.  I will be building on these same principles to reach a bizarre conclusion to a simple math problem about counting.  If you are unsettled by this post, I recommend a Google search.  What I have done here is just a sample; .999… has its own Wiki page, visit it, and you will find lots of different and varied proofs.   

 

A Pitcher in Zipper Boots

I had an uncle named Dallas.  This post is about him and a couple things he did during his life, random and unusual things I will never forget.

Dallas used to wear a leather band on his watch, an extraordinarily thick one.  The watch was always worn with the dial under his wrist, not above it.  Why?  I have no idea.  I asked him about it once, and he rotated his left wrist up and to the left and said: “If I want to know what time it is, I do this.”  Fair enough.

Dallas was a big wrestling fan.  Andre the Giant was the strongest, baddest man on the planet, he wouldn’t let anyone dispute that.  I remember him booing The Shiek, an apparent and blatant cheater.  How is the ref not seeing that?  He cheered Bruno Sammartino and got riled up when Gorilla Monsoon got up to his usual shenanigans.  That world was black and white, no one was wearing a grey hat, and Dallas loved it. 

He had a great sense of humor, totally out of proportion to everything else about him.  And, believe me,  that was an excellent thing.  He used to hand me a hammer as he held a piece of rebar vertically with the end touching the ground.  He would say, “OK…when I nod my head hit it.”  He thought that was hilarious, but not nearly as funny as his favorite comedian, the remarkably unfunny Raymond  J. Johnson, Jr.

As far as I can tell, Johnson had one bit.  People would address him by his name, and he would say to them that there were numerous other names they could call him by; they didn’t have to use the particular one that they just used.  Here is a typical Ray Jay Johnson inspired encounter between my uncle and me:

Hi, Dallas.

Dallas, you doesn’t hasta call me Dallas.  You can call me Dal, or you can call me Donley, or you can call me Sonny, or you can call me Junior…but you doesn’t hasta call me Dallas.

Now, this went on whenever I mentioned his name.  He loved that bit.  Ray Jay Johnson has clips on the internet, some of them are national beer commercials.  Such was the fame of Ray Jay Johnson. 

We used to go bowling when I was a kid.  One Saturday night, we went to a local bowling alley for what they called Razzle Dazzle.  There were colored pins mixed in with the regular white ones.  If a head pin came up a particular color, you got money if you threw a strike.  Different color pins were worth different amounts of money.  The red pin in the headpin position was worth $25, a nice chunk of change back in the 1970s.

You guessed it, it was Dallas’ turn, and there it was front and center,  the red headpin.  He waited for the person at the desk to acknowledge the situation.  It only took a few seconds for the loudspeaker to engage.  “Red pin on lane 16.”  The other bowlers stopped.  The $25 shot was the big one.  Some nights went by without it ever coming up.  This was a big deal.

Dallas took his ball and cradled it as he dried his hand.  He might have said a silent prayer, I really don’t know.  With all eyes upon him, Dallas went through his regular routine.  He raised the ball up in the air with both hands as he took a giant step to his right.  As the ball dropped, he slowly started his approach.  He reared back and released, as the ball left his hand it drifted right, completely missing the headpin.  Dallas turned and started walking back toward the seats, totally dejected.  Then something happened, something I had never seen before or since.  The pins started dropping from the back forward, slowly one after the other as if they were in slow motion.  Dallas saw me point down the lane, he turned just as the headpin, the last pin standing, started to slowly wobble and then fall.  The place exploded in cheers as Dallas jogged up to the counter to get his money.  Simply remarkable.

Dallas was not just a bowler, he, along with my friends and I, used to play a lot of softball when we were younger.  I had a long list of names and numbers by the telephone at my parent’s house.  I would call someone to try to get a game together, they would make some calls, and then those people would make some calls, and when everyone was done, we could usually get a bunch of people to play.  We would have neighborhood games, and then we would often challenge people from other schools to play against us.  We played a lot of those types of games.

One day we played a bunch of kids from the local Catholic school.  The games could get pretty competitive.  Most of the kids who showed up played high school baseball, along with lots of other sports.  In fact, those kids from the Catholic school would go on to win a state championship in baseball a few years later.  And yes, among their ranks was a young man who would grow up to become a famous football coach.  I can’t quite remember if Urban Meyer was there on the day my story takes place, he certainly could have been.  Lots of his teammates used to show up for these games.

We were all warming up when Dallas appeared just as the game was about to begin.  I asked him if he was ready, and if he wanted to pitch.  He said sure and took the mound with no warm-up.  The first three batters were mowed down in quick succession.  Then something unusual happened.  He did it the next inning and the next and the next.

Around the fourth or fifth inning, I realized Dallas hadn’t allowed a run.  He was pitching a shutout, in a softball game, against a group of young men who were to become state champions in a few years.  When I mentioned to one of the other players that Dallas hadn’t given up a run yet, he nodded and said: “Yeah, I know.  I can’t believe it.”

Keep in mind that many of these games finished with scores in the 20s or maybe even the 30s.  Pitchers did not fare well in our games, offense dominated…except for that day.  Dallas pitched a shutout.  He hadn’t realized what he had done, and no one made that big of a deal of it.  We all got on with our day after the last out was recorded.  And here I am, over four decades later, checking the time on my upside-down watch.  Every time I look at it, I am reminded of the day my Uncle Dallas pitched a shutout against a team of future state champions while wearing zipper boots.         

The Notorious MFT: The Checkered Story of the GOAT of GOATS

On April 3, 1995, the human race lost the GOAT of GOATS, a stone-cold assassin, a man whom Michael Jordan and Wayne Gretzky can only admire from down the road.  As for Wolfgang Mozart and Isaac Newton, let’s just say that the three of them can argue over which appetizer to order with dinner.  The subject of this essay belongs at that table; those three would have a lot to talk about.  And yes, five days after his death, The New York Times gave him a healthy two-column obituary.

The Notorious MFT was a bad man, how bad?  Humans posed such a weak challenge that in 1958, he gave up his world title out of boredom.  For the next 50 years or so, he would become World Champion whenever he wanted.  Everyone knew he was the GOAT, so he didn’t need to rub elbows with us mere mortals.  He could do whatever he wanted, his legacy was secure.  If he felt like playing, he did; if not, he stayed home.

Before I get to this man and his remarkable story, I have a few thoughts on the word goat and the now ubiquitous acronym GOAT.  When I was younger, the word goat had a negative context when it came up in sports.  The goat was the person responsible for their team losing.  Poor Bill Buckner, who booted a ground ball for the Boston Red Sox in the 1986 World Series, is a famous example.  I still remember where I was when I saw the ball roll by him as much of New England screamed in dread.

Not too long ago, something interesting happened, the word goat became the acronym GOAT, and everything changed.  Now when I hear anyone mention The GOAT, they are always speaking of The Greatest Of All Time.  Many people attribute this change in meaning to the great Muhammed Ali, a man who was much more than one of the greatest boxers who ever lived.  Ali’s wife, Lonnie, incorporated G.O.A.T. Inc. in 1992.  That was the beginning of the metamorphosis.

Ali fought in and outside the ring.  As much as he was a fantastic fighter, he was undoubtedly a historic crusader for social justice.  Our man, while not nearly as famous, also dedicated his life to improving the circumstances of those born less fortunate.  Few would argue that Ali was one of the greatest boxers who ever lived.  No one would ever say that The Noriorious MFT was anything other than the greatest in his field.  It’s not even up for debate.   

Now we get to the man for whom this essay is named.  The Notorious MFT, also known as Marion Franklin Tinsley, was the greatest checkers player who ever lived.  He never lost a match, you read that right, he never lost a single match!  He only lost four games his entire life when he sat down to play checkers against a fellow human being.  Can you imagine?  I don’t know what to say in the face of such a ridiculous record.  All I can do is stand in awe of the genius that was Marion Tinsley.

Tinsley was a mathematician and a lay preacher.  He got his Ph.D. in mathematics from The Ohio State University.  The records at that university will show that Tinsley concentrated in combinatorial analysis, those same archives will not document all the time he spent studying checkers while there.  The man never married, he lived checkers, the game was his one true love.

Tinsley left his position teaching math at Florida State University for a similar post at Florida A&M, a public university historically attended by African-Americans.  Instead of becoming a missionary to Africa, Tinsley decided to stay closer to home to spread the word about mathematics and his faith.  I have been searching, and I can not find anyone who has gone on record with a single bad word to say about him.  By all accounts, he was a kind and gentle soul, except when seated to play checkers.  Then he transformed into an aggressive menace. 

Tinsley’s full story can not be told without considering the development of computers and the software that runs them.  Many people took it upon themselves to try to defeat Tinsley.  When the humans failed and failed again, a man in Canada decided to write some code.  He and his team made it their mission to create a computer program that could defeat the most magnificent checkers player of all time.    

Jonathan Schaeffer of the University of Alberta in Canada led a team that dared to believe that they could beat Tinsley.  How did they fare?  Do you have any guesses?  What do you think happened?

They failed.  Schaeffer’s program, named Chinook, defeated Tinsley twice in individual games but lost the match.  It is essential to note that no human ever beat Tinsley twice in a game of checkers.  His four losses were to four different people.  

After Tinsley’s death, the team did something extraordinary.  They designed a software program that solved checkers.  What does this mean?  The best any opponent can hope for is a tie.  The software can not be defeated.  It plays perfectly every time it is engaged. 

It took the team decades to dial the software in.  Obviously, this is a significant accomplishment, one worthy of world acclaim.  Think about this: there are 5 x 10²⁰ possible moves on a standard checkerboard.  Imagine the computing power, as well as the brainpower, required to attack that problem.

Schaeffer and his team were motivated and inspired by the greatness of Tinsley.  They were driven to build a program that could defeat him.  They were on the cusp of perfecting the program when Tinsley succumbed to pancreatic cancer at the age of 68.     

Tinsley’s grave is in Columbus, Ohio.  Schaeffer hopes to make a pilgrimage to the site one day.  Chinook lives on, you can find it with a Google search.  You can even challenge the program to a game if you dare.  If you play, prepare yourself to lose, you certainly will.  Same as with the people who came up against The Notorious MFT, the undeniable GOAT of GOATS.