THINKER'S ALMANAC - December 21

How, using a barometer, did a student give his teachers a lesson in creativity?

Subject: Creative Thinking - Functional Fixedness

Event:  The story “Angels on the Head of a Pin” appears in The Saturday Review, 1968

Children must be taught how to think, not what to think. -Margaret Mead

On this day in 1968, Alexander Calandra published a story in The Saturday Review magazine entitled “Angels on the Head of a Pin.”

In the story, Calandra recounts his interaction with a physics student who was referred to him by another instructor who requested that Calandra referee the student’s unconventional answer to a test question.

The question on the exam was “Show how it is possible to determine the height of a tall building with the aid of a barometer.”  

                                                            Image by OpenClipart-Vectors from Pixabay 

The student responded to the question as follows:  “Take a barometer to the top of the building, attach a long rope to it, lower the barometer to the street and then bring it up, measuring the length of the rope.  The length of the rope is the height of the building.”

Although the student’s answer was correct, it clearly did not reflect the instructor’s expectation that a student answers the question in a way that reveals a competence in physics.  A correct answer would involve using the barometer to measure the difference between the pressure at the top of the building and the bottom.

Offering the student a second chance to answer the question, Calandra gave the student six minutes.  This time the student-generated the following answer: 

"Take the barometer to the top of the building and lean over the edge of the roof. Drop that barometer, timing its fall with a stopwatch. Then using the formula S = ½ a t2, one could easily calculate the height of the building.”

Intrigued by the student’s thinking, Calandra asked him what other solutions he had to the problem.  The student then proceeds to give four more possible methods.  One, involving a comparison of the shadows cast by the barometer and the building; two, using the barometer as a ruler and marking off the length of the barometer on the wall while climbing the stairs; three, using the barometer on the end of a string to make a pendulum; and four, knocking on the janitor’s door and asking him the following: "I have a fine barometer which will be yours if you tell me the height of this building.”

The truly fascinating thing about Calandra’s parable is that it is the student who is being tested who becomes the teacher, supplying Calandra and the reader with a powerful lesson in flexible thinking.  Too often students are taught one, supposedly acceptable way to solve a problem, rather than being encouraged to use their creativity to explore multiple correct possibilities.  

The student was courageously resisting functional fixedness, the type of thinking that limits solutions to conventional, acceptable answers and discourages new ideas and innovative thinking.  

For example, try the following brain teaser:

What is the capital of Antarctica?

If you Google the question, searching for a city, you’ll discover that Antarctica has no cities, let alone a capital city.  However, if you look at the question with a bit more of a flexible mindset, you might realize that the word “capital” can also refer to letters; therefore, the answer is capital A.

 

Recall, Retrieve, Recite, Ruminate, Reflect, Reason:  What is functional fixedness, and how does it limit creative thinking?

Challenge - Defenestrate The Box:  As the student illustrated in the story, functional fixedness can hinder creative thinking.  Do a bit of research on creative problem solving, and write a public service announcement that encourages people to think outside of the box.  What are important characteristics and habits of creative thinking, and how can people apply these habits to think more creatively?

ALSO ON THIS DAY:

December 21, 2002:  On this day, President George W. Bush was meeting with his closest advisors in the Oval Office to review the evidence for the existence of weapons of mass destruction (WMD) in Iraq.  Determining whether or not Iraq had such weapons was crucial in the president’s decision on whether or not to commit U.S. forces to the invasion of Iraq.  At one point in the meeting, President Bush turned to CIA Director George Tenet, asking him how confident he was that Iraq had WMDs.  His reply was, “Don’t worry, it’s a slam dunk!” In using a basketball metaphor, Tenet was expressing his belief that the presence of WMDs was a sure thing.  History tells us that Tenet might have been better served by selecting a different metaphor considering the fact that the eventual absence of WMDs became a huge embarrassment for the Bush administration after the U.S. invaded Iraq in March 2003.

Sources:

1-Calandra, Alexander. “Angels on a Pin.” Saturday Review 21 Dec. 1968.

THINKER'S ALMANAC - December 22

How did a failed doomsday prophecy in 1954 lead to an essential psychological insight into how humans rationalize failure?

Subject:  Cognitive Dissonance - The Seekers

Event: Dorothy Martin’s Prophecy, 1954

 

We are all capable of believing things which we know to be untrue, and then, when we are finally proved wrong, impudently twisting the facts so as to show that we were right. -George Orwell

In 1954, psychologist Leon Festinger saw an intriguing headline in the newspaper:  “Prophecy From Planet Clarion Call to City:  Flee That Flood.”  The article explained the strange beliefs of a Chicago cult called the Seekers, led by housewife Dorothy Martin, who claimed to be receiving communications from the planet Clarion.  Based on these communications, Martin revealed that on December 21, 1954, the world would end.  Prior to the event, however, Martin also explained that aliens would come via flying saucers to collect her faithful followers and take them to safety on Clarion.

Assuming that Martin’s proclamations were incorrect, Festinger arranged for some of his students to infiltrate the Seekers in order to observe them up close.  Festinger was especially interested in how the group would react on this day, December 22, when they learned that the flying saucers did not arrive as scheduled and that the world did not end.

As Festinger expected, the morning of December 22 dawned without the arrival of any alien visitors.  Early that morning at 4:45 AM Martin called the Seekers together to deliver her latest message from Clarion.

Martin’s message totally reframed the Seekers’ situation, turning it from tragedy to triumph.  She proclaimed that because her people had shown how much faith, the earth had been spared:

 “…by his word have ye been saved -- for from the mouth of death have ye been delivered and at no time has there been such a force loosed upon the Earth.  Not since the beginning of time upon this Earth has there been such  force of Good and light as now floods this room.”

Festinger documented the story of the Seekers in his 1956 book When Prophecy Fails, and he called the phenomenon of clashing beliefs experienced by the Seekers cognitive dissonance.  And as he further explained, cognitive dissonance is a type of thinking all humans experience:  facing incompatible beliefs, we rationalize a situation or justify a failure. Who hasn’t, for example, gone on a diet one day and then gone on a junk food binge the next.  We might be disappointed with ourselves, but we are also capable of buoying our self esteem by rationalizing our behavior by explaining it away as a minor indiscretion.

                                                                    Image by Maddy Mazur from Pixabay 

To establish the reality of cognitive dissonance under experimental conditions, Festinger set up a study that he called “The Boring Task.”  It began by giving subjects an hour-long task:  simply turning pegs monotonously on a wooden board.  Once that task was completed, he offered half the subjects one dollar to tell the next person waiting to complete the task that it was fun and interesting.  The other half of the subjects were offered twenty dollars to tell the next person in line that the task was fun and interesting.  Finally, all participants were interviewed by researchers and asked what they really thought about the task.  The results showed that subjects who had been paid one dollar reported that the task was enjoyable, while subjects who were paid twenty dollars reported that the task was terribly dull.

Festinger interpreted the results as consistent with how ordinary people adjust their beliefs when faced with cognitive dissonance.  The people who were given just one dollar to lie experienced an uncomfortable clash of belief between their true feelings about the task being boring and the fact that they had told someone else it was fun.  This clash of beliefs was resolved by simply altering their beliefs and reporting that the task was actually fun.  In contrast, the people who were given twenty dollars felt no need to alter their beliefs because they had been fairly compensated to lie and thus felt no need to justify their actions (1).

Recall, Retrieve, Recite, Ruminate, Reflect, Reason:  How did Festinger’s boring task show that ordinary people experience cognitive dissonance?

Challenge - Franklin and the Fish:  In his autobiography, Benjamin Franklin recounts the following incident.  Read it carefully, and explain how specifically Franklin experienced cognitive dissonance:

I believe I have omitted mentioning that , in my first voyage from Boston, being becalmed off Block Island, our people set about catching cod, and hauled up a great many. Hitherto I had stuck to my resolution of not eating animal food, and on this occasion I considered, with my master Tryon, the taking every fish as a kind of unprovoked murder, since none of them had or ever could do us any injury that might justify the slaughter. All this seemed very reasonable. But I had formerly been a great lover of fish, and when this came hot out of the frying-pan, it smelt admirably well. I balanced some time between principle and inclination, till I recollected that, when the fish were opened, I saw smaller fish taken out of their stomachs. Then thought I, "If you eat one another, I don't see why we mayn't eat you." So I dined upon cod very heartily, and continued to eat with other people, returning only now and then occasionally to a vegetable diet. So convenient a thing it is to be a reasonable creature, since it enables one to find or make a reason for everything one has a mind to do.

 

ALSO ON THIS DAY:

December 22, 1944:  On this day in 1944, American soldiers of the 101 Airborne Division at the Belgian town of Bastogne were surrounded by German forces.  In what later became known as the Battle of the Bulge, the American forces were caught off guard when Hitler launched a surprise counteroffensive.  At 11:30 on the morning of December 22, German couriers with white flags arrived at the American lines, delivering a letter demanding the surrender of the Americans.  The acting commander of the 101st, Brigadier General Anthony McAuliffe, read the letter.  After pausing for a moment to reflect and to ask for input from his subordinates, he scribbled the following laconic reply:

 

To the German commander:

 

Nuts!

 

The American commander

 

The German couriers spoke English, but they were puzzled by the general’s reply.  As U.S. officers escorted them back to the defensive line, they explained to the Germans that “nuts” meant the same thing as “go to hell.” The soldiers of the 101st continued to hold their ground under the attacks of the Germans for the four days that followed until the siege was finally broken with the arrival of U.S. tank forces of the Third Army, led by Lieutenant General George S. Patton. The laconic reply has a long military tradition that dates back to the Spartans of ancient Greece, who were known for their blunt statements and dry wit.  In fact, the word “laconic,” meaning “concise, abrupt” is a toponym originating from a region of Sparta known as Laconia.  In Spartan schools, for example, a boy whose reply to a question was too verbose was subject to being punished by having his thumb bitten by his teacher (3).  When Philip II of Macedon - father of Alexander the Great - invaded Greece in the third century BC, he sent the following threat to the Spartans:   “You are advised to submit without further delay, for if I bring my army into your land, I will destroy your farms, slay your people, and raze your city."  The Spartan’s replied:  “If.”  (4).

 

Sources:  

1-Grimes, David Rober.  Good Thinking.  New York:  The Experiment, 2019.

2-The Electric Ben Franklin.  The Autobiography of Benjamin Franklin (1793).

3-Cartledge, Paul.  Spartan Reflections. University of California Press, 2003:  85.

4-http://www.etymonline.com/index.php?term=laconic. https://www.army.mil/article/92856

THINKER'S ALMANAC - December 22

Subject:  Cognitive Dissonance - The Seekers

Event: Dorothy Martin’s Prophecy, 1954

 

We are all capable of believing things which we know to be untrue, and then, when we are finally proved wrong, impudently twisting the facts so as to show that we were right. -George Orwell

In 1954, psychologist Leon Festinger saw an intriguing headline in the newspaper:  “Prophecy From Planet Clarion Call to City:  Flee That Flood.”  The article explained the strange beliefs of a Chicago cult called the Seekers, led by housewife Dorothy Martin, who claimed to be receiving communications from the planet Clarion.  Based on these communications, Martin revealed that on December 21, 1954, the world would end.  Prior to the event, however, Martin also explained that aliens would come via flying saucers to collect her faithful followers and take them to safety on Clarion.

Assuming that Martin’s proclamations were incorrect, Festinger arranged for some of his students to infiltrate the Seekers in order to observe them up close.  Festinger was especially interested in how the group would react on this day, December 22, when they learned that the flying saucers did not arrive as scheduled and that the world did not end.

As Festinger expected, the morning of December 22 dawned without the arrival of any alien visitors.  Early that morning at 4:45 AM Martin called the Seekers together to deliver her latest message from Clarion.

Martin’s message totally reframed the Seekers’ situation, turning it from tragedy to triumph.  She proclaimed that because her people had shown how much faith, the earth had been spared:

 “…by his word have ye been saved -- for from the mouth of death have ye been delivered and at no time has there been such a force loosed upon the Earth.  Not since the beginning of time upon this Earth has there been such  force of Good and light as now floods this room.”

Festinger documented the story of the Seekers in his 1956 book When Prophecy Fails, and he called the phenomenon of clashing beliefs experienced by the Seekers cognitive dissonance.  And as he further explained, cognitive dissonance is a type of thinking all humans experience:  facing incompatible beliefs, we rationalize a situation or justify a failure. Who hasn’t, for example, gone on a diet one day and then gone on a junk food binge the next.  We might be disappointed with ourselves, but we are also capable of buoying our self-esteem by rationalizing our behavior by explaining it away as a minor indiscretion.

To establish the reality of cognitive dissonance under experimental conditions, Festinger set up a study that he called “The Boring Task.”  It began by giving subjects an hour-long task:  simply turning pegs monotonously on a wooden board.  Once that task was completed, he offered half the subjects one dollar to tell the next person waiting to complete the task that it was fun and interesting.  The other half of the subjects were offered twenty dollars to tell the next person in line that the task was fun and interesting.  Finally, all participants were interviewed by researchers and asked what they really thought about the task.  The results showed that subjects who had been paid one dollar reported that the task was enjoyable, while subjects who were paid twenty dollars reported that the task was terribly dull.

Festinger interpreted the results as consistent with how ordinary people adjust their beliefs when faced with cognitive dissonance.  The people who were given just one dollar to lie experienced an uncomfortable clash of belief between their true feelings about the task being boring and the fact that they had told someone else it was fun.  This clash of beliefs was resolved by simply altering their beliefs and reporting that the task was actually fun.  In contrast, the people who were given twenty dollars felt no need to alter their beliefs because they had been fairly compensated to lie and thus felt no need to justify their actions (1).

Challenge - Franklin and the Fish:  In his autobiography, Benjamin Franklin recounts the following incident.  Read it carefully, and explain how specifically Franklin experienced cognitive dissonance:

I believe I have omitted mentioning that , in my first voyage from Boston, being becalmed off Block Island, our people set about catching cod, and hauled up a great many. Hitherto I had stuck to my resolution of not eating animal food, and on this occasion I considered, with my master Tryon, the taking every fish as a kind of unprovoked murder, since none of them had or ever could do us any injury that might justify the slaughter. All this seemed very reasonable. But I had formerly been a great lover of fish, and when this came hot out of the frying-pan, it smelt admirably well. I balanced some time between principle and inclination, till I recollected that, when the fish were opened, I saw smaller fish taken out of their stomachs. Then thought I, "If you eat one another, I don't see why we mayn't eat you." So I dined upon cod very heartily, and continued to eat with other people, returning only now and then occasionally to a vegetable diet. So convenient a thing it is to be a reasonable creature, since it enables one to find or make a reason for everything one has a mind to do.

 

Sources:  

1-Grimes, David Rober.  Good Thinking.  New York:  The Experiment, 2019.

2-The Electric Ben Franklin.  The Autobiography of Benjamin Franklin (1793).

THINKER'S ALMANAC - September 21

What is the connection between the actor Bill Murray and philosopher Friedrich Nietzsche? 

  

Subject: Amor Fati - Groundhog Day, The Movie

Event:  Birthday of Bill Murray, 1950

Cease to fume at destiny by ever grumbling at today or lamenting over tomorrow. -Marcus Aurelius

What if there were no tomorrow?  What if, instead, each day were the same day -- day after day ad infinitum.  This is the premise of the 1993 film Groundhog Day, starring Bill Murray, who was born on this day in 1950.  In the film, Murray plays a self-consumed Pittsburgh weatherman who travels to Punxsutawney, Pennsylvania, to cover the annual Groundhog Day festivities.  When he wakes the next morning, Connors discovers that it is not, in fact, the day after Groundhog Day; instead, it is once again February Second, Groundhog Day.

Image by Karen Burke from Pixabay

For the rest of the film, Phil struggles to cope and adapt to his fate, living the same day over and over.  At first, he faces disbelief, then desperation, then decadence, and then depression.  Finally, near the film’s end, he begins to embrace his fate and look beyond his own selfish desires.  Rather than seeing each day as a living nightmare, Phil now sees each day as an opportunity to serve others.

When the film Groundhog Day first came out in 1993, most saw it as merely another entertaining romantic comedy; however, as it has aged, the film has become more and more a philosophical film.  Could it be that the name of the main character Phil is meant to prime viewers to think about the classic ‘phil’osophical questions of life:  What is the meaning of my life?  How should I spend my time each day? What am I learning from my experiences each day?

As mentioned earlier, Phil Connors finally learns to embrace his fate rather than to curse his existence. Like Sisyphus, Phil cannot die and is stuck in the hell of repeating the same day over and over.  Change comes for him, however, when he stops struggling against his fate and instead begins to focus on the things that he can control.  As the Stoic philosopher Epictetus, a slave who faced much adversity himself, said, “Do not seek for things to happen the way you want them to; rather, wish that what happens happens the way it happens: then you will be happy” (1).

The Stoics called this mindset amor fati, the love of fate.  It’s an acknowledgment that much of life consists of good and bad circumstances that are out of our control.  What is in our control, however, is our thoughts, attitudes, and reactions to those life events.  These thoughts are what allow us to make the best out of anything that happens.

One anecdote that illustrates the amor fati mindset comes from the life of the great American inventor Thomas Edison.  On the evening of December 10, 1914, a chemical-fueled inferno engulfed his New Jersey invention factory.  As Edison stood watching the conflagration, he calmly turned to his young son and said, “Go get your mother and all her friends.  They’ll never see a fire like this again.”

Another philosopher who advocated amor fati was Friedrich Nietzsche: “My formula for greatness in a human being is amor fati: that one wants nothing to be different, not forward, not backward, not in all eternity. Not merely bear what is necessary, still less conceal it… but love it.” 

Philosophy means “the love of wisdom.”  In this sense, Groundhog Day is a true love story.  Phil finds love through a relationship with a romantic partner; more importantly, however, he finds love through examining his own life, gaining wisdom, and embracing his fate.

 

Recall, Retrieve, Recite, Ruminate, Reflect, Reason:  What is amor fati?  Contrast what Phil’s life looked like before and after he embraced the amor fati philosophy?

Challenge - Thinking “Filmosophically”: Brainstorm a list of films that you would classify as philosophical, that is, films that help you reflect on the meaning of life or on the nature of reality (metaphysics) or truth (epistemology).  Which one film on your list would you recommend most highly for its ability to get the audience to contemplate philosophical questions?

Also on This Day:  

September 21, 1756:  The Scottish engineer John Loudon McAdams was born on this day.  McAdams’ revolutionary idea was to solve the problem of muddy and impassable roads by using layers of rock and gravel to raise the level of the road, making it more stable and less muddy.  In his 2014 book Brain Rules, neuroscientist John Medina employs McAdams’ road innovation as an analogy for exercise.  Just as the macadamization of roads gave people better access to goods and services, so too does exercise provide your body better access to the oxygen and food it needs to survive and thrive (3).

September 21, 1897:  One of the most famous editorials ever written was published on this day.  After 8-year-old Virginia O’Hanlon wrote a letter to the New York Sun asking to know the truth about Santa Claus, Francis Pharcellus Church wrote her editorial reply saying:   

Yes, Virginia, there is a Santa Claus. He exists as certainly as love and generosity and devotion exist, and you know that they abound and give to our life its highest beauty and joy. . . . Nobody sees Santa Claus, but that is no sign that there is no Santa Claus The most real things in the world are those that neither children nor men can see. (5)

September 21, 1937:  J.R.R. Tolkien’s The Hobbit was published.  Tolkien began the book in a rather unexpected way.  As a professor of Anglo-Saxon at Oxford University, Tolkien would augment his salary in the summers by marking School Certificate exams, a test taken by 16-year-olds in the United Kingdom.  In a 1955 letter to the poet W.H. Auden, Tolkien recounted the moment that launched what was to become a classic in fantasy and children’s literature:

 

All I remember about the start of The Hobbit is sitting correcting School Certificate papers in the everlasting weariness of that annual task forced on impecunious academics with children. On the blank leaf I scrawled: 'In a hole in the ground there lived a hobbit.' I did not and do not know why (4).

 

September 21, 1947:  Today is the birthday of the writer Stephen King, known best for his horror stories.  He once said, “People think that I must be a very strange person. This is not correct. I have the heart of a small boy. It is in a glass jar on my desk.” 

Sources:

1-Williams, Mary Elizabeth. “Lessons from ‘Groundhog Day’: More resonant than ever today.”  Salon.com  2 Feb. 2018.

2-Muyskens, K.L. -

“What if There is No Tomorrow? There Wasn’t One Today.” Elephantjournal.com 2 Feb. 2015.

3-Medina, John. Brain Rules: 12 Principles for Surviving and Thriving at Work, Home, and School. Seattle, WA: Pear Press, 2008. ISBN 978-0979777707: 30.

4-http://www.theguardian.com/books/2014/jun/12/jrr-tolkien-teaching-exhausting-depressing-unseen-letter-lord-rings

5-”Text of ‘Yes, Virginia, There is a Santa Claus.’"  www.cs.cmu.edu.  

 

THINKER'S ALMANAC - December 21

Subject: Creative Thinking - Functional Fixedness

Event:  The story “Angels on the Head of a Pin” appears in The Saturday Review, 1968

Children must be taught how to think, not what to think. -Margaret Mead

On this day in 1968, Alexander Calandra published a story in The Saturday Review magazine entitled “Angels on the Head of a Pin.”

In the story, Calandra recounts his interaction with a physics student who was referred to him by another instructor who requested that Calandra referee the student’s unconventional answer to a test question.

The question on the exam was “Show how it is possible to determine the height of a tall building with the aid of a barometer.”  

The student responded to the question as follows:  “Take a barometer to the top of the building, attach a long rope to it, lower the barometer to the street and then bring it up, measuring the length of the rope.  The length of the rope is the height of the building.”

Although the student’s answer was correct, it clearly did not reflect the instructor’s expectation that a student answers the question in a way that reveals a competence in physics.  A correct answer would involve using the barometer to measure the difference between the pressure at the top of the building and the bottom.

Offering the student a second chance to answer the question, Calandra gave the student six minutes.  This time the student-generated the following answer: 

"Take the barometer to the top of the building and lean over the edge of the roof. Drop that barometer, timing its fall with a stopwatch. Then using the formula S = ½ a t2, one could easily calculate the height of the building.”

Intrigued by the student’s thinking, Calandra asked him what other solutions he had to the problem.  The student then proceeds to give four more possible methods.  One, involving a comparison of the shadows cast by the barometer and the building; two, using the barometer as a ruler and marking off the length of the barometer on the wall while climbing the stairs; three, using the barometer on the end of a string to make a pendulum; and four, knocking on the janitor’s door and asking him the following: "I have a fine barometer which will be yours if you tell me the height of this building.”

The truly fascinating thing about Calandra’s parable is that it is the student who is being tested who becomes the teacher, supplying Calandra and the reader with a powerful lesson in flexible thinking.  Too often students are taught one, supposedly acceptable way to solve a problem, rather than being encouraged to use their creativity to explore multiple correct possibilities.  

The student was courageously resisting functional fixedness, the type of thinking that limits solutions to conventional, acceptable answers and discourages new ideas and innovative thinking.  

For example, try the following brain teaser:

What is the capital of Antarctica?

If you Google the question, searching for a city, you’ll discover that Antarctica has no cities, let alone a capital city.  However, if you look at the question with a bit more of a flexible mindset, you might realize that the word “capital” can also refer to letters; therefore, the answer is capital A.

Challenge - Defenestrate The Box:  As the student illustrated in the story, functional fixedness can hinder creative thinking.  Do a bit of research on creative problem solving, and write a public service announcement that encourages people to think outside of the box.  What are important characteristics and habits of creative thinking, and how can people apply these habits to think more creatively?

 

Sources:

1-Calandra, Alexander. “Angels on a Pin.” Saturday Review 21 Dec. 1968.