Life Lessons from Mathematics

Here’s a question for you:  Suppose that one in a thousand people have a serious disease and there is a medical test which determines whether or not a person has it. However, as with all tests, it is not 100% accurate. If you have the disease, it will give the correct diagnosis 100% of the time. If you don’t have the disease it will give the correct diagnosis 97% of the time. You take the test and it indicates you have the disease. Should you be concerned? What’s the probability that you actually have it?

You may be surprised to learn that you can breath a sigh of relief.  Chances are only about 3% that you have the disease!  Surprised?  Think of it this way: If 1000 people get tested, just one of those will likely have the disease and will be diagnosed as such. However, 3% of the 1000 – that is, 30 people - who are healthy will also be diagnosed as diseased.  Thus there are a total of 31 people who test positive, but only one of them – about 3% - is actually sick.

OK – now that you’re thinking more clearly, try this one: How many people need to be in a room before you can be absolutely certain that at least two of them have the same birthday (just the day, not the year)?  Well, allowing for leap year, it’s possible (though highly unlikely) that 366 people can each have a different birthday – each on a different day of the year. However, as soon as one more person enters the room, s/he HAS to share a birthday with one of the 366 already there. Thus 367 people GUARANTEES that two will have the same birthday.

Sorry, that wasn’t the question. Here it is: How many people need to be in a room before the probability is greater than one-half that two will have the same birthday?  That is, if you had to bet, you’d do better to guess that somewhere in the room two people share a birthday.  What do you think?  A common guess is 183 (half of 366).  However, you’re likely to be just as surprised as before. It turns out that if the room has just 23 people in it, chances are better than 50% that two will have the same birthday. Don’t believe me? The math is too involved for this column, but try it out.  Have everyone in a room write down their birthday (and relatives as needed) so that the total number of birthdays is, say, over 35.  Then go around and have everyone give the dates - - you’ll very likely find a match.

I have spent the last fifteen years going to high schools, colleges, and universities around the country telling about Elvis, my (late) Welsh Corgi. When I threw a ball down the beach and into the water, he ran down the beach and jumped into the lake at just the right point to retrieve the ball in minimum time. (For details, google: elvis, corgi, calculus.)

My favorite part of the talk was when I asked what Elvis should do if we backed up another 20 yards, but still threw the ball to the same place in the water.  Most everyone guessed that Elvis’s water-entry point should also back up a bit.  Using calculus, I showed them that their intuition was wrong. Elvis’s entry point remained the same.

These examples show the power of mathematics.  They also show the value of a formal education.  As I tell students, one can learn much about life by getting a job, or traveling the world, or joining the military, or just living out on the street. However, a formal education provides valuable and life-changing insights in mathematics, literature, and science – insights that one won’t likely learn on one’s own.  That is why a liberal arts education is truly liberating.

These examples provide another lesson as well. Our gut intuition and beliefs – our common sense – may well be dead wrong, even when others are in agreement with us.  Think about that. There may be things that you and those around you are convinced are true, but in fact are not. In mathematics it’s relatively easy to prove the error. In other areas we have no choice but to hold our beliefs with a dose of humility realizing that maybe – just maybe – we’re all mistaken.

That’s not a bad lesson to learn – at least that’s what my gut tells me.

Bobby Kennedy’s Legacy

Bobby Kennedy is a hero of mine.  I’m just old enough to remember a little about him first hand, and recently began a new biography,  “Bobby Kennedy: The Making of a Liberal Icon” by Larry Tye.

Who can forget the iconic image of him sitting crouched face to face with his brother, the President, during the Cuban Missile Crisis. President Kennedy had been challenged as to the wisdom and appropriateness of appointing his younger  brother, just in his mid thirties, as Attorney General. JFK quipped, “I can't see that it's wrong to give him a little legal experience before he goes out to practice law.”  

That quote is significant. The 1960’s under Kennedy and the Civil War period under Lincoln were two of the most turbulent times in the history of our nation. Yet in the midst of troubled times, these presidents led with gentleness and humor.  Lincoln was famous for his stories. A favorite was of the Revolutionary War hero Ethan Allen who visited England a few years after the war ended. England was still smarting from the loss, so when Allen asked to use the outhouse, he discovered that his host had hung a picture of George Washington in it. Upon exiting Allen announced, “Very appropriate – nothing makes an Englishman shit faster than a picture of General Washington.”  I digressed intentionally. It is good to remember the character – the wit and wisdom  - of our great leaders.

Lincoln, though assassinated, accomplished his great mission – he saw the Civil War end and the Union restored.  President Kennedy was killed before his first term ended, but not before he put this nation on bold new trajectories of humanitarian work abroad, a space program, physical fitness, and civil rights.

But Bobby’s potential legacy remains the great unknown. Not knowing what he would have accomplished as president, we shouldn’t forget the lesson he taught us while still a senator and presidential contender.

The date was April 4, 1968. The place was Indianapolis. Bobby was scheduled to give a campaign speech in anticipation of the Indiana primary.  As Bobby’s plane landed, he learned that Martin Luther King Jr. had been assassinated.  Fearing riots, the mayor and chief of police advised him to cancel his speech to a largely black audience set in the ghetto of Indianapolis.  Rejecting their advice, Bobby addressed the shocked crowd with words just as appropriate for today (find the full speech  online):

“In this difficult day, in this difficult time for the United States, it’s perhaps well to ask what kind of nation we are, and what direction we want to move in . . . We can make an effort, as Martin Luther King did, to understand, and to comprehend, and to replace that violence, that stain of bloodshed that has spread across our land, with compassion and love  . . . My favorite poet was Aeschylus – he once wrote: `He who learns must suffer. And even in our sleep, pain that cannot forget, falls drop by drop upon the heart. And in our own despair, against our will, comes wisdom to us, by the awful grace of God. ‘ . . . What we need in the United States is not division. What we need in the United States is not hatred. What we need in the United States is not violence and lawlessness, but love and wisdom, and compassion toward one another – and justice for those who still suffer within our country – whether they be white or whether they be black.”   

“We have had difficult times in the past, and we will have difficult times in the future. It is not the end of violence. It is not the end of lawlessness. It is not the end of disorder. The vast majority want to live together, and want to improve the quality of our lives, and want justice for all human beings that abide in our land. Let’s dedicate ourselves to what the Greeks wrote so many years ago, `To tame the savageness of man, and make gentle the life of this world.’  Let us dedicate ourselves to that, and say a prayer for our country, and for our people.”

Riots broke out in over one hundred major U.S. cities, but Indianapolis remained calm.

Bobby was assassinated two months later.

Friends – this is the heritage of leadership and behavior to which we should aspire.  Bobby was speaking, in the words of Lincoln, to our better angles. We’d do well to reflect and remember.