Pi Day

English: Pi Pie, created at Delft University o...
English: Pi Pie, created at Delft University of Technology, applied physics, seismics and acoustics Deutsch: Pi Pie (π-Kuchen), hergestellt an der Technischen Universität Delft (Photo credit: Wikipedia)

For all of the nerds out there, including me, today is international Pi Day, the day when we celebrate our favorite mathematical constant. Pi Day is best celebrated by pi memorization contests, walking in circles, and, of course, eating pies, or is it pis? I think I will celebrate by writing a little about pi.

Pi or π is, as everyone should know, the ratio between a circle’s diameter and its circumference. Pi is an irrational number. By this, they do not mean that pi makes no sense but rather that pi is a constant that cannot be expressed as a ratio of two integers. Numbers like 2 or .445 or 1/2 can be expressed as a ratio of two integers and so are rational. Numbers like pi or the square root of any number that is not a perfect square, the square root of 2 for instance, are irrational. An irrational number expressed in decimal form never ends or repeats but continues to infinity. Thus, there can never be a last digit of pi.

The symbol π was first used by the mathematician William Jones in 1706 and was popularized by another mathematician, Leonhard Euler. They chose π, the Greek equivalent of the Latin letter p because it is the first letter of the word periphery. Π, by the way, is not pronounced “pie” in Greek but “pee”, just like our p. I don’t think that international “pee” day would be nearly so appealing.

Although the symbol for pi is relatively recent, the concept is very old. The ancient Egyptians and Babylonians knew about it. Pi is even mentioned in the Bible.

23 He made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits[o] to measure around it. 24 Below the rim, gourds encircled it—ten to a cubit. The gourds were cast in two rows in one piece with the Sea. (1 Kings 7:23-24)

Properly speaking, the line around the “Sea” should have been 31.5 cubits but the ancient Hebrews were not very knowledgeable about geometry and measuring techniques were crude.

There is no particular reason to calculate pi to so many digits. No conceivable application of pi would possibly take more than 40 digits. Still, the challenge of calculating pi to the farthest digit possible has been an irresistible one for mathematicians over the years.

Around 250 BC, Archimedes was the first mathematician to seriously try to calculate pi. He used a geometric method of drawing polygons inside and outside a circle and measuring their perimeters. By using polygons with more and more sides he was able to calculate pi with more precision and ended determining the value of pi as somewhere between 3.1408 and 3.1429. Archimedes’s method was used in the west for more than eighteen hundred years. The Chinese and Indians used similar methods. The best result using the geometric method was the calculation of pi to 38 digits in 1630.

With the development of calculus by Isaac Newton and Gottfried Leibniz in the 1660’s, it was possible to calculate pi using infinite series, or the sum of the terms of an infinite sequence. The best calculations with these methods were done by the mathematician Zacharias Daze who calculated pi to 200 places in 1844 and William Shanks who spent fifteen years calculating pi to 707 digits. Unfortunately, he made a mistake with the 528th digit. Meanwhile, in 1761 Johann Heinrich Lambert proved that pi is irrational.

Computers made the calculation of pi much faster so pi could be calculated to more digits. ENIAC calculated pi to 2037 places in 1949. This record didn’t last long. A million digits were reached in 1970. As of  2011, pi has been calculated to 10,000,000,000,050 places.

Pi is not just used in geometry. There are a number of applications of pi in the fields of statistics, mechanics, thermodynamics, cosmology, and many others. Here is a list of just some of the formulae that use pi. It seems you can find pi everywhere.

With that in mind then, happy pi day! For your enjoyment here are the first thousand digits of pi.

3.14159265358979323846264338327950288419716939937510
  58209749445923078164062862089986280348253421170679
  82148086513282306647093844609550582231725359408128
  48111745028410270193852110555964462294895493038196
  44288109756659334461284756482337867831652712019091
  45648566923460348610454326648213393607260249141273
  72458700660631558817488152092096282925409171536436
  78925903600113305305488204665213841469519415116094
  33057270365759591953092186117381932611793105118548
  07446237996274956735188575272489122793818301194912
  98336733624406566430860213949463952247371907021798
  60943702770539217176293176752384674818467669405132
  00056812714526356082778577134275778960917363717872
  14684409012249534301465495853710507922796892589235
  42019956112129021960864034418159813629774771309960
  51870721134999999837297804995105973173281609631859
  50244594553469083026425223082533446850352619311881
  71010003137838752886587533208381420617177669147303
  59825349042875546873115956286388235378759375195778
  18577805321712268066130019278766111959092164201989

Books of Color

You would think that the late-night show comedians would find all sorts of fodder for comedy in the ongoing campaign to cancel anything and everything that might possibly be the slightest bit offensive, especially such silliness as putting warnings on the Muppet Show and canceling six Dr. Seuss books, but you would be wrong. According to this recent article at the blog Hollywood in Toto, the comedians didn’t find the cancellations worth making fun of. Instead, they mocked those silly conservatives who just don’t see the necessity of eliminating every vestige of racism from our culture and who imagine there is really some sort of cancel culture going on.

It goes without saying that today’s late night comics won’t mock the new Biden administration.

They’ve made it crystal clear their shows are progressive propaganda first and foremost. Speaking “truth to power” comes in a distant second. Some nights it ranks dead last.

When you wait nearly a year to call out a corrupt governor, that’s all the proof you need.

These comedians still could, in theory, pay attention to the culture wars attacking beloved institutions. Take Disney+ inexplicably slapping warning labels on classic episodes of “The Muppets.” Just this week the Dr. Seuss estate decided to stop publishing six of the author’s works because a very select few believe they contain racist imagery.

That’s despite Dr. Seuss’s own stepdaughter swearing he didn’t have a racist bone in his body.

Enter Stephen Colbert.

The far-left “Late Show” host chortled about the Dr. Seuss cancellation, ignoring the decades of joy his books have given children across the globe.

Nothing to see here, folks. Move along.

“It’s a responsible move on their part … they recognize the impact of these images on readers, especially kids,” he said. What impact? Kids have read these books for decades without any impact save giggles and hugs from their parents.

So Colbert is firmly on the side of the cancellers and the censors. I guess he is less a comedian than a propagandist. That might be why he is not very funny. Comedy, by its nature, tends to be subversive. Authoritarian comedy is seldom very funny.

But it is this next part that made me stop and think.

He then cued up Fox News clips to mock anyone calling this another “Cancel Culture” moment.

If you’re worried your books shelves just got a bit duller, he advised, why not add tomes written by authors of color to cushion the blow?

“It’s fun to read books written after the ’40s,” he said with a twinkle.

Authors of color? What kind of an idiot selects books based on the color of the author? All last month, during Black History Month, Amazon kept offering me suggestions for Black authors I might be interested in, I wasn’t the slightest bit interested. My reasons for choosing a book to read simply do not include the race of the author. For nonfiction, I want a book about a subject I am interested in learning about and I want the author to present the information clearly and interestingly. For fiction, I want an interesting and entertaining story with characters I can relate to. I do not see how, in either case, the race or nationality of the writer matters at all. I could not possibly say how many of the books I own were written by authors of color. I would have to pull down each book from the shelf and look to see if there is a picture of the author on the cover to get an idea. I am not that interested.

As for the comment about books written since the 1940s, well many of my favorite authors, J. R. R. Tolkien, C. S. Lewis, George Orwell, wrote their best works during the 1940s, and most of the greatest books ever written were written decades and centuries ago. I am not sure if there have been all that many books that have been written in recent years that can compare with the great classics, certainly, none that have, as yet, stood the test of time. If the censors and the wokescolds have their way there won’t be any books worth reading at all.

So, what kind of a person chooses books based on the color of the author? Maybe the sort of person who buys Books by the Foot. The sort of superficial person who is not so interested in the ideas contained in books as much as impressing people by seeming to read the correct books. Why else would someone care about the race or color of the author, than to demonstrate that they are woke or politically correct in their reading and thinking? Maybe the sort of person that becomes a late-night propagandist.

As for me, I am going to keep on reading the books I want to read and am going to ignore the suggestions from Amazon and Stephen Colbert that I should read authors because of their color because, unlike the people on the left, I am not a racist.

The Indispensable Man

It may not be the popular or politically correct thing to believe, but I hold fast to the opinion that our founding fathers, men like Benjamin Franklin, Thomas Jefferson, Alexander Hamilton, John Adams, and the rest are among the greatest men who have ever lived. Our nation would be blessed to have even one such great men at its founding. The fact that we had so many great men must surely attest that America is under the protection of divine providence. Of these great men, George Washington stands head and shoulders above the rest. For his contribution to the cause of liberty, leading the fight for American independence, and then not making himself a king or president for life, Washington is surely one of the greatest men who have ever lived.

It is no easy task to write a biography of Washington. For too many people, Washington seems to be too distant a marble statue of implacable virtue that normal people cannot relate to. The man, with his very real flaws, disappears behind the image. More recently, there is a tendency, among the ignorant woke, to dismiss Washington as merely a slaveholder, never mind the fact that Washington grew up in a time in which slavery was accepted and uncontroversial, that he came to have misgivings about the institution of slavery, and he, almost alone among his contemporary planter class, actually made a real effort to prepare his slaves for the freedom he believed they would gain when slavery, being obsolete, would die out. A candid assessment of Washington’s life and works runs the risk of seeming to be a hagiography, and yet to focus too much on his flaws, does the man an injustice.

James Thomas Flexner’s Washington: The Indispensible Man tries to thread the needle of writing a biography of Washington that makes him be a paragon of virtue while not dwelling overmuch on his flaws. In this effort, Flexner is mostly successful doing a passable job of relating Washington’s life and accomplishments and establishing that Washington was, indeed, the indispensable man without whom the American colonies could not have gained their independence. If you want to know about Washington’s life and accomplishments, this is a good book to read.

I cannot help, however, but feel a little disappointed when I finished Washinton: The Indispensable Man. It is a good work but there are some flaws. For one thing, there are no maps. This might be a fatal flaw in the sections dealing with Washington’s military career in the French and Indian War, and particularly in the Revolutionary War. How is the reader expected to follow the movements of the Continental and British armies without any maps? How can we understand the course of the battles? If I were not already familiar with the battles of the War of Independence, I would have been lost.

The lack of maps is somewhat frustrating, but I had a more serious problem with this book, it is too short, or too long. The problem is that Washington: The Indispensable Man is not the right length for what Flexner is trying to do. It is too long for a mere summary, but not long enough to get to know Washington. The author seems to hint at things but then moves on without going any deeper. I learned about Washington’s deeds, but I did not feel that I got to know Washington the man. I do not feel I got to know any of the people Washington interacted with, his friends, mentors, officers, subordinates. Flexner mentions names, tells a little about what they did and how Washington acted, and then moves on. I don’t get to know how Washington really felt about people he shared his life with.

Part of the problem is that Washington: The Indispensable Man is a condensation of James Thomas Flexner’s earlier four-volume biography of Washington. Flexner asserts in the preface that the text in this book is almost entirely new and not a series of patched together extracts, and while I have no reason to doubt his word, the book does indeed read as if he took out selections from his longer work. It summarizes but leaves tantalizing hints that there is more.

As I said, I can recommend this book to anyone wanting to know more about Washington, but I fear that the reader is going to end the book unsatisfied. It is a good book to begin to learn about Washington, but not to end one’s study of the great man.

 

Nineteen Years

It has been nineteen years since the terrorist attack on September 11, 2001, and I still remember it as if it were yesterday.

On that Tuesday morning, I was at work, driving from Madison to North Vernon when I got a call from my wife. She asked me if I was listening to the radio. I was not. She told me to turn it on because something terrible was happening. I turned my car radio on and listened to the coverage of the attack.

I went about my duties at the stores in North Vernon in a sort of state of shock.  The North Vernon Walmart and Jay C played continuing news coverage of the day’s events instead of the usual soothing Musak. Not too many people were working or shopping in the stores. They were mostly just listening.

I had to go to Seymour for a meeting that afternoon. On the way, I noticed that some gas stations had raised the price of gasoline to a then unheard of price of $5 per gallon. At the meeting, no one wanted to discuss the business at hand. Instead, we talked about the terrorist attack. It seemed certain to us all that more attacks were on the way and that this time we couldn’t just launch a few missiles, blow up some tents, and then move on. We were in for a long fight.

I don’t remember much about the rest of that day. I went home but I don’t remember much about it.

I was once in the World Trade Center. I was in New York with some friends as a sort of tourist and we took the elevator to the top floor of one of the twin towers. There was a gallery up there where you could look out over the city of New York. The day was foggy so I didn’t see anything. They had a gift shop in the center section of the floor. It sickens me to think that the people who worked there went to work one morning, and then had to choose between burning to death or jumping, Not to mention the tourists, who only wanted to look at the city.

It still sickens me to think about the people who were only doing their jobs having to lose their lives.

twin

Al Jolson

I remember going through an old record collection, when I was a child, and seeing an album cover with the picture of a man with what appeared to be a very dirty face. His face was black, except around the eyes and mouth, as if he had just emerged from a coal mine or had rubbed his face with black mud. I had never heard of entertainers performing in blackface and since the man has caucasian features and his makeup did not resemble any natural skin tone, I did not know what this was all about until I turned the album over and read the description on the back. The man was Al Jolson, the entertainer who was famous in the early twentieth century for performing in blackface.

What are we to do with Al Jolson today? His performances are undoubtedly offensive to today’s more racially aware audiences. Perhaps his present-day obscurity is deserved. Maybe Al Jolson ought to disappear down the memory hole along with so much of our shameful past. Then again, maybe not. I am not a fan of airbrushing away historical figures just because they offend contemporary sensibilities. I think the past ought to be remembered.  Al Jolson was the most famous entertainer of his time. He definitely had talent. Moreover, his relationship with the African-American community was not as straightforward as we might expect.

Al Jolson

Who was Al Jolson anyway? Al Jolson was born to a Jewish family as Asa Yeolson, on June 8, 1886, in the village of Srednike in Lithuania, then part of the Russian Empire. Yeolson’s father, Moses Rubin Yeoson, was a rabbi and cantor or Hazzan who immigrated to New York in 1891. In 1894 he was able to bring his family to the United States and they settled in Washington DC, where the elder Yeolson found work as a cantor. Young Asa seemed to have inherited his father’s singing voice, and he and his brother Hirsch begin singing on street corners for money in 1897, using the names, Al and Harry. Asa Jeolson began working in show business in 1902, with his name anglicized to Al Jolson. After a somewhat fitful start. Jolson’s career in vaudeville and musicals took off, particularly after he started performing in blackface in 1904. By the 1920s, Al Jolson was one of the most successful entertainers in the United States.

Al Jolson in blackface

In 1927, Al Jolson began acting in movies, starring in The Jazz Singer, generally regarded as the first talkie. Jolson went on to star in a number of successful movies. His career and personal life went into something of a slump in the late 1930s but after the Japanese bombed Pearl Harbor, Jolson was the first star to entertain for the troops, before the USO had even been organized. He was praised for the service he provided for American soldiers fighting overseas, but Jolson also contracted malaria and had to have a lung removed. Jolson was also the first entertainer to perform for the soldiers fighting in the Korean War. Al Jolson’s service in Korea proved to be exhausting for him and he died of a heart attack in San Francisco on October 23, 1950

This biographical sketch might give the impression that Al Jolson was the worst sort of racist who made his fortune exploiting the most degrading negative Black stereotypes. What else are we to think of a man who was most famous for performing in blackface? Should Al Jolson be relegated to obscurity as a forgotten relic of America’s racist past? Not quite. As is often the case, the truth is not what it seems at first glance. The fact is that Al Jolson used his position as America’s highest-paid entertainer to fight against discrimination against Blacks. He insisted on equal treatment for his Black co-stars and consistently stood up for the rights of Blacks at a time when this was, by no means, a popular position to take.

So, how do we resolve this paradox? Al Jolson was an entertainer who made millions by wearing blackface and demeaning African Americans, yet was an undoubted benefactor of the Black race. How do we reconcile these two very different sides of this man?

I would suggest that Al Jolson did not put on blackface to insult or demean Blacks. Al Jolson had many Black friends in his youth and later and it is hard to imagine that we would have knowingly done something that they might have found insulting. Blackface was an accepted genre of entertainment at the time, and not necessarily seen as degrading to Blacks. I suspect that Al Jolson might have believed that his blackface performances were a sort of tribute to his Black colleagues. He might have found something in African-American culture that was lacking in his own Jewish-Russian heritage and putting on blackface might have been his way of celebrating the culture of his Black friends. In fact, if you think about it, the practice of White performers blackening their faces and pretending to be Black was a sort of backhanded compliment to Blacks. Yes, these performers disseminated demeaning stereotypes about Blacks, yet they had to believe something was appealing about African American culture for them to pretend to emulate it. We ought to look on Al Jolson’s performances, and perhaps those of other entertainers in blackface as celebrations of African American culture rather than deliberate insults.

Now the reason I am writing this, aside from the fact that  I find Al Jolson’s life and career to be interesting, is that I have found it helpful to try to impute the best possible motives for the actions of the people I run into. That is to say, rather than assuming they are acting from rudeness or malice, I try to think of good reasons for why people do what they do. I cannot say that I am very accomplished in this way of thinking. It seems to run against human nature. It is natural for us to make excuses for our own actions while judging others more harshly. I am trying to reverse this natural tendency by trying to make excuses for others while judging myself more harshly, or at any rate more honestly. Some might say that if I succeed in this endeavor I might become something of a Pollyanna, but I think that it would be worth risking becoming more naive to become more tolerant and charitable in my thinking. I might manage to make myself a genuinely good person.

I think that our country as a whole might be better off, especially in racial matters, if we applied this method to each other. What if, instead of seeking out evidence of racism everywhere, we focus on the real progress in racial relations we have made over the last decades? What if instead of canceling people for a bad joke or unfortunate remark made years ago, we accept that they made a mistake and have moved on? What if, in other words, instead of believing the worst of our fellow Americans, that we are a people seething with systemic racism, we assume the best, that we are human beings and like all human beings we make mistakes but we are trying to do better? We might actually make this country a better place.

Pi Day

English: Pi Pie, created at Delft University o...
English: Pi Pie, created at Delft University of Technology, applied physics, seismics and acoustics Deutsch: Pi Pie (π-Kuchen), hergestellt an der Technischen Universität Delft (Photo credit: Wikipedia)

For all of the nerds out there, including me, today is international Pi Day, the day when we celebrate our favorite mathematical constant. Pi Day is best celebrated by pi memorization contests, walking in circles, and, of course, eating pies, or is it pis? I think I will celebrate by writing a little about pi.

Pi or π is, as everyone should know, the ratio between a circle’s diameter and its circumference. Pi is an irrational number. By this, they do not mean that pi makes no sense but rather that pi is a constant that cannot be expressed as a ratio of two integers. Numbers like 2 or .445 or 1/2 can be expressed as a ratio of two integers and so are rational. Numbers like pi or the square root of any number that is not a perfect square, the square root of 2 for instance, are irrational. An irrational number expressed in decimal form never ends or repeats but continues to infinity. Thus, there can never be a last digit of pi.

The symbol π was first by the mathematician William Jones in 1706 and was popularized by another mathematician, Leonhard Euler. They chose π, the Greek equivalent of the Latin letter p, because it is the first letter of the word periphery. Π, by the way is not pronounce “pie” in Greek but “pee”, just like our p. I don’t think that international “pee” day would be nearly so appealing.

Although the symbol for pi is relatively recent, the concept is very old. The ancient Egyptians and Babylonians knew about it. Pi is even mentioned in the Bible.

23 He made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits[o] to measure around it. 24 Below the rim, gourds encircled it—ten to a cubit. The gourds were cast in two rows in one piece with the Sea. (1 Kings 7:23-24)

Properly speaking, the line around the “Sea” should have been 31.5 cubits but the ancient Hebrews were not very knowledgeable about geometry and measuring techniques were crude.

There is no particular reason to calculate pi to so many digits. No conceivable application of pi would possibly take more than 40 digits. Still, the challenge of calculating pi to the farthest digit possible has been an irresistible one for mathematicians over the years.

Around 250 BC, Archimedes was the first mathematician to seriously try to calculate pi. He used a geometric method of drawing polygons inside and outside a circle and measuring their perimeters. By using polygons with more and more sides he was able to calculate pi with more precision and ended determining the value of pi as somewhere between 3.1408 and 3.1429. Archimedes’s method was used in the west for more than a eighteen hundred years. The Chinese and Indians used similar methods. The best result using the geometric method was the calculation of pi to 38 digits in 1630.

With the development of calculus by Isaac Newton and Gottfried Leibniz in the 1660’s it was possible to calculate pi using infinite series, or the sum of the terms of an infinite sequence. The best calculations with these methods were done by the mathematician Zacharias Daze who calculated pi to 200 places in 1844 and William Shanks who spent fifteen years to calculate pi to 707 digits. Unfortunately he made a mistake with the 528 digit. Meanwhile, in 1761 Johann Heinrich Lambert proved that pi is irrational.

Computers made the calculation of pi much faster so pi could be calculated to more digits. ENIAC calculated pi to 2037 places in 1949. This record didn’t last long. A million digits were reached 1970. As of  2011, pi has been calculated to 10,000,000,000,050 places.

Pi is not just used in geometry. There are a number of applications of pi in the fields of statistics, mechanics, thermodynamics, cosmology, and many others. Here is a list of just some of the formulae that use pi. It seems you can find pi everywhere.

With that in mind then, happy pi day! For your enjoyment here are the first thousand digits of pi.

3.14159265358979323846264338327950288419716939937510
  58209749445923078164062862089986280348253421170679
  82148086513282306647093844609550582231725359408128
  48111745028410270193852110555964462294895493038196
  44288109756659334461284756482337867831652712019091
  45648566923460348610454326648213393607260249141273
  72458700660631558817488152092096282925409171536436
  78925903600113305305488204665213841469519415116094
  33057270365759591953092186117381932611793105118548
  07446237996274956735188575272489122793818301194912
  98336733624406566430860213949463952247371907021798
  60943702770539217176293176752384674818467669405132
  00056812714526356082778577134275778960917363717872
  14684409012249534301465495853710507922796892589235
  42019956112129021960864034418159813629774771309960
  51870721134999999837297804995105973173281609631859
  50244594553469083026425223082533446850352619311881
  71010003137838752886587533208381420617177669147303
  59825349042875546873115956286388235378759375195778
  18577805321712268066130019278766111959092164201989

 

Eighteen Years

It has been eighteen years since the terrorist attack on September 11, 2001, and I still remember it as if it were yesterday.

On that Tuesday morning, I was at work, driving from Madison\ to North Vernon when I got a call from my wife. She asked me if I was listening to the radio. I was not. She told me to turn it on because something terrible was happening. I turned my car radio on and listened to the coverage of the attack.

I went about my duties at the stores in North Vernon in a sort of state of shock.  The North Vernon WalMart and Jay C played continuing news coverage of the day’s events instead of the usual soothing Musak. Not too many people were working or shopping in the stores. They were mostly just listening.

I had to go to Seymour for a meeting that afternoon. On the way, I noticed that some gas stations had raised the price of gasoline to a then unheard of price of $5 per gallon. At the meeting, no one wanted to discuss the business at hand. Instead, we talked about the terrorist attack. It seemed certain to us all that more attacks were on the way and that this time we couldn’t just launch a few missiles, blow up some tents, and then move on. We were in for a long fight.

I don’t remember much about the rest of that day. I went home but I don’t remember much about it.

I was once in the World Trade Center. I was in New York with some friends as a sort of tourist and we took the elevator to the top floor of one of the twin towers. There was a gallery up there where you could look out over the city of New York. The day was foggy so I didn’t see anything. They had a gift shop in the center section of the floor. It sickens me to think that the people who worked there went to work one morning, and then had to choose between burning to death or jumping, Not to mention the tourists, who only wanted to look at the city.

It still sickens me to think about the people who were only doing their jobs having to lose their lives.

twin

 

 

Pi Day

English: Pi Pie, created at Delft University o...
English: Pi Pie, created at Delft University of Technology, applied physics, seismics and acoustics Deutsch: Pi Pie (π-Kuchen), hergestellt an der Technischen Universität Delft (Photo credit: Wikipedia)

For all of the nerds out there, including me, today is international Pi Day, the day when we celebrate our favorite mathematical constant. Pi Day is best celebrated by pi memorization contests, walking in circles, and, of course, eating pies, or is it pis? I think I will celebrate by writing a little about pi.

Pi or π is, as everyone should know, the ratio between a circle’s diameter and its circumference. Pi is an irrational number. By this, they do not mean that pi makes no sense but rather that pi is a constant that cannot be expressed as a ratio of two integers. Numbers like 2 or .445 or 1/2 can be expressed as a ratio of two integers and so are rational. Numbers like pi or the square root of any number that is not a perfect square, the square root of 2 for instance, are irrational. An irrational number expressed in decimal form never ends or repeats but continues to infinity. Thus, there can never be a last digit of pi.

The symbol π was first by the mathematician William Jones in 1706 and was popularized by another mathematician, Leonhard Euler. They chose π, the Greek equivalent of the Latin letter p, because it is the first letter of the word periphery. Π, by the way is not pronounce “pie” in Greek but “pee”, just like our p. I don’t think that international “pee” day would be nearly so appealing.

Although the symbol for pi is relatively recent, the concept is very old. The ancient Egyptians and Babylonians knew about it. Pi is even mentioned in the Bible.

23 He made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits[o] to measure around it. 24 Below the rim, gourds encircled it—ten to a cubit. The gourds were cast in two rows in one piece with the Sea. (1 Kings 7:23-24)

Properly speaking, the line around the “Sea” should have been 31.5 cubits but the ancient Hebrews were not very knowledgeable about geometry and measuring techniques were crude.

There is no particular reason to calculate pi to so many digits. No conceivable application of pi would possibly take more than 40 digits. Still, the challenge of calculating pi to the farthest digit possible has been an irresistible one for mathematicians over the years.

Around 250 BC, Archimedes was the first mathematician to seriously try to calculate pi. He used a geometric method of drawing polygons inside and outside a circle and measuring their perimeters. By using polygons with more and more sides he was able to calculate pi with more precision and ended determining the value of pi as somewhere between 3.1408 and 3.1429. Archimedes’s method was used in the west for more than a eighteen hundred years. The Chinese and Indians used similar methods. The best result using the geometric method was the calculation of pi to 38 digits in 1630.

With the development of calculus by Isaac Newton and Gottfried Leibniz in the 1660’s it was possible to calculate pi using infinite series, or the sum of the terms of an infinite sequence. The best calculations with these methods were done by the mathematician Zacharias Daze who calculated pi to 200 places in 1844 and William Shanks who spent fifteen years to calculate pi to 707 digits. Unfortunately he made a mistake with the 528 digit. Meanwhile, in 1761 Johann Heinrich Lambert proved that pi is irrational.

Computers made the calculation of pi much faster so pi could be calculated to more digits. ENIAC calculated pi to 2037 places in 1949. This record didn’t last long. A million digits were reached 1970. As of  2011, pi has been calculated to 10,000,000,000,050 places.

Pi is not just used in geometry. There are a number of applications of pi in the fields of statistics, mechanics, thermodynamics, cosmology, and many others. Here is a list of just some of the formulae that use pi. It seems you can find pi everywhere.

With that in mind then, happy pi day! For your enjoyment here are the first thousand digits of pi.

3.14159265358979323846264338327950288419716939937510
  58209749445923078164062862089986280348253421170679
  82148086513282306647093844609550582231725359408128
  48111745028410270193852110555964462294895493038196
  44288109756659334461284756482337867831652712019091
  45648566923460348610454326648213393607260249141273
  72458700660631558817488152092096282925409171536436
  78925903600113305305488204665213841469519415116094
  33057270365759591953092186117381932611793105118548
  07446237996274956735188575272489122793818301194912
  98336733624406566430860213949463952247371907021798
  60943702770539217176293176752384674818467669405132
  00056812714526356082778577134275778960917363717872
  14684409012249534301465495853710507922796892589235
  42019956112129021960864034418159813629774771309960
  51870721134999999837297804995105973173281609631859
  50244594553469083026425223082533446850352619311881
  71010003137838752886587533208381420617177669147303
  59825349042875546873115956286388235378759375195778
  18577805321712268066130019278766111959092164201989

 

Seventeen Years

It has been seventeen years since 9/11. We said that we would never forget, but I am afraid we are already forgetting. They are even starting to teach in colleges that it was our fault.   A person turning eighteen this year, old enough to vote, was only three on that fateful day. I don’t imagine that they would have any clear personal memories of that day, unless they or someone close was personally affected. I am afraid that we are trying to forget the most important lesson of 9/11, that the world is a dangerous place, and there are people out there who would like to destroy us. I suppose that even memorializing 9/11 is considered Islamophobia today.

Well, I will never forget that dreadful day seventeen years ago, no matter how long I live. We will just have to keep telling the story to the younger generations so they will not have to experience any such attacks for themselves. With that in mind, I am going to copy what I wrote three years ago.

On that Tuesday morning, I was at work, driving from Seymour to North Vernon when I got a call from my wife. She asked me if I were listening to the radio. I was not. She told me to turn it on because something terrible was happening. I turned my car radio on and listened to the coverage of the attack.

I went about my duties at the stores in North Vernon in a sort of state of shock.  The North Vernon WalMart and Jay C played continuing news coverage of the day’s events instead of the usual soothing Musak. Not too many people were working or shopping in the stores. They were mostly just listening.

I had to go to Seymour for a meeting that afternoon. On the way I noticed that some gas stations had raised the price of gasoline to a then unheard of price of $5 per gallon. At the meeting, no one wanted to discus the business at hand. Instead we talked about the terrorist attack. It seemed certain to us all that more attacks were on the way and that this time we couldn’t just launch a few missiles, blow up some tents, and then move on. We were in for a long fight.

I don’t remember much about the rest of that day. I went home but I don’t remember much about it.

I was once in the World Trade Center. I was in New York with some friends as a sort of tourist and we took the elevator to the top floor of one of the twin towers. There was a gallery up there where you could look out over the city of New York. The day was foggy so I didn’t see anything. They had a gift shop in the center section of the floor. It sickens me to think that the people who worked there went to work one morning, and then had to choose between burning to death or jumping, Not to mention the tourists, who only wanted to look at the city.

It still sickens me to think about the people who were only doing their jobs having to lose their lives.

twin

 

Suicide is Painful

My brother committed suicide last week. I am not going to relate the details on when and how this tragedy happened nor will I speculate on his motives. I will respect his privacy, and the privacy of his family. The only reason that I am writing this post for the sake of any reader who may be considering suicide

Contrary to what the theme song of M*A*S*H declares, suicide is not painless. It is painful, very painful, perhaps for the person who has killed himself but certainly for the loved ones left behind. They are left with questions that will never be answered. Why did their friend or relative choose suicide? Was there any way it could have prevented? Did they do anything to trigger the decision? When a person takes their life, they leave a hole in the hearts of everyone who was close to them.

No matter how bad things may seem, they can get better. As long as there is life, there is hope, that whatever problems you may have can get resolved, but once dead, that is the end of any hope. The problems do not go away, however. They become other people’s problems, along with the mess that any death creates. If you believe that your burdens are too much to bear, why would you want to shift them onto the shoulders of the people you love most?

My brother meticulously planned his death, for over a year. In hindsight There were signs that he was preparing to end his life, but no one put the pieces together until it was too late. How could they? He seemed content with his life, despite some setbacks. He hid his distress well.

Part of my brother’s planning was insuring that his children would be well provided for after his death. He believed that his death would ensure an inheritance large enough to take care of them. I do not know how much money they are going to inherit. I do know, looking at their faces, that they would rather have their Dad back thaany amount of money

If anyone reading this post is considering suicide, please, please get help. Talk to someone, a friend, a counselor, clergy, anyone. If there is something eating away at you, don’t keep it to yourself. Open up to someone. If everything seems hopeless, think  again. You cannot know what new reasons for hope tomorrow may bring. If you do not care about yourself, think about the impact on the people around you. Suicide is never the answer.

National Suicide Prevention Lifeline

1-800-273-8255