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.

 

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

 

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

 

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

 

Toys Were Us

This is sad. Toys R Us is closing all of its stores. Here’s the report from the Washington Post.

Toy store chain Toys R Us is planning to sell or close all 800 of its U.S. stores, affecting as many as 33,000 jobs as the company winds down its operations after six decades, according to a source familiar with the matter.

The news comes six months after the retailer filed for bankruptcy. The company has struggled to pay down nearly $8 billion in debt — much of it dating to a 2005 leveraged buyout — and has had trouble finding a buyer. There were reports earlier this week that Toys R Us had stopped paying its suppliers, which include the country’s largest toymakers. On Wednesday, the company announced it would close all 100 of its U.K. stores. In the United States, the company told employees closures would likely occur over time, and not all at once, according to the source, who spoke on the condition of anonymity because they were not authorized to discuss internal deliberations.

Toys R Us, once the country’s preeminent toy retailer, has been unable to keep up with big-box and online competitors. The recent holiday season dealt another blow to the embattled company, which struggled to find its footing even as the retail industry racked up its largest gains in years. In January, the retailer announced it would close 182 U.S. stores, or about one-fifth of its remaining Toys R Us and Babies R Us locations.

What is going to happen to all the Toys R Us kids?

I guess they all grew up and kids today get their toys from WalMart and Amazon.com.

The glory of capitalism is its ability to engage in creative destruction. Businesses and industries are all subject to the strict discipline of the market. If they can no longer serve their customers in an efficient manner, they are destroyed to make way for businesses that can. The result is, hopefully, ever-increasing prosperity. We ought not to be over sentimental about the loss of Toys R Us. The company has not been functioning well for some time. If Amazon or Walmart can deliver toys to children cheaper and more efficiently, than so much the better for all of us.

I cannot help, though, thinking that we are losing something. I know using e-commerce to deliver products right to your door is more convenient. I know superstores like WalMart are cheaper. But, I am afraid that the children of the future are going to be missing out on something special, the delight in stepping into a store full of nothing but toys. Maybe smaller toy store chains will take Toy R Us’s place. Maybe not. I guess there is no stopping progress, if that is what this is, but I regret the losses along the way.

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

One Horn

I have been studying German lately, mostly by using Duolingo, and I have noticed an interesting difference between English and German. This article I read about Ira Einhorn, the founder of Earth Day who murdered and composted his girlfriend brought the difference to mind.

Ira Einhorn was on stage hosting the first Earth Day event at the Fairmount Park in Philadelphia on April 22, 1970. Seven years later, police raided his closet and found the “composted” body of his ex-girlfriend inside a trunk.

A self-proclaimed environmental activist, Einhorn made a name for himself among ecological groups during the 1960s and ’70s by taking on the role of a tie-dye-wearing ecological guru and Philadelphia’s head hippie. With his long beard and gap-toothed smile, Einhorn — who nicknamed himself “Unicorn” because his German-Jewish last name translates to “one horn”  —advocated flower power, peace and free love to his fellow students at the University of Pennsylvania. He also claimed to have helped found Earth Day.

Einhorn is actually the German word for unicorn. What I have noticed is that English tends to create new words for new or abstract concepts by taking words from other languages, particularly Latin and Greek and often combining them in new ways not found in the original languages. German tends to create new words from other German words and seems to be less eager to take words from other languages.

In English we watch television (Greek tele “far” + Latin visionem, participle of videre “to see”). Germans watch the Fernseher (literally “far-seer” in German). We may study science (Latin scientia “knowledge) in school while Germans study Wissenschaft (“knowledge” in German). If you study chemistry you may be familiar with the elements, like hydrogen (Greek Hydr “water” + gen “produces or born from” thus “made from water”) or oxygen (Greek oxys “acid”+ gen so “made from acid). In German they are Wasserstoff (waterstuff) and Sauerstoff (sourstuff). Carbon comes from Latin carbonem “coal” Germans call it Kohlenstoff, “coalstuff”.

Electricity (Latin electrum and Greek elektron both meaning amber) is one of humanity’s greatest inventions. The Germans do have the word Elektrizität but they also call it Strom “stream, current”. We may be afraid of exposure to radiation(Latin radiationem “shining” from radius “beam of light). A German would prefer not to be exposed to Strahlung “beaming”.

You don’t have to study science to notice the difference. English speakers may vote (Latin votus “to vow”) in an election (Latin ex “out of” + legere “to choose”) for Congress (Latin congressus from com “with” + gradus “to walk” thus walking or meeting together) or Parliament (French from parler “to speak”). Germans may abstimmen (choose or coordinate) in a Wahl (choice) for the Bundestag (Bundes “Federal” Tag literally “day” from Latin diet “daily” the name of various representative assemblies in the Holy Roman Empire and elsewhere). This body may pass legislation (Latin legis latio “proposing a law”). In German it is Gesetzgebung (Gesetz “law” + gebung “-tion” so “lawization”. In English, we may participate (Latin participare “to share”) in and organization (Latin organizationem from organum “organ”). In German they teilnehmen (take part) in a Unternehmen (undertaking). I could go on and on but you get the idea.

I don’t want to exaggerate the contrast between the two languages. German does have plenty of words derived from Latin, mostly taken, like English through French, and English, of course, does make new words out of older English words, just like German. We can say we take part in an “undertaking” too. In fact, English seems to have a double vocabulary, one made up of simpler words derived from Anglo-Saxon and another composed of fancier words from French and Latin. Which approach is better, the German or the English is a matter of taste, I think. English perhaps has more words and is more eager to appropriate words from other languages, but all those Latin words may make English a more abstract language in some respects, one more easy to obfuscate in. German seems somehow homier, yet as anyone who tried to read Hegel or some of the other German philosophers can attest, German can also be an obfuscating language with dense verbiage.

So, why is English half a romance language, while German remains, well, Germanic? Part of the reason must be that there was nothing like the Norman Conquest in German history. Germany was not conquered by a nation that spoke a Romance Language as England was conquered by the French speaking Normans and so there was not the huge influx of Latin derived words into German as there was with English.

Yet, I also think that there is another reason why English has generally been careless about adopting words. from other languages. For some reason, English speakers seem to lack the concern about language purity found in the speakers of many other languages. The French have the Academie Francaise, an official institution that tries to safeguard the purity of the French language by setting standards for usage and inventing proper French words to replace any foreign words that have managed to slip in. Almost every major language has a similar official organization to set standards, with one exception, English. There has never been any sort of official or semi-official body in the English speaking world with any authority to set official standards for usage, or even for spelling, nor has there been any serious movement to purify the English language by purging it of “foreign” words. Other languages have had spelling reforms sponsored by various governments. German spelling was reformed in 1901 and again in 1996. The People’s Republic of China simplified the characters used in written Chinese, and there was even a proposal, shortly after the Communists came to power to abandon the characters altogether in favor of romanization. Ataurk ordered the Turks to abandon their traditional use of the Arabic script to write Turkish in favor of the Latin alphabet. Nothing like that is likely to occur in English, even though English orthography is a mess and badly needs to be simplified.

It seems that there is simply about the Anglophone mind and culture that tends to resist regimentation and regularization imposed from above, even when such such regularization might make things easier. English speakers have generally been the most reluctant to adopt the metric system, and the United States still uses the traditional system of measurements. We seem to prefer things haphazardly and chaotically rather than rational and regular, and we don’t mind speaking a language where every rule has an exception and in which if we don’t have a word for something, we have no trouble stealing words from other languages. If the new words aren’t proper English words, we don’t care.

Maybe if English were more regular, it would be an easier language for foreigners to learn. Since English is rapidly becoming the Common Tongue of the whole world, maybe we owe it to the poor souls who have to learn the language to make it easier for them. On the other hand, the fact that English has at least one word from almost every other language may make it at least a little familiar to others. English is certainly a more interesting and dynamic language because of its propensity to borrow shamelessly from other languages and maybe that is part of the reason English is the primary international  language.

 

It’s Greek to Me

My favorite YouTube channel is, without question, the Langfocus  channel, created by Paul Jorgenson, a Canadian who teaches English in Japan. Paul is fascinated by language and he shares his knowledge and fascination in his videos. Paul makes videos about particular languages, language families and general concepts about language. Whatever the specific topic he covers, Paul’s videos are always interesting and informative.

Not too long ago, Paul made a video on the Greek language.

I have studied Koine or New Testament Greek a little bit and it is amazing to me just how little the language has actually changed over the centuries. I can tell there are some differences in grammar and vocabulary. Some of the verb inflections have changed a little and Modern Greek seems to have lost the dative case. I also notice that the middle and passive voices have combined into a mediopassive voice. The Greek word for speak has changed from λαλεω (laleo) to μιλεω (mileo) and dog from κυων (cuon) to σκυλος (skylos). I think that a speaker of Modern Greek could read the New Testament in its original Koine Greek without too much trouble and could even read Plato and Homer with varying degrees of difficulty. I suppose that the sounds or phonology of spoken Greek have changed quite a bit more than written Greek so a modern Greek transported back to Periclean Athens might have quite a bit of difficulty making himself understood in conversation, but perhaps not much more than speakers of related languages might have. Despite the changes, Modern Greek is recognizably the same language as the Greek spoken two thousand or more years ago.

Now look at this sample of English from about one thousand years ago.

Hwæt. We Gardena in geardagum,
þeodcyninga, þrym gefrunon,
hu ða æþelingas ellen fremedon.
Oft Scyld Scefing sceaþena þreatum,
monegum mægþum, meodosetla ofteah,
egsode eorlas. Syððan ærest wearð
feasceaft funden, he þæs frofre gebad,
weox under wolcnum, weorðmyndum þah,
oðþæt him æghwylc þara ymbsittendra
ofer hronrade hyran scolde,
gomban gyldan. þæt wæs god cyning.
These are the first lines of Beowulf, an Anglo-Saxon epic poem that was probably the first work of literature written in Old English. Here is a translation.
LO, praise of the prowess of people-kings
of spear-armed Danes, in days long sped,
we have heard, and what honor the athelings won!
Oft Scyld the Scefing from squadroned foes,
from many a tribe, the mead-bench tore,
awing the earls. Since erst he lay
friendless, a foundling, fate repaid him:
for he waxed under welkin, in wealth he throve,
till before him the folk, both far and near,
who house by the whale-path, heard his mandate,
gave him gifts: a good king he!
It doesn’t seem to be the same language at all. If you look closely, some of the words are recognizable, “god cyning”= good king, but the grammar is very different and there are even some strange letters not used in Modern English. The text looks more like a dialect of German than the English we are familiar with. This is not too surprising. German and English originated on the same branch of West Germanic in the Germanic language family. There would probably be a closer resemblance between Modern English and German if it weren’t for the infusion of so many words from French and Latin after the Norman conquest. As it is, English is less of a strictly Germanic language, at least in vocabulary, and more of a hybrid between Germanic and the Romance languages. (Paul has a couple of videos on this)
Besides the unfamiliar words, you might notice that Modern English has lost the inflections that Old English had. This may also be due to the Norman conquest, or perhaps the earlier Danish or Viking invasions. Britain seems to have been something of a magnet for settlers during the tenth and eleventh centuries and since the Danes, Normans, etc had to communicate with the Anglo-Saxons who already lived there, they used a simplified form of Old English that developed into the language we speak today.
Here are the first lines of Chaucer’s Canturbury tales, written in Middle English around 1300.
Whan that aprill with his shoures soote
The droghte of march hath perced to the roote,
And bathed every veyne in swich licour
Of which vertu engendred is the flour;
Whan zephirus eek with his sweete breeth
Inspired hath in every holt and heeth
Tendre croppes, and the yonge sonne
Hath in the ram his halve cours yronne,
And smale foweles maken melodye,
That slepen al the nyght with open ye
(so priketh hem nature in hir corages);
Thanne longen folk to goon on pilgrimages,
And palmeres for to seken straunge strondes,
To ferne halwes, kowthe in sondry londes;
And specially from every shires ende
And the translation:
When April’s gentle rains have pierced the drought
Of March right to the root, and bathed each sprout
Through every vein with liquid of such power
It brings forth the engendering of the flower;
When Zephyrus too with his sweet breath has blown
 Through every field and forest, urging on
The tender shoots, and there’s a youthful sun,
His second half course through the Ram now run,
And little birds are making melody And sleep all night, eyes open as can be
So Nature pricks them in each little heart), On pilgrimage then folks desire to start.
The palmers long to travel foreign strands
To distant shrines renowned in sundry lands;
And specially, from every shire’s end
This is recognizably English even if the spelling looks strange. There are some unfamiliar words and some differences in grammar. Chaucer can be read by an English speaker, but it is not easy. Shakespeare and the King James Bible are the most familiar examples of Early Modern English. They are essentially the same language spoken today, but even after a mere four hundred years they already seem quaint and old-fashioned, requiring a glossary to fully understand the text.
How is it that a language like Greek has changed slowly enough over the centuries that the Greeks can read the classics of Ancient Greek literature without too much difficulty while anything written in English more than about five hundred years ago is incomprehensible to the modern reader? Has Greek been unusually conservative or has English changed faster than most languages. Maybe it is both. Latin has changed quite a bit in the transition to the Romance Languages, particularly in the loss of the noun case system, loss of the neuter gender and changes in verb tenses. The vocabulary of the Romance Languages is still largely based on Latin and I think that a modern speaker of Italian or Spanish could still get the basic meaning of a Latin text.
Part of the reason might be because Greek has a much longer written history than English. Writing does tend to make a language more conservative, at least in its written form, particularly when the older version of the language is seen as somehow more pure while innovations are viewed as corruptions. This has long been the case in Greek where until recently it was common for Greek writers to use a formal and archaic version of Greek that resembled Ancient Greek more than the Greek actually spoken. (This is actually a common phenomenon found on many languages with a long literary history.) It seems the greatest changes in English came in the centuries after the Norman Conquest when French was the official language at court and English was mostly a language of illiterate peasants. Another possible reason for the continuity of Greek as opposed to the development of the Romance Languages from Latin might be that the Greek speaking Eastern Roman (or Byzantine) Empire survived as a nation until 1453 while the Latin speaking Western Roman Empire broke up causing regional dialects to become separate languages.
Whatever the reasons, the relatively rapid development of English from its Germanic, Anglo-Saxon origins to the useful language we speak today with its large vocabulary and relatively simple grammar has helped to make English the lingua franca of the modern world. I’m sure I’d rather speak Modern English than Anglo-Saxon, but I wish there had been a greater continuity over the centuries.
  • The Anglish Moot-They want to restore English to its native roots. The result of writing English without any Latin, Greek, or other words is truly weird and helps to demonstrate just how much English has borrowed from other languages.
  • Day of the Dead Languages (feedproxy.google.com)