Pi Day

English: Pi Pie, created at Delft University of Technology, applied physics, seismic 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 up 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 1660s, 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

Pride

Dennis Prager has always been one of my favorite conservative commentators. Back when I had time, I used to love to listen to his radio show. He always seemed to know what he was talking about, and I was particularly impressed with the calm and rational way he handled hostile callers.

I am no longer able to listen to his show, but I still read Prager’s columns, and I found this recent one about pride to be especially illuminating.

I’ve never understood ethnic, race, gender or sex pride. Even as a kid.

For my bar mitzvah, someone gave me a book titled “Great Jews in Sports” or something like it.

.Aside from the usual jokes — it was not a long book; the print and the photos were very large — what I remember best was that I had little interest in the book. I loved sports. And I strongly identified as a Jew — I was raised in an Orthodox Jewish home and attended yeshivas until the age of 19. So, my disinterest in the book didn’t emanate from either disinterest in sports or disinterest in Jews. I was keenly interested in both.

But even at the age of 13, the idea of ethnic pride meant little to me.

As far as I could tell, my friends — and, of course, the relative who gave me the book — considered the book quite meaningful. They were proud of Detroit Tigers Hall of Famer Hank Greenberg, of the great Cleveland Indians third baseman Al Rosen, of the lightweight boxing champ Benny Leonard, and the other Jews who were featured.

I apparently marched to the beat of a quirky drummer. It turned out, however, that my attitude at 13 wasn’t a quirk. Though I didn’t realize it then, it was actually the dawning of a conviction — that maybe group pride wasn’t a great idea.

I agree with Mr. Prager. I don’t think group pride is a great idea either. I used to know a man who was heavily into White Pride. He often also posted on social media how proud he was to be White. Now, White people have accomplished quite a bit. In fact, it would be fair to say that White people largely created the modern world, including almost all of its science and technology. This is not to put down people of other races or even to elevate the White race. It is a simple historical fact. I have no doubt that the people who lived in the temperate climate of Europe with the same sort of cultural background would have invented the modern world, no matter what the color of their skin. Race had nothing to do with it.

Should I be proud that I am White? Well, the fact is that all those discoveries and inventions were made by other White people. I didn’t have anything to do with it. The only trait I share with those scientists and inventors is the color of my skin, a trait I did not choose for myself. Should I be proud of my German ancestors because Germans made many scientific discoveries? Why should I? Should I be proud to be an American? I love my country and think it is the greatest country in the world, but I have had little part in making America great.

But Dennis Prager is not writing about racial pride but Pride Month, the month of June when all things LGBTXYZ are celebrated.

The most recent incarnation of group pride is LGBTQ pride. Every company, every professional sports team, every Democratic politician, even the armed forces and American embassies around the world are expected to celebrate Pride Month, Pride Night and year-round LGBTQ Pride.

This is problematic for at least two reasons.

First, what exactly is one proud of? What accomplishment is involved in being gay, lesbian or bisexual? Even trans is allegedly built into one’s nature. Isn’t the entire premise of the LGBTQ movement that one does not choose one’s sexual orientation or sexual identity? Wasn’t anyone who argued that homosexuality is a choice declared a hater and a science denier? So, then, if no choice is involved, no effort on the part of the individual — let alone no moral accomplishment — what is there to be proud of? Maybe I couldn’t identify with Jewish pride over great Jewish athletes, but at least they all actually accomplished something.

The other problematic element has to do with why the LGBTQ movement does everything possible to bludgeon every institution into celebrating Pride Nights, Days, Weeks and Months. The reason is the totalitarian nature of all left-wing movements. Unlike liberal and conservative movements, every left-wing movement is totalitarian. Therefore, it is not enough for people to tolerate or even show respect to LGBTQ individuals. We must all celebrate lesbianism, male homosexuality, the transgendered and queers. No left-wing movement is a movement for tolerance. They are movements that demand celebration.

Pride month wouldn’t concern me at all if it weren’t for the coercive aspect of it all. I wouldn’t care if the LBGTABC crowd celebrated Pride Day or Pride Year so long as I was left out of it. I feel, however, that I am obliged to be part of it, with the corporate-sponsored rainbows showing up everywhere. I feel as if I am being made to celebrate something I don’t really approve of.

Not a good thing

But what’s wrong with pride? As I have said I share Dennis Prager’s wariness about group pride, but I would add one or two things. First, it is not clear to me that being a sexual deviant is anything to be proud of. Mr. Prager steers clear of the subject of homosexuality, but the scripture and traditions of both Judaism and Christianity (and really every other major religion) condemn homosexuality as sinful. The inclination is not, of course, a sin. Temptation is never sinful in itself. The action is a sin. If this is true, then being proud of committing acts that our creator disapproves of seems impudent at best.

Second, I am not sure where Judaism stands, but to Christians the greatest sin is pride. This is a sin worse than any sexual sin. As C. S. Lewis put it:

According to Christian teachers, the essential vice, the utmost evil, is Pride. Unchastity, anger,
greed, drunkenness, and all that, are mere fleabites in comparison: it was through Pride that the
devil became the devil: Pride leads to every other vice: it is the complete anti-God state of mind.

Now what you want to get clear it that Pride is essentially
competitive – is competitive by its very nature – while the other vices are competitive only, so to
speak, by accident. Pride gets no pleasure out of having something, only out of having more of
it than the next man. We say that people are proud of being rich, or clever, or good-looking, but
they are not. They are proud of being richer, or cleverer, or better-looking than others. If
someone else became equally rich, or clever, or good-looking there would be nothing to be
proud about. It is the comparison that makes you proud: the pleasure of being above the rest.
Once the element of competition has gone, pride has gone. That is why I say that Pride is
essentially competitive in a way the other vices are not. The sexual impulse may drive two men
into competition if they both want the same girl. But that is only by accident; they might just as
likely have wanted two different girls. But a proud man will take your girl from you, not because
he wants her, but just to prove to himself that he is a better man than you. Greed may drive men
into competition if there is not enough to go round; but the proud man, even when he has got
more than he can possibly want, will try to get still more just to assert his power. Nearly all
those evils in the world which people put down to greed or selfishness are really far more the result of Pride.

The problem with group pride of any sort is that if you are proud of belonging to your group then it follows that you must look down on the people who don’t belong to your group. This is why the Pride movement is totalitarian in nature. The proud person must feel superior to and have contempt for anyone who is not an enthusiastic supporter of the cause. You can’t be tolerant towards others if you are proud because you are competing with them.

Maybe instead of Pride Month, we should have Humility Month, a month in which we all reflect on how we have not lived up to our promise. We should consider ways in which we can become better people. Maybe we should try to be more tolerant and compassionate towards people we don’t like or agree with. Humility Month would certainly be healthier than Pride Month.

Pi Day

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

Pi Day

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 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 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.

Related articles

• Toys ‘R’ Us is a shell of its old self. How it got this way is a lesson for retail (business.financialpost.com)
• How Small Biz Owners Can Take Advantage of Small Business Saturday This Year (grasshopper.com)