Pi day (π day) comes every year, but this year’s pi day is special and there won’t be another one like it for a hundred years. If you write pi to two decimal places, you have π=3.14, and you can read that as March 14. But if you write it out to four decimal places you have π=3.1415. That’s March 14th, 2015 and that happens only once every hundred years!
Some of you reading this don’t feel the excited need for an exclamation point at the end of that previous sentence. We’re sorry about that. We realize that you have to have a certain affection for mathematics and a love for pi in particular to get excited about seeing it carried it out to four places in decimal notation and on your calendar.
Though pi may not be exactly loveable, it’s definitely special. There are certain numbers that keep turning up again and again, and some of them are so omnipresent that mathematicians, wanting to save time and space, have used symbols to represent them. Pi, as we say it, or π, as we write it in mathematics, is certainly the most famous. Among mathematicians, e is almost as famous as π, but if you gave up on math when you left high school you may still remember something about π while you haven’t heard a thing about e. But let’s put e aside and get back to pi.
In mathspeak, pi is an irrational number — not to imply that 3.14159 is a particularly wacky numeral, but simply that you cannot get it by dividing a number by another number. Or, to speak mathematically, it isn’t the ratio of two numbers and, hence, it’s irrational. So, it’s not equal to 22/7, which many students pick up in high school.
You can calculate pi by drawing a regular hexagon inside and outside a circle, and you can use the sides of the hexagon as the base of triangles whose vertex is at the center of the circle. It’s simple enough to calculate the areas of the triangles and hence the hexagons, and you know that the area of the circle is bigger than the inside hexagon and smaller than the outside hexagon. Archimedes did that and kept doubling the number of sides until he had a 96-sided polygon. Then he was able to show that pi was bigger than 223/71 and smaller than 22/7. And that’s where 22/7 comes from.
Our pi is transcendental. That sounds more unusual and ecstatic than it is. Again, in mathspeak, a transcendental number is not algebraic, which is to say that it’s not a root of a non-zero polynomial equation with rational coefficients. (Satisfied?) Most real numbers are transcendental, but if we start discussing what we mean by that previous sentence we won’t enjoy much of the day.
Pi — everyone knows you know this — is the number you get when you divide the circumference of a circle by it’s diameter.What’s interesting — or amazing, if you’re in the mood — is that when you compare the diameter and circumference and try to divide the circumference by the diameter, you get a number which is clearly just a little bit bigger than three, but it’s impossible to discover exactly how much bigger. Or look at it this way, you can divide the diameter into little equal pieces with nothing left over, or you can divide the circumference into little equal pieces with nothing left over, but you’ll never find a size of equal little pieces that that will work on the circumference and on the diameter, too, with nothing left over. Far better to eat your Pi pie.
David Brooks, the conservative columnist at the New York
times, recently wrote a provocative piece about secularists. Ordinarily, his
focus is politics; he’s well connected in Washington, he’s reasonable and he writes well. Brooks occasionally comments on society and culture, and there his conservative vision can lead him astray. His column on secularists sprang from his reading a book, Living the Secular Life, by the sociologist Phil Zuckerman. Brooks didn’t review the book, but used it as a jumping off point for his own views on “secular individuals” and “secular people.”
He makes a number of observations which we can agree with, or debate, or think are plain silly. Here they are in his own words:
•“Secular individuals have to build their own moral philosophies. Religious people inherit creeds that have evolved over centuries.”
•“Secular individuals have to build their own communities. Religions come equipped with covenantal rituals that bind people together, sacred practices that are beyond individual choice.”
•“Religious people are commanded to drop worldly concerns. Secular people have to create their own set times for when to pull back and reflect on spiritual matters.” It’s hard to believe but, yes, he’s serious here.
•“Secular people have to fashion their own moral motivation. Religious people are motivated by their love of God and their fervent desire to please Him.”
As you can see, secular people have a very hard life, having to build their own philosophies, communities and rituals, having to make choices, needing to decide when to reflect on life, and having to create their own moral motivations. On the other hand, religious people have it, oh — so easy.
Brooks comes to the point of his piece, beginning with a couple of things that it is not:
“The point is not that secular people should become religious. You either believe in God or you don’t. Neither is the point that religious people are better than secular people. That defies social science evidence and common observation. The point is that an age of mass secularization is an age in which millions of people have put unprecedented moral burdens upon themselves. People who don’t know how to take up these burdens don’t turn bad, but they drift. They suffer from a loss of meaning and an unconscious boredom with their own lives.”
So that’s the point, that life is really, really really hard for secular people, even if they don’t know it — like when they’re bored with their lives and aren’t even conscious of their boredom and go around thinking that they’re not bored.
In his conclusion, Brooks offers some suggestions to secular people.
“It seems to me that if secularism is going to be a positive creed, it can’t just speak to the rational aspects of our nature. Secularism has to do for nonbelievers what religion does for believers — arouse the higher emotions, exalt the passions in pursuit of moral action. Christianity doesn’t rely just on a mild feeling like empathy; it puts agape at the center of life, a fervent and selfless sacrificial love. Judaism doesn’t just value community; it values a covenantal community infused with sacred bonds and chosenness that make the heart strings vibrate. Religions don’t just ask believers to respect others; rather each soul is worthy of the highest dignity because it radiates divine light.”
Of course, secularism isn’t a religion and it doesn’t have a creed the way religions have creeds and one wonders how a religious person, like David Brooks, would respond to a secularist’s suggestions for ways to improve religion. Because Brooks is religious, he knows what he’s talking about when he speaks about a certain kind of spiritual inspiration and feeling. But he doesn’t understand the secular temperament and his his characterization of the secular person is a clownish caricature. And although his lines about Christianity and Judaism speak powerfully, he strangely portrays religious people as passive sheep.
Christianity and Judaism impose the same ethical “burden” on their faithful as is imposed on the secular person. Though religious and secular people may phrase the process differently, they both, at times, have difficulty in distinguishing the right moral choice and both recognize their self-deception and folly.
Yes, being part of a religious group does give meaning to the lives of many people, but it’s witless to think it gives meaning to all of them. Furthermore, many secular minded people find meaning in their family, in their love for their husband or wife, their children, in their daily work for their daily bread, in their pursuit of justice and social good – there are numberless ways in which people find meaning in life without being affiliated with a church.
Brooks concludes by saying “The only secularism that can really arouse moral motivation and impel action is an enchanted secularism, one that puts emotional relations first and autonomy second. I suspect that over the next years secularism will change its face and become hotter and more consuming, less content with mere benevolence, and more responsive to the spiritual urge in each of us, the drive for purity, self-transcendence and sanctification.”
Only David Brooks knows what an “enchanted secularism” is. Maybe there is in each of us a spiritual urge, a drive for purity, self-transcendence and sanctification. But in the context of his essay those words have specific religious meanings and a secularist wouldn’t use those words that way. The secularism and the sanctification he’s been defining throughout his piece are clearly incompatible.
David Brooks isn’t a dummy. Liberals read Brooks and generally can follow his reasoning even when they disagree with views. So it may be that a newspaper column isn’t large enough to allow a well reasoned exploration of secularism and religion. But one thing’s sure, on this subject his writing — though serious and well intended — is a confused and confusing muddle.
In the aftermath of the slaughter in Paris our instinct is to condemn the killers and mourn their victims and to defend — defend to the death, as some have said — the right of editors and cartoonists to write and draw what they please. If they want to satirize Moses or the Pope or Jesus or Mohammed, fine, let them do it.
The offices of Charlie Hebdo had been firebombed in the past by Islamic extremists, so the editors and cartoonists there knew what they were doing. Workers on the magazine weren’t constrained by prudence or the unwritten rules of ordinary decent behavior, such as civility, politeness, and live and let live. They were, as their publication says of itself, irresponsible. We know that.
We also know that safe speech that offends no one, and safe cartooning that ridicules only the conventionally ridiculous, doesn’t maintain or test the limits of free speech. People on the social margin — anarchistic, pornographic, outrageous and disobedient — people working at the disreputable edge, they’re the ones who keep the mainstream free. We have no qualms or quibbles, no questions about any of that.
But we do question whether they had the right target when they lampooned Muhammad. Every nation engaged in fighting Islamic extremists has said over and over again that it is not at war with Islam — it’s at war with Islamic extremists. French President François Hollande has distinctly and emphatically said it many times this past week. About 18 percent of the French population is Muslim. Those Muslims aren’t visitors; they are citizens of France, they are French.
Satirists have generally aimed their barbs at the rich and powerful, at the people in charge who lord it over the poor and downtrodden. But in creating cartoons of the prophet Muhammad, Charlie Hebdo offended all French Muslims — a group made up, by and large, of poor and marginalized citizens. Yes, yes, the cartoons were visual statements against Muslim extremists and terrorists. But extremists and terrorists don’t change their behavior by being bashed in a low circulation satirical magazine. Charlie Hebdo’s broad brush cartoons injured the religious sensibilities of all Muslims.
In France, as in the United Sates, there aren’t laws prohibiting the publication of magazines such as Charlie Hebdo. Open, pluralistic, democratic societies don’t pass laws against publishing satirical cartoons, no matter how offensive, nor do they punish editors for adolescent rebelliousness or gross misjudgment. They don’t even pass laws against cartoonists for being offensive simply for the sake of offending. An open and democratic society puts up with a lot. It’s worth it.
A couple of years ago we published a post about taking down the Christmas tree. Whereas it is now a lazy New Year’s Day, and whereas we haven’t finished straightening up the house from our Christmas feast and our jolly guests, and whereas we celebrated the arrival of the New Year late last night, probably too late last night, we’re simply going to republish our old post:
Taking down the Christmas tree is one of the saddest domestic chores. For a week or longer this evergreen has been standing in the room with us, filling the air with the scent of balsam or other pines, glittering with lights and sparkling ornaments. And those ornaments are so important, so beautiful, no matter that they’re inexpensive baubles or, say, ordinary pine cones tinted with gold-like paint, or paper and glitter glued together by one of the children a dozen years ago. Each ornament has it’s family history — the history of which grandparents had it on their tree a generation ago, or who brought it as a gift, or made it just this year.
There’s no joy of recognition when taking these ornaments from the tree. That delight happened two weeks ago when, after an absence of a year, we carefully lifted this delicate trinket from it’s wrapping and — oh, yes! — we remember that one, the Santa with the paint chipping off, the glass sphere with Mother and Child inside, or those tiny gold balls we got forty years ago for our first Christmas. And if you turn off all the lamps in the room and leave only the strings of tiny tree lights — how magically beautiful it is!
Now we’re simply returning the faded old ornaments to their little egg-crate boxes, if we can find the right boxes that fit, and stacking them one upon the other in a corner of the attic, or in a closet behind the bag of swim suits and beach clothes. Then, after struggling to unfasten the tree from the stand, and after spilling water on the floor, we finally grapple with the brittle tree amid a shower of dried pine needles, drag it out the door and toss it on the snowbank down by the road. And there it will lie until the town truck comes to take it away, bits of glittering tinsel still fluttering here and there.
One of the curses or blessings of contemporary life is that we get news instantaneously from all over the world, and a lot of days it’s truly depressing news. Whether or not you believe in angels singing over a stable in Bethlehem, whether or not you credit the tale of shepherds startled in their fields, and magi who traveled to Bethlehem bearing gifts, magi who got there by following a star — surely the news of that event would be better than what we’re getting these days. So enjoy this event, this balm for the soul. Use your imagination.
The painting is a detail from a much larger work, The Adoration of the Magi, painted by Domenico Ghirlandaio,the Italian Renaissance painter. Along with two brothers and a brother-in-law, he managed a studio workshop that turned out a number of paintings, a sort of “school of Ghirlandaio.” His most famous student-apprentice was Michelangelo. Those angels, or ones resembling them, appear in some other of the works to come out of that workshop, not quite mass production, but not unique either, and, indeed, how much was done by Domenico and how much by someone else is unknowable. The music that the Angels are singing is largely unknowable and quite inaudible. Do use your imagination.
Gene Mirabelli, who writes most of the posts here, is working on another book. (Another damned book, to quote him.) And it’s taking him longer than he had hoped. He’s older now and getting slower. He was 84 on his last birthday, whenever that was, so he may be older than that by now. Still, he considers himself most fortunate. “When I get up in the morning almost everything almost works almost all the time.” In any case, he’s writing fewer posts. In fact, he’s asked us to remove some of the older topical posts which have lost there relevance — and we shall do that in our spare time, whenever we get any spare time, which isn’t often, and which we’ll probably want to spend doing something more entertaining. If you’re interested in his works, and we hope you are, you can find his literary web site and some notes about his publications at www.mirabelli.net
Some theories just feel right and true. They appeal to our common sense so strongly that we believe in them as soon as we hear them. And if the theory is about language, the language we speak and write, we feel pretty certain that we’re familiar enough with the way it works to assess whether some theory about it is true. Now, here’s a theory about language:
• Language channels the way we think and view the world.
That theory became popular among certain linguists in the 1930s and still circulate among many, perhaps most, educated people today.
One thing we know for certain, languages vary widely. One language may have only a single word for eating and drinking, still another makes uniquely fine discriminations between different shades of a color, yet another has no articles such as the or a.
Native American Hopi have no tense markers to indicate time and no words like later. And that led Benjamin Lee Whorf to propose that since the Hopi language has no way indicate past, present or future, they view time differently from English speakers and, further, the cyclical Hopi cosmology reflects this difference.
Whorf was not a professional linguist, but his ideas looked right to his mentor, the linguist Edward Sapir, and soon the theory — called the Sapir-Whorf hypothesis — spread among linguists, academics and the general public. However, no examination of people speaking one language or another has found evidence to support the theory. It’s generally conceded now that such linguistic differences as Whorf had in mind don’t actually channel thought or create a particular view of the world.
And now we have John McWhorter’s The Language Hoax: Why the World Looks the Same in Any Language. McWhorter is a Professor of Linguistics at Columbia University and the author of The Power of Babel: A Natural History of Language, an excellent book that is both scholarly and readable. He’s the author of many other books on language, as well as works on race and cultural issues, and his articles have appeared in the New York Times, and the New Yorker, among other publications.
The Language Hoax is a short book. The pages are small, only about 5 by 7 inches, and there are about 168 pages, excluding the introduction, notes and index. Even so — as an admirer of John McWhorter’s work I hate to say this — it’s too long.
McWhorter demonstrates again and again the inability of the neo-Whorfians to come up with credible evidence to support their theory. His examples of wild differences over a spectrum of languages are interesting and often amusing. But after a while even the most indulgent reader will wonder why McWhorter bothered to write this book if, as he says repeatedly and credibly, there’s no support for the theory he’s attacking.
He has been careful to acknowledge and praise academic work that does show how the workings of language can have a tiny, marginal effect on thought, and he’s shown the difference between those studies and the general notion held by some people that such differences in language guide thought and shape culture. McWhorter writes in a readable and engaging style — he’s a good writer — but his passion for bashing this moribund theory is hard to understand. And there is certainly no hoax involved in whatever misunderstanding the lay public may have about languages.
Languages change and develop in the most amazing ways, and the variety of ways that languages differ is wonderful. McWhorter believes linguistic changes come about spontaneously. They just bubble up, he says. How those bubble are made and where they come from — well, that would make a very interesting book.
There’s a little story about a nun and a dog. A dead dog. Fortunately, everything turns out well in the end. The story is set to music and both the story and the music were composed by Marilyn Robertson. And Yes, that’s Marilyn playing the guitar and singing. It’s a simple whimsical tale and we think you’ll like it. Ms Robertson has a way with words and she manages some delightfully sly puns along the way.
The nuns in the image we’ve posted here are from way back in Medieval times, but our nun is quite contemporary — she rides trolley cars and deals with the hazards of life in the city. The only recording of “The Nun’s Story” is located at SoundCloud.com, which you may not be familiar with, so we’ve made it easy and all you have to do is click HERE. And after you’ve listened to Marilyn you can explore the other music on the site, too. Then return to Critical Pages.
While our fellow humans are drowning themselves in each other’s blood, it’s consoling to remember Steven Pinker’s great book, The Better Angels of Our Nature. The author’s preface begins with these words:
“This book is about what may be the most important thing that has ever happened in human history. Believe it or not – and I know that most people do not — violence has declined over long stretches of time, and today we may be living in the most peaceable era in our species’ existence. The decline, to be sure, has not been smooth; it has not brought violence down to zero; and it is not guaranteed to continue. But it is an unmistakable development, visible on scales from millennia to years, from the waging of wars to the spanking of children.”
Pinker’s book, including notes and index, is 802 pages long. It’s overwhelmingly convincing. You may not want to choose a work of such length for summer reading, or for reading in any season, but even a random walk through these pages will be a corrective to the view that history is on a long downhill trajectory. Some readers may dispute his statistical methodologies, but by and large the trends he focuses on are beyond question.
There are passages describing what humans no longer do to each other, and those pages may be hard to take. The record of violence and cruelty increases as we read further and further back in history, and we’ve forgotten or averted our eyes from the bloody chronicle because we can no longer stomach thinking about what we have done to each other. If you lived in medieval times your chances of being murdered would be thirty times greater than today.
In Steven Pinker’s words “The centuries for which people are nostalgic were times in which the wife of an adulterer could have her note cut off, children as young as eight could be hanged for property crimes, a prisoner’s family could be charged for easement of irons, a witch could be sawn in half, and a sailor could be flogged to a pulp. The moral commonplaces of our age, such as that slavery, war, and torture are wrong, would have been seen as saccharine sentimentality, and our notion of universal human right almost incoherent. Genocide ad war crimes were absent from the historical record only because no one at the time thought they were a big deal.”
The Better Angels of Our Nature is an important book not only because it adds to our understanding of human history, not only because it is a corrective to fanciful notions of a more just and peaceful past, but also because – and this is crucial – it encourages us to persist in our struggle to overcome what Steven Pinker calls “the tragedy of the inherent appeal of aggression.” Our progress has been straight or smooth, and it is certainly uneven today, but clearly we are moving in the right direction. Because we know we can live better, we should keep pressing forward.
Most people know what a turnip is. But not so many are sure they know a rutabega when they see one. Assuming you know what a turnip is and you also know what a cabbage is, we can tell you that a rutabega came about as a cross between the turnip and the cabbage. Yes, we know that’s unlikely, but it seems to be so.
Turnips and rutabegas are members of the plant genus Brassica. In fact, among people who care about such things there’s a theory known as the Triangle of U which diagrams the relationship between members of the Brassica — a theory which has been proven true by DNA studies. But that takes us very far afield. All we wanted to do was to introduce this light, whimsical poem by Marilyn Robertson. It’s called “Roots” and it goes like this…
Is this a turnip? I ask the man arranging vegetables
in the markeet. No, he says, that’s a rutabega.
Here’s a turnip — and he holds up a roundish
white and purple root. The colors are nice,
but the name is not half so musical as rutabega.
It makes me think of jumprope rhymes,
cheerleaders at football games:
Rutabega, Rutabega, sis boom bah.
Or the melodies of old songs: Rutabega moon,
keep shining…Rutabega, here I come,
right back where I started from.
I put a few in my shopping cart.
At the check-out counter,
I ask the young man bagging groceries,
Pardon me, boy, is that the Rutabega choo-choo?
He has no idea what I’m talking about.