My Best Resolution

My Best Resolution

With the end of the year just around the corner, it’s time to think about the resolutions for 2011. People all over the world seem to dedicate at least a few minutes to thinking about what changes they want to make in their lives in the new year. But where does this tradition come from? It’s generally accepted that Babylonians were the first to want to start the new year (on the night of the first new moon after the first day of spring) with a clean state, mostly by returning borrowed farm equipment. As far as Western civilization is concerned, the tradition may be traced all the way to 153 B.C., when the Roman god Janus was placed at the head of the Roman calendar. Janus was always depicted with two faces, one on the front of his head and one on the back. Thus he could look backward and forward at the same time. At midnight on December 31, the Romans imagined Janus looking back at the old year and forward to the new. The god became the ancient symbol for resolutions and many Romans looked for forgiveness from their enemies and also exchanged gifts before the beginning of each year. Later on, the early Christians believed the first day of the new year should be spent reflecting on past mistakes and resolving to improve oneself during the year. No matter where the tradition of making New Year’s resolutions originates, most seem abandoned in a matter of weeks. Working harder, going back to school, losing weight, quitting smoking, eating healthy and balanced meals: all seem short-lived goals. I have had plenty of unfulfilled ones. After some heavy-duty self-analysis, I have decided that the best resolution for 2011 is to have no resolutions. No scuttled plans, no broken promises . . . that’s a pretty responsible way to start the new year.

Thank You, Santa Baby

Thank You, Santa Baby

What’s Christmas without Santa Claus? When we were kids, most of us expected a jolly, red-cheeked man to slide down our chimneys with the gifts we wanted most. Maybe because we had no chimney (I was the only kid at school who lived in a tiny apartment and not in a house.), I realized that my Pop was behind it. I never got the gift I wanted most (a house with a chimney!), but isn’t it the thought that counts?

The origin of Santa dates back to the 4th century. Nikolaos of Myra, who later became St. Nicholas, inspired the folk hero. Nikolaos used to give secret gifts. People would leave their shoes out, and he’d leave coins in them. I bet he never expected that would lead to the super-commercial “Xmas” people experience today.

Aside from traditional holiday stories like “A Visit from St. Nicholas,” which was actually a poem, also known as “Twas the Night Before Christmas,” and Charles Dickens‘s A Christmas Carol, sometimes a story shows up with a whole new angle. I’m going to acquaint you with two spirited Santa stories.

In O. Henry‘s “A Chaparral Christmas Gift,” (1903), Rosita McMullen is loved by two guys: Madison Lane and Johnny McRoy. When she marries Lane on Christmas, McRoy loses it. He shows up (uninvited, natch!), at Sundown Ranch while the festivities are in full swing. “I’ll give you a Christmas present!” he announces, and shoots into the hall. He misses the bride, but shoots off the groom’s earlobe.

“ ‘I’ll shoot better next time,’ ” he vows, “ ‘and there’ll be a next time.’ ” Later, he becomes the Frio Kid, a bloodthirsty outlaw.

Years later, on another Christmas, the Frio Kid gets a whiff of the ratama bloom. O. Henry writes, “The rich, sweet scent touched him somewhere beneath his ice and iron.” Suddenly, he’s thinking of Rosita again, and the vow he made...

There’s a big party going on at Sundown Ranch. The Lanes have a three-year-old son, and there are kids everywhere. Of course, Santa shows up. “That’s my Papa!” six-year-old Billy Sampson says, as his dad plays Santa every year for them.

But it’s not Billy’s dad.

And since O. Henry is the master of the twist ending, you can guess who Santa really is!

In Damon Runyan’s “Dancing Dan’s Christmas” (1932), it’s Christmas Eve at Good-Time Charley’s speakeasy. The narrator and his pals are having a roaring good time, when Dancing Dan comes in carrying this huge package. Dancing Dan is a fun-loving guy who’s been spending too much time with Muriel O’Neill, who’s loved by mobster Heine Schmitt.

The guys are busy toasting everybody in the whole world when vagrant Ooky shows up. “Ooky,” Runyan writes, “is going around all week dressed like Santa Claus and carrying a sign advertising Moe Lewinsky’s clothing joint around in Sixth Avenue.”

As the party goes on, Dancing Dan gets schmaltzy. It seems Muriel’s senile grandmother, Gammer O’Neill, still hangs a stocking up for Santa to fill. Muriel has always sneaked small gifts in Gammer’s stocking. Dancing Dan tells the guys, “ ‘Miss Muriel O’Neill is saying to me that she only wishes she can give Gammer O’Neill one real big Christmas before the old doll puts her checks back in the rack.’ ”

When Ooky falls asleep, Dancing Dan and the guys pull off Ooky’s Santa Claus suit, and Dancing Dan puts it on. He fills up the Santa bag with stuff from that big package he’d brought in, and they head for the O’Neill’s tenement near Madison Square Garden.

As old Gammer sleeps, “Santa” fills up the stocking with diamonds: rings, brooches, and necklaces. “There are enough diamonds to fill the stocking to the muzzle,” Dunyan writes, “and it is no small stocking, at that, and I judge that Gammer O’Neill has a pretty fair set of bunting sticks when she is young.” Plus there are leftover gems, which Dancing Dan and the guys leave in “a nice little pile on the chair.”

Later the narrator remembers seeing huge headlines in the day’s paper about the monumental stickup of a diamond merchant. . . .

But it’s the best Christmas the old doll ever has.

Thanks to you, Santa, baby.

Storytelling and Math, Part 3

Storytelling and Math, Part 3

As promised, I added another chapter to the saga of Dawn of the Deadheads: A Choose Your Own Math Adventure. It's the last school day before vacation, a day of daydreaming about a fun camping trip, but you, the "hero" of the story, slowly start to awaken to the horrible reality of what is happening in your town and in the rest of the world.

As the suspense builds, so do the mathematical challenges. In this chapter, students need to know and understand the Pythagorean Theorem and have experience (but not proficiency) working with rectangular prisms. Believe it or not, in some states, these topics are required in as early as 7th grade. Alas, to solve the "fishing rod" problem, students also need to know how to approximate the square roots of non-perfect squares. That topic is usually reserved for 8th grade.

Next year, I'll kick off my posts with Bloom's Taxonomy, a popular topic in education. In the meantime, enjoy Dawn of the Deadheads: A Choose Your Own Math Adventure.

Antiquity Corner: From Solstice to Santa

Antiquity Corner: From Solstice to Santa

The basic theme of Paul Frodsham’s book From Stonehenge to Santa Claus (The History Press, 2008) is that Christmas has been celebrated since the Neolithic Age (c. 8000–5000 years ago) and that even if Christianity had never been, we would still be celebrating Christmas, but calling it something else. Frodsham references great megalithic monuments in Europe, such as Stonehenge, and the frequency with which they are aligned with the winter solstice. To the people of antiquity, the dying and reviving of the sun, the lengthening of days, and the return of warmth and growth was a matter of survival. They were affected by the movement of the sun and its relation to the natural forces of the earth in ways that would not occur to most modern people. Even without calendars, therefore, December 21 was the occasion for celebration.

In Celtic and Germanic Europe, the solstice was the occasion for the Midwinter Feast. Since November 1 (Samhain) marked the beginning of the cold season and Spring began with Imbolc in February, the solstice was the winter midpoint. The feasting was to celebrate the returning power of the sun and to encourage it. In this context, the evergreen tree, the holly, and the mistletoe had magical and ritual significance as they remained green and alive even in the depth of winter. For pre-Christian Celts, midwinter was celebrated with sacrifices, both human and animal.

These were placed in wicker cages, which were hung from the boughs of the evergreen. In a ceremony presided over by the druids, the sacrifices were set on fire and perished in the flames. Today, of course, we simply hang crystal balls and candy on the tree, accompanied by electric light bulbs. No sacrifices and no druids. As for the mistletoe, belief in its magical power to ensure life and fertility came from the fact that it grew high on the tree, close to the gods. It could only be cut by a druid with a golden sickle. (For a more detailed analysis of all this, refer to Sir James George Frazer’s book The New Golden Bough.)

At this point, logical questions would be about why Christmas Day is on December 25 if the solstice occurs around the 21st and how it all became identified with the birth of Christ. The answer to the first question lies with the fallacies in the Julian calendar. When this was devised by Julius Caesar in the first century B.C., he identified December 25 as the day of the winter solstice. However, he did not account for the effect of the movement of the earth on the calendar year. More modern calendars shifted the solstice to its present date of December 21or 22. As for the second question, the answer has to do with the traditional Roman celebration of the Dies Natalis Sol Invictus (the Day of the Birthday of the Unconquered Sun) on December 25. At some point in the 4th century, a Bishop of Rome decreed that henceforth the birthday of Christ would be celebrated on December 25. This was in keeping with the practice of the early Church of preempting pagan festivals and replacing them with Christian rituals. This is no evidence that Jesus was born on that date. There is some evidence that his birthday was actually in April. However, belief in December 25 as the Nativity took root and so it is celebrated today with all the traditional trappings.

During the European Middle Ages, Christmas Day itself was less important than the nighttime celebrations culminating in the Twelfth Night. The Christmas celebrations with which we are familiar today were largely developed in 19th century Victorian England. Charles Dickens’ A Christmas Carol will give you a good description. That is why stores which sell Christmas decorations usually feature a Victorian village complete with glowing houses, shops, evergreens, snow, and often an electric train running around or through it. The image of Father Christmas is also a product of Victorian England. At the risk of outraging many, however, I must tell you that the American Santa Claus is a 19th-century invention of the Coca Cola Company, although, as Frodsham points out, its origins can be traced to a fourth-century Saint Nicholas.

Regardless of origins, Christmas is always a lot of fun. So Ho! Ho! Ho! And a merry Christmas to all.

To Refudiate, Or Not to Refudiate?

To Refudiate, Or Not to Refudiate?

One of my favorite pastimes is celebrity-watching. I especially love keeping track of those celebrities who set off firestorms of commentary everywhere they go—recent favorites have included Lady Gaga, Paris Hilton, Kate Middleton, and of course, Sarah Palin. That’s why I was more excited than usual by the Oxford American Dictionary’s word of the year: refudiate.

Ms. Palin coined the word in a July 18 tweet, when she wrote: “Ground Zero Mosque supporters: doesn't it stab you in the heart, as it does ours throughout the heartland? Peaceful Muslims, pls refudiate.” The tweet, along with two others, started media outlets buzzing not only about the messages’ controversial politics but also about the hybrid word Sarah Palin had created. The buzz only got louder when Palin covered her mistake by writing, “ ‘Refudiate,' 'misunderestimate,' 'wee-wee'd up.' English is a living language. Shakespeare liked to coin new words too. Got to celebrate it!"

Sentence fragments aside, Sarah Palin is actually right about this one, and that’s exactly why the Oxford American Dictionary gave the former governor a nod with the word of the year. Each year, the organization chooses a word that’s new to the English language, one that they think reflects movements in popular culture and that they think will have lasting use. In fact, new technology has been a source for many past word-of-the-year finalists and winners, like “unfriend,” “intexticated,” and “webisode.” (Personal side note here: one of the finalists for this year was the South African vuvuzela!)

According to the Oxford American Dictionary, refudiate is a combination of refute and repudiate, and it broadly means “to reject.” The word’s new status has itself been rejected; media outlets are now abuzz with whether the Oxford American Dictionary has the authority to name the word of the year. The practice of choosing one word above all others was started by the American Dialect Society (ADS), who announces their word of the year in January. Merriam Webster started trumping the ADS by announcing their own word in December. Now the Oxford University Press, publishers of the Oxford American Dictionary, is announcing their word of the year in November!

Irregardless (that’s another “word” made famous by a politician, although this one didn’t win any prizes), the debate over Ms. Palin’s word and its nomination by lexicographers serve as a reminder that our language is not static, even after hundreds of years of development. Even if the word isn’t officially making it into the dictionary any time soon, I’ll be on Palin-watch for any other new additions!

The Heart of Argentina

The Heart of Argentina

While I was thinking about a topic for my December post, I realized that my trip to Argentina is coming soon. So, I decided my next two posts will be about my unconventional tourist destination in Argentina, the city of Córdoba. I lived there for about ten years and although I now live in the most amazing and exciting city in the world, New York, I still miss Córdoba. This time I am traveling with my husband and a friend of ours. I am hoping to see the city from a different perspective, as a tourist.

The following is just a short description of my upcoming destination so you will have some background information when you read my January post.

What You Need to Know About Córdoba

Córdoba is the second-largest city in Argentina and is located in the center of the country, about 470 miles northwest of Buenos Aires. It has 1.3 million inhabitants and it was founded on the Suquía River by the Spanish Noble Jerónimo Luis de Cabrera in 1573.

The Jesuits, a Catholic religious order, played a very important role in the city’s history and development. They founded the first university in Argentina, Universidad Nacional de Córdoba. As a matter of fact, Córdoba is popularly known as La Docta (translated as the "Learned Lady") due to the large number of universities and students it has. It´s also called La ciudad de las campanas (The City of the Bells) because of the presence of numerous churches built during colonial times.

Córdoba’s streets and avenues combine modern buildings with colonial architecture. One of the most identifiable historical monuments is the Jesuit Block or Manzana Jesuítica, declared in 2000 as a World Heritage Site by UNESCO.

Cordobeses have the reputation of being fun-loving, something that is compounded by their distinctive accents, which, to other Argentines, sound like an amusing song regardless of what they are saying.

In my next post, I will include a detailed account and photos of my trip.

A Christmas Carol: Caribbean Style

A Christmas Carol: Caribbean Style

Most everybody knows what Christmas caroling is, but who goes caroling anymore? Have people become too busy, lazy, or intimidated to sing in public? Are they afraid of offending neighbors or interrupting their privacy? Even I, the poster child for all things secular, enjoy the Christmas season and miss those traditions.

In the Spanish-speaking world, however, caroling is still alive and kicking. In Puerto Rico, for example, caroling is known as parranda, asalto, or trulla. It goes like this: a group of friends gathers together to surprise another friend. They arrive at the destination and then very quietly assemble by the front door. At a signal, all start playing their instruments and singing traditional songs. The parrandas usually begin after 10 P.M. in order to wake the sleeping friend. (Of course, the parranderos are given plenty of "hints" beforehand by the homeowner that he or she is ready to receive a parranda.)


The party goes on for an hour or two, then everyone, including the homeowners, takes the party to someone else. The group grows as they offer their parranda at several houses during that night. At the last house, probably around 3 or 4 A.M., the homeowner offers the traditional chicken soup (asopao de pollo) or mondongo (beef tripe soup). The party is over at dawn.


I hope you will appreciate the difference between a mild-mannered 10-member choir singing "Silent Night" and 10 people blasting away with brass, wind, and percussion instruments, backed up by 20 singers. It’s a different ball game, all right.


What they have in common, though, is that they both are expressions of happiness and celebrations friendship. I sure wouldn’t mind experiencing more of that in this neck of the woods.

Me, My “Self” and My Son

Me, My “Self” and My Son

The other night, my son and I attended a panel discussion at the New York Academy of Sciences called “To Be or Not To Be: The Self as Illusion.” This was the first such event in a six-part series called Perspectives on the Self: Conversations on Identity and Consciousness. The panel was moderated by Krista Tippett, the creator/host of Public Radio’s Being, and included the following people: Dutch cardiologist and expert in near-death experiences (NDEs), Dr. Pim van Lommel; philosopher Thomas Metzinger (Univ. of Mainz, Germany); and philosopher Evan Thompson (Univ. of Toronto, Canada).

I usually attend lectures that concern my main areas of academic interest, such as animal behavior. However, I had a more personal reason for attending this event―I was interested in the neurobiology and the data on NDEs. My son, a budding philosophy major in college, was interested in going to the event, too, since he had read about Metzinger. To quote from the Academy’s flyer, the discussion aimed “to examine recent developments in neuroscience and philosophy that shed light on whether our conscious experience of a unified self is a reality or illusion.” How lucky that science (biology) and philosophy collided to produce an academic event that I could share with my son!

Metzinger stated that, in his opinion, there is no true self; he seemed to think that the experience of such is limited by the biology of the brain and by the social connections we share, which produce a sense of self. The other philosopher, Thompson, was concerned with the ethical implications of the concept of a self. Interestingly, van Lommel, who began his career as a “rational” scientist, had a more spiritual concept of the self as a transcendent entity that may exist beyond the physical functioning of the brain. This was based on hundreds of conversations with his patients who had had NDEs and/or OBEs (out-of-body experiences).

In terms of people finding a meaningful sense of self, Metzinger said that this is a great challenge, given that we are all products of random and non-directional evolution (a point I appreciated). I still struggle in my understanding of the biological and spiritual aspects of the self. But what rings most true for me can be paraphrased from a recent e-mail about this very conflict: “If there is no self, then whose arthritis is this?”

December 7, 1941

December 7, 1941

On this anniversary of Japan’s attack on Pearl Harbor, I want to present a different perspective on that tragic event and, at the same time, plug one of Amsco’s textbooks. Most U.S. history and world history textbooks (including our own) spend only a few sentences explaining why Japan took this drastic action, which Japanese leaders must have known would lead the United States to take rigorous measures to retaliate and try to defeat Japan.

But one of our textbooks, Enjoying Global History, by Henry Abraham and Irwin Pfeffer, spends more time on the Japanese motives than most other high school textbooks. It presents an imaginary discussion among Japanese leaders in November 1941 as to how to react to U.S. actions. This book is aimed at reluctant readers who need a high-interest approach to history. Every chapter includes a dramatized discussion by notable figures from the past. Let’s look at how the Pearl Harbor dramatization reads:

Tokyo November 1941. Setting: the headquarters of the Japanese Imperial High Command in Tokyo.

“Gentlemen, let us come to order,” said Prime Minister Tojo. “The United States says it will not recognize our territorial gains in China. We must now decide how to deal with the United States.”

There was a sharp outcry from the admirals and generals. All agreed that something had to be done.

The prime minister continued. “We all know that Japan is the most advanced nation in Asia. Therefore, the people of Asia look to us for leadership and protection. Now that the Western imperialists are fighting a war to the death among themselves, we have our chance to rid all Asia of those vultures! I say let us strike fear in the American heart and send it back to the other side of the sea where it belongs!”

Prime Minister Tojo

At this, the military officers in the room leaped to their feet and shouted their approval. Only one man––Admiral Yamamoto––remained seated. It was obvious that he did not entirely share Tojo’s opinions.

Admiral Yamamoto spoke. “Gentlemen, we enjoy a profitable friendship with the United States. It supplies us with oil, scrap iron, and many other valuable materials. We need these things, and the United States needs our business. We all know that the Americans still suffer from an economic depression. I do not think that they can afford to stop trading with us. Americans are reasonable people. I do not think that they are looking for trouble. Let our ambassadors, and not our guns, convince the Americans to mind their own business. Remember, gentlemen, war is costly. The United States may not be as weak and foolish as it appears.”

Admiral Yamamoto

The men spoke excitedly to one another. While they did not cheer the admiral, they were impressed by what he had said. Suddenly, an official rushed into the room and gave a message to the prime minister. The room was hushed as Tojo read the message.He looked up with flashing eyes and said, “My brothers, the United States has just turned down every one of our demands.”

“The message says that, if we wish to continue to trade, we must give up the parts of Asia that we now protect. They order us about as if we were mindless children! We have taught the Chinese to respect us. Now I say that it is time to let the Americans feel our sting! Let us invade their bases in Hawaii!”

The officers stood once more and flooded the room with cries of agreement. This time, not a single officer remained seated.

Postholing. Rather than cover all topics in a world history curriculum, Enjoying Global History uses the postholing technique. It picks key concepts and events and presents them in more depth than most other world history textbooks. Moreover, it presents them in such a way that students are more likely to remember the events and concepts. Not all the dramatizations are as controversial as the one above, but they are all memorable.

Critical Thinking. The book does not do away with the historical narrative altogether. Each chapter begins with an introduction that puts the following dramatization in context. Then after each dramatization, the narrative tells the student what happened next and interprets the events. And of course, each chapter has a set of review questions and other activities to further the students’ understanding of the subject of the chapter.

Big Nothing: The History of Zero

Big Nothing: The History of Zero

While rocking out to Patti Smith, in celebration of her victory winning the National Book Award, I rediscovered her tribute, “Radio Baghdad.” The song celebrates the Iraqi city’s rich cultural and intellectual history, and as a refrain she specifically mentions its involvement in the invention of zero: “We created the zero/But we mean nothing to you.”

Smith honors Baghdad’s intellectual contribution to the establishment of zero as a number. Zero deserves her praise for its usefulness as a placeholder (as in the number 306), for its role as the additive identity element (if you add zero to any number, you get that number—in symbols, n + 0 = n for any number n), and for its contribution to the development of calculus. As the late writer David Foster Wallace elegantly claimed, “The invention of calculus was shocking because for a long time it had simply been presumed that you couldn't divide by zero.” Zero is a game-changer, a distinct value, and the barrier between positive and negative.

The richly informative book 100 Greatest Science Inventions of All Time tells the story of Al-Khwarizmi. In 810 A.D., this famous Baghdad mathematician convinced a group of fellow scholars that zero must be a number by demonstrating that zero behaves like a number when subject to common operations. Not only did Al-Khwarizmi thus effectively demonstrate zero as a number, but he also established himself as the founder of algebra. 
I love this story because I think it eloquently demonstrates the following dispositions that are essential to the study of mathematics: engagement in abstract thought, the use of objects to represent numbers and demonstrate their properties, scholarly debate, and the necessity of proof.

Even before Al-Khwarizmi, the Indian mathematician Brahmagupta was the first to write about zero in a text, in 628 A.D. He describes the properties of zero, detailing how zero computes with both positive and negative numbers. There is evidence that the Mayans used zero as a number long before 810 A.D. The influential mathematician Ptolemy used a symbol for zero in a text he wrote in 130 A.D., the first instance where zero was not used as merely a placeholder (as it is used in the number 100, for instance.) All of these origins of the use of zero as a number helped contribute to the way it is used in mathematics. Reading about the origins of mathematical ideas or discussing them in your classroom can honor the thinkers involved and give you and your students a different way to think deeply about the ideas that we all use in mathematics every day. Encourage students to meditate on these ideas. Let them debate and imagine and doubt. Let them demonstrate and let them marvel. I marvel, like Patti Smith marvels, at the “invention of zero.” I marvel at the fact that rigorous mathematicians can really make something out of nothing.

Let’s Talk Turkey

Let’s Talk Turkey

Here it is, early December, and I am already thinking about a Christmas turkey. I remember when it was my mom and dad who were in charge of making our Thanksgiving and Christmas turkeys. When I was really young, deciding when the turkey was cooked was pretty much guesswork. When the bird looked brown enough, my dad would wiggle one of the drumsticks. If the leg moved easily, he pronounced the bird done.

Later on, they used a meat thermometer, which was a more reliable indicator of “doneness.” (A turkey is cooked when its internal temperature is 185°F (85°C).) They had to be careful, however,  not to let the bulb of the thermometer come too near or touch a bone because the reading would be too high and the turkey may not have been cooked all the way through. In addition, there was the problem of reading the thermometer.

Next, came turkeys with those little built-in, pop-up turkey timers. They took the guesswork out of turkey cooking, which made mom and dad very happy. From that time on, our turkeys were perfectly cooked every time.

The scientist in me has always wondered how those little devices work. Through the magic of Google, I was able to find out. Now, I will share that information with you. As you can see from the diagram, the pop-up timer has four basic parts: (A) the indicator, which is usually red; (B) the case, which is usually white; (C) a spring; and (D) a bit of metal with a melting point of about 185°F. While the turkey is refrigerated and while it is cooking, the metal remains a solid. When the internal temperature of the turkey reaches 185°F, the metal melts, becoming a liquid, and releases the indicator. The spring pushes the indicator out of the case. No more guesswork; a perfectly cooked turkey every time.

Did you know that these pop-up timers are reusable? To reuse a timer, wash it thoroughly, then, to melt the metal, hold it in water that is above 185°F, push in the indicator, take the timer out of the hot water, and wait a bit until the metal solidifies.

Now that I think about my guest list, I guess I won’t need a really big turkey because several of those coming to my home for the holidays are vegetarians. Maybe I’ll just make a big chicken or skip meat altogether and make a big pan of lasagna or baked ziti. I still have time to make up my mind.