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Babylonian Math

June 17, 2010

Until I can locate my camera’s power cord, there will be no vacation photos. Try to restrain your disappointment. ;)

While the kids were at Vacation Bible School yesterday (a concept I find simultaneously delightful and mystifying given my secular upbringing — but that’s a whole other post) I spent an hour avoiding cleaning the house and instead watching the first two lectures in a series devoted to the history of mathematics.

I’ve really come around to liking math lately. It’s a foreign language I never bothered to learn well when I was in school. I’m slowly fixing that.

I especially like learning about ancient math and science. It’s riveting to discover that people 4,000 years ago were far more advanced and modern in thinking than I’d realized. The ancient Babylonians predicted eclipses and planetary alignments centuries into the future, they calculated the square root of 2 to six decimal places, they figured out a geometrical solution to quadratic equations, and they used the Pythagorean theorem 1,500 years before Pythagoras was born.

I wish I had learned in school that algebra is shorthand for something that can be solved using geometry — visually. And had been shown those visuals. I think it would have been a lot easier to grasp.

Take the Pythagorean theorem. The algebraic equation is

a^2 + b^2 = c^2\!\,

where a and b represent two sides of a right triangle and c is the hypotenuse. When we visualize it, this is probably what we see:

It doesn’t really tell us much.

But what if we think about it like this: a square with sides of length A will have an area that, when added to the area of a square with the sides of length B, will equal the area of a square with the sides of length C.

We’ll use the classic 3/4/5 triangle:

This makes more sense to me. And it’s how the Babylonians derived the theorem themselves. When the numbers of the three sides are all whole numbers we call them Pythagorean triples. The Babylonians calculated this triple: 4601 (squared) + 4800 (squared) = 6649 (squared). Crazy.

How about quadratic equations? Let’s say we’re staring at this quadratic equation in 10th-grade algebra and trying to figure out how to solve it:

x² + 2x = 15

Before this concept could be represented algebraically, the Babylonians figured it out geometrically. Let’s say you wanted to construct a rectangular building and you knew you only had 15 square units of ground space to work with. You know that you’d like to divide it into two rooms, and one of those rooms needs to have a wall that is 2 units long. The other room needs to be a square. How long will the walls of the square room be? You can draw it like this:

Can you see it?  x² + 2x = 15

Now you can split the rectangle with a known side of 2 units into equal pieces:

Next you move these two pieces around like this:

Now comes the part known as “completing the square”. You create a little square to fill in the missing space in the bigger square. We can tell from the drawing that the new square will be 1 unit by 1 unit.

You’re going to need to add an equal square to the other side to keep the equation equal:

The little square has an area of 1 unit. We can think of the big square this way: its area is the same as 15 plus 1. We can write it out showing that one side multiplied by the other side equals 15 plus 1:

(x + 1)(x + 1) = 15 + 1

We’ll write it out a new way:

(x + 1)² = 16

And now we need to take the square root of each side, something the Babylonians were good at doing.

(Square root, by the way, is the length of a side of the square that can be divided into equal squares of a given number. So 16 little equal squares can be combined to form a larger square with sides the length of 4. The square root of 16 is therefore 4. This becomes more complicated to do geometrically when you’re not using whole numbers, like say, finding the square root of 15. But it works for square roots that are whole numbers.)

Anyway, taking the square root of each side gives us:

x + 1 = 4

Now it’s simple to solve for the unknown. Simply subtract 1 from each side and:

x = 3

Now we know our square room is 3 by 3 units, and the total rectangle building is 3 by 5 units.

Algebraically speaking, x also could equal -5, but I don’t know if the Babylonians could calculate that. While I’m aware that there must be some use for -5 as an answer to this equation, it isn’t practical for the question I posed above about building dimensions, so it doesn’t much bother me whether the Babylonians could calculate it or not.

When I learned how to solve equations like this in high school, we did what is called “factoring”, meaning that you have to figure out what numbers can be multiplied together to get 15, and then insert them, one at a time, into the equation. One would be positive and the other negative, and so you would reason out 3 and -5 after trying them in the equation. It seemed so arbitrary to me at the time, and I had completely forgotten how to do it at all until I looked it up on the internet.

But I think I can remember how to complete the square. Pretty neat, huh?

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Byeya’s Irises

April 10, 2010

Somewhere close to 60 years ago my grandmother planted these “champagne” irises. They’ve survived droughts, freezes, and then 18 years of neglect after she died. More recently they survived being dug up and moved to my house.

I’ve been watching them, anticipating the day they would burst forth.

Today was a perfect spring day. I brought Augustine’s Confessions outside to read after it got too sunny to keep weeding. A small hill in my backyard proved magnetic after awhile, and I was drawn out of my shaded spot to lie there on my stomach and read.

Back in college, half my life ago, I used to lie outside on a hill reading in a sunny area between dorms, my friends to either side of me, listening to the music of Pearl Jam’s Ten blaring from a stereo propped in the open window of the boys’ dorm to our right combined with the music of romping 19-year-olds hitting volleyballs, throwing frisbees, and reveling in the freedom of new adulthood.

Today I listened to the music of neighborhood lawnmowers, the TV in the garage where my husband worked, and the shouts of my children romping with their neighbors in the yard next door, reveling in the freedom of a sunny Saturday with no homework.

“Time does not stand still, nor are the rolling seasons useless to us, for they work wonders in our minds,” Augustine said.

I took in the beauty around me, noting the prickle of last year’s grass thatch against my wrists, the contrast of the gentle warmth of the April sun soaking through my clothes and a light, cool breeze on my face, the visual punch of reborn plants bursting with foliage in the slanting light, and the smell of mulch and new growth.

“Yet were these beautiful things not from you [God], none of them would be at all. They arise and sink; in their rising they begin to exist and grow toward their perfection, but once perfect they grow old and perish; or, if not all reach old age, yet certainly all perish. So then, even as they arise and stretch out toward existence, the more quickly they grow and strive to be, the more swiftly they are hastening toward extinction. This is the law of their nature. You have endowed them so richly because they belong to a society of things that do not all exist at once, but in their passing away and succession together form a whole, of which the several creatures are parts. So it is with our speaking as it proceeds by audible signs: it will not be a whole utterance unless one word dies away after making its syllables heard, and gives place to another.”

And I saw what he was saying. We are part of a greater whole. We can’t see it because we are just parts, but for the whole to exist we must grow and eventually die, as did those before us and those yet to come. It is like we are the individual words of a spoken sentence, one that will not have meaning until all the words are spoken. It is bittersweet to see this beauty and to know its temporariness and yet it must be. We grow toward perfection in our mortal selves, and if we’re lucky we grow old before we perish. But always we are moving on, moving toward the true perfection of the whole.

Before I went inside I took a picture of Byeya’s irises. Today another part reached perfection.

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On Friendship

April 5, 2010

Friendship can only exist between good men.

This is what Cicero said in his letter called On Friendship. I decided to read it tonight after seeing it referenced in St. Augustine’s Confessions, which I’m working my way through this month.

Is it true that friendship can only exist between good men?

Well, to parse it some, I’d argue that friendship can exist between good women as well as between a good man and a good woman. And before you go and say that it’s 21st-century feminist mumbo jumbo that’s making me claim that Cicero meant only a man-to-man relationship I will tell you that he meant exactly that. He said so explicitly. Repeatedly. Only. Between. Men.

Moving on, do both parties have to be good? I got a kick out of his definition of “good”. Cicero was Roman, the speakers in his story are Romans, and while they acknowledge some indebtedness to the Greeks, they’re not going to blindly accept Greek philosophy. So where Socrates would have spent 20,000 words building an imaginary city to define “good”, Cicero (or his narrator, Laelius) snorts at the philosophers:

I do not, however, press this [definition] too closely, like the philosophers who push their definitions to a superfluous accuracy. They have truth on their side, perhaps, but it is of no practical advantage. Those, I mean, who say that no one but the “wise” is “good.” Granted, by all means. But the “wisdom” they mean is one to which no mortal ever yet attained. We must concern ourselves with the facts of everyday life as we find it — not imaginary and ideal perfections.

The argument Cicero makes as his letter drags goes on is that people who aren’t good can’t be good friends and therefore can’t have good friends. Or something like that.

Aside from a few snarky remarks, this was a pretty dry read. It ended up, in fact, being an occasion where the book itself became more interesting than the contents.

Take this excerpt from the introduction:

The evils which were undermining the Republic bear so many striking resemblances to those which threaten the civic and national life of America today that the interest of the period is by no means merely historical.

The edition I’m reading was published in 1909.

More fun are the notes a previous owner made in the margins, helpfully dated July 28, 1951. This passage was underlined:

There are people who give the palm to riches or to good health, or to power and office, many even to sensual pleasures.

And next to it, double-underlined and with an exclamation point is:

Tom!

So of course my imagination has drifted away from what Cicero had to say about friendship and toward whatever Tom must have done 60-some-odd years ago to merit double-underlining and immortality in my book. Was he into money or politics or *gasp* sensual pleasures? I want to know, RBJ (I only have your initials) … it must be a good story.

And now you see why I have trouble finishing tough reads.

But I did finish this one.

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Happy Easter

April 4, 2010

Did you know that St. Augustine was responsible for infant baptism? In his time (the 4th century AD) baptism was reserved until the last possible instant. You had only one chance to be completely cleansed of sin, so Christians in the 300′s held out until they were close to death, thinking that they had a better likelihood of achieving heaven if they were close to sinless at the time they met their maker.

Augustine reasoned that his delayed baptism led him to act worse than he otherwise would have. He lied, he stole, he took a mistress and fathered a child with her, and all of this was excused by his elders because he had not yet been baptized. He had no incentive to behave. Or so he said.

We went to the Easter Vigil service on Saturday night. It’s the biggest celebration of the year in the Catholic Church. (Christmas is secondary because without the belief in the resurrection, there’s no point in celebrating some prophet’s December birthday.)

It was our first time to bring the kids. Easter Vigil is a tough service because it’s very long — nearly three hours. But it’s a special service. It’s the service of adult baptism.

Seven years ago at Easter I converted to the Catholic Church. I was baptized a Methodist in my infancy, and when I attended services occasionally someone would be inspired to join the church. When that happened, the Reverend would welcome him to the front, ask him a few questions, and *bam* we had a new Methodist.

Not so with the Catholics. To join their church (if you’re not born into it), you have to go through RCIA, the Rite of Christian Initiation of Adults. It’s a nine-month-long process requiring weekly classes and weekly church services. You have to really want to do it to go through with it — this is no spur-of-the-moment commitment.

Sometime in the future I may discuss why I chose to convert, but for now I’ll simply say that I’m grateful to my generous, wonderful parents who supported me throughout the process, even as they must have wondered what kind of crazy thing their daughter was getting herself into.

The Easter Vigil was where I became confirmed as a Catholic. (I was already baptized a Christian in the Methodist Church, and the Catholic Church respected that.) I like to go back and revisit the Vigil, see my old friends from RCIA, and watch people become new Catholics. There’s something very moving about it; they’ve worked so hard for this moment, and they’re so excited to have made it. Some are on their second or third try, having dropped out of previous classes.

When Father Bill doused each catechumen three times with water in the name of the Father and of the Son and of the Holy Spirit, I could feel the joy radiating out from the baptismal font to the back of the church where I sat. Really. That’s a special feeling that more than makes up for three hours of cranky six-year-old, bless her little heart. (I think a Sunday of sleeping in, chocolate, treats from the Easter Bunny, and hunting for eggs with the neighbor kids made up for three hours of torture in her little mind. Her brother was perfectly cool throughout the Mass, as it was something “adult”, and therefore something he wanted to do. Plus he got all of the Sunday benefits his sister got.)

It tied in nicely that this month my online reading group is discussing St. Augustine’s Confessions, a work to which I alluded back in September. I alternated reading it and listening to excellent lectures from The Teaching Company about it this weekend while I worked out in the garden between family times.

I don’t have a deep conclusion to draw about adult baptism and whether or not Augustine was right. It’s a point to ponder. Would I now be better behaved if I had not received that sacrament until age 29? I don’t really know.

I can say this much, however: this Easter weekend, I am grateful to be with the people I am with, in the place that I am, in the life that God has given me. I pray that I will continue to feel gratitude, no matter my life’s circumstances. Amen.

Blessings to you and your family this Easter.

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Flatland

March 30, 2010

I’ve been thinking about how to finish up my post on the Fibonacci sequence, and what’s been holding me up is how to illustrate my point. I mean that literally. How am I going to draw a golden rectangle and the spiral that can be formed inside repeated rectangles that corresponds perfectly to certain shells in nature? I can’t find my compass, and I’ve lost my momentum.

So here’s a Fibonacci spiral from wikipedia:

The ratio of the larger side of the rectangle to the smaller is the same as the ratio of a larger Fibonacci number to one just preceding it, a number that approximates 1.61803.  It’s known as the golden ratio, and it’s been used since ancient times in art and architecture.

I’m stopping there because I have become completely absorbed in something else: the concept of dimensions.

This was a later lecture in my math series, and it touched on a subject that I’ve run across in various books by physicists like Brian Greene and Richard Feynman. Every time I read something about dimensions beyond the third, I get curious. The physicists think they’ve proved 17 dimensions now, but it’s all theoretical. Still, I like the idea.

One of the math professors in this lecture series began to illustrate the dimensions we have experience with. First we start with a point. A point is invisible, mathematical, and has no dimension. It is completely self-contained.

Next we have a line. A line stretches between two points. It moves only in a forward or backward direction. It is one-dimensional.

Next would be two perpendicular lines. Together they would form a plane. We could draw a square on the plane, and it would have four corners, or vertices. It would have four sides, all made of one-dimensional lines. The square is two-dimensional.

And finally we could draw a line perpendicular to the plane (to go up and down). We could turn the square into a cube. It would have eight corners, or vertices, and six sides made up of two-dimensional squares. The cube is three-dimensional.

If we kept up this pattern, a four-dimensional cube would have 16 vertices and eight sides made of three-dimensional cubes. To see the fourth dimension we’d need to be able to draw a line perpendicular to the third dimension. And of course we can’t do that, so this theoretical concept is one we can’t visualize.

You know how you can draw a cube, a three-dimensional object, in 2-D? Example:

You look at it, and the sides are not all equal and the angles aren’t all 90 degrees, but it doesn’t matter because we have experience with cubes and so are able to visualize that this drawing represents one.

Well, one of the professors constructed a 3-D model of a 4-D cube. It was sort of the same thing as the drawing above, only it was three-dimensional and had eight sides. He suggested that to someone in the fourth dimension it would make sense, like the drawing above makes sense to us. Click here for a movie of what it looks like.

Science fiction writers call the 4-D cube a tesseract. I first ran across that term as a kid reading A Wrinkle in Time. It’s still one of my favorite books.

The professors suggested that a better way to wrap our brains around the concept of dimensions is to go lower rather than higher. We live in 3-D. But what would be different about life if we lived in only two dimensions?

This is a concept Edwin A. Abbott explored in his groundbreaking 1884 novel, Flatland. The book is in the public domain now, and you can read it in its entirety here.

The main character is a square, and he describes his existence. Take a penny, for instance. You lay it on a table, and you can see that it’s round. But what happens if you put it on the edge of the table and lower your eye so that your view is in the same plane as the penny? It becomes a small, copper, horizontal line. In Flatland, the square explains, everything is on a plane, so everything to the creatures in Flatland appears to be a line. He goes into a bit of detail about how they learn to recognize people and places, and if you’re interested, you can check out the link.

This was a part that grabbed my interest: in Flatland, the surface of each figure is its outline. To a square then, the outline of a square is its skin. It is incapable of seeing anything contained within the outline without cutting itself open. So far as a square is concerned, the area within it is as contained as our organs are within our bodies. But to a three-dimensional creature, the insides are visible.

Below is an example I drew. On the left is a girl as we would expect to draw her in a 2-D space. On the right is a girl as Abbott might have drawn her. For her to see or hear, her eyes and ears would need to be on the perimeter (surface) of her body. Additionally, her insides, while invisible to her and her compatriots, would be visible to us.

So, to extrapolate this idea to the fourth dimension, fourth-dimensional creatures would be able to see our insides just as we can see those of two-dimensional creatures. Pretty freaky.

If you’re wondering why such a weird concept has grabbed my attention, the answer is that I’m reworking a time-travel novel I wrote, and I’ve been looking for a good way to explain how it works. So I’m kicking these thoughts around in my head. Perhaps time travel can be explained through other dimensions, blah, blah… I’m still figuring it out. But it’s fun for me.

Hope you enjoy it too!

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Everything is Golden

March 25, 2010

I like pineapples, despite their being a complete PITA* to cut up. They’re tart and tangy and a little bit sweet, which is a lovely combination of flavor. They’re even the secret ingredient in every episode of Psych, one of my favorite TV shows, which you can watch here.

But pineapples have their own little secret.

Have you ever noticed that the basket-weave look to a pineapple is just spirals that go in two different directions? Here’s a weird factoid: all pineapples have the same number of spirals. In one direction that number is 8. Guess what the number is in the other direction. Go on. Guess.

What’d you say? If you’re like me, you figured it’s somewhere between 7 and 9.

But it’s not. Its 13.

Don’t believe me? That’s okay. I was told this in my latest nerdy endeavor, which is to watch a series of lectures called The Joy of Thinking: The Beauty and Power of Classical Mathematical Ideas. And I didn’t believe it either.

So, Doubting Thomasina that I am, I went into the kitchen, pulled a whole pineapple out of the refrigerator**, and counted the spirals. Sure enough, there were 8 one way and 13 the other.

Turns out pinecones have 8 spirals one way and 5 the other. Cone flowers have 13 spirals in one direction and 21 in the other. And daisies have 21 spirals in one direction and 34 in the other. Sunflowers have 55 and 89.

Yadda, yadda, who cares, right? Well I do, because I’m nerdy that way.

You may notice that some of these numbers overlap. (Weirdly, so do some of the names, like pine/cone/flower. But that’s neither here nor there.) If you line them up you get 5, 8, 13, 21, 34, 55, 89. This makes a pattern whereby the first two numbers in the series add up to the third number, the second two add up to the fourth number, and so on. So you can extrapolate the series forward and backwards to be 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc.

The guy who first noticed this phenomenon and put it all together into a sequence of numbers was Leonardo of Pisa. So in his honor it’s named the Fibonacci Sequence.

Yeah, I don’t get it either.

But Leonardo did this in 1202, when he published a mathematical paper about rabbits propagating. His question was — how many rabbits would you get if you stuck a pair of baby rabbits in a fenced-in area for a year?

Here are the rules: 1) rabbits take two months to mature, 2) after those first two months they will produce a pair of rabbits every month, and 3) we won’t worry about real-life concerns like feeding all these rabbits, cleaning up after all these rabbits, smelling all these rabbits, or freaking out that all of these rabbits are blood relatives and probably genetic mutants.

In January, we’ve got 1 pair of baby rabbits. In February, they reach maturity and we’ve still got 1 pair of rabbits. March, we’ve got a pair of baby rabbits and a pair of adult rabbits, making 2 pair. April, it’s two pairs of adults, 1 pair of babies, for 3 pair. Then it’s 5 pair, 8 pair, 13 pair, on up the Fibonacci sequence until December, when we hit 233 pairs. You can see this idea demonstrated (in a G-rated way) here.

It’s looking like this sequence is repeated in nature quite a bit already, but it goes even farther. And it gets more interesting. I promise.

But I’m tired, so I need to call it a night. More to come later.

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*Pain In The Ass

**On a recent visit to a Costa Rican pineapple plantation, my parents learned many facts about how to choose a good pineapple. Among other things, they were told unequivocally to refrigerate the pineapple as soon as they brought it home from the store. So now I do that too.

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Filling My Nerdy Heart with Joy

March 24, 2010

Tomorrow I’ll write about what I’m up to on the learning front. Tonight I want to mention a site I stumbled upon called Freerice.com. It is weirdly addictive and purportedly works for a good cause. Good, clean nerdy fun.

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Friday Afternoon Blues

February 26, 2010

It has not yet been recorded that any human being has gained a very large or permanent contentment from meditation upon the fact that he is better off than others.

Main Street, a 1920 bestselling novel by Sinclair Lewis* that I finished this week, includes several of these little bon mots, but this particular line leaps to mind today. I know people with bigger troubles, but that’s not taking my mind off my little ones.

Mostly I’m focused on the fact that I had the first part of a root canal today and now my mouth is halfway numb and not working (making my coffee difficult to drink) while simultaneously throbbing with a deep, burning pain. (Not from the coffee.) I’m impatiently waiting for the painkillers to kick in. And contemplating how I have a minimum of four more dentist visits to finish this fix, all of which will require shots in the mouth that will heighten my paranoia that Dr. Bill or Dr. Dennis will sever a facial nerve in the process.

It could happen. Dr. Dennis told me so.

Also, The Big M has been out of town on business. I miss him. At least he’s coming back today.

And I’ve been working on my taxes. That’ll depress anyone.

And … (this is the embarrassing one) … I dropped my iPhone in the toilet. At least that didn’t happen today. I dropped it earlier this week. Today it’s working, thanks to a relatively inexpensive fix at a shop appropriately named Cell Phone Repair. I didn’t tell the Cell Phone Repair people *how* I got the water damage because I didn’t want to end up on Not Always Right.com. Unfortunately, Cell Phone Repair doesn’t guarantee their fixes in case of water damage, so my phone could crap out again at any time.

Ha ha. But really, it could.

Would you like to know what happens when you drop your iPhone in the toilet? First, your heart sinks at approximately the same rate as the phone does. Then you reach your hand into the toilet and pull the phone out in one swift motion while exclaiming, “Ick! Ick! Ick!” Then, as you do a quick visual scan of the bathroom to find a towel appropriate for drying the toilet victim, you glance down at the iPhone screen and see that a message has popped up. It says (and I am not making this up): “This accessory is not compatible with the iPhone. Would you like to switch to airplane mode?”

As I went through the drying out process, I wondered what kind of toilet might be compatible with the iPhone. Because apparently I could use one of those.

As I sit here planning out my pity party, I think to myself — What Would The Girl Do? If one were to throw a Pity Party Parade, she’d be the Grand Marshal. The child knows how to do it.

And then I chanced upon this:

Now the other side:

Open it up and:

Cuut! I love it!

She got exactly what she wanted in a card because she made it for herself! Now it’s my turn:

To Me, From Me:

Cute! I love it!

I feel better already. Part of that is because the painkillers are finally kicking in. But still.

Next week we’ll get flooring, and at that point I’ll get fully moved in to the library. Then I’ll post more pictures.

Have a great weekend!

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* Sinclair Lewis is not to be confused with Upton Sinclair, author of The Jungle. I tell you this because I used to confuse the two of them and I want to spare you from having this problem. And now, looking at the Wiki entries, I see that not only did they know each other, but Lewis lived in Sinclair’s cooperative-living colony in New Jersey. Weird.

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Dido’s Lament

February 9, 2010

I may previously have mentioned that I’m not particularly cultured. For instance, I share in my late grandmother’s opinion of opera. Grandma would hear an aria on the radio and demand, “Whose cat’s dying?”

She got a universal laugh with this line until the day when she said it and the feline death wail in question turned out to be sung by her granddaughter Kim, who had presented Grandma with a CD of her senior musical thesis. Oooh, Grandma was embarrassed. She flushed brighter red than she used to after a margarita at Nuevo Leon.

She and Kim made up, and Kim went on to sing karaoke to a devoted West Coast audience. (She currently is traveling in Laos, attempting to fulfill her goal of singing karaoke in every Asian country she’s visited. Laos makes number five.)

But I digress.

My point is that I’m doing a musical course entitled How to Listen to and Understand Great Music, and I may be coming around on opera.

I decided to listen to this course to deepen my understanding of what I’m reading. Writers do not write in a vacuum, but rather process the culture surrounding them as they develop their worldview on the page. I have no real understanding of the musical side of past culture despite years of piano lessons and a childhood of Music Memory in public school.

I’ve heard of composers, sure. I’ve played some of them. I’ve listened to many of them. But before this course I couldn’t have told you that Bach preceded Mozart (who studied as a child with Bach), who preceded Beethoven (who studied as a teenager with Mozart). Or that Bach’s death marked the end of the Baroque period and Beethoven’s death marked the end of the Classical period.

I couldn’t have told you that Beethoven was five years old when the Declaration of Independence was signed in the American colonies or that Mozart was already enormously famous by 1776 and Thomas Jefferson probably was familiar with his work. Ben Franklin, who was hanging out in Paris and (successfully) convincing King Louis XVI to send the American revolutionaries arms and money, probably saw Mozart perform at Versailles in the late 1770’s. Louis loved music, and Mozart was a European rock star.

Cultural context is important for seating all of the facts floating around in my brain. It’s like historical facts in my head have been randomly scattered on a large piece of fabric, all unrelated to each other, and now they are suddenly coming together and synthesizing into a linear, orderly structure that makes sense. That’s why I’m doing this — to bring order to the nebulous mishmash up there in the gray matter. It seems to be working.

Back to opera.

Its invention in 1598 marked a cultural shift from focus on the group (usually in the context of worshipping God) to focus on the individual (how do I feel about things?). Shakespeare had written Romeo & Juliet a couple of years before and was working on Henry V and Julius Caesar (both based closely on Plutarch’s Lives.)

Old-school opera performances were something like today’s minor-league hockey games. You’d have your food vendors walking around in the stands hawking beer and something hot on a stick, and you’d talk to your friends, and shush them if some singer came on that you liked and maybe boo and hiss if another came on that you didn’t. The opera (like the minor-league hockey game) was secondary to the experience of just being there and enjoying yourself.

I could get behind a revival of this kind of opera. My friends and I could chat and drink beer, and when someone tried to shush us, we could say — hey, we’re just being historically accurate.

As it is, I’ve been walking around for the last week (badly) singing an aria called “Dido’s Lament” from a 1689 English-language opera by Henry Purcell and wondering about who might have been walking around London that year humming the same tune. John Dryden, for one, might have been. He did the translation of Plutarch’s Lives that I’m reading.

So there you have it. Opera has connected me with someone I was already reading. That’s pretty cool.

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The Sabine Women

January 22, 2010

I finished Plutarch’s life of Romulus, which reads a lot like one of Rudyard Kipling’s Just So Stories. Just as Kipling mythologizes animal history such as how the leopard got its spots or how the camel got its hump, Plutarch explains the beginnings of Roman history, including such tidbits as why fast people are said to have celerity, why lawyer-client privilege exists, and even why the bridegroom carries his new bride across the threshold.

Romulus and his twin brother Remus were the mythical founders of Rome. They were said to have been born of a virgin mother and an apparition that came out of an evil king’s fireplace. The king had the twins cast into the river at birth, but the servant tasked with this chore put them in a trough first. The babies floated safely to shore, where a wolf suckled them and a woodpecker fed them bits of food until they were rescued by a swineherd and his wife. Here is a famous statue of the wolf suckling the twins:

The Big M says that this statue looks like a chupacabra, the legendary goat sucker that people periodically claim to see around our part of the country. So would that make Romulus and Remus … chupalobos?

Now, according to Plutarch, the legendary wolf may have been a misnomer. He acknowledges that “wolf” was another name for a woman of “loose morals.” Immediately I pictured the equivalent modern predator:

I suppose if a Courteney Cox-type found the twins and fed them, that would be a bit more plausible than a wolf doing the same.

Anywho, the most interesting part of the story (as far as I was concerned) is the infamous Rape of the Sabine Women. Seems ol’ Romulus had knocked off his brother Remus and was now the ruler of a little town full of men. These men were cast-offs from the surrounding communities and, as such, could not find women willing to marry them.

After unsuccessfully negotiating for women with the nearby Sabine tribe, Romulus got an idea. He would claim to have found a hidden altar, and then throw a giant festival in celebration. There would be a huge sacrifice and food, performances, and—best of all—games in the Circus Maximus.

It worked. All of the surrounding tribes showed up for the festival. Romulus had pre-arranged a signal with his men: at a certain time during the races he would throw his robe over his shoulder, and this would mean “attack.” Swish goes the robe, and suddenly hundreds of men draw swords and rush upon the crowd. They steal away the Sabine women, taking care only to kidnap the marriageable virgins (I’m going to assume they had some sort of distinctive dress that would allow for their quick identification in the melee. ‘Cause otherwise, how would one go about identifying marriageable virgins in a melee?).

By the time the Sabine men finally got around to battling the Romans, their women had had children with their new husbands and in some cases had adjusted well to marriage. The women ran out on the battlefield and entreated the Sabines and the Romans to reconcile, which they did. I imagine it made for a strange family reunion.

“Dad, this is Romulus. You’ll remember him as the guy who kidnapped me and committed an outrage on me to make me his wife. We’re in love now.”

The Rape of the Sabine Women has been a popular subject in art from the Renaissance forward. It’s been covered in sculpture:
(Giambologna, 1582)

and painting (Peter Paul Rubens, 1640),

Jacques Louis David (1799),

and even Pablo Picasso (1962).

If you like musical theater, you’ll recognize the theme in Seven Brides for Seven Brothers. (Which may be the only musical that actually names Plutarch in a song.) Seven mountain men kidnap seven unmarried ladies after unsuccessfully wooing them from their families, and eventually the girls fall in love with their kidnappers. Here’s a performance of “Sobbin’ Women”:

Strange aside: when The Big M’s high school put on a production of this musical, the choir kids weren’t allowed to have a bed on the stage because it might imply sex. Never mind that the subject of the play was kidnapping women for sex. No bed, and it’s all good.

Actually, that wasn’t entirely true. The kids also had to change the lyrics of another song from “we’ve got to make it through the winter or else we won’t get lovin’ in the spring” (and later “…or Billy says we won’t get a doggone thing”) to “we’ve got to make it through the winter or else we won’t get to wear a ring.”

So a bed implying married sex was still bad. Kidnapping the brides, okay.

Anyway, Romulus had a long rule as Rome’s head of state before eventually disappearing. Legend had it that members of the Senate he created dismembered him into tiny chunks. At any event his body was never found.

As for why the bridegroom carries his new bride across the threshold?

It is done “in memory that the Sabine virgins were carried in by violence, and did not go in of their own will.”

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