Things that make you go hmmmm. Coincidi (isn’t that better than coincidences?) are eerie, even when concerning such ordinary things as mugs. It makes one want to cry, ’twas meant to be! But was it? Does the cosmos care if your father gets the right mug, no disrespect to your father? Or possibly we have some kind of power to make coincidences happen for ourselves? But then why the weird ones? Why????

Well, to play devil’s advocate, let’s assume the cosmos doesn’t care. But just think of all the events that occur in a given day that aren’t coincidental. Could it be that the laws of probability dictate that out of all the events that occur, some are bound to be coincidental, and occasionally even weird? Wouldn’t it be weirder if there were no weird coincidences?

Anyway, my dad suggested that we revisit the clerihew. We’ve had clerihews before at Le Blog Bookworm, but it was quite a while ago, and perhaps the topic is worth reviving. Here is the detailed explanation of this venerable art form — and it’s worth clicking the link just to read the marvelous clerihews in the comments — but just in case you don’t, clerihews are four-line poems. Rhyme scheme: AABB. Meter: any. Topic: A famous person, whose name must be mentioned somewhere in the first line. Goal: gentle humor.

Here is a recent one of my dad’s:

All the world’s heard of Mother Theresa,

and that’s why she never requires a visa

as she visits Macao and Lower Tobago

to cure the folks of mumps and lumbago.

Here is one of mine:

Dame Muriel Spark

Liked to write in the dark.

And she wasn’t even sorry

About all the typos in Memento Mori.

How about you? I’d love to add some more to my collection and the comment section awaits, hint, hint.

* * *

If clerihews aren’t really your thing, may I offer another option? Have you ever heard of a Fib? No, not that kind of fib. Fib, as in Fibonacci sequence. It’s a form of poetry that was invented by a blogger. It’s a six-line poem, and the number of syllables in each line is dictated by the Fibonacci sequence, i.e., 1, 1, 2, 3, 5, 8. How cool is THAT?

So, here’s one to start you off:

Read!

Write!

Express

yourself and

have fun doing it!

Enter the blogosphere today!

God, that was stupid. Let me try again.

Fire.

Trucks.

Add them

together

and you have toddler

heaven. Daniel is transported.

Hm. A little better. Certainly topical, as I’m writing with this in the background. As usual.

Ok, your turn now.

This was an odd little . . . volume. I can’t really call it a novel, although it’s certainly novel. It takes place in a world where — well, A. Square describes it better than I can:

Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows — only hard and with luminous edges — and you will then have a pretty correct notion of my country and countrymen.

That is, it’s a world with only two dimensions. The first half of the book (60 pages) consists of the description of this world. It’s written like a treatise. No dialogue, all exposition. It covers everything from the floor plans of their houses to the details of their sexist, classist society. Abbott intended this to be a satire of Victorian society, and it is so extremely scathing that it’s actually painful to read. The Flatland class hierarchy is based on the number of sides a person has — the more the better, with Circles at the very top (infinite sides). The wider your angles, the more intelligent you are. Bottom of the heap are Isosceles Triangles, who suffer the added indignity of not having all their sides the same length. They make up the very lowest class, and are considered to be disposable, expendable — the red-shirts, if you will. And women? They’re Straight Lines. No angles at all! Which of course makes them lower than the lowest Isosceles. ‘Nuff said!

The second, more interesting, half of the book (58 pages) is also treatise-like, but now the subjects are math and philosophy. A. Square discovers Lineland, a world of only one dimension, and then a three-dimensional entity — a sphere — discovers him. There are some funny moments here, such as this bit of dialogue:

“Pardon me,” said I, “O Thou Whom I must no longer address as the Perfection of all Beauty; but let me beg thee to vouchsafe thy servant a sight of thine interior.

SPHERE. My what?

I. Thine interior: thy stomach, thy intestines.

SPHERE. Whence this ill-timed impertinent request?

A. Square initially considers the sphere to be the Perfection, etc., because a sphere comprises an infinite number of circles, and Circles are the pinnacle of Flatland society. But it occurs to him that if there are worlds of one, two and three dimensions, couldn’t there also be worlds of four, five, or six? And wouldn’t a four-dimensional being comprising an infinite number of spheres be even more perfectly beautiful than a mere three-dimensional sphere? Ad infinitum? And the most interesting part of the whole book is the Sphere’s reaction to this idea: even though the Sphere is well aware that there are worlds of one and two dimensions, he is so angered by A. Square’s assertion that he evicts him out of Spaceland forever. Is this a wry comment on the way we humans cannot see ourselves as anything less than the crown of creation?

One of the strangest things about this book is its half-and-half structure. Stories are supposed to be divided in thirds, not halves. Beginning, middle, end. Just two feels unstable, unfinished. I liked the math, though. I actually found myself awake in the middle of the night after I finished it, pondering geometry. I tried to remember the formula for calculating the measurements of the angles of regular polygons. I came up with this: if n is the number of angles (or sides), the measurement of each angle is (n-2) times 180, all divided by n. Then I attempted some calculations in my head . . . and soon drifted off to sleep.

* * *

This reminds me, too, that I have another anecdote about Cousin Ward. (Please click on the link to refresh your memory about Cousin Ward; he’s well worth the effort.) Anyway, I’m sitting next to him at Easter dinner. Conversation with him is awkward because he’s a mathematician, but I do my best. I ask him how his grandkids in Pittsburgh are doing. They are well. The older one is, what? 8? 9? Neither of us can remember.

“It’s hard to tell them apart at that age,” says Ward.

“Very true,” I agree, going off into a little reverie about kids getting older. When they’re babies, a difference of three months seems insurmountable, but the older they get the less it matters. My train of thought is heading toward Maudlin.

“Because, you know,” he continues, “one is two to the power of three and the other is three to the power of two.”

I love this guy. Betcha he’s read Flatland.

Can you picture the scene? Imagine the cozy living room, fire crackling merrily, cousins playing happily at one end, Ward and I ensconced in a fabulous leather sofa at the other. “So,” I say to him conversationally, “Tell me some more about perfect numbers.” Being a mathematician, conversation is not his strong point and I have to do most of the work, though being an introverted bookworm, conversation is not my strong point either. But I am thinking that perfect numbers would make a great blog post, not only because they are interesting in themselves but also because the topic is a perfect way for me to casually let slip that my birthday is tomorrow — on the TWENTY-EIGHTH of December.

In fact, I first learned about perfect numbers at a long-ago family dinner when I confessed to Ward my life-long fascination with the number 28. He could not have made me happier than when he told me that mathematically speaking 28 is a rare bird — a “perfect” number. Six is a perfect number too. And the next one after 28 is four-hundred-and-something.

A perfect number is one that equals the sum of its factors. Factors of 6 = 1, 2, 3. Factors of 28 = 1, 2, 4, 7, 14. Factors of four-hundred-and-something? Um. This would make a much better post if I knew four-hundred-and-what, which is why I ask Ward: “Four-hundred-and-what?” Suddenly he is staring off into space, lips moving slightly. I stare at his skull, wondering what’s going on inside.

“Well,” he says finally, “What’s 31 x 16? Whatever is 31 x 16, that’s a perfect number.” By this time Uncle Brad is listening too, and the three of us attempt to multiply 31 x 16 in our heads. Of course Ward comes up with the answer first: 496. There is some joking about whether he’d get the same answer in subsequent attempts, but — check it yourself — he was right.

Meanwhile, I am astounded. What does 31 x 16 have to do with anything? I press Ward for details and he tells me that there’s a formula for finding perfect numbers. He tells me the formula but I have trouble hearing because Daniel is busily drilling my knee with a fairly loud toy electric drill. But this is too good to let go. “Hold that thought,” I say to Ward. I push Daniel away, and run off to find my dear hubby. And of course he has pen and paper on hand, because he is Steve. So I run back to Ward with pen and paper, and here it is:

A perfect number equals (2^p-1)(2^p-1), where p is a prime number.

So if p=3 you get 2³ = 8, minus 1 is 7, and 2² = 4. And voilà! 7 x 4 = 28! And when p = 5 you get 31 x 16.

I ask Ward whether perfect numbers are, you know, useful. Do they have any practical application?

Ward laughs. “None whatsoever.”

Speaking of husband, he did answer his five questions, but he posted them down here. By the way, I loved reading everyone’s answers! I hope you’ll follow the links and see what they wrote.

I was going to write about home birth but something infinitely more fascinating and fun came up. I have to tell you about this right away:

So, my dad calls me last night. His friend, a musicologist, had asked him whether he thought Bach and Handel might have learned about the golden section in school; or if not, where did my dad think they would have learned about it. Never mind why the musicologist thought my dad might have known the answer to this question. He didn’t; but it got him thinking about the golden section.

If you already know what it is, skip this paragraph. I first learned about it in elementary school when they showed this movie; if you saw it, you might remember too. Basically, picture a line segment, AC. AC is divided at point B at a particular place so that AB is to BC as BC is to AC. This is called the golden section (or the divine proportion) because it’s supposed to be so aesthetically pleasing. It’s in classical architecture, you can find it in many paintings, it’s in the human body, etc., etc., and it’s in the music of Bach and Handel (and others). Now. If you know the length of the segment AB, there is a number you multiply it by to get BC. BC multiplied by the same number gives you the length of AC. This number, called Phi (?), is an irrational number, approximately 1.618…, and it shows up everywhere. Phi has many fascinating and spooky properties, including being related to the Fibonacci sequence.

So. Pops decides he wants to prove that the answer is Phi. He’s at his office in the psych department, which happens to be next door to the math department. He wanders over next door and finds a math grad student to ask. The grad student sits him down in front of a blackboard and does the math. But she does it too fast for him to follow. So he calls me up and says, “Hey, Jules, you like algebra, right?” Um. Okay.

Over the phone, Pa and I figure out an equation. We start doing algebra. Somehow, we manage to arrive at a quadratic equation. Remember those?

ax² + bx + c = 0

Once you have that, it’s easy to solve (ha ha). There’s a formula. Two days ago I would not have remembered that this formula existed, let alone its content. Nor would have my dad. But thanks to the math grad student, my dad was able to start me off. “Negative b,” he said, “plus or minus the square root of…” And it came flooding back to me. “Plus or minus the square root of b² minus 4ac, all over 2a!” I shouted.The feeling of this memory coming back was so cool. It was like that tickle in the back of your nose before you sneeze. Ah, ah, ah… b-squared minus four a c!!!

Anyway, Papa and I spent some hours separately and together over the phone trying to work out this problem. We encountered other obstacles. For example, do you remember this one? I sure didn’t.

(a – b)² = a² – 2ab + b²

It was so fun. How the heck Dad knew I liked algebra, I have no idea. I didn’t even know it myself until yesterday.