by Michael Rossman
I go out to summon the third-graders from recess for our science class, but check myself, on seeing their handiwork. Using juice-cups as molds, they've made a city of small sand-castles. Hundreds of truncated cones stretch across the porch, decorated with little sprigs of leaves, flowers, and berries. It's a marvelous construction, and I pause to admire their industry and grace. Finally they notice me. I ask, "Where do you want to have class today?"
"Out here! Right here!" I agree: the sun's so nice. Immediately, they start brushing the little castles off the porch.
"Hey, why do that? It's really lovely. We've got plenty of space." I marvel at how well-trained they are already, how ready to discount and sweep aside their own spontaneous creation, to make way for the Official Business of schooling. Yet what should a teacher's business be, if not to be conscious and open? And how many times have I come with a lesson prepared, and not recognized a lesson present and waiting? We settle ourselves around the sandcastle city and admire it in silence for a while, until I ask, "So what do you notice?"
A truly open question can lead almost anywhere. Annie notices a road leading through the city, beyond that castle crowned with hemlock to signify its owner's poisonous occupation. Perhaps Prince Vartan stopped there, one rainy night, in the adventure we could go on spinning together. Carol notices how the castles are placed, not randomly but almost equidistantly; and we might well wonder why cities tend to grow this way. Kelly notices how their decorations survey the nearby vegetation, presenting the leaf-samples as in an exhibit, to be identified, compared, contrasted; and Royce notices how complex and subtle a spectrum of "green" they offer. Alta notices the very fact that the children have decorated their small heaps, as some birds and packrats do. Is it for the same reason, is an impulse to beauty inborn?
I can't bear to notice so much, wonder so much. And I'm not free, I'm here to teach "science," whatever that is, and however one goes about separating it from the rest of life. I should have taught the class inside. To encounter the world in its richness is too much, disorienting. To keep it simple, I focus on Danny, who has noticed that the sand atop each castle, right at the sharp edge, has turned a different color, lighter than the main body.
"How come?" I ask.
"The water vaporated."
"E-vaporated. Is he right?" The others agree: sand looks lighter when it's dry.
"So what does the water look like, when it's in the sand?" Someone suggests it's in round drops. This is how they're used to imagining small quantities of liquid, but it's clearly absurd, and they realize that no one has any real idea. So I become water, and curve my body around a magnified sand-grain, showing them how I spread over its surface. And then it hits me.
"Hey, why can you make a sand-castle, anyway? Can you make one out of dry sand?"
Annie tries, and of course her castle slumps down when she lifts the cup. We agree: the sand has to be wet. Somehow the water makes the grains stick together. I ask them how that might happen. They have no idea, no images, no gut feel for what's going on.
"Okay. We call it surface tension,” I say, starting with extremes -- with the abstract language, and the concrete kinesthetic feeling. "Let's hear it."
"Sir-fuss ten-shun." Their chorus is ragged and uncertain. I beckon them to repeat. "Sur-face! ten-sion!" they shout, crisply, proudly, perfectly together.
"So a surface is a surface," I say, running my hands over one in the air before me. "But what is 'tension'?"
"It's like when grownups get angry," says Ruth.
"You're right. But the word also has a physical meaning. Give me your hand." I reach across the castles, as she leans forward to join hands. "Now lean back a bit. Feel the pull? That's a tension, a force along our arms, holding us together. Come on, folks, try it."
After the brief chaos of tugging that follows, I sum up. "So a surface tension is a force pulling on the surface of a liquid, holding it together. Makes sense?"
Their nods reassure me. "Now, some liquids have stronger surface tensions, and some have weaker tensions. Water's is pretty strong." I set up one of their juice-cups in a plaza of Castle City, dash inside to grab the watering-pitcher, and say, "Look here," as I start pouring.
The water reaches the top, brims up and up above the rim as I keep adding drop after drop. "Get down, get down!" they tell each other, putting their cheeks almost on the sandy floor. "You've got to get down to see!" When they do, their sense of scale changes abruptly, as they sight between the huge castles to where sunlight gleams refracted through a great smooth bulge of water hanging over the cup's lip.
"So what force keeps it up? Why doesn't gravity just pull it down?"
I raise my hands, and the chorus comes sharp and clear: "Surface tension!"
I pick up a pinch of sand. "Now, what is sand?" Real small rocks, they agree. "And which is denser, rock or water?" Everyone knows. "So a rock should sink in water. So look." I pick out a grain and drop it on the bulging film. It sinks like a stone. "Oops!" I find a smaller, dry, rounded grain to drop. This time it just sits there, in a small dimple on the water's surface.
"So what's holding it up?" Same conductor, same chorus. I drop a few more grains, but won't let them drop any. "Hey, lay off, you'll make it spill. Try it at home yourself if you want. See how heavy a grain you can use, before it forces its way through the surface. Find out if the surface will hold up a needle.
"Now let's look at why water has surface tension." I level a dozen castles, spreading their sand in a thin plane, on which I sketch a large angle, with a broad curve bulging beyond its vertex. "So here's the lip and side of the cup, and the bulge of the water. Let's see what the molecules of the water are doing."
I set small leaves on the diagram to represent molecules. "Pretend they aren't all moving around and tumbling over each other.” The image has been familiar ever since we danced the Dance of the States of Matter together, turning from jittery crystal to flowing liquid to agitated vapor and back again in the empty space of the gym. “Take a picture to stop their motion. This is how they are just at one moment.
"Now here's the complicated part. You know that molecules hold on to each other when they're in a crystal, in Solid State. They can't hold on strongly unless they're standing still. When they're moving fast, in the Gas State, they don't hold on at all. But when they're moving slowly, in the Liquid State, they pull on each other a bit. Put your hands like this, and imagine a magnet in each hand." I hold mine near each other. "Feel your magnets pulling on each other. This is how the molecules feel, pulling on each other as they pass by.
"Now look at the diagram, think of the molecules all pulling on each other." I scribe short lines connecting the leaves to each other, and then point to one near the center. "Let's take this molecule. Its neighbors to the left are pulling it left, and these to the right are pulling it right. So which way is it being pulled?" The answer is clear, in their kinesthetic imagination: the pulls cancel out. I repeat for the neighbors pulling up, pulling down. "So which way is a molecule inside the water being pulled as it moves, by all of its neighbors together?"
"No way!" they affirm.
"Now look at this molecule on the surface. Here's neighbors on the right, neighbors on the left. Which way are they pulling all together?"
"Here's neighbors on the inside, neighbors on the .... whoops! No neighbors on the outside! So ...?"
"The inside ones are pulling him in?" ventures Marshall.
"That's right. Now look." I tug on the lines leading inward, as if they were strings. "They pull it in. But it can't go alone, it's pulling on its neighbors." I tug on the surface-lines. "And they're being pulled the other way by their other neighbors on the surface. So there's a tension between them. Now think of the whole surface." I sweep my hand over its sandy profile. "All over it, the molecules moving. Between them these lines of tension, pulling on each other."
My finger goes poke-poke-poke for the molecules, zig-zag-zig for the lines between them, until Amon says, "It looks like a net."
"Uh-huh. The whole surface is a net of tension, getting pulled inward at each knot, each molecule, holding the whole water-mass together. Now get up, c'mon over here."
We go into the yard, where I stand them a comfortable distance apart. "With your right hand grab someone else's clothing, at a place where it's okay to pull it a bit. But don't grab anyone who's grabbed you first." They sort it out quickly. "With your left hand grab someone else, who you're not already grabbing and who's not grabbing you." It takes longer this time, not so many arrangements are possible under these constraints. Finally they develop one.
"Now tug a bit on each person's clothing, and pull away a bit from whoever's tugging on yours. Do it gently, and don't move your feet." As they lean away from each other, their net expands slightly. "So here you are, you're a molecule inside the water, or on the surface, the outside. Close your eyes, lean away a little bit harder from whoever's holding you. Feel that net of tension?" A chorus of exclamations rises, as the feeling of being webbed in a coherent fabric of force penetrates their bodies, their minds. "You there, Alison, on the inside. Which way are you being pulled?"
"Every way, I mean no way."
"And you, Seth, on the outside?"
"They're pulling me in."
"Okay. Now lean a bit more, get that tension tight. Now FREEZE!" I yell. "Don't move! Open your eyes! What do you see?" They see their peers in the inside standing straight, and those on the edge tilted outward, some dangling from sleeves that threaten to rip. "What keeps those molecules on the edge from falling off?"
"And what would happen if you leaned over farther, if gravity pulled you harder? C'mon, you're not welded together, you're just pulling like magnets. Loosen up." They are glad to comply. The edge tumbles outward, leading us to a brief intermission of scuffling. Finally I pull the group back together, and pick up the pitcher. Silently, I pour drop by drop into the brimming cup, until the bulging surface finally overloads and breaks, in a swift trickle down the side -- rewarding me with several oh!s of comprehension.
"Now, about those sand-castles. There's one more thing you need to know. Water molecules tend to hold onto other kinds of molecules too, in most solid things. So stick your thumb and forefinger in your mouth, get them real sloppy with saliva. Now point them downward. How come the liquid doesn't just drip off your fingertip, what's holding it up?"
"Surface tension!" they yell.
"Between the water molecules?"
"Between them and the finger molecules," says Seth.
"But is that still surface tension?" Annie asks.
"Well, it's between the water and another surface, and the forces are pretty much the same, so we can still call it that, Now put your fingers together like this." I make an O, touching the tips of thumb and forefinger. "Pull them apart, very gently. What can you feel?" I'm cheating a bit, for saliva's more viscous than pure water, but it does make a dandy demonstration.
The more careful children crow with delight immediately, and coax the hastier ones to try again, until they too can feel the slight pull between their fingertips and watch the smooth liquid curve stretch before it breaks, releasing them. "Now lick three fingers sloppy, and put them together. Pretend that your fingertips are grains of sand, covered with thin films of water. Feel how the castle holds itself together?" With three the sensation is not only clearer but three-dimensional, you begin to feel how the wet grains adhere in a form.
"Okay. Now go pick two short stems of grass." While they rummage in the weeds, I fill a bucket. When they return, I show them how to strip the leaves, leaving the stems bare. Then I tip the bucket over. "Earthquake! Tidal wave! Watch out!" The flood surges over the nearest castles and around the rest, to threaten laggard toes. As they jump back, Castle City is melting in the tide, castles slumping gracefully as their modest weights press on saturated foundations.
The porch looks like Venice, noble ruins studding the placid water. "Take your two stems, dip them in the water, and put them together. What happens?" They quickly discover how the stems cling together once their fluid films are joined. But no one grasps how strong the binding is, until I show them how to gauge its maximum by pulling the stems apart at the midpoint of their joined length.
We might go on actually to measure the binding-force. By stringing hollow stems on long loops of thread, joining them with water, and loading one loop with paper-clips until the stems pull apart, we could learn that the force is nearly proportional to the length of wet contact between two stems. In such an inquiry is borne the very essence of mathematical physics. I think children of this age, who are moving beyond concrete-operational to abstract thought, can be led to comprehend it genuinely, as well as to feed back the sorts of test answers so often mistaken for proof of understanding. But I also think they're too young yet to benefit from the investment of time and concentration it takes, to experience the birth of formal conclusion from the texture of real numbers.
Meanwhile, the sand is still drying on the castle crests, while surface tension leads the dark stain of capillary action up their slumping bodies; and I need to give our inquiry a form to rest in. "Now save the stem with the sharpest point, dry your hands, and pick up a few grains of dry sand. Let them lie together in your palm. Now roll a few apart from each other with your stem. Is any force holding them together?"
"Gravity!" pipes up Seth, quoting from a lesson I thought he'd slept through. Everyone laughs. He thinks the laugh's at him, and says defensively, "But you said any two bodies have attraction!"
"I did, you're right. But sand-grains are so small, that their gravitational attraction is almost too small to imagine. Is any force between them strong enough to feel?"
"They're leaning on each other," says Amon, glad to keep me off balance.
"Can you feel it?" I ask snappishly, leaning on him in turn.
"No, but I can prove it!"
"Sometimes when I roll one grain away, another tumbles after it. So it must have been leaning."
"No way!" says Alice scornfully. Several start rechecking their own observations, less for science's sake than to support me, since Amon gets on other nerves than mine. Seth is quick to confirm that Amon's wrong. But Amon points out how he's cupping his hand, forcing the grains to stay together.
"All right," I say, relieved to be the judge again rather than the target. "Amon, that's a sharp observation. But your grains lean together because the earth's gravity is pulling each one down, not because they're pulling each other. Can you show us an attractive force between them?"
No one can, so I have them repeat the experiment with a pinch of damp sand. This time when I ask, "Do you see any evidence of an attractive force between them?" even the slowest can see that some grains tend to hold onto each other as they're moved. We observe that the damper grains hold together more strongly; and agree that thin films of water between them must be holding the grains together, just as they held the straws.
"Okay. Now cup that hand with the sand, and put a little puddle in it." I show them how to scoop a bit of water from the floor. "Try to roll some grains away from each other underwater. What do you notice?" I have led them to an abrupt reversal in the chain of evidence that seemed to say the wetter the tighter, for the grains can be moved apart from each other quite freely underwater. "So what does that tell us?"
"There's no force between them," suggests Annie.
"No significant force," I agree, forestalling the gravity kid. "In particular, then, there's no ..."
I can hardly start my gesture before the roar begins: "Surface tension!"
As they rest in satisfaction, I say, "How come?" No one quite follows me. "How come there's no surface tension force between them? Think about it, but don't say anything."
Five faces have brightened with comprehension, and grown fidgety to blurt out their answers, by the time I get the response I'm fishing for. Danny cracks up when he gets it, laughing so hard that he slips to his knees in the puddle. Half the faces are still blank. "Go on," I urge, as his straight man. "So why is there no surface tension?"
"Because there's no surface!" he gasps out, kicking his heels in joy, spattering his neighbors and me too.
"Hey, quit it! Explain!"
"The surface is above them. It isn't between them any more, so it can't pull them together."
"That isn't funny, Danny!" Annie cries, referring mainly to the mess on her blouse. But she is bright enough to be distracted by an idea, and I intervene.
"Hey, how come that wet sand's sticking to the fibers of your blouse?" She gets it at once, and smiles. "So what's going to happen to the surface when the water dries? How much water surface will there be?"
"No surface," she says gladly.
"No surface, no tension. No tension, no sand. You can brush it off then, it won't stain, there's no dirt in it. And we'd better clean off the porch anyway before you all track it in. Go get the hose and the brooms."
It's an invitation to soak themselves, as our hour has still ten minutes to run and half of them have damp shoes already. But school's over after that, and they deserve an appropriate celebration. Castle City fades into memory as they dissolve the force that held its material together, spraying and splashing behind the brooms as I stand by content, not bothering to restore a semblance of order as parents start arriving to pick them up.
Let them greet their daughters and sons as if they had just returned from a day's expedition cross-country through lush and demanding terrain. Let them recognize the badge of the experience on their clothes and their hands, in their faces, their eyes.