Lockhart's Lament and The Physics of Lenses

Week 12, Day One

There's a centrally bulging piece of spherical glass mounted on a stand with a curved depression to hold it. A wooden box with a triangular hole houses a tiny bulb with a cord plugged into the mains. The box is placed 30 centimeters from the glass. A white screen is placed at the same distance on the other side of the glass. The light is switched on. The magic begins.

Unfortunately, science lessons in schools do not begin in the lab, rather, on a chalkboard. The fast pace of life is no excuse to forget that Newton started thinking about gravity after the apple fell to the ground before him, not the other way round. Everyone with a secondary school education knows that convex lenses converge light rays and concave lenses diverge them. How do they know this? Because they're told. They're told what happens before they had a chance to discover. That's what science has been reduced to. Replication, not discovery. Drab fact regurgitation. Well, close enough.

Think about the description in the first paragraph. When the light was switched on, was there an image on the white screen? Think about the things that could be done with that set-up. Logically. The centrally bulging glass can be replaced by a flat piece, or a centrally thinning one, maybe a wavy one too. Or whatever else. The screen and box can be moved relative to the centrally-placed glass. The screen could be moved to the other side with the box as well! If the image caught is enlarged or shrinking, the trends can be recorded- where does the image start shrinking? At what distance from the glass piece are the screen and light box? Are they on the same side, or opposite sides of the glass? Granted, it'll take longer to beat well-established facts out of schoolchildren. What is harder to fathom however, is that the widespread understanding of the delivery of science and mathematics education has come to mean anything but self-discovery? And frankly, even if that comes at the cost of knowing lesser stuff within the same period of time, it would be totally worth it. How logic has come to be divorced from science, I don't know and couldn't care less about. What I do care about is why it should be rectified, and how.

A widely (and yet not widely enough) circulated little paper of the nature of school education is Lockhart's Lament (PDF file: http://www.maa.org/devlin/LockhartsLament.pdf). I came across this wonderful piece of work a year ago, and re-discovered it in my pile of keepsakes a few days ago. Curious about the man who spoke about the flaws of current school education in a manner similar to my own thoughts, I google-d Paul Lockhart. Not the astronaut. Paul is a mathematics teacher at Saint Ann's School in Brooklyn, New York. His article has been circulating through math-ed communities since 2002, but he never published it. It is one of the best critiques of current K-12 mathematics education, made no less important by the fact that it has been written by a first-class research mathematician who elected to devote his career to teaching schoolchildren.

What drew me to his work was the utter semblance of what he said with my own experience and consequential understanding of learning science. Having come from an Indian school before I went to McGill for a Bachelors, I can safely say that I was in a deep rut when it came to understanding science, particularly biology. See, Indians make for amazing workers. Only the Asians could give us any competition in clocking study hours. We have tiny, error-laden textbooks, and 3-4 reference books that are so humongous that the only way they can fit into a book bind that isn't breaking apart is to have ultra-thin pages with alphanumeric page numbers. The easiest way to kill, KILL, our own version of O and A-levels is to work on over 20 past exams per subject. While this needn't necessarily involve rote learning, there are no traces of independent thought. Shame.

The average science student is first compelled to do full-blown independent work at the graduate level. Through schooling and undergraduate years, they can slip conveniently through the cracks of small-scale independent work, failure at which can be more than compensated by the fact and formula-based tests and exams. Even labs are a sham. Independent work, with less reading and more hands-on lab or field work, and informal sit-down sessions with the professor where ideas are beaten out...these should be the foci of primary testing. Having no background in the variety of education systems of the world, my viewpoint reflects strictly one side of the argument. It is nonetheless a strong one because if students feel unprepared for the scientific process, or daunted by the seemingly copious work, then there is a serious problem. Education communities should seriously exchange notes and hammer out a feasible and flexible solution that addresses this issue. I wrote notes for students in Physics, Chemistry and Biology as an undergrad, and realized how easy it was for people to get everything they needed to get a 3.0+ GPA without the effort, and honestly, without the fun. So most science graduate students, unless under the tutelage of a phenomenal supervisor, will be left to replicate someone else's study by changing one tiny factor. It's enough to get published in an obscure journal, but what was new? What was learnt?

Science is about progressing, in painfully slow steps. Not a lot of scientists have leaped, not even most Nobel Laureates. The Nobel-worthy culmination of decades of work starts with an obscure idea that doesn't receive much endorsement. It's only when the results start to show that some support starts to flow in. What about the investment that goes into work before the monetary support? Until results don't show, scientists follow their instincts. Instincts that are obviously based on logic-derived hypotheses. However, given that many logical explanations can be drafted for any phenomenon, trusting one of them to be the focus of your work, is a gut-thing.

Halfway into my flailing research, I was told to look up an alternative, short experiment to complete so I could at least get a publication for all that labour. Last week, the sixth week into perfecting and testing my experiment design, I got a result that gave an indication of the system finally working. No more meter hiccups, no leaking, no dying tadpoles, no clogged tubes, no toppled cages with escaped tadpoles. Nada. One smooth run with distinguishable difference between the two treatments.

Were the fast-piling failures, the uncertainty of the sustenance of the system design, the doubts at probably aiming too far, was it all worth it? Oh Hell yes.

Cough, sputter, sputter.....hiccup

Week 11, Day Three

A black cylinder, 10 centimeters long and barely over 1 centimeter in diameter ends in a thin, thin glass nib housed in a teeny transparent plastic cup. A squirt of distilled water and an abrasive rub later, it is plunged into a yellow solution droppered flimsily into the small plastic cup. The cylinder is inverted, its wiring carefully set aside. The curved end of the 1 centimeter diameter plastic cup is draped with a membrane held in place by an ultra-thin rubber ring made visible only because its black colour is conspicuous against the transparent background. So far, so good. The last leg involves pushing this delicate assembly of rubber, plastic and glass into a cylindrical hold barely larger in diameter than the cylinder itself. The membrane and rubber ring assembly go in unharmed, the black body of the cylinder starts to move in. And then gets stuck. No amount of force can get it in, the only way out is pulling it back out and destroying the little membrane and rubber ring assembly. Dratted, dainty little equipment that costs over 2000$.

Another hour of re-doing the whole process, and my supervisor successfully installs it in the holder. The holder goes on the clamp, the wires into the meter. Switch on.

The manual says it draws its numbers every 18 seconds. Mine takes 60 times that time. Multiply by six experimental set-ups, and I'm sashaying around the meter for almost an hour and a half. Not to mention the predicament of comparing numbers from the chamber measured at 10:15am with those from the one measured at 11:30am.

Six concurrent set-ups and one precariously functioning respirometer.

Everything here is old school, and not in a good way. With no software for the meter to record the readings all day for weeks, a lot of trials were underway to determine the appropriate timeline for making the recordings. And it doesn't help that the meter sputters like an old engine that just refuses to die and thus be better used as scrap metal.

One, Two, Three, One, Two, Three

Week 11, Day Two

I underestimated kinks. Kinks are interesting. Kinks keep monotony at bay. Once the kinks diminish, there's no...fire! The burning curiosity to find a solution so you can move on keeps the bulb inside burning, keeps things fresh.

Now it's all routine. The counts are at half-hour intervals, the feeding every 24 hours. Uber thin tubes glued into the glassware making for water entry and exit. The tubes go from the tanks to the pumps, the pumps to the glass chambers, the chambers to the meter. The glassware rinsed with fresh, warm, distilled water with its flush-distill-flush-distill prep routine. Nets scooping up the scurrying tadpoles. 60 milliliters of aged tap water in beakers with five tadpoles weighing below 100 milligrams each poured into the little glass chambers. Six glass chambers neatly fitted into their seats on an iron stand, one set of tubes bursting out like a single spout of water from atop one set of glass arms. The hum of the now-running flow pumps. The water slowly surging up the tubes from the tanks, into tinier tubes hidden behind the opaque pump, into visible tubes flowing into the glass chambers, and emerging as dew droplets from their make-believe fountain heads. Pitter patter, plop.

Twenty hours later, the first recordings are drawn. Another in two. After twenty-fours hours, the flow goes off. And I watch as in each chamber, five little critters frisk about, from tube to tube, still hoping to exit their small, crowded (and temporary) lodging. I hope the meter can catch what obviously happens: oxygen depletion. Just to be sure, I put in five of them into one chamber, yet I hope they breathe fast enough and the meter is alive and kicking so it can catch the oxygen decline substantially well. Lower numbers make my heart swell.

Four hours later, the flow goes back on, running overnight. Pitter patter, plop.

Meet the cast

Week 11, Day One

Pictures and videos of the lead cast:

A 100 milligram Arabian tadpole:

Several dozen, actually. Plus, a 100 milligram dragonfly larva:

The tadpoles are stored in small tanks with small rocks as refuges and anchorage points for both algae and tadpoles:

After several casualties- upstream swimmers that got caught in the multiple sponge and cloth layers in the filter- wire mesh was used to cover the inlet and outlet pipes. Sometimes though, the odd mini tadpole finds its way into an alternate tank in the array of tanks.

Some unfortunate tadpoles will wind up as dinner, like this one:

...others just get the aftertaste.

I basically watch what they do once they've got a whiff (literally) of the dinner I fed their predators. Amphibian young are famous for their ability to detect the presence of predators through little chemical cues dispersed in the water. These cues have been found to be quite specific, and reveal both qualitative and quantitative information. It tells them which predator is nearby, how near it is, if it's been killing their kin or is just an opportunistic feeder, and varies with time as well. Sound and smell have always been the best developed senses in all aquatic creatures.

So, I keep tabs on any behavioural or morphological changes in large set-ups like these:

I'm also trying to figure out if their respiration rate rises, which is the hard part. After much reading, hunting, improvising, tweaking and testing, I concocted this set-up:

Water is pumped out of two tanks- one without any predators, and another with a predator in its cage fed at regular intervals- into identical glass chambers with five tadpoles and the controls without them. Based on previous studies, the larvae predators release chemical substances as do the dead tadpoles. These diffuse through the water and alert the tadpoles of the impending danger. Once the tadpoles in the glass chambers sense this in the water that's flowing in, their respiration rate should rise. The tubes coming out of these chambers are periodically attached to the meter at the end that records oxygen concentration. Should the decline in oxygen be significantly different between the predator tank and control tank, it would constitute a viable experiment.

The whole idea behind setting this up is to get small doses of pesticides and metals into the tanks as well. If respiration increases, toxin uptake will increase as well, resulting in mortality. Given the (still) widespread use of pesticides, such studies are strong scientific evidence that specify appropriate (if that's what they are!) concentrations of such potent chemicals in natural water sources. And for the fast declining amphibians water contamination can be a death sentence because of the synergistic effects of predation and toxin intake.

Labour day

Week 9, Day One

It's hot, dry-hot. And the glare is astounding. Summer is officially here.

I try hard not to focus on the tiny, excessively rusted- and therefore creaking- pushcart I'm wheeling on my three kilometer trek from the lab to the greenhouse, but the stillness of the air muffles not an iota of the rasping and grating. To think this was the best of the lot of wheelers available. Empty carts go easy on the inclined planes, but thankfully drivers here actually adhere to speed limits. I get some respectful passes as the they let me take my noisy machine and wincing face across the street and up the next inclined plane. The last one goes up to the greenhouse, all the way behind the closed gate. No parking spot. Yay, windfall. I walk up, swing the noisy green gate open, block it with the massive boulder, and slide down to where I left my creaky companion. I haul it up, and meander it through the narrow paths with way too many right angles and park it in front of the tents housing the plants and tanks. I sniff around for aquariums. There is a mountain of dirty ones, brown-dust-and-dry-leaf dirty ones. I have no idea where to hold it without breaking it or collapsing with the sheer weight. After two minutes, I grasp two edges of one, pushing its entire bottom against my chest, secretly thanking the one stroke of luck I've had all day: my labcoat. I walk half inclined myself, reach the cart, and make another incline with my legs over which I slide the aquarium down onto the cart. Five more trips to go.

Another three kilometers and one more respectful driver later, I reach the lab. My pile of aquariums, all neatly balanced on top of each other with no edge sticking out, now poses another hassle. A little forethought, and I start manage to remove them without toppling the whole darn pile over. The aquarium just about fits into the sink where they're to be scrubbed and cleaned. I fold up the arms of my sleeves and dive in with a metal scrubber, dishwashing liquid, pure ethanol, and very, very hot water. Two hours later, they're all done. I squirt some ethanol onto a cloth, followed by a bout with distilled water as finishing touches. The clear, glistening aquariums are my pride and joy.

I wheel them into the lab, assemble them on the shelving unit, hoping they don't crash, now or ever. My back is as hard as a rock right now.

10-minute walks in the warm sun and dry warm breeze are never enough to satiate the back stiffening that comes from a combination of hard labour and excessive air-conditioning. And bending over aquariums for nearly three hours, netting tadpoles as little as 4mm long to those over 30mm and sorting them right after that, makes it worse.

Which is why you cover the connecting drains through which they escape and- if lucky enough to survive- enter other aquariums BEFORE you add them in the first place.

And despite desperate measures to prevent casualties, I killed two and nicked the tails of three others in the process. Between this, and my tadpole-prodding episode from two weeks ago, I have acquired a ticket to hell.

My two-inch Frankenstein

Week 7, Day Two

It fell three feet to the ground. Again. The tail wriggled and momentarily stopped me from bending down to pick it up.

It was supposed to be dead.

I gave it another minute, but the tadpole lay lifeless in a tiny pool of water on the floor. My heart sank all over again and I picked it up gingerly. I scooped it up on the foil and lay it stomach-down on my palm once again. The beady black eyes were always motionless against the equally black, shiny body. But the nostrils don't flare and no suction on the ventral surface, the tailspin a far cry. I rubbed the pad of my forefinger against the bulgy part of its body, the slimy surface soft, pudgy. Carefully. As if it were still alive.

Less than two months ago, they were barely a centimeter in length. You could just make out the pin-sized head and wriggly tail. Three weeks ago, they'd all grown to more than twice that length, lateral bulk now added. A week ago, they were five to seven times that length; eyes, nostrils and suction cup-like mouths obvious. I got curious, and after handling them during wadi sampling, tank transfers and set-up construction, I got accustomed to the wriggling on my palm. So I scooped one up from the storage tank to have a closer look. I nabbed a rather feisty one because he jumped right off my palm onto the floor over three feet down. Oops. Took me long enough to find something flat yet thin enough to slide between its belly and the floor and once back on my palm, it wriggled and then curled into a jet black oval, motionless. A hint of moisture from the spray bottle, and it sprang back to life wriggling in the newly deepened pool. The suction began as it swam from crevice to crevice in my cupped hand. I opened my palm wide, straight, and then watched the eyes, the cheeks underneath bloating and sinking quickly with gulps of air. I lowered my finger and barely touched the surface. Satisfied, but more wary of the stress that may have been invoked with its high jump, I lifted my eyes off my palm, hunting for a beaker in which to deposit the creature.

I grabbed one and looked down, and there was no movement. No suction, no makeshift cheeks. Oh god.

I touch the sensitive tail hoping for a reaction. Nothing. I touch the head, spray some water and dunk it into the beaker, sitting still for a minute. Nothing. Nothing. I lift it out of the beaker and onto my palm, remembering the two dead tadpoles from the wadi samples that had to be dunked into the drain. I can't throw this creature there. I killed a tadpole. I killed the tadpole.

I must have killed a dozen insects every few weeks unknowingly. This one dead tadpole is making me more miserable than all those dead insects in two decades. Since I couldn't bare the dark, smelly burial ground, I dunk it into the storage tank instead, half hoping it springs back to life. Nada.

I follow it as it sinks to the bottom like a wisp of snow, my face wrinkled.

Two minutes later it joins the other milling tadpoles.

Grey checkered American Eagle ballet flats

(for SATURDAY, March 20)

Week 7, Day One

There's a part of the Muscat landscape we don't see much of. Industry. With all this open sandy land to use, the concrete maze grows horizontally here. And the mills get built far, far away. But on the impromptu trip to a new wadi, we take the Nizwa freeway from Al-Khoud towards the township of Sa'al. And I discover one of Muscat's industrial pastures on the way. Lone, white and steel structures rising from the sand, seemingly lost amongst the many orange mountains.

Sa'al is built near an oasis under the foot of a comparatively large mountain, the summit gleaming, sharp, sun-thrashed. The drive ends halfway up a dirt path and we get out into the crazy afternoon sun. It is deathly silent. There are no date palms in sight, no towering hills for shade. The fifteen-minute walk to the wadi is traumatic when you're not dressed for the occasion. My grey checkered American Eagle ballet flats have long run their course, but I had no other alternative on this impromptu trip up to the wadi. So I walk past the stinging needles of the desert plants that are hoping to land their seeds near the vernal pools by latching onto the thin, really thin, spun cotton on my feet.

The elephant grey rocks housing the intermittent pools of water run like frozen waves along the entire length of the stream. Somewhere beneath all those hard rocks must lie tiny gullets linking the pools. Red dragonflies buzz between pools, sampling their prey. Fish and metamorphosing tadpoles dart between pebbles, not much silt here anyhow. The pools are relatively transparent. We hunt for pools housing newly-spawned tadpoles. The terrain is death sentence to my cute ballet flats, and I'm afraid by the time I'm done with this little trip, my beloved American Eagles will topple into their graves. I don't care if they die bravely. I want them to be preserved.

The combination of the silence and the heat is shockingly calming. But it's still March. The boiling, blistering heat is yet to come. A goat bleats in the distance. But it's hard to see where, what with all the jutting mounds of grey blocking the only view spared by the blinding sun. I get back to the tadpoles and I hear it bleat again. I can't resist cocking my head up to look again. I get my fill of tadpoles, skip from rock to rock, and collect more stinging needles on the way back to the car.

My legs will be crying tonight.