A tale of negative density
April 10th, 2013
While thinking about some of my research problems today, my mind wandered off to a time many years ago when on one morning during an undergrad class of solid mechanics I was first introduced, rather unceremoniously I must say, to the revolutionary concept of negative density.
We were trying to figure out some academic arcana about a pendulum, a water tank, an accelerating vehicle, and that universal scourge of high flyers everywhere, gravity and as it often happens in matters of little consequence, the stakes were enormously high. I was standing at the blackboard having just drawn a schematic of the problem under discussion, the quality of which stood as a testimony to the complete lack of the artistic strain in my blood. My sorry efforts at trying to draw a container of water had given it the kind of waves which the moon would be proud of generating in the Pacific on one of its 'in the zone' days. And the pendulum hung there inside the bowl with the pathetic visage of one who has just learnt that his parole application has been denied. The motion of the vehicle on to which my ghastly contraption was supposed to have been placed was indicated by a few swooshes in the opposite direction - an effect that was no doubt the result of having read one too many comics.
So there I stood fidgeting alongside my hesitating contribution to postmodern sketching and it should not be hard to imagine that in that moment of vulnerability in front of my classmates, my attitude towards the problem at hand was inspired by the old adage of attack being the best form of defense. I don't remember the exact train of arguments but I do remember it being broken by the voice of a friend who has always been surer of himself than I have been of myself. Confrontation with him on a good day is quite an ordeal but he had chosen to speak up at a time when the iron had just been removed from the kiln and lay red and embarrassed on the side of the subpar schematic.
What about negative density, he asked. I eyed him suspiciously unable to comprehend the level at which I should refute that incongruous little quip of his. Suddenly I found myself face to face with a question far greater than any that I could have dreamed of. Not only was I not able to establish my position as to the effect of negative density on the problem, I was not even able to comprehend if he was joking or not. I eyed him suspiciously like I have often found myself doing when faced with someone whose character evinces a certain unidentifiable shiftiness and asked after much internal deliberation, what about it.  What if the liquid had negative density, he persisted? What happens to your pendulum then? I looked at my sorry pendulum in my sorry jar and wondered how much more it would have to go through at the hands of sadists such as him. It had already been through enough under my penmanship, its whole substance reduced to a dented bob of arbitrary circularity flimsily attached to a feeble wire and left to brave the torrential waves of a bowl of badly drawn liquid. Surely the pendulum had been through enough and could do without further torment. And moreover, said I to myself, what the hell is a negative density liquid anyway. In the face of a complete lack of evidence that such liquids existed, I promptly concluded that subjecting my down and out pendulum to such an alien ambiance must constitute as some sort of a violation of the Geneva convention or something. In fact I was so incensed by the suggestion that I instantly snapped at my friend for the mere mention of so ghastly a possibility.
I have since realized that my impatience that day was misplaced and that fate, in the semi cruel and semi sadistic sort of way in which it likes so much to operate, designed my life so that eventually I ended up doing a major part of my research in the field of materials with negative densities. And that one question on that fair day in Guwahati which elicited such a visceral response from me has come to serve as a persistent reminder that the true worth of an idea, howsoever ridiculous it may appear at the first, second, and fifth glances, must never be judged based upon irrational emotional attachments to one's sketching abilities, especially to sad looking pendulum faces. I also realize now that I need to learn how to extract useful morals out of life events.
Would you call it a quirk of fate or a fait accompli?
It so happens that I was also there and my memory of it is somewhat different of it that yours. He merely was using the notion of negative density as a mathematical tool to solve an unsymmetric problem, by subtracting a symmetric portion of problem (by way of negative density) to make the whole problem symmetric and then superimpose later that effect of what was removed earlier on to make the solution complete. This is something which is done routinely in other aspects of physics such as FFT, or in Complex mathematics.
Wut?
Exactly! And you got stuck at the negative density part, refusing to listen to whatever else he was trying to say. haha. May lord have mercy on your students.