Beware of the Asymptotes

Yesterday marked day seven of straight fieldwork with no breaks. For a few days I’ve been pulling double shifts—measuring diameters with the Bosques crew in the morning and doing my own work in the afternoon. For the past few days, Bess has been out of town with her parents. I’ve devoted the time to a side project I’m doing with my friend Kelly, studying mycorrhizae (the interactions of plant roots and fungi in the soil). Kelly’s going to do the boring part, staining the roots and inspecting them under a microscope for fungus, and I get to do the fun part, collecting roots. Fun, if you like mud.

I went with a very low-tech approach to sampling. In the field, I carried a notebook and pencil, some garbage bags, a sturdy digging stick (yay for Stone Age technology!), and my special innovation: a stash of plastic sandwich bags, each of which contained a scrap of flagging tape with a number written on it. I would locate a seedling of a species on our list that was small enough that I could trace the roots and be sure I was getting the right ones, but not so small that I’d kill it by taking a few roots. I’d dig around the base, extract a few roots, stash them in one of the baggies, wipe the mud off my hands, write the number and species in my notebook, take a leaf sample to press, swat some mosquitoes, and repeat.

At first, sampling was easy. Almost every plant of the right size that I came across was a species I didn’t have yet. With time, though, it became harder and harder to find the ones I was looking for: everything I came across was already in the bag. It’s like baseball cards, or those movie trading cards that were popular when I was a kid. My little sister must have had eight or nine copies of “Robin gets the worst of it” (i.e., Kevin Costner meets the beam end of a quarterstaff) before she ever got that one of Maid Marian. It’s an inevitable consequence of finite biodiversity (or trading card diversity, I suppose). Except in a theoretical, infinitely diverse ecosystem where each individual is a different species (θ→∞, for you Hubbell fans out there!), you’re going to start coming across the same ones again and again, and it takes a lot more time and effort to find anything new. If you plot the number of species you find vs. the number of individuals you encounter, the curve levels off eventually. In mathematical terms, you approach an asymptote.

And that was where I found myself yesterday afternoon, hunting through the underbrush in search of the elusive Strychnos panamensis and Rourea glabra. I only needed one more sample of each to complete my planned collections for the day. There are a lot of plants that look similar from a distance, but disappoint on closer inspection. As the afternoon wore on, I accumulated mosquitoes rather than new species. A thick, humming cloud of the little bloodsuckers followed my every move, despite repeated applications of bug dope and the formidable mud layer I had built up on all my exposed skin from repeated attempts to swat them.

In an effort to stay sane, I thought about species accumulation curves (the generally accepted name for the plot of species vs. individuals). I know it’s not a great strategy for maintaining sanity, but hey, it’s what I had. I started wondering what other things follow the same kind of curve. There are so many repeated patterns in nature that correspond to elegant mathematical descriptions—the logarithmic spirals of snails, fern fiddleheads, and certain vine tendrils; the fractal patterns of shorelines and leaf veins; the endless applications of the Fibonnaci series. I’m not a good enough mathematician to really understand them; just good enough to puzzle over them, smile, and turn back to my little logistic regressions.

I started wondering if you could plot an idea accumulation curve, tracing the ideas that have really shaped human history. Agriculture, the city-state, writing. Penicillin, air travel, fast food. It seems that it’s getting harder and harder to come up with an idea that’s actually novel. When I was about fourteen, I kept a notebook of all the truly original ideas I came across or formulated, but I gave it up when I realized that the notebook was filling very, very slowly, and nothing in it was invented by me. Standing in a muddy peccary trail and peering into a dense thicket of spiny palms, I wondered where we are on the idea accumulation curve. Are we nearing the asymptote, where everything will be derivative of everything else? And the truly novel ideas of the recent past—TV, weapons of mass destruction, genetic engineering—are moving us in a direction that doesn’t seem very positive.

I’ve just been re-reading Jonathan Safran Foer’s stunning novel Extremely Loud and Incredibly Close, about an orphan of the World Trade Center attacks. September 11^th wasn’t a new idea at all, though the enormity of it certainly made it seem like one at the time, at least to most Americans I know. It was a blending of some ideas of the recent past (airplanes, skyscrapers) with some of the oldest ideas: fear and hate, which have been with us since before we came down out of the trees, and divinely ordained righteousness; an idea that, more than any other, makes the little hairs on my neck stand straight up. September 11^th was a derivative idea, an idea for the asymptote. In my darker moments I wonder whether the human brain is such an evolutionary advantage as we often seem to believe. We have such enormous potential and so little foresight.

I also thought, along the same lines, about how much easier it is to have a lasting impact by destroying rather than creating. No one remembers the names of the thousands of workers who built the World Trade Center, girder by girder, floor by floor. The names of Mohammed Atta and Osama bin Laden are household words. When I was younger I used to think that I wanted to be one of those people who makes a splash in the world. But looking back through history, the people we remember are most often the destroyers rather than the builders. We remember the generals and not the farmers, not the mothers. I would so much rather be a part of the undistinguished masses, weaving my little part in the scrambled tapestry we call civilization than one of those egregious few who rips a hole in the fabric.

People sometimes ask me what I think about when I’m out in the field alone all day. Usually nothing; I can go for hours with the pleasant background mind-numbness of I wonder what’s for lunch… any snakes behind that log?... I bet that root’s slippery… any ants on that leaf?...do I need to go to town tomorrow to replenish my chocolate stash?.. any snakes behind that log? Yesterday I managed to maintain a few other lines of thought, a small and not unpleasing anomaly. But between that, looking for those last few plants, and the usual vigilance for snakes, stinging ants, scorpions, etc., I didn’t notice the howler monkeys’ warnings until too late. Howler vocabulary is rather limited: “aroo-gah-roo-gah-roo-gah!” at 90 decibels just about covers it. To really get what they’re saying, you have to pay attention to the context. Two or three monkeys exchanging howls across several kilometers means, “this is my territory and stay the hell out!” But if they all get going at once, not pausing to wait for answers, it means, “va a llover.” And llover it did, so intensely that I was soaked to the skin in about 30 seconds and sloshing in my boots before I could even get back to my bike. And I never did find those last two plants. Shows what you get for thinking.