Fun times in leaf estimation

Don't be fooled into notions of simplicity

Don't be fooled into notions of simplicity

One of the things that I love about biological systems is how messy they are. Leaving issues of random mutations, and loose enzyme kinetics aside, you don’t have to look too far to see just how much of life likes to live outside of neat little boxes. The tension between the sloppy reality of life, and the human desire to neatly categorize all things is something that I relate to, and hopefully something that I can get my students to appreciate in the time they spend with me. A recent lab provided me with one such opportunity.

The lab is a classic: measuring the effect of environmental variables on the rate of transpiration. My preferred methodology for this activity is as simple as they come. Students tightly bag the root ball of whatever cheap plants I can find at the local greenhouse, take an initial mass, set up their experimental and control treatments, and let the system run for a week, massing every day. The lost mass serves as an analogue for the rate of transpiration, since this is the major process that is contributing to the change. Like I said, simple.

The real cognitive fun comes from the math involved. In discussing the results, we work our way around to the notion that if we are going to be able to compare results among plants, we’ll need to transform our “mass lost” data into a more universal measurement. This is not so tough (though I won’t deign to give you the easy answer here). The tricksy bit comes in once we determine that the surface area of the leaves on the plant are going to have a major effect on the rate of transpiration. So…let’s measure the surface area of the leaves.

Leaves are funny things. If you don’t think about it too much, you probably conceive of them as vaguely triangular in shape. In fact, the shape of leaves are much more complex than any simple geometric. Leaves are actually fractal, and their geometry is just as complex as any other fractal pattern. As such, it’s not all that possible to get a “true” measurement of the surface area of a leaf. All methodologies are going to involve some level of estimation.*

I keep this little bit to myself, and let my students begin the “simple” process of figuring out how to accomplish this task. After a few minutes, students begin to grasp the problem. This moment signifies itself when they start coming to me, asking me if the method they have decided to use “is okay”. As far as I’m concerned, as long as it’s a rational attempt to get at the problem, it always is. I keep my opinions as to what I would do if I were in their shoes firmly to myself.**

This is the beauty of this lab. It’s also the beauty of Biology, and science at large. I don’t know of any other subject that can take such a simple starting point, and build it in to a major understanding about the nature of the world that we inhabit. The point is not to get the right answer. A much better point is to understand that even though the world is a messy place, with precious few absolutes, we have a way of understanding it that still works, and that works really, really well. If that’s not something worth teaching students, I don’t know what is.

*By the way, the necessity of estimation is not restricted only to leaves. Functionally every object that exists outside the realm of mathematical abstraction has some level of indeterminacy that is beyond our ability to measure it.

**Here’s a hint.