One activity I’ve been doing to teach my 8th graders at Chrysalis about time lags – and give them an introduction to calculus – is maintaining two graphs throughout the school year. The first graph is of daylength. The second graph is of change in daylength.
At the beginning of the school year in late August, both the graphs were moving downward. But after Autumn Equinox, the change in daylength started moving up (from a very down position) while the daylength graph was moving down for three more months. And now, in May, as the daylength graph is moving towards its peak (Beginning of the Long Days), the change in daylength graph has been heading down for several weeks. (If this is confusing, that’s why I am giving kids this experience. Time lags are one of the great conceptual challenges for our species.) For example, the change in daylength graph last week went from a weekly change of the days growing longer by 14 minutes to a weekly change of the days growing longer by 12 minutes. So the graph of the change dropped from 14 to 12 even though the meaning of the graph is that days are still growing longer at a rate where the daylength today is 12 minutes longer than the daylength of a day one week ago. We periodically have discussions of why the two graphs can be moving in different directions at certain times of the year. Tanya summarized the April-May situation nicely in her immortal phrase: “It’s growing longer shorterly.”
Accurately describing underlying dynamics like this is challenging. For example, last week I got clearer on two of the effects my erosion work is actually having. When I diverge runoff and slow it down so that more of it soaks in, what I am doing is “decreasing the rate at which the rain’s potential energy transforms into kinetic energy.” And one of the consequences of that is “decreasing the average distance eroded material travels before being deposited.”
When I am sloppy in my thinking, I say that my work reduces erosion and increases deposition. But that is inaccurate because deposition is the ending phase in a cycle of erosion. The only way to increase deposition is to increase erosion (somewhere else). So increasing deposition is not my goal. Decreasing the average distance travelled is. Soil is moving down “shortily”. And the effect of that is slowing down the gravity-powered conveyor belt which has the effect of the soil cycle “backing up”. Soil accumulates more on the slopes and earth rises.
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