The shortest physically productive pre-activity

It’s common knowledge among ESL teachers that any activity should be prefaced with a pre-activity. Not only textbooks, but handouts, powerpoint presentations, and even off-the-cuff improvisations by the teacher are prefaced by some schemata-activating questions, discussion points or pictures, the theory being that students are better able to engage with the main activity after their brains have all the context-appropriate neurons firing.

I have never seen any evidence that the principle of preparing students for any activity should only apply to main activities, however, so it stands to reason if we are right about the importance of schema activation that these pre-activities could use pre-activities of their own. If you follow my logic, responsible pedagogy should involve a pren+1-activity before any pren-activity.

This presents a philosophical and practical pedagogical problem, as responsible language teaching now seems to entail an infinite series of increasingly small pren-activities, which in an echo of Zeno’s arrow, mean that we can never actually physically reach the start of our main activity.

With an eye toward helping my fellow language teachers out of this conundrum, I would like to propose a pragmatic (no pun intended) solution to the pren-activity dilemma, which is this:

Teachers should not have pre-activities whose length would be shorter than the time it takes for light to travel from the teacher to the nearest student. The last pre-activity whose length is longer than this time will be called the shortest physically productive pre-activity.

I will illustrate this principle by assuming a few values:

  • The speed of light is 3.08 * 108 m/s
  • Our main activity is planned for 20 minutes (1200 seconds).
  • Our pre1-activity is 5 minutes, or 1/4 the main activity, and schemata-activating pre-activities for other pre-activities will also last 1/4 as long as the activity that they prepare for.
  • For the sake of simplicity, the nearest student is seated 3.08 m from the teacher.


Given our values for the distance between the teacher and the nearest student, it takes 1/108 seconds for light to travel from the teacher to the nearest student. Any pren-activity that takes less time than that will be over before the last one can be physically sensed by the students.

It’s worth pointing out that light is the fastest known physical phenomenon in the universe; no cognitive activity (or any activity with a physical substrate) can outpace it, no matter how “quick” the student. The speed of light is, therefore, a crucial property to consider when planning pren-activities whose length is measured in millionths of seconds.

The question then is what value of n in a pren-activity yields an activity whose length is less than 1/108 seconds. I solved for n by plugging in the values above:

1200/4n = 1/108




Doing these calculations the old-fashioned way, I come up with a value of 18 for n as the last pren-activity whose length is longer than the time it takes for light to travel from the teacher to the student. Therefore, with the assumptions above, a main activity should be preceded by exactly 18 pre-activities, the 18th pre-activity being the shortest physically productive pre-activity.

It is to be hoped that teachers integrate this knowledge into their lesson planning thoughtfully and responsibly.

Clichés of polyrhythm/meter in metal

Here is my fourth-ever metal post. The others continue to get a few views every day from people who are probably disappointed by the rest of the content of this blog (and vice versa for English teachers who collide with metal posts). Obviously, my music theory metalanguage is quite shabby, but I’m going to try here to describe a few things I’ve heard over and over again in metal bands.

Continue reading “Clichés of polyrhythm/meter in metal”