Rare, frequent, improbable, probable

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What is rare? Is a recurring event that happens once every decade rare or common? Is an event that occurs once a century rare? Looking to the dictionary we can find that “rare” is “an event, situation, or condition that does not occur very often.” It depends, of course, on the temporal frame of reference. Someone who has well-developed timefulness skills may respond “Duh, of course it depends on the timescale of investigation.” But, would the student new to geoscience (or other areas of inquiry that work in longer timescales) or the person in your family or community who rarely thinks beyond the timescale of their lived experience consider this obvious and trivial?

In our lived experience we can naturally shift our understanding of what is ‘frequent’ versus ‘rare’ based on the timescale. For example, if you do some activity (go for a jog, a bicycle ride, etc.) once a week, this might be quite frequent for some people or contexts but infrequent for others. We’ll add phrases like “which is a lot for me” or “which is pretty rare for us” as a way to communicate the temporal reference. Or, if we don’t add that, someone will ask “So, is that often for you?”. The point is that, in the context of the range of timescales we experience, we are pretty good at incorporating the temporal reference without thinking about it too much.

Coupled with how common or rare an event is over time is the significance or ‘size’ of the event (i.e., frequency-magnitude relationship). Humans have internalized this in numerous contexts. For example, as I write this post (April 2021) the pandemic is still affecting the globe, to varying degrees, and a phrase we find ourselves saying is “this is a once-in-a-century event!”. Implicit in such a statement is that this event we are experiencing is both rare and of significant magnitude. In turn, we often link this to some vague idea of probability — because an event is significant and infrequent it’s likely not to happen again for a long time.

We can consider these ideas for timescales longer than the human lived experience and for ‘prehistorical’ times (before the collective memory or spoken/written record of humans). While this may not come as naturally to us, it’s a skill we can develop. While thinking about this, I was reminded of this 1967 paper from Gretener that I read many years ago (as part of a grad-level stratigraphy course). I won’t summarize the details of this paper here, I encourage you to read it.

Gretener’s main point, which I’ve highlighted in the image of the Abstract above, is that, given enough time, an event that is exceedingly rare becomes probable if not certain. We could apply this notion to the huge range of timescales represented in Earth history. For example, a rare event at the scale of 100,000 years might be considered ‘common’ when viewing 10,000,000 years. How can this stretching of time and the associated frequency-magnitude relationships help us think about and cope with the ‘rare’ events in our society?

Another thought-provoking paper along these lines is this 1989 paper from Kenneth Hsu. This paper focuses on extinction events but the message is very similar to the Gretener paper.

Why is this important? Related to these ideas is the notion of shifting baselines, or a gradual change in what is considered a “normal” range of conditions due to lack of memory and/or knowledge of past conditions. The idea of shifting baselines has been discussed in the context of environmental issues for decades and, more recently, for climate change. And the relationship to hazards and how we collectively assess risk (e.g., “a 100-year flood”) is particularly relevant. As geoscientists, we make the case that the enhanced temporal perspectives gained from studying Earth history provides insight into contemporary challenges. In addition to the technical insights, I think we can also highlight the development of temporal reasoning itself.

As the previous posts in this series (clock time and event time and what is an event?) discussed, my motivation in thinking about timefulness is to move towards developing activities/assignments in my courses that are more explicit about temporal reasoning. One way to do this is develop specific activities centered on temporal reasoning as the primary learning objective. And/or it could be embedded within activities/assignments that have other learning goals, but it would be highlighted and intentionally discussed as part of the activity (a temporal reasoning ‘check’).

In the context of this post, a bunch of potential ideas — e.g., analyze the frequency/magnitude relationships of well-dated sedimentation events and include a class discussion (even just 5 minutes) or reflection question about the dependency of terms like ‘rare’ versus ‘frequent’. If such temporal reasoning ‘checks’ occur many times throughout the course there could then be a more lengthy summary-style activity near the end of the semester to tie them together. 🤔