panta rhei — Everything flows. If your perspective is right, you see the motion.

Ed Lachapelle introduced quite a few of us to the Deborah Number, while talking about glaciology and about politics out by his shed in McCarthy, where he was splitting firewood.

The Deborah Number comes from rheology, the study of how materials deform and flow. It compares two timescales: the time an event takes to occur, and the time over which we observe it.

In its more precise technical form, the Deborah number is:

Deborah number = relaxation time ÷ observation time

Here, the relaxation time is the characteristic time over which a material relaxes stress, while the observation time is the period over which we observe or test its response.

When the relaxation time is short compared with the observation time, a material has time to relax and may respond predominantly through flow. When the relaxation time is long compared with the observation time, the material may appear elastic or solid-like. The comparison depends on the material, its conditions, and the timescale of the observation.

Markus Reiner named the number after a passage in the biblical Song of Deborah, which he rendered as “The mountains flowed before the Lord.” The name brings an ancient image into a precise scientific question about time and material behavior.

For me, its significance also lies in the question it encourages us to ask: what processes does the duration of our attention allow us to perceive, and what does it conceal? In observing a landscape—or considering a community or institution—that question can change what we notice and investigate. Applying the numerical measure beyond its physical setting requires identifying meaningful relaxation and observation times; the broader question can travel further.

See Markus Reiner. “The Deborah Number.” Physics Today 17 (1964): 62.

For more about Ed LaChapelle, including his essay, “The Ascending Spiral,” which discusses the Deborah Number and much else, see the retrospective on his life in The Avalanche Review April, 2007.