Stable and Unstable Equilibria

The cat is staring at me through the conservatory doors.  He wants in.  Now.  If I let him in, he will take over my lap and there will be no room for my journal.  Ah well, he’s a good cat and I’ll let him in.

He is now docked on my lap and I have muddy footprints all over my trousers.  He doesn’t seem willing to share the space with my journal this morning.  He keeps biting the pen and swiping his tail across the page.  At last, he is beginning to purr and settle down.  His warm belly makes me sleepy.   I think we might have reached a compromise:  cat on the left side, journal on the right.  If he’d just put away his teeth and claws we all could relax.   We seem to have reached an unstable equilibrium.

In physics, an unstable equilibrium is drawn as a peak on a graph.  The very top of the peak is the point of unstable equilibrium.  A small nudge in any direction would make the ball roll off the peak.

But we also consider stable equilibria, or equilibrium wells.  And if the ball is perturbed a bit in either direction, it will roll back and forth, back and forth, and eventually return to the lowest energy state at the bottom of the well.

I wonder, do our days move from unstable equilibrium to unstable equilibrium, from peak to peak, never quite knowing what will knock us off one perch or lift us unexpectedly to the next?  Or do we oscillate around a center, a lower energy point governed by restoring forces that, with time and in space, return us to a stable equilibrium?

I suppose we have measures of both.  We balance on a peak in moments of exhilaration:  A story published! A painting finished!  A baby born!  A stone added to a mountaintop cairn!  Each peak is an event we mark with a flag, it takes a huge amount of energy to climb, perhaps more than we’ve ever needed before.    And each peak, by its very nature, is an unstable equilibrium point.  With time, in space, we roll off the peak, into a well of learning, of development, of memory and reflection.

In the wells, we oscillate.  Sometimes, we are pulled back and forth by the drama of the everyday.  Sometimes, we swing with greater amplitudes as we adopt and adapt to different perspectives.  Occasionally, we almost rest at the bottom but never quite come still.  Quantum mechanics reminds us that there is no such thing as zero energy; there will always be a small vibration, some uncertainty in position and time, energy and momentum.  We are cradled around a center.   Yet, with time, space and perhaps a catalyst, we summit the next peak.

These are cycles, yet there is little predictable about their content and causes.  All that is certain is that we will travel these peaks and valleys.   At points of unstable equilibrium, we command the long view.  Looking back, we see the travelled paths.  Future vistas expand ahead.    With the descent, we can trust in the restoring forces of the next green valley.

Throughout the journey is the deep recognition that all of it: the peaks, the valleys, the long views, the oscillations around still points, the footsteps from point to point, the forces that keep us moving along this non-parabolic trajectory, all of these create a landscape for our adventures as grand and awe-inspiring as the Rocky Mountains.

Grizzly Peak, Loveland Pass, CO 2009

Grizzly Peak, Loveland Pass, CO 2009. Photo Credit: Brian Beeghly

This entry was posted in Non-parabolic trajectory and tagged , . Bookmark the permalink.