#physicsofacoffeecup

“It little profits that an idle king,

By this still hearth, among these barren crags,

Match’d with an aged wife, I mete and dole

Unequal laws unto a savage race,

That hoard, and sleep, and feed, and know not me.

I cannot rest from travel: I will drink

Life to the lees…”

And so begins Alfred, Lord Tennyson’s truly wonderful poem Ulysses. There are a lot of life lessons to be learned from that poem, about perseverance, endurance, and living. “Lees” are, of course, the sediment at the bottom of a bottle of wine. And the phrase “drinking life to the lees” means “to the very last drop.” I first read that in High School and this phrase, and others from that poem, are never far from the conscious surface of my mind.

And so this morning, as I was drinking my morning coffee and staring into the nearly finished cup, the physicist within me marveled at the pattern of the residual grounds, the lees, and Tennyson came to my mind and it is all captured in The figure below.

But there is more, the physicist within me once stirred is not easily quieted, and I find took great joy in the little fractal rivers that carve the “Mississippi Delta” out of the caffeine laden mud. They are fractal yes, random little twists and turns of unpredictability. But they are not fractal in the sense that there is a physics driven size scale to the pattern that we see – driven by surface tension, ground size, and imperfections in the surface of the cup. Famously. in the movie Jurassic Park Ian Malcolm explains to Ellie Satler how subtle variations cause chaos in the descent of a drop of water down her hand. It is a great seduction scene and presents the essence of chaos theory right there in the bottom of the coffee cup.

When I was in graduate school there was the proud tradition of coffee and donuts before seminars. And there was a great black indolent dog, named KT, whom everybody loved and who only came alive for donut time. You would bring your little styrofoam cup into the seminar with you and then quietly massage it into a work of art – the best being to turn it inside out patiently until it resembled a sombrero. Then too there is the tradition of studying the physics of the coffee cup. Upon looking carefully you truly may find the universe in a cup of coffee. It so wonderfully mimics the physics of mega-scale phenomena like stellar dynamics and the thermal engines that drive the currents of the terrestial atmosphere and oceans.