A Cathedral member here in Phoenix sent me a short note from a local “human potential” organization. In a nutshell it was arguing that the only way to live our lives was to follow the teaching of the Stoics. Except it didn’t use the word Stoic.

So I was trying to explain the stoic ideals as I wrote up my response, and googled the wikipedia article on Zeno of Citium so as to link to it in my email. And whilst I was mucking around in Wikipedia I thought I’d read the entry of Zeno of Elea; the maker of wondrous paradoxes.

Zeno’s paradox of the Dichotomy (which some argue is the same as Achilles and Tortoise) is one of the ways I used to argue that space was fundamentally quantized when I was teaching the Philosophy of Physics. Basically, if you go halfway to the wall, and then halfway again, and again, and again, conceptually you’ll never actually reach the wall. Except we know that we do.

Mathematics solves the problem by demonstrating that convergent series have limits. A physicist would say that ultimately after a number of steps, you get to the point where you can no longer subdivide space-time. (You’ve reached the Plank Scale.)

While I was reading the paradoxes, I came across this interesting adaption of one of Zeno’s ideas (the Paradox of the flight of the arrow) to quantum decay:

“The quantum Zeno effect is a name coined by George Sudarshan and Baidyanath Misra of the University of Texas in 1977 in their analysis of the situation in which an unstable particle, if observed continuously, will never decay.[1] One can nearly ’freeze’ the evolution of the system by measuring it frequently enough in its (known) initial state. The meaning of the term has since expanded, leading to a more technical definition in which time evolution can be suppressed not only by measurement: The quantum Zeno effect is the suppression of unitary time evolution caused by quantum decoherence in quantum systems provided by a variety of sources: measurement, interactions with the environment, stochastic fields, and so on.[2] As an outgrowth of study of the quantum Zeno effect, it has become clear that application to a system of sufficiently strong and fast pulses with appropriate symmetry also can decouple the system from its decohering environment.[3]”

Read the full entry here.

So, in other words, if you pin a system into a specific quantum state by making an observation, and then repeat rapidly enough that the system’s wave function cannot evolve, you’ve effectively frozen the system.

And therefore, we can show that if you watch a pot of water on the stove carefully enough, it can never actually boil.

And yet it does.

A paradox to the paradox!

I love it when that happens.