Posted by: Brad Nixon | February 10, 2016

On the Pier: The Cape Zeno Infinite Pier

I’m pleased to welcome guest blogger, Dr. Alfredo Cabezaloco. Professor Cabezaloco is an eminent authority who stepped forward to offer further information in response to the previous post about the piers of California. Take it away, Professor.

Thank you, blaknissan. Hello, everyone. As soon as I read blaknissan’s blog post about Redondo Beach Pier, I realized you fans of California travel would be interested to hear about a unique California pier: the Cape Zeno Infinite Pier.

The pier is remote — almost inaccessible — and doesn’t have a ferris wheel, shops, stores or restaurants. It’s a simple structure. It does have one characteristic that distinguishes it from all other piers, everywhere, not only in California:

You can never reach the end of it.

Some time in the early 1900s, an eccentric individual known to us only as “Achilles” amassed a fortune in northern California: probably through the unscrupulous clear-cut logging of redwoods. He owned a vast tract of land there.

This Achilles was obsessed with paradoxes. He reportedly invested enormous sums in an attempt to build a palace along the lines of one of M. C. Escher’s structures with infinitely repeating passageways. If he succeeded, there’s no evidence of it. But he did apparently succeed in realizing his fascination with Zeno’s Paradox, embodied in the Cape Zeno Infinite Pier.

rugged coast Brad Nixon 7755 (640x480)

On the rugged Cape Zeno coast

For those not familiar with it, Zeno’s Paradox states that before you walk across a certain distance, you have to cover half the distance. Then you must cross half the remaining distance, then half the remaining quarter of the distance, half the remaining eighth, and so on. You can, in fact, according to the paradox, never cover an entire distance, because there is always some fraction of the distance yet to be traversed.

If — as is claimed — Achilles succeeded in constructing his Infinite Pier (reportedly of robust redwood timber), it stands at rugged and nearly inaccessible Cape Zeno on a remote portion of the northern California coast.

One can walk out on the pier halfway, enjoying the sight of the vast Pacific, the sound of breakers rolling in, the feel of the sun and the wind. And then one can walk half the remaining distance, perhaps pausing to look over the railing to watch dolphins or even a whale. Then, one covers half the remaining distance, and so on.

But you can never reach the end of the pier.

There’s heated debate about this matter, naturally, and I’ve taken part in vetting scholarly publications about the Pier for several decades.

Skeptics have asked if perhaps Achilles managed to construct a one-way, “unidirectional” phenomenon, meaning the paradox only applies going out. Otherwise, how would one return? Does a person who covers only that initial half the distance and decides to return find themselves trapped, only able to cover the first half of the return span, then half of the remainder, etc? Is the pier inevitably the final bourne of all who set foot on it? A chilling prospect.

Others have questioned how the workers and materials could have been moved from land out along the pier as construction continued outward. Did they work from boats?

In my capacity as Director of Unidirection at the Multidirectional Directorate, I’ve been studying this paradox for many years. I’m planning a trip now to visit and test the validity of these, we’ll call them assertions, for want of a better term. I hope blaknissan will allow me to write a followup article once I have better data.

Thank you,

Dr. Alphonse Cabezaloco, Director of Unidirection, The Multidirectional Directorate.

Thank you, Professor Cabezaloco. We look forward to your report. In the mean time, I suggest that any of you traveling in California stay off that pier! blaknissan

© Brad Nixon 2016, 2017



  1. Highly fascinating! I’ve never heard of this. It seems too outlandish to be valid.


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