Gödel’s Door

Conner Roberts
Jul 20, 2017 · 3 min read

An old Christian mystic saying from the 1200s goes like this:

The wall turns out to be a door. A door open all along. A breeze rolls through, barely gracing your skin, carrying the scent of something you’ve felt you’ve always known.

I’d like to think he had this in mind when, in 1931, the mathematician Kurt Gödel, came upon a principle, nested in two theorems. He suggested that within any system (of claims, truths, assertions) there will always be un-provable terms. That is, no closed system of statements can completely prove itself — without, crucially, the existence of another system outside of itself. Term after term, eventually there will be known true and false statements with no definitive foundation. Assumptions, he concluded, not formal proof.

Math, logic, reasoning down to the atoms (axioms). Gödel showed this principle across sets and systems without fail. The philosopher Alfred Whitehead’s famous set of foundational logic also suffered this truth. Bertrand Russell’s system, was also subject to this young logician’s annoying math.

Gödel simply called this “Incompleteness”:

A closed formal system will never attain completion — pock marked or porous, here was a math of imperfection. A bit of uncertainty leaked back into philosophy.

~~~

What does this mean for you, traveler? The mountains and rivers don’t lend themselves to abstraction. A theorem won’t chase your bag as it rolls down a hill. Maybe, after 14 hours on a bus your mind wanders into these sort of waters, murky and untethered from real matter. Where then does this play out?

Symbols, formulas, Signs and systems, Belief, truth… Language, ideas.

Each with uncertain border towns. A traveler’s less-explicit medium.

In 1931, Gödel laid bare a cornerstone of human conversation:

Reconsider it this way, an Ideology is just a system of associated ideas that relate, define, describe or judge the world. And it seems that ever since humans attained abstract thought we’ve been submerged in every kind of ideology.

Dogma being the particular kind of belief that your ideology is complete, totally and safely secure in its unique description of reality. We also call this “hard line ideology”, “extremism” or “dogmatic faith”. AS a traveler, these are perhaps the most dangerous things you will encounter in the world. (It is best not to try and Gödel your way into a dogmatists system unless you have an exit strategy or a local intoxicant.)

In conversation we find ourselves negotiating our own contradictory ideologies against another’s. “Incompleteness” tells us that neither he nor I have an absolute system of truth — just bits, angles, experiences. There is always more to explore in another as we communicate with words and postures. From this principle we seek out the pores between us, potentially becoming a bit more human within every encounter. We are bits meeting bits. Finding inkling proof of our world across the, at times, seemingly infinite divide between personal experiences.

Travel affords us with the basic tools to negotiate this Gödellian bind: The improvable nature our own beliefs. When abroad: in the variety of worldviews and languages, with new ideas, concepts, postures, foods, smells, tones of voice, our internal system is exposed to the elements. Like a backpacker caught in a rainstorm. The question gets prompted at every market, at every cross roads:

Isn’t this idea of Me a careful ideology too?

The wall turns out to be a door. A door open all along. A breeze rolls through, barely gracing your skin, carrying the scent of something you’ve felt you’ve always known.

The math here gets us down finally to our own incompleteness of our ideas of ourselves. The math doesn’t lie but it’s only the door. On the other side is the You you haven’t known yet, the old memories felt anew, and the traveler is the one who crosses the threshold with all her senses, seeing who in time will return.

(excerpt from a larger project I’m working on “Daemon Guide to Travel”)

the Tangled Snarl

A Journal

)

writer and other

A Journal

Welcome to a place where words matter. On Medium, smart voices and original ideas take center stage - with no ads in sight. Watch
Follow all the topics you care about, and we’ll deliver the best stories for you to your homepage and inbox. Explore
Get unlimited access to the best stories on Medium — and support writers while you’re at it. Just $5/month. Upgrade