062: Metamathematics is fun!

Elizabeth Marro asks, and I answer: travel, heat, playlists, work-noise, spilt nail polish, suitcase detritus, books--especially Douglas Hofstadter--and the reassuring beauty of logic

As we go on, the theme of Strange Loops will recur again and again. Sometimes it will be hidden other times it will be out in the open; sometimes it will be right side up, other times it will be upside down, or backwards.

—Douglas R. Hofstadter in Gödel, Escher, Bach

Elizabeth Marro opened her latest issue of “Spark” with a series of questions: Think about the week that is ending today. What will you remember? What gave you the most peace? What gave you a reason to smile? It’s been a long, hot, strange summer and this week I’m looking for beauty. How about you?

After I read this, my mind set a new personal best for “number of images sent to the conscious self on a loop.”

What will you remember? What gave you the most peace? What gave you a reason to smile? 

~ Walking around the Marineterrein neighborhood of Amsterdam. Scenes of Dutch modernist buildings, a canal cordoned off into swim lanes, an eco-restaurant-biolab-arts-centre with mycelium-based panels (i.e. mushroom huts), a vegetable garden, a glass-paneled science lab, a child-sized bicycle, abandoned in the middle of a narrow lane.

~Listening to the same songs over and over on an airplane over the Atlantic, thinking back and forth across time and lives.

~ Driving north from Boston in 95 degrees, air conditioning broken, windows down, sunroof open, hair whipping everywhere, spectacular hot pink and disco-orange sunset. Later, lying in the dusk-cool grass, in front of a tavern, somewhere in the Connecticut river valley, waiting for friends to arrive.

~Distractedly taking an extra loop around winding New Hampshire roads on the way home afterwards, then leaving looping voice texts for a friend while circling the perimeter of my garden in the summer dark: scent of late roses and Russian sage and dry earth.

~Holding a first ripe tomato, still warm from the sun in my hand.

~ Dropping a bottle of cherry red nail polish and it shatters. Red is splattered everywhere: tiles, toilet, tub, towels, and skin, it is a slasher murder scene, nothing can be done about it without acetone polish remover. I laugh out loud at the sight of this because the only provable truth is that it’s funny. There’s no one in my life anymore who would be angry that I did this, no one to chastise or demean me.

~ Walking out under the full moon with my neighbors, carrying shovels and buckets to dig peony bushes from the yard of an abandoned house. I put mine in my kitchen sink and go elsewhere for the night, so I am momentarily surprised to find a peony nursery in my kitchen when I come home in the morning.

~ Hanging laundry on a line. Later, folding it up, smell of sunshine and green grass.

~ Accidentally getting drunk while mowing the lawn, because a podcast I’m listening to is giving me ideas and I keep stopping to write them down, and every time I stop, I take a sip from a glass of wine. It’s a long podcast. It becomes the weirdest-ever drinking game for one: Mow, listen, write, drink, repeat—working my way around the gardens of my house-shaped house.

*

It’s been a long, hot, strange summer and this week I’m looking for beauty. How about you?

Yes. Always.

I feel like some part of my life is ending and some new thing is beginning and it’s bewildering, a bit. I do this every ten years or so, just shed a chrysalis, so I know what it is, but I’m in the middle of it right now, and I can’t see what’s next, and the only respite, if there is any, is if something is beautiful. Beauty floats above the detritus of living and apart from time and identity. It has nothing to do with deadlines for grant applications, or home repairs, nor hurt feelings or ambitions, or not-ambitions, or crises-that-are-not-real, or crises that are real, nor sweet-natured, bewildered-eyed men, nor even sunburnt skin and bug-bitten ankles.

And this week, oh my god, this week, the beautiful cure was Douglas Hofstadter’s Gödel, Escher, Bach: an Eternal Golden Braid.

It was too hot to go jogging, too hot to go anywhere, too hot to cook, too hot to do anything but maybe sit around watching a show, but I was craving beauty—not entertainment. I wanted something nourishing, something that would make me feel like I had a soul. I dug in.

I got to the section called “The MU-puzzle.”

It completely blew my mind.

I was just reading along, thinking about the MU-puzzle, just as Hofstadter invites you to. (He does this delightful thing where he puts forth a puzzle and then basically says “go ahead and try it, I’ll wait.”) Then, suddenly, I could see it, both the shape of the MU-puzzle and the whole point of it as a thought exercise. How it shows how mathematical logic works: how axioms lead to theorems, how systems have rules of production, how you can work inside and outside of systems, how there are meaningless and meaningful interpretations of mathematical proofs, how the whole system must be fit together so that any input you encounter can be organized into a form that can be tested.

Then, it got even better:

In the chapter “Meaning and Form in Mathematics” Hofstader introduces a second, slightly more complicated puzzle (the pq-system) about which he draws a comparison between formal (mathematical) systems and language, saying,

Our command of language is not like a finished product: the rules for making sentences increase when we learn new meanings. On the other hand, in a formal system, the theorems are predefined, by the rules of production. We can choose “meanings” based on an isomorphism (if we can find one) between theorems and true statements. But this does not gives us the license to go out and add new theorems to the established theorems.

This filled me with joy.

It doesn’t matter how many ideas (theorems) there are—how many permutations, extensions, escalations, or proliferations, there is a mechanism by which they can be sorted and found to be true or false. There is no strip-mined digital flood plain in metamathematics, there is no drowning in too muchness; there are systems and ways to make new systems, there is even a system for incompleteness.

The beauty of this. The order made out of chaos.

Reading about mathematical systems is giving me a means to sort through all of that incoming stuff that my mind served up to me as memories in response to a writing prompt—and all of the other stuff, too, everything from global inflation and fuel shortages, to pandemics, to hornets nests under a bedroom window, to the hundreds of other things that have happened in the past week and months.

The relief of this: there are theorems that can occur along well-formed strings and they can be tested. They can be found to be true or false. In other words, there are things that can be known.

*

There was that time I argued about the nature of truth with the ex-spouse who would have shamed me about spilling nail polish. I had told some version of a story to him, and then told another version of it to someone else, and he wanted to know if I knew which one was true. I told him that both of them were true.

Which they were, within the rules of language and storytelling. I had rearranged facts for effect and audience, but the truth was still intact. He didn’t like this answer, and I couldn’t understand why not. What other answer is there, for a storyteller, to the question of “what is true?”

Now, I know another answer. If he really needed something to hold on to, we could define a system of rules for the stories I told, a string-series of premises inside an agreed upon logic of stories. He could check them. He would then know that they were true. (I would have already known.)

Before this week it was not clear to me that the boundaries of logic (truth, meaning) can be agreed upon. In my world, until last week, there existed only infinite meanings for anything I’ve ever experienced and given language to. I don’t mean this in the Trumpian sense of “alternative facts.” I mean that there are a lot of meanings for every word, and there are a lot of ways to arrange words, and unless you are writing formal verse, there really isn’t even a Requirement of Formality for writing—not in these post-modern times, there isn’t. Every rule can—and arguably should—be broken when it comes to words. A very simple version of this is “the power of positive thinking.” Another is “spin.” We can make meaning almost ‘on-demand’ in how we use language to express ourselves.

You’re going to have to take it on face value that I’m not talking about lying; I’m talking about the exponential diversity that is encoded in human expression—which is a good and powerful thing.

The infinite possibilities of my own small piece of human existence has become, well, dizzying. Just getting older means I know more things and have had more experiences, and then there’s an information firehose that is pointed at me now, that I do enjoy drinking from. It’s harder and harder to hold the shape of a strange loop—of a formal, ever more complex beauty—and not just descend into anarchy.

I’m only just getting started with Gödel, Escher, Bach: an Eternal Golden Braid, but I can feel my mind starting to right itself now. It’s building a logical set of rules so that I can keep ahold of the complexity that I love, like a just-ripe tomato, still warm from the sun.

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• This essay by Jean Ganet, “Scenes From An Open Marriage,” in Paris Review is absolutely beautiful writing—a masterclass in rhetorical style, courageously and sensitively described, and just so utterly human in its approach.
  

• The whimsical dialog with an AI on the occasion of the Sturgeon Moon by Will Dowd in “The Lunar Dispatch”

Sturgeon Super Moon

• Doodle Dispatches was a featured writer on Substack last week—did you see it? All you got to do is click and you’ll see why.

• Finally, this meme which, honestly, does give me a feeling of power.

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Now, About You

What’s your take on Elizabeth’s questions? You can answer by comment, or head on over to “Spark” newsletter to see what folks are saying there. (Or do both!)

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