Endless Thread - The Lost Loophole

Episode Date: July 24, 2026

Kurt Gödel was a genius mathematician and logician, considered by many scholars to be as influential as Aristotle. He was also buddies with fellow geniuses Albert Einstein and Oskar Morgenstern, the co-creator of Game Theory. In 1947, Gödel told Morgenstern and Einstein he had identified an inner contradiction in the U.S. Constitution while studying for his citizenship test: the type of loophole that could plunge the United States into a dictatorship not unlike the Nazi regime Gödel had escaped when he immigrated from Austria. So, what was the loophole? Over the years, everyone from Constitutional law scholars to laypeople on Reddit have wondered. Endless Thread plumbs the depths of Gödel's galaxy brain with the help of philosopher, writer and Gödel expert Rebecca Newberger Goldstein — and learns some surprising lessons about artificial intelligence, a German shorthand called Gabelsberger, and democracy along the way. Show notes: Incompleteness: The Proof and Paradox of Kurt Gödel, by Rebecca Newberger Goldstein (Amazon) Oskar Morgenstern's account of Kurt Gödel's naturalization (Institute of Advanced Study) This episode was produced by Grace Tatter. It was co-written by Grace Tatter and Ben Brock Johnson, co-hosted by Ben Brock Johnson and Amory Sivertson, and edited by Meg Cramer and Dave Shaw. Mix and sound design by Paul Vaitkus.

WBUR Podcasts, Boston. It starts like a joke. A mathematician, a physicist, and an economist get into a car headed to Trenton, New Jersey. It's December 5, 1947. One of these men created the theory of relativity, which changed humanity's understanding of space and time. Albert Einstein. Another, Oscar Morganstern,

co-created game theory, which would change how governments around the world strategized for greater power. These two are in the front seat. And the third guy sitting in the back? Well, right now, he's just hoping to pass his citizenship test. This third guy, Kurt Goodle, is on the brink of royally mucking it up. Not because he isn't smart. In fact, he might almost be too smart. for his own good. In preparation for this citizenship test, he's been over-preparing,

studying the entirety of U.S. history. This is how game theory economist Oscar Morgan Stern would remember it in a memo years later. While we were driving, Einstein turned around a little and said, now, Kirtle, are you really well prepared for this examination? Of course, this remark upset Kirtle tremendously, which was exactly what Einstein intended. and he was greatly amused when he saw the worry on Gertl's face. Gertl's not just on edge because Einstein is screwing with him. He's nervous because as he's been over studying for his citizenship test, which will allow him to secure his safety in the U.S.

and leave the fascism-wrecked Europe in the rear view, he's discovered something in the American system of governance that he thinks could lead America down the same perilous path followed by Italy and Germany, into dictatorship, despotism, and destruction. Kurt Goetel's buddies in the car, Albert and Oscar, say, Kurt, maybe don't mention the whole critical failure point in American democracy thing to the judge. And then, according to the story told by Morgan Stern years later, when these guys get to Trenton, New Jersey, and get in front of the judge, Gertel can't help himself. He has to tell

people. Now, Mr. Girdle, where do you come from? Where I come from, Austria? What kind of government did you have in Austria? It was a republic, but the Constitution was such that it finally was changed into a dictatorship. Oh, this is very bad. This could not happen in this country. Oh, yes. I can prove it. Einstein and Morgan Stern are horrified. But the judge helps Girdle out. Judges like, hey man, you know what, we don't need to get into all that. Let's save that for later. You're in. He's in. And here in the U.S., Goetel builds on the contributions he's made to our understanding of the foundations of mathematics. But this little vulnerability in America's system that you might be able to drive a tank through? Goodell never really piped up about it again, as far as we know. All we seem to know is that he found something.

And he was worried. The story about Goetle's loophole, this inner contradiction he found, may be embellished, but it's still going almost 80 years later. And that's because it's a perfect example of something that Kurt Gödel was really good at. He had an extraordinary capacity to identify loopholes in things that we all take for granted. We found Reddit posts about the mystery of Goetel's Lost Loophole, and it's one of those stories that's just too damn good to let go of, especially now.

President Trump has expanded the scope of presidential power and denounced... Trump has targeted judges in the past, he's doing it again. Frankly, the president is trying to take the power of the purse away from the legislative branch. Some of his orders have tested the lengths of presidential power. And we're not the only ones who've become obsessed with. with this loophole. A lot of people have bugged you about this thing. Oh, yeah.

I've been getting emails about this. Really? I'm Amory Siebertson. I'm Ben Brock Johnson, and you're listening to Endless Thread. Coming to you from WBUR, Boston's NPR. Today's episode, The Lost Loophole. How do you say? I say goodle.

Goodle. Yeah. Goodell. Yeah. You need to work on that. When I was writing the book, so this woman, you know, she asked me what I was writing about, and I said, Goodell, and she said, You're writing about women's undergarments?

Rebecca Newberger Goldstein is a philosopher. She's an important one. She got a medal from Obama. She's a best-selling author in multiple genres, like Goetle. She crosses fields of study. She's influential in her own right. In 2005, Rebecca wrote a book about Goetle called Incompleteness, because even though Goetel was born almost a

century before then, we were and are still grappling with his ideas, which are relevant right now. Rebecca dove right into Goethe's origin story with us. So Goetal had been born in what was the Austro-Hungarian Empire, but it collapsed after World War I, and it became the Czech Republic. In 1924, Goetel moves to Vienna for university. And those were some pretty dramatic years to be in Vienna. So it seems like it. Yeah.

And in fact, to be in Europe in general. He did see a lot of governments, Austria, Germany, but also Poland, the Baltic states, Hungary, Romania, Yugoslavia, devolved from parliamentary democracies to dictatorships. Amid all this unrest, Gerdl is pretty focused on his research. He gets his doctorate, becomes a professor. And he gets a reputation for using mathematical concepts to reveal fundamental truths about how math works. It's as if a painter had painted a beautiful picture that was not only a representation of a beautiful scene, but could tell us about the nature of beauty itself and its power to move us. That's what he did in mathematics.

This was also the work of a logician. A philosopher. Goetle had a galaxy brain. And by the time he's in his 20s, Goodell's had some very big and very influential ideas. For instance, he came up with this way of encoding information into long strings of numbers. It's called Goodle numbering. Storing data inside numbers is really important for machine code. But Goetle was best known by his contemporaries for another set of big ideas, his incompleteness theorems, which really blew wide open ideas about how math worked. And for now, we are going to leave the explanation of those incomplete.

Point is, at least in the beginning, many of Goetal's ideas are theoretical and not necessarily super useful ideas. Which makes them perfect for the recently established Institute for Advanced Study at Princeton, which is dedicated to the pursuit of useless ideas, ideas that have no practical implications of my kind of ideas and his kind of ideas, right? Ideas like Einstein's unified field theory. And John von Neumann's electric computer project.

Von Neumann was real controversial. He outraged the other members of the Institute because he created a computer, largely out of Gittle's ideas, but it was a computer. It was practical, and they were outraged. And after von Neumann died, they moved it over to Princeton outside of the Institute of that study because they just didn't want anything that useful.

While Princeton is wrangling geniuses, the spread of Nazism is totally changing borders in geopolitics in Europe. It's also changing the map of where the world's intellectuals live, which is also why people like Einstein, von Neumann are hanging out in Jersey. The guy who developed the Institute for Advanced Studies said, Hitler shakes the apple tree and I gather up the apples that fall to the ground. They were just scooping up European intellectuals who did not find favor with the powers that be. Goodell visits the Institute throughout the 1930s, but in 1938, the Nazis take control of Vienna.

Since the German troops crossed the Austrian border on the historic invasion last Friday, news has flowed across the Atlantic in a steady stream. The German Chancellor now winds his way through the conquered nation in a parade of triumph to end in a tremendous spectacle in Vienna. Goethe still 1940. At the time, many of the intellectuals in Vienna are Jewish. Goetel isn't, but because he is an intellectual in Vienna, people think he is Jewish. He got really beaten up by a bunch of thugs. His wife, Boydor, Hedell, who had been a cabaret dancer, get that. So she beat them off with an umbrella.

Oh. Whoa. And they decided back to New Jersey. This time, they're going to New Jersey for good. Goetel's not really a social guy, so he doesn't really make strong connections with most of his fellow geniuses at the Institute. except for Albert Einstein. Einstein and Goethe walk to and from campus together every day. They're kind of an odd couple.

Einstein, he was a much older man, and Goethe at this point is, you know, in his early 30s. And Einstein was somewhat depressed. His unified field theory wasn't panning out. And he actually said to Oscar Borgonstern that his own work doesn't mean much to him anymore. he only goes to his office at the Institute to have the privilege of being able to walk home with Goethe. So that's why Einstein is in the car with Goethe and Morgan Stern on December 5, 1947, on the way to his citizenship test. When Rebecca was writing her book about Goetle, she tried to find out more about the constitutional loophole he supposedly discovered. I did research. I tried to find out. But another quirk.

of Goetal. He kept everything, so it's wonderful. I found bills for coal that he had been delivered to him when he was a student in Vienna. He kept everything. But he took notes and he took many notes. He himself had journals, notebooks and notebooks of journals. But he wrote it in this shorthand that he had learned as a high school student in Austria called Gobblesburger that nobody knows how to read anymore. You're telling me

the shorthand is called Gobblesburger? It really is. It really is. So all we had to do is find the notes, learn this shorthand no one knows anymore

and solve the mystery? How hard can it be? Fortunately, guess who knows where all those notes are? I do. Producer Grace Tatter, you're here

because you've laid eyes on these notes. Nay, hands on them because after all this time, they're still at one of Princeton's libraries, a stones throw away from the Institute of Advanced Study. Grace, did they feel weighty? Did they feel useless? It definitely felt useless. Grace and I both can probably gobble burgers and Amory can gobble a veggie burger, but none of us can read gobbles burger. Exactly. Not yet, at least. So first, I

reached out to another one of Goetal's dedicated biographers, John Dawson. He's a mathematician, and he spent years cataloging Goetal's papers and notes. Turns out Rebecca had also been reaching out to Dawson because Dawson's wife had learned Gobblesberger just to help him translate all those notes. We all need a wife like that, yeah. And so I said, well, what about the loophole? And they said, well, it's not a mathematical interest. That's not what we've, you know, been interested in interpreting. And I just wrote to him again recently because so many people have been writing to me about what is the loophole. And this time he didn't answer me.

He didn't answer me either. Okay. So back to square one. Rebecca had recently met a German professor at Harvard who thought he might know people who know Gobelpsberger. So I reached out to him. He reached out to a colleague in Germany, who reached out to another colleague, who finally connected me to Max Cricker, an expert in German manuscripts in shorthand. Max is an expert in Gobelsberger.

So he translated some of the pages into German, and then we worked together to translate them into English. So after all this, Grace, what did we find? Well, that story we heard at the beginning, I can confirm that Goodell studied real hard for the citizenship exam. His notes go into a lot of detail, like the fact that revenue bills must originate in the House of Representatives. We call this the power of the purse, which means that Congress, not the president, decides how to collect and spend taxpayer money. Goodall wrote in his notes that this was one of the most important checks and balances. And this has actually been popping up a lot recently.

Remember Doge? Remember our episode about the Fed News subreddit? If for whatever reason, you don't. In the early months of the Trump administration, federal officials canceled or froze trillions of dollars in funding that had already been appropriated by Congress. Is this it? Is this our loophole? Did we find it?

Not so fast. No. Come on. To be clear, I don't think this is the loophole. This is just something that Goodle thought was interesting. But so far, we've only made it through seven pages, and there are many more. Because it turns out, hiring a guy in Germany to translate a niche, nearly extinct form of shorthand, is not something that public media has a ton of money lying around for.

You don't say. This is a good time here to remind you to donate to your local public radio station, yes? I have to say, when I first reached out to our friendly translator, Max, I didn't quite realize how time-consuming translating Gobblesberger could be. Which got us thinking, Goodell, grandfather of computer science, galaxy brain, who is still haunting the conversations we are having about artificial intelligence. Could we get AI to do this? Well, good news for Max's job security.

translating Gobelsberger, not a thing that machines are good at. In fact, I talked to an AI expert in Germany who is specifically researching how to train AI to translate Gobelsberger. And even he doesn't think that AI will ever be able to do it perfectly, at least without an assist from experts like Max. AI Zero, Humans, One. Okay, thank you, Grace. Gobblesberger is, I guess, a dead end, at least for now. But that doesn't mean we can't keep searching for our answer because we may not be Gobblesburger translators, but are we quitters? No, no we are not.

We press on after the break. There is something powerful about the sound of the human voice. Beautifully produced audio has the unique power to connect and inspire. Tell your organization's story with a custom podcast from CitySpace Productions, the creative studio from WBURs, business partnerships team. Become a thought leader. Recruit new talent. Reach new audiences. Whatever your goal, we can help. Discover how the magic is made at wbUR.org slash creative studio. So we're on a mission to solve this mystery, to find this supposed loophole in the system of

American government that is like a trapdoor that will drop us into fascism. We've been asking around, and we are not the first people to ask our good old expert, Rebecca Newberger Goldstein. Everybody thinks it's terrifically relevant right now. Separation of powers, checks and balances, and, you know, the legislature and the judiciary are supposed to be able to check the power of the executive, and it doesn't seem to be happening. In 2025, a survey of more than 500 political scientists.

found that the majority believed that the United States was moving away from a liberal democracy and towards authoritarianism. So the people on Reddit, the people endlessly emailing Rebecca, they're all wondering, did Kurt Goetel see this coming? I actually think he didn't. I don't think... You don't think he found a loophole?

I think he found a loophole. But I don't think... It's such a Goodellian loophole. That is, it is theoretically possible, but so unlikely, so impractical, but just the kind of thing that he would have really appreciated. Appreciated because Gerdl really loved a few particular concepts that became folded into his work. For instance, the idea of self-reference. It's really interesting and it can be explained very, very easily.

For example, take this statement. This proposition consists of six words. It refers to itself, and it's true. It actually does consist of six words. No problem. Not very interesting, but no problem. Okay. Here's a proposition.

this very proposition is false. Now, if this proposition is false, then it's true. But if it's true, then it's false. So self-reference can get us into the realm of paradoxes. Contradictions. Contradictions are terrible. They boggle the rational mind. Goodell's big contribution to mathematics and logic was saying that to avoid contradictions in a system or way of thinking, you will end up with a conclusion that a true statement is actually unprovable.

This is at the heart of the thing he's really known for, his famous incompleteness theorems. What Goodell did is that he actually use a statement that can refer to itself to produce the same. to produce this amazing theorem, the first incompleteness theorem, I'm just going to state it, which says that in any formal system of mathematics, which is rich enough to express arithmetic, there are propositions which, although true, can't be provable. So our formal systems are either inconsistent or they're incomplete. But we wanted to formalize mathematics to root out all inconsistencies and to show that anything that's mathematically true can be provable.

And that's what Goetle proved was impossible. That's what his proof is about. By the way, Goetel wrote two incompleteness theorems, packaged deal, but the only one you really need to worry about here is the first one, the one that Rebecca just read, which again boils down to there are true statements that cannot be proven. As demonstrated by statements like, this sentence is false, self-referential statements,

which finally brings us back to the loophole. DeV I haven't said at all what we think. the loophole was, right? No, I'm still. Yeah. Okay, long build up. Yeah, that's good. Long drum roll.

What many people think the loophole could be, given Goodell's appreciation for self-referencing contradictions. It involves Article 5 of the Constitution. Which, as Amory knows very well, is something very similar to you, which we all know is. Yes. Article 5 sets out the amendment. process, that the Constitution can be amended if two-thirds of both houses of Congress vote on a proposed amendment and three-quarters of state legislatures vote to ratify it.

The amendment process can be used to apply to itself. So self-referential. Yeah, here we go. And let's see there's a very determined, majority in the House and in the Senate. They could vote to amend the amendment process. Perhaps they'll say it only takes a majority in the two houses or maybe only one of the houses.

There's nothing to rule out. They're amending the amending the process itself. amendment process can be amended. Yep. Self-reference, right? And then once that happens, the bar is lowered to all further amendments. So in theory, Congress could amend the Constitution to make it easier to amend the Constitution. And then they could do all sorts of things, like get rid of judicial review, suspend term limits, limit the freedom of the press.

Anything can happen. Anything can happen, but it's unlikely because the first step, getting both houses of Congress and most of state legislatures to agree on anything would be pretty hard. Self-reference be damned. Still, this is what a lot of scholars and lawyers and redditors think Goetel might have meant when he said he found a loophole. But we don't know, because as far as we know, he never spoke of it after his citizen. If I knew a specific loophole that could lead to the immediate unraveling of American democracy, I would become a superhero and try to protect it. Or I would maybe tell somebody about it other than myself.

But, you know, Goethe had other existential questions on his mind. He dabbled in physics and showed that Einstein's theory of relativity suggests the possibility of time travel. He wrote philosophical papers about the nature of truth. He also struggled. His friend Einstein died in 1955, and Goetal became increasingly withdrawn and paranoid. Not about democracy, but about his own health. He became more and more convinced that people were trying to poison him, and he would only eat food prepared by his wife, Adele. In 1977, Adele was hospitalized for several months.

Goetle essentially stopped eating. He died of starvation in January the following year, weighing only 65 pounds. But since Goetl suggested the possibility of time travel, let's rewind to just a couple of years before he died. His old friend Morgan Stern wrote that for a few weeks, Goodle came out of his shell. And during that rare and fleeting moment, Goodle and Rebecca, our Goodell guide, who is a little bit of his guide, who is a few weeks, Gordell came out of his shell. getting her PhD in the philosophy of science at the time, ended up at the same party. When I entered, he was like the Greta Garbo of pure reason. You know, I want to be alone. You know, he was very antisocial after Einstein died.

The Greta Garbo of Pure Reason. He would not like that analogy, but that's how I thought of him. You know, Greta Garbo, 1930s actress. We want to be alone. We want to be alone. But one day I shall find myself alone. So when I came to this party and I walked in, all of these people rushed over to me and said, he's here, he's here. Rebecca had one question for her idol. And it wasn't about the loophole.

It was a question that went all the way back to his theory of incompleteness. But also, a question that felt increasingly relevant in the 1970s. I wanted to ask him a question so much, but I was so intimidated. It was like, you know, asking. That question, did he think that his first incompleteness there implied that our minds can't be digital computers? Did he make that leap? One thing I wish I could wind back the clock and go back to and change in my own behavior. Of course, there are many things.

But one of them is that I didn't ask Good Goodell that question, you know? I've regretted that my entire life. Rebecca's not the only one who regrets not being able to ask Goethe about how his ideas might connect to artificial intelligence. A lot of what he created has since been heavily applied to a theoretical world of AI that is, becoming real at breakneck speed. Here's one more little loop for you. Gertl's incompleteness theorem talks about how things that are true might not necessarily be provable. Let's go back around to a contemporary of Gertl whose ideas are still echoing in our

AI present. Alan Turing, the famous codebreaker from World War II, who invented the test for figuring out when a machine can exhibit behavior equivalent to a human, the term. Turing test, which is really important now that we are always trying to figure out whether something is AI or not. Well, Alan Turing was reportedly directly inspired by Goetel's incompleteness theorem. In fact, Turing developed his own math problem inspired by the incompleteness theorem. The so-called halting problem is the problem of figuring out whether or not any computer program with an input will stop running or keep running forever. It's theoretical.

You're dang right it is. But have you ever seen the beginning of the movie Fantasia? Where Mickey Mouse uses the Sorcerer's Wahn to get a broom and a bucket to do some cleanup work. And then he can't stop them. And they just keep going and going and it's a disaster. The Sorcerer's Apprentice. In this example, the brooms are AI. Mickey is us.

We are Mickey. Yes, eventually the sorcerer returns puts a stop to it all, but we don't really have a sorcerer. It's us and the machines. Or at least we want to get to sorcerer level, where we can keep control of the machines in a responsible way. We still want to sit above them. We don't want them running our lives. When it comes to this relationship between us and the machines, Gerdl's incompleteness theorem and connected ideas don't.

don't just have mathematical utility. They also have philosophical utility. Because if algorithms fundamentally can't, for instance, prove a theorem is true no matter how hard they try, but humans can conceptualize something that is true even if it isn't provable, this is perhaps a permanent crucial difference between people and machines, a place that artificial intelligence will actually never be able to reach. A key difference between the sorcerer and the broom with the bucket. It's a deeper understanding of truth and magic.

It led many people to say, well, our minds can't be at least digital computers because it's not that we fall in love and that we can do poetry and write novels and all of that mushy stuff. When it comes to math itself, rule following math itself, it seems that we can do something that the computer can't do, the computer running on normal systems. Falling in love, writing real poetry that captures the human spirit, translating Gobblesberger,

we're three and oh against the machines. Rebecca might never know or be able to prove what Goodell actually thought about computers and our minds. And we might never know what the loophole he supposedly found in the Constitution was, or why he didn't ever write it down in a way future generations would be able to decode. Was it because it seemed unlikely? Did he just move on to another logical contradiction after his citizenship test? Did Einstein convince him it wasn't a concern?

Because we don't know, we'll probably keep coming back to this, a recursive search for Goethe's loophole. And whether we're talking about artificial intelligence or sliding into fascism, sometimes humanity's ability to know what is true despite missing the exact definitive proof is where we have to land. Some version of making peace with incompleteness. Rebecca Newberger Goldstein has a new book, by the way. It's called The Mattering Instinct, How Our Deepest Longing Drives Us and Divides Us. You should check it out.

Thanks to Derek Penzler, professor of German at Harvard University, who, with help from Leah Simon at the Jewish Museum of Berlin, and Professor Dr. Irmila Fondullo helped us find Gobblesberger translator Max Cricka. Thank you to all of these people for aiding our quest to translate Gerdl's loophole. Also, thank you as well to my neighbor, Tom O'Feldman, for some quick live interpretation and to Vincent Christline for speaking to Grace about Gobelzberger and AI. If you want to try your hand at learning Gobblesberger and translating some of the notes, we've uploaded scans to our website, wbUR.org slash endless thread.

Good luck. Thank you to the Institute. Good luck. That's pretty good. Thank you. Thank you to the Institute of Advanced Study at Princeton for permission to let us upload those. This episode was produced by Grace Tatter and written by Grace Tatter and me, Ben Brock Johnson.

I also co-hosted it with me. Amory Sievertson. Editing by Meg Kramer and Dave Shaw, mix and sound design by our production manager, Paul Vikis. The rest of our team is Dean Russell, Kalyani Saxana, Emily Jankowski, and our senior managing producer, Summit to Joshi. Endless Thread is a show about the blurred lines between dictatorship and a functioning democracy. If you have an untold history and unsolved mystery or some other wild story from the internet, hit us up. Endless thread at WBUR.org. And good luck to us all.