The Lost Loophole

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 https://www.amazon.com/Incompleteness-Proof-Paradox-G%C3%B6del-Discoveries/dp/0393327604) Oskar Morgenstern's account of Kurt Gödel's naturalization (Institute of Advanced Study https://albert.ias.edu/entities/archivalmaterial/9fd45e83-9706-4c1f-92de-302efdc85561) 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.

Speaker names marked ? are inferred from speaking time and the show’s known hosts — they are not voice-verified.

• 0:00Speaker 00

  Support for this podcast comes from Is Business Broken?, a podcast from the Marotra Institute at BU Questrom School of Business. A recent episode explores how AI is reshaping our schools. Stick around until the end of this podcast to preview the episode.

• 0:17Amory Sivertson?

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• 1:03Amory Sivertson?

  WBUR Podcasts, Boston.

• 1:14Ben Brock Johnson?

  It starts like a joke.

• 1:18Amory Sivertson?

  A mathematician, a physicist, and an economist get into a car headed to Trenton, New Jersey.

• 1:25Ben Brock Johnson?

  It's December 5th, 1947. One of these men created the theory of relativity, which changed humanity's understanding of space and time. Albert Einstein.

• 1:38Amory Sivertson?

  Another, Oscar Morgenstern, co-created game theory, which would change how governments around the world strategized for greater power. These two are in the front seat.

• 1:49Ben Brock Johnson?

  And the third guy, sitting in the back? Well, right now, he's just hoping to pass his citizenship test.

• 1:56Amory Sivertson?

  This third guy, Kurt Gödel, is on the brink of royally mucking it up.

• 2:04Ben Brock Johnson?

  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 US history. This is how game theory economist Oscar Morgenstern would remember it in a memo years later.

• 2:26Speaker 03

  While we were driving, Einstein turned around a little and said, "Now, Gödel, are you really well-prepared for this examination?" Of course, this remark upset Gödel tremendously, which was exactly what Einstein intended. And he was greatly amused when he saw the worry on Gödel's face.

• 2:49Amory Sivertson?

  Gödel'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 US and leave the fascism-wrecked Europe in the rearview, 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.

• 3:18Ben Brock Johnson?

  Kurt Gödel'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."

• 3:29Amory Sivertson?

  And then, according to the story told by Morgenstern years later, when these guys get to Trenton, New Jersey and get in front of the judge, Gödel can't help himself. He has to tell people.

• 3:42Speaker 03

  "Now, Mr. Gödel, 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."

• 4:05Ben Brock Johnson?

  Einstein and Morgenstern are horrified. But the judge helps Gödel out. Judge is like, hey, man, you know what? We don't need to get into all that. Let's save that for later. You're in.

• 4:18Amory Sivertson?

  He's in. And here in the US, Gödel 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?

• 4:34Ben Brock Johnson?

  Gödel 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.

• 4:46Amory Sivertson?

  The story about Gödel's loophole, this inner contradiction he found, may be embellished, but it's still going, almost 80 years later.

• 4:57Ben Brock Johnson?

  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.

• 5:11Amory Sivertson?

  We found Reddit posts about the mystery of Gödel's lost loophole. And it's one of those stories that's just too damn good to let go of. Especially now.

• 5:21Speaker 04

  President Trump has expanded the scope of presidential power and denounced-

• 5:25Speaker 05

  Trump has targeted judges in the past. He's doing it again.

• 5:27Speaker 06

  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.

• 5:37Amory Sivertson?

  And we're not the only ones who've become obsessed with this loophole.

• 5:41Ben Brock Johnson?

  A lot of people have bugged you about this thing.

• 5:44Amory Sivertson?

  Oh, yeah. I've been getting emails about this.

• 5:47Ben Brock Johnson?

  Really?

• 5:52Amory Sivertson?

  I'm Anne Marie Sivertson.

• 5:53Ben Brock Johnson?

  I'm Ben Brock Johnson, and you're listening to Endless Thread.

• 5:56Amory Sivertson?

  Coming to you from WBUR, Boston's NPR.

• 5:59Ben Brock Johnson?

  Today's episode, The Lost Loophole.

• 6:09Ben Brock Johnson?

  How do you say?

• 6:10Speaker 06

  I say Gödel.

• 6:11Ben Brock Johnson?

  Gödel?

• 6:12Speaker 06

  Yeah.

• 6:12Ben Brock Johnson?

  Okay.

• 6:12Amory Sivertson?

  Gödel. We need to work on that.

• 6:14Speaker 06

  When I was writing the book, so this woman, you know, she asked me what I was writing about, and I said Gödel, and she said, "You're writing about women's undergarments?"

• 6:26Ben Brock Johnson?

  Rebecca Newberger-Goldstein is a philosopher. She's an important one. She got a medal from Obama. She's a bestselling author in multiple genres like Gödel. She crosses fields of study. She's influential in her own right.

• 6:41Amory Sivertson?

  In 2005, Rebecca wrote a book about Gödel called Incompleteness, because even though Gödel 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 Gödel's origin story with us.

• 7:03Speaker 06

  So Gödel had been born in, what was the Austro-Hungarian Empire, but it collapsed after World War I, and it became the Czech Republic.

• 7:16Ben Brock Johnson?

  In 1924, Gödel moves to Vienna for university.

• 7:20Speaker 06

  And those were some pretty dramatic years to be in Vienna.

• 7:24Ben Brock Johnson?

  So it seems like it, yeah.

• 7:25Speaker 06

  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. It devolved from parliamentary democracies to dictatorships.

• 7:46Amory Sivertson?

  Amid all this unrest, Gödel is pretty focused on his research. He gets his doctorate, becomes a professor.

• 7:53Ben Brock Johnson?

  And he gets a reputation for using mathematical concepts to reveal fundamental truths about how math works.

• 8:01Speaker 06

  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.

• 8:19Ben Brock Johnson?

  This was also the work of a logician, a philosopher. Gödel had a galaxy brain. And by the time he's in his twenties, Gödel'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 Gödel numbering. Storing data inside numbers is really important for machine code.

• 8:45Amory Sivertson?

  But Gödel 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.

• 8:58Ben Brock Johnson?

  And for now, we are going to leave the explanation of those incomplete. Point is, at least in the beginning, many of Gödel's ideas are theoretical and not necessarily super useful ideas.

• 9:12Amory Sivertson?

  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, my kind of ideas and his kind of ideas, right?

• 9:31Ben Brock Johnson?

  Ideas like Einstein's unified field theory.

• 9:34Amory Sivertson?

  And John von Neumann's electric computer project. Von Neumann was real controversial.

• 9:40Speaker 06

  He outraged the other members of the institute because he created a computer largely out of Gödel'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 for Advanced Study because they just didn't want anything that useful.

• 9:59Ben Brock Johnson?

  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.

• 10:17Speaker 06

  The guy who developed the Institute for Advanced Study 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 do not find favor with the powers that be.

• 10:38Ben Brock Johnson?

  Gödel visits the Institute throughout the 1930s. But in 1938, the Nazis take control of Vienna.

• 10:45Speaker 06

  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.

• 11:01Ben Brock Johnson?

  Gödel sticks it out until 1940.

• 11:05Amory Sivertson?

  At the time, many of the intellectuals in Vienna are Jewish. Gödel isn't, but because he is an intellectual in Vienna, people think he is Jewish.

• 11:16Speaker 06

  He got really beaten up by a bunch of thugs. His wife, who I adore, Adele, who had been a cabaret dancer, get that. So she beat them off with an umbrella.

• 11:30Amory Sivertson?

  Ooh.

• 11:30Speaker 06

  Whoa. And they decided back to New Jersey.

• 11:34Ben Brock Johnson?

  This time, they're going to New Jersey for good. Gödel'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.

• 11:49Amory Sivertson?

  Einstein and Gödel walk to and from campus together every day. They're kind of an odd couple.

• 11:55Speaker 06

  Einstein, he was a much older man. And Gödel, 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 Morgenstern 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 Gödel.

• 12:24Amory Sivertson?

  So that's why Einstein is in the car with Gödel and Morgenstern on December 5, 1947, on the way to his citizenship test.

• 12:33Ben Brock Johnson?

  When Rebecca was writing her book about Gödel, she tried to find out more about the constitutional loophole he supposedly discovered.

• 12:41Speaker 06

  I did research. I tried to find out. But another quirk of Gödel, he...

• 12:48Speaker 06

  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 had, 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 Gabelsberger, that nobody knows how to read anymore.

• 13:20Ben Brock Johnson?

  You're telling me the shorthand is called Gabelsberger?

• 13:23Speaker 06

  It really is. It really is.

• 13:29Ben Brock Johnson?

  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?

• 13:40Speaker 06

  I do. Producer Grace Tatter, you're here because you've laid eyes on these notes, nay, laid hands on them. Because after all this time, they're still at one of Princeton's libraries, a stone's throw away from the Institute of Advanced Study. Grace, did they feel weighty? Did they feel useless?

• 14:01Speaker 07

  They definitely felt useless.

• 14:08Ben Brock Johnson?

  Grace and I both can probably gobble burgers, and Amory can gobble a veggie burger, but none of us can read Gobblesburger.

• 14:15Speaker 07

  Exactly. Not yet, at least. So first, I reached out to another one of Goodall's dedicated biographers, John Dawson. He's a mathematician, and he spent years cataloging Goodall's papers and notes. Turns out Rebecca had also been reaching out to Dawson, because Dawson's wife had learned Gobblesburger just to help him translate all those notes.

• 14:40Speaker 06

  We all need a wife like that, yeah. And, and so I said, well, what about the loophole? And he said, well, it's not of 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 he, this time, he didn't answer.

• 15:03Speaker 07

  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 Gabelsberger. 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 Kricker, an expert in German manuscripts in shorthand.

• 15:26Speaker 05

  Damals, in the time when Gabelsberger was studied and it was usual that one said Gabelsberger.

• 15:32Speaker 07

  Max is an expert in Gabelsberger. So he translated some of the pages into German, and then we worked together to translate them into English.

• 15:40Ben Brock Johnson?

  Phew, so after all this, Grace, what did we find?

• 15:44Speaker 07

  Well, that story we heard at the beginning, I can confirm that Goodall 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

• 16:29Speaker 07

  or froze trillions of dollars in funding that had already been appropriated by Congress.

• 16:34Ben Brock Johnson?

  Is this it? Is this our loophole? Did we find it?

• 16:37Speaker 07

  Not so fast.

• 16:39Ben Brock Johnson?

  Ah, come on.

• 16:41Speaker 07

  To be clear, I don't think this is the loophole. This is just something that Goodall 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.

• 17:02Amory Sivertson?

  You don't say. This is a good time here to remind you to donate to your local... Public radio station, yes?

• 17:10Speaker 07

  I have to say, when I first reached out to our friendly translator, Max, I didn't quite realize how time-consuming translating Gobblesburger could be.

• 17:20Ben Brock Johnson?

  Which got us thinking. Good old 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?

• 17:33Speaker 07

  Well, good news for Max's job security. Translating Gobblesburger, 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 Gobblesburger. 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.

• 17:57Amory Sivertson?

  AI zero, humans one.

• 18:00Ben Brock Johnson?

  Okay, thank you, Grace. Gobblesburger 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?

• 18:13Amory Sivertson?

  No, no, we are not. We press on after the break.

• 18:38Speaker 00

  Support for this podcast comes from Is Business Broken?, a podcast from the Marotra Institute at BU Questrom School of Business. How should employers measure real skills in the age of AI? Instead of observing the final artifact, instead of observing the final essay or the final program, observe the entire process of creation. Follow Is Business Broken? wherever you get your podcasts, and stick around until the end of this podcast for a preview of a recent episode on rethinking academic and job assessment when AI can do the work.

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• 19:48Ben Brock Johnson?

  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 Gödel expert Rebecca Newberger-Goldstein.

• 20:05Speaker 06

  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 to check the power of the executive, and it doesn't seem to be happening.

• 20:31Ben Brock Johnson?

  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.

• 20:45Amory Sivertson?

  So the people on Reddit, the people endlessly emailing Rebecca, they're all wondering, did Kurt Gödel see this coming?

• 20:53Speaker 06

  I actually think he didn't. I don't, I don't think-

• 20:58Amory Sivertson?

  You don't think he found a loophole?

• 20:59Speaker 06

  I think he found a loophole. But I don't think... It's a, it's such a Gödelian loophole. That is, it is theoretically possible, but so unlikely, so impractical. But just the kind of thing- That he would have really appreciated.

• 21:23Ben Brock Johnson?

  Appreciated because Gödel really loved a few particular concepts that became folded into his work. For instance, the idea of self-reference.

• 21:33Speaker 06

  It's really interesting and it can be explained very, very easily. For example, take this statement. This proposition consists of six words.

• 21:49Speaker 06

  It refers to itself, and it's true. It actually does consist of six words. No problem, not very interesting, but no problem. Okay.

• 22:02Speaker 06

  Here's a proposition. This very proposition is false.

• 22:11Speaker 06

  Now, if this proposition is false, then it's true.

• 22:18Speaker 06

  But if it's true, then it's false.

• 22:24Amory Sivertson?

  So self-reference can get us into the realm of paradoxes, contradictions.

• 22:29Speaker 06

  Contradictions are terrible. They boggle the rational mind.

• 22:35Ben Brock Johnson?

  Gödel'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.

• 22:49Amory Sivertson?

  This is at the heart of the thing he's really known for, his famous incompleteness theorems.

• 22:56Speaker 06

  What Gödel did is that he actually used a statement that can refer to itself 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...

• 23:38Speaker 06

  To formalize mathematics, to root out all inconsistencies, and to show that anything that's mathematically true can be provable. And that's what Gödel proved was impossible. That's what his proof is about.

• 23:59Ben Brock Johnson?

  By the way, Gödel wrote two incompleteness theorems, package 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.

• 24:14Amory Sivertson?

  As demonstrated by statements like, "This sentence is false," self-referential statements, which finally brings us back to the loophole.

• 24:24Speaker 06

  Have I? I haven't said at all what we think the loophole was, right?

• 24:30Ben Brock Johnson?

  No, I'm still waiting.

• 24:31Speaker 06

  Okay, long build up.

• 24:34Ben Brock Johnson?

  Yeah, that's good.

• 24:35Speaker 06

  Long drum roll.

• 24:36Ben Brock Johnson?

  What many people think the loophole could be, given Gödel's appreciation for self-reference and contradictions.

• 24:43Speaker 06

  It involves Article 5 of the Constitution.

• 24:48Ben Brock Johnson?

  Which, as Anne Marie knows very well, is--

• 24:51Amory Sivertson?

  Something very similar to you, which we all know is--

• 24:54Speaker 06

  Yes.

• 24:55Amory Sivertson?

  Article 5 sets out the amendment process, that the Constitution can be amended if 2/3 of both Houses of Congress vote on a proposed amendment and 3/4 of state legislatures vote to ratify it.

• 25:10Speaker 06

  The amendment process can be used to apply to itself. So self-referential.

• 25:22Ben Brock Johnson?

  Yeah, here we go.

• 25:23Speaker 06

  And let's say there's a very determined majority in the House and in the Senate.

• 25:33Ben Brock Johnson?

  Okay.

• 25:34Speaker 06

  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 process itself. The amendment process can be amended.

• 26:00Ben Brock Johnson?

  Yep.

• 26:00Speaker 06

  Self-reference, right? And then-- Once that happens, the bar is lowered to all further amendments.

• 26:11Ben Brock Johnson?

  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.

• 26:27Speaker 06

  Anything can happen.

• 26:30Ben Brock Johnson?

  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.

• 26:43Amory Sivertson?

  Still, this is what a lot of scholars and lawyers and reditors think Goedel 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 citizenship test.

• 26:58Ben Brock Johnson?

  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, Goedel had other existential questions on his mind.

• 27:18Amory Sivertson?

  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.

• 27:29Ben Brock Johnson?

  He also struggled. His friend Einstein died in 1955, and Goedel 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.

• 27:49Amory Sivertson?

  In 1977, Adele was hospitalized for several months. Goedel essentially stopped eating. He died of starvation in January the following year, weighing only 65 pounds.

• 28:08Ben Brock Johnson?

  But since Gödel 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, Gödel came out of his shell.

• 28:21Amory Sivertson?

  And during that rare and fleeting moment, Gödel and Rebecca, our Gödel guide, who was getting her PhD in the philosophy of science at the time, ended up at the same party.

• 28:33Speaker 06

  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.

• 28:45Ben Brock Johnson?

  The Greta Garbo of pure reason.

• 28:47Speaker 06

  Oh, my God. He would not like that analogy. But that's how I thought of him.

• 28:53Amory Sivertson?

  You know, Greta Garbo, 1930s actress.

• 28:57Speaker 06

  I 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.

• 29:10Ben Brock Johnson?

  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.

• 29:26Speaker 06

  I wanted to ask him a question so much, but I was so intimidated. It was like, you know, asking...

• 29:34Amory Sivertson?

  What did you want to ask?

• 29:35Speaker 06

  That question. Did he think that his first incompleteness theorem implied that our minds can't be digital computers? Did he make that leap?

• 29:52Speaker 06

  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 Gödel that question, you know? I've regretted that my entire life.

• 30:11Amory Sivertson?

  Rebecca's not the only one who regrets not being able to ask Gödel 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.

• 30:27Ben Brock Johnson?

  Here's one more little loop for you. Gödel's incompleteness theorem talks about how things that are true might not necessarily be provable. Let's go back around to a contemporary of Gödel 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 Turing test, which is really important now that we are always trying to figure out whether something is AI or not.

• 31:02Amory Sivertson?

  Well, Alan Turing was reportedly directly inspired by Gödel's incompleteness theorem. In fact, Turing developed his own math problem inspired by the incompleteness theorem.

• 31:14Ben Brock Johnson?

  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.

• 31:26Amory Sivertson?

  You're dang right it is.

• 31:28Ben Brock Johnson?

  But have you ever seen the beginning of the movie Fantasia?

• 31:31Amory Sivertson?

  Where Mickey Mouse uses the sorcerer's wand 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.

• 31:46Ben Brock Johnson?

  The Sorcerer's Apprentice. In this example, the brooms are AI, Mickey is us, we are Mickey.

• 31:57Amory Sivertson?

  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.

• 32:20Amory Sivertson?

  When it comes to this relationship between us and the machines, Gödel's incompleteness theorem and connected ideas don't just have mathematical utility, they also have philosophical utility.

• 32:33Ben Brock Johnson?

  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.

• 33:06Speaker 06

  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 not well 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 formal systems.

• 33:35Amory Sivertson?

  Falling in love, writing real poetry that captures the human spirit, translating Goebbelsberger, we're 3-0 against the machines.

• 33:51Amory Sivertson?

  Rebecca might never know or be able to prove what Gödel 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.

• 34:09Ben Brock Johnson?

  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 Gödel'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.

• 34:39Ben Brock Johnson?

  Is where we have to land, some version of making peace with incompleteness.

• 34:56Ben Brock Johnson?

  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.

• 35:06Amory Sivertson?

  Thanks to Derek Pensler, professor of German at Harvard University, who, with help from Lea Simon at the Jewish Museum of Berlin, and professor Dr. Irmela von der Ley, helped us find Gobbelsberger translator Max Kricker. Thank you to all of these people for aiding our quest to translate Gödel's loophole.

• 35:25Ben Brock Johnson?

  Also, thank you as well to my neighbor, Tomo Feldman, for some quick live interpretation, and to Vincent Kristlein for speaking to Grace about Gobbelsberger and AI.

• 35:36Amory Sivertson?

  If you want to try your hand at learning Gobbelsberger and translating some of the notes, we've uploaded scans to our website, wbur.org/endlessthread. Good luck. Thank you to the Institute.

• 35:48Ben Brock Johnson?

  Good luck.

• 35:49Amory Sivertson?

  Good. It's pretty good. Thank you, thank you to the Institute of Advanced Study at Princeton for permission to let us upload those.

• 35:57Ben Brock Johnson?

  This episode was produced by Grace Tatter and written by Grace Tatter and me, Ben Brock Johnson. I also co-hosted it with?

• 36:05Amory Sivertson?

  Me, Amory Sivertson, editing by Meg Cramer and Dave Shaw, mix and sound design by our production manager, Paul Vikes. The rest of our team is Dean Russell, Kalyani Sikhsana, Emily Jankowski, and our senior managing producer, Sumit Joshi.

• 36:19Ben Brock Johnson?

  Endless Thread is a show about the blurred lines between dictatorship and a functioning democracy. If you have an untold history, an unsolved mystery, or some other wild story from the internet, hit us up, [email protected]. And good luck to us all.

• 36:57Speaker 00

  Support for this podcast comes from Is Business Broken?, a podcast from the Marotra Institute at BU Questram School of Business. Follow Is Business Broken? wherever you get your podcasts and listen on for a preview of a recent episode featuring Janet Kang, Executive Director of the Just Horizons Alliance, on who stands to benefit from AI in education.

• 37:19Speaker 06

  I am absolutely in favor of AI in learning in the right context. And just to claim why you're excited about it. Oh my gosh, individualized support, right? Personalization and to be able to scale quality education in places where it was historically impossible. So for certain kinds of learners with different kinds of learning styles and disabilities, for example, speakers of different languages, there are amazing ways AI can boost learning. It just has to be with the right context and age appropriateness is something we do a lot of work in because it is very different depending on where in that maturity cycle you are in terms of how your brain develops.

• 37:58Speaker 00

  Find the full episode by searching for Is Business Broken? wherever you get your podcasts and learn more about the Marotra Institute for Business Markets and Society at ibms.bu.edu.

• 38:18Speaker 07

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• 38:46Speaker 06

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