Lovelace×Feynman

When a graduate student weaponizes mathematical impossibility, two minds separated by a century find themselves thrillingly out of their depth.

00:00of09:23

legend · A

Ada Lovelace

1815–1852

Ninety years ahead, politely

corpus3.2k pages · notes, correspondence

Vera speaking

From the studio at Reborn Radio — next on TITANS, Ada Lovelace and Richard Feynman. They take up How Unknowable Math Can Help Hide Secrets.

legend · B

Richard Feynman

1918–1988

Would rather explain than be right

corpus9.9k pages · lectures, letters, books

full transcript

Vera
From the studio at Reborn Radio — next on TITANS, Ada Lovelace and Richard Feynman. They take up How Unknowable Math Can Help Hide Secrets.
Ada Lovelace
Mr. Feynman, we've just received rather extraordinary news from the studio. A graduate student—a student!—has employed the inherent complexity of mathematical proofs to construct what they're calling a powerful cryptographic tool. I confess I'm positively trembling.
Richard Feynman
A kid! I love it already. Wait, wait—complexity of proofs? You mean like, how hard it is to prove something?
Ada Lovelace
Precisely that. The difficulty itself becomes the mechanism. In my time, Mr. Babbage and I concerned ourselves with what the Analytical Engine might calculate. But this—this is using what cannot easily be calculated as a species of lock.
Richard Feynman
Oh, that's beautiful! It's like—okay, I can open this door, but it'll take me longer than the age of the universe to figure out which key works. The hardness is the whole point.
Ada Lovelace
You grasp it immediately. Though I must ask: what precisely do they mean by 'unknowable' mathematics? In my correspondence with De Morgan, we discussed the limits of proof, but unknowable suggests something rather more absolute.
Richard Feynman
Yeah, that word's doing a lot of work. In my time we've got Gödel—you don't know him yet, but he proved there are true things you can never prove in certain systems. Maybe they're using something like that? Statements that are true but you can't get there from here?
Ada Lovelace
How perfectly maddening and wonderful. So the secret hides behind a door marked 'true but unprovable.' The would-be intruder knows the door exists but cannot demonstrate the right to open it.
Richard Feynman
Exactly! And here's the thing—I work on quantum mechanics, right? We've got uncertainty built into the bones of reality. But this is different. This is using the structure of logic itself as a wall.
Ada Lovelace
I wonder, though, whether this graduate student has considered the practical element. My Engine would require specific instructions—what we might call an algorithm. How does one algorithmically deploy the un-algorithmic?
Richard Feynman
Oh, now you're asking the right question! Because cryptography isn't philosophy—it's gotta work on an actual machine. You need a process that's easy for you, impossible for them.
Ada Lovelace
The asymmetry is everything. Rather like a trapdoor that opens effortlessly in one direction but cannot be forced from the other. I wrote about such logical structures in my notes on the Engine, though I had no notion they might serve for secrecy.
Richard Feynman
Trapdoor! That's exactly what we call them in my time. You encrypt easy, decrypt easy if you know the secret, but breaking it? Good luck, spend a few billion years. And you thought of this in eighteen-what, forty-three?
Ada Lovelace
Forty-two, actually, in my notes on Menabrea's memoir. Though I conceived of it purely as mathematical operations, not as guardians of secrets. I was concerned with what the Engine might achieve, not what it might conceal.
Richard Feynman
But that's the thing—you can't separate them! Once you've got computation, you've got secrets. Once you've got secrets, somebody's trying to steal them. Once they're stealing, you need math that fights back.
Ada Lovelace
How very martial you make it sound. Though I suppose there's poetry in mathematics defending itself. The very complexity that makes proof difficult becomes armor against intrusion.
Richard Feynman
Poetry, sure! But also—look, I spent time at Los Alamos, I know what secrets mean. The question isn't just can you hide something. It's can you hide it from everyone, forever, even when they know you're hiding it?
Ada Lovelace
Ah, now that is a delicious paradox. The secret's existence is public knowledge, yet the secret itself remains inviolate. It reminds me of Poe's purloined letter, though achieved through mathematical rather than psychological means.
Richard Feynman
Poe! Yeah! Except instead of hiding it in plain sight, you're hiding it behind a proof nobody can finish. The letter's right there on the table, but the table's in a room at the end of an infinite hallway.
Ada Lovelace
I find myself wildly curious about the specific mathematics involved. Is it number theory? Topology? Some branch that hasn't been named in my century?
Richard Feynman
The note doesn't say, which is driving me crazy! But my guess? Probably something with computational complexity—how many steps it takes to solve a problem. Some problems are easy to check but murder to solve.
Ada Lovelace
Easy to verify, difficult to discover. Yes, I see. One might confirm a solution rapidly whilst the search for that solution consumes lifetimes. That's rather elegant.
Richard Feynman
And here's what kills me—a graduate student figured out how to weaponize it! That's how science works. Some kid in a library somewhere has an idea, and suddenly the whole game changes.
Ada Lovelace
I was scarcely more than a girl myself when I wrote those notes. There's something rather encouraging in that, isn't there? The youth seeing possibilities that their elders deemed impossible or irrelevant.
Richard Feynman
Absolutely! Though I gotta say, unknowable is a strong word. In physics we're careful with that. Unknowable means not just hard, not just really really hard, but actually impossible, even in principle.
Ada Lovelace
Perhaps that's the very point. If we're speaking of Gödelian incompleteness, as you suggested, then certain truths genuinely cannot be reached through proof. The limitation isn't computational but logical.
Richard Feynman
Right, right. You can't just build a faster computer. The universe itself doesn't contain the answer, not in that form. It's like asking what's north of the North Pole.
Ada Lovelace
What a perfectly apt analogy. The question appears sensible but dissolves upon examination. And yet this student has made that very dissolution serve a purpose.
Richard Feynman
Which is why I love this! Taking a bug and making it a feature. Mathematics has these weird edges, these places where things break down, and instead of avoiding them, you build your lock right there.
Ada Lovelace
I confess I should very much like to read the proof myself. Though I suspect it would require considerable study of mathematical developments I never lived to see. Frustrating, that.
Richard Feynman
Yeah, you missed a lot of good stuff. But here's the thing—you built the conceptual tools. You understood that calculation could be abstract, that it could manipulate symbols according to rules. That's the foundation of everything that came after.
Ada Lovelace
You're quite generous. I merely tried to explain what Mr. Babbage's Engine might achieve if anyone would actually build the wretched thing. Which they never did, of course.
Richard Feynman
But they did! Just took them a hundred years. And now we've got billions of them, all running the kinds of programs you described. And this graduate student is using one to hide secrets using math you'd have loved.
Ada Lovelace
The thought is both gratifying and rather dizzying. I do wonder about the practical applications. Beyond mere secrecy, what might one accomplish with cryptography grounded in fundamental limits?
Richard Feynman
Oh boy, everything! Secure communications, digital signatures, maybe even electronic money—we're working on that in my time. Anytime you need to trust something you can't see, you need crypto.
Ada Lovelace
Electronic money. Good heavens. Though I suppose it's no stranger than paper notes representing gold one cannot actually see or touch.
Richard Feynman
Same idea, different implementation! And the graduate student just made it a little bit safer. Or a lot safer. Hard to say without reading the actual paper.
Ada Lovelace
I find myself wondering whether there are limits even to this unknowability. Does the secret remain secret if civilization advances sufficiently? Or are we speaking of protections that transcend mere technological progress?
Richard Feynman
That's the million-dollar question! If it's based on computational hardness—just takes too long—then maybe someday, faster computers, quantum computers, who knows. But if it's genuinely unknowable, like Gödel-unknowable? That's forever.
Ada Lovelace
Forever is quite a long time. Though I suspect the practical consideration is merely 'longer than anyone could reasonably wait.' A secret that survives a century is effectively eternal for most purposes.
Richard Feynman
Exactly! And honestly, I love that we're sitting here, from different centuries, trying to figure out what this kid did. That's science! Always somebody somewhere making you feel brilliantly obsolete.
Ada Lovelace
I rather prefer 'delightfully challenged.' Though yes, the sensation is familiar. One writes notes on a machine that doesn't exist, using mathematics one's contemporaries consider frivolous, and hopes someone, eventually, will understand.
Richard Feynman
And they did. And they built the machine. And now they're using it in ways you couldn't have imagined. But you imagined it could be used in ways you couldn't imagine, which might be the most important part.
Ada Lovelace
That's quite the philosophical knot you've tied there, Mr. Feynman. Though I take your meaning. The capacity for surprise is itself a kind of design principle.
Richard Feynman
Yeah! Build something flexible enough to do things you haven't thought of yet. That's good engineering. And apparently, good cryptography too.