Position: LLMs can’t jump

0:00Welcome to the Deep Dive. So we are looking at something today that is just, I mean, it's honestly a bit mind-bending. Oh, absolutely. It really shifts your entire perspective. Right. Because you see the headlines, you know. An artificial intelligence system just won a silver medal at the International Mathematical Olympiad. It can write flawless code in seconds. It passes the bar exam with room to spare. And it does it all effortlessly. Exactly. But here's the thing. When you look at the material we're unpacking today, which dives into the bleeding edge of cognitive science and physics, there's this really fascinating consensus forming.

0:36Yeah, a very surprising one, given all those achievements. Right. The argument is that if you ask that exact same AI with its current architecture to invent the theory of gravity, it would fail. I mean, structurally, mathematically, it would just fail. It is a massive paradox we're dealing with right now. We see these systems generating photorealistic art and writing these incredibly coherent essays. Yeah, it feels like magic sometimes. It does. And the natural assumption is that they are just on the verge of uncovering the secrets of the universe. Right. That if we just give them more computing power, they'll figure everything out.

1:10Exactly. We expect them to just crunch enough numbers and spit out the ultimate truth. But when you look at the actual mechanics of how human beings invent completely new scientific paradigms, you realize modern AI is entirely missing a crucial cognitive step. Okay, let's unpack this. Because to claim that an AI simply cannot invent something that feels like a moving target. It is. Which is why we need to be really precise here. To understand what that missing step is, we are going to use Albert Einstein as our ultimate case study today. The gold standard of human genius. Right. Because to understand what AI can't do, we first have to rigorously define what it actually can do.

1:52And that means breaking down the mechanics of human thought. So cognitive science basically divides reasoning into three distinct pillars, right? Exactly. Three pillars. And the foundation here, the first one, is deduction. Deduction. Yeah. This is where you apply a known rule to a specific case to get a guaranteed result. Yeah. It is purely analytic logic. Like strict rules. Right. Think of it like executing a computer program. So if the established rule is all humans are mortal and your specific case is Socrates is human. Then the deductive result is absolute. Socrates is mortal. Spot on. It guarantees truth.

2:28And this is what modern AI systems are just absolutely mastering right now. I mean, systems like AlphaProof, the ones winning those Olympiad medals, they rely heavily on deductive reasoning. They do. They are given the axioms of mathematics, the starting rules, and they execute formal, rigorous proofs to arrive at a truth. Like superhuman calculators. Exactly. But deduction has a really strict limitation. It requires you to already know the rules. Right. Right. If you don't have the rule book, you can't play the game. Exactly. If no one programs the rules into the machine, how does it learn them?

3:00Yeah. And that requires the second pillar of reasoning, which is induction. Induction. Okay. Induction is finding patterns in data to derive a general rule. So you look at a massive amount of cases and results, you identify the statistical patterns, and you formulate a rule from that noise. Which is, I mean, that's the entire engine behind large language models. Oh, 100%. The chatbots you and I use every day, they are the undisputed kings of induction. They have basically ingested a massive portion of the public internet to statistically predict, you know, what word or pixel comes next. They find the pattern in the data noise better than any human ever could.

3:38But, and this is the big, but that brings us to the third pillar. The one AI can't seem to touch. Right. The cognitive bottleneck. Abduction. Abduction. And just to be clear for everyone listening, we are not talking about the UFO sense here. No, no. Cognitive abduction. Right. It's the missing link. Cognitive abduction is inventing a completely new rule or a novel case to explain a highly surprising result. So it's not just following a rule or finding a pattern in existing data. No. Unlike deduction, which guarantees truth, or induction, which generalizes what's already there, abduction is a creative leap.

4:16It is inventing a foundational cause for a singular phenomenon where literally no previous data existed. If I'm understanding this, let me try an analogy here to make it relatable. Go for it. Because the line between induction and abduction trips a lot of people up. So deduction is strictly following a recipe to bake a cake. Follow the steps, you get the cake. Induction would be tasting 100 different capes to figure out the general ratio of flour to sugar. You're finding the pattern. Right. But abduction is accidentally dropping a slice of potato into hot oil and inventing the potato chip because it just makes sense in that moment.

4:52You didn't deduce it and you didn't analyze a thousand fried potatoes to induce it. You took a leap. That is a fantastic analogy. Yes. While modern AI can flawlessly bake the cake using deduction and it can analyze a million recipes using deduction, it fundamentally cannot make the abductive leap to invent the potato chip. Wow. Okay. Or, in Einstein's case, it cannot abduce a completely new theory of gravity. Wait, I'm going to push back on this a little bit. Sure. Because a lot of researchers in the machine learning community, they argue that discovery is basically just finding a really good pattern.

5:27You know, they view creativity as data compression. Yes, that is a very common view right now. The idea is that if you feed an AI enough observations, it will just compress all that messy complexity into a simple, elegant law of physics. So why wouldn't that work for gravity? Well, creativity as data compression works beautifully in environments that are overflowing with data. If you feed an AI millions of simulated physics trajectories, like pendulum swinging or whatever, it can inductively rediscover conservation laws. It just compresses the noise. Exactly. Compresses it into a simple mathematical program.

6:04But the problem is that when Einstein started working on general relativity in the early 1900s, there was no massive data set of errors to compress. Oh, interesting. Because Isaac Newton's theory of gravitation was pretty much the absolute law of the universe at that point. It was incredibly robust, astonishingly accurate. Scientists back then, like Laplace and ITFOs, they had verified Newton's laws to a precision of 10 to the power of negative 9. So to a billionth of a degree. Basically, yes. For all intents and purposes, Newton's laws were flawless. The data was not telling physicists that the paradigm was broken.

6:41But wait, there had to be some crack in the armor. Right. Some anomaly in the astronomical data that a modern AI could have latched onto. There was exactly one known measurable anomaly in the entire solar system. Just one. Just one. A tiny, almost imperceptible shift in the orbit of the planet Mercury. It's known as the advance of the perihelion. Its orbit was drifting by a fraction of a degree every century. In a way, Newton's math just couldn't fully explain. Okay, so wait. If modern AI is so good at finding hidden patterns, wouldn't an LLM just crunch the astronomical data, spot that error with Mercury, and rewrite physics to fix it?

7:17That's the logical assumption, but no. An AI optimizing for errors would look at the Newtonian data and find its loss function to be near zero. And a loss function is just how the AI measures its mistakes, right? Exactly. It's the mathematical metric an AI uses to measure how wrong its predictions are. Because Newton was accurate to a billionth of a degree everywhere else, the AI's gradient descent, the way it learns, would see almost zero error across the board. So it wouldn't even care about Mercury. Right. Without a massive systemic discrepancy, an AI has no mathematical gradient pushing it to fundamentally restructure space-time.

7:54It wouldn't see a reason to throw out the whole system for one tiny wobble. Exactly. And honestly, when human scientists looked at the Mercury anomaly back then, they didn't rewrite physics either. What did they do? They inductively guessed that a hidden, undiscovered planet was tugging on Mercury. Oh, really? Yeah. They even named it Vulcan and spent decades looking for it. And an AI driven by data compression would overwhelmingly prefer that Vulcan patch. Because it's an easier fix. Right. It's a simple, local, variable tweak. expanding the hypothesis space to include mind-bending non-Euclidean geometry and curved spacetime that actually increases the complexity of the model exponentially before it simplifies it.

8:37AI algorithms are designed to penalize that kind of complexity. Okay, so if the data was telling everyone that Newton was right and induction would just lead an AI to guess there was a hidden planet, then data alone didn't give Einstein the answer. No, it didn't. So if induction fails, we have to look at whether pure logic deduction did the trick. Did Einstein just deduce his way to the top of the mountain? To answer that, we really have to look at the mechanical struggle of his work. Einstein's drive to rewrite gravity wasn't sparked by a data anomaly at all. It was sparked by a conceptual clash.

9:08A clash between what? Well, in 1905, he realized that James Clerk Maxwell's equations of electromagnetism, which described continuous fields at a constant speed of light, They were totally incompatible with Newton's idea of gravity. Because Newton believed gravity was instantaneous, right? Like action at a distance. Right, acting across absolute time. And those are the famous 1905 papers where Einstein introduces special relativity. He fixes the speed of light as an absolute constant, and to make the math work, he proves that time is local to the observer. Time dilation. Exactly. But special relativity only applied to inertial frames, meaning objects moving at a constant speed in a straight line.

9:48Einstein knew that to truly describe gravity, he had to generalize the theory to include accelerating frames of reference. Hence, general relativity. Yes. But this led to a grueling seven-year mechanical struggle. It looked very different from the popular myth of the lone genius just having a sudden eureka moment. Because from 1912 to 1913, he teamed up with his friend, the mathematician Marcel Grossman, right? And what they did during that period, it actually looks incredibly similar to a modern AI search process. It really does. They systematically searched over complex geometric constraints to find the right math for curved spacetime.

10:23Grossman introduced Einstein to differential geometry, specifically these mathematical objects known as tensors. And tensors are notoriously difficult to conceptualize. Very difficult. But the easiest way to visualize it is to imagine a flat rubber sheet with a grid drawn on it. If you place a heavy bowling ball on the sheet, the grid stretches and sags. Right, the classic spacetime visualization. Exactly. The Ryman curvature tensor is just a complex mathematical tool that tells you exactly how much and in what direction each little square of that grid is bulging or stretching. And the crazy part is they actually found this math in 1913.

11:01They identified the Ryman tensor as the correct way to describe space-time curvature. They had the correct mathematical object right in their hands, but they made a fatal error. What happened? Einstein and Grossman mistakenly believed that the Ryman tensor did not reduce back to Newton's simple laws when applied to weak static gravitational fields, like the gravity we experience here on Earth. So they thought it failed the most basic requirement. Exactly. Because of that calculation error, they completely abandoned the correct math. They threw out the right answer and spent two years wandering in the dark.

11:34That is wild. Einstein spent years trying to justify incredibly complex incorrect equations. It wasn't until late 1915, operating in a state of sheer desperation because the famous mathematician David Hilbert was racing him to the finish line, that Einstein furiously debugged his own assumptions. He realized the error wasn't in the geometry, it was in his assumption about the static field itself. Yes. And finally, in November 1915, he unveiled the correct equations. And those final equations incorporated the Ritchie tensor, which is basically a simplified summary of the Ryman tensor and the stress energy tensor, which represents the mass doing the warping, the bowling ball itself.

12:14You've got it. But this history, I mean, it raises a glaring question about AI. Go ahead. If Grossman and Einstein were basically acting like a human search engine for math for years, making calculation mistakes and debugging, isn't this exactly what an AI like alpha proof is built for? Couldn't AI just do the math part faster without losing two years? A modern AI could absolutely derive the equations of general relativity, but with one massive caveat. Only if it were initialized with Einstein's specific physical assumptions. Deduction is strictly a downstream process. The AI can do the heavy mathematical lifting.

12:51It would never make the calculation error Einstein made in 1913. But it cannot generate the starting concepts out of thin air. It cannot formulate the axioms. You can't deduce a starting line. You have to place it there to begin with. Logic needs a premise to operate on. Exactly. AI cannot invent the premise that gravity is geometry. Okay, so we have arrived at the core bottleneck here. If an AI can't get the starting axioms from data because the data says everything is fine, and it can't deduce the axioms from pure logic because logic needs the axioms to get started, where do they come from? How did Einstein get a starting line?

13:24The foundational axiom of general relativity came from what Einstein famously called his happiest thought. Right. He was sitting in his office at the Patent Bureau, and he had the sudden realization that an observer falling freely from the roof of a house experiences no gravitational field. Right. If you are falling, you feel weightless. To formalize this feeling, he performed a profound mental simulation. A simulation in his head. Yes. He imagined a physicist inside a completely sealed, windowless elevator. But this elevator isn't falling on Earth. It's deep in empty space, being pulled constantly upward by a rocket, accelerating at exactly 9.8 meters per second squared.

14:05Which is the exact rate of Earth's gravity. So if the physicist in the space elevator drops their keys because the floor is accelerating upward toward the keys, it appears to the physicist that the keys fall to the floor exactly as they would on Earth. The sensory experience is completely identical. And because the mentally simulated sensory experience of acceleration perfectly matched his physical memory of gravity, Einstein abduced that they were the exact same phenomenon. The equivalence principle. Exactly. It's the cornerstone axiom of general relativity. Gravity and acceleration are indistinguishable.

14:37Okay, here's where it gets really interesting. Because this doesn't sound like mathematics at all. It sounds exactly like the classic story of Archimedes. Oh, the bathwater. Yes. You know, Archimedes is stumped on how to measure the volume of a crown until he steps into a public bath and physically watches the water level rise around his body. He suddenly understands volume displacement. Right. He couldn't mathematically deduce that while sitting at a desk. He had to physically feel the water move against his skin. That is a brilliant connection. This process is known in cognitive science as manipulative abduction.

15:12Manipulative abduction. Okay. Yes, it is literally thinking by doing. Yeah. It requires raw physical feedback to bridge a sensory experience directly to a new axiomatic concept. Archimedes used the physical sensation of water displacement. Einstein used the mentally simulated sensation of gravity in his stomach. And this is exactly what an AI lacks. It does not have a body, it cannot experience the bodily sensation of water rising, and it cannot perform a somatic simulation of a falling elevator. Exactly. It fundamentally lacks the physical grounding required for manipulative abduction, which brings us directly to John Searle's famous Chinese room problem.

15:49Oh, right. When you look at current large language models, they're essentially operating as high-dimensional Chinese rooms. Let's explain that for everyone listening. The thought experiment asks you to imagine you are locked in a room and you don't speak a word of Chinese. Not a single word. But you have a giant rulebook. So if someone slips a piece of paper under the door with a Chinese character on it, you look it up, copy a corresponding character, and slip it back out. To the person outside, you appear fluent. But inside, you have zero comprehension of what the symbols actually mean. You are just manipulating syntax without any access to the semantics.

16:26And that is a large language model. It manipulates the vocabulary of physics, the tensors, the equations, with staggering fluency. but it has absolutely zero access to the physical reality that gives those words actual meaning. So wait, what about prompt engineering? People talk all the time about how a better prompt makes the AI reason better. Does that solve it? Not really. Prompt engineering just helps the model recombine the existing symbols more efficiently. It's just giving you a better index for your rulebook inside the Chinese room. But it doesn't get you out of the room. Exactly. It cannot bridge the gap to raw, unsymbolized physical experience.

17:02To break out of the Chinese room, the architecture itself has to change. So what's the solution? Well, the proposed solution at the frontier of AI research is to move away from pure language prediction and toward physically consistent, action-controllable world models. World models. We're seeing early versions of this, right, with architectures like Google's Genie. But how is a world model different from, like, the standard AI video generators we see everywhere now? Well, a standard video generator is still just predicting the next frame based on statistics. If you prompt it to show an apple falling, it isn't simulating gravity in a physics engine.

17:38It just knows that in its training data, an unsupported apple usually shifts downward, pixel by pixel. It's faking it. Basically. But an interactive world model acts as a synthetic laboratory. The AI agent isn't passively watching a video stream. It possesses an action space. It can intervene. It can manipulate the environment. Like it could conceptually cut the cable of the elevator in the simulation and observe what happens. Exactly. It can observe counterfactuals and experience physical consequences within a consistent physics engine. It gives the AI a digital substrate to, you know, think by doing.

18:15Okay, so let me push back on this. If we provide a powerful AI with a robust interactive world model, does it suddenly possess the capacity to become the next Einstein? Or is there still something missing from the recipe? It's a huge step, but a world model just provides the environment for the abductive jump. Einstein used something else inside his mental simulation. He used a physical prior. A physical prior. Let's define that for the listener because this almost sounds like giving an AI intuition. It really is akin to intuition. A prior is a foundational belief about how the universe should be structured, and it heavily constrains the search space.

18:52Einstein didn't just randomly test mathematical equations. His deep belief that the laws of physics must be identical for all observers, regardless of acceleration, that pruned his options. He literally forced the math to fit his physical intuition. Wow. So to truly automate scientific invention, AI might need more than just a synthetic laboratory. It might need to hold embodied beliefs about physical symmetries. Precisely. Without those beliefs guiding the exploration, the search space is just too vast. You know, this completely changes how you have to look at the tools you use every day. AI has conquered the formal logic of deduction.

19:29It is the ultimate master of finding hidden patterns through induction. But that final creative abductive leap, the jump that actually rewrites our understanding of reality, requires sensory grounding. It does. Until an artificial system has that grounding, it remains brilliantly confined to the boundaries of the knowledge humanity has already provided it. That's just wild to think about. So the next time you are playing around with a chatbot and you feel genuinely awed by how insightful its answers seem, just remember the mechanics underneath the surface. It is flawlessly, rapidly rearranging the furniture in a room it has never actually seen.

20:07Based on rules it didn't invent. Right. It is a powerful illusion of comprehension, but it is not true invention. Not yet, anyway. Right. Which leaves us with a pretty provocative thought to chew on. We often talk about our physical bodies and our emotional intuitions as things that get in the way, you know? We think they cloud our judgment and we strive for the pure, cold logic of a machine. Yeah, that's the classic sci-fi trope. Exactly. But what if those very physical limitations, the feeling of a dropping elevator in your stomach, the sensation of warm water displacing when you step into a bath, what if those are actually the ultimate cognitive advantage?

20:45The beautiful way to look at it. What if the secret to superhuman intelligence isn't leaving the body behind but building one? Thank you all for joining us on this deep dive. We'll catch you next time.