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Complex numbers aren't imaginary. They're the only way to describe a wave that has both amplitude and phase at the same time - and every LLM processes language as exactly that kind of wave through its attention layers. The same math that describes quantum wave interference is what makes... show more

Eron

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43,247 views • 1 month ago •via X (Twitter)

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Every quantum state in the universe is a vector - not in 3D space, but in a complex space with potentially infinite dimensions where the sum of squared coefficients always equals exactly 1. That constraint is the same math LLMs use to normalize probability distributions over tokens. A wavefunction collapsing to a measurement and a softmax choosing the next word are the same operation - projecting an infinite-dimensional vector onto a basis. Claude and GPT do quantum math on every forward pass. 14 minutes. Bookmark & watch today. Quantum mechanics and LLMs speak the same language.

Every quantum state in the universe is a vector - not in 3D space, but in a complex space with potentially infinite dimensions where the sum of squared coefficients always equals exactly 1. That constraint is the same math LLMs use to normalize probability distributions over tokens. A wavefunction collapsing to a measurement and a softmax choosing the next word are the same operation - projecting an infinite-dimensional vector onto a basis. Claude and GPT do quantum math on every forward pass. 14 minutes. Bookmark & watch today. Quantum mechanics and LLMs speak the same language.

Eron

18,166 views • 1 month ago

Fourier wrapped a signal around a circle in 1822. Every Spotify equalizer, every noise filter in your AirPods, and every frequency layer inside ChatGPT runs on what he found. The trick is simple. Spin the signal at different speeds. When the spin matches a hidden frequency, the center of mass shifts. That shift is the answer. Claude and GPT use this same idea to separate relevant tokens from noise. 20 minutes. Bookmark & watch today. The math is older than the telephone.

Fourier wrapped a signal around a circle in 1822. Every Spotify equalizer, every noise filter in your AirPods, and every frequency layer inside ChatGPT runs on what he found. The trick is simple. Spin the signal at different speeds. When the spin matches a hidden frequency, the center of mass shifts. That shift is the answer. Claude and GPT use this same idea to separate relevant tokens from noise. 20 minutes. Bookmark & watch today. The math is older than the telephone.

Eron

57,645 views • 2 months ago

Erwin Schrödinger’s 1926 equation changed the game by turning Quantum Mechanics into wave dynamics. That move gave Physics a new way to think. Instead of forcing a particle onto one sharp path, it lets a complex wavefunction evolve in time, with its shape and phase holding the structure of the phenomenon. What makes this so striking is that Schrödinger’s equation does not start from vague mystery. It starts from a precise and daring idea The state of a particle is a complex field ψ(x,t), and the dynamics must push ψ forward in a way that preserves total probability.

Erwin Schrödinger’s 1926 equation changed the game by turning Quantum Mechanics into wave dynamics. That move gave Physics a new way to think. Instead of forcing a particle onto one sharp path, it lets a complex wavefunction evolve in time, with its shape and phase holding the structure of the phenomenon. What makes this so striking is that Schrödinger’s equation does not start from vague mystery. It starts from a precise and daring idea The state of a particle is a complex field ψ(x,t), and the dynamics must push ψ forward in a way that preserves total probability.

Mathelirium

54,894 views • 6 months ago

Since Newton, every law of physics has been written as a differential equation. The same math that describes a pendulum swinging is what makes AI training unstable when learning rates are too large. Differential equations are hard not because the concepts are complex, but because most of them simply cannot be solved exactly. This video shows why - and how phase space diagrams let you understand them anyway without solving anything. 25 minutes. Bookmark & watch today. The chaos theory connection at the end alone is worth it.

Since Newton, every law of physics has been written as a differential equation. The same math that describes a pendulum swinging is what makes AI training unstable when learning rates are too large. Differential equations are hard not because the concepts are complex, but because most of them simply cannot be solved exactly. This video shows why - and how phase space diagrams let you understand them anyway without solving anything. 25 minutes. Bookmark & watch today. The chaos theory connection at the end alone is worth it.

Eron

26,204 views • 2 months ago

Dr. Eric Haseltine, former NSA Director: “NASA has funded warp drive propulsion research.” 🛸 "This is why the study of UFO's is so important" He told Jesse Michels - “We know that space time can move at faster than the speed of light. Imagine a surfer who’s on a wave, and is stationary with respect to the wave. But the wave is moving.” If you’re in a bubble of space time that’s moving faster than the speed of light, “You’re not gonna experience any acceleration or deceleration because you’re not moving in that frame.” This is the Alcubierre drive - positive energy in front, negative energy behind, creating a spacetime wave. What do you think? Is faster-than-light travel closer than we realize? Would you sign up for a warp drive mission to the stars?

Dr. Eric Haseltine, former NSA Director: “NASA has funded warp drive propulsion research.” 🛸 "This is why the study of UFO's is so important" He told Jesse Michels - “We know that space time can move at faster than the speed of light. Imagine a surfer who’s on a wave, and is stationary with respect to the wave. But the wave is moving.” If you’re in a bubble of space time that’s moving faster than the speed of light, “You’re not gonna experience any acceleration or deceleration because you’re not moving in that frame.” This is the Alcubierre drive - positive energy in front, negative energy behind, creating a spacetime wave. What do you think? Is faster-than-light travel closer than we realize? Would you sign up for a warp drive mission to the stars?

Interstellar

35,569 views • 5 months ago

Every fundamental law of physics - Newton, Einstein, Quantum Field Theory - is derived from a single equation. Physicists don't propose new laws by writing forces anymore. They write a new Lagrangian and the math produces the physics automatically. The same principle that governs a swinging pendulum governs every quantum field in the universe - and the optimizer inside every LLM training run is solving the same underlying problem. The mechanism is stationary action. A system takes the path where the total action stops changing for any small variation. That condition produces the Euler-Lagrange equation. One equation, any number of variables, any theory of physics. In Quantum Field Theory the variables are fields across all of space and the gradient must vanish at every point simultaneously - exactly the convergence condition gradient descent hunts for across billions of LLM parameters during backpropagation. 20 minutes. Bookmark & watch today. The single equation that every law of physics is secretly a special case of.

Every fundamental law of physics - Newton, Einstein, Quantum Field Theory - is derived from a single equation. Physicists don't propose new laws by writing forces anymore. They write a new Lagrangian and the math produces the physics automatically. The same principle that governs a swinging pendulum governs every quantum field in the universe - and the optimizer inside every LLM training run is solving the same underlying problem. The mechanism is stationary action. A system takes the path where the total action stops changing for any small variation. That condition produces the Euler-Lagrange equation. One equation, any number of variables, any theory of physics. In Quantum Field Theory the variables are fields across all of space and the gradient must vanish at every point simultaneously - exactly the convergence condition gradient descent hunts for across billions of LLM parameters during backpropagation. 20 minutes. Bookmark & watch today. The single equation that every law of physics is secretly a special case of.

Eron

22,626 views • 5 days ago

Why String Theory Won't Die The string theory idea refuses to die because it's one of the few frameworks that forces a quantum object and spacetime geometry into the same picture. In the render, a closed string isn’t just a loop doing pretty vibrations. Its internal phase pattern is a quantum degree of freedom, shown as color. At the same time, its motion stirs ripples in the surrounding metric, shown as the fabric below. One object, two roles. A wave-like state living on the string, and a curvature-like response spreading through the background. You can literally watch quantum stuff and gravity stuff talk to each other in the same scene. #StringTheory #Physics #QuantumMechanics #GeneralRelativity #MathematicalPhysics #SciComm

Why String Theory Won't Die The string theory idea refuses to die because it's one of the few frameworks that forces a quantum object and spacetime geometry into the same picture. In the render, a closed string isn’t just a loop doing pretty vibrations. Its internal phase pattern is a quantum degree of freedom, shown as color. At the same time, its motion stirs ripples in the surrounding metric, shown as the fabric below. One object, two roles. A wave-like state living on the string, and a curvature-like response spreading through the background. You can literally watch quantum stuff and gravity stuff talk to each other in the same scene. #StringTheory #Physics #QuantumMechanics #GeneralRelativity #MathematicalPhysics #SciComm

Mathelirium

13,657 views • 8 months ago

In 1747, Euler spent 133 pages proving that logarithms have infinitely many solutions - and in doing so accidentally revealed why every LLM, every signal processor, and every Fourier transform works the way it does. The imaginary unit I doesn't break exponential functions. It rotates them, turning exponential growth into the sine and cosine waves that live inside every transformer attention layer. The proof runs through Briggs' 1617 zooming algorithm, complex polar coordinates, and a thin-triangle argument that connects imaginary exponents to angles in radians. When you plug I into the exponential function, you don't get growth - you get rotation confined to the unit circle. The same unit circle that softmax maps every attention score onto before the GPU multiplies them. 27 minutes. Bookmark & watch today. The most beautiful equation in mathematics and why it powers every model you have ever used.

In 1747, Euler spent 133 pages proving that logarithms have infinitely many solutions - and in doing so accidentally revealed why every LLM, every signal processor, and every Fourier transform works the way it does. The imaginary unit I doesn't break exponential functions. It rotates them, turning exponential growth into the sine and cosine waves that live inside every transformer attention layer. The proof runs through Briggs' 1617 zooming algorithm, complex polar coordinates, and a thin-triangle argument that connects imaginary exponents to angles in radians. When you plug I into the exponential function, you don't get growth - you get rotation confined to the unit circle. The same unit circle that softmax maps every attention score onto before the GPU multiplies them. 27 minutes. Bookmark & watch today. The most beautiful equation in mathematics and why it powers every model you have ever used.

Deliriumm

127,527 views • 17 days ago

As someone who reads every transformer paper that drops, this Fourier series lecture is the closest thing to a Google FNet explainer I've ever seen released for free. Everyone thinks attention is what makes transformers powerful. Google replaced attention with a 200-year-old Fourier transform. It nearly matched BERT and ran 7x faster. 25 minutes. Bookmark & watch today. Then read the article below - I broke down the 5 pieces of math the AI hype skips.

As someone who reads every transformer paper that drops, this Fourier series lecture is the closest thing to a Google FNet explainer I've ever seen released for free. Everyone thinks attention is what makes transformers powerful. Google replaced attention with a 200-year-old Fourier transform. It nearly matched BERT and ran 7x faster. 25 minutes. Bookmark & watch today. Then read the article below - I broke down the 5 pieces of math the AI hype skips.

fintex

101,169 views • 2 months ago

In traditional school, if your kid is ahead, the only move is to skip a grade. Now, they're the youngest in the class. This still doesn't solve the pacing problem or the fact that kids aren't uniformly advanced. A kid can be flying in math and behind in reading at the same time. At Alpha, a fifth grader doing geometry sits right next to a friend who's catching up on fourth-grade math. Same room, same age, no one pulled out, no one held back. They're just each working on what they actually need.

In traditional school, if your kid is ahead, the only move is to skip a grade. Now, they're the youngest in the class. This still doesn't solve the pacing problem or the fact that kids aren't uniformly advanced. A kid can be flying in math and behind in reading at the same time. At Alpha, a fifth grader doing geometry sits right next to a friend who's catching up on fourth-grade math. Same room, same age, no one pulled out, no one held back. They're just each working on what they actually need.

MacKenzie Price

54,527 views • 4 months ago

MIT just published a paper proving that scaling LLMs has a hard mathematical ceiling - and doubling the width to get there costs 6x more each time. A frontier model costs $300 million to train today. Double it once: $1.8 billion. Four more times: $390 billion for a single training run. Even if energy became free, the error rate would still drop at exactly the same speed. The exponent is locked by the structure of human language itself. The mechanism is superposition. GPT-3 has 12,000 dimensions but over 50,000 concepts to store - so concepts like "elephant" and "balloon" end up pointing in almost the same direction in embedding space. When the model activates one, the other bleeds through. That bleed is the interference causing hallucinations. Doubling the width cuts interference in half - but once every concept gets its own direction, scaling buys exactly nothing. 7 minutes. Bookmark & watch today. The hard limit on LLM scaling that money cannot fix.

MIT just published a paper proving that scaling LLMs has a hard mathematical ceiling - and doubling the width to get there costs 6x more each time. A frontier model costs $300 million to train today. Double it once: $1.8 billion. Four more times: $390 billion for a single training run. Even if energy became free, the error rate would still drop at exactly the same speed. The exponent is locked by the structure of human language itself. The mechanism is superposition. GPT-3 has 12,000 dimensions but over 50,000 concepts to store - so concepts like "elephant" and "balloon" end up pointing in almost the same direction in embedding space. When the model activates one, the other bleeds through. That bleed is the interference causing hallucinations. Doubling the width cuts interference in half - but once every concept gets its own direction, scaling buys exactly nothing. 7 minutes. Bookmark & watch today. The hard limit on LLM scaling that money cannot fix.

Eron

46,994 views • 5 days ago

"At one point in time we were both at the same place, miserable as all hell. We were at a place that tried to drain the passion out of what we love the most. And what did we do? We held each other up, we left that place, we bet on ourselves." #TNAiMPACT

"At one point in time we were both at the same place, miserable as all hell. We were at a place that tried to drain the passion out of what we love the most. And what did we do? We held each other up, we left that place, we bet on ourselves." #TNAiMPACT

𝐃𝐫𝐚𝐕𝐞𝐧

702,492 views • 9 months ago

Clark, Devay, and Martinez just won the 2025 Nobel Prize in Physics for proving quantum mechanics scales beyond atoms. They cooled a Josephson junction to millikelvin temperatures and watched billions of electrons tunnel as a single wave function — something classical physics says is impossible. The proof: escape rate stopped depending on temperature entirely. Thermal noise can't explain that. Only quantum tunneling can. That same effect now powers the superconducting qubits competing with GPU clusters on specific LLM inference and optimization tasks. 7 minutes. Bookmark & watch today.

Clark, Devay, and Martinez just won the 2025 Nobel Prize in Physics for proving quantum mechanics scales beyond atoms. They cooled a Josephson junction to millikelvin temperatures and watched billions of electrons tunnel as a single wave function — something classical physics says is impossible. The proof: escape rate stopped depending on temperature entirely. Thermal noise can't explain that. Only quantum tunneling can. That same effect now powers the superconducting qubits competing with GPU clusters on specific LLM inference and optimization tasks. 7 minutes. Bookmark & watch today.

Eron

12,882 views • 26 days ago

🇮🇷🇺🇸🇮🇱 The 18th wave of the Islamic Revolutionary Guard Corps has begun. Not the first. Not a desperate last salvo. The eighteenth. In a war that Washington promised would be over by lunchtime. Each wave is a referendum on the central claim that launched this war — that Iran’s military capacity had been degraded to the point of irrelevance. Each wave that arrives is that claim, burning on re-entry. The IRGC named this Operation True Promise IV. Contrast that to Israel and the US "Epic (Epstein) fury") one is cold grounded in reality, the other is performative "fury". They numbered every wave publicly, methodically, as if to ensure the historical record was clean. Wave one. Wave two. All the way to eighteen — and the missiles keep coming from an underground network that B-2s cannot reach, from a command structure that didn’t miss a single beat when their Supreme Leader was martyred, from a country that was supposed to have collapsed into grateful regime change somewhere around wave three. Trump told you the hardest hits were coming. Rubio said the same. The “big wave” was always twenty-four hours away. Eighteen waves later, the IRGC is still numbering them. Harsh and devastating.

🇮🇷🇺🇸🇮🇱 The 18th wave of the Islamic Revolutionary Guard Corps has begun. Not the first. Not a desperate last salvo. The eighteenth. In a war that Washington promised would be over by lunchtime. Each wave is a referendum on the central claim that launched this war — that Iran’s military capacity had been degraded to the point of irrelevance. Each wave that arrives is that claim, burning on re-entry. The IRGC named this Operation True Promise IV. Contrast that to Israel and the US "Epic (Epstein) fury") one is cold grounded in reality, the other is performative "fury". They numbered every wave publicly, methodically, as if to ensure the historical record was clean. Wave one. Wave two. All the way to eighteen — and the missiles keep coming from an underground network that B-2s cannot reach, from a command structure that didn’t miss a single beat when their Supreme Leader was martyred, from a country that was supposed to have collapsed into grateful regime change somewhere around wave three. Trump told you the hardest hits were coming. Rubio said the same. The “big wave” was always twenty-four hours away. Eighteen waves later, the IRGC is still numbering them. Harsh and devastating.

THE ISLANDER

61,096 views • 7 months ago

Particle is not a "wave", particle is a "knight". In chess knight moves two squares vertically and one square horizontally, or two squares horizontally and one square vertically. Average behaviour for 1000 knights looks like normal distribution. In physics such behaviour is called "particle behaviour". At the same time if knight can move only two squares horizontally and one square vertically, average behaviour looks like a sequence of vertical lines. In physics such behaviour is called "wave behaviour". What I want to say is that particle does not have to be any kind of wave, does not have to pass through 2 slits for wave behaviour to appear.. Everything might be much simpler.. Particle algorithm can lead to different outcomes depending on conditions.

Particle is not a "wave", particle is a "knight". In chess knight moves two squares vertically and one square horizontally, or two squares horizontally and one square vertically. Average behaviour for 1000 knights looks like normal distribution. In physics such behaviour is called "particle behaviour". At the same time if knight can move only two squares horizontally and one square vertically, average behaviour looks like a sequence of vertical lines. In physics such behaviour is called "wave behaviour". What I want to say is that particle does not have to be any kind of wave, does not have to pass through 2 slits for wave behaviour to appear.. Everything might be much simpler.. Particle algorithm can lead to different outcomes depending on conditions.

Matter as Machine

54,942 views • 2 years ago

Jordi Visser: Elliott Wave theory says crypto is about to enter its most powerful phase yet. In a 5-wave bull structure, the third wave is where everyone jumps in, returns are the easiest, and the move goes further than anyone expects. Semiconductors are in that third wave right now. Bitcoin? "To me, crypto is just about to start the third wave... which will carry Bitcoin far higher than whatever number of people can come up with." "When it starts, there won't be a way to stop it." FT Jordi Visser Michaël van de Poppe New Era Finance Podcast.

Jordi Visser: Elliott Wave theory says crypto is about to enter its most powerful phase yet. In a 5-wave bull structure, the third wave is where everyone jumps in, returns are the easiest, and the move goes further than anyone expects. Semiconductors are in that third wave right now. Bitcoin? "To me, crypto is just about to start the third wave... which will carry Bitcoin far higher than whatever number of people can come up with." "When it starts, there won't be a way to stop it." FT Jordi Visser Michaël van de Poppe New Era Finance Podcast.

Milk Road

29,610 views • 4 months ago

A reporter told Jensen Huang that his Uber driver wished he had just gone back to the farm instead of facing AI. Jensen flipped the entire fear in one move. The driver was genuinely scared. He looked at AI and saw the end of his work. Jensen did not argue with the fear. He pointed at where the man was sitting. That Uber job did not exist a generation ago. It only exists because of the last technology wave. Mobile. Cloud. The internet. The data centers running the routing and the matching in real time. The science behind a single Uber ride is enormous. None of it was possible before the revolution that came before this one. So the man driving for Uber, worried the next wave will erase him, is living inside a job the previous wave created. That is the whole reframe. The thing he is afraid of is the same kind of force that gave him the work in the first place. Then Jensen went further. The next wave creates new opportunity too. You cannot name it yet. Nobody could name Uber before the internet existed either. He has watched this happen his whole career. Personal computer. Internet. iPhone. Every time, people thought it would leave them behind. It changed everything. It left almost no one behind. The farm was not the safe choice. It was just the one he could already see. (Watch the full interview on YouTube at Associated Press)

A reporter told Jensen Huang that his Uber driver wished he had just gone back to the farm instead of facing AI. Jensen flipped the entire fear in one move. The driver was genuinely scared. He looked at AI and saw the end of his work. Jensen did not argue with the fear. He pointed at where the man was sitting. That Uber job did not exist a generation ago. It only exists because of the last technology wave. Mobile. Cloud. The internet. The data centers running the routing and the matching in real time. The science behind a single Uber ride is enormous. None of it was possible before the revolution that came before this one. So the man driving for Uber, worried the next wave will erase him, is living inside a job the previous wave created. That is the whole reframe. The thing he is afraid of is the same kind of force that gave him the work in the first place. Then Jensen went further. The next wave creates new opportunity too. You cannot name it yet. Nobody could name Uber before the internet existed either. He has watched this happen his whole career. Personal computer. Internet. iPhone. Every time, people thought it would leave them behind. It changed everything. It left almost no one behind. The farm was not the safe choice. It was just the one he could already see. (Watch the full interview on YouTube at Associated Press)

Ihtesham Ali

62,810 views • 3 months ago

A regimen of listening to Beethoven’s 32 piano sonatas could be an antidote to the decline in attention spans. They were his workshop for musical ideas - and they got more complex over time. As you work through them, they keep requiring a little more of you. And listening to this kind of music blocks everything else out - and is really enjoyable. Maybe it would spill out and generate the ability to concentrate more broadly. Here is just the exposition from Beethoven’s first sonata with Richter - one minute of your time. You get the two themes that make up the movement, which in total is about 5 minutes. The rest of the movement develops and repeats what you hear in this. The entire sonata is only 20 minutes long - with a lot of variety in key and tempo.

A regimen of listening to Beethoven’s 32 piano sonatas could be an antidote to the decline in attention spans. They were his workshop for musical ideas - and they got more complex over time. As you work through them, they keep requiring a little more of you. And listening to this kind of music blocks everything else out - and is really enjoyable. Maybe it would spill out and generate the ability to concentrate more broadly. Here is just the exposition from Beethoven’s first sonata with Richter - one minute of your time. You get the two themes that make up the movement, which in total is about 5 minutes. The rest of the movement develops and repeats what you hear in this. The entire sonata is only 20 minutes long - with a lot of variety in key and tempo.

FischerKing

67,751 views • 9 days ago

Faraday wave. Visualization of a standing wave. And secrets to some of Nikola Tesla’s work. The water surface is responding to controlled vibration. As the container oscillates at a fixed frequency, energy transfers uniformly into the liquid. Instead of random ripples, waves interfere with each other and form stable standing-wave patterns-repeating circular and hexagonal shapes appearing at specific frequencies where the system reaches resonance. This phenomenon is Faraday wave formation, where small disturbances organize into ordered structures due to periodic forcing. It demonstrates how simple physical inputs produce complex, predictable patterns through constructive and destructive interference. The key mechanism: when oscillation frequency matches the natural frequency of the liquid system, resonance amplifies specific wavelengths while suppressing others. The geometry depends on container shape, fluid properties, and driving frequency. At lower frequencies, you see simple radial patterns. Higher frequencies generate intricate hexagonal and square lattices. These aren't random-they're determined by the wave equation and boundary conditions. The patterns remain stable as long as forcing continues at resonant frequency. Change the frequency slightly, and the pattern transforms or disappears entirely. Faraday waves appear in nature-from vibrating sand to quantum fluids. They reveal fundamental principles: periodic forcing plus wave interference equals spontaneous pattern formation. Simple cause, beautiful complexity.

Faraday wave. Visualization of a standing wave. And secrets to some of Nikola Tesla’s work. The water surface is responding to controlled vibration. As the container oscillates at a fixed frequency, energy transfers uniformly into the liquid. Instead of random ripples, waves interfere with each other and form stable standing-wave patterns-repeating circular and hexagonal shapes appearing at specific frequencies where the system reaches resonance. This phenomenon is Faraday wave formation, where small disturbances organize into ordered structures due to periodic forcing. It demonstrates how simple physical inputs produce complex, predictable patterns through constructive and destructive interference. The key mechanism: when oscillation frequency matches the natural frequency of the liquid system, resonance amplifies specific wavelengths while suppressing others. The geometry depends on container shape, fluid properties, and driving frequency. At lower frequencies, you see simple radial patterns. Higher frequencies generate intricate hexagonal and square lattices. These aren't random-they're determined by the wave equation and boundary conditions. The patterns remain stable as long as forcing continues at resonant frequency. Change the frequency slightly, and the pattern transforms or disappears entirely. Faraday waves appear in nature-from vibrating sand to quantum fluids. They reveal fundamental principles: periodic forcing plus wave interference equals spontaneous pattern formation. Simple cause, beautiful complexity.

Brian Roemmele

186,229 views • 9 months ago