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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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42,680 次观看 • 6 天前 •via X (Twitter)

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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

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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

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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

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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?

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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

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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

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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.

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"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

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🇮🇷🇺🇸🇮🇱 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

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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 次观看 • 2 年前

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.

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29,610 次观看 • 3 个月前

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)

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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 次观看 • 8 个月前

FOR THOSE WHO ARE CONFUSED… We experience TIME as a straight line, one moment after another, PAST TO PRESENT TO FUTURE. But that is only how it appears from inside the system. Beings in higher dimensions, what some call “ORACLES” OR “GODS,” do not experience time like this. They do not move through it. They observe it in its entirety. A closer analogy would be CHANNELS ON A SCREEN. What is playing on FOX and what is playing on CBS is not separate in existence, it is only separated by perspective. Both are happening at the same time, fully active, fully real. In the same way, what we call 1950 and what we call 2004 are not distant points moving away from each other. They are both present within the same total field of reality. From that level of awareness, nothing is being “waited on.” There is NO DELAY. There is only ACCESS. A shift of perception is all that is needed, like changing the channel. So if everything exists at once, then your FUTURE is not something that is coming toward you. It is something that already exists. The version of you 20 YEARS FROM NOW is already there. You have already CHOSEN THAT PATH, you have already GONE THROUGH WHAT COMES WITH IT, you have already LIVED THROUGH IT ALL. And what you are doing now is not creating it. You are MOVING THROUGH IT. Slowly remembering why you are there at all.

FOR THOSE WHO ARE CONFUSED… We experience TIME as a straight line, one moment after another, PAST TO PRESENT TO FUTURE. But that is only how it appears from inside the system. Beings in higher dimensions, what some call “ORACLES” OR “GODS,” do not experience time like this. They do not move through it. They observe it in its entirety. A closer analogy would be CHANNELS ON A SCREEN. What is playing on FOX and what is playing on CBS is not separate in existence, it is only separated by perspective. Both are happening at the same time, fully active, fully real. In the same way, what we call 1950 and what we call 2004 are not distant points moving away from each other. They are both present within the same total field of reality. From that level of awareness, nothing is being “waited on.” There is NO DELAY. There is only ACCESS. A shift of perception is all that is needed, like changing the channel. So if everything exists at once, then your FUTURE is not something that is coming toward you. It is something that already exists. The version of you 20 YEARS FROM NOW is already there. You have already CHOSEN THAT PATH, you have already GONE THROUGH WHAT COMES WITH IT, you have already LIVED THROUGH IT ALL. And what you are doing now is not creating it. You are MOVING THROUGH IT. Slowly remembering why you are there at all.

THE VOICE 🌹 🗣🎙🇺🇸🦅🌎⚓💜♠️CHRIST CONSCIOUSNESS

40,362 次观看 • 2 个月前

Using the BLUEPRINT of reality? Classical computers compute with BITS: 0 or 1 - ONE state at a time. Quantum computers use QUBITS: 0 and 1 or both "simultaneously" through superposition. These states EVOLVE continuously on something like a Bloch sphere - the same MATHEMATICS that describes spin, atoms and electron orbitals. The GEOMETRY feels familiar. Wheels within wheels. Computation, now operating in the rule-set of REALITY itself. Engineering in the same language of nature. THIS is a profound shift. So what follows? 📽 credits: uncover.quantum

Using the BLUEPRINT of reality? Classical computers compute with BITS: 0 or 1 - ONE state at a time. Quantum computers use QUBITS: 0 and 1 or both "simultaneously" through superposition. These states EVOLVE continuously on something like a Bloch sphere - the same MATHEMATICS that describes spin, atoms and electron orbitals. The GEOMETRY feels familiar. Wheels within wheels. Computation, now operating in the rule-set of REALITY itself. Engineering in the same language of nature. THIS is a profound shift. So what follows? 📽 credits: uncover.quantum

WhatdoIknow

21,109 次观看 • 6 个月前

These young ladies were waiting for their luggage, over a half an hour went by and still nothing. They were later called over to the airline kiosk and they got their luggage back. According to the representative, the luggage was damaged in transit. What makes it strange is it was all of the luggage from the same family, what are the odds of that happening since they weren’t all checked in at the same time. Does the airline owe them a better explanation as well as a check for their belongings?

These young ladies were waiting for their luggage, over a half an hour went by and still nothing. They were later called over to the airline kiosk and they got their luggage back. According to the representative, the luggage was damaged in transit. What makes it strange is it was all of the luggage from the same family, what are the odds of that happening since they weren’t all checked in at the same time. Does the airline owe them a better explanation as well as a check for their belongings?

SonnyBoy🇺🇸

922,226 次观看 • 5 个月前

From Eric Vishria on how the top AI founders are building products completely opposite of the SaaS era: "One of the things that is really different in the AI world versus the SaaS world, is that in the SaaS world, over and over again, you had people who really understood the customer. And the problem. And then they understood a domain. They understood what the technology was more or less capable of. But it wasn't a real question of if you could build something or not. For example, take Salesforce, Workday, and ServiceNow. CRM existed before Salesforce. HR management existed before Workday. Same thing with ServiceNow. So in every case, Salesforce followed Siebel. Workday followed Peoplesoft. ServiceNow followed Peregrine and Remedy, and others. So they were just kind of, cloud SaaS versions of the prior generation product. They just understood the customers. They understood the problem. And they were just like, here's a better version. And that evolved a little bit over time in SaaS land. But that's what it is. And so product development in that way was done by people who really understood the customer and the problems. And then just took advantage of the next wave. And this is almost diametrically opposite of product development in the AI era. When I look at the teams that are having the most success today, they have intimate knowledge of the models. They are right on the frontier of understanding which models are better at what, and why, and when. And what they're going to be good at and what they're not going to be good at. And what they're spending their time on, is figuring out how do I apply this capability of this model to this domain or to this user. So they're actually working inside out or technology out, versus customer problem in. And of course, they understand the customer problem. And a lot of times they have firsthand knowledge of it. But they're really close to the metal and capability, and they're applying it. And I think this is a really different way to develop products than in SaaS. I started my career as a product manager a long time ago, and it's almost the complete opposite of everything you learned. "Listen to the customer, understand it, then bring it back to the engineering and product teams." If you did that right now, ask a bunch of customers what they want out of AI, and you brought it back, for the most part, it may not be possible today with today's technology. Whereas the teams that are winning right now really understand the technology and are applying it out. And so I think this reversal matters. I think it's a big difference in terms of how companies are getting built. And maybe even the types of entrepreneurs that will be successful. I'm not sure. You're seeing some real change there. Look at the Bret Taylor's at Sierra. That's a super, super technical founder who really gets it. Brett and Clay really get it. You look at Michael and his co-founders at Cursor. They're super technical founders and they get it. They all really understand what these things can and can't do. And that's a pretty different dynamic relative to the way the best SaaS companies got built." Link in bio for the full conversation going deep on the current class of startups going from zero to $100m+ in ARR within 12 months.

From Eric Vishria on how the top AI founders are building products completely opposite of the SaaS era: "One of the things that is really different in the AI world versus the SaaS world, is that in the SaaS world, over and over again, you had people who really understood the customer. And the problem. And then they understood a domain. They understood what the technology was more or less capable of. But it wasn't a real question of if you could build something or not. For example, take Salesforce, Workday, and ServiceNow. CRM existed before Salesforce. HR management existed before Workday. Same thing with ServiceNow. So in every case, Salesforce followed Siebel. Workday followed Peoplesoft. ServiceNow followed Peregrine and Remedy, and others. So they were just kind of, cloud SaaS versions of the prior generation product. They just understood the customers. They understood the problem. And they were just like, here's a better version. And that evolved a little bit over time in SaaS land. But that's what it is. And so product development in that way was done by people who really understood the customer and the problems. And then just took advantage of the next wave. And this is almost diametrically opposite of product development in the AI era. When I look at the teams that are having the most success today, they have intimate knowledge of the models. They are right on the frontier of understanding which models are better at what, and why, and when. And what they're going to be good at and what they're not going to be good at. And what they're spending their time on, is figuring out how do I apply this capability of this model to this domain or to this user. So they're actually working inside out or technology out, versus customer problem in. And of course, they understand the customer problem. And a lot of times they have firsthand knowledge of it. But they're really close to the metal and capability, and they're applying it. And I think this is a really different way to develop products than in SaaS. I started my career as a product manager a long time ago, and it's almost the complete opposite of everything you learned. "Listen to the customer, understand it, then bring it back to the engineering and product teams." If you did that right now, ask a bunch of customers what they want out of AI, and you brought it back, for the most part, it may not be possible today with today's technology. Whereas the teams that are winning right now really understand the technology and are applying it out. And so I think this reversal matters. I think it's a big difference in terms of how companies are getting built. And maybe even the types of entrepreneurs that will be successful. I'm not sure. You're seeing some real change there. Look at the Bret Taylor's at Sierra. That's a super, super technical founder who really gets it. Brett and Clay really get it. You look at Michael and his co-founders at Cursor. They're super technical founders and they get it. They all really understand what these things can and can't do. And that's a pretty different dynamic relative to the way the best SaaS companies got built." Link in bio for the full conversation going deep on the current class of startups going from zero to $100m+ in ARR within 12 months.

The Peel

209,752 次观看 • 1 年前