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Markov Proved that Randomness With Memory Can Still Settle Into Law Markov’s 1906 result was a major turning point in Probability Theory. He showed that even when successive events are dependent, long-run averages can still stabilize. That broke the old habit of tying the Law of Large Numbers only...

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Mathelirium

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15,338 просмотров • 5 месяцев назад •via X (Twitter)

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In 1906, the world-renowned Russian mathematician Andrey A. Markov asked a heretic question of that time: if randomness has memory, do averages still behave or does probability theory collapse? His answer was a new kind of dependence where the next step only remembers the present, P(X_{n+1}=j | X_n=i, X_{n-1}, …) = P_ij, and yet the law of large numbers survives. The path stays noisy, while long-run state frequencies converge to a fixed profile pi = pi P. Markov’s idea is now the workhorse behind estimates by random-walks. MCMC (Markov Chain Monte Carlo) builds a chain whose stationary distribution is the target (posteriors, partition functions, constrained geometries), then uses time-averages as estimates. The same Markov structure shows up in hidden Markov models for time series, in biophysics as channels switching between states, and in control/RL as Markov decision processes. #ProbabilityTheory #Markov #MCMC
0:58

In 1906, the world-renowned Russian mathematician Andrey A. Markov asked a heretic question of that time: if randomness has memory, do averages still behave or does probability theory collapse? His answer was a new kind of dependence where the next step only remembers the present, P(X_{n+1}=j | X_n=i, X_{n-1}, …) = P_ij, and yet the law of large numbers survives. The path stays noisy, while long-run state frequencies converge to a fixed profile pi = pi P. Markov’s idea is now the workhorse behind estimates by random-walks. MCMC (Markov Chain Monte Carlo) builds a chain whose stationary distribution is the target (posteriors, partition functions, constrained geometries), then uses time-averages as estimates. The same Markov structure shows up in hidden Markov models for time series, in biophysics as channels switching between states, and in control/RL as Markov decision processes. #ProbabilityTheory #Markov #MCMC

Mathelirium

288,693 просмотров • 9 месяцев назад

In 1905, Russian Mathematician Andrey Andreyevich Markov asked a heretic question for the time: if randomness is allowed to remember something, do averages still behave or does probability theory fall apart? His answer was a very specific kind of memory. The next step only depends on the present, P(Xₙ₊₁=j | Xₙ=i, Xₙ₋₁, …) = Pᵢⱼ, and yet the law-of-large-numbers stability survives. The bead jitters forever, but long-run occupation settles. Time-averaged state frequencies converge to a fixed profile π satisfying π = πP. Fast-forward to 1931, another Russian Andrey Nikolaevich Kolmogorov, takes the same Markov mechanism and turns it into dynamics. Instead of only asking where does the chain spend its time?, you watch the whole distribution move in real time through the Kolmogorov forward (master) equation dp/dt = pQ, where Q is the generator of the continuous-time chain. That’s exactly what the render is showing as the same mechanism wearing two different lenses. The fog is p(t) spreading through the labyrinth, the flux layer is the net current pushed through corridors and the portal, and the particles are just sample paths driven by the same generator. One Markov engine...either you look at the evolving law, or you watch trajectories and let ergodic averages do the estimating. That’s also why Markov’s "memory without collapse" became a workhorse. MCMC engineers a chain whose stationary distribution is the target, then uses time-averages to estimate things you can’t integrate directly (posteriors, partition functions, constrained geometries). The same skeleton appears in hidden Markov models for time series, in biophysics as channels switching between states, and in control/RL through Markov decision processes. #ProbabilityTheory #MarkovChains #ContinuousTimeMarkovChains #KolmogorovForwardEquation #StochasticProcesses #Kolmogorov #Markov #MCMC
0:59

In 1905, Russian Mathematician Andrey Andreyevich Markov asked a heretic question for the time: if randomness is allowed to remember something, do averages still behave or does probability theory fall apart? His answer was a very specific kind of memory. The next step only depends on the present, P(Xₙ₊₁=j | Xₙ=i, Xₙ₋₁, …) = Pᵢⱼ, and yet the law-of-large-numbers stability survives. The bead jitters forever, but long-run occupation settles. Time-averaged state frequencies converge to a fixed profile π satisfying π = πP. Fast-forward to 1931, another Russian Andrey Nikolaevich Kolmogorov, takes the same Markov mechanism and turns it into dynamics. Instead of only asking where does the chain spend its time?, you watch the whole distribution move in real time through the Kolmogorov forward (master) equation dp/dt = pQ, where Q is the generator of the continuous-time chain. That’s exactly what the render is showing as the same mechanism wearing two different lenses. The fog is p(t) spreading through the labyrinth, the flux layer is the net current pushed through corridors and the portal, and the particles are just sample paths driven by the same generator. One Markov engine...either you look at the evolving law, or you watch trajectories and let ergodic averages do the estimating. That’s also why Markov’s "memory without collapse" became a workhorse. MCMC engineers a chain whose stationary distribution is the target, then uses time-averages to estimate things you can’t integrate directly (posteriors, partition functions, constrained geometries). The same skeleton appears in hidden Markov models for time series, in biophysics as channels switching between states, and in control/RL through Markov decision processes. #ProbabilityTheory #MarkovChains #ContinuousTimeMarkovChains #KolmogorovForwardEquation #StochasticProcesses #Kolmogorov #Markov #MCMC

Mathelirium

96,504 просмотров • 7 месяцев назад

Wall Street does not try to predict one future. It generates thousands of them and lets probability decide what the answer should be. The model is Monte Carlo Simulation: π ≈ 4 · Ninside / Ntotal Throw random points into a square with a circle inside it. Some land inside the circle, some outside. One point means nothing. A hundred are noisy. But as N grows, the ratio starts converging toward 3.14159. That is the law of large numbers in motion. The same idea is used in finance. If a payoff is too complex to solve directly, quants simulate thousands of possible market paths, calculate the result in each one, and average them. The breakthrough came from Stanislaw Ulam, John von Neumann and Nicholas Metropolis at Los Alamos. The strange idea was that randomness itself could be turned into a computational tool. But the math has a cost: error ∝ 1/√N Cut the error in half, and you need roughly 4x more simulations. Want 10x more precision, and you may need about 100x more work. That is why early estimates jump everywhere. Then the cloud fills in, the noise cancels, and one stable number emerges. Wall Street uses the same structure for option pricing, risk models and portfolio simulations. the edge was never removing randomness. it is generating enough of it that the randomness averages itself out.
0:20

Wall Street does not try to predict one future. It generates thousands of them and lets probability decide what the answer should be. The model is Monte Carlo Simulation: π ≈ 4 · Ninside / Ntotal Throw random points into a square with a circle inside it. Some land inside the circle, some outside. One point means nothing. A hundred are noisy. But as N grows, the ratio starts converging toward 3.14159. That is the law of large numbers in motion. The same idea is used in finance. If a payoff is too complex to solve directly, quants simulate thousands of possible market paths, calculate the result in each one, and average them. The breakthrough came from Stanislaw Ulam, John von Neumann and Nicholas Metropolis at Los Alamos. The strange idea was that randomness itself could be turned into a computational tool. But the math has a cost: error ∝ 1/√N Cut the error in half, and you need roughly 4x more simulations. Want 10x more precision, and you may need about 100x more work. That is why early estimates jump everywhere. Then the cloud fills in, the noise cancels, and one stable number emerges. Wall Street uses the same structure for option pricing, risk models and portfolio simulations. the edge was never removing randomness. it is generating enough of it that the randomness averages itself out.

Di Krass

103,040 просмотров • 26 дней назад

Have You Ever Heard of Molecular Communication Systems? Instead of using radio waves or light, molecular communications send information carefully through released chemical particles. A transmitter emits molecules into a medium, the channel reshapes that signal through diffusion, flow, and randomness. The receiver reads the message from the molecules that arrive and bind. It is communication theory at microscopic scale, where physics, probability and biology all become part of the channel. Some applications you may know: Targeted drug delivery inside the body, microscopic health monitoring with nanosensors, and lab-on-a-chip.
0:48

Have You Ever Heard of Molecular Communication Systems? Instead of using radio waves or light, molecular communications send information carefully through released chemical particles. A transmitter emits molecules into a medium, the channel reshapes that signal through diffusion, flow, and randomness. The receiver reads the message from the molecules that arrive and bind. It is communication theory at microscopic scale, where physics, probability and biology all become part of the channel. Some applications you may know: Targeted drug delivery inside the body, microscopic health monitoring with nanosensors, and lab-on-a-chip.

Mathelirium

19,452 просмотров • 6 месяцев назад

Russian Genius Found Structure in The Mess of Turbulence In 1941, Andrey Kolmogorov proposed a simple but powerful picture of turbulence: Energy does not disappear where it is injected but moves. Large eddies pass energy to smaller ones, those smaller ones feed even finer motion, and viscosity finally removes it at the tiniest scales. That cascade picture became one of the foundations of modern turbulence theory. The point is not just that turbulence looks messy. The point is that the mess has structure, and Kolmogorov’s great insight was to treat that structure statistically.
0:30

Russian Genius Found Structure in The Mess of Turbulence In 1941, Andrey Kolmogorov proposed a simple but powerful picture of turbulence: Energy does not disappear where it is injected but moves. Large eddies pass energy to smaller ones, those smaller ones feed even finer motion, and viscosity finally removes it at the tiniest scales. That cascade picture became one of the foundations of modern turbulence theory. The point is not just that turbulence looks messy. The point is that the mess has structure, and Kolmogorov’s great insight was to treat that structure statistically.

Mathelirium

59,102 просмотров • 5 месяцев назад

There’s a random curve that is perfectly continuous in time, never jumps, models smooth noise in physics and finance… and yet with probability 1 it has no derivative at any point. If you zoom in anywhere, it never straightens out. Brownian motion started as a physics headache long before it became a clean mathematical object. In 1827, Robert Brown watched pollen grains jitter under a microscope and had no microscopic theory to blame; almost a century later, Einstein and Smoluchowski explained that jitter as the visible effect of countless molecular collisions, and then Wiener turned that physical picture into a precise random function of time that now underpins much of modern probability, physics, and quantitative finance. #BrownianMotion #ProbabilityTheory #StochasticCalculus #RandomWalks #MathematicalPhysics #QuantFinance
1:00

There’s a random curve that is perfectly continuous in time, never jumps, models smooth noise in physics and finance… and yet with probability 1 it has no derivative at any point. If you zoom in anywhere, it never straightens out. Brownian motion started as a physics headache long before it became a clean mathematical object. In 1827, Robert Brown watched pollen grains jitter under a microscope and had no microscopic theory to blame; almost a century later, Einstein and Smoluchowski explained that jitter as the visible effect of countless molecular collisions, and then Wiener turned that physical picture into a precise random function of time that now underpins much of modern probability, physics, and quantitative finance. #BrownianMotion #ProbabilityTheory #StochasticCalculus #RandomWalks #MathematicalPhysics #QuantFinance

Mathelirium

33,072 просмотров • 9 месяцев назад

The most important tool in Probability and Statistics - Markov Chain Monte Carlo (MCMC) Method Fresh out of undergraduate Probability and Stats courses, it’s easy to feel invincible. You’ve tamed Gaussians, gammas, betas, all those neat closed-form toy distributions. Then research hits and you meet the harsher truth. Real posteriors and energy landscapes are jagged, asymmetric, multimodal, and too high-dimensional to integrate or sample from directly. You can’t compute the normalising constant. You can’t do the integrals by hand. And i.i.d. samples are basically science fiction. Markov Chain Monte Carlo is the hack we invented to survive that reality. Instead of drawing perfect samples, you send a carefully designed random walk wandering through the landscape, then use its long-run positions as your window into the target distribution. Here’s the problem. Standard trace plots and diagnostics can still cheerfully lie to you. High-dimensional geometry can make a chain that looks healthy while it’s effectively frozen. Multimodal targets, bad tuning, and hidden correlations can quietly wreck your posterior summaries. This series is about those blind spots. We’ll use visuals like this one to show how MCMC actually moves, where the guarantees get slippery, and how to think clearly about convergence and diagnostics in serious Bayesian, physics, and ML work. #BayesianInference #MCMC #MonteCarloMethods #ProbabilityLandscape #StatisticsEducation #ComputationalScience
0:59

The most important tool in Probability and Statistics - Markov Chain Monte Carlo (MCMC) Method Fresh out of undergraduate Probability and Stats courses, it’s easy to feel invincible. You’ve tamed Gaussians, gammas, betas, all those neat closed-form toy distributions. Then research hits and you meet the harsher truth. Real posteriors and energy landscapes are jagged, asymmetric, multimodal, and too high-dimensional to integrate or sample from directly. You can’t compute the normalising constant. You can’t do the integrals by hand. And i.i.d. samples are basically science fiction. Markov Chain Monte Carlo is the hack we invented to survive that reality. Instead of drawing perfect samples, you send a carefully designed random walk wandering through the landscape, then use its long-run positions as your window into the target distribution. Here’s the problem. Standard trace plots and diagnostics can still cheerfully lie to you. High-dimensional geometry can make a chain that looks healthy while it’s effectively frozen. Multimodal targets, bad tuning, and hidden correlations can quietly wreck your posterior summaries. This series is about those blind spots. We’ll use visuals like this one to show how MCMC actually moves, where the guarantees get slippery, and how to think clearly about convergence and diagnostics in serious Bayesian, physics, and ML work. #BayesianInference #MCMC #MonteCarloMethods #ProbabilityLandscape #StatisticsEducation #ComputationalScience

Mathelirium

32,296 просмотров • 7 месяцев назад

According to Bentov, consciousness evolves to the 'absolute' which is the source of all consciousness. Matter, composed of quanta of energy, is the vibrating, changing component of pure consciousness. The absolute is fixed, manifest and invisible. Bentov proposed that the brain acts as a transducer, converting the energy of consciousness into the electrical and chemical signals that are used to communicate information within the body. He also believed that the brain has the ability to tune into different frequencies of consciousness, allowing individuals to experience different states of awareness. Bentov's theory is based on the idea that consciousness is a fundamental aspect of the universe and is not limited to the brain or the body. He argued that consciousness is non-local, meaning it is not bound by space and time and can exist independently of the physical body. Bentov's theory has been influential in the field of consciousness studies, but it remains a subject of debate and is not widely accepted by mainstream science.
2:39

According to Bentov, consciousness evolves to the 'absolute' which is the source of all consciousness. Matter, composed of quanta of energy, is the vibrating, changing component of pure consciousness. The absolute is fixed, manifest and invisible. Bentov proposed that the brain acts as a transducer, converting the energy of consciousness into the electrical and chemical signals that are used to communicate information within the body. He also believed that the brain has the ability to tune into different frequencies of consciousness, allowing individuals to experience different states of awareness. Bentov's theory is based on the idea that consciousness is a fundamental aspect of the universe and is not limited to the brain or the body. He argued that consciousness is non-local, meaning it is not bound by space and time and can exist independently of the physical body. Bentov's theory has been influential in the field of consciousness studies, but it remains a subject of debate and is not widely accepted by mainstream science.

Vicky Verma

390,608 просмотров • 2 лет назад

Why Are Some People Still Taking String Theory Seriously? String theory is controversial, but it is still one of the few ideas that tries to describe Quantum Physics and Gravity in one picture. This animation points to one of its best-known ideas: Holography. What happens on the boundary helps determine what happens in the interior, so the edge seems to shape the bulk.
0:30

Why Are Some People Still Taking String Theory Seriously? String theory is controversial, but it is still one of the few ideas that tries to describe Quantum Physics and Gravity in one picture. This animation points to one of its best-known ideas: Holography. What happens on the boundary helps determine what happens in the interior, so the edge seems to shape the bulk.

Mathelirium

29,696 просмотров • 5 месяцев назад

A woman who spent nine years gluing paper models in a print shop just told a room of physicists their whole field stands on a mistake, one line, no hedging: "Every theory we have takes space and time for granted, like a bagel that forgot it was once a flat sheet of paper." That's Bianca Dittrich. She has a free lecture course that asks one question: what is left of geometry once you quantize it? The answer is: far less than you can picture. Quantum gravity looks like one more field theory. Buried inside is something stranger. Every quantum theory we have puts fields on a fixed stage, flat or curved, and does the physics on top of it. Here the stage itself is the thing being quantized. Your gut reads an atom of spacetime as a tiny grain sitting somewhere. Wrong. It cannot sit anywhere, because it is the somewhere. The move is invisible to human intuition, which is exactly why the people who get anywhere stop asking where the pieces are and start asking what a measurement even means. In 3D the whole thing collapses in a way that should scare you. No matter, no cosmological constant, and gravity is locally flat everywhere. Six degrees of freedom per point, all of them eaten by diffeomorphism symmetry. A field theory that ends up with finitely many real degrees of freedom, sometimes zero. None of it is hidden. Cut a parallelogram out of paper, glue the edges, and you have a torus. Flat everywhere, and yet two numbers survive that no local measurement can see. The lecture is free. Here is the trap: you feel every equation you can solve, every geometry you can draw, as progress. What you cannot feel is the gap you have to cross. Ten to the forty-one, from the Planck scale back up to the world you live in. And crossing it is the only thing that pays. Almost every approach still cannot show it recovers ordinary physics at the far end, and almost everyone quits long before then. The math is free to learn. The nerve to stop trusting your picture of space, that part you still have to bring yourself.
1:02:52

A woman who spent nine years gluing paper models in a print shop just told a room of physicists their whole field stands on a mistake, one line, no hedging: "Every theory we have takes space and time for granted, like a bagel that forgot it was once a flat sheet of paper." That's Bianca Dittrich. She has a free lecture course that asks one question: what is left of geometry once you quantize it? The answer is: far less than you can picture. Quantum gravity looks like one more field theory. Buried inside is something stranger. Every quantum theory we have puts fields on a fixed stage, flat or curved, and does the physics on top of it. Here the stage itself is the thing being quantized. Your gut reads an atom of spacetime as a tiny grain sitting somewhere. Wrong. It cannot sit anywhere, because it is the somewhere. The move is invisible to human intuition, which is exactly why the people who get anywhere stop asking where the pieces are and start asking what a measurement even means. In 3D the whole thing collapses in a way that should scare you. No matter, no cosmological constant, and gravity is locally flat everywhere. Six degrees of freedom per point, all of them eaten by diffeomorphism symmetry. A field theory that ends up with finitely many real degrees of freedom, sometimes zero. None of it is hidden. Cut a parallelogram out of paper, glue the edges, and you have a torus. Flat everywhere, and yet two numbers survive that no local measurement can see. The lecture is free. Here is the trap: you feel every equation you can solve, every geometry you can draw, as progress. What you cannot feel is the gap you have to cross. Ten to the forty-one, from the Planck scale back up to the world you live in. And crossing it is the only thing that pays. Almost every approach still cannot show it recovers ordinary physics at the far end, and almost everyone quits long before then. The math is free to learn. The nerve to stop trusting your picture of space, that part you still have to bring yourself.

Zyron

110,850 просмотров • 2 месяцев назад

Here’s the video of the TISZA Party's heartwarming national march. It took two hours for the end of the crowd to even leave the starting point, and by then Heroes' Square was already packed. By the end of the event, the tail end of the half-million crowd was still only halfway along the route. Fidesz and its propaganda machine could once again produce nothing but pathetic lies, along with a provocation involving a Ukrainian flag. The "hate march" that Fidesz organized with billions in funding turned out to be one of the smallest so far — even though the ruling party bused large numbers of people into Budapest using pressure and money. The comrades are well aware that in 27 days, it’s all over.
0:39

Here’s the video of the TISZA Party's heartwarming national march. It took two hours for the end of the crowd to even leave the starting point, and by then Heroes' Square was already packed. By the end of the event, the tail end of the half-million crowd was still only halfway along the route. Fidesz and its propaganda machine could once again produce nothing but pathetic lies, along with a provocation involving a Ukrainian flag. The "hate march" that Fidesz organized with billions in funding turned out to be one of the smallest so far — even though the ruling party bused large numbers of people into Budapest using pressure and money. The comrades are well aware that in 27 days, it’s all over.

Magyar Péter (Ne féljetek)

39,980 просмотров • 6 месяцев назад

I was watching a lecture on YouTube by David Tse from Stanford (see link below), and he quoted his advisor Bob Gallager: "Good theory should prune rather than grow the knowledge tree." To demonstrate what Gallager meant, we takes one idea… "how do you move mass from one shape to another as cheaply as possible?" and watch 200 years of mathematics cut that idea down to its clean geometric core. Monge (1781, "Mémoire sur la théorie des déblais et des remblais") A mound on the left, a trench on the right, and every grain of earth has to choose one destination and stick to it. In the animation that’s strict one-to-one matching: each point marches to a single partner, no splitting, no sharing. It’s beautiful but rigid and hard to work with. Kantorovich (1942, "On the Translocation of Masses"; 1948, "On a Problem of Monge") Kantorovich relaxes the rules. Instead of forcing each point to pick exactly one target, he allows mass to split: part of it can go here, part of it can go there. On screen you see packets of mass spraying from one source cell to several targets along smooth arcs. The problem becomes a clean convex optimisation problem. Brenier (1991, "Polar factorization and monotone rearrangement of vector-valued functions"); McCann (1995, "Existence and uniqueness of monotone measure-preserving maps"; 1997, "A convexity principle for interacting gases") Bernier then shows that, in the most natural cost setting, the best way to move mass always comes from a hidden height function whose slopes tell you where to send things. McCann shows that many natural energy functionals behave nicely along the paths generated this way. In the animation you see contour lines of that hidden landscape, with particles gliding along the most economical path between the two shapes. Jordan-Kinderlehrer-Otto (1998, "The variational formulation of the Fokker-Planck equation") JKO change the question from "what is the best single shuffle?" to "how does a whole cloud evolve in time?". They show that a familiar diffusion-with-drift equation can be reinterpreted as steepest descent of a free energy in the space of probability distributions. In the scene, a blob both smooths out and gets pulled toward the embankment while a free-energy counter steadily drops. Ambrosio-Gagli-Savaré (2005, "Gradient flows in metric spaces and in the spaces of probability measures") Ambrosio-Gigli-Savaré take that idea and generalise it far beyond this one setting. They build a theory of gradient flows on abstract metric spaces: you only need a notion of distance and an energy, and you can talk about curves of maximal slope. Wasserstein spaces become one important example among many. In the final scene the probability field evolves in the top panel while its energy traces a clean descending curve below.
1:12

I was watching a lecture on YouTube by David Tse from Stanford (see link below), and he quoted his advisor Bob Gallager: "Good theory should prune rather than grow the knowledge tree." To demonstrate what Gallager meant, we takes one idea… "how do you move mass from one shape to another as cheaply as possible?" and watch 200 years of mathematics cut that idea down to its clean geometric core. Monge (1781, "Mémoire sur la théorie des déblais et des remblais") A mound on the left, a trench on the right, and every grain of earth has to choose one destination and stick to it. In the animation that’s strict one-to-one matching: each point marches to a single partner, no splitting, no sharing. It’s beautiful but rigid and hard to work with. Kantorovich (1942, "On the Translocation of Masses"; 1948, "On a Problem of Monge") Kantorovich relaxes the rules. Instead of forcing each point to pick exactly one target, he allows mass to split: part of it can go here, part of it can go there. On screen you see packets of mass spraying from one source cell to several targets along smooth arcs. The problem becomes a clean convex optimisation problem. Brenier (1991, "Polar factorization and monotone rearrangement of vector-valued functions"); McCann (1995, "Existence and uniqueness of monotone measure-preserving maps"; 1997, "A convexity principle for interacting gases") Bernier then shows that, in the most natural cost setting, the best way to move mass always comes from a hidden height function whose slopes tell you where to send things. McCann shows that many natural energy functionals behave nicely along the paths generated this way. In the animation you see contour lines of that hidden landscape, with particles gliding along the most economical path between the two shapes. Jordan-Kinderlehrer-Otto (1998, "The variational formulation of the Fokker-Planck equation") JKO change the question from "what is the best single shuffle?" to "how does a whole cloud evolve in time?". They show that a familiar diffusion-with-drift equation can be reinterpreted as steepest descent of a free energy in the space of probability distributions. In the scene, a blob both smooths out and gets pulled toward the embankment while a free-energy counter steadily drops. Ambrosio-Gagli-Savaré (2005, "Gradient flows in metric spaces and in the spaces of probability measures") Ambrosio-Gigli-Savaré take that idea and generalise it far beyond this one setting. They build a theory of gradient flows on abstract metric spaces: you only need a notion of distance and an energy, and you can talk about curves of maximal slope. Wasserstein spaces become one important example among many. In the final scene the probability field evolves in the top panel while its energy traces a clean descending curve below.

Mathelirium

65,705 просмотров • 9 месяцев назад

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.
0:33

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 просмотров • 6 месяцев назад

What I saw was an ICE vehicle attempting to leave an area that was in a near riot condition, a civilian vehicle then suddenly moved in front of it to block its departure. I then saw an ICE officer approach that vehicle and issue a lawful order to the driver to get out of the car. Instead of complying with that order, the driver backed up, pointed the car in the direction of another officer, and then shifted into drive, stepping on the gas while an officer had his hand on the door then accelerated in the direction of the other ICE officer at the moment he fired into the vehicle. That’s what the video shows, and we all have eyes and we all can see it. There are a lot of questions that it raises, starting with the perspective of the officer who fired at this approaching vehicle. Was the car indeed pointed directly at him when he fired? It certainly appeared that way to me from the video we’ve seen. I assume the officer was wearing a body camera and we’ll get a better idea of his perspective in the course of the investigation. There’s the question of why the driver attempted to block the ICE vehicle as it was leaving, why the driver felt motivated to obstruct clearly uniformed federal law enforcement officers in the performance of their duties, why she willfully refused to comply with a lawful order by those officers, and why she pointed her vehicle toward another officer while hitting the gas. I suspect that a great deal of motivation was exactly from the kind of incendiary rhetoric we hear everyday from our radical democratic colleagues. It is a direct attack on the rule of law. Our ICE officers are enforcing federal law as the Congress wrote it. The Democrats here don’t like that law, they object to its enforcement, and they are actively encouraging citizens to obstruct its enforcement. In a nation of laws, the answer is not to obstruct the law, but to change it. We’re sitting in the very institution that writes these laws. If they believe the laws that enforce our nations sovereignty are wrong? Then they should make the case to change them. And Ms. Ross, I point out that when the Democrats had the majority and our nation was suffering through the worst illegal mass migration in its history, the immigration subcommittee under Democratic control held not a single hearing on that crisis as it unfolded, not one. I suspect their encouragement of disobedience to the law had a large role to play in the mind of the driver and in the minds of the increasingly violent mobs that our colleagues are deliberately inciting. As Lincoln said to their predecessors, “There is no grievance is a fit object for redress by mob law.” How sad the same words need to be repeated here. Before the House Judiciary Committee that’s supposed to be dedicated to the rule of law.
3:14

What I saw was an ICE vehicle attempting to leave an area that was in a near riot condition, a civilian vehicle then suddenly moved in front of it to block its departure. I then saw an ICE officer approach that vehicle and issue a lawful order to the driver to get out of the car. Instead of complying with that order, the driver backed up, pointed the car in the direction of another officer, and then shifted into drive, stepping on the gas while an officer had his hand on the door then accelerated in the direction of the other ICE officer at the moment he fired into the vehicle. That’s what the video shows, and we all have eyes and we all can see it. There are a lot of questions that it raises, starting with the perspective of the officer who fired at this approaching vehicle. Was the car indeed pointed directly at him when he fired? It certainly appeared that way to me from the video we’ve seen. I assume the officer was wearing a body camera and we’ll get a better idea of his perspective in the course of the investigation. There’s the question of why the driver attempted to block the ICE vehicle as it was leaving, why the driver felt motivated to obstruct clearly uniformed federal law enforcement officers in the performance of their duties, why she willfully refused to comply with a lawful order by those officers, and why she pointed her vehicle toward another officer while hitting the gas. I suspect that a great deal of motivation was exactly from the kind of incendiary rhetoric we hear everyday from our radical democratic colleagues. It is a direct attack on the rule of law. Our ICE officers are enforcing federal law as the Congress wrote it. The Democrats here don’t like that law, they object to its enforcement, and they are actively encouraging citizens to obstruct its enforcement. In a nation of laws, the answer is not to obstruct the law, but to change it. We’re sitting in the very institution that writes these laws. If they believe the laws that enforce our nations sovereignty are wrong? Then they should make the case to change them. And Ms. Ross, I point out that when the Democrats had the majority and our nation was suffering through the worst illegal mass migration in its history, the immigration subcommittee under Democratic control held not a single hearing on that crisis as it unfolded, not one. I suspect their encouragement of disobedience to the law had a large role to play in the mind of the driver and in the minds of the increasingly violent mobs that our colleagues are deliberately inciting. As Lincoln said to their predecessors, “There is no grievance is a fit object for redress by mob law.” How sad the same words need to be repeated here. Before the House Judiciary Committee that’s supposed to be dedicated to the rule of law.

Tom McClintock

354,708 просмотров • 8 месяцев назад

Google presents AudioPaLM: A Large Language Model That Can Speak and Listen paper page: introduce AudioPaLM, a large language model for speech understanding and generation. AudioPaLM fuses text-based and speech-based language models, PaLM-2 [Anil et al., 2023] and AudioLM [Borsos et al., 2022], into a unified multimodal architecture that can process and generate text and speech with applications including speech recognition and speech-to-speech translation. AudioPaLM inherits the capability to preserve paralinguistic information such as speaker identity and intonation from AudioLM and the linguistic knowledge present only in text large language models such as PaLM-2. We demonstrate that initializing AudioPaLM with the weights of a text-only large language model improves speech processing, successfully leveraging the larger quantity of text training data used in pretraining to assist with the speech tasks. The resulting model significantly outperforms existing systems for speech translation tasks and has the ability to perform zero-shot speech-to-text translation for many languages for which input/target language combinations were not seen in training. AudioPaLM also demonstrates features of audio language models, such as transferring a voice across languages based on a short spoken prompt.
4:10

Google presents AudioPaLM: A Large Language Model That Can Speak and Listen paper page: introduce AudioPaLM, a large language model for speech understanding and generation. AudioPaLM fuses text-based and speech-based language models, PaLM-2 [Anil et al., 2023] and AudioLM [Borsos et al., 2022], into a unified multimodal architecture that can process and generate text and speech with applications including speech recognition and speech-to-speech translation. AudioPaLM inherits the capability to preserve paralinguistic information such as speaker identity and intonation from AudioLM and the linguistic knowledge present only in text large language models such as PaLM-2. We demonstrate that initializing AudioPaLM with the weights of a text-only large language model improves speech processing, successfully leveraging the larger quantity of text training data used in pretraining to assist with the speech tasks. The resulting model significantly outperforms existing systems for speech translation tasks and has the ability to perform zero-shot speech-to-text translation for many languages for which input/target language combinations were not seen in training. AudioPaLM also demonstrates features of audio language models, such as transferring a voice across languages based on a short spoken prompt.

AK

290,517 просмотров • 3 лет назад

DeepMind CEO Demis Hassabis says the AI bottleneck is already moving from model ideas to physical supply chains. "How much of the restriction at this point is physical? I am talking memory shortage, GPU shortage, and electricity." Demis: "That is constraining a lot of the deployment for sure. We see so much more demand for our models - Gemini and the other models that we have - than we can possibly serve." Then the less obvious part: "It does constrain a little bit the research, because you need a lot of chips to be able to experiment on new ideas at big enough scale that you can actually see if they are going to work." And on memory: "The whole supply chain is kind of strained... It still in the end actually comes down to a few suppliers of a few of the key components. Anywhere where there is some kind of constraint on the capacity, there is a sort of choke point." Important framing: The next AI race is not just who has the best model architecture. It is who can secure memory, chips, power, suppliers, and enough experimental capacity to find the next breakthrough before everyone else.
1:09

DeepMind CEO Demis Hassabis says the AI bottleneck is already moving from model ideas to physical supply chains. "How much of the restriction at this point is physical? I am talking memory shortage, GPU shortage, and electricity." Demis: "That is constraining a lot of the deployment for sure. We see so much more demand for our models - Gemini and the other models that we have - than we can possibly serve." Then the less obvious part: "It does constrain a little bit the research, because you need a lot of chips to be able to experiment on new ideas at big enough scale that you can actually see if they are going to work." And on memory: "The whole supply chain is kind of strained... It still in the end actually comes down to a few suppliers of a few of the key components. Anywhere where there is some kind of constraint on the capacity, there is a sort of choke point." Important framing: The next AI race is not just who has the best model architecture. It is who can secure memory, chips, power, suppliers, and enough experimental capacity to find the next breakthrough before everyone else.

Karl Mehta

25,716 просмотров • 2 месяцев назад

CITADEL QUANTS HIDE THE GAME BEHIND A FORMULA WITH TEN TERMS, PREDICTION MARKETS RUN ON EXACTLY ONE The secret is one line. Edge = P(model) − P(market) That Z-field monster on screen is a stack of simple signals wearing a costume. A prediction market strips all of it down to one number, the crowd's guess at a probability. In plain words. If you can turn fresh news into a probability before the crowd reprices, the gap between your number and their price is the whole edge. That is why the game is not IQ, it is speed to a number. An AI that reads live news does in ninety seconds what the tab takes hours to price in. I broke down the four exact prompts that turn Grok into a probability desk, the sizing rules and the ten minute daily routine in the article. Still bets, not a salary, so size like it & the full playbook is in the article. Read it ↓
0:46

CITADEL QUANTS HIDE THE GAME BEHIND A FORMULA WITH TEN TERMS, PREDICTION MARKETS RUN ON EXACTLY ONE The secret is one line. Edge = P(model) − P(market) That Z-field monster on screen is a stack of simple signals wearing a costume. A prediction market strips all of it down to one number, the crowd's guess at a probability. In plain words. If you can turn fresh news into a probability before the crowd reprices, the gap between your number and their price is the whole edge. That is why the game is not IQ, it is speed to a number. An AI that reads live news does in ninety seconds what the tab takes hours to price in. I broke down the four exact prompts that turn Grok into a probability desk, the sizing rules and the ten minute daily routine in the article. Still bets, not a salary, so size like it & the full playbook is in the article. Read it ↓

slash1s

15,977 просмотров • 1 месяц назад

A lot of people have asked me whether FOMO can ever really be overcome. The problem with FOMO isn’t just that it can lead to one bad trade. It can become the starting point of a whole chain of mistakes. Even after more than 16 years of trading, I still feel FOMO sometimes. The difference is that I’ve learned to become much more aware of it — and to manage it before it takes over. The real turning point often starts with understanding what’s actually happening underneath the feeling. Why do you feel FOMO in the first place? Does FOMO really help you become a better trader? Once you realize that FOMO isn’t something you need to act on, you can start looking at it differently. Instead of being pulled around by the emotion, you gradually learn to take control of it. That was one of the most important shifts in my journey from a beginner to a professional trader.
1:09

A lot of people have asked me whether FOMO can ever really be overcome. The problem with FOMO isn’t just that it can lead to one bad trade. It can become the starting point of a whole chain of mistakes. Even after more than 16 years of trading, I still feel FOMO sometimes. The difference is that I’ve learned to become much more aware of it — and to manage it before it takes over. The real turning point often starts with understanding what’s actually happening underneath the feeling. Why do you feel FOMO in the first place? Does FOMO really help you become a better trader? Once you realize that FOMO isn’t something you need to act on, you can start looking at it differently. Instead of being pulled around by the emotion, you gradually learn to take control of it. That was one of the most important shifts in my journey from a beginner to a professional trader.

J Law

15,456 просмотров • 1 месяц назад

When I look at the US and global debt burdens and how countries are likely to respond, I worry about the possibility of creating a stagflationary environment. Our financial system is dependent on the idea that you can take a debt asset and convert it into money. But now there’s not enough money to go around. That makes the idea of devaluing the dollar relative to other currencies appealing — but the other currencies won’t want much of an appreciation either. That’s one of the reasons I say that gold will be a better performing asset.
1:13

When I look at the US and global debt burdens and how countries are likely to respond, I worry about the possibility of creating a stagflationary environment. Our financial system is dependent on the idea that you can take a debt asset and convert it into money. But now there’s not enough money to go around. That makes the idea of devaluing the dollar relative to other currencies appealing — but the other currencies won’t want much of an appreciation either. That’s one of the reasons I say that gold will be a better performing asset.

Ray Dalio

253,673 просмотров • 1 год назад