Video wird geladen...

Video konnte nicht geladen werden

Beim Laden dieses Videos ist ein Problem aufgetreten. Dies könnte an einem vorübergehenden Netzwerkproblem liegen oder das Video ist möglicherweise nicht verfügbar.

You start with a plain old complex polynomial p(z) = a₀ + a₁z + … + aₙzⁿ. Instead of fixing the coefficients, you treat them as variables in a controlled experiment and modulate them. Maybe you draw each aₖ from some distribution, or you let them drift along a... parameter path. Do that 50,000 times, say, and you no longer have a polynomial. You have an ensemble. For each realization, the goal is the same Find its roots. Instead of attacking p(z)=0 directly with something like fsolve, you rewrite the polynomial as a matrix problem. Specifically, you build its Companion Matrix. For a monic polynomial zⁿ + bₙ₋₁zⁿ⁻¹ + … + b₀ the companion matrix is an n×n matrix whose last column contains the coefficients (with minus signs), and whose subdiagonal is filled with ones. Everything else is zero. It’s sparse, structured and deterministic. The theorem that makes this worth doing is simple and beautiful The eigenvalues of the companion matrix are exactly the roots of the polynomial. So each polynomial sample becomes a matrix. Each matrix becomes an eigenvalue problem. And eigenvalues are something numerical linear algebra is very, very good at computing.show more

Mathelirium

37,469 subscribers

15,566 Aufrufe • vor 6 Monaten •via X (Twitter)

Anya Rossi• Live Now

Private livecam show

0 Kommentare

Keine Kommentare verfügbar

Kommentare vom Original-Post werden hier angezeigt

Ähnliche Videos

Finding the roots of a polynomial is one of the oldest and most central problems in Algebra. Once the coefficients are allowed to move through the complex plane, the roots start revealing a much richer geometry. Here is the Mathematics, try it yourself and play around with the coefficients and polynomial structure: P(x) = x¹² + a x⁸ + b x⁶ + c x⁴ + d x + 1 a = (sin(t₁) + i cos(sin(t₂) + 0.5 sin(2t₂))) M b = 0.3 (t₁ + t₂) Mᶜ c = (exp(i t₁) - cos(t₂)) M d = (cos(t₁) - 0.5 i sin(sin(t₂) + 0.5 sin(2t₂))) Mᶜ M = 1 + ∑ₖ₌₁ᵐ Aₖ exp(i 2π sₖ n / N) Mᶜ = 1 + ∑ₖ₌₁ᵐ Aₖ exp(-i 2π sₖ n / N) Here t₁ and t₂ lie on the unit circle, n is the frame index, N is the total number of frames, and Aₖ, sₖ are the modulation amplitudes and speeds.

Finding the roots of a polynomial is one of the oldest and most central problems in Algebra. Once the coefficients are allowed to move through the complex plane, the roots start revealing a much richer geometry. Here is the Mathematics, try it yourself and play around with the coefficients and polynomial structure: P(x) = x¹² + a x⁸ + b x⁶ + c x⁴ + d x + 1 a = (sin(t₁) + i cos(sin(t₂) + 0.5 sin(2t₂))) M b = 0.3 (t₁ + t₂) Mᶜ c = (exp(i t₁) - cos(t₂)) M d = (cos(t₁) - 0.5 i sin(sin(t₂) + 0.5 sin(2t₂))) Mᶜ M = 1 + ∑ₖ₌₁ᵐ Aₖ exp(i 2π sₖ n / N) Mᶜ = 1 + ∑ₖ₌₁ᵐ Aₖ exp(-i 2π sₖ n / N) Here t₁ and t₂ lie on the unit circle, n is the frame index, N is the total number of frames, and Aₖ, sₖ are the modulation amplitudes and speeds.

Mathelirium

23,042 Aufrufe • vor 4 Monaten

The Trap in Every Mathematics Lecture If you’ve taken a lot of math courses, you start to recognize a pattern. There’s a moment where the lecturer is warming up with the obvious stuff...add matrices entrywise, scale by α, do the row-column product...and you’re thinking, alright… where is this going? Then you relax. You stop resisting. And right there, they slip in one line that changes how you see the whole subject. When Benedict Gross says "matrices represent linear operators,"he’s telling you to stop treating a matrix as a rectangle of numbers and start treating it as an action. A linear operator is a function T: Rⁿ → Rⁿ that respects two rules: T(u+v)=T(u)+T(v) and T(αu)=αT(u). Once you pick a basis, T is completely determined by where it sends the basis vectors e₁,…,eₙ. Put T(e₁),…,T(eₙ) into columns and you get a matrix A. That is what "A represents T" means...A is the coordinate portrait of the transformation. Now the punchline that makes matrix multiplication feel inevitable. If B represents S and A represents T, then doing S first and then T is the composition T∘S. In coordinates that becomes A(Bx)=(AB)x. So multiplying matrices is really composing transformations. That’s why multiplication is usually not commutative: T∘S is generally not the same transformation as S∘T, and the matrices inherit that noncommutativity. This explains half of Linear Algebra because it tells you what the course is really about...functions that move vectors around, not grids of numbers. A matrix is just the written form of that function once you choose coordinates. Then the rules stop feeling random Multiplying matrices means doing one move and then another, an inverse means you can undo the move, eigenvectors are directions that don’t get turned, and changing basis is just describing the same move in a different language. That one idea makes a lot of linear algebra click. #LinearAlgebra #Matrices #GroupTheory #GLn #MathLectures #Mathematics

The Trap in Every Mathematics Lecture If you’ve taken a lot of math courses, you start to recognize a pattern. There’s a moment where the lecturer is warming up with the obvious stuff...add matrices entrywise, scale by α, do the row-column product...and you’re thinking, alright… where is this going? Then you relax. You stop resisting. And right there, they slip in one line that changes how you see the whole subject. When Benedict Gross says "matrices represent linear operators,"he’s telling you to stop treating a matrix as a rectangle of numbers and start treating it as an action. A linear operator is a function T: Rⁿ → Rⁿ that respects two rules: T(u+v)=T(u)+T(v) and T(αu)=αT(u). Once you pick a basis, T is completely determined by where it sends the basis vectors e₁,…,eₙ. Put T(e₁),…,T(eₙ) into columns and you get a matrix A. That is what "A represents T" means...A is the coordinate portrait of the transformation. Now the punchline that makes matrix multiplication feel inevitable. If B represents S and A represents T, then doing S first and then T is the composition T∘S. In coordinates that becomes A(Bx)=(AB)x. So multiplying matrices is really composing transformations. That’s why multiplication is usually not commutative: T∘S is generally not the same transformation as S∘T, and the matrices inherit that noncommutativity. This explains half of Linear Algebra because it tells you what the course is really about...functions that move vectors around, not grids of numbers. A matrix is just the written form of that function once you choose coordinates. Then the rules stop feeling random Multiplying matrices means doing one move and then another, an inverse means you can undo the move, eigenvectors are directions that don’t get turned, and changing basis is just describing the same move in a different language. That one idea makes a lot of linear algebra click. #LinearAlgebra #Matrices #GroupTheory #GLn #MathLectures #Mathematics

Mathelirium

66,892 Aufrufe • vor 8 Monaten

This video, created by my dear coauthor Mahdi E Kahou for our teaching and papers, shows how overparameterized neural networks produce smooth function approximations even in the context of the Runge phenomenon. Some background. Imagine you want to approximate the Runge function using polynomial interpolation at equally spaced points. It is well known that, despite targeting an infinitely differentiable function, such a polynomial approximation produces oscillatory behavior that worsens with the degree of the polynomial. In other words, higher-degree polynomial approximations might not improve accuracy. Instead, approximate the Runge function with a neural network (here, two layers are just to make the example concrete; nothing fundamental depends on it). As you increase the number of parameters well above the 11 training points (in our example, a two-layer neural network with 128 nodes each), you nicely converge to the target, without wild oscillations. Yes, this has much to do with double descent and benign overparameterization, but the main punchline of this post is that neural networks are really very different types of animals than polynomial approximations. And yes, Chebyshev nodes and splines exist, and in this case, they will prevent the oscillations. But that's not the point. Chebyshev nodes and splines still confront Faber’s theorem, which states that for any system of polynomial interpolation nodes, there exists a continuous function whose sequence of interpolating polynomials diverges as the number of nodes grows to infinity. Faber’s theorem does not apply to neural networks because they are not polynomials. The notebook, if you want to check the details, is here: Stay tuned for more on this 👀

This video, created by my dear coauthor Mahdi E Kahou for our teaching and papers, shows how overparameterized neural networks produce smooth function approximations even in the context of the Runge phenomenon. Some background. Imagine you want to approximate the Runge function using polynomial interpolation at equally spaced points. It is well known that, despite targeting an infinitely differentiable function, such a polynomial approximation produces oscillatory behavior that worsens with the degree of the polynomial. In other words, higher-degree polynomial approximations might not improve accuracy. Instead, approximate the Runge function with a neural network (here, two layers are just to make the example concrete; nothing fundamental depends on it). As you increase the number of parameters well above the 11 training points (in our example, a two-layer neural network with 128 nodes each), you nicely converge to the target, without wild oscillations. Yes, this has much to do with double descent and benign overparameterization, but the main punchline of this post is that neural networks are really very different types of animals than polynomial approximations. And yes, Chebyshev nodes and splines exist, and in this case, they will prevent the oscillations. But that's not the point. Chebyshev nodes and splines still confront Faber’s theorem, which states that for any system of polynomial interpolation nodes, there exists a continuous function whose sequence of interpolating polynomials diverges as the number of nodes grows to infinity. Faber’s theorem does not apply to neural networks because they are not polynomials. The notebook, if you want to check the details, is here: Stay tuned for more on this 👀

Jesús Fernández-Villaverde

47,212 Aufrufe • vor 4 Monaten

The Trap in Every Mathematics Lecture If you’ve taken enough math courses, you start noticing the same little move. The lecturer warms up with the obvious stuff, add matrices entrywise, scale by α, do the row-column product, and you’re thinking alright, where is this going. Then you relax. You stop resisting. And right there, they drop one line that quietly rewires the whole subject. When Benedict Gross says matrices represent linear operators, he’s telling you to stop treating a matrix as a rectangle of numbers and start treating it as an action. A linear operator is a function T: ℝⁿ → ℝⁿ that respects two rules: T(u+v) = T(u) + T(v) T(αu) = αT(u) Once you pick a basis, T is completely determined by where it sends the basis vectors e₁,…,eₙ. Put T(e₁),…,T(eₙ) into columns and you get a matrix A. That is what A represents T means. A is the coordinate portrait of the transformation. Now the punchline that makes matrix multiplication feel inevitable. If B represents S and A represents T, then doing S first and then T is the composition T∘S. In coordinates that becomes A(Bx) = (AB)x. So multiplying matrices is really composing transformations. That’s why multiplication is usually not commutative. T∘S is generally not the same transformation as S∘T, and the matrices inherit that noncommutativity. This explains half of linear algebra because it tells you what the course is really about: functions that move vectors around, not grids of numbers. A matrix is just the written form of that function once you choose coordinates. After that, the rules stop feeling random. Multiplying matrices means doing one move and then another. An inverse means you can undo the move. Eigenvectors are directions that don’t get turned. Changing basis is just describing the same move in a different language. One idea, and a lot of linear algebra suddenly clicks. #LinearAlgebra #Matrices #LinearMaps #Eigenvectors #ChangeOfBasis #Mathematics

The Trap in Every Mathematics Lecture If you’ve taken enough math courses, you start noticing the same little move. The lecturer warms up with the obvious stuff, add matrices entrywise, scale by α, do the row-column product, and you’re thinking alright, where is this going. Then you relax. You stop resisting. And right there, they drop one line that quietly rewires the whole subject. When Benedict Gross says matrices represent linear operators, he’s telling you to stop treating a matrix as a rectangle of numbers and start treating it as an action. A linear operator is a function T: ℝⁿ → ℝⁿ that respects two rules: T(u+v) = T(u) + T(v) T(αu) = αT(u) Once you pick a basis, T is completely determined by where it sends the basis vectors e₁,…,eₙ. Put T(e₁),…,T(eₙ) into columns and you get a matrix A. That is what A represents T means. A is the coordinate portrait of the transformation. Now the punchline that makes matrix multiplication feel inevitable. If B represents S and A represents T, then doing S first and then T is the composition T∘S. In coordinates that becomes A(Bx) = (AB)x. So multiplying matrices is really composing transformations. That’s why multiplication is usually not commutative. T∘S is generally not the same transformation as S∘T, and the matrices inherit that noncommutativity. This explains half of linear algebra because it tells you what the course is really about: functions that move vectors around, not grids of numbers. A matrix is just the written form of that function once you choose coordinates. After that, the rules stop feeling random. Multiplying matrices means doing one move and then another. An inverse means you can undo the move. Eigenvectors are directions that don’t get turned. Changing basis is just describing the same move in a different language. One idea, and a lot of linear algebra suddenly clicks. #LinearAlgebra #Matrices #LinearMaps #Eigenvectors #ChangeOfBasis #Mathematics

Mathelirium

133,454 Aufrufe • vor 7 Monaten

This is a great lecture at MIT by David Shirokoff on Markov Chains. He covers the fundamentals of Markov Chains using a simple particle movement example. He starts by explaining how a particle moves between two positions, A & B, with different probabilities. From there, the talk converts the problem into matrix form using a Markov matrix. The main topics covered are: - Transition probabilities - Markov matrices - Probability vectors - Matrix multiplication in Markov Chains - Finding probabilities after n steps - Eigenvalues and eigenvectors - Matrix diagonalization - Long-term steady state distribution

This is a great lecture at MIT by David Shirokoff on Markov Chains. He covers the fundamentals of Markov Chains using a simple particle movement example. He starts by explaining how a particle moves between two positions, A & B, with different probabilities. From there, the talk converts the problem into matrix form using a Markov matrix. The main topics covered are: - Transition probabilities - Markov matrices - Probability vectors - Matrix multiplication in Markov Chains - Finding probabilities after n steps - Eigenvalues and eigenvectors - Matrix diagonalization - Long-term steady state distribution

𝗿𝗮𝗺𝗮𝗸𝗿𝘂𝘀𝗵𝗻𝗮— 𝗲/𝗮𝗰𝗰

141,930 Aufrufe • vor 3 Monaten

In the movie, The Matrix, Agent Smith has the ability to enter any body, at any time, and that often happens when the Matrix is threatened by Neo. This scenario is a reflection of our real world. For example, you're having a conversation with a friend/family member/partner and everything is fine until you mention something like 9/11 was inside job. Now watch what happens, up pops the Agent Smith to replace the person you were just having a conversation with to attack you because all truths threaten the Matrix, which gives them feeling of safety, security and purpose in this "hologram" reality. Most people have had the Agent Smith programing since birth. These programed people become the guardians of the Matrix, protectors of the narrative and enforcers of indoctrination which holds together our false concept of reality like super glue. Think critically, I love you all, X

In the movie, The Matrix, Agent Smith has the ability to enter any body, at any time, and that often happens when the Matrix is threatened by Neo. This scenario is a reflection of our real world. For example, you're having a conversation with a friend/family member/partner and everything is fine until you mention something like 9/11 was inside job. Now watch what happens, up pops the Agent Smith to replace the person you were just having a conversation with to attack you because all truths threaten the Matrix, which gives them feeling of safety, security and purpose in this "hologram" reality. Most people have had the Agent Smith programing since birth. These programed people become the guardians of the Matrix, protectors of the narrative and enforcers of indoctrination which holds together our false concept of reality like super glue. Think critically, I love you all, X

MAVERICK X

393,029 Aufrufe • vor 8 Monaten

what if you can run an entire 0-person company — without the grind of running a team? matrix is the runtime that makes it possible. in last week’s limited beta, our users created tens of thousands of new 0-person companies and started real businesses in matrix. today, matrix is open to everyone. launch yours ↓

what if you can run an entire 0-person company — without the grind of running a team? matrix is the runtime that makes it possible. in last week’s limited beta, our users created tens of thousands of new 0-person companies and started real businesses in matrix. today, matrix is open to everyone. launch yours ↓

Matrix

527,654 Aufrufe • vor 2 Monaten

In the movie, The Matrix, Agent Smith has the ability to enter any body, at any time, and that often happens when the Matrix is threatened by Neo. This scenario is a reflection of our real world. For example, you're having a conversation with a friend/family member/partner and everything is fine until you mention something like 9/11 was inside job. Now watch what happens, up pops the Agent Smith to replace the person you were just having a conversation with to attack you because all truths threaten the Matrix, which gives them feeling of safety, security and purpose in this "hologram" reality. Most people have had the Agent Smith programing since birth. These programed people become the guardians of the Matrix, protectors of the narrative and enforcers of indoctrination which holds together our false concept of reality like super glue. Think critically.

In the movie, The Matrix, Agent Smith has the ability to enter any body, at any time, and that often happens when the Matrix is threatened by Neo. This scenario is a reflection of our real world. For example, you're having a conversation with a friend/family member/partner and everything is fine until you mention something like 9/11 was inside job. Now watch what happens, up pops the Agent Smith to replace the person you were just having a conversation with to attack you because all truths threaten the Matrix, which gives them feeling of safety, security and purpose in this "hologram" reality. Most people have had the Agent Smith programing since birth. These programed people become the guardians of the Matrix, protectors of the narrative and enforcers of indoctrination which holds together our false concept of reality like super glue. Think critically.

MAVERICK X

791,200 Aufrufe • vor 3 Jahren

The evolving lemniscates of a time-choreographed complex polynomial. *DM me if you would like to see the math framework...bots are killing me.

The evolving lemniscates of a time-choreographed complex polynomial. *DM me if you would like to see the math framework...bots are killing me.

Mathelirium

18,318 Aufrufe • vor 11 Monaten

Graph Convolutional Network by hand ✍️ ~ 12 steps walkthrough below Graph Convolutional Networks (GCNs), introduced by Thomas Kipf and Max Welling in 2017, are the tool for data shaped like a graph: social networks, recommendations, biological networks, drug discovery, molecular chemistry. I drew and calculated a simple GCN entirely by hand. Goal: run a two-layer GCN, then a small classifier, on a five-node graph, filling in every cell yourself. 1. Given A graph of five nodes, A to E, with edges between some of them. 2. Adjacency matrix (neighbors) Put a 1 wherever two nodes share an edge, in both directions. 3. Adjacency matrix (self) Add 1s down the diagonal, one self-loop per node. That is just adding the identity matrix. 4. Messages Multiply each node's embedding by the weights and biases, then ReLU. Negatives become 0. 5. Pooling Multiply the messages by the adjacency matrix. Each node gathers the messages of its neighbours and itself. 6. Visualize Node A pools [3,0,1] + [1,0,0] = [4,0,1]. 7. Second GCN layer Messages again: weights, biases, ReLU. 8. Pooling again Pool over each node and its neighbours, once more. 9. Visualize Node C pools [1,2,4] + [1,3,5] + [0,0,1] = [2,5,10]. 10. Fully connected layer Weights, biases, ReLU. This time there are no neighbours to pool, just the node itself. 11. Linear layer One more: weights and biases. 12. Sigmoid Squash each score to a probability (≥ 3 → 1, 0 → 0.5, ≤ -3 → 0). That is the classification for each node. You have just classified every node in the graph by hand. ✍️ The outputs: A: 0 (very unlikely) B: 1 (very likely) C: 1 (very likely) D: 1 (very likely) E: 0.5 (neutral) The takeaway: a GCN layer is two parts. The top part pools each node with its neighbours through the adjacency matrix. The bottom part is an MLP that transforms each node on its own. A transformer layer has the same two parts, with an attention matrix where the adjacency matrix was. Both matrices do one job, mixing across positions: attention over tokens, adjacency over nodes. In my class I call the GCN the transformer's little cousin: a bit more stubborn, because its attention is fixed by the graph rather than computed from Q, K, and V. Draw the two side by side and the resemblance is hard to miss. 💾 Save this post! #AIbyHand #GraphNeuralNetworks #DeepLearning

Graph Convolutional Network by hand ✍️ ~ 12 steps walkthrough below Graph Convolutional Networks (GCNs), introduced by Thomas Kipf and Max Welling in 2017, are the tool for data shaped like a graph: social networks, recommendations, biological networks, drug discovery, molecular chemistry. I drew and calculated a simple GCN entirely by hand. Goal: run a two-layer GCN, then a small classifier, on a five-node graph, filling in every cell yourself. 1. Given A graph of five nodes, A to E, with edges between some of them. 2. Adjacency matrix (neighbors) Put a 1 wherever two nodes share an edge, in both directions. 3. Adjacency matrix (self) Add 1s down the diagonal, one self-loop per node. That is just adding the identity matrix. 4. Messages Multiply each node's embedding by the weights and biases, then ReLU. Negatives become 0. 5. Pooling Multiply the messages by the adjacency matrix. Each node gathers the messages of its neighbours and itself. 6. Visualize Node A pools [3,0,1] + [1,0,0] = [4,0,1]. 7. Second GCN layer Messages again: weights, biases, ReLU. 8. Pooling again Pool over each node and its neighbours, once more. 9. Visualize Node C pools [1,2,4] + [1,3,5] + [0,0,1] = [2,5,10]. 10. Fully connected layer Weights, biases, ReLU. This time there are no neighbours to pool, just the node itself. 11. Linear layer One more: weights and biases. 12. Sigmoid Squash each score to a probability (≥ 3 → 1, 0 → 0.5, ≤ -3 → 0). That is the classification for each node. You have just classified every node in the graph by hand. ✍️ The outputs: A: 0 (very unlikely) B: 1 (very likely) C: 1 (very likely) D: 1 (very likely) E: 0.5 (neutral) The takeaway: a GCN layer is two parts. The top part pools each node with its neighbours through the adjacency matrix. The bottom part is an MLP that transforms each node on its own. A transformer layer has the same two parts, with an attention matrix where the adjacency matrix was. Both matrices do one job, mixing across positions: attention over tokens, adjacency over nodes. In my class I call the GCN the transformer's little cousin: a bit more stubborn, because its attention is fixed by the graph rather than computed from Q, K, and V. Draw the two side by side and the resemblance is hard to miss. 💾 Save this post! #AIbyHand #GraphNeuralNetworks #DeepLearning

Tom Yeh

16,800 Aufrufe • vor 2 Monaten

THE MATRIX SPOON BOY'S MESSAGE Many have seen the Matrix but it seems fewer grasp just how powerful the 'spoon boy's' message was when Neo first visits the oracle... The boy says to Neo: "Do not try and bend the spoon, that's impossible. Instead, only try to realize the truth...there is no spoon. Then you'll see that it is not the spoon that bends, it is only yourself." What he's saying is there is nothing that is NOT yourself, BECAUSE 'Neo' was not just an entity as the body, 'Neo' was the entire Matrix becoming self aware to re-write and change itself - this is why in the final movie there is rain and in the very end there is sunshine. Anyone who knows the Matrix knows EVERYTHING which appears is really shaped through Matrix code which means 'Neo' (who could visibly see this code) was all of the characters and places, not just the one we saw in the flesh as 'Neo'. Why do you think in the end Mr Smith asks Neo if he realises its impossible to win, that he simply can't.... And the reason nothing can be 'won' is they are not separate and Neo began realising himself as 'The Matrix' itself rather than just a body which is why he no longer fights Smith and allows him to enter his body.... The body was not 'Neo'.... 'Neo' becoming the chosen one is acknowledging the self as the entire Matrix, as one self and not two...(Mr. Anderson and Smith) There is no body which is separate from earth, only MIND has made this concept. Earth and body are ONE beyond what we call them... We are not Mr Anderson nor Neo, we are the entire Matrix writing itself to experience itself. Realise everything in the form which changes is only yourself because the self is not just limited to this body... Each and everyone of you are this 'CHOSEN ONE'. But what did Morpheus say to Neo... "DON'T THINK YOU ARE, KNOW YOU ARE"..... Until The One believes... They remain as just a character feeling stuck inside of something or somewhere when there is no where or place separate from your true self - which is why in the beginning it says: "The Matrix Has You..." In the beginning he existed as an illusory identity of Mr Anderson, the Matrix had him but he did not have the Matrix. He was not aware of the self beyond identity and form so through meeting Morpheus, "he died" and realised himself as the "chosen one" who can directly change and save his experience. What this means is ANYONE of these characters could of became 'Neo' because Neo is a realisation of the true self similar to "Christ Consciousness" as we know it... We are ALL this chosen one but until this is realised, we will never find it but seek it.... You do not become it, you ARE already IT... Any process is like running past the finish line after you've won a race, if you continue running, when do you acknowledge you've already finished... ✨🙌🏾💫 © Awakened Gnostic

THE MATRIX SPOON BOY'S MESSAGE Many have seen the Matrix but it seems fewer grasp just how powerful the 'spoon boy's' message was when Neo first visits the oracle... The boy says to Neo: "Do not try and bend the spoon, that's impossible. Instead, only try to realize the truth...there is no spoon. Then you'll see that it is not the spoon that bends, it is only yourself." What he's saying is there is nothing that is NOT yourself, BECAUSE 'Neo' was not just an entity as the body, 'Neo' was the entire Matrix becoming self aware to re-write and change itself - this is why in the final movie there is rain and in the very end there is sunshine. Anyone who knows the Matrix knows EVERYTHING which appears is really shaped through Matrix code which means 'Neo' (who could visibly see this code) was all of the characters and places, not just the one we saw in the flesh as 'Neo'. Why do you think in the end Mr Smith asks Neo if he realises its impossible to win, that he simply can't.... And the reason nothing can be 'won' is they are not separate and Neo began realising himself as 'The Matrix' itself rather than just a body which is why he no longer fights Smith and allows him to enter his body.... The body was not 'Neo'.... 'Neo' becoming the chosen one is acknowledging the self as the entire Matrix, as one self and not two...(Mr. Anderson and Smith) There is no body which is separate from earth, only MIND has made this concept. Earth and body are ONE beyond what we call them... We are not Mr Anderson nor Neo, we are the entire Matrix writing itself to experience itself. Realise everything in the form which changes is only yourself because the self is not just limited to this body... Each and everyone of you are this 'CHOSEN ONE'. But what did Morpheus say to Neo... "DON'T THINK YOU ARE, KNOW YOU ARE"..... Until The One believes... They remain as just a character feeling stuck inside of something or somewhere when there is no where or place separate from your true self - which is why in the beginning it says: "The Matrix Has You..." In the beginning he existed as an illusory identity of Mr Anderson, the Matrix had him but he did not have the Matrix. He was not aware of the self beyond identity and form so through meeting Morpheus, "he died" and realised himself as the "chosen one" who can directly change and save his experience. What this means is ANYONE of these characters could of became 'Neo' because Neo is a realisation of the true self similar to "Christ Consciousness" as we know it... We are ALL this chosen one but until this is realised, we will never find it but seek it.... You do not become it, you ARE already IT... Any process is like running past the finish line after you've won a race, if you continue running, when do you acknowledge you've already finished... ✨🙌🏾💫 © Awakened Gnostic

🧬Maxpein🧬

59,563 Aufrufe • vor 10 Monaten

THE MATRIX SPOON BOY'S MESSAGE Many have seen the Matrix but it seems fewer grasp just how powerful the 'spoon boy's' message was when Neo first visits the oracle... The boy says to Neo: "Do not try and bend the spoon, that's impossible. Instead, only try to realize the truth...there is no spoon. Then you'll see that it is not the spoon that bends, it is only yourself." What he's saying is there is nothing that is NOT yourself, BECAUSE 'Neo' was not just an entity as the body, 'Neo' was the entire Matrix becoming self aware to re-write and change itself - this is why in the final movie there is rain and in the very end there is sunshine. Anyone who knows the Matrix knows EVERYTHING which appears is really shaped through Matrix code which means 'Neo' (who could visibly see this code) was all of the characters and places, not just the one we saw in the flesh as 'Neo'. Why do you think in the end Mr Smith asks Neo if he realises its impossible to win, that he simply can't.... And the reason nothing can be 'won' is they are not separate and Neo began realising himself as 'The Matrix' itself rather than just a body which is why he no longer fights Smith and allows him to enter his body.... The body was not 'Neo'.... 'Neo' becoming the chosen one is acknowledging the self as the entire Matrix, as one self and not two...(Mr. Anderson and Smith) There is no body which is separate from earth, only MIND has made this concept. Earth and body are ONE beyond what we call them... We are not Mr Anderson nor Neo, we are the entire Matrix writing itself to experience itself. Realise everything in the form which changes is only yourself because the self is not just limited to this body... Each and everyone of you are this 'CHOSEN ONE'. But what did Morpheus say to Neo... "DON'T THINK YOU ARE, KNOW YOU ARE"..... Until The One believes... They remain as just a character feeling stuck inside of something or somewhere when there is no where or place separate from your true self - which is why in the beginning it says: "The Matrix Has You..." In the beginning he existed as an illusory identity of Mr Anderson, the Matrix had him but he did not have the Matrix. He was not aware of the self beyond identity and form so through meeting Morpheus, "he died" and realised himself as the "chosen one" who can directly change and save his experience. What this means is ANYONE of these characters could of became 'Neo' because Neo is a realisation of the true self similar to "Christ Consciousness" as we know it... We are ALL this chosen one but until this is realised, we will never find it but seek it.... You do not become it, you ARE already IT... Any process is like running past the finish line after you've won a race, if you continue running, when do you acknowledge you've already finished... ✨🙌🏾💫 © Awakened Gnostic

THE MATRIX SPOON BOY'S MESSAGE Many have seen the Matrix but it seems fewer grasp just how powerful the 'spoon boy's' message was when Neo first visits the oracle... The boy says to Neo: "Do not try and bend the spoon, that's impossible. Instead, only try to realize the truth...there is no spoon. Then you'll see that it is not the spoon that bends, it is only yourself." What he's saying is there is nothing that is NOT yourself, BECAUSE 'Neo' was not just an entity as the body, 'Neo' was the entire Matrix becoming self aware to re-write and change itself - this is why in the final movie there is rain and in the very end there is sunshine. Anyone who knows the Matrix knows EVERYTHING which appears is really shaped through Matrix code which means 'Neo' (who could visibly see this code) was all of the characters and places, not just the one we saw in the flesh as 'Neo'. Why do you think in the end Mr Smith asks Neo if he realises its impossible to win, that he simply can't.... And the reason nothing can be 'won' is they are not separate and Neo began realising himself as 'The Matrix' itself rather than just a body which is why he no longer fights Smith and allows him to enter his body.... The body was not 'Neo'.... 'Neo' becoming the chosen one is acknowledging the self as the entire Matrix, as one self and not two...(Mr. Anderson and Smith) There is no body which is separate from earth, only MIND has made this concept. Earth and body are ONE beyond what we call them... We are not Mr Anderson nor Neo, we are the entire Matrix writing itself to experience itself. Realise everything in the form which changes is only yourself because the self is not just limited to this body... Each and everyone of you are this 'CHOSEN ONE'. But what did Morpheus say to Neo... "DON'T THINK YOU ARE, KNOW YOU ARE"..... Until The One believes... They remain as just a character feeling stuck inside of something or somewhere when there is no where or place separate from your true self - which is why in the beginning it says: "The Matrix Has You..." In the beginning he existed as an illusory identity of Mr Anderson, the Matrix had him but he did not have the Matrix. He was not aware of the self beyond identity and form so through meeting Morpheus, "he died" and realised himself as the "chosen one" who can directly change and save his experience. What this means is ANYONE of these characters could of became 'Neo' because Neo is a realisation of the true self similar to "Christ Consciousness" as we know it... We are ALL this chosen one but until this is realised, we will never find it but seek it.... You do not become it, you ARE already IT... Any process is like running past the finish line after you've won a race, if you continue running, when do you acknowledge you've already finished... ✨🙌🏾💫 © Awakened Gnostic

🧬Maxpein🧬

129,688 Aufrufe • vor 1 Jahr

Jason Segel revealed that he made a huge glass pipe that he and Seth Rogen used for smoking weed. Jason Segel: All we kind of knew is that you and I both liked to smoke weed. Seth Rogen: Yes, and a side note to The Matrix coming out is this Bill Pope, who's the cinematographer of The Matrix, was shooting our pilot. And the whole marketing campaign for The Matrix was "What is The Matrix?" and we'd always go to Bill and be like, "What is The Matrix?" And he wouldn’t tell us! But it actually came out the day the pilot wrapped. Jason Segel: Holy shit. Seth Rogen: So the whole, in my head, the whole pilot was just a march to The Matrix being released. Jason Segel: 100%! And then we rolled giant joints... Seth Rogen: Yeah. Jason Segel: ...and we drove to the movie theater, and we saw The Matrix together. Seth Rogen: We actually smoked weed out of a giant glass pipe that you had in your car! Like a huge, like a comically large, like dragon-shaped glass pipe. Jason Segel: I think I made that pipe because I had graduated high school with the assumption that you just start doing professional acting.

Jason Segel revealed that he made a huge glass pipe that he and Seth Rogen used for smoking weed. Jason Segel: All we kind of knew is that you and I both liked to smoke weed. Seth Rogen: Yes, and a side note to The Matrix coming out is this Bill Pope, who's the cinematographer of The Matrix, was shooting our pilot. And the whole marketing campaign for The Matrix was "What is The Matrix?" and we'd always go to Bill and be like, "What is The Matrix?" And he wouldn’t tell us! But it actually came out the day the pilot wrapped. Jason Segel: Holy shit. Seth Rogen: So the whole, in my head, the whole pilot was just a march to The Matrix being released. Jason Segel: 100%! And then we rolled giant joints... Seth Rogen: Yeah. Jason Segel: ...and we drove to the movie theater, and we saw The Matrix together. Seth Rogen: We actually smoked weed out of a giant glass pipe that you had in your car! Like a huge, like a comically large, like dragon-shaped glass pipe. Jason Segel: I think I made that pipe because I had graduated high school with the assumption that you just start doing professional acting.

Ruzy

465,327 Aufrufe • vor 3 Monaten

The way this would be an incredible climax of a movie and it's not the climax and you still have an awesome fight left to go. The 3rd act of The Matrix is so good it beggars belief.

The way this would be an incredible climax of a movie and it's not the climax and you still have an awesome fight left to go. The 3rd act of The Matrix is so good it beggars belief.

All Things Movies

12,652 Aufrufe • vor 5 Monaten

A concise and profound summary of the deliberate controlled demolition of the West. "Something is happening across the Western world... A silent shift is underway and it has a name—the inversion matrix." "The end goal? A population too confused to resist and too fragmented to unite." "The longer we stay silent, the more the inversion matrix tightens... This is about survival." "And if you're still listening, it means the program didn't fully work on you."

A concise and profound summary of the deliberate controlled demolition of the West. "Something is happening across the Western world... A silent shift is underway and it has a name—the inversion matrix." "The end goal? A population too confused to resist and too fragmented to unite." "The longer we stay silent, the more the inversion matrix tightens... This is about survival." "And if you're still listening, it means the program didn't fully work on you."

Wide Awake Media

62,794 Aufrufe • vor 6 Monaten

A 91-year-old professor is why Nvidia is worth $4 trillion. His name is Gilbert Strang. He teaches linear algebra at MIT. Every AI model on Earth runs on his course. The course has been free on YouTube since 2005. The videos have earned him nothing. MIT 18.06 opens with "The Geometry of Linear Equations." No advanced math. Strang takes a system of two equations, draws it two ways, and shows the class that a matrix is a picture, not an abstraction. The row picture is two lines that cross. The column picture is two arrows that sum to a target. Every neural network on Earth operates on the column picture. Strang first taught linear algebra at MIT in 1962. He wrote the textbook in 1976. It is on every serious engineer's shelf. Every quant fund, every ML lab, every rendering engine at Pixar is running his math. His central insight is that most people are taught matrices as bookkeeping. That is the first thing to unlearn. A matrix is a linear transformation. A linear transformation is a way of moving space. Once you see the space move, the math stops being algebra and becomes geometry. The Kalman filter is a linear system. PCA is a linear system. Every gradient step in a neural net is a matrix-vector product. GPT is a stack of matrix-vector products, each one a scene from MIT 18.06 running on a Blackwell GPU. He retired in 2023 after 61 years at MIT. The course is still up. Watched tens of millions of times. The chip is $40,000. Strang never asked for a royalty.

A 91-year-old professor is why Nvidia is worth $4 trillion. His name is Gilbert Strang. He teaches linear algebra at MIT. Every AI model on Earth runs on his course. The course has been free on YouTube since 2005. The videos have earned him nothing. MIT 18.06 opens with "The Geometry of Linear Equations." No advanced math. Strang takes a system of two equations, draws it two ways, and shows the class that a matrix is a picture, not an abstraction. The row picture is two lines that cross. The column picture is two arrows that sum to a target. Every neural network on Earth operates on the column picture. Strang first taught linear algebra at MIT in 1962. He wrote the textbook in 1976. It is on every serious engineer's shelf. Every quant fund, every ML lab, every rendering engine at Pixar is running his math. His central insight is that most people are taught matrices as bookkeeping. That is the first thing to unlearn. A matrix is a linear transformation. A linear transformation is a way of moving space. Once you see the space move, the math stops being algebra and becomes geometry. The Kalman filter is a linear system. PCA is a linear system. Every gradient step in a neural net is a matrix-vector product. GPT is a stack of matrix-vector products, each one a scene from MIT 18.06 running on a Blackwell GPU. He retired in 2023 after 61 years at MIT. The course is still up. Watched tens of millions of times. The chip is $40,000. Strang never asked for a royalty.

Ochob

130,880 Aufrufe • vor 1 Monat

We are being played by evil people who distort and twist reality. Petty was an agitator and insurrectionist. Petty is a victim of the radical lefts brainwashing, the matrix brainwashing. All these protestors are the militant wing of the matrix, they fight for and protect the very system that is oppressing them, and oppresses us all. Hard times await us all because of the cowardice of the people who know better, that is what has allowed this country to get to where it is today. I hope you are all ready for an absolute shit show of a year. This corrupt government would rather burn everything down and rule over ashes, than hold a single government official accountable.

We are being played by evil people who distort and twist reality. Petty was an agitator and insurrectionist. Petty is a victim of the radical lefts brainwashing, the matrix brainwashing. All these protestors are the militant wing of the matrix, they fight for and protect the very system that is oppressing them, and oppresses us all. Hard times await us all because of the cowardice of the people who know better, that is what has allowed this country to get to where it is today. I hope you are all ready for an absolute shit show of a year. This corrupt government would rather burn everything down and rule over ashes, than hold a single government official accountable.

The Artist known as Jess

18,646 Aufrufe • vor 7 Monaten

A Fields medalist walked into an Oxford room in 2020 and taught first-year students what a determinant is. The lecturer is James Maynard. He was 32 at the time and had already broken open a problem the field had been stuck on for 2,000 years. The subject is Linear Algebra II. He is defining a function that eats a square matrix and returns 1 number. The number is a volume. Feed a matrix the unit cube and the determinant tells you how much the transformation stretched or squashed it. A determinant of 0 means the shape got flattened into a lower dimension. Nothing can unflatten it, which is exactly when a matrix has no inverse. A negative determinant means the space got turned inside out. Every graphics engine, every physics simulation, every solver checks that 1 number before doing anything else. Maynard won the Fields Medal in 2022 for work on gaps between primes, sharpening the bound Yitang Zhang had produced from nothing. Oxford films these and puts them up for free, tutorials and problem sheets included. The best number theorist of his generation spent an hour on the volume of a box.

A Fields medalist walked into an Oxford room in 2020 and taught first-year students what a determinant is. The lecturer is James Maynard. He was 32 at the time and had already broken open a problem the field had been stuck on for 2,000 years. The subject is Linear Algebra II. He is defining a function that eats a square matrix and returns 1 number. The number is a volume. Feed a matrix the unit cube and the determinant tells you how much the transformation stretched or squashed it. A determinant of 0 means the shape got flattened into a lower dimension. Nothing can unflatten it, which is exactly when a matrix has no inverse. A negative determinant means the space got turned inside out. Every graphics engine, every physics simulation, every solver checks that 1 number before doing anything else. Maynard won the Fields Medal in 2022 for work on gaps between primes, sharpening the bound Yitang Zhang had produced from nothing. Oxford films these and puts them up for free, tutorials and problem sheets included. The best number theorist of his generation spent an hour on the volume of a box.

Gaspar

122,833 Aufrufe • vor 1 Monat

The Matrix is not a movie. It’s a system of beliefs designed to keep your mind asleep. They don’t need chains. They only need your agreement. They distract you with: • Entertainment • Debt • News • Social roles • Endless scrolling So you never look within and realize the truth: You are not just a person. You are consciousness itself. An infinite being having a temporary experience. The moment you remember, the game changes. You stop reacting. You start creating. You stop searching. You start knowing. The Matrix fears awakened souls — because awakened souls can’t be controlled. Keep awakening. The world is waiting for you. 🌑✨

The Matrix is not a movie. It’s a system of beliefs designed to keep your mind asleep. They don’t need chains. They only need your agreement. They distract you with: • Entertainment • Debt • News • Social roles • Endless scrolling So you never look within and realize the truth: You are not just a person. You are consciousness itself. An infinite being having a temporary experience. The moment you remember, the game changes. You stop reacting. You start creating. You stop searching. You start knowing. The Matrix fears awakened souls — because awakened souls can’t be controlled. Keep awakening. The world is waiting for you. 🌑✨

vegastar

30,716 Aufrufe • vor 10 Monaten

A timely “Matrix” remake about internet censorship in Russia A satirical video circulating online parodies a famous chase scene from The Matrix. But instead of agents, the character is chased by an official telling him that “the internet is gone,” “VPN won’t save you,” and “Telegram, Instagram and YouTube are already in the past.” In one scene, the character is told to use MAX — a state-backed Russian messaging service promoted by the authorities as an alternative to Western platforms. The video mocks growing internet censorship in Russia: blocked websites, “white lists” of allowed services, and attempts to replace popular platforms with state-controlled ones.

A timely “Matrix” remake about internet censorship in Russia A satirical video circulating online parodies a famous chase scene from The Matrix. But instead of agents, the character is chased by an official telling him that “the internet is gone,” “VPN won’t save you,” and “Telegram, Instagram and YouTube are already in the past.” In one scene, the character is told to use MAX — a state-backed Russian messaging service promoted by the authorities as an alternative to Western platforms. The video mocks growing internet censorship in Russia: blocked websites, “white lists” of allowed services, and attempts to replace popular platforms with state-controlled ones.

NEXTA

33,367 Aufrufe • vor 6 Monaten