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Geometry of Machine Learning Models - Gaussian Process Kernel In 1948 Norbert Wiener framed prediction as a correlation problem, and in the 1970s George Wahba clarified that picking a smoothness preference is the same as picking a kernel. The motivation is that whenever data i s sparse and noisy,... show more

Mathelirium

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15,661 次观看 • 6 个月前 •via X (Twitter)

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We often hear that machine learning models "learn patterns in data". But what does that actually look like in geometry? If you dropped a little elastic mesh into a cloud of points and let it learn, how would it fold itself to match the shape of the data? In this scene we watch a self-organizing map...a simple unsupervised neural model...learn the shape of a two-dimensional dataset arranged in a spiral arm. On top of this, we lay down a square grid of neurons whose weights live in the same plane. At the start, this grid is just a flat net floating across the cloud...it knows nothing about the structure underneath. Learning is a repeated game: pick a random data point, find the neuron whose weight is closest, and then nudge that neuron and its neighbours toward the point. Do this again and again, while slowly shrinking how far the neighbourhood influence spreads. #MachineLearning #ManifoldLearning #UnsupervisedLearning #NeuralMaps #GeometricML

We often hear that machine learning models "learn patterns in data". But what does that actually look like in geometry? If you dropped a little elastic mesh into a cloud of points and let it learn, how would it fold itself to match the shape of the data? In this scene we watch a self-organizing map...a simple unsupervised neural model...learn the shape of a two-dimensional dataset arranged in a spiral arm. On top of this, we lay down a square grid of neurons whose weights live in the same plane. At the start, this grid is just a flat net floating across the cloud...it knows nothing about the structure underneath. Learning is a repeated game: pick a random data point, find the neuron whose weight is closest, and then nudge that neuron and its neighbours toward the point. Do this again and again, while slowly shrinking how far the neighbourhood influence spreads. #MachineLearning #ManifoldLearning #UnsupervisedLearning #NeuralMaps #GeometricML

Mathelirium

139,757 次观看 • 9 个月前

We often hear that Machine Learning models learn patterns in data. But what does that actually look like in Geometry? If you dropped a little elastic mesh into a cloud of points and let it learn, how would it fold itself to match the shape of the data? In this scene we watch a Self-Organizing Map (SOM), a simple unsupervised neural model, learn the shape of a 3D datasets l, one static and the other dynamic. On top of this, we lay down a square grid of neurons whose weights live in the same plane. At the start, this grid is just a flat net floating across the cloud. It knows nothing about the structure underneath. Learning is a repeated game: Pick a random data point, find the neuron whose weight is closest, and then nudge that neuron and its neighbours toward the point. Do this again and again, while slowly shrinking how far the neighbourhood influence spreads. Python code is available for Subscribers. #MachineLearning #ManifoldLearning #UnsupervisedLearning #NeuralMaps #GeometricML

We often hear that Machine Learning models learn patterns in data. But what does that actually look like in Geometry? If you dropped a little elastic mesh into a cloud of points and let it learn, how would it fold itself to match the shape of the data? In this scene we watch a Self-Organizing Map (SOM), a simple unsupervised neural model, learn the shape of a 3D datasets l, one static and the other dynamic. On top of this, we lay down a square grid of neurons whose weights live in the same plane. At the start, this grid is just a flat net floating across the cloud. It knows nothing about the structure underneath. Learning is a repeated game: Pick a random data point, find the neuron whose weight is closest, and then nudge that neuron and its neighbours toward the point. Do this again and again, while slowly shrinking how far the neighbourhood influence spreads. Python code is available for Subscribers. #MachineLearning #ManifoldLearning #UnsupervisedLearning #NeuralMaps #GeometricML

Mathelirium

76,335 次观看 • 6 个月前

We often hear that Machine Learning models learn patterns in data. But what does that look like in geometry? Picture dropping an elastic mesh into a cloud of points and letting it adapt. How would it bend, stretch, and settle so it matches the shape hiding in the data? In this scene we watch a self-organizing map(SOM)...a classic unsupervised neural model...learn a 2D dataset arranged like a spiral arm. Over the points we place a square grid of neurons whose weights live in the same plane. At the start it’s just a flat net drifting across the cloud. No clue what the structure is. Fir the SOM, learning is a repeated game: Pick a random data point, find the neuron whose weight is closest, then nudge that neuron and its neighbours toward the point. Repeat, repeat, repeat...while gradually shrinking how wide the neighbourhood influence spreads. The result is satisfying...the grid stops being a grid and turns into a coordinate sheet wrapped onto the spiral. #MachineLearning #ManifoldLearning #UnsupervisedLearning #NeuralMaps #GeometricML #SelfOrganizingMap #Topology

We often hear that Machine Learning models learn patterns in data. But what does that look like in geometry? Picture dropping an elastic mesh into a cloud of points and letting it adapt. How would it bend, stretch, and settle so it matches the shape hiding in the data? In this scene we watch a self-organizing map(SOM)...a classic unsupervised neural model...learn a 2D dataset arranged like a spiral arm. Over the points we place a square grid of neurons whose weights live in the same plane. At the start it’s just a flat net drifting across the cloud. No clue what the structure is. Fir the SOM, learning is a repeated game: Pick a random data point, find the neuron whose weight is closest, then nudge that neuron and its neighbours toward the point. Repeat, repeat, repeat...while gradually shrinking how wide the neighbourhood influence spreads. The result is satisfying...the grid stops being a grid and turns into a coordinate sheet wrapped onto the spiral. #MachineLearning #ManifoldLearning #UnsupervisedLearning #NeuralMaps #GeometricML #SelfOrganizingMap #Topology

Mathelirium

23,021 次观看 • 7 个月前

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 次观看 • 7 个月前

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.

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.

Mathelirium

15,566 次观看 • 6 个月前

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 次观看 • 6 个月前

In 1998, Japanese Mathematician, Engineer and Machine Learning pioneer Shun-ichi Amari published "Natural Gradient Works Efficiently in Learning (722 Cites in Papers and 9 Cites in Patents)" and made a point that still feels fresh even today If your loss is L(θ), then the usual update θ̇ = −∇ L(θ) quietly assumes your parameter space is flat. Amari asked what happens when the model itself has geometry, described by G(θ), the Fisher information. Then the more natural direction becomes θ̇ = −G(θ)⁻¹∇ L(θ). This is the same loss, but with a different notion of distance. As the animation shows, ordinary Gradient Descent follows the raw slope and gets dragged around by distortion, while the natural gradient moves in a way that respects the geometry of the statistical model itself.

In 1998, Japanese Mathematician, Engineer and Machine Learning pioneer Shun-ichi Amari published "Natural Gradient Works Efficiently in Learning (722 Cites in Papers and 9 Cites in Patents)" and made a point that still feels fresh even today If your loss is L(θ), then the usual update θ̇ = −∇ L(θ) quietly assumes your parameter space is flat. Amari asked what happens when the model itself has geometry, described by G(θ), the Fisher information. Then the more natural direction becomes θ̇ = −G(θ)⁻¹∇ L(θ). This is the same loss, but with a different notion of distance. As the animation shows, ordinary Gradient Descent follows the raw slope and gets dragged around by distortion, while the natural gradient moves in a way that respects the geometry of the statistical model itself.

Mathelirium

45,802 次观看 • 5 个月前

The goal isn't despair, it's indifference. It's enlightenment. It's having the ability to step in and out of the muck as you see fit without a handler or a sponsor coming down on you for it. I get fired up about things but this isn't my entire identity. I can put my phone down and walk away whenever I want and what a blessing that is.

The goal isn't despair, it's indifference. It's enlightenment. It's having the ability to step in and out of the muck as you see fit without a handler or a sponsor coming down on you for it. I get fired up about things but this isn't my entire identity. I can put my phone down and walk away whenever I want and what a blessing that is.

Shipwreck

20,812 次观看 • 7 个月前

I don't want the Mormons to think we're picking on them, Jehovah's Witnesses are every bit as much of a cult as they are. What they both share in common is that they have a false occult 'Jesus' who is nothing like the Jesus of the Bible.

I don't want the Mormons to think we're picking on them, Jehovah's Witnesses are every bit as much of a cult as they are. What they both share in common is that they have a false occult 'Jesus' who is nothing like the Jesus of the Bible.

Now The End Begins

24,705 次观看 • 11 个月前

A lot of robot learning pipelines treat embodiment mismatch as a software problem. Collect data with one device, retarget the motion to another robot, and try to deal with the differences later. TwinDEX flips that idea around. This system is from a Chinese robotics company called X Square. Instead of starting with a generic data-collection device, the team co-designs a wearable three-finger end-effector and a robotic hand as two sides of the same learning system. They align the things that actually matter during manipulation: joint structure, link proportions, contact geometry, surface properties, visual appearance, sensing, and timing. That matters because dexterous manipulation is much more than matching hand poses. A few millimeters of contact error or a different force relationship can completely change how a task is executed. In the collection evaluation, TwinDEX delivered up to 5.3 times the effective throughput of on-robot teleoperation. It’s a useful reminder that scaling robot learning may not only be about bigger models and more data. Sometimes the hardware collecting the data is part of the data problem itself.

A lot of robot learning pipelines treat embodiment mismatch as a software problem. Collect data with one device, retarget the motion to another robot, and try to deal with the differences later. TwinDEX flips that idea around. This system is from a Chinese robotics company called X Square. Instead of starting with a generic data-collection device, the team co-designs a wearable three-finger end-effector and a robotic hand as two sides of the same learning system. They align the things that actually matter during manipulation: joint structure, link proportions, contact geometry, surface properties, visual appearance, sensing, and timing. That matters because dexterous manipulation is much more than matching hand poses. A few millimeters of contact error or a different force relationship can completely change how a task is executed. In the collection evaluation, TwinDEX delivered up to 5.3 times the effective throughput of on-robot teleoperation. It’s a useful reminder that scaling robot learning may not only be about bigger models and more data. Sometimes the hardware collecting the data is part of the data problem itself.

Alamin

48,112 次观看 • 8 天前

String Theory is one of the few frameworks that tries to describe Quantum Physics and Gravity in the same mathematical language. In this animation, the glowing loop is the string, the shifting color along it represent its quantum vibration modes, and the surrounding fabric is a proxy for Spacetime responding. When you quantize a string, one of its vibration modes behaves like a graviton. So, geometry shows up as part of the same quantum system. #StringTheory #QuantumGravity #GeneralRelativity #QuantumPhysics #TheoreticalPhysics #PhysicsVisualization

String Theory is one of the few frameworks that tries to describe Quantum Physics and Gravity in the same mathematical language. In this animation, the glowing loop is the string, the shifting color along it represent its quantum vibration modes, and the surrounding fabric is a proxy for Spacetime responding. When you quantize a string, one of its vibration modes behaves like a graviton. So, geometry shows up as part of the same quantum system. #StringTheory #QuantumGravity #GeneralRelativity #QuantumPhysics #TheoreticalPhysics #PhysicsVisualization

Mathelirium

42,221 次观看 • 6 个月前

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

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

Mathelirium

13,657 次观看 • 7 个月前

James Fishback says Byron Donalds is LYING about data centers! Says this has nothing to do with China and it’s all about GREED. “There are 4,200 data centers in the United States. There are 470 in China. We've already won the AI war. My grandfather was a computer science major at Florida Atlantic University about 30 minutes south of here in Boca. And he would tell you that in the 1970s and 80s, computers were the size of Costco warehouses and now those same computers fit in our pocket. Why are we building an AI data center that in five years is going to be obsolete, is going to be one one hundredth of the size. And so I fear it's because a lot of the big land developers want to buy up cheap land, flip it for the next AI data center. So it's a greedy thing. It's a greed thing. And I don't want that to happen in our state because you know what? If you buy something and you screw up, you can return it. You could sell it. If you pave over citrus groves or the Everglades or a wetlands to build the data center, you cannot easily undo that. And so I don't want our farmers, I don't want our rural towns to be run roughshod over. My opponent, Byron Donalds, will say, well, what about the AI data center? Don't they have property rights? And I would say to him, what about the property rights of the people who live a hundred feet from the data center? Where there is EMF, where there is audible noise pollution, where there is the potential even for small radioactive waves? What happens in that case? Do they not have property rights? They don't have to live next to something like that.”

James Fishback says Byron Donalds is LYING about data centers! Says this has nothing to do with China and it’s all about GREED. “There are 4,200 data centers in the United States. There are 470 in China. We've already won the AI war. My grandfather was a computer science major at Florida Atlantic University about 30 minutes south of here in Boca. And he would tell you that in the 1970s and 80s, computers were the size of Costco warehouses and now those same computers fit in our pocket. Why are we building an AI data center that in five years is going to be obsolete, is going to be one one hundredth of the size. And so I fear it's because a lot of the big land developers want to buy up cheap land, flip it for the next AI data center. So it's a greedy thing. It's a greed thing. And I don't want that to happen in our state because you know what? If you buy something and you screw up, you can return it. You could sell it. If you pave over citrus groves or the Everglades or a wetlands to build the data center, you cannot easily undo that. And so I don't want our farmers, I don't want our rural towns to be run roughshod over. My opponent, Byron Donalds, will say, well, what about the AI data center? Don't they have property rights? And I would say to him, what about the property rights of the people who live a hundred feet from the data center? Where there is EMF, where there is audible noise pollution, where there is the potential even for small radioactive waves? What happens in that case? Do they not have property rights? They don't have to live next to something like that.”

Chris Nelson 🏝️🇺🇸

27,295 次观看 • 29 天前

Stealing Energy from a Rotating Black Hole A rotating black hole doesn’t just pull things in. It drags spacetime itself into motion. In the spinning region just outside the horizon, nothing can remain still in any normal sense. That strange rule opens a loophole. One incoming body can split, with one piece swallowed while the other escapes with more energy than it came in with. A Penrose-style heist where the difference is paid for by the black hole’s rotation. The same idea shows up in wave form. A coherent packet can skim that region and return brighter, as if the geometry itself acted like an amplifier. Split near the ergosphere and you can steal spin. Skim it as a wave and you can come back louder.

Stealing Energy from a Rotating Black Hole A rotating black hole doesn’t just pull things in. It drags spacetime itself into motion. In the spinning region just outside the horizon, nothing can remain still in any normal sense. That strange rule opens a loophole. One incoming body can split, with one piece swallowed while the other escapes with more energy than it came in with. A Penrose-style heist where the difference is paid for by the black hole’s rotation. The same idea shows up in wave form. A coherent packet can skim that region and return brighter, as if the geometry itself acted like an amplifier. Split near the ergosphere and you can steal spin. Skim it as a wave and you can come back louder.

Mathelirium

20,314 次观看 • 7 个月前

Christian Kirk explained the process of how he ended up signing with the #49ers this offseason: “I was in a position where I could be a little more picky on where I wanted to go at this point in my career. It just all depended on being in the right situation.……You know a lot of respect for that organization and the more I started thinking about it I’m like yes, that’s a great fit and you know I fit into that locker room really well and you know I want to be a part of what they’re doing.” Via: In Good Company with Mitch Morse

Christian Kirk explained the process of how he ended up signing with the #49ers this offseason: “I was in a position where I could be a little more picky on where I wanted to go at this point in my career. It just all depended on being in the right situation.……You know a lot of respect for that organization and the more I started thinking about it I’m like yes, that’s a great fit and you know I fit into that locker room really well and you know I want to be a part of what they’re doing.” Via: In Good Company with Mitch Morse

OurSF49ers

70,858 次观看 • 5 个月前

Club fitting must be married with instruction. A golfer adapts to whatever is in their hands, so poorly fit clubs can train compensations that a lesson might have to fight. When the fitting is dialed in, the coaching and the clubs are able to pull in the same direction. As Dave Phillips says, "Make sure your clubs are working toward where you want to go, not stopping you from where you want to go."

Club fitting must be married with instruction. A golfer adapts to whatever is in their hands, so poorly fit clubs can train compensations that a lesson might have to fight. When the fitting is dialed in, the coaching and the clubs are able to pull in the same direction. As Dave Phillips says, "Make sure your clubs are working toward where you want to go, not stopping you from where you want to go."

TPI

16,638 次观看 • 3 个月前

Robert Benzie: "What Danielle Smith has done is open a can of worms to solve a problem within the United Conservative Party just as David Cameron opened a can of worms to solve a problem in the UK Conservative Party ... why would you ask a question at the risk of finding an answer that you don't want. I think it's just insane on many levels."

Robert Benzie: "What Danielle Smith has done is open a can of worms to solve a problem within the United Conservative Party just as David Cameron opened a can of worms to solve a problem in the UK Conservative Party ... why would you ask a question at the risk of finding an answer that you don't want. I think it's just insane on many levels."

Scott Robertson

40,521 次观看 • 4 个月前