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More on the system used for the Eyebrows. As shown before, a curve is projected on the face, and then the eyebrow mesh is wrapped onto the curve. Unlike before, there is now a second layer of projection that guarantees the eyebrow mesh stays above the surface of the... show more

aVersionOfReality

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20,028 Aufrufe • vor 1 Jahr •via X (Twitter)

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The #geometrynodes Curve Normals Proxy Rig is almost ready! You place it on the face and adjust some controls to line things up, and it just works. The controls can be worked with in lots of different ways. You can attach it to an existing rig or animate it. Those bones are controlling a mesh which controls the curve points, so you can also make Shapekeys on the meshes instead and Drive them to match other expression keys! The forehead above the top curve blends to Radial Normals, and under the chin blends to the actual mesh Normals. I'm adding the rest of the controls to allow completely arbitrary Normals per curve point, and then its just cleanup and it can be released! (There's lots more that can be added to it like falloff and interpolation controls, but if I try to put everything into the first version it'll never release.)

The #geometrynodes Curve Normals Proxy Rig is almost ready! You place it on the face and adjust some controls to line things up, and it just works. The controls can be worked with in lots of different ways. You can attach it to an existing rig or animate it. Those bones are controlling a mesh which controls the curve points, so you can also make Shapekeys on the meshes instead and Drive them to match other expression keys! The forehead above the top curve blends to Radial Normals, and under the chin blends to the actual mesh Normals. I'm adding the rest of the controls to allow completely arbitrary Normals per curve point, and then its just cleanup and it can be released! (There's lots more that can be added to it like falloff and interpolation controls, but if I try to put everything into the first version it'll never release.)

aVersionOfReality

57,639 Aufrufe • vor 1 Jahr

This is how the eyes have been modelled! it has an eye white mesh, iris mesh, a mesh for shadow and then the eyelids. The eyelids can move separately for more emotion. And the eyes can look around through blendshapes but there is clipping because of curved surfaces.

This is how the eyes have been modelled! it has an eye white mesh, iris mesh, a mesh for shadow and then the eyelids. The eyelids can move separately for more emotion. And the eyes can look around through blendshapes but there is clipping because of curved surfaces.

Zel Kanis 🦾 3DVartist (@zelkanis.com 🦋)

38,811 Aufrufe • vor 10 Monaten

In Calculus of Variations, we give up the idea of only optimizing values and start optimizing geometries instead. The unknown is not a single x. It is a whole curve/surface y(x). The object you are minimizing is usually not a simple formula that you can guess. It is an integral that judges the whole shape. In our first lecture, we discuss the famous Brachistochrone problem. You choose two points, turn on gravity and ask a question which almost sounds too simple...which track will allow a bead to move from A to B in the minimum time? At your first attempt, your instinct will lead you astray. It is not the straight line. It is not the drop hard then cruise sketch either. The winner turns out to be a cycloid...the curve a point on a rolling circle traces. The track is the moving character in the animation. We begin with a flawed curve, perform gradient descent in curve-space, and observe the geometry change frame by frame as T[y] collapses to the brachistochrone. Please see the comment below for the math breakdown. #CalculusOfVariations #Brachistochrone #Cycloid #Physics #Optimization #Mathematics

In Calculus of Variations, we give up the idea of only optimizing values and start optimizing geometries instead. The unknown is not a single x. It is a whole curve/surface y(x). The object you are minimizing is usually not a simple formula that you can guess. It is an integral that judges the whole shape. In our first lecture, we discuss the famous Brachistochrone problem. You choose two points, turn on gravity and ask a question which almost sounds too simple...which track will allow a bead to move from A to B in the minimum time? At your first attempt, your instinct will lead you astray. It is not the straight line. It is not the drop hard then cruise sketch either. The winner turns out to be a cycloid...the curve a point on a rolling circle traces. The track is the moving character in the animation. We begin with a flawed curve, perform gradient descent in curve-space, and observe the geometry change frame by frame as T[y] collapses to the brachistochrone. Please see the comment below for the math breakdown. #CalculusOfVariations #Brachistochrone #Cycloid #Physics #Optimization #Mathematics

Mathelirium

23,254 Aufrufe • vor 3 Monaten

$Math. Truchet tiles. As you randomly orient the tiles, is a closed smooth curve always produced? (For random orientations, what is the fraction of closed circles?) By Frédéric Vayssouze-Faure, Used with permission.$

Math. Truchet tiles. As you randomly orient the tiles, is a closed smooth curve always produced? (For random orientations, what is the fraction of closed circles?) By Frédéric Vayssouze-Faure, Used with permission.

Cliff Pickover

14,464 Aufrufe • vor 1 Jahr

While hiking, these people come across a Ford Mustang 5.0 that had missed a curve and flipped over the guardrail above. There are marks on the car where the jaws of life were used along with a pair of shoes on the ground near the wreck. Why was this left there and not removed?

While hiking, these people come across a Ford Mustang 5.0 that had missed a curve and flipped over the guardrail above. There are marks on the car where the jaws of life were used along with a pair of shoes on the ground near the wreck. Why was this left there and not removed?

Blonde of War (JJ)

237,827 Aufrufe • vor 6 Monaten

I'm putting a lot of attention into getting a high quality transfer for the Face Proxy Mesh we're adding to the Fondant Custom Normals Blender addon. Even if the proxy has great Normals, it will not matter if the transfer is distorted. A basic world space Nearest Surface (aka Nearest Face Interpolated) transfer can get screwed up if there are gaps between the meshes. And if they are different shapes and poly counts, there will be! So the first big piece of the puzzle is getting a clean transfer. Before transferring Normals, a transfer space is made and a UV map is transferred from the proxy. Then any other data needed can be transferred in that UV space. As long as it is right, any other data will be clean! (Normals or anything else you might want.) And a UV map is easy to debug because you can put a grid texture on it. If the grid is evenly spaced, then distortion is minimal. This clip shows the differences in distortion between a basic World Space transfer and a better transfer space made by blending Sphere projection and a simple projection of the face forward onto the proxy (used down the center line.) Different faces will need slightly different configuration. Most of this is automatic, but the addon will have some simple controls to adjust it to different face shapes.

I'm putting a lot of attention into getting a high quality transfer for the Face Proxy Mesh we're adding to the Fondant Custom Normals Blender addon. Even if the proxy has great Normals, it will not matter if the transfer is distorted. A basic world space Nearest Surface (aka Nearest Face Interpolated) transfer can get screwed up if there are gaps between the meshes. And if they are different shapes and poly counts, there will be! So the first big piece of the puzzle is getting a clean transfer. Before transferring Normals, a transfer space is made and a UV map is transferred from the proxy. Then any other data needed can be transferred in that UV space. As long as it is right, any other data will be clean! (Normals or anything else you might want.) And a UV map is easy to debug because you can put a grid texture on it. If the grid is evenly spaced, then distortion is minimal. This clip shows the differences in distortion between a basic World Space transfer and a better transfer space made by blending Sphere projection and a simple projection of the face forward onto the proxy (used down the center line.) Different faces will need slightly different configuration. Most of this is automatic, but the addon will have some simple controls to adjust it to different face shapes.

aVersionOfReality

14,935 Aufrufe • vor 1 Jahr

$The Bonding Curve Documentation for It is super comprehensive and gives you an idea of how to build any Bonding Curve on AO. With on-chain curve math (Newton’s method, integer exponent, fractional powers).$

The Bonding Curve Documentation for It is super comprehensive and gives you an idea of how to build any Bonding Curve on AO. With on-chain curve math (Newton’s method, integer exponent, fractional powers).

Ivan

12,207 Aufrufe • vor 1 Jahr

Calculus of Variations is what happens when you stop optimizing values and start optimizing geometries. The unknown isn’t a single x...it’s a whole curve y(x). And the thing you’re minimizing usually isn’t a formula you can eyeball...it’s an integral that judges the entire shape. For our first lecture, we look at the famous Brachistochrone problem. Fix two points, switch on gravity, and ask a question that sounds too simple...which track gets a bead from A to B in the least time? Your intuition will betray you on the first try. It’s not the straight line. It’s not the drop hard then cruise sketch either. The winner is a cycloid...the curve traced by a point on a rolling circle. In the animation, the track is the moving character. We start with an imperfect curve, run gradient descent in curve-space, and watch the geometry reshape frame by frame as T[y] collapses until it locks into the brachistochrone. Pls see the comment below for the math breakdown. #CalculusOfVariations #Brachistochrone #Cycloid #Physics #Optimization #Mathematics

Calculus of Variations is what happens when you stop optimizing values and start optimizing geometries. The unknown isn’t a single x...it’s a whole curve y(x). And the thing you’re minimizing usually isn’t a formula you can eyeball...it’s an integral that judges the entire shape. For our first lecture, we look at the famous Brachistochrone problem. Fix two points, switch on gravity, and ask a question that sounds too simple...which track gets a bead from A to B in the least time? Your intuition will betray you on the first try. It’s not the straight line. It’s not the drop hard then cruise sketch either. The winner is a cycloid...the curve traced by a point on a rolling circle. In the animation, the track is the moving character. We start with an imperfect curve, run gradient descent in curve-space, and watch the geometry reshape frame by frame as T[y] collapses until it locks into the brachistochrone. Pls see the comment below for the math breakdown. #CalculusOfVariations #Brachistochrone #Cycloid #Physics #Optimization #Mathematics

Mathelirium

106,981 Aufrufe • vor 8 Monaten

Boop says there is a lot more pressure on Clix than on Veno right now "The comparison will be that Veno won FNCS with Curve but can he do that with Clix now, that will be the pressure on Clix"

Boop says there is a lot more pressure on Clix than on Veno right now "The comparison will be that Veno won FNCS with Curve but can he do that with Clix now, that will be the pressure on Clix"

Stack

51,003 Aufrufe • vor 3 Monaten

Oil sold off the moment the Iran peace deal appeared. That part makes perfect sense. Nobody wants to be long crude into open supply routes and normalizing tanker flows. The fundamental value of oil is closer to 50 a barrel than 150. But here is where it gets interesting. If this were only supply normalizing, the curve would still hold its shape. Inventories are drained. Tankers are disrupted. Refineries are scrambling. As long as demand is firm, the curve should stay in strong backwardation. Backwardation means front-month crude trades above later contracts. It is the market telling you it wants barrels today. It is a sign of tightness. That backwardation is nearly gone. The prompt spread, the first two contracts, has narrowed to under a buck. The three-month spread has dropped to just over 2, after being 30 not long ago. The front is selling off far harder than the back. Some of that is supply normalizing. The good kind. But when the curve gets this close to contango this fast, it points to something more troubling. Contango is what a glut looks like in the futures market. Too much oil for the demand in front of it. The curve is not there yet. But it is moving that way. And that is the warning. You have to be careful about exactly why oil is plunging this far, this fast.

Oil sold off the moment the Iran peace deal appeared. That part makes perfect sense. Nobody wants to be long crude into open supply routes and normalizing tanker flows. The fundamental value of oil is closer to 50 a barrel than 150. But here is where it gets interesting. If this were only supply normalizing, the curve would still hold its shape. Inventories are drained. Tankers are disrupted. Refineries are scrambling. As long as demand is firm, the curve should stay in strong backwardation. Backwardation means front-month crude trades above later contracts. It is the market telling you it wants barrels today. It is a sign of tightness. That backwardation is nearly gone. The prompt spread, the first two contracts, has narrowed to under a buck. The three-month spread has dropped to just over 2, after being 30 not long ago. The front is selling off far harder than the back. Some of that is supply normalizing. The good kind. But when the curve gets this close to contango this fast, it points to something more troubling. Contango is what a glut looks like in the futures market. Too much oil for the demand in front of it. The curve is not there yet. But it is moving that way. And that is the warning. You have to be careful about exactly why oil is plunging this far, this fast.

Jeffrey P. Snider

50,006 Aufrufe • vor 3 Monaten

A physical system, its phase-space state, and the energy function that governs the flow, all linked together. The point of the animation is that these are not three different objects. They are three views of the same dynamics. The pendulum on the left is the physical motion. The curve on the floor is the evolution of its state. The translucent surface shows the energy landscape that organizes that motion.

A physical system, its phase-space state, and the energy function that governs the flow, all linked together. The point of the animation is that these are not three different objects. They are three views of the same dynamics. The pendulum on the left is the physical motion. The curve on the floor is the evolution of its state. The translucent surface shows the energy landscape that organizes that motion.

Mathelirium

19,894 Aufrufe • vor 5 Monaten

There’s going to be a demolition of the Accra-Kumasi highway, which will commence soon. The demolition start-point will be at Ablekuma curve as seen on the video

There’s going to be a demolition of the Accra-Kumasi highway, which will commence soon. The demolition start-point will be at Ablekuma curve as seen on the video

𝔸𝕝 𝕍𝕒𝕣𝕠 𝕏

42,602 Aufrufe • vor 6 Monaten

Lecture 4 on Calculus of Variations You might wonder...If I’m optimizing a shape...a curve, a surface, a whole path, what does "take the derivative and set it to zero" even mean? Do I take the damn derivative with respect to a curve/surface? 🤔 In normal calculus the variable is a number x, so the reflex is clean...f′(x)=0. In calculus of variations the variable is a whole function...the geometry itself, like a curve y(x) (or a surface z(x,y)). So the derivative can’t be a single slope. It has to be a pointwise sensitivity, i.e. how the objective reacts to tiny local deformations. You’re holding a whole shape, like a curve y(x). Your objective isn’t f(x) anymore, it’s a functional J[y], and as we've seen with our first there examples, usually an integral that depends on the entire curve (often through y and y’). To talk about a “derivative”, you do the only thing that makes sense: you nudge the entire curve by a tiny amount and see how J changes. Pick a wiggle shape η(x). It’s not random...it’s any admissible deformation direction. Admissible just means it obeys the constraints. If the endpoints are fixed, you force η(0)=η(1)=0 so the wiggle doesn’t move the endpoints. Then scale that wiggle by a small number ε and define the perturbed curve yε(x)=y(x)+εη(x). Now treat ε like the usual scalar in a Taylor expansion. As ε→0, J[y+εη] expands as J[y+εη] = J[y] + ε · (first-order term depending linearly on η) + o(ε). So the difference is J[y+εη] - J[y] = ε · (linear functional of η) + o(ε). For the standard integral of a Lagrangian problems, that linear functional can be written as an inner product with some function of x: J[y+εη] - J[y] = ε ∫ (δJ/δy)(x) η(x) dx + o(ε). That’s the definition-level meaning of δJ/δy: it’s the unique pointwise sensitivity function that makes this identity true for every admissible η. If δJ/δy is positive at some x, then choosing η negative there decreases J; if δJ/δy is negative there, pushing y upward locally decreases J. It’s literally a map along the curve saying push this way to go downhill. Now translate “set the derivative to zero.” At a minimizer y*, the first-order change must vanish for every admissible wiggle: J[y*+εη] − J[y*] = o(ε) for all η. Plug in the expansion and the ε-term must be zero: ∫ (δJ/δy)(x) η(x) dx = 0 for all admissible η. Here’s the crucial logic step: the only way an integral against every test function η can be zero is if the integrand itself is zero (in the usual sense used in analysis). So you get δJ/δy = 0. For the common case J[y]=∫ L(x, y, y’) dx, you can compute δJ/δy explicitly and it becomes the Euler–Lagrange expression δJ/δy = ∂L/∂y − d/dx(∂L/∂y’). So if you name the Euler–Lagrange residual as “left-hand side” R(x) = ∂L/∂y − d/dx(∂L/∂y’), then “set the derivative to zero” is exactly R(x)=0. That’s why animation works so well. You don’t have to solve R=0 in one shot. You can evolve the curve in an artificial time τ by pushing it in the downhill direction: ∂y/∂τ = −R(y). Where the residual is large, the curve moves a lot; as the residual drains toward zero, the motion dies out and the curve settles into an extremal. In our animations, we start from an intentionally ugly curve/surface. Frame by frame the functional drops, the residual drains away, and the geometry relaxes into an extremal. #CalculusOfVariations #EulerLagrange #FunctionalDerivative #GradientFlow #Optimization #MathAnimation

Lecture 4 on Calculus of Variations You might wonder...If I’m optimizing a shape...a curve, a surface, a whole path, what does "take the derivative and set it to zero" even mean? Do I take the damn derivative with respect to a curve/surface? 🤔 In normal calculus the variable is a number x, so the reflex is clean...f′(x)=0. In calculus of variations the variable is a whole function...the geometry itself, like a curve y(x) (or a surface z(x,y)). So the derivative can’t be a single slope. It has to be a pointwise sensitivity, i.e. how the objective reacts to tiny local deformations. You’re holding a whole shape, like a curve y(x). Your objective isn’t f(x) anymore, it’s a functional J[y], and as we've seen with our first there examples, usually an integral that depends on the entire curve (often through y and y’). To talk about a “derivative”, you do the only thing that makes sense: you nudge the entire curve by a tiny amount and see how J changes. Pick a wiggle shape η(x). It’s not random...it’s any admissible deformation direction. Admissible just means it obeys the constraints. If the endpoints are fixed, you force η(0)=η(1)=0 so the wiggle doesn’t move the endpoints. Then scale that wiggle by a small number ε and define the perturbed curve yε(x)=y(x)+εη(x). Now treat ε like the usual scalar in a Taylor expansion. As ε→0, J[y+εη] expands as J[y+εη] = J[y] + ε · (first-order term depending linearly on η) + o(ε). So the difference is J[y+εη] - J[y] = ε · (linear functional of η) + o(ε). For the standard integral of a Lagrangian problems, that linear functional can be written as an inner product with some function of x: J[y+εη] - J[y] = ε ∫ (δJ/δy)(x) η(x) dx + o(ε). That’s the definition-level meaning of δJ/δy: it’s the unique pointwise sensitivity function that makes this identity true for every admissible η. If δJ/δy is positive at some x, then choosing η negative there decreases J; if δJ/δy is negative there, pushing y upward locally decreases J. It’s literally a map along the curve saying push this way to go downhill. Now translate “set the derivative to zero.” At a minimizer y, the first-order change must vanish for every admissible wiggle: J[y+εη] − J[y*] = o(ε) for all η. Plug in the expansion and the ε-term must be zero: ∫ (δJ/δy)(x) η(x) dx = 0 for all admissible η. Here’s the crucial logic step: the only way an integral against every test function η can be zero is if the integrand itself is zero (in the usual sense used in analysis). So you get δJ/δy = 0. For the common case J[y]=∫ L(x, y, y’) dx, you can compute δJ/δy explicitly and it becomes the Euler–Lagrange expression δJ/δy = ∂L/∂y − d/dx(∂L/∂y’). So if you name the Euler–Lagrange residual as “left-hand side” R(x) = ∂L/∂y − d/dx(∂L/∂y’), then “set the derivative to zero” is exactly R(x)=0. That’s why animation works so well. You don’t have to solve R=0 in one shot. You can evolve the curve in an artificial time τ by pushing it in the downhill direction: ∂y/∂τ = −R(y). Where the residual is large, the curve moves a lot; as the residual drains toward zero, the motion dies out and the curve settles into an extremal. In our animations, we start from an intentionally ugly curve/surface. Frame by frame the functional drops, the residual drains away, and the geometry relaxes into an extremal. #CalculusOfVariations #EulerLagrange #FunctionalDerivative #GradientFlow #Optimization #MathAnimation

Mathelirium

12,186 Aufrufe • vor 8 Monaten

Everyone was positioned for oil at 200 a barrel. Inventories were low. The trade made sense. Then the curve flattened. In two weeks. Almost overnight. A flat curve after a supply shock is not supposed to happen. Normal shortage logic says near term prices trade at a premium while the market waits on inventories to refill. Instead the front of the curve collapsed hardest. That is not a supply story. That is the market pricing in demand disappearing faster than constrained supply can even matter. Stack it next to the household employment numbers, the drop in labor force participation, falling real incomes. The oil curve is not an isolated signal. It is confirmation.

Everyone was positioned for oil at 200 a barrel. Inventories were low. The trade made sense. Then the curve flattened. In two weeks. Almost overnight. A flat curve after a supply shock is not supposed to happen. Normal shortage logic says near term prices trade at a premium while the market waits on inventories to refill. Instead the front of the curve collapsed hardest. That is not a supply story. That is the market pricing in demand disappearing faster than constrained supply can even matter. Stack it next to the household employment numbers, the drop in labor force participation, falling real incomes. The oil curve is not an isolated signal. It is confirmation.

Jeffrey P. Snider

57,605 Aufrufe • vor 2 Monaten

Here's what's coming next for the Fondant Custom Normals Addon: Adjustable 3D anime face proxy mesh! If you've tried the proxy method before, you know that it can be difficult to get good results as you need the right topology and shape for good Normals, and also for it to fit to the face properly for a clean transfer. The solution is to use two proxies: one for the shape, and one for the fitting. But that gets cumbersome! And it is still often unintuitive to get the correct shading shapes. The next major feature of the addon will be aiming to solve these problems by providing a convenient proxy mesh that you can fit to your character's face with some rig controls, and then handles the rest under the hood with Geometry Nodes. All the benefits of complexity without having to deal with it yourself! This clip shows the general idea, but is early stages. I'll be sharing more as I build it out.

Here's what's coming next for the Fondant Custom Normals Addon: Adjustable 3D anime face proxy mesh! If you've tried the proxy method before, you know that it can be difficult to get good results as you need the right topology and shape for good Normals, and also for it to fit to the face properly for a clean transfer. The solution is to use two proxies: one for the shape, and one for the fitting. But that gets cumbersome! And it is still often unintuitive to get the correct shading shapes. The next major feature of the addon will be aiming to solve these problems by providing a convenient proxy mesh that you can fit to your character's face with some rig controls, and then handles the rest under the hood with Geometry Nodes. All the benefits of complexity without having to deal with it yourself! This clip shows the general idea, but is early stages. I'll be sharing more as I build it out.

aVersionOfReality

107,211 Aufrufe • vor 1 Jahr

Women's hockey continues to grow, and ice hockey legend Hilary Knight thinks there is a lot of catching up to be done now. "We need to cut that curve of not having investment for as many years as we haven't had," Knight said during the TIME100 gala red carpet. One of the greatest players in the history of women's hockey, Knight is on the TIME100 list this year. Read more about her legacy here:

Women's hockey continues to grow, and ice hockey legend Hilary Knight thinks there is a lot of catching up to be done now. "We need to cut that curve of not having investment for as many years as we haven't had," Knight said during the TIME100 gala red carpet. One of the greatest players in the history of women's hockey, Knight is on the TIME100 list this year. Read more about her legacy here:

TIME

23,097 Aufrufe • vor 4 Monaten

Slowly adding to my tool stack for Hallway . This is a spline patch making a mesh that is wrapped from UV space onto the model. There's also setups to unwrap meshes on the surface back to UV space. Working in UV space enables a lot of procedural workflows. #b3d

Slowly adding to my tool stack for Hallway . This is a spline patch making a mesh that is wrapped from UV space onto the model. There's also setups to unwrap meshes on the surface back to UV space. Working in UV space enables a lot of procedural workflows. #b3d

aVersionOfReality

81,464 Aufrufe • vor 3 Jahren

The value of the work we're doing at Optimum is encapsulated quite well by the phrase "speed is money". In modern markets there are real economic advantages to latency reduction. This is nothing new. Wall Street firms have long been optimizing on latency, primarily through colocation and top of the line hardware. However, when it comes to decentralized systems, expensive hardware and geographic concentration are antithetical to their purpose. Therefore we should optimize decentralized network latency through software, which I'm thrilled about because it's exactly what I've spent the better part of the past 2 decades working on with Random Linear Network Coding. Now let’s talk about networking economics, the relationship between speed and money. First, it's important to note that users will only pay for low latency if it can be consistently guaranteed. Second, you can only make that latency guarantee for a certain number of users. This is a universal law of networking. We can model this relationship on a delay curve, shown below. The delay curve is determined by the utilization rate of the network, meaning how much traffic is flowing through the network divided by the network's throughput. As you approach a level of traffic equal to the available throughput, latency trends infinitely higher. On this delay curve we can impose some utility thresholds. These thresholds are the levels of latency which are important to different groups of users because of how that latency guarantee improves their economic outcomes. Finding the point on the curve where each threshold intersects will tell us what level of traffic we can guarantee that level of latency for. Essentially, there exists a finite supply of speed on a network and the highest utility users of that speed are willing to pay more for it. I like to think of this similarly to expedited shipping options on Amazon. This is why we say speed is money, and why we can create a Latency Marketplace. The only way to increase the supply of speed is to fundamentally increase network throughput. This is what we work on at Optimum by using Random Linear Network Coding. The same relationship between traffic and throughput still applies, but now the delay curve is shifted out further to the right. Now more traffic can be processed at the same latency, or the same traffic can be processed at a lower latency. More speed available to the network. More value unlocked for the network’s users. Crucially, that value is no longer only reserved for those who can afford to sit closest to the machine. Expanding the supply of speed widens who can reach each latency threshold, keeping the network's advantage decentralized rather than concentrated in the hands of a few. When nodes join Optimum and participate, they reap the benefits, but they also add to the capacity. Rather than vying against each other in a zero-sum game, nodes help themselves and others.

The value of the work we're doing at Optimum is encapsulated quite well by the phrase "speed is money". In modern markets there are real economic advantages to latency reduction. This is nothing new. Wall Street firms have long been optimizing on latency, primarily through colocation and top of the line hardware. However, when it comes to decentralized systems, expensive hardware and geographic concentration are antithetical to their purpose. Therefore we should optimize decentralized network latency through software, which I'm thrilled about because it's exactly what I've spent the better part of the past 2 decades working on with Random Linear Network Coding. Now let’s talk about networking economics, the relationship between speed and money. First, it's important to note that users will only pay for low latency if it can be consistently guaranteed. Second, you can only make that latency guarantee for a certain number of users. This is a universal law of networking. We can model this relationship on a delay curve, shown below. The delay curve is determined by the utilization rate of the network, meaning how much traffic is flowing through the network divided by the network's throughput. As you approach a level of traffic equal to the available throughput, latency trends infinitely higher. On this delay curve we can impose some utility thresholds. These thresholds are the levels of latency which are important to different groups of users because of how that latency guarantee improves their economic outcomes. Finding the point on the curve where each threshold intersects will tell us what level of traffic we can guarantee that level of latency for. Essentially, there exists a finite supply of speed on a network and the highest utility users of that speed are willing to pay more for it. I like to think of this similarly to expedited shipping options on Amazon. This is why we say speed is money, and why we can create a Latency Marketplace. The only way to increase the supply of speed is to fundamentally increase network throughput. This is what we work on at Optimum by using Random Linear Network Coding. The same relationship between traffic and throughput still applies, but now the delay curve is shifted out further to the right. Now more traffic can be processed at the same latency, or the same traffic can be processed at a lower latency. More speed available to the network. More value unlocked for the network’s users. Crucially, that value is no longer only reserved for those who can afford to sit closest to the machine. Expanding the supply of speed widens who can reach each latency threshold, keeping the network's advantage decentralized rather than concentrated in the hands of a few. When nodes join Optimum and participate, they reap the benefits, but they also add to the capacity. Rather than vying against each other in a zero-sum game, nodes help themselves and others.

Muriel Medard

45,497 Aufrufe • vor 2 Monaten