Dr. Rook Bridson
@rookbridson.bsky.social
she/her 🏳️⚧️🏳️🌈
Mathematician in metro Vancouver, working on VFX software in simulation/numerics/geometry. You may know me as the inventor of FLIP for incompressible flow, curl-noise, a very simple fast Poisson disc algorithm, my fluids book, cloth stuff…
Mathematician in metro Vancouver, working on VFX software in simulation/numerics/geometry. You may know me as the inventor of FLIP for incompressible flow, curl-noise, a very simple fast Poisson disc algorithm, my fluids book, cloth stuff…
But this is a case where it's certified okay. But I won't dive into why today...
November 27, 2025 at 11:12 PM
But this is a case where it's certified okay. But I won't dive into why today...
r here is a length. Surely this suggests we rescale it with a characteristic length for the problem R, using log(r/R) instead... but (1) there is no intrinsic characteristic length for the Laplacian and (2) we also know log(r/R)=log(r)-log(R) so that hardly does anything meaningful.
November 27, 2025 at 11:12 PM
r here is a length. Surely this suggests we rescale it with a characteristic length for the problem R, using log(r/R) instead... but (1) there is no intrinsic characteristic length for the Laplacian and (2) we also know log(r/R)=log(r)-log(R) so that hardly does anything meaningful.
Generally the arguments to a special function like exp() or log() must be nondimensional, coming straight from their Taylor series — exp(x)=1+x+x^2/2+... so x (and x^2 etc) all have to have the same units as 1, i.e. none.
But the fundamental solution of the Laplacian in 2D is -log(r)/2π ?!
But the fundamental solution of the Laplacian in 2D is -log(r)/2π ?!
November 27, 2025 at 11:12 PM
Generally the arguments to a special function like exp() or log() must be nondimensional, coming straight from their Taylor series — exp(x)=1+x+x^2/2+... so x (and x^2 etc) all have to have the same units as 1, i.e. none.
But the fundamental solution of the Laplacian in 2D is -log(r)/2π ?!
But the fundamental solution of the Laplacian in 2D is -log(r)/2π ?!
...by getting a "characteristic" length scale X and time scale T, then using non-dimensional variables x/X and t/T before even beginning classic steepest descent.
The * above highlights one vexing case that many people are confused by at some point (at least me, i was confused)...
The * above highlights one vexing case that many people are confused by at some point (at least me, i was confused)...
November 27, 2025 at 11:12 PM
...by getting a "characteristic" length scale X and time scale T, then using non-dimensional variables x/X and t/T before even beginning classic steepest descent.
The * above highlights one vexing case that many people are confused by at some point (at least me, i was confused)...
The * above highlights one vexing case that many people are confused by at some point (at least me, i was confused)...
If you're minimizing f(x,t) where f is dimensionless, x is a length, and t is a time, say, then the gradient g is a vector with units (1/length, 1/time). There is no step size scalar α that can make (x,t)+α*g dimensionally correct. This indicates you probably should non-dimensionalize...
November 27, 2025 at 11:12 PM
If you're minimizing f(x,t) where f is dimensionless, x is a length, and t is a time, say, then the gradient g is a vector with units (1/length, 1/time). There is no step size scalar α that can make (x,t)+α*g dimensionally correct. This indicates you probably should non-dimensionalize...
For example, Newton's method is "dimensionally correct", and sure enough, if you were to change the units of your inputs (changing all their values), it will produce the equivalent algorithmic results up to rounding error.
Steepest Descent, as typically written, is _not_ dimensionally correct...
Steepest Descent, as typically written, is _not_ dimensionally correct...
November 27, 2025 at 11:12 PM
For example, Newton's method is "dimensionally correct", and sure enough, if you were to change the units of your inputs (changing all their values), it will produce the equivalent algorithmic results up to rounding error.
Steepest Descent, as typically written, is _not_ dimensionally correct...
Steepest Descent, as typically written, is _not_ dimensionally correct...
The Shipping News, but then ... Kevin Spacey 😬
November 27, 2025 at 10:42 PM
The Shipping News, but then ... Kevin Spacey 😬
aaaah! thank you! this paper was half in my memory for some stuff i have been doing, but too hazy to even be able to search for it :)
November 26, 2025 at 6:34 PM
aaaah! thank you! this paper was half in my memory for some stuff i have been doing, but too hazy to even be able to search for it :)
…the writing be a dull slog that simply copies an “academic” style seen in too many past papers. If your math actually needs to be super rigorous, so be it, but don’t try to just give the illusion of rigour with pedantic text obfuscating the plain ideas.
November 26, 2025 at 6:27 PM
…the writing be a dull slog that simply copies an “academic” style seen in too many past papers. If your math actually needs to be super rigorous, so be it, but don’t try to just give the illusion of rigour with pedantic text obfuscating the plain ideas.
What I AM saying is write clearly. Get the critical insights and intuition you gained through arduous research across in a clear memorable way, maybe tied to a concise phrase or a demonstrative image or perfect “toy” problem that encapsulates it all. Even if the details are a slog, don’t let all…
November 26, 2025 at 6:27 PM
What I AM saying is write clearly. Get the critical insights and intuition you gained through arduous research across in a clear memorable way, maybe tied to a concise phrase or a demonstrative image or perfect “toy” problem that encapsulates it all. Even if the details are a slog, don’t let all…
But I guess the real lesson I wanted to say here is that quality writing matters, even in highly technical math/engineering/science/computer papers!
I am NOT saying to choose a cute title: that can work (like this one) but is besides the point, and can backfire and cause eye rolls if badly done.
I am NOT saying to choose a cute title: that can work (like this one) but is besides the point, and can backfire and cause eye rolls if badly done.
November 26, 2025 at 6:27 PM
But I guess the real lesson I wanted to say here is that quality writing matters, even in highly technical math/engineering/science/computer papers!
I am NOT saying to choose a cute title: that can work (like this one) but is besides the point, and can backfire and cause eye rolls if badly done.
I am NOT saying to choose a cute title: that can work (like this one) but is besides the point, and can backfire and cause eye rolls if badly done.
…for what is happening (say in a linearized toy problem) in Fourier space, and in particular: are there high frequencies in what you are attempting to solve that you can’t actually represent, and if so are they going to be filtered out in a way you understand or will they alias?
November 26, 2025 at 6:20 PM
…for what is happening (say in a linearized toy problem) in Fourier space, and in particular: are there high frequencies in what you are attempting to solve that you can’t actually represent, and if so are they going to be filtered out in a way you understand or will they alias?
…it is really important to make sure that you actually understand the nature of the approximations, what the errors you will be making “mean”, what is actually justifiably negligible and what is actually important.
And to be honest, often a lot of this just comes down to getting a gut feeling …
And to be honest, often a lot of this just comes down to getting a gut feeling …
November 26, 2025 at 6:20 PM
…it is really important to make sure that you actually understand the nature of the approximations, what the errors you will be making “mean”, what is actually justifiably negligible and what is actually important.
And to be honest, often a lot of this just comes down to getting a gut feeling …
And to be honest, often a lot of this just comes down to getting a gut feeling …
And while the paper focuses only on finite element methods, this actually leads to a bigger picture insight about numerically discretizing differential equations — and even modelling as a step before that. Before jumping to a method that offers some nice qualities you associate with true solutions,
November 26, 2025 at 6:20 PM
And while the paper focuses only on finite element methods, this actually leads to a bigger picture insight about numerically discretizing differential equations — and even modelling as a step before that. Before jumping to a method that offers some nice qualities you associate with true solutions,
The paper in question: www.sciencedirect.com/science/arti...
Don't suppress the wiggles—They're telling you something!
The subject of oscillatory solutions (wiggles), which sometimes result when the conventional Galerkin finite element method is employed to approximate…
www.sciencedirect.com
November 26, 2025 at 6:11 PM
The paper in question: www.sciencedirect.com/science/arti...
I sometimes feel like I belabour the point (“always work out 1D or 2D first!”) but goodness me, it’s not just my own experience, I have seen so many projects through the cg industry where going straight to 3D (often forced by the 3D-only platforms we’re working in) caused unnecessary roadblocks
November 20, 2025 at 5:04 PM
I sometimes feel like I belabour the point (“always work out 1D or 2D first!”) but goodness me, it’s not just my own experience, I have seen so many projects through the cg industry where going straight to 3D (often forced by the 3D-only platforms we’re working in) caused unnecessary roadblocks
and yet I have only ever gotten to a 3D solution faster and with more confidence through starting with 1D and 2D models. Or turning things around, so many times I have been able to efficiently figure out what was going wrong in a 3D code by reduction to lower dimensional toy problems
November 20, 2025 at 4:44 PM
and yet I have only ever gotten to a 3D solution faster and with more confidence through starting with 1D and 2D models. Or turning things around, so many times I have been able to efficiently figure out what was going wrong in a 3D code by reduction to lower dimensional toy problems
even if it’s just to quickly rule out approaches which by dint of failing in 2D will definitely not work in 3D, or simply gaining more insight inti how to think about the problem space.
Much more common I think is curse of dimensionality stuff, where 3D is exponentially, combinatorially harder
Much more common I think is curse of dimensionality stuff, where 3D is exponentially, combinatorially harder
November 20, 2025 at 4:44 PM
even if it’s just to quickly rule out approaches which by dint of failing in 2D will definitely not work in 3D, or simply gaining more insight inti how to think about the problem space.
Much more common I think is curse of dimensionality stuff, where 3D is exponentially, combinatorially harder
Much more common I think is curse of dimensionality stuff, where 3D is exponentially, combinatorially harder
It’s an interesting point — I have hit a few things where 3D is fundamentally just different, with simplex-mesh-related spatial tilings and subdivision coming to mind in particular. However I think even then it’s always been the case that I benefit from looking at the 2D version in depth first,
November 20, 2025 at 4:44 PM
It’s an interesting point — I have hit a few things where 3D is fundamentally just different, with simplex-mesh-related spatial tilings and subdivision coming to mind in particular. However I think even then it’s always been the case that I benefit from looking at the 2D version in depth first,
...and sure enough it was a mistake. I got stuck in the 3D derivation, started the 2D, and almost immediately realized some simplifications I had missed when overwhelmed with the 3D expressions, and it's all so much simpler and quicker now!
November 19, 2025 at 7:49 PM
...and sure enough it was a mistake. I got stuck in the 3D derivation, started the 2D, and almost immediately realized some simplifications I had missed when overwhelmed with the 3D expressions, and it's all so much simpler and quicker now!
Reposted by Dr. Rook Bridson
transness is a gift. i need every trans woman to understand that by nature of their existence they have been blessed with the ability to pluck the strands of fate with their hands if they choose to. it is not always easy and it is not without hardship but every trans woman is capable of greatness.
November 14, 2025 at 1:15 AM
transness is a gift. i need every trans woman to understand that by nature of their existence they have been blessed with the ability to pluck the strands of fate with their hands if they choose to. it is not always easy and it is not without hardship but every trans woman is capable of greatness.