Mike Henderson
@mhender.bsky.social
Retired Applied Mathematician. Computational Dynamical Systems.
Still trying to understand how things work.
https://multifario.sourceforge.io/henderson/
I might be wrong.
Still trying to understand how things work.
https://multifario.sourceforge.io/henderson/
I might be wrong.
One of the things about Lagrangian Descriptors is that it seems to go against the conv. wisdom that finding every trajectory in (part of) phase space is too expensive.
Things are different now, and there are situations where that's no longer true. And hey, look what you can do.
Things are different now, and there are situations where that's no longer true. And hey, look what you can do.
November 28, 2025 at 4:12 PM
One of the things about Lagrangian Descriptors is that it seems to go against the conv. wisdom that finding every trajectory in (part of) phase space is too expensive.
Things are different now, and there are situations where that's no longer true. And hey, look what you can do.
Things are different now, and there are situations where that's no longer true. And hey, look what you can do.
I've been reading about Lagrangian Descriptors.
champsproject.github.io/lagrangian_d...
Seems expensive, but makes intriguing pics
www.researchgate.net/profile/Fabi...
champsproject.github.io/lagrangian_d...
Seems expensive, but makes intriguing pics
www.researchgate.net/profile/Fabi...
The Method of Lagrangian Descriptors — Lagrangian Descriptors
champsproject.github.io
November 26, 2025 at 4:29 PM
I've been reading about Lagrangian Descriptors.
champsproject.github.io/lagrangian_d...
Seems expensive, but makes intriguing pics
www.researchgate.net/profile/Fabi...
champsproject.github.io/lagrangian_d...
Seems expensive, but makes intriguing pics
www.researchgate.net/profile/Fabi...
These are out-takes from
www.worldscientific.com/doi/10.1142/...
A very weird surface. Points on it satisfy 3d ODE with bcs and four parameters. It can be embedded in 4d, but projected into 3d it crosses itself.
The colors have to do with a classification of the solutions - # loops and twists.
www.worldscientific.com/doi/10.1142/...
A very weird surface. Points on it satisfy 3d ODE with bcs and four parameters. It can be embedded in 4d, but projected into 3d it crosses itself.
The colors have to do with a classification of the solutions - # loops and twists.
October 30, 2025 at 5:22 PM
These are out-takes from
www.worldscientific.com/doi/10.1142/...
A very weird surface. Points on it satisfy 3d ODE with bcs and four parameters. It can be embedded in 4d, but projected into 3d it crosses itself.
The colors have to do with a classification of the solutions - # loops and twists.
www.worldscientific.com/doi/10.1142/...
A very weird surface. Points on it satisfy 3d ODE with bcs and four parameters. It can be embedded in 4d, but projected into 3d it crosses itself.
The colors have to do with a classification of the solutions - # loops and twists.
This is the same algorithm (and code) as for the torus. The continuation is limited to the inside of a box, so you only see the yellow spheres until they cross that. The polyhedra around the spheres are more visible. They're used to find the boundary of the union of spherical balls.
October 27, 2025 at 1:42 PM
This is the same algorithm (and code) as for the torus. The continuation is limited to the inside of a box, so you only see the yellow spheres until they cross that. The polyhedra around the spheres are more visible. They're used to find the boundary of the union of spherical balls.
This is an animation of an algorithm for covering a torus with the projection of disks tangent to the surface. Red is the boundary, and the yellow contribute to the boundary. Blue ones are interior.
Each step picks a point on the boundary for a new disk. The boundary is a simple list.
Each step picks a point on the boundary for a new disk. The boundary is a simple list.
October 26, 2025 at 7:17 PM
This is an animation of an algorithm for covering a torus with the projection of disks tangent to the surface. Red is the boundary, and the yellow contribute to the boundary. Blue ones are interior.
Each step picks a point on the boundary for a new disk. The boundary is a simple list.
Each step picks a point on the boundary for a new disk. The boundary is a simple list.
I have always had a blind spot for people who say things with confidence. I need to think about things, and can't seem to avoid reacting as if confidence means that they've thought about what they're saying. I know I'm not alone in this.
So not surprised that LLMs come across as intelligent.
So not surprised that LLMs come across as intelligent.
October 18, 2025 at 1:28 PM
I have always had a blind spot for people who say things with confidence. I need to think about things, and can't seem to avoid reacting as if confidence means that they've thought about what they're saying. I know I'm not alone in this.
So not surprised that LLMs come across as intelligent.
So not surprised that LLMs come across as intelligent.
Ugh. I moved my stuff to a new machine, and when I ran configure on my code I goofed and told it to use lapack64 instead of lapack. Strange messages about subroutine arguments having bad values.
I hate debugging. I hate installing and configuring code.
I hate debugging. I hate installing and configuring code.
October 17, 2025 at 8:40 PM
Ugh. I moved my stuff to a new machine, and when I ran configure on my code I goofed and told it to use lapack64 instead of lapack. Strange messages about subroutine arguments having bad values.
I hate debugging. I hate installing and configuring code.
I hate debugging. I hate installing and configuring code.
On the question about what counts as a solution, I've seen people spend a lot of time and doing some brilliant things to get a closed form solution. It's nevertheless 10 lines long and the response is usually -- "Oh, good".
October 14, 2025 at 6:53 PM
On the question about what counts as a solution, I've seen people spend a lot of time and doing some brilliant things to get a closed form solution. It's nevertheless 10 lines long and the response is usually -- "Oh, good".
Something we used to talk about all the time is what counts as "solving" a differential equation? Does it require a (simple) closed form? An asymptotic expansion? A numerical solution?
And I've yet to discover what "solving" the 3-body problem means. Stop that.
I do have my opinions.
And I've yet to discover what "solving" the 3-body problem means. Stop that.
I do have my opinions.
October 13, 2025 at 8:13 PM
Something we used to talk about all the time is what counts as "solving" a differential equation? Does it require a (simple) closed form? An asymptotic expansion? A numerical solution?
And I've yet to discover what "solving" the 3-body problem means. Stop that.
I do have my opinions.
And I've yet to discover what "solving" the 3-body problem means. Stop that.
I do have my opinions.
I'm just trying to imagine if the amount of attention (and money) that goes into college football went instead into Applied Math (just a random alternative).
October 11, 2025 at 10:18 PM
I'm just trying to imagine if the amount of attention (and money) that goes into college football went instead into Applied Math (just a random alternative).
I 'm reading Hermann's "Geometry, Physics, and Systems", 1973. It's got a chapter on Thermo. I love this guy.
He doesn't like the (dU/dP)_V notation or mysticism (his word) about entropy.
But what's with the bibliography? All references are labelled 1? Later there are some 2's.
He doesn't like the (dU/dP)_V notation or mysticism (his word) about entropy.
But what's with the bibliography? All references are labelled 1? Later there are some 2's.
October 1, 2025 at 6:19 PM
I 'm reading Hermann's "Geometry, Physics, and Systems", 1973. It's got a chapter on Thermo. I love this guy.
He doesn't like the (dU/dP)_V notation or mysticism (his word) about entropy.
But what's with the bibliography? All references are labelled 1? Later there are some 2's.
He doesn't like the (dU/dP)_V notation or mysticism (his word) about entropy.
But what's with the bibliography? All references are labelled 1? Later there are some 2's.
Since grad school I never let myself play computer games. Novels were bad enough. But now I play solitaire. It's as much about dodging the ads. One claims I'm out of date (maybe true). If I press the wrong button I have to uninstall all sorts of games and find how to get the screen manager back 1/x
September 24, 2025 at 3:47 PM
Since grad school I never let myself play computer games. Novels were bad enough. But now I play solitaire. It's as much about dodging the ads. One claims I'm out of date (maybe true). If I press the wrong button I have to uninstall all sorts of games and find how to get the screen manager back 1/x
A question: this thermo stuff uses the notation
(\frac{\partial T}{\partial V})_S
Why the subscr\frac{\partial T}{\partial V}ipt? Isn't that what the partial means? If S was a function of V it'd be
\partial T/\partial V+ \partial T/\partial S \partial S/\partial V
No?
(\frac{\partial T}{\partial V})_S
Why the subscr\frac{\partial T}{\partial V}ipt? Isn't that what the partial means? If S was a function of V it'd be
\partial T/\partial V+ \partial T/\partial S \partial S/\partial V
No?
September 20, 2025 at 2:40 PM
A question: this thermo stuff uses the notation
(\frac{\partial T}{\partial V})_S
Why the subscr\frac{\partial T}{\partial V}ipt? Isn't that what the partial means? If S was a function of V it'd be
\partial T/\partial V+ \partial T/\partial S \partial S/\partial V
No?
(\frac{\partial T}{\partial V})_S
Why the subscr\frac{\partial T}{\partial V}ipt? Isn't that what the partial means? If S was a function of V it'd be
\partial T/\partial V+ \partial T/\partial S \partial S/\partial V
No?
So we (USA) live in a democracy and are free. Except if you work for a company, which is kind of hard to avoid in one way or another. And the company is pretty much a dictatorship. Who says what goes? The shareholders? (Not in little things at least). The CEO? Anyone in "Management"? Not right.
September 19, 2025 at 5:18 PM
So we (USA) live in a democracy and are free. Except if you work for a company, which is kind of hard to avoid in one way or another. And the company is pretty much a dictatorship. Who says what goes? The shareholders? (Not in little things at least). The CEO? Anyone in "Management"? Not right.
I'm used to conservation laws. Navier Stokes and so on. So div f=0 in spatial vars. Thermo eqs seem to instead be "Irrotational", or path independent, so curl f=0. And not in space, but in pairs of the phase variables? Related to the second partials being the same (d^2U/dSdV=d^2U/dV/dS).
Head hurts
Head hurts
September 15, 2025 at 5:50 PM
I'm used to conservation laws. Navier Stokes and so on. So div f=0 in spatial vars. Thermo eqs seem to instead be "Irrotational", or path independent, so curl f=0. And not in space, but in pairs of the phase variables? Related to the second partials being the same (d^2U/dSdV=d^2U/dV/dS).
Head hurts
Head hurts
Is our goal to accurately simulate systems? If you can, and you match "reality" it says the model is probably right and we understand the important forces. But all you've got now is the ability to do forecasts or clean experiments. That's just the beginning.
September 14, 2025 at 6:00 PM
Is our goal to accurately simulate systems? If you can, and you match "reality" it says the model is probably right and we understand the important forces. But all you've got now is the ability to do forecasts or clean experiments. That's just the beginning.
Always wondered why they wrote thermodynamics equations as differentials. Of course Navier Stokes writes a temperature equation as a PDE, but ..
Am reading www.fys.ku.dk/~andresen/BA... and trying to get my head around work and heat flow being differential forms on the manifold of state (???!)
Am reading www.fys.ku.dk/~andresen/BA... and trying to get my head around work and heat flow being differential forms on the manifold of state (???!)
September 14, 2025 at 3:52 PM
Always wondered why they wrote thermodynamics equations as differentials. Of course Navier Stokes writes a temperature equation as a PDE, but ..
Am reading www.fys.ku.dk/~andresen/BA... and trying to get my head around work and heat flow being differential forms on the manifold of state (???!)
Am reading www.fys.ku.dk/~andresen/BA... and trying to get my head around work and heat flow being differential forms on the manifold of state (???!)
Wow. Has the Heisman hype always been this bad? Watched the Ducks game and the QB is apparently a superhero level athlete who is a fine upstanding young man who writes children's books on wanting to be a super duper football player. The announcers even read us a page.
Was assured the A&M QB is too.
Was assured the A&M QB is too.
September 14, 2025 at 1:54 PM
Wow. Has the Heisman hype always been this bad? Watched the Ducks game and the QB is apparently a superhero level athlete who is a fine upstanding young man who writes children's books on wanting to be a super duper football player. The announcers even read us a page.
Was assured the A&M QB is too.
Was assured the A&M QB is too.
I read a scary article on Russian social media interference.
The internet was great. Didn't have to rely on gate keepers with low bandwidth for "what is interesting". There are lots of interesting people/things out there!
Now back to gatekeepers because some exploit it? Or intrusive verification?
The internet was great. Didn't have to rely on gate keepers with low bandwidth for "what is interesting". There are lots of interesting people/things out there!
Now back to gatekeepers because some exploit it? Or intrusive verification?
September 9, 2025 at 3:36 PM
I read a scary article on Russian social media interference.
The internet was great. Didn't have to rely on gate keepers with low bandwidth for "what is interesting". There are lots of interesting people/things out there!
Now back to gatekeepers because some exploit it? Or intrusive verification?
The internet was great. Didn't have to rely on gate keepers with low bandwidth for "what is interesting". There are lots of interesting people/things out there!
Now back to gatekeepers because some exploit it? Or intrusive verification?
I don't want to live in a world where I have to decide if the person I'm reading is sincere or trying to fool me. Is that too much to ask? Are you pretending to know what you're talking about? Or worse are you just saying that to take advantage.
Yes. I've been reading AI/ML papers.
Yes. I've been reading AI/ML papers.
September 6, 2025 at 4:16 PM
I don't want to live in a world where I have to decide if the person I'm reading is sincere or trying to fool me. Is that too much to ask? Are you pretending to know what you're talking about? Or worse are you just saying that to take advantage.
Yes. I've been reading AI/ML papers.
Yes. I've been reading AI/ML papers.
So, if the gov't refunds the tariffs they've illegally collected they give the money to the companies that imported the stuff? The ones who turned around and charged consumers more for the stuff? Hmmm.
September 4, 2025 at 2:17 PM
So, if the gov't refunds the tariffs they've illegally collected they give the money to the companies that imported the stuff? The ones who turned around and charged consumers more for the stuff? Hmmm.
These are from the periodically forced damped pendulum, showing how points near the unstable fixed point (up) evolve. W/o forcing they'd spiral to the stable fixed point (down).
The surface is rendered as white with black polygons. Hidden line removal but still black and white.
The surface is rendered as white with black polygons. Hidden line removal but still black and white.
August 31, 2025 at 5:47 PM
These are from the periodically forced damped pendulum, showing how points near the unstable fixed point (up) evolve. W/o forcing they'd spiral to the stable fixed point (down).
The surface is rendered as white with black polygons. Hidden line removal but still black and white.
The surface is rendered as white with black polygons. Hidden line removal but still black and white.
These are three very old (1987) figures showing the cusp, swallowtail and butterfly catastrophes and the complex sheets associated with them. These were done in CATIA. Yep. Not many choices back then.
August 31, 2025 at 5:25 PM
These are three very old (1987) figures showing the cusp, swallowtail and butterfly catastrophes and the complex sheets associated with them. These were done in CATIA. Yep. Not many choices back then.
August 30, 2025 at 4:43 PM