I am shocked by how well this runs
Show HN: Strange Attractors
61–70 of 83 posts
Re: Show HN: Strange Attractors
#62> A small change in the parameter a can lead to vastly different particle trajectories and the overall shape of the attractor. Change this value in the control panel and observe the butterfly effect in action.
I think this is slightly inaccurate. The butterfly effect is about the evolution of two nearby states in phase space into well-separated states. But the parameter a is not a state. To see the butterfly effect by changing a we would need to let the system settle down, give the parameter a small change, and then change it back. The evolution during the changed time acts as a perturbation on states.
Instead, showing that the attractor changes qualitatively as a function of the parameter is more akin to a phase transition.
Re: Show HN: Strange Attractors
#63Earlier quoted context omitted.
Do you think an AI can learn this intuition by training it in similar environment?
Can we train our neurons? Like the experiment where human vision adapted to upside down image, could our brains somehow adapt to understanding 4D data from VR headset?
Yes, I believe it's possible to train our brains and learn to perceive better in higher dimensions. There's a great description in the science-fiction book Neverness, where pilots meld their minds with the spaceship computer to visualize and navigate hyperspace.
Re: Show HN: Strange Attractors
#64[deleted]
Re: Show HN: Strange Attractors
#65Earlier quoted context omitted.
The conclusion I’ve come to from works like Flatland, 4D toys, etc., is that we simply don’t have the neural circuitry to grasp anything beyond three dimensions. We can reason about them, we can make inferences about the whole from partial understanding, but we cannot truly grasp more than three, or perhaps only for an instant of forced conceptualization using heuristics like you mentioned. Even three is a stretch, o…
I've managed to visualize a Klein bottle in 4d. I easily visualize 3d objects. However I can't really do color - I startled myself recently when I briefly saw red. On that aphantasia test with an apple, I can hold it's 3d shape, but no surface texture or color. People seem to have surprisingly different internal experiences. I don't know how common 4d visualization is, and I suspect even those capable require exposur…
For me, being able to visualize 4D would imply that I can picture four mutually perpendicular axes, something which I find completely impossible for me to do. And I thought it is impossible for any human brain. It would be fascinating if I am wrong.
Re: Show HN: Strange Attractors
#66Earlier quoted context omitted.
The conclusion I’ve come to from works like Flatland, 4D toys, etc., is that we simply don’t have the neural circuitry to grasp anything beyond three dimensions. We can reason about them, we can make inferences about the whole from partial understanding, but we cannot truly grasp more than three, or perhaps only for an instant of forced conceptualization using heuristics like you mentioned. Even three is a stretch, o…
I've managed to visualize a Klein bottle in 4d. I easily visualize 3d objects. However I can't really do color - I startled myself recently when I briefly saw red. On that aphantasia test with an apple, I can hold it's 3d shape, but no surface texture or color. People seem to have surprisingly different internal experiences. I don't know how common 4d visualization is, and I suspect even those capable require exposur…
[deleted]
Re: Show HN: Strange Attractors
#67Earlier quoted context omitted.
The conclusion I’ve come to from works like Flatland, 4D toys, etc., is that we simply don’t have the neural circuitry to grasp anything beyond three dimensions. We can reason about them, we can make inferences about the whole from partial understanding, but we cannot truly grasp more than three, or perhaps only for an instant of forced conceptualization using heuristics like you mentioned. Even three is a stretch, o…
I've managed to visualize a Klein bottle in 4d. I easily visualize 3d objects. However I can't really do color - I startled myself recently when I briefly saw red. On that aphantasia test with an apple, I can hold it's 3d shape, but no surface texture or color. People seem to have surprisingly different internal experiences. I don't know how common 4d visualization is, and I suspect even those capable require exposur…
The blind French mathematician Bernard Morin is well-known for creating the first visualization of a sphere eversion, a method for turning a sphere inside out without creasing it. His work was based on Stephen Smale's 1958 proof of sphere eversion's existence and on ideas shared by Arnold Shapiro. Morin's method involved constructing a sequence of models, including his "Morin surface," to demonstrate the process.
Re: Show HN: Strange Attractors
#68Earlier quoted context omitted.
The conclusion I’ve come to from works like Flatland, 4D toys, etc., is that we simply don’t have the neural circuitry to grasp anything beyond three dimensions. We can reason about them, we can make inferences about the whole from partial understanding, but we cannot truly grasp more than three, or perhaps only for an instant of forced conceptualization using heuristics like you mentioned. Even three is a stretch, o…
I've managed to visualize a Klein bottle in 4d. I easily visualize 3d objects. However I can't really do color - I startled myself recently when I briefly saw red. On that aphantasia test with an apple, I can hold it's 3d shape, but no surface texture or color. People seem to have surprisingly different internal experiences. I don't know how common 4d visualization is, and I suspect even those capable require exposur…
Your hippocampus has several special clusters of neurons whose members activate and deactivate based on your body's understanding of your position and momentum in a 3D world.
The arrangement of these neurons physically corresponds to reality, and so things are pretty hardwired.
Repurposing these neurons might be possible with advanced training and nootropics, but I'm not sure. You might have better luck engaging other parts of your brain, for example using metaphor or abstraction such as mathematics.
Re: Show HN: Strange Attractors
#69Earlier quoted context omitted.
Well, what's interesting about 4D is that's not just an extra dimension slapped on top, it's extra rotational degrees of freedom. You can't really get that with time (at least not until you get relativistic, and it still would be hyperbolic rotation, not euclidean).
Sure you do - waves only exist in 4D as they have a time vector (frequency).
What I'm talking about is something like this: https://en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euc...
You can either sweep a cutting hyperplane through time or rotate a fixed projection or cut through time, but not both simultaneously.
Re: Show HN: Strange Attractors
#70I bought "Strange Attractors: Creating Patterns in Chaos" (1993) by J. C. Sprott recently, which is a fun book about these kinds of attractors. The whole book can be downloaded online [1] from the author's web site [2]. It's such a typical object of its time. Garishly colored cover, comes with a floppy disk (!) and there are even 3D glasses to view some of the stereoscopic color plates (unfortunately these were missi…
The book software https://sprott.physics.wisc.edu/fractals/bookdisk/