Animating the hypergraph with Dugan Hammock
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- Опубликовано: 21 апр 2023
- Dugan Hammock creates beautiful animations of three-dimensional cross-sections through four-dimensional spaces.
But his animations aren’t mere mathematical abstractions. He has also applied his geometrical skills to animating the hypergraph of Wolfram Physics, in such a way that it doesn’t jump from frame to frame.
In this second part of my recent conversation with Dugan, we talk about his extending spring-electrical embedding into an additional time dimension...
...and we show some of the beautifully smooth animations that come out of it.
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Dugan Hammock
• Dugan Hammock’s videos on RUclips www.youtube.com/@VJDugan/videos
• Dugan Hammock on Twitter / duganhammock
• Dugan Hammock at The Wolfram Physics Project education.wolfram.com/summer-...
• Plotting the evolution of a Wolfram Model in 3-dimensions community.wolfram.com/groups/...
• Temporally coherent animations of the evolution of Wolfram Models community.wolfram.com/groups/...
People and concepts mentioned by Dugan
• Coulomb’s law en.wikipedia.org/wiki/Coulomb...
• Hooke’s law en.wikipedia.org/wiki/Hooke%E...
• Spring-electrical embedding reference.wolfram.com/languag...
• Charles Pooh community.wolfram.com/web/cha...
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Prefer to listen to the audio? Search for The Last Theory in your podcast player, or listen at lasttheory.com/podcast/036-an...
Kootenay Village Ventures Inc.
Beautiful
Thanks Nik! This is pretty amazing work by Dugan, isn't it?
Holy cow what an amazing idea! And the results just speak for themselves 😲
Thanks for sharing, I have some hypergraph videos to binge.
Can't wait for the next dimension 🤗 (and why stop at 4?! 😆)
Yes, it's fun to see those hypergraphs smoothly evolve!
Something else seriously-cool in the Kingdom of Multiple Dimensions, is complex time (or "two-dimensional time").
Curious about "moving into the past" without squeezing through a singularity at "zero?" Rotate there.
So is the optimization done one layer at a time, with previous layers (time steps) held fixed as the layout for a new layer / time-step is generated; or is the layout of the entire sequence optimized together, so that in principle what the graph will look like in the future could affect how it is laid out now?
That's a good question, thanks Kevin.
I believe what Dugan is doing is a _global_ optimization, i.e. generating _all_ the layers of the hypergraph and applying the optimization _across_ the layers. The only constraint he's imposing is that each time slice remains in its own plane.
So yes, with this optimization method, the future connectivity of the graph can affect how it's laid out now.
This is very different from the way I do it in my animations, where I lay out the hypergraph at the first time step, then use that layout as the initial conditions for laying out the hypergraph at the next time step, and so on.
The hypergraph animations are great. Are there mathematica notebooks for doing these animations? Is there other software available for doing these animations where one could play with the transformation rules to see what graphs are generated? Thanks!
Thanks! The best place to start is the software tools page of the Wolfram Physics Project: www.wolframphysics.org/tools/
As far as I understand, you'll be able to play around with different rules of Wolfram Physics using these tools, and see what graphs are generated.
Dugan's animation techniques aren't publicly available, though, since they're only just done! I believe he's in touch with Wolfram Research, so I hope they'll do whatever they need to do to make these animations available soon!
Thanks for the channel! Watched all vids in two days. When will you add consciousness to the mix? ))
That makes me happy, thanks Vladislav!
It's going to be a little while before I get to consciousness, since I have to work through the multiway graph and multiple threads of time before I get to how Stephen Wolfram postulates consciousness might be involved in collapsing it all to a single thread of time.
This is fascinating stuff... I'll get there!
Yes, it is fascinating and complicated. I only came across Stephen's theory two weeks ago, but I have been thinking in a similar key for many years: a self evolving information universe (software or consciousness). I described this idea in my book on the evolution of financial derivatives in 2012, but it was only published in Russian. I am glad that such a renowned mathematician has formulated and is pursuing such an idea right now!
Where are more videos with hypergraphs? On Hammocks channel there is only confusing 4d animations 😵💫
Yes, Dugan's channel has mostly his 3D cross-sections through 4D spaces... which is always going to be confusing for 3D creatures like me! He has, however, published a couple more of his hypergraph animations on Twitter recently, and with any luck he'll be tweeting more. Check them out at twitter.com/DuganHammock
@@lasttheory Sry, I dont do twitter. And the 4D vis, I am used to that, but without any meta information (angles, parameters) it's kinda useless.
@@harriehausenman8623 Not doing Twitter is a good way to stay sane!
@@lasttheory for me it's self defense: I know myself enough that I know it would immediately get me 🤭
Does this display method (beautiful and useful as it is) break down at very large scales, under the weight of computation, visualizability, or interpretation?
If so, do investigators' intuitions indicate that something like purpose or teleology or value "is being sought" at these scales, and not reflected in the animation?
If so, I suggest that a framework like Active Inference be investigated as a way of supplementing the more point-to-point techniques already in use. AcI allows characterization of the dynamics of self-governing complex systems by simultaneously improving (I dare not say "optimizing") pragmatic value and epistemic value in a single number-valued formalism.
There's a whole course on the quantum-informational aspect of the Active Inference framework (and courses and talks on other aspects):
ruclips.net/video/SV0glS6stuA/видео.html
That’s interesting, thanks. I would say that these visualizations are just an aid to understanding. Precise results, such as determining the dimensionality of a hypergraph, can be arrived at through precise measurements. It’s good to be able to “see” these universes, but to determine whether they match our own we need to do calculations.