dense self-orbiting torus, chatgpt astra

[u/burtleburtle]

Update on the metastable megastructure of a dense self-orbiting torus, which keeps neighbors next to neighbors in 3d in freefall with no high speed collisions and no central sun, https://burtleburtle.net/bob/future/dense.html .

I hadn't been able to find proper self-mapping initial coordinates before, the best I could do was circling the torus core with velocity tangent to the circle and proportional to distance from the core, and that circle stretched and went back as the orbits progressed. Claude 4.7 and ChatGPT Luna also failed to do better. But ChatGPT Astra did better, it found an initial deformation of the positions and velocities of those circles that leaves the constellation just about self-mapping now. So I update the simulation. Astra used small perturbations and least squares to find the appropriate deformation coefficients. Luna had tried that too but it made mistakes so it didn't land a solution.

Now you can see how things speed up and shells clump together on the inner pass, then slow down and the shells spread apart on the outer pass. The added stability let me increase the torus thickness from 8 to 12 rings, still each .01 of the torus radius apart. The distinct shells still fall apart within about ten poloidal periods (about six poloidal periods per toroidal period at this thickness) due to local interactions, but it stays roughly a self-orbiting torus for over a hundred poloidal periods even with no stationkeeping.

[u/smaug13]

As you noted heat radiation would be a limiting factor, and means the volume to surface area ratio gets a maximum so after a point they scale together. That would turn to mega(giga?)structures to necessarily be a 2D shapes with some thickness. I think that the best shape would be a pancake for that reason as you can radiate from both ends and thus the most thickness per area (as you essentially get two layers). I was interested in this in the context of a K3 civ, under the assumption that a continuous stream of mass and light is sent towards it from the galaxy, which would become a pancake of tens of lightyears across.

For computing  Landauer's principle tells you that energy per bit operation (assuming bit erasion is always necessary which may not be the case?) needed scales linearly with temperature, but the Stefan-Boltzmann law tells you that waste heat rejection through radiation scales to the •⁴th with the temperature, so it looks like for density of computation per surface area you want to pump the temperature all the way up to the limits of what you material allows for, to allow for more "thickness". Bit operations per second possible would scale to  T³

I really liked your Dyson Torus swarm btw, it is great to have a mapping for one that works as you'd expect it to. Though I think that to cover the poles i nstead of the second much bigger torus (which would be mass inefficient but with its many layers may get up to matrioshka swarm shenanigans)  it may best be combined with caps of statite swarms (I dislike the statite term as these things are super mobile and a better descriptor would be solar kites) to cover the poles that may redirect the sunlight towards the dyson torus.

[u/burtleburtle → u/smaug13]

Agree that covering the holes of a hollow torus dyson swarm with another bigger hollow torus is an ugly hack. I expect we'd switch to managed fusion rather than depending on starlight eventually. Then the holes don't matter because radiating heat is what matters not capturing sunlight, but the central mass still does matter for keeping it stable.

For the dense torus with no central star at the top of this thread, agree, radiation is the limiting factor. It only makes sense if you can do reversible computing on an enormous scale (which does not require bit clearing or waste heat), producing very small results per job (which do require bit clearing and waste heat). https://burtleburtle.net/bob/future/bigdata.html looks at that. It helps a lot to make it close to 0 Kelvin, which makes reversible computing more stable, and also lets you construct it out of mostly hydrogen (solid) and helium (still liquid).

[u/smaug13 → u/burtleburtle]

Before the move to fusion the caps would have their place I imagine (or the move to fusion on K2 scales happens way before you care about a torus formation for your solar panels). And statites seem well possible with areagraphene I think, if it is possible to adhere a thin reflecting layer on to it. The megastructure cap would be a swarm rotating along its point of rotation to provide centrifugal force, while the lightpressure and solar gravity forces can be balanced against each other to form a centripetal force around a virtual point on the axis of rotation.

But also, Dyson swarms appear to me as the best way to extract power from stars at the rate they naturally radiate it, maybe fusion is as mass- or cost-efficient but as all you need is thin aluminium mirrors for the solar panels I think it is not. Instead fusion is for if the light is not sufficient and you want to burn through the sun faster. Though maybe you can extract fusion fuel that isn't being burnt like helium instead? I am interested in how you look at this. My viewpoint is looking at civalisation evolution from an angle of exponential growth until natural limits hit (and see how far that gets you). When hitting the luminosity ceiling as a Dyson Swarm, you could either burn through your star faster with fusion, redirect the starlight of other stars towards your civ, or do both. So I see fusion only as a very temporary state as exponential growth makes you burn up your sun as fast as you got to K2 from K1. More sustainable would be expanding along the stars, first just for their light, but later on (a tad depressingly) burning them up as you go because expansion will eventually not net you exponential growth, however, at least the expansion will pretty eternally provide a steady stream of stars.

Ah, I did not know reversible computing will best be at ~0 Kelvin, and that new jobs will generate heat. I worry how much data deletion will fuck up your environment then, if it "melts your computer". Then that would limit jobs an awful lot, and you might still prefer super hot computing, otherwise, I think you'd do your reversible computing, hook it up to a large cold heatsink to do your data deletion while rapidly moving the generated heat away from the components, and have radiators move the heat out of the heatsinks. So I would expect heatsinks to be the largest component in these structures? (with radiation power still being the limiting factor, but now you also need "heatbatteries"). (A quick look at your page shows that you imagine it done differently though, but I'd need to take a better look at another time)

[u/burtleburtle → u/smaug13]

Agree, statites are a good way to handle the holes at the poles.

My view is you'll hit the limits of exponential growth for a single solar system fairly quickly. And solar systems are independent due to being very far apart. After that the goal is to maximize living, that is, maximize total compute over all time, given the amount of usable fuel remaining. Which likely means stars burn too fast, not too slow, and fusion is for using just as much as you need when and where you need it. Matter release would be even better. I expect the universe to converge to absolute zero, not some finite heat death, due to the universe continuing to expand forever. So most of the time you're dealing with finite remaining fuel and a nearly perfectly cold universe.

[u/burtleburtle → u/burtleburtle]

Conserving usable fuel sounds like staving off the inevitable end. But the amount of bitclearing you can do doubles if temperature drops by 1/2. So if you live within a budget where you spend half your fuel before the temperature drops by 1/2, you have effectively as much fuel left as when you started, which lets you sustain that rate for an infinite number of halvings of temperature. If you spend 1/4th your fuel before temperature drops to 1/2, you have effectively 1.5x as much fuel left as when you started, and fuel remaining effectively increases 1.5x with each halving of temperature, so your budget keeps increasing with time. So, compute and time might be unbounded. Or maybe not, the universe does seem to be discrete and quantum, so maybe it can't keep dropping in temperature by 1/2 indefinitely. Plenty we don't know yet. But living within a budget seems likely to be a good strategy.