There is absolutely no reason to beleive that any kind of machine will ever exist that can "make it fairly fast" to disassemble an entire planet. You're probably entirely ignoring any kind of wear and tear on the machine itself, which could easily be outpaced by the rate of creating new machines for anything approaching the billions of years this would actually take using any imaginable fuel.
Assume humans are the VN machine. We can make space suits and greenhouses etc., so it's not crazy.
Assume reproduction such that population doubles every 25 years. Fast, but not insane.
(1000/25) = 40 doubling periods
8e9 * 2^40 * 100kg = 2.7 Mercury masses, or 12 lunar masses, or 1.3 Mars masses
That's a worst-case bound using a biological anchor. Dedicated VN machines can plausibly be faster: even if it's something weird like staying with biology and uplifting dogs, that's now 75 years, a plausible but currently hypothetical self-replicating 3D printer could make the timescales even shorter.
The sun provides enough power to do it in a week or two, though anything less than decades may have thermodynamics issues.
I'm not sure where your 8e9 number is coming from. Population doubling every year but the parents leaving the planet after mating?
In your calculation, after 1000 years, there would be 2^40 humans, each weighing 100kg - many orders of magnitude less than Mercury's mass.
Still, if we give it a few thousand more years of exponential growth, you will eventually reach such masses.
However, these numbers are meaningless - you are assuming that doubling the size of a population that's 2^39 individuals will take roughly the same time as a population that's 64 individuals individuals, which is not even close to plausible - especially when we reach ideas like a population weighing as much as half a planet.
You're also assuming that it's even possible for a mahcine to convert a significant proportion of a planet's crust to copies of itself - which is obviously false, as the crust is mostly rock, and machines require plenty of liquids and water to be produced (whether biological or mechanical or electronic). And that doing so will not affect the growth rate at all, even as the planet starts being formed of molten magma once all of the crust has been used up. And not to mention the gigantic earthquakes and supervolcaones they would have to deal with as a significant portion of continental mass gets shifted around.
Overall, you are only extrapolating some numbers to a completely absurd conclusion, and calling it plausible. There is nothing even close to realistic in your scenario, and indeed we have no idea if it's even close to possible to strip a planet down to create a Dyson swarm. I very much doubt your energy calculation as well, but that's already beside the point.
> I'm not sure where your 8e9 number is coming from. Population doubling every year but the parents leaving the planet after mating?
That's the current human population.
> In your calculation, after 1000 years, there would be 2^40 humans, each weighing 100kg - many orders of magnitude less than Mercury's mass.
You start with one human, I didn't. What are you even imagining that I'm describing, Adam-only parthenogenesis?
> Still, if we give it a few thousand more years of exponential growth, you will eventually reach such masses.
Even with Adam-only parthenogenesis, log2(8e9)*25 years is 822 years, less than one, definitely not plural, millennia.
Material science isn't my field, though it doesn't need to be given how many other places there are for whichever chemicals we want. Water? Oxides in the local rock, and four massive hydrogen gas giants (don't need much proportionally as H2O is 89% oxygen by mass).
> I very much doubt your energy calculation as well, but that's already beside the point.
Gravitational binding energy of Earth: 2.2e32 J; Mercury: 1.8e30 J; Mars: 4.9e30 J; Luna: 1.2e29 J
Luminosity Sol: 3.8e26 W
Time required to explosively disassemble (i.e. each part reaching escape velocity) each object: Earth: 6.6 days; Mercury: 1.3 hours; Mars: 3.6 hours; Luna: 313 seconds.
To preempt the obvious, yes I know that's the number for total luminosity and not the power available at any given moment given how many space habs have been built part way through the process, but that makes very little difference: Given the way the functions behave, you don't need most of the power of the sun until you can harness a significant percentage of it anyway.
I mean, this toy model also assumes that the only thing these humans do with their lives is reproduction, with the average individual adding only a little more than their own body mass to the VN swarm each generation, and not, e.g., building themselves a nice little space hab that's unlikely to mass less than 10,000 kg/person even if I make the grossly simplifying assumption of just adding life support to a tiny house or a camper van. It makes very little difference to exponential growth.
You haven't addressed the most important points at all, and keep coming up with toy models based on exponential growth. All of the models ignore the realities of how mechanical things work and how they can break and how they actually operate (just for a basic example, there is no mechanical system we have any idea how to build that could move any amount of the Earth's mantle in any way, since the mechanisms would simply melt) and rely on the ridiculous idea that this exponential growth can actually be maintained indefinitely to paper over various other omissions.
You also don't need to be a materials scientist to know that you can't get water or oxygen out of rock with sheer mechanical force.
Your estimate for the energy of the sun takes into account all of the energy sent in all directions in all spectra. The amount reaching the earth is significantly less - 1.73e15 W, or about 10^9 times less - and the amount that can realistically be captured is far less than that.
Overall, don't worry: there is exactly 0 chance that any human advancement will disassemble even a dwarf planet in the next millennium in the real world. Just because Freeman Dyson could write some back of the napkin computations it doesn't mean this is actually possible in any meaningful way.
> just for a basic example, there is no mechanical system we have any idea how to build that could move any amount of the Earth's mantle in any way, since the mechanisms would simply melt
You know stuff cools down, right? Power loss to radiation is proportional to T^4.
> You also don't need to be a materials scientist to know that you can't get water or oxygen out of rock with sheer mechanical force.
Good thing you're putting words into my mouth, then. Hint 1: How do we do this for aluminium? Hint 2: I didn't say "mechanical" for this.
> Your estimate for the energy of the sun takes into account all of the energy sent in all directions in all spectra
I know, and I said as much with different words.
Do you perchance know what a mirror is? Or how light they are? How little of (insert-planet-here)'s mass you need to turn into PV and/or mirrors to get to covering the planet, how little time it takes to use those to gather the energy needed to run a launch loop to get a second planet-tiling-quantity to orbit?
That's why I preemptively made the point that you're ignoring here.
> You know stuff cools down, right? Power loss to radiation is proportional to T^4.
It only took around 160 million years for the Earth's crust to form, so yeah, sure, stuff cools down, eventually.
> Hint 1: How do we do this for aluminium? Hint 2: I didn't say "mechanical" for this.
Ok, mechanical was my idea - but chemical extraction of oxygen requires some other compounds to form, potentially making the whole thing even less usable for future conversion into more copies. Plus, it requires an input of some other materials, which may not be easy to create.
> Do you perchance know what a mirror is? Or how light they are? How little of (insert-planet-here)'s mass you need to turn into PV and/or mirrors to get to covering the planet, how little time it takes to use those to gather the energy needed to run a launch loop to get a second planet-tiling-quantity to orbit?
That still only gives you the 10^15 watts that reach the Earth, not the 10^26 number you were citing. Also, covering the whole planet with mirrors or PVs is again not nearly as trivial as you make it out to be, and this "launch loop" idea is just some abstract design, not something we can actually build (despite what the author would have you believe).
> Assume reproduction such that population doubles every 25 years. Fast, but not insane.
This is already completely implausible given everything we know about human behavior, but it reaches impossibility very quickly when you consider the possibility of humans becoming more than a negligible fraction of the mass of their single host planet. We aren't machines that can trivially reproduce ourselves from commonly available materials and then eject into space. Feeding ourselves is hard, getting to space (alive) is harder. And once the overwhelming majority of us are in space because there's no more room down below, how are we supposed to meet up to keep up the 25 year doubling rate. How are we supposed to keep up the rate of resource extraction from Earth?
> We aren't machines that can trivially reproduce ourselves from commonly available materials and then eject into space.
Nah, we use plants to turn raw materials into what we can consume. And in the other direction, we can only make stuff on this scale with factories that take a while to build. But in both cases, that's a distinction without a difference. A farm and a factory rather than a spacesuit, makes no difference on this scale, so long as they feed themselves while growing their families.
> Feeding ourselves is hard, getting to space (alive) is harder.
Feeding ourselves is about 1% of our current labour. Getting into space is only hard because we use rockets, but at this scale we'd use launch loops, atlas towers, orbital rings, or similar. Those are extremely cheap, like "$300 to LEO" cheap for this thought experiment's ("spherical cow in a vacuum" model of a) 100 kg human.
> And once the overwhelming majority of us are in space because there's no more room down below, how are we supposed to meet up to keep up the 25 year doubling rate. How are we supposed to keep up the rate of resource extraction from Earth?
There's lots of ways I've seen suggested. Even without the exotic options like the Dyson Motor (would take too long, at 40k years for Earth, not seen the numbers for Luna or Mars) or redirecting Kupier Belt Objects to blow off percentage points of the target planet mass at a time, even just with traditional digging, at that scale it's "how fast can you drill vertically?" and "how many launch loops can you wrap the target planet in?", followed by "how fast does the deep ground cool down when exposed?" — the latter being why I said thermodynamics probably gets in the way when the timeline gets down to decades; this is radiative-dominated cooling in a better vacuum (insulator!) than most laboratories let alone thermos-flasks.
Interestingly, rocky planet disassembly isn't horribly complicated and is a well solved problem. Just need large scale rail and satellite manufacturing.
Only requires more structures and geoengineering larger than humans have bever done before.
We know how, and we know it doesn't require more than operating at higher scales of industry than ever before. Any interplanetary or kardishev 1+ venture makes those assumptions.
