Why isn’t it likely, given that you can “burn” more resources in order to grab a larger share of the lightcone? If you’re saying that the outcome of burning the cosmic commons isn’t likely because everyone will negotiate to avoid it, I’m saying that the game structure itself isn’t zero-sum, which is needed to show that strategy-stealing applies in theory.
And that this type of negotiation seems particularly easy given the distribution of values I expect for the actors negotiating (e.g., strongly locust-like values aren’t that likely).
I do not know of a result, or have the intuition, that if negotiation is “easy” then strategy-stealing (approximately) applies. My intuition is that even in this case (like in my toy game) some parties can credibly threaten to burn down the world (or to risk this), and others can’t, and this gives the former a big advantage that the latter can’t copy. Negotiation is “easy” in my game too (note that the outcome is pareto optimal, and no risky action is actually taken), but the more cautious or altruistic party is disadvantaged.
I don’t currently think you can burn more resources to grab a larger fraction of the light one. Or like, I think the no-negotiation equilibrium burns a small fraction of resources. I don’t feel super confident in this view, but that was my understanding of our current best guess. I haven’t looked into this seriously because it didn’t seem like a crux for anything. Maybe I’m totally wrong!
My cached view is something like “you can send out an absurd number of probes at ~maximal speed given very small fractions of resources, so burning resources more aggressively doesn’t help”.
The following LLM output matches my own understanding:
Ryan’s crux is his “cached view” that you can send probes at nearly maximal speed using very small fractions of resources, so burning extra resources doesn’t help. This violates the physics of relativistic travel.
Because of relativity, kinetic energy scales non-linearly as you approach the speed of light (). The energy required to accelerate an object approaches infinity as its speed approaches .
If Actor A wants to beat Actor B to an uncolonized star system, and Actor B launches a probe at , Actor A must launch at to get there first.
Upgrading a probe’s speed from to , and then from to , requires exponentially more energy for the same payload mass.
Furthermore, if you want your probe to actually do something when it arrives (like decelerate, build infrastructure, and defend itself), it needs mass. To decelerate without relying entirely on ambient interstellar medium, you have to carry fuel for the deceleration phase, which exponentially increases the launch mass required (the Tsiolkovsky rocket equation).
Therefore, Robin Hanson’s “Burning the Cosmic Commons” scenario is physically accurate. In an uncoordinated race for the universe, colonizers must convert almost all available local mass/energy into propulsion to outpace competitors. Securing a larger share of the lightcone absolutely requires burning vastly more resources.
LLM output doesn’t seem nearly quantitative enough. With some numbers of 9s, it surely doesn’t give you a meaningful advantage to go at 0.99...99c rather than merely 0.99...9c — especially when you factor in that it probably takes time to convert energy/mass into the additional speed (most mass will be in between your origin and the farthest reaches of the universe, and by the time some payload have decelerated and started harvesting significant energy from the middle mass, the frontier of the colonization wave will likely already be quite distant). I share Ryan’s guess that you can get close enough to optimum without burning a large fraction of all energy in the universe. (That’s a lot of energy!)
I think you’re right that wasn’t really conclusive. Will try to address your arguments below.
With some numbers of 9s, it surely doesn’t give you a meaningful advantage to go at 0.99...99c rather than merely 0.99...9c
This seems right but you can (probably) still gain a meaningful advantage by sending more colony ships (and war/escort ships) instead of pushing for more speed.
especially when you factor in that it probably takes time to convert energy/mass into the additional speed (most mass will be in between your origin and the farthest reaches of the universe, and by the time some payload have decelerated and started harvesting significant energy from the middle mass, the frontier of the colonization wave will likely already be quite distant)
Are you assuming either that it’s possible to launch colony ships directly across the universe, or that it takes millions/billions of years to fully harvest a star (e.g. using a Dyson sphere while the star burns naturally)? If instead there’s a distance beyond which it’s infeasible or uncompetitive to try to directly colonize, like 10x the average distance between neighboring galaxies, and also possible to quickly harvest a star using direct mass to energy conversion (e.g., via Hawking radiation of small black holes), then the colonies in the middle should have plenty of tempting new targets to try to colonize (before someone else does), at the edge of the feasible range?
I share Ryan’s guess that you can get close enough to optimum without burning a large fraction of all energy in the universe.
I’ll describe a toy model to convey my intuitions here.
Setup
Two players each own 0.5 of Galaxy 1. They compete for Galaxy 2 by consuming their Galaxy 1 resources as colonization effort (c).
Payoff
Player A’s total utility is their retained Galaxy 1 plus their competitively won share of Galaxy 2. U = (0.5 - cA) + cA / (cA + cB).
Solution
To find the Nash Equilibrium, we maximize Player A’s utility by taking its derivative and setting it to zero. Because the game is symmetric, both players will invest equal effort (cA = cB). Solving this yields an equilibrium effort of c = 0.25.
Outcome
Both players sacrifice exactly half of their initial resources (0.25 out of 0.5). Because they invest equally, they split Galaxy 2 evenly (0.5 each). Their final score is 0.75 each.
P.S., what do you think about my earlier points about war and black hole negentropy, which could end up being stronger (or easier to think about) arguments for my position?
Why isn’t it likely, given that you can “burn” more resources in order to grab a larger share of the lightcone? If you’re saying that the outcome of burning the cosmic commons isn’t likely because everyone will negotiate to avoid it, I’m saying that the game structure itself isn’t zero-sum, which is needed to show that strategy-stealing applies in theory.
I do not know of a result, or have the intuition, that if negotiation is “easy” then strategy-stealing (approximately) applies. My intuition is that even in this case (like in my toy game) some parties can credibly threaten to burn down the world (or to risk this), and others can’t, and this gives the former a big advantage that the latter can’t copy. Negotiation is “easy” in my game too (note that the outcome is pareto optimal, and no risky action is actually taken), but the more cautious or altruistic party is disadvantaged.
I don’t currently think you can burn more resources to grab a larger fraction of the light one. Or like, I think the no-negotiation equilibrium burns a small fraction of resources. I don’t feel super confident in this view, but that was my understanding of our current best guess. I haven’t looked into this seriously because it didn’t seem like a crux for anything. Maybe I’m totally wrong!
My cached view is something like “you can send out an absurd number of probes at ~maximal speed given very small fractions of resources, so burning resources more aggressively doesn’t help”.
The following LLM output matches my own understanding:
Ryan’s crux is his “cached view” that you can send probes at nearly maximal speed using very small fractions of resources, so burning extra resources doesn’t help. This violates the physics of relativistic travel.
Because of relativity, kinetic energy scales non-linearly as you approach the speed of light (
If Actor A wants to beat Actor B to an uncolonized star system, and Actor B launches a probe at
Upgrading a probe’s speed from
Furthermore, if you want your probe to actually do something when it arrives (like decelerate, build infrastructure, and defend itself), it needs mass. To decelerate without relying entirely on ambient interstellar medium, you have to carry fuel for the deceleration phase, which exponentially increases the launch mass required (the Tsiolkovsky rocket equation).
Therefore, Robin Hanson’s “Burning the Cosmic Commons” scenario is physically accurate. In an uncoordinated race for the universe, colonizers must convert almost all available local mass/energy into propulsion to outpace competitors. Securing a larger share of the lightcone absolutely requires burning vastly more resources.
LLM output doesn’t seem nearly quantitative enough. With some numbers of 9s, it surely doesn’t give you a meaningful advantage to go at 0.99...99c rather than merely 0.99...9c — especially when you factor in that it probably takes time to convert energy/mass into the additional speed (most mass will be in between your origin and the farthest reaches of the universe, and by the time some payload have decelerated and started harvesting significant energy from the middle mass, the frontier of the colonization wave will likely already be quite distant). I share Ryan’s guess that you can get close enough to optimum without burning a large fraction of all energy in the universe. (That’s a lot of energy!)
I think you’re right that wasn’t really conclusive. Will try to address your arguments below.
This seems right but you can (probably) still gain a meaningful advantage by sending more colony ships (and war/escort ships) instead of pushing for more speed.
Are you assuming either that it’s possible to launch colony ships directly across the universe, or that it takes millions/billions of years to fully harvest a star (e.g. using a Dyson sphere while the star burns naturally)? If instead there’s a distance beyond which it’s infeasible or uncompetitive to try to directly colonize, like 10x the average distance between neighboring galaxies, and also possible to quickly harvest a star using direct mass to energy conversion (e.g., via Hawking radiation of small black holes), then the colonies in the middle should have plenty of tempting new targets to try to colonize (before someone else does), at the edge of the feasible range?
I’ll describe a toy model to convey my intuitions here.
Setup
Two players each own 0.5 of Galaxy 1. They compete for Galaxy 2 by consuming their Galaxy 1 resources as colonization effort (c).
Payoff
Player A’s total utility is their retained Galaxy 1 plus their competitively won share of Galaxy 2. U = (0.5 - cA) + cA / (cA + cB).
Solution
To find the Nash Equilibrium, we maximize Player A’s utility by taking its derivative and setting it to zero. Because the game is symmetric, both players will invest equal effort (cA = cB). Solving this yields an equilibrium effort of c = 0.25.
Outcome
Both players sacrifice exactly half of their initial resources (0.25 out of 0.5). Because they invest equally, they split Galaxy 2 evenly (0.5 each). Their final score is 0.75 each.
P.S., what do you think about my earlier points about war and black hole negentropy, which could end up being stronger (or easier to think about) arguments for my position?
IIRC someone I know tried to look into this at some point (at least the physics). I’ll see if I can learn what they found.