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Really cool thought experiment but it's hard to imagine making significant investments on a project that wouldn't produce any results until ~250 years. Any project on that time scale and that distance from "home" would likely need to be completely self sufficient so I would image the project would need a fully capable AI and self replication or at least some sort of very advanced manufacturing capabilities. Autonomous self replicating drones like in universal paperclips are likely the answer.
You'll probably be less disappointed if you read this as a paper about VRP using genetic algorithms as opposed to space exploration
Agreed. I'm actually doing a VRP using genetic algorithms for a final project right now. That said I feel like I know enough about the problem to know that I don't know enough about the problem to contribute to HN about it. Space missions are much closer to my wheelhouse.
> I'm actually doing a VRP using genetic algorithms for a final project right now

Don't forget to compare it with simulated annealing to find out if Skiena was right about GA in The Algorithm Design Manual when he said that he "[has] never seen any computational results reported using genetic algorithms that have favorably impressed [him]".

Yeah, the time scales involved are my go-to counterargument to the people who say other intelligent creatures should have conquered the galaxy by now.

I suspect that for all realistic lifeforms, given travel at a few percent of lightspeed max, the ROI on interstellar travel (both on the financial and the individual-sacrifice-vs-benefit level) is so bad that you'll essentially only do it when your solar system is doomed.

And that takes you from exponential growth down to essentially zero growth.

I think the time-scale argument lacks a little bit of imagination. Time scales are very relative.

There could easily be organisms that have lifespans in the thousands of years due to a variety of unique selective pressures (or no concept of a lifespan at all). Or species that have technology that can augment their lifespans to be thousands of years long. I can certainly see humans getting to that point in the next 10-thousand years.

Given a thousand year lifespan, what is a few hundred years in terms of commitment to a project? It would be something akin to working a job for 10 years or so, which is not entirely unheard of.

The ROI argument is more interesting! Although there are way too many factors to consider to have a definitive answer one way or another.

250 years hardly sounds outrageous.

https://en.wikipedia.org/wiki/Sagrada_Fam%C3%ADlia has been under construction for nearly 150 years; "construction passed the midpoint in 2010".

Some of the European cathedrals took centuries to build. The people who started them knew they'd never see the result.
St. Vitus cathedral in Prague: constructed between 1344-1929. That's not "centuries" -- that's a better part of a millennium.
Once the technology exists to allow cults and misfits to build self sustatining asteroids and stick an engine on them, then it will.

However as there would be no meaningful communication outside of a solar system, a single civilisation wouldn't spread to the stars

Of course, even better strategy is to just sit at home and create a small fleet of drones that can use Sun's gravity as a lens to observe planet surfaces in nearby stellar systems with resolution in kilometers per pixel.

At least this could be accomplished within our lifetimes.

Do you have any reference links? This sounds amazing.
The one downside is that you need multiple missions to observe just single target. The mission could potentially be modified to be good for more than one target but at the cost of length of the mission. The path of drones would have two intersect two points that need to be reached to observe two targets, but that would require most likely less hyperbolic (meaning slower) escape trajectory.

The major benefit is that we don't need to invent anything new -- all required technology already exists. And the mission wouldn't even be that costly (at least in comparison). Just select the target, build (a dozen?) drones, shoot them on a right orbit into the Sun's gravity well and wait something like 20 years until they reach destination.

Definitely seems like the kind of thing that would be made way more feasible with the advent of Starship bringing down launch costs 100x
Holy cow, this is incredible. How have I not heard of this concept before?? Guess I'm one of today's lucky 10,000
10,000 only applies to a concept that reasonably is known to everybody or almost everybody before they die (like the fact mentos thrown into bottle of pepsi does funny things).

I suspect that only very, very small number of people are aware of this mission profile:)

Not very easy. Focal point needs to be dynamic and is very far away. Also the receivers are complex and not just a piece of mirror. Doable yes, but extremely costly. James Webb is nothing compared to a sun telescope
You compliment me by thinking it is my idea.

No, it is not. It is actually being seriously worked on by Nasa.

Also, they use the word "affordable". Now, in case if NASA this can mean practically anything, but there is chance it is not prohibitively expensive.

https://www.nasa.gov/directorates/spacetech/niac/2020_Phase_...

This is awesome!

Another reason to be bullish on SpaceX starship. Being able to send mass to space on the cheap opens up many new astronomical exploration avenues.

I still argue for autonomous vehicles with sentient robots that come alive in orbit and go down to the planet and explore. I very much doubt that humans will ever leave the solar system. Sadly our lifespans are just too short. One possibility is constructing very large telescopes. I stress very large! A properly constructed telescope could see enormous distances and eliminate the concern about travelling to the particular target. Let's see what the scientists cook up.