Your argument shows a lack of understanding of exponential growth.

Any given colony has to create only slightly more than 1 additional colony in order to drive exponential growth. There doesn't have to be any coordinated action by a central authority for it to happen. For it not to happen (if it is physically feasible), in contrast, every species has to refrain from doing it at all points in their history, almost without exception. And those that do the colonization will seed additional colonies with a mindset that led to colonization; such mindsets will be selected for for further expansion.

Permanent exponential growth is very rare in nature, and even rarer in biological systems. What we observe as exponential growth is usually only a partial observation of a logistical curve or is missing a system collapse at the end of the curve.

We have no reason to believe alien (or even human) civilization will continue to grow and expand forever. Heck even the human population curve has started to slow down and is now revealing it self to be a logistical curve.

But regardless of this, space is very very very big. And there are a lot of extremely hostile worlds out there. Any civilization will experience biological limitation to which worlds they can (and will want to) colonize. Likewise they will experience both economical and physical limitations to how far they will send their machines. Lets say an alien species is lucky and has a habitable world inside their solar system which they will colonize. I think this is likely. They also spot another world in a nearby solar system which takes them 200 years to travel to, eager colonists travel in a generational ship, and 600 years later the colony is thriving. Now they run out of nearby habitable worlds. There is a world of questionable quality 500 years away and they are unable to persuade enough people to fill a generational ship. Also they learned the stories of the passengers in the generational ship, their lives kind of sucked, we have it much better on this world. So it is better to just stay here. This might happen after 1 or 100 successful colonizations, but I think space is so freaking large, it will happen to all civilizations. At some point they will run out of worlds to colonize, and they will never expand far outside of some local area near their home world.

It's rare in biological systems because it's terminated by running out of some resource.

But you're saying galactic colonization would terminate without running out of new systems to colonize.

There would be a slowdown due to geometric constraints -- only so many new systems adjacent the boundary of the colonized zone -- but that hardly solves your problem.

My speculation is that the size of space is an obvious geometric constraint which will limit the span of any civilizations almost immediately.

If we look at humans, we have both the space, technology, and the resources to expand even further on earth, yet our span only marginally larger then it was 10 000 years ago. We can have permanent settlements on Antarctica, floating on the ocean, etc. but we don’t. We can increase our population by another order of magnitude, but again, it looks like we won’t. This follows the same population dynamics as most other species on earth. I think aliens will be no different.

Unless some means of communicating faster than light is found a galactic colonisations is not a civilisation, its multiple ones. A colony ship heading in one direction at 0.1c will never interact with one heading the other way at the same speed. After 10,000 years the civilisations will be very different, after 100,000 years they will barely be the same species.

Even if 99% stop and fail, the 1% will continue and continue expanding.

The only way to stop would be to run out of planets, which would mean every habitable planet and star system has been populated. There wouldn’t be a biological urge to stop, as the successful colonies are ones which have the urge to expand. An environmental need wouldn’t affect every colony and ship short of a galaxy spanning event of some sort which we can’t even conceive.

Yes, I think that will never happen. My prediction is that generational ships are super rare in the universe, and may only happen ones or twice in the entire history of a civilization, and for a tiny portion of civilizations. Meaning by far majority of all civilization will have zero generational ships. Maybe a single civilization somewhere in a distant galaxy will have hundreds, but nowhere near enough to cover an entire galaxy, not even if we count decedent civilizations.

I also think fast space travel (like 0.1c) is rare among civilizations, and may only happen in the order of hundreds of time in the history of some civilizations. And most of these fast space travel will scientific instruments for curiosity and exploration, not for colonization. And that a technologically advanced civilization would favor doing their explorations with telescopes, not probes. So probes would only be sent long distance for rare occasions.

This would mean that almost no civilizations will be expand beyond their solar system, and those that do, will only do it a handful of times, and the expansion will finally stop.

It doesn’t matter how rare it is to get started once it starts. Every ship is a new civilisation that is created, one predisposed culturally and perhaps genetically to spreading out.

Especially once you reach the “hundreds” level then given the technology exists and the people exist why would it stop, until there’s nowhere else to go.

There is the light cage issue where a civilisation can only spread so far with exponential growth before internal pressures overwhelm it (the leading edge never gets a chance to continue as it is overwhelmed by trailing edges)

Even in that situation though you’d still have self replicating probes - likely at a far lower tech level than biological. Once you reach the tech to send one probe which can duplicate itself more than once using resources in a new system then its game over.

Send 50 probes to each of the 50 stars within 15 light years at 0.01c. If 10% make it they then use local materials and send 50 more, that’s 250 out in 1500 years. Then it’s 1250 out in 3000 years. Within a few millennia years you’ve got millions of probes spreading in an unstoppable way. The ones heading back “inwards” will fail, but those heading outwards will reach each new star dozens of times, only one will need to get there. Within 10 million years you’ve reached the entire galaxy.

To stop it you’d have to make a self replicating probe which was faster and did exactly the same thing and caught the earlier probe, but then when would that probe itself stop, it would have no way of knowing if there were any other “bad” probes to find without becoming the bad probe itself.

Living beings are the same. Once a few dozen have made it and passed on, it’s inevitable it will continue. It may leave out a hollowed husk in the origin point with all resources having being consumed in the centre, but that doesn’t matter as the centre has no way of affecting what happens on the edge, and one edge has no way of affecting another edge.

von Neumann probes are a fantasy. I see no reason why any civilization in the entire universe will ever build a successful self replicating probes, let alone ones that are still replicating dozens of millennia later. The reasons include that targeted probes and telescopes can give you pretty much the same amount of knowledge for far cheaper and much quicker then random walking probes across the galaxy. There is also a technical limitation to self replicating probes, even if a civilization will build one, we cannot expect the self-replicating mechanism to last dozens of millennia. Some generations will fail to replicate, and in the vastness of space that may mean the entire lineage will go extinct.

I think you may be expecting an exponential growth when population dynamics almost always favor logistical growth. At some point your machines, or your colonial behavior hits a limit and your growth starts to slow down. I suspect that limit is within the solar system for the vast vast vast majority of civilization. And even if one escapes their own solar system and starts anew on a new home world, they most likely will not colonize another. The space is just so big, and habitable worlds so far away from each other that I find it extremely improbable that any civilization (and their ancestor civilization) will survive more than 5-6 colonization (by far most will see 0).

> Living beings are the same.

They are not. You are describing living beings like viruses (fair enough; viruses are worthy to be considered lifeforms) that spread from host to host until they infect everybody. But viruses don‘t behave like that. The vast majority of them only infect their closest neighbors, and those that do spread towards the limit of all members of the species (like Covid) still fall short and eventually start to slow down their spread in a logistical manner. Growth only looks exponential while you are at the initial stages of spread. This behavior is not only common among viruses, but in fact most population dynamics can be described with logistical growth.

> von Neumann probes are a fantasy.

Well pack it up folks, we've been told what would be possible for any alien civilization, even given millions of years of effort.

Yes, theorizing a future possibility that has no president is, by definition, fantasy. I mean, you can do fantasy, it makes good science fiction, but until we have evidence that von Neumann probes exist and are capable of colonizing the entire galaxy, it remains fantasy. Theoretically we could build a high speed rail between Seattle and LA, we could build a permanent settlement on Antarctica, and we could replace our jet-planes with hydrogen powered flying wings, but until we do, a world with those things are just fantasy.

The only argument for von Neumann probes that I can think of is as a specific answer to the Fermi paradox. The universe should be filled with these probes, but since it obviously isn’t, we can infer that no civilization has reach the interstellar age.

I reject this framing, the Fermi paradox is only a paradox if you assume that space colonization is a thing that is not just possible, but inevitable. My solution to the Fermi paradox simply rejects this assumption. Civilization will not colonize definitely, they will do their space explorations with telescopes and targeted probes, and they won‘t build any von Neumann probes (at least not ones continue to replicate for dozens millennia).

Aside: I am aware of the irony that my description of civilizations outside of our solar system is also a fantasy.