epistemic status: I suspect these thoughts are not novel and are potentially wrong. I still think there's some value in recording my thought process
tl;dr: Selection effects from not being annihilated by aliens may explain why we don't see any very advanced aliens, but it doesn't explain why don't see any as advanced as we are. This may suggest a filter behind us.
Civilisations may sometimes become sufficiently advanced to spread across the stars. Perhaps they would even expand outwards in a near light-speed "shockwave" that converts all available resources into something that they value (like copies of their mind). Perhaps they send seed ships across intergalactic voids. Wherever they go, no new civilisations arise: all matter and energy is used by their civilisation.
Suppose we live in a universe of infinite spatial extent, and that there's some chance of intergalactic civilisation arising in any unoccupied spatiotemporal region. If these civilisations spread out at near light-speed and the chance of civilisational genesis is less than a certainty, there will always be an infinite extent of uncolonised space throughout the history of this universe. The picture below shows an example of such a region in a world where civilisations arise relatively often.
After a little thought, it might appear that we have an anthropic solution to the Fermi Paradox here: of course we don't observe any aliens, for if if we were in their future light cone, the matter we are made of would be used for something else, so we wouldn't exist.
Before we rush ahead with this line of thinking, let's look at a couple of caveats with this idea. The first is that civilisations may exist in states that are observable but not subsuming. I'll specifically consider the case where civilisations start of as observable for a period, then become subsuming. The second is the observed age of the Universe and its implications for this argument.
Visible but not subsuming
On the first, our civilisation has probably been observable for awhile, given the amount and structure of electromagnetic radiation we produce. If we presume that this "young" period is typical for civilisations, we have to explain why we don't observe any young civilisations that wouldn't have subsumed us yet.
Let's take a model where a young civilisation deterministically becomes an intergalactic civilisation over some period τ. Then we have to wonder why there are no young civilisations in the red loveheart region of the picture below.
The volume of a past light cone at time t scales like t⁴, and if p is the probability that a civilisation arises in a volume of spacetime, the probability that a light cone contains no civilisations scales like (1 - p)^(t⁴). This of course drops off very fast with increasing t.
The probability, B, that there are no civilisations arising in the red region looks like (1 - p)^(t⁴ - (t - τ)⁴).
Perhaps we think we are relatively close to becoming intergalactic (even up to a million years away would count for my purposes). That suggests that τ is very much smaller than the period of the Universe's history in which life might have arisen. Therefore, we might kill off terms in the exponent of B that are in higher powers of τ. This gives us a probability that scales like (1 - p)^(τ⋅t³). This still scales very fast with t, so p still can't be very great, but given low τ, higher values of p become plausible.
Young in an old world
Now to the age of the Universe. For a young civilisation to come into existence in some region, it has to be the case that no mature civilisations exist in that region's past light cone and that the appropriate conditions are met for civilisation to arise.
The chance that a spatiotemporal region's past light cone doesn't include mature civilisations declines with that region's position in time (very quickly, as seen above): later regions have larger past light cones that we require no civilisations to have existed within. If we assume that the chance of a civilisation arising in a region does not increase throughout time, the probability a young civilisation observes a young universe is far greater than that it observes an old universe. Our infinite universe argument says that there are young-old civilisation-universe combinations, but that young-young is more probable.
Given that it seems plausible that the Universe could have sustained life for a long time before we came around, this pushes us back towards something like a Fermi paradox. Not: "where is everyone?", but: "(why) are we late to the party?"
A filter behind
This can be resolved with a Rare Earth hypothesis, just like the normal Fermi paradox. That is, we could say it's very difficult to become an intergalactic civilisation. Even though that doesn't change the fact that early intergalactic civilisations are more probable, if it really is astoundingly difficult to become intergalactic, the probability of observing an old(ish) Universe is not appreciably less than observing a young one.
One might even be tempted (insufficiently, according to me) to say that young civilisations are very common, but that all of them die out. That way, you don't need to worry about expansion-shockwaves in your past light cone. In fact, pretty much the same proportion of space will be available for new civilisations for all time.
I don't think the last paragraph holds. Consider again the picture with the blue teardrop and red loveheart regions. Whatever the normal lifetime of a young civilisation (even if it inevitably never becomes old), there is some red region where young civilisations would be observed.
Let's model becoming an intergalactic civilisation as a two step process. Becoming a young civilisation with probability y and (after time τ), going from young to intergalactic with probability i. The probability of an intergalactic civilisation arising in an appropriate region then is c = y⋅i.
The age of the Universe suggests c is low. So at least one of y and i must be low. If i were very low and y high, then we might expect a teeming red region -- we would observe a lot of young civilisations. So that suggests that (at least) y is low and that there is a Great Filter is behind us.
The argument above is essentially using the self-sampling assumption. We consider a world with various young civilisations, and imagine we are drawn from the set of these young civilisations. What is the probability that we see empty skies? What is the probability that we see the Universe is old?
How does the above argument need to be changed under the self-indication assumption? I'm not that confident in this bit, but here's my thinking: if the possible worlds we select from are obtained by varying the parameters i and y in the above model, we expect y to be high (as Katja Grace has pointed out) because that results in more observers that we could be chosen from. The only other way to increase the probability of empty skies (in this model) is to shrink down τ, thus reducing the volume of the red region and suggesting that the time from transmitting signals to judgment day is short.
Some parts of your anthropic argument don't seem right... and it's lead me to a related thought
It seems likely that an expanding civilization would capture much more anthropic measure than what exists on earth. Billions of times more. So, why should we find ourselves here where the cosmic body of life is still so small? Why weren't we born hundreds of thousands of years later in the heavenly gardens of an alien diaspora?
What if... Siblings Are Dangerous: What if most life-supporting universes have in common a dynamic where technology significantly increases the danger of coexisting with other living things. Creating new life on a grand scale is made unviable, our gardens will tend to evolve competitors who will eventually kill everything around them until only they are left, or until nothing is left. The theory is that life is at its most numerous when it is too dumb and too weak to pose much of a threat to itself, as we are.
I'd guess that expanding one's own mind into well-controlled slave cortexes would capture similar amounts of new anthropic measure.. but maybe once you go over a certain scale, having those be independent minds, sufficient to observe their own existence, maybe it just isn't possible to keep that many star-sized consciousnesses under control.
(You might ask why anthropic measure should be tied to independently-intelligent minds. I don't know. It just seems to be. I don't make the rules.)
Any late filter would explain it, though.
It sounds like in the first part of your post you're disagreeing with my choice of reference class when using SSA? That's reasonable. My intuition is that if one ends up using a reference class-dependent anthropic principle (like SSA) that transhumans would not be part of our reference class, but I suppose I don't have much reason to trust this intuition.
On anthropic measure being tied to independently-intelligent minds, what is the difference between an independently- and dependently-intelligent mind? What makes you think the mind needs to be specifically independently-intelligent?
Mm. I think I oppose that intuition. It's hard to see how there can be much of a distinction between existing at low measure and simply existing less, or being less likely to have occurred, or to have been observed. So, for a garden to be considered successful I would expect its caretakers to at least try to ensure that its occupants have high anthropic measure, and at least some of the time they would succeed.
Incisive question... All I can think of is... human organizations are often a lot more conscious- behaviorally- than any individual pretends to be, and I find that I am an individual rather than an organization. I am immersed the sensory experience of one human sitting at one terminal, rather than the immense, abstract sensory experience of, say, wikipedia, or the US intelligence community. It's conceivable that organizations with tightly integrated knowledge-bases and decisionmaking processes do have a lot of anthropic measure, but maybe there just aren't very many of them yet.
I'm trying to imagine speaking to some representative of the state of knowledge of a highly integrated organization, and hearing it explain that its subjective experience anthropic measure prior for organizations is higher than its anthropic measure for individuals (multiplied by the number of individuals), but I don't know what a hive-mind representative would even act like, at what point does it stop saying "we" and start saying "I"? Humans' orgs are more like ant colonies than brains, at this point, there is collective intelligence but there's no head to talk to.
This was really interesting. I've thought of this comment on-and-off for the last month.
You raised an interesting reason for thinking that transhumans would have high anthropic measure. But if you have a reference-class based anthropic theory, couldn't transhumans have a lot of anthropic measure, but not be in our reference class (that is, for SSA, we shouldn't reason as if we were selected from a class containing all humans and transhumans)?
Even if we think that the reference class should contain transhumans, do we have positive reasons for thinking that it should contain organisations?
One thought is that you might reject reference classes in anthropic reasoning (even under SSA). Is that the case?
I think you are overestimating the observability of our civilization. https://what-if.xkcd.com/47/ has an analysis of it. A galactic civ with huge telescopes could easily spot us and a Dyson sphere would be easily visible to us. However our telescope sensitivity and signal strength mean we might detect aliens a few light years away, if we were pointing a telescope at them when they were broadcasting. However its possible that we will go through a highly observable stage before our light speed expansion, sitting round a dyson sphere for 100's of years, so this analysis is still useful.
Yeah, that's a good point. I will amend that part at some point.
Also, the analysis might have some predictions if civilisations don't pass through a (long) observable stage before they start to expand. It increases the probability that a shockwave of intergalactic expansion will arrive at Earth soon. Still, if the region of our past light cone where young civilisations might exist is small enough, we probably just lose information on where the filter is likely to be
If shock wave is anything below с, something like 0.9c, when we could observer the incoming shockwave, and also, because of t^4 volume rule, the chances that we are in the outer volume of the cone where we could observer the incoming shock wave are larger and are 0.35 for 0.9c.
I think that the shock originators know all this and try to send information signals ahead of physical starships, in what I call SETI-attack.
Yes, I suppose the only way that this would not be an issue is if the aliens are travelling at a very high fraction of the speed of light and inflation means that they will never reach spatially distant parts of the Universe in time for this to be an issue.
In SETI-attack, is the idea that the information signals are disruptive and cause the civilisations they may annihilate to be too disrupted (perhaps by war or devastating technological failures) to defend themselves?
The idea is that aliens purposely send dangerous AI-code aimed on self-replication and transmitting the code farther. There are a lot of technical details how it could happen, which I described in the recently published article, available here: https://philpapers.org/rec/TURTRC
This is a bit unrelated to the original post, but Ted Kaczynski has an interesting hypothesis on the Great Filter, mentioned in Anti-Tech Revolution: Why and How.