So I've revisited the carter catastrophe using the mediocrity principle and also looked at a possible extinction event with relevance to us (competition from an equally intelligent competitor species).
Life has existed for approximately 3.5 billion years and the sun has existed for approximately 4.5 billion years.
Since we have no evidence of life other than our own and our sun has existed for only 4.5 billion years then by the principle of mediocrity we have to say that every newborn star in the galaxy that fits the category of our sun (i.e. G class stars) will develop life after 1 billion years and life will continue once it has gotten started in spite of extinction events and that there shall be at least five extinction events during the 3.5 billion years of life.
What can we say about the species existing? Well nothing much during the entire period because we don't have the data but we can say that right now we have about 10 million species right now and approximately 1 in 100,000 species are what can be classified as "living fossils" or in other words species that have survived a significant percentage of the time that animal life has existed. Some of these living fossils have been around for 450 million years and it's therefore arguable that they have been around since the beginning of vertebrate life. Thus we can say that some species have existed unchanged and have not gone extinct in the entire period that animal life has been around and have passed through 5 major extinction events. That said since we have no examples of living fossils longer than the period of animal life (500 million years) we cannot argue that they last any longer than 500 million years. We have to say that's the top line.
If we accept the principle of mediocrity for species we can therefore say that 0.001 percent of all species will be long lived during the 4.5 billion years after a star forms. According to the principle of mediocrity we also have to say that 1 in 100,000 of all *intelligent* species will be long lived. Intelligent species are us. Only one species. 1 in 10 million. So one in 100,000 x 10 million intelligent species should therefore last 500 million years and the rest will last the normal period of time at the most which is 2 million years for a species.
Now 100,000 x 10 million makes 100,000,000,000 is 100 billion. Which gives us an answer that there are *no* long lived intelligent species in our galaxy and in fact there is only 1 long lived species in 100 galaxies. But let's ignore that inconvenient fact for now.
Since we have no evidence of any intelligent species that last 500 million years unless it is us (and we're not there yet) then we have to leave the putative long lived species out of the picture. Even though right there we have resolved the fermi paradox.
Now the interesting thing is this: intelligence clearly isn't normal because it's only 1 in 10 million species. So can we apply the principle of mediocrity to it? Hard to say, but let's say that we can at least with regards to *other* potential intelligent signal transmitting species.
We need big brains, hands, and communication in order to generate human like intelligence (i.e. a species that can send signals. We have to exclude the possibility that stellar travel is possible because we haven't done it but since we have sent signals then by the principle of mediocrity so can other intelligent species like ourselves). How common are the conditions that lead to the development of intelligence? Big brains obviously, but that's not all. Whales, Elephants and Dolphins all have big brains and though it can be argued that they communicate, that's not enough. We need coordinated communication, big brains and tool making. Tool making requires hands. There are several species with hands but only us with big brains.
Coordinated communication exists in wolf packs and other pack animals. Coordinated communication also exists in herds of prey animals. So we can argue that the three things that together can lead to an intelligent species that can make tools are fairly common. We can likewise argue that the thing required to kickstart civilization in addition to tool making, coordinated communication and big brains is agriculture. There are several species that do this such as ants among others and if you broaden the definition to symbiosis there are many many species. So the conditions for the development of agriculture by tool making, big brained coordinated communication intelligent creatures are common. It just takes a long time. Not till the last 10,000 years. We can also say that it's only during the last 100 years of a 4.5 billion period since a new star formed that a species can send a signal. We can also say that it can't possibly have happened in the *first* 4.5 billion year period of the universe since all stars in that period were only type I stars (i.e. no heavy elements surrounding them) and we have to wait until type II stars are formed. So that cuts out the possibility of a long lived species appearing in the first part of the history of the universe. Now the first type II stars formed around 9 billion years ago so that means that in our galactic space we ought to have had at least two intelligent species that lasted 500 million years within the sphere of the nearest 200 galaxies. But we're talking GALAXIES!!! It's one thing to meet the ridiculous challenge of interstellar colonization and quite another to meet the challenge of intergalactic. Never mind that we have to assume that the two putative civilizations *stayed civilized* during the entire period *and* coincided with us. Likely? I think not.
But lets get back to signals from our putative signalling civilization.
What we can't say is whether such a signal will be received or indeed whether it can even be understood over stellar distances because although we have been sending signals for some 100 years via radio waves we haven't in fact received anything, so it may in fact be impossible to receive signals stellar distances via our level of technology.
But we can't say anything about that because we have no evidence so instead looking at the evidence (i.e. we can SEND signals and nothing about whether they can be received) let's ask the question how many species can send signals?
About 1 in 13 stars in the Galaxy are G Class stars which are the same type of star as the sun.
Since the principle of mediocrity demands that we aren't special we have to say therefore that all G type stars in the galaxy have life and the capacity to generate intelligent species.
That is to say there are 100 billion stars in the galaxy approximately 7 billion of which are G class. If G class stars are evenly distributed then since the average distance between stars is about 5 light years then that means the average distance between civilizations like ours ought to be 5x13 = 65 light years.
In our sphere shaped region of space we will have thousands of stars capable of signalling us at
the current time if the principle of mediocrity is true. So either we're not listening or
we can't hear or there are no signals.
But... the ingredients for life seem to be pretty common all throughout the universe so that's
probably not it. And if life gets started we have to assume that it will eventually lead
to something like us, so something else must be happening...
If we argue that over the last million years there has been at least one other contender intelligent species but only we discovered agriculture then that pushes the light cone out to 130 light years. There we have one possible explanation for why we haven't received any signals yet if they are understandable or receivable over stellar distances: the signal hasn't reached us yet.
So that's fairly straightforward. We're going to receive signals sometime in the next 50 years if we're not unique and we are capable of receiving or understanding the signal at our current level of technology.
So now let's look and see if we can determine how long we're going to last.
We can conjecture that we have about a 1 in 100,000 chance of surviving 500 million years
and 99,999 chance of surviving less than that. Australopithecines lasted about 2 million years
so we can argue that we have an evens chance of lasting 2 million years. Homo Sapiens has been
around for about 200,000 years and neanderthals also lasted about 200,000 years.
So we can say we have close to evens chance of lasting 200,000.
So our time could be up about now or else we have about a 49% chance of lasting another 1.8 million years and about a 1 in 100,000,000,000 chance of surviving 500 million years.
So most species around us last somewhere from 200,000 to 2 million years and hardly anyone lasts 500 million years. We have to rule out the possibility that any species lasts 4.5 billion years which are our time chunks for the formation of intelligent species from single celled life beginning to end.
So which is it? How long do *we* last.
Unfortunately we can't know without receiving any more signals. If we don't receive *any* signals within the next 65 years that would indicate that civilizations that are capable of signalling other civilizations are rarer than can be predicted just from obverving us which in turn says that we are missing something in our predictions from the principle of mediocrity. On the other hand, if we receive signals from *all* of the predicted civilizations then we can fairly confidently say that in a sphere of space containig 100,000,000,000 civilizations, one of them will be composed of a species that will last for 500 million years. It doesn't, however, say that during that 500 milllion years it will maintain the ability to signal for that entire length of time, just that there should be one long lived species.
It's also interesting to note that dinosaur killer events take place approximately 700 million years so it's quite possible that a long lived species will be born, life it's life and then die out in between those large extinction events, so large extinction events might not be what put an end to it.
In the case of the short lived species (200,000 to 2 million years) it's even less likely that
a dinosaur killer event would put an end to them because they simply don't happen often enough
and if there are lots in a volume of space then the small chance of an extinction event taking
place during the 2 million years for all of them is vanishingly small.
What *can* we say?
Well during the last 200,000 years there were at least two and potentially up to five competing
intelligent species in the same spot and only one of us survived so we can say that in a 200,000
year space an intelligent species has about a 50% to an 80% chance of being outcompeted by another intelligent species and about a 50% to a 20% chance of surving the competition.
Since we can rule out extinction events such as dinosaur killers doing us in and we can rule out visitation by star faring aliens we have to assume that it's competition from another intelligent species right here on Earth. We do in fact have a candidate: sufficiently intelligent machines. So let's look at that.
If we then take the roughly 49.999999% chance of being wiped out right now multiplied by 20-50%
we have thus about 10-25% chance of surving competition by another species plus 49.999999% of surviving at least 1.8 million years and some small fraction of surving 500 million years then it's at worst about a 40 per cent chance of extinction with a 60% survival likelihood and at best 75% of surving *if* we are the better fitted to the conditions.
Now that's where it gets interesting.
Since the only example we have is of a fitter species outcompeting less fit species, what's so
special about us? Are we more violent, more cooperative, simply better at acquiring resources or what?
In fact in the case of the neanderthals and the denisovans they have left 6% of their DNA in us and somewhat around 10% in total including
other species. So statistically if it's us that get outcompeted it looks like we don't get wiped out, we get absorbed.
Since what we're most likely to be facing in the near future in terms of competition is that from our machines and
more specifically competition from intelligent machines we can argue that if we are to go extinct we probably will hold out for quite
some time and eventually get absorbed by our machines which will be somewhat like us and have some
of us in them and thus we can probably safely rule out an extinction event predicated by an unfriendly AI
in a hard takeoff scenario, though we cannot rule out partial extinction by machines.
So somewhere between 40% likely we will be absorbed by machines and 60% likely we will still be
recognizably human in 1.8 million years with a vanishingly small chance that we will be recognizably human in 500 million years.
Interestingly, we're going to have to become significantly more intelligent to defeat machine intelligences or else our machine intelligences will be incapable of becoming much more intelligent than us and we outcompete them in some other way but in either case it's likely that our ability to process data will increase significantly. What's interesting about that is it could answer the question of whether we are capable of understanding or receiving messages transmitted over stellar distances but we just don't have the technologies.
In any case, as far as I'm concerned the fermi paradox is resolved. Putative signalling civilizations are too far apart, there's no proof we are even capable of hearing their signal, they won't coincide with us in time *and* there might be a "great filter" which wipes them out.