<p>The answer is, it <em>could</em> be non-zero (some would argue it must be non-zero), but since we don't know what the probability of life emerging on Earth was, it is impossible to quantify.</p>
<p>This is why this question is normally turned around - if we find life elsewhere in the Solar System (and it is independently developed), then what is the probability that life can emerge given reasonable circumstances?</p>
<p>The occurrence of a second instance <em>would</em> allow us to put a number on the probability. That number would be high enough that, since the Sun is a fairly ordinary star and that Solar System architectures <em>may</em> also be reasonably frequent, life ought to be common throughout the Galaxy.</p>
<p>There won't be any drastic changes in the habitable zone location for the next few billion years - it slowly moves outwards as the Sun's luminosity increases. Perhaps Mars will warm up a bit and become habitable again? If so, there is certainly the time available (still a couple of billion years before the Sun becomes a red giant and Mars gets much hotter) for primitive lifeforms to develop, given that life on Earth seems to have come into existence very soon (less than a few hundred million years) after the conditions became suitable.</p>
<p>The asteroid belt and outer planets? Much less likely. The habitability or not of the Jovian and Saturnian moons is unlikely to be affected by gradual changes in the solar luminosity during the main sequence and the habitable zone remains well inside the orbit of Jupiter.</p>
<p>Once the Sun does become a red giant, then the habitable zone does move outwards maybe as far the Neptunian moons and Kuiper belt (<a href="https://pubmed.ncbi.nlm.nih.gov/14577880/" rel="nofollow noreferrer">Stern 2003</a>). There are plenty of icy bodies with organic materials that might have the raw materials to form life. The difficulty here might be the rapidly changing luminosity of the Sun as it approaches the end of it's life. It will not be stable on timescales of billions of years like it is as a main sequence star. Other authors disagree on the exact location of the habitable zone during this phase, probably because of its exact definition and because of difficulties in modelling the final stages of the Sun (see below). Below is a plot from <a href="https://arxiv.org/abs/1605.04924" rel="nofollow noreferrer">Ramirez &amp; Kaltenegger (2016)</a> showing how the habitable zone (between the solid lines) changes rapidly during the final billion years of the Sun's life. There is a period of about 100 million years when the habitable zone is between 5 and 15 au (i.e. the Jovian moons), and an even briefer period before that when where there could be habitability out to 30 au.</p>
<p><a href="https://i.sstatic.net/6M4MU.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/6M4MU.png" alt="Ramirez and Kaltenegger 2016" /></a></p>
<p>But again, given we don't know exactly how quickly life can develop, although there is an <em>opportunity</em> for life, we can't quantify what the probability is.</p>
<p>Note that all of of the above is uncertain in three ways. First, not everyone agrees on what defines the habitable zone and what temperature range it should encompass. Second, we don't know <em>exactly</em> how the Sun will behave when it becomes a red giant because much depends on the mass-loss rate, for which there is no fundamental theory at present. Third, the behaviour of the atmospheres and albedos of the planetary bodies or moons, which can change, will play an important role. For example, Mars is actually in the habitable zone now, according to simplistic calculations that just use the solar luminosity, and will be for many billions of years. It could <em>just</em> be suitable for life as we find it on Earth (antarctic microbes). On the other hand, if we demand a temperature range of 270K-300K, then Mars may only be habitable for a very <em>brief</em> period in the future (11.6-11.7 billion  years from the birth of the Sun, according to <a href="https://academic.oup.com/astrogeo/article/42/6/6.26/293074" rel="nofollow noreferrer">Schroder et al. 2001</a>) and this may be insufficient time for life to develop.</p>

CC BY-SA 4.0
2021-07-22T07:20:27.580Z
Thanks for your answer. Maybe probability is the wrong term? I don't want to extrapolate any chances from one occurrence (on earth). That would be a bit difficult. I simply want to take the time span and maybe a few factors like temperature into account. So Mars might have been habitable before. Thus it might become habitable again, e.g. ice would melt. But would it be long enough to at least match earths timeframe?
steros
CC BY-SA 4.0
2021-07-22T07:23:00.877Z
@steros well your comment illustrates the difficulties. The Sun was *less* luminous in the past, so Mars was outside the habitable zone. However, Mars was much *more* habitable in the past because it had liquid water, an atmosphere and was warmer. Anyway, I think I have added some detail along the lines you suggest.
ProfRob
CC BY-SA 4.0
2021-07-22T07:24:42.377Z
Okay I see thank you. Maybe it's a bit too "unscientific" for this stack and should move to worldbuilding 
steros
CC BY-SA 4.0
2021-07-22T07:47:16.840Z
@steros Part of it is astrophysics, part of it is planetary science, since the influence of an atmosphere on whether a planet is habitable can be enormous. I've given you the astrophysical bit.
ProfRob
CC BY-SA 4.0
2021-07-22T08:28:41.477Z
@steros, I think that your question is: can life be extinct then NATURALLY restart again when conditions change? Because, there are people believing that hunanity can make Mars habitable (i.e. Terraforming Mars). This is not part of your question, right?
Ng Ph
CC BY-SA 4.0
2021-07-22T23:42:27.207Z
@NgPh No it's not my question. My question is only if the timespan of a planet or other body being in the habitable zone is long enough to make life possible. E.g. a body that already has all elements would maybe take millions of years whereas a body without elements would need much longer due to bombardment of elements needed.
steros
CC BY-SA 4.0
2021-07-22T23:49:20.240Z
@ProfRob Thank you for your update. This is what I was thinking about! :)
steros
CC BY-SA 4.0
2021-07-25T23:47:12.127Z
I removed some off-topic parts. If the edit is accepted, I'll accept this answer. Thanks!
steros
CC BY-SA 4.0
2021-07-26T23:36:12.493Z
@ProfRob it was rejected -_-
Could you edit your answer and remove the first three paragraphs until "There won't be any drastic changes". It's offtopic and not what I was asking about. Thank you!
steros
CC BY-SA 4.0
2021-08-31T16:02:36.183Z
@steros You asked about the "probability" of life forming elsewhere in the Solar System, and the first three paragraphs are essential in establishing that this probability CANNOT be estimated and are therefore essential to answer the question as stated (and please do not now edit your question).
ProfRob
CC BY-SA 4.0
2021-07-22T07:04:11.223Z
2021-07-26T09:27:25.163Z
2021-07-26T09:27:25.163Z
ProfRob
<p>There's nothing wrong with asking a question to which the answer is &quot;nobody knows&quot; -- so long as you are willing to accept that the answer is essentially &quot;nobody knows&quot;.</p>
<p>The only thing we do know is that the probability you are asking about is non-zero because life does exist on the Earth. Some argue that the probability you are asking about is very close to zero. This is the <a href="https://en.wikipedia.org/wiki/Rare_Earth_hypothesis" rel="noreferrer">Rare Earth hypothesis</a> -- the Earth happened to pick the one out of a trillion life lotto ticket.</p>
<p>Others argue that the probability you are asking about is very close to one. This is the basis of the <a href="https://en.wikipedia.org/wiki/Mediocrity_principle" rel="noreferrer">mediocrity principle</a> which implies that life is common; that there's nothing special about the Earth. Astronomers have detected Earth-like exoplanets orbiting in the habitable zone of other stars.</p>
<p>That completely fuzzy range between nearly zero and nearly one is just life as we know it. This falls into the &quot;known unknown&quot; category. What about life as we don't know it? That's an unknown unknown.</p>

CC BY-SA 4.0
2021-07-22T18:56:59.183Z
Non only the 1/trillion lucky lotto ticket (to harbor life). To harbor it long enough so that A form of life starts to ask questions, of which "who organized this lotto?". That's a 1/zillion chance.
Ng Ph
CC BY-SA 4.0
2021-07-22T21:07:28.700Z
@NgPh Strictly speaking, even if we assume the rare Earth hypothesis to be true, that does not tell us anything about the probability of us happening to develop the required level of intelligence to ask questions. For all we know, both the rare Earth hypothesis and the strong anthropic principle are true, we quite simply have insufficient evidence to render a conclusion on either point.
Austin Hemmelgarn
CC BY-SA 4.0
2021-07-22T23:44:13.577Z
Thanks for your answer but I understand my question must be misleading. I am not asking about this kind of aspect. I think it has been discussed a lot and there is a lot material available (which you linked already).
steros
CC BY-SA 4.0
2021-07-22T11:45:30.220Z
2021-07-22T11:45:30.220Z
David Hammen
<p>The answer is nobody knows, but we can structure the ignorance with some rigor.</p>
<p>If you have a planet where life could emerge and observe that it emerged after a certain time <span class="math-container">$t_L$</span> (<span class="math-container">$t_L\approx0.7$</span> Gy), then you can model this as a random event having an unknown rate of occurrence <span class="math-container">$\lambda$</span> per unit of time and calculate a maximum likelihood estimate of <span class="math-container">$\lambda$</span> if you are a frequentist, and a posterior distribution if you are Bayesian.</p>
<p>In the latter case, you use <span class="math-container">$$\Pr[\lambda|\text{no life before } t_L]\propto \Pr[\text{no life before } t_L|\lambda] \Pr[\lambda]$$</span> where <span class="math-container">$\Pr[\lambda]$</span> is the super-tricky to decide prior where we put our assumptions. For a Poisson process and a uniform prior on <span class="math-container">$\lambda$</span> (nontrivial assumption!) <span class="math-container">$$\Pr[\lambda|\text{no life before } t_L] = \Pr[\text{no life before } t_L|\lambda]=(1/\lambda)\exp(-t_L/\lambda).$$</span>  So if you had a bunch of planets that would each become habitable for a period of time <span class="math-container">$T_i$</span> and assuming everything the same, you can now estimate that life might emerge with probability <span class="math-container">$p_i(\lambda)=1-(1/\lambda)\exp(-T_i/\lambda)$</span> and the chance that at least one lifebearing world emerges is <span class="math-container">$1-\prod_{i=1}^N (1-p_i(\lambda))$</span>, giving a distribution depending on <span class="math-container">$\lambda$</span>. Unfortunately, <span class="math-container">$T_i$</span> tends to be short, just hundreds of millions of years at most (and often much less) and <span class="math-container">$N$</span> is small, so the chances are not good.</p>
<p>At this point everybody is shouting about the tower of assumptions going into this calculation. That is fine: we can be explicit about assumptions and analyse them, including extending the model to take them into account. It is still &quot;nobody knows&quot;, but we can characterize our ignorance.</p>
<p>The biggest and likely most important problem is that assuming that <span class="math-container">$t_L$</span> has no restrictions. It is somewhat plausible that after a certain time interval <span class="math-container">$[0,t_X]$</span> life cannot have emerged on Earth since whatever resources were needed could have run out. Another obvious but tricky restriction is that <span class="math-container">$0&lt;t_L&lt;t_{now}$</span>: life <em>must</em> have emerged so that we observers can talk about it! Lifeless and observer-less planets are not going to be sampled. Furthermore, even if life emerges it might be that there are several hard steps one needs to go through to end up with observers. These objections can be dealt with if one builds <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7997718/" rel="nofollow noreferrer">a fairly elaborate Bayesian model</a>, and ends up being pretty pessimistic about at least intelligent life if one uses Earth evolutionary history.</p>
<p>The prior for <span class="math-container">$\lambda$</span> is debatable. It cannot be too large for rapid life formation, or we would see abiogenesis in the lab and presumably life everywhere in the sky. This likely rules out log-uniform priors. There is a tremendous uncertainty about what even the range of plausible values could be.</p>
<p>We could also make an elaborate model where each planet has its own rate, perhaps depending on amount of water, and use this more elaborate two-parameter form above. To be really fancy we could have an abiogenesis model and a panspermia model, where there is a certain rate of cross contamination between worlds that have life. These can be studied using Monte Carlo methods.</p>
<p>But the more parameters you have, the dearth of data (just Earth, and maybe the lack of life at present on some bodies) means you get both very broad probability distributions, and that instead of some peak for some parameters being most likely you end up with ridges or surfaces in parameter space corresponding to plausible scenarios that fit the data. The problem is really underdetermined.</p>

CC BY-SA 4.0
2024-08-28T09:58:44.097Z
2024-08-28T09:58:44.097Z
Anders Sandberg
<p>I'm sorry I am not quite sure this question satisfies this point:</p>
<blockquote>
<p>Questions that are purely hypothetical, for example a question such as 'Could a black hole destroy the universe' or 'What if our solar system had two suns' (however, feel free to visit World Building)</p>
</blockquote>
<p>But actually I am not asking hypothetically.
Given the timespan it took to develop life on earth, I wonder if we can project this to life having already developed once or going to develop again in the solar system.
I'm referring to the fact that during suns lifespan the habitable zone shifts towards other areas.
This won't last only for a few centuries, right? But for millions to billions of years.
Some of the planets and other celestial bodies contain the basic elements to host life (as we know it) already. And then there's stuff floating around in the belts that could bombard those bodies.</p>
<p>E.g. this article claims a study found:</p>
<blockquote>
<p>Researchers studying the crater said investigations by the Mars Science Laboratory have confirmed the presence of an ancient lake that existed in the Gale crater for up to 10 million years, indicating that parts of Mars may once have been habitable for thousands of years.</p>
</blockquote>
<p><a href="https://www.indiatoday.in/science/story/life-on-mars-curiosity-rover-nasa-jpl-1820677-2021-06-29" rel="nofollow noreferrer">https://www.indiatoday.in/science/story/life-on-mars-curiosity-rover-nasa-jpl-1820677-2021-06-29</a></p>
<p>I'm not sure how to go from 10 million years to thousands of years. Thousands of years might not have been enough for substantial life to develop, but millions of years sounds more possible.</p>
<p>Just for reference this video got me to the question:
<div class="youtube-embed"><div>
                <iframe width="640px" height="395px" src="https://www.youtube.com/embed/521omVSc8kM?start=0"></iframe>
            </div></div>
(of course it's just a fun video)</p>

CC BY-SA 4.0
2021-07-22T06:51:35.673Z
This is absolutely "nobody knows" type question.  We only have a single example of life developing, it seemed to do so pretty quickly after liquid water appeared on Earth.  But with only a sample of 1, we can't do much statistical analysis.
James K
CC BY-SA 4.0
2021-07-22T07:01:03.083Z
Hmm, I thought more in the sense of:
- from since habitability was reached to development of first life
- take that span and check if some body will be in the habitable zone for the same amount of time (or longer)
- also consider if some body already has all elements vs. needs outside source
I mean of course no one will know if it will actually develop, aka if just being in the habitable zone is enough.
steros
CC BY-SA 4.0
2021-07-22T22:41:46.997Z
See https://en.wikipedia.org/wiki/Fermi_paradox and https://en.wikipedia.org/wiki/Drake_equation. They apply to the full Galaxy rather than just the Solar System, but the underlying questions are very similar, especially the difficulty in the estimates and the very very wide range of both inputs and results. See also https://en.wikipedia.org/wiki/Rare_Earth_hypothesis.
jcaron
CC BY-SA 4.0
2021-07-22T23:50:28.427Z
@jcaron Thanks for the comment, but actually I was thinking a different direction. ProfRob updated his answer and now it's much close to what I had in mind.
steros
CC BY-SA 4.0
2024-08-26T20:54:16.077Z
Why do you assume life can only arise on the surfaces of planets?  Large liquid water oceans are now known to exist in the interiors of moons and asteroids. Heated by internal heat, they would have hot vents on their bottoms releasing extra energy and nutrients.
eshaya
<the-sun><planet><solar-system><life><astrobiology>
What is the probability of life having developed or going to develop in our solar system another time?
steros
# What is the probability of life having developed or going to develop in our solar system another time?

(Asked by: username_0 on 2021-07-22)

I'm sorry I am not quite sure this question satisfies this point:

> Questions that are purely hypothetical, for example a question such as 'Could a black hole destroy the universe' or 'What if our solar system had two suns' (however, feel free to visit World Building)

But actually I am not asking hypothetically.
Given the timespan it took to develop life on earth, I wonder if we can project this to life having already developed once or going to develop again in the solar system.
I'm referring to the fact that during suns lifespan the habitable zone shifts towards other areas.
This won't last only for a few centuries, right? But for millions to billions of years.
Some of the planets and other celestial bodies contain the basic elements to host life (as we know it) already. And then there's stuff floating around in the belts that could bombard those bodies.

E.g. this article claims a study found:

> Researchers studying the crater said investigations by the Mars Science Laboratory have confirmed the presence of an ancient lake that existed in the Gale crater for up to 10 million years, indicating that parts of Mars may once have been habitable for thousands of years.

<https://www.indiatoday.in/science/story/life-on-mars-curiosity-rover-nasa-jpl-1820677-2021-06-29>

I'm not sure how to go from 10 million years to thousands of years. Thousands of years might not have been enough for substantial life to develop, but millions of years sounds more possible.

Just for reference this video got me to the question:(of course it's just a fun video)

**Tags:** the-sun, planet, solar-system, life, astrobiology
> **Comments:**
> **username_1**: This is absolutely "nobody knows" type question.  We only have a single example of life developing, it seemed to do so pretty quickly after liquid water appeared on Earth.  But with only a sample of 1, we can't do much statistical analysis.  
> **username_0**: Hmm, I thought more in the sense of: - from since habitability was reached to development of first life - take that span and check if some body will be in the habitable zone for the same amount of time (or longer) - also consider if some body already has all elements vs. needs outside source I mean of course no one will know if it will actually develop, aka if just being in the habitable zone is enough.  
> **username_2**: See https://en.wikipedia.org/wiki/Fermi_paradox and https://en.wikipedia.org/wiki/Drake_equation. They apply to the full Galaxy rather than just the Solar System, but the underlying questions are very similar, especially the difficulty in the estimates and the very very wide range of both inputs and results. See also https://en.wikipedia.org/wiki/Rare_Earth_hypothesis.  
> **username_0**: @jcaron Thanks for the comment, but actually I was thinking a different direction. ProfRob updated his answer and now it's much close to what I had in mind.  
> **username_3**: Why do you assume life can only arise on the surfaces of planets?  Large liquid water oceans are now known to exist in the interiors of moons and asteroids. Heated by internal heat, they would have hot vents on their bottoms releasing extra energy and nutrients.  

---

## 3 answers

### Answer by username_4 on 2021-07-22. Score: 17

The answer is, it *could* be non-zero (some would argue it must be non-zero), but since we don't know what the probability of life emerging on Earth was, it is impossible to quantify.

This is why this question is normally turned around - if we find life elsewhere in the Solar System (and it is independently developed), then what is the probability that life can emerge given reasonable circumstances?

The occurrence of a second instance *would* allow us to put a number on the probability. That number would be high enough that, since the Sun is a fairly ordinary star and that Solar System architectures *may* also be reasonably frequent, life ought to be common throughout the Galaxy.

There won't be any drastic changes in the habitable zone location for the next few billion years - it slowly moves outwards as the Sun's luminosity increases. Perhaps Mars will warm up a bit and become habitable again? If so, there is certainly the time available (still a couple of billion years before the Sun becomes a red giant and Mars gets much hotter) for primitive lifeforms to develop, given that life on Earth seems to have come into existence very soon (less than a few hundred million years) after the conditions became suitable.

The asteroid belt and outer planets? Much less likely. The habitability or not of the Jovian and Saturnian moons is unlikely to be affected by gradual changes in the solar luminosity during the main sequence and the habitable zone remains well inside the orbit of Jupiter.

Once the Sun does become a red giant, then the habitable zone does move outwards maybe as far the Neptunian moons and Kuiper belt ([Stern 2003](https://pubmed.ncbi.nlm.nih.gov/14577880/)). There are plenty of icy bodies with organic materials that might have the raw materials to form life. The difficulty here might be the rapidly changing luminosity of the Sun as it approaches the end of it's life. It will not be stable on timescales of billions of years like it is as a main sequence star. Other authors disagree on the exact location of the habitable zone during this phase, probably because of its exact definition and because of difficulties in modelling the final stages of the Sun (see below). Below is a plot from [Ramirez & Kaltenegger (2016)](https://arxiv.org/abs/1605.04924) showing how the habitable zone (between the solid lines) changes rapidly during the final billion years of the Sun's life. There is a period of about 100 million years when the habitable zone is between 5 and 15 au (i.e. the Jovian moons), and an even briefer period before that when where there could be habitability out to 30 au.

[![Ramirez and Kaltenegger 2016](https://i.sstatic.net/6M4MU.png)](https://i.sstatic.net/6M4MU.png)

But again, given we don't know exactly how quickly life can develop, although there is an *opportunity* for life, we can't quantify what the probability is.

Note that all of of the above is uncertain in three ways. First, not everyone agrees on what defines the habitable zone and what temperature range it should encompass. Second, we don't know *exactly* how the Sun will behave when it becomes a red giant because much depends on the mass-loss rate, for which there is no fundamental theory at present. Third, the behaviour of the atmospheres and albedos of the planetary bodies or moons, which can change, will play an important role. For example, Mars is actually in the habitable zone now, according to simplistic calculations that just use the solar luminosity, and will be for many billions of years. It could *just* be suitable for life as we find it on Earth (antarctic microbes). On the other hand, if we demand a temperature range of 270K-300K, then Mars may only be habitable for a very *brief* period in the future (11.6-11.7 billion years from the birth of the Sun, according to [Schroder et al. 2001](https://academic.oup.com/astrogeo/article/42/6/6.26/293074)) and this may be insufficient time for life to develop.

> **Comments:**
> **username_0**: Thanks for your answer. Maybe probability is the wrong term? I don't want to extrapolate any chances from one occurrence (on earth). That would be a bit difficult. I simply want to take the time span and maybe a few factors like temperature into account. So Mars might have been habitable before. Thus it might become habitable again, e.g. ice would melt. But would it be long enough to at least match earths timeframe?  
> **username_4**: @steros well your comment illustrates the difficulties. The Sun was *less* luminous in the past, so Mars was outside the habitable zone. However, Mars was much *more* habitable in the past because it had liquid water, an atmosphere and was warmer. Anyway, I think I have added some detail along the lines you suggest.  
> **username_0**: Okay I see thank you. Maybe it's a bit too "unscientific" for this stack and should move to worldbuilding   
> **username_4**: @steros Part of it is astrophysics, part of it is planetary science, since the influence of an atmosphere on whether a planet is habitable can be enormous. I've given you the astrophysical bit.  
> **username_5**: @steros, I think that your question is: can life be extinct then NATURALLY restart again when conditions change? Because, there are people believing that hunanity can make Mars habitable (i.e. Terraforming Mars). This is not part of your question, right?  
> **username_0**: @NgPh No it's not my question. My question is only if the timespan of a planet or other body being in the habitable zone is long enough to make life possible. E.g. a body that already has all elements would maybe take millions of years whereas a body without elements would need much longer due to bombardment of elements needed.  
> **username_0**: @ProfRob Thank you for your update. This is what I was thinking about! :)  
> **username_0**: I removed some off-topic parts. If the edit is accepted, I'll accept this answer. Thanks!  
> **username_0**: @ProfRob it was rejected -_- Could you edit your answer and remove the first three paragraphs until "There won't be any drastic changes". It's offtopic and not what I was asking about. Thank you!  
> **username_4**: @steros You asked about the "probability" of life forming elsewhere in the Solar System, and the first three paragraphs are essential in establishing that this probability CANNOT be estimated and are therefore essential to answer the question as stated (and please do not now edit your question).  

---

### Answer by username_6 on 2021-07-22. Score: 6

There's nothing wrong with asking a question to which the answer is "nobody knows" -- so long as you are willing to accept that the answer is essentially "nobody knows".

The only thing we do know is that the probability you are asking about is non-zero because life does exist on the Earth. Some argue that the probability you are asking about is very close to zero. This is the [Rare Earth hypothesis](https://en.wikipedia.org/wiki/Rare_Earth_hypothesis) -- the Earth happened to pick the one out of a trillion life lotto ticket.

Others argue that the probability you are asking about is very close to one. This is the basis of the [mediocrity principle](https://en.wikipedia.org/wiki/Mediocrity_principle) which implies that life is common; that there's nothing special about the Earth. Astronomers have detected Earth-like exoplanets orbiting in the habitable zone of other stars.

That completely fuzzy range between nearly zero and nearly one is just life as we know it. This falls into the "known unknown" category. What about life as we don't know it? That's an unknown unknown.

> **Comments:**
> **username_5**: Non only the 1/trillion lucky lotto ticket (to harbor life). To harbor it long enough so that A form of life starts to ask questions, of which "who organized this lotto?". That's a 1/zillion chance.  
> **username_7**: @NgPh Strictly speaking, even if we assume the rare Earth hypothesis to be true, that does not tell us anything about the probability of us happening to develop the required level of intelligence to ask questions. For all we know, both the rare Earth hypothesis and the strong anthropic principle are true, we quite simply have insufficient evidence to render a conclusion on either point.  
> **username_0**: Thanks for your answer but I understand my question must be misleading. I am not asking about this kind of aspect. I think it has been discussed a lot and there is a lot material available (which you linked already).  

---

### Answer by username_8 on 2024-08-28. Score: 1

The answer is nobody knows, but we can structure the ignorance with some rigor.

If you have a planet where life could emerge and observe that it emerged after a certain time $t\_L$ ($t\_L\approx0.7$ Gy), then you can model this as a random event having an unknown rate of occurrence $\lambda$ per unit of time and calculate a maximum likelihood estimate of $\lambda$ if you are a frequentist, and a posterior distribution if you are Bayesian.

In the latter case, you use $$\Pr[\lambda|\text{no life before } t\_L]\propto \Pr[\text{no life before } t\_L|\lambda] \Pr[\lambda]$$ where $\Pr[\lambda]$ is the super-tricky to decide prior where we put our assumptions. For a Poisson process and a uniform prior on $\lambda$ (nontrivial assumption!) $$\Pr[\lambda|\text{no life before } t\_L] = \Pr[\text{no life before } t\_L|\lambda]=(1/\lambda)\exp(-t\_L/\lambda).$$ So if you had a bunch of planets that would each become habitable for a period of time $T\_i$ and assuming everything the same, you can now estimate that life might emerge with probability $p\_i(\lambda)=1-(1/\lambda)\exp(-T\_i/\lambda)$ and the chance that at least one lifebearing world emerges is $1-\prod\_{i=1}^N (1-p\_i(\lambda))$, giving a distribution depending on $\lambda$. Unfortunately, $T\_i$ tends to be short, just hundreds of millions of years at most (and often much less) and $N$ is small, so the chances are not good.

At this point everybody is shouting about the tower of assumptions going into this calculation. That is fine: we can be explicit about assumptions and analyse them, including extending the model to take them into account. It is still "nobody knows", but we can characterize our ignorance.

The biggest and likely most important problem is that assuming that $t\_L$ has no restrictions. It is somewhat plausible that after a certain time interval $[0,t\_X]$ life cannot have emerged on Earth since whatever resources were needed could have run out. Another obvious but tricky restriction is that $0: life *must* have emerged so that we observers can talk about it! Lifeless and observer-less planets are not going to be sampled. Furthermore, even if life emerges it might be that there are several hard steps one needs to go through to end up with observers. These objections can be dealt with if one builds [a fairly elaborate Bayesian model](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7997718/), and ends up being pretty pessimistic about at least intelligent life if one uses Earth evolutionary history.

The prior for $\lambda$ is debatable. It cannot be too large for rapid life formation, or we would see abiogenesis in the lab and presumably life everywhere in the sky. This likely rules out log-uniform priors. There is a tremendous uncertainty about what even the range of plausible values could be.

We could also make an elaborate model where each planet has its own rate, perhaps depending on amount of water, and use this more elaborate two-parameter form above. To be really fancy we could have an abiogenesis model and a panspermia model, where there is a certain rate of cross contamination between worlds that have life. These can be studied using Monte Carlo methods.

But the more parameters you have, the dearth of data (just Earth, and maybe the lack of life at present on some bodies) means you get both very broad probability distributions, and that instead of some peak for some parameters being most likely you end up with ridges or surfaces in parameter space corresponding to plausible scenarios that fit the data. The problem is really underdetermined.


---

