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The SETI project analyzes signals and looks for patterns, some of which include prime number sequences that have an absurdly low improbability of occurring. It does this to detect intelligent life.

However, we have no independent evidence of life outside earth. Life occurring on earth does not imply life elsewhere especially since we don’t understand how life originated.

But even if we could say life could possibly exist elsewhere, we have no knowledge by which to assume very complex life forms can evolve elsewhere, much less have the capability to send radio signals down to earth. On what basis can we ever say, even if this pattern was detected, that this was generated by intelligent lifeforms outside earth?

Even if the probability of the pattern occurring was 1/2^100, one would have to justify a higher probability of intelligent lifeforms outside earth being able to create signals existing. There is nothing indicating this.

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Scientists use statistical significance measures all the time, discussed here: How improbable does an event have to be before we can say it didn't happen by chance?

"Life occurring on earth does not imply life elsewhere especially since we don’t understand how life originated."

On the contrary, life here indicates life elsewhere is possible. And it beginning within 0.5b years of the Earth's surface solidifying, possibly with 0.2b years, implies a reasonably high likelihood of life beginning in a similar situation, though with low confidence statistically.

Why do scientists do what they do? Because they are curious, and pursuaded someone to fund them. SETI succeeded on both grounds, so the more pertinent question is, 'Why shouldn't SETI happen?', but you don't seem to be complaining that something else should get the funding. And, you seem unaware that failing to find life is data too.

People generally don't realise what a minimal amount of searching SETI projects have been able to do, and this relates to the fact they have been funded, but not very well. It has involved scanning a particular band of radiofrequencies that don't get absorbed by interstellar gases. That would have to be a strong signal intentionally sent out to the cosmos, intended to communicate with new species; and for most of the cosmos it would have to be quite an old signal. It's also likely use of radio waves will be limited to a tiny window of time in human development, judged by geological epochs. There may be far more suitable media yet to be discovered, like say involving dark-matter, which would make radio redundant.

Planet-hunting has allowed the hunting for Earth-like planets and stellar systems, which could allow much more targetted scrutiny. And will allow some indications of atmospheric gases, especially teactive ones that indicate life like oxygen and phosphine. Currently, we are limited by our telescopes to higher mass planets, and most stars are noisier than our Sun. The neccessary observations typically involve stellar dimming of a few percent once every decade or when the planet is in near-conjuction to the star towards us, which requires new wide-field and patient telescopes, which are being developed. Working out how special our solar system is, is also useful data for modelling how likely abiogenesis was here.

With sustained intention, it would likely be possible to use current human technology to colonise another star system, with small probes capable of self-replication, accelerated to high speed from Earth, and sent in high enough numbers to overwhelm losses. Because of this, we think life getting to a similar stage to Earth and continuing to thrive, seems to be rare, because it would rapidly get everywhere, and lead to astro-engineering like habitat-rings. So it's reasonable to think there may be a Great Filter, which has prevented other cosmic ecologies reaching such a breakout phase. Narrowing the parameters on that, working out if we have already passed it (eg abiogenesis, formation of cell nucleus, formation of multi-celled life, or a very fine balance between environmental catastrophes and stability) or not is arguably one of the most important things to know (eg globally-connected life might be deeply insrable like suggested in this paper: Asymptotic burnout and homeostatic awakening: a possible solution to the Fermi paradox.

Plus, finding aliens, or finding evidence we live in a Dark Forest scenario, could be the most important results ever discovered by science, for our planet's future. These results may be unlikely, our finding the information about them may be far even less likely. But it definitely merits some measure of human effort to investigate them, probably more than they currently have alloted.

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    – V2Blast
    Jul 14, 2023 at 0:23
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Let's focus on this part of the question: "On what basis can we ever say, even if this pattern was detected, that this was generated by intelligent lifeforms outside earth?"

Bayesian inference framework

One common approach is to apply Bayesian inference as a method to compute a new hypothesis credence (posterior probability) from an old credence (prior probability), a new observation, and the compatibility of the evidence with the hypothesis. So let's do that to the radio SETI problem.

Bayes' theorem is frequently written:

         P(E|H) P(H)
P(H|E) = -----------
             P(E)

where:

  • H is the hypothesis of interest, in this case, that extra-terrestrial technological civilizations currently exist nearby, or existed in the past at the proper distance for their signal to reach us now.

  • E is the evidence, in this case the detection of a radio signal with a particular structure, originating from outside our solar system.

  • P(H|E), the "probability of H given E", is the updated probability (credence) that H is true, given we have detected E, and is what we want to compute.

  • P(E|H) is the probability that E happens if we assume H is true. We'll have to make an assumption here, so I'll explore multiple possible values.

  • P(H) is the credence we assign H before detecting E. This also requires an assumption.

  • P(E) is the probability of detecting E, independent of H.

Let's first deal with P(E). Typically when making scientific measurements, we don't estimate P(E), but instead P(E|¬H), i.e., the probability of observing E assuming that H is false. We can then compute P(E) by breaking it down into the two cases depending on whether H is true or false:

P(E) = P(E|H) P(H) + P(E|¬H) P(¬H)

and:

P(¬H) = 1 - P(H)

What value should we use for P(E|¬H)? In physics, it is common to use a "five sigma" detection threshold, meaning that the probability that E would be detected if H were false (that is, due to random chance) is less than 0.00006%. Astronomers often use three sigma, but for a discovery of this importance, the more rigorous threshold is appropriate, so I will use 0.00006% as my baseline. You've contemplated 2^-100 so I'll consider that too.

What about P(E|H)? That is, assuming there is currently at least one extra-terrestrial technological civilization (ETTC), what is the probability that we would detect a structured signal from it? There doesn't seem to be a good way to estimate this since it depends on so many unknowns, so I'll consider a range of values, with a somewhat arbitrary 1% as the baseline.

Finally, what about P(H)? That is, prior to any detection, what should we assume is the probability that there is at least one ETTC? This is the subject of the Drake equation, but in practice that doesn't help much. Again, I'll consider a range of values, again using 1% as a baseline.

Baseline calculation

With baseline assumptions, we find that a five sigma detection leads to over 99% updated credence despite only 1% prior credences:

P(H|E) = P(E|H) * P(H) / P(E)
       = P(E|H) * P(H) / ( P(E|H) * P(H) + P(E|¬H)   * P(¬H)      )
       = P(E|H) * P(H) / ( P(E|H) * P(H) + P(E|¬H)   * (1 - P(H)) )
       = 0.01   * 0.01 / ( 0.01   * 0.01 + 0.0000006 * (1 - 0.01) )
       = 0.0001        / ( 0.0001        + 0.0000006 * 0.99       )
       = 0.0001        / ( 0.0001        + 0.000000594            )
       = 0.0001        / (                 0.000100594            )
       = 0.994

Moreover, we can see from the structure of this calculation that the result is primarily determined by how P(E|H)P(H) (the product of our priors) compares to P(E|¬H) (the probability of detection under the null hypothesis).

More skeptical priors

With five sigma detection, how low do our priors have to be to significantly degrade the final credence? Let's try a few values:

P(E|H)  P(H)    P(H|E)
------  ------  ------
0.01    0.01    0.994       baseline
0.001   0.001   0.625       more skeptical
0.0001  0.0001  0.016       initially highly skeptical, first detection
0.0001  0.016   0.730       initially highly skeptical, second detection
0.0001  0.730   0.998       initially highly skeptical, third detection

So, if you think there's only a 0.01% chance an ETTC exists, and a 0.01% chance that we would detect one if it did exist, then even with a five sigma signal detection, your updated credence that an ETTC exists is only 2%. But then, further detections, if they occur, would quickly push the credence to near certainty.

Extreme detection

What if P(E|¬H), the probability of observing the evidence due to random chance, is very low, say, 2^-100 = 7.89e-31? Let's try it:

P(E|¬H)     P(E|H)  P(H)    P(H|E)
----------  ------  ------  ------
0.0000006   0.0001  0.0001  0.016       highly skeptical from above
7.89e-31    0.0001  0.0001  1.000       P(E|¬H) = 2^-100
7.89e-31    1e-10   1e-10   1.000       absurdly skeptical
7.89e-31    1e-15   1e-15   0.559       ... and then some

We find that, if the chance of the detected signal occurring by chance is 2^-100, then we'd need the product of our priors to be comparable to that value to have any posterior doubt, which requires at least one to be, in my opinion, unjustifiably small.

Conclusion

Bayesian inference provides one possible answer to how a rational agent should update its credences in light of new evidence. Applying it to the problem of a potential detection of extra-terrestrial technology, we see that when using reasonably but not excessively skeptical prior credences (1% each), a five sigma signal detection ought to be regarded as very convincing, and that with either repeated detection or a signal with greater structure, even extreme skeptics ought to be persuaded.

But, I can't tell you your priors! Every rational agent arrives at the inference problem with their own, and for any given detection and accompanying probability of occurrence by chance, there are priors that make that (single) detection unpersuasive.

Addendum: Regarding selection of priors, see follow-up question: Can a zero prior probability for some theories be justified?

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    Not being able to tell the priors is unfortunately key and without it, the inference framework doesn’t seem useful. If lifeforms outside earth do not exist, or if they do but aren’t capable of generating radio signals, then no pattern, regardless of the probability, will justify believing in them. If they do exist, then of course, it is reasonable to conclude that they may have played a role in a pattern. Note that a very low likelihood doesn’t make P(H) higher. So even an absurdly improbable pattern doesn’t increase the prior. They seem independent. Jul 10, 2023 at 7:35
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    Note that if one does assign a non zero prior, it would be due to practical reasons. This is different from assigning a non zero prior to aliens causing things due to evidence, such as atleast observing one instance of an alien causing things directly. Jul 10, 2023 at 7:47
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    Indeed the framework does not tell you what priors to use, although I do not agree that makes it useless. I see you've asked a good follow-up question regarding zero priors, so I've added a link to it. Jul 10, 2023 at 16:57
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A major false premise, considering how surely almost everyone thinks of it due to news and movies, is the detection capability of radio SETI. It would have an extremely difficult time detecting us from any star if the roles were reversed. So no - the aliens aren't watching Hitler at the Olympics or I Love Lucy or even Ally McBeal.

I'm not going to try digging up numbers but consider the Sun is emitting radio waves too now factor in the signal intensity dropping by the inverse square law.

Quoting from an answer here by ProfRob - which quotes some relevant papers https://physics.stackexchange.com/questions/245505/from-how-far-away-could-earths-telescopes-detect-earth-like-radio-signals

The SETI Phoenix project was the most advanced search for radio signals from other intelligent life. Quoting from Cullers et al. (2000): "Typical signals, as opposed to our strongest signals fall below the detection threshold of most surveys, even if the signal were to originate from the nearest star". Quoting from Tarter (2001): "At current levels of sensitivity, targeted microwave searches could detect the equivalent power of strong TV transmitters at a distance of 1 light year (within which there are no other stars)...".

Cullers et al. (2000): https://adsabs.harvard.edu/full/2000ASPC..213..451C

Tarter (2001) https://ui.adsabs.harvard.edu/abs/2001ARA%26A..39..511T/abstracts

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  • "the detection capability of radio SETI. It would have an extremely difficult time detecting us from any star. So no the aliens aren't watching Hitler " Aliens are using radio wave detection? Are you implying it's impossible for aliens to detect Earth comms? I feel like this phrasing could be clearer.
    – CriglCragl
    Jul 10, 2023 at 11:23
  • @CriglCragl I added a line about if the roles were reversed. But yes the point is we are basically not detectable. So we shouldn't expect to be able to detect aliens. Alien SETI as portrayed in Contact for example likely can't pick up the radio signals of our civilization. Jul 10, 2023 at 16:06
  • We do occasionally beam signals at nearly planet systems just in case someone is listening.
    – user253751
    Jul 11, 2023 at 13:50
  • Re " ... targeted microwave searches could detect the equivalent power of strong TV transmitters at a distance of 1 light year ..." --> That indicates that an order of magniture increase in sensitivity would allow detection at Alph Centauri. If Aliens exist them an increase in technical capability of several orders of magnitude is entirely likely, and an increase of a ginormous magnitude is not inconceivable. || Also, Aliends who wish to dvertise their presence, which may be unwise for them, or a honeypot trap for us, may be able to "transmit" at Pulsar level. ... Jul 11, 2023 at 14:00
  • The first known Pulsar PSR B1919+21 discovered in 1967 was (allegedly) jokingly named LGM-1 for a reason. || " ... The discoverers jokingly named it little green men 1 (LGM-1), considering that it may have originated from an extraterrestrial civilization, but Bell Burnell soon ruled out extraterrestrial life as a source after discovering a similar signal from another part of the sky..." Jul 11, 2023 at 14:05
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"However, we have no independent evidence of life outside earth."  Of course not.  That’s why SETI is looking for it.

To me, the flaw in SETI is tunnel vision.  If intelligence evolved somewhere too far away to be influenced by earth, wouldn't it seem highly likely that it would be so different from us that the "patterns" it might send out would be ones that wouldn't occur to us?  But, looking for those patterns is better than not looking for any.

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