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Not sure if this is the correct site on Stack Exchange to ask this, please let me know if there is a better one.

If civilizations were distributed fairly evenly in the habitable region of the galaxy, how many civilizations would there have to be for us to be able to detect at least one, assuming all civilizations had approximately the same level of science as us. (i.e. How many of "us" would there need to be for us to be able to detect one of "us")

There are some assumptions that I'm making that may be incorrect:

  • The habitable region of the galaxy is not the entire galaxy. I believe the center of the galaxy is deemed to be uninhabitable due to the levels of radiation, but I'm unaware of other regions are considered uninhabitable, or how large this region is.
  • It's generally only possible to detect another civilization from their broadcast emissions, which would probably limit detection range to somewhere around 50 LY or less.
Tibrogargan
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  • This list contains 971 known stars with a distance less than 50 lightyears. – Uwe Jul 15 '18 at 22:15
  • The center of the galaxy is not radiated by anything. The stars are far closer to eachother, it might decrease the number of the planets on a stable, near-circular orbit, that is all. – peterh Jul 16 '18 at 01:27
  • @peterh While perhaps not the most reliable of references, this wikipedia article suggests otherwise. – Tibrogargan Jul 16 '18 at 02:22
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    I asked a similar question: https://space.stackexchange.com/questions/17765/from-how-far-away-could-our-seti-searches-detect-and-recognize-our-technological?rq=1 and was referred to something on Worldbuilding: https://worldbuilding.stackexchange.com/questions/39571/how-far-away-would-an-alien-civilization-need-to-be-for-us-to-not-notice-them - upshot: likelihood is zero because the threshold distance is actually only about 1 LY and there are no other stars that close. – Anthony X Jul 16 '18 at 02:57
  • @AnthonyX So pretty much ... every star in the galaxy could have a civilization similar to ours and we probably wouldn't detect a single one unless we got lucky. – Tibrogargan Jul 16 '18 at 04:08
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    There is a really excellent answer to the question Are we alone after all? Understanding the recent re-evaluation of the Drake Equation that you may find helpful, or at least interesting. – uhoh Jul 16 '18 at 05:13
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    @uhoh I'm aware of the Drake Equation and the recent discussion/publicity - which is pretty much why I'm asking the question, especially concerning the "Fraction of the above revealing their existence via signal release into space". We [effectively] don't do that, and even if we did it sounds like we couldn't see it anyway, so that fraction is probably exceedingly small – Tibrogargan Jul 16 '18 at 05:19
  • Several prominent scientists such as Michio Kaku have stated that they expect detection of intelligent aliens before 2100. People like to overstate how good our technology is currently but really the range at which we could find life is pretty short. Hell, we didn't even have pictures of Pluto consisting of more than 16 pixels before 2015 and new moons around Jupiter and Saturn are still discovered reasonably often. – Dragongeek Jul 16 '18 at 12:10

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There are already some very good comments that address detection issues themselves (e.g., difficulty detecting signals at the necessary distances), so let me add another major factor: time.

Your hypothetical supposes that any nearby civilizations would be on a comparable technological level to our own, but this is a huge assumption if you want to draw any sort of realistic conclusion. Consider the age of our planet compared to the length of time humanity has inhabited it; that's a very tiny percentage. A lot of things had to happen in particular ways over incredible lengths of time in order for humanity to be right here right now. Even if there are thousands of life supporting bodies in our galaxy, each of them has its own unique geological, astronomical, and evolutionary history. In other words, your question is very, very different if you don't assume everyplace else is on Earth's time table and conditions. And sadly, that fact makes the likelihood of finding any neighboring civilizations out there even less probable.

Dan
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    Thanks for the comment. This is actually covered by one of the factors of the Drake Equation (Years a civilization remains detectable). Perhaps I should explicitly call it out in my question - since it would probably increase the number of civilizations required dramatically. It's beginning to look like earth equivalent civilizations could be as common as dirt and we still wouldn't be aware of any – Tibrogargan Jul 16 '18 at 19:55
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    @Tibrogargan Ah, I'd forgotten that was one of the parameters of the equation. Well, if it's all right with you, I'll leave this answer posted in case any other passers-by have the same thought. – Dan Jul 16 '18 at 22:34
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    I think the reason we ask about civilizations on a technological par with us is because it defines a worst-case - we have only recently begun emitting radio signals into space and even more recently became capable of and interested in detecting signals from space. No less-developed world would be doing either, and any more developed world could be reasonably assumed to do better. – Anthony X Jul 17 '18 at 00:54