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德雷克方程的重要意义.地外生命何以被探测到. Sal Khan 创建




some of you might be wondering why are we even worried about this Drake Equation or the number or why are we even tempted to go through this thought experiment of the number of detectable civilizations in the galaxy when we don't have a clue of some of these assumptions we don't know what fraction of planets capable of sustaining life actually do generate life we don't know of all of the the planets that have life what fraction of those planets go on to have intelligent life and what fractions of those civilizations go on to having to using electromagnetic radiation as a form of communication we don't know these answers in fact we probably won't know some of these answers for some sometime so what's the point of going through this exercise and that is a valid point of view the Drake Equation or even this little equation that we've set up here it's not an equation in the traditional sense we can immediately apply it to some engineering problem or some physical problem or anything like that I view it more as a bit of a thought experiment and what's interesting about it is it kind of can structure our thought around the problem and I think that's where it has the most value will probably not get a solid number on this anytime soon but it does lead us to thinking about these interesting problems of what does it mean or what what do we think has to happen for a planet to start sisty getting life even if it has all the right ingredients and then what and then what does it mean for things to eventually get to the point that you have in telogen life and you know in all fairness to this is that probably 200 years ago there would have been no way to even have a decent estimate of the number of stars in the galaxy now we're starting to do an okay job on that twenty or thirty years ago it would have been viewed impossible to say the fraction of stars that have planets but now we're finding exoplanets we're seeing stars wobble we're finding we're getting more and more accurate instruments so we can start to think about planets that are closer to the size of Earth so we're even we're making we're making headway there there's other indirect methods to think about well you know some of these exoplanets look like they're in the right zone and they look like they have the right chemical signature based on other information that we're getting that then maybe they are capable of sustaining life so as time goes on in this technology improves we might be able to get better and better and better at this but with that said it was not gonna happen anytime soon and the real value of all of this is really to structure our thought about really a super super interesting topic now the other thing I want to talk about is a slight clarification of what I talked about in the last video in the last video for this L I said it's the civilizations lifespan but what's actually relevant is the civilization the lifespan of the civilization while it is detectable so detectable so it doesn't matter if the civilization is around a hundred thousand years but it's not releasing any type of thing that we can detect that's not what we care about we care about that the five thousand years or the ten thousand years or the hundred thousand years when they are actually using some type of some type of communications or some type of some type of electromagnetic radiation that we can eventually detect once those things reach us now the other thing I want to make it clear is we're talking about the number of detectable civilizations in the galaxy right now and I'll right now in in quotation marks because we're not talking about a civilization that is maybe even a peer civilization with us that developed developed radio communication on the order of a hundred years ago because frankly they would have to be no more than a hundred light years away for us to be able to detect those signals now if they were on the other side of the galaxy we wouldn't be able to detect their signals for another for tens of thousands of years so when I talk about now I'm saying that the signals are getting to us signals getting signals received the signals are being are being received right now signals are so you could have a civilization that developed radio 70,000 years ago but there's 70,000 light-years away and maybe they collapsed ten thousand years later but we're just receiving their first radio signals so that's that would be a civilization that I would count in this in this equation we're setting up and so just to make sure we understand it just so and then we can play with some numbers let's remind ourselves this is the number of stars our estimate of the number of stars in the galaxy multiplied by this you now know the number of stars in the galaxy that have planned you multiply by this n sub P the the average number of planets capable of sustaining life and these first three terms will give you the average number of planets in the galaxy that the number the total number of planets in the galaxy that have been capable of sustaining life at some point in their history multiply it by this this is the number of planets in the galaxy that have sustained actual life not just capability of it they actually had life on them at some point in their history multiply it by this this is the fraction that have developed intelligent life on these planets the number of planets with intelligent life at some point in their history multiply it by this fraction all of these terms you have the number of planets in the galaxy that have developed that have had intelligent life that got became detectable that started emitting some type of radio signature we don't know some type of thing like that at some point in their history so it over here all of these first six terms tell us the number of detectable civilizations that occurred at some point in the history of the the stars the solar systems the planets that are out there right now but we care about the ones that are detectable now we don't care about the ones that came and went and their radio signature went past us while we were you know still living in caves or we were hunter-gatherers we care about the ones that the radio signatures are receiving us now and that's why we have this little term right over here so this is the civilization of I guess you could say this is the length of the detectable civilization so while they were actually releasing a radio signature divided by the life of that planet or that solar system or that star so for any given star or planet it meets all of these criteria what's the probability that it's releasing its so it's it's at some point in the history it was there was a detectable civilization or more that was releasing a some type of a radio signature but what's the probability that it's doing it right now and so that's the detectable lifespan of that civilization divided by the life of that solar system or of that planet because frankly the the the star and the solar system of the planet they're all going to essentially have give or take a few hundred thousands of years or even a few millions of years because we're thinking in the billions here they're gonna have roughly the same lifespan and so if you have if if let's say let's give and just to make this a little bit a little bit more tangible let's say that the Sun the Sun has a lifespan and let's say that with the earth and our solar system has a lifespan of approximately ten billion years ten billion years and let's say let's say that us as humans let me be pretty optimistic about it let's say that we are detectable as a civilization for 1 million years so you know we have our best days are ahead of us so we have we are we are detectable for 1 million years so this term right over here will be 1 million over 10 billion so this will be 1 over 10,000 so even though we might be around sending out detectable signals 4 million years the odds relative to the entire span of the history of our and I'm making some simplifying assumptions here but relative to the entire span of the history of our planet and our Sun if someone is just randomly sampling our solar system at a random time in its history in a random part of this 10 billion years there's only a 1 in 10,000 chance that they'll still they'll be sampling us at a time that we are releasing signals assuming that there weren't any other civilizations on Mars or Venus or whatever else or that there weren't any other civilizations on earth hundreds of thousands of years ago that we're doing this they would only have a what they'll definitely only have a 1 in 10,000 chance of detecting us assuming that they're sampling you know there could have been a civilization that was around 3 million years ago and they did this whole search for extraterrestrial life maybe they're you know maybe they're 20 or 100 or a thousand light years away and they pointed their radio telescopes at us but a million or two million years ago they were pointed at the direction of our Sun and they would have not gotten any radio signals and they're like man when is this when is extraterrestrial life going to show up even though the Sun and Earth does eventually develop us they weren't able to observe us because when they sampled was outside of that 1 in 10,000 window