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Current time:0:00Total duration:7:18

Video transcript

what I want to do in this video is reconcile the more traditional Drake Equation with the stuff that we derived or that we came up with we kind of thought through it in the last several videos so the more known Drake Equation is this the number of detectable civilizations in the galaxy is equal to and they'll have this and this is not the number of stars in the galaxy this is the average rate of star formation per year in the galaxy so star so let me write this down average rate of star formation which seems kind of unintuitive and frankly it is but hopefully will reconcile to show you that this and what we're going to show with the traditional Drake Equation are actually the same thing so that's the average rate of star formation so I don't know what it is maybe it's ten stars a year or something on that order and then the rest of it looks pretty similar so times the fraction of stars that have planets so this product would give you the average point that the average stars with planet formations per year you multiply that times the average number of the average number of planets capable of sustaining life for a star that has planets for a solar system that has planets so essentially if you multiply this this is the average new planets per year in our galaxy capable of sustaining life you multiply that x times this which is the same exact fraction the fraction of those planets that are capable of sustaining life that are actually that this is capable of sustaining life now we're saying that the fraction that actually do develop life and then of the life we care about the fraction that actually does become intelligent and of the fraction that actually does become intelligent we care about the fraction we care about the fraction that eventually becomes detectable that can actually communicate and then in the traditional Drake equation we multiply that times this L over here times the detectable life of the civilization so how long is that civilization detectable are they releasing radio waves or some like it that a civilization like ours can detect maybe there are other ways to communicate and we're just not advanced enough maybe in a few years we'll discover in a few decades or a few hundreds of years we'll discover that all of the other advanced civilizations are using a much more sophisticated way of communicating that doesn't involve electromagnetic waves who knows but this is what we're thinking right now but anyway the whole point here is to reconcile this thing which is less intuitive for me at least than with this thing because I started up here with the total number of stars in the galaxy the traditional Drake Equation stars with the starts with the average rate of star formation so it's like well how does the average rate of star formation gel with the total number of stars or civilizations that are now detectable what I want to do is diagram that out a little bit and I'm gonna make a few assumptions I'm gonna assume that this is kind of constant that we're in a steady state so this is constant and we are in a steady state the reality is that what would matter is the rate of star formation maybe four or five six billion years ago I don't know how long it has to be ago so that now that it starts to become realistic for real intelligence and real detectable intelligence to exist but let's just assume that this number is constant for most of the life of the galaxy obviously we're making all sorts of crazy assumptions here so why not why not make another one but what I want you to show is that this is equivalent to the number of stars in the galaxy divided by the average life divided by the average life of a star or the average life of a solar system and if n divided by this T sub s if that's the same thing as our star then essentially we have the same formulas and to see that they're the same imagine this imagine this that these that this year so this is this year so this is 2,000 and well let me say this year this year let's say that we have our star let's say that this number is 10 we have 10 new stars in the galaxy so this is I'll just say it's 10 so our star is equal to 10 so this height over here is 10 that's what I'm depicting so if I were to slide I could show this is 10 units high or whatever and then last year there was also and so on and so forth now let's go to let's go to whatever let's say that this number this number right over here is 10 billion years the average star life is 10 billion years so let's go back 10 billion years into the past so this so the average the average life of a star is equal to 10 billion years and we're assuming that this is constant so 10 billion years ago this year they were also they were also they were also 10 new stars came about and every year in between every year in between you had 10 stars come about now how many total stars would there be in our galaxy well any star that came about so we could go beyond that we could go 2 stars that that were born more than 10 billion years ago more than this T sub s years ago so you could have a star that was born that was born 10 billion in 1 years ago on average we're talking about on average here on average that star will not exist anymore so that is not an odd in existence the stars that are in existence once again on average are the ones that were born 10 billion years ago all the way to the ones that were born this year so you have 10 billion years of star birth the ones that are still around each year there's 10 of those years so the total number of stars the total number of stars should be equal to the number of stars that are born each year assuming that that is constant times the average lifespan of the stars x times the average lifespan of the stars and if you look at it and once again this is the that this works because if the stars that were before born before this lifespan don't exist anymore they've died out on average we care about kind of this area right over here 10 stars per year times 10 billion years and now if you manipulate this a little bit you'll see that we'll get the result we want let's solve for R so we could just divide both sides by this T so you get n star so the number of stars in our galaxy now making a bunch of assumptions divided by the Everage life of the stars is equal to the average is equal to the average number of new stars per year is equal to the average number of new stars per year and we get our result if you replace this if you replace this with this with the total number of stars divided by T total number of stars divided by T you get the exact same result that we had before you just change the order a bit we can take this divided by T put it under this n take it out of here and then you get the exact same thing so hopefully that reconciles it a little bit for you