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Some of you might be wondering, why are we even worried about this Drake equation, 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 planets that have life, what fraction of those planets go on to have intelligent life, and what fractions of those civilizations go on 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 time. 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, where 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. We'll probably not get a solid number on this any time soon, but it does lead us to thinking about these interesting problems of what does it mean, or what do we think has to happen for a planet to start getting life, even if it has all the right ingredients? And then what does it mean for things to eventually get to the point that you have intelligent life? And 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 OK job on that. 20 or 30 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 getting more and more accurate instruments. So we can start to think about planets that are closer to the size of Earth's. We're making headway there. There's other indirect methods to think about, well, 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, and that maybe they are capable of sustaining life. So as time goes on, and as technology improves, we might be able to get better and better and better at this. But with that said, it's not going to happen any time soon, and the real value of all of this is really to structure our thoughts 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 civilization's lifespan, but what's actually relevant is the lifespan of the civilization while it is detectable. So, detectable. So it doesn't matter if the civilization is around 100,000 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 5,000 years, or the 10,000 years, or the 100,000 years when they are actually using some type of communications, or some type of electromagnetic radiation that we can eventually detect once those things reach us. Now, the other thing I want to make clear is we're talking about the number of detectable civilizations in the galaxy right now. And I'll write now in quotation marks, because we're not talking about a civilization that is maybe even a peer civilization with us that developed radio communication on the order of 100 years ago, because frankly, they would have to be no more than 100 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 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 received right now. So you could have a civilization that developed radio 70,000 years ago, but they're 70,000 light years away, and maybe they collapsed 10,000 years later, but we're just receiving their first radio signal. So that would be as a civilization that I would count in this equation we're setting up. And so just to make sure we understand it, 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 of the galaxy. Multiplied by this, you now know the number of stars in the galaxy that have planets. You multiply by this n sub p, the average number of planets capable of sustaining life, and these first three terms will give you the average number of planets-- or I should say 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. We have the number of planets in the galaxy that have had intelligent life that 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 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 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 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-- or 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 that meets all of these criterion, what's the probability that it's releasing its-- so at some point in the history, there was a detectable civilization or more that was releasing some type of a radio signature. But what's the probability that it's doing it right now? And so that's the detectable life span of that civilization divided by the life of that solar system, or of that planet. Because frankly, the star and the solar system and the planet, they're all going to essentially have, give or take, a few hundreds of thousands of years, or even a few millions of years, because we're thinking in the billions here, they're going to have roughly the same life span. And so let's say, and just to make this a little bit more tangible, let's say that the sun has a lifespan, and let's say that with the Earth and our solar system, has a lifespan of approximately 10 billion years. 10 billion years. And 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 one million years. Our best days are ahead of us. We are detectable for one million years. So this term right over here will be 1 million over 10 billion. So this will be 1/10,000. So even though we might be around sending out detectable signals for a million years, the odds relative to the entire span of the history of-- 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 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, that there weren't any other civilizations on Earth hundreds of thousands of years ago that were doing this, they'll definitely only have a 1 in 10,000 chance of detecting us, assuming that they're sampling. There could have been a civilization that was around three million years ago, and they did this whole search for extraterrestrial life. Maybe they're 20, or 100, or 1,000 light years away, and they pointed their radio telescopes at us. But a million or two million years ago, they would have pointed at the direction of our sun, and they would have not gotten any radio signals, and they're like, man, 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.