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Some of you might be wondering

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Why are we even worried about this drake equation?

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Or why are we even tempted to go through

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this thought experiment of the number of

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detectable civilizations in the galaxy,

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when we dont have a clue of some of these

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assumptions. We dont know what

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fraction of planets capable of sustaining life

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actually do generate life. We dont know of all of

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the planets that have life what fraction of those

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planets go on to have intelligent life and what

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fraction of those civilizations go on to using

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electromagnetic radiation as a form of

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communication. We don't know these answers.

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In fact, we probably won't know some of

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these answers for some time.

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So what's the point of going through this

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exercise? And that is a valid point of view.

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The drake equation or even this little equation that

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we have set up here, it's not an equation in the

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traditional sense where we can immediately apply

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it to some engineering problem or some physical

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problem or anything like that. I view it

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more as a bit of a thought experiment.

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And what's interesting about it is that

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it can kinda structure our thought around the

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problem and I think that's where it has

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the most value.

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We'll probably not get a solid number

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on this any time soon, but it does lead

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us to thinking about these interesting problems

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of what does it mean or what do we think has

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to happen for a planet to start getting life

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even if it has all the right ingredients?

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Then what does it mean for things to eventually get

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to the point that you have intelligent life?

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You know, in all fairness to this, is

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that probably two hundred years ago there

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would have been no way to even have

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a decent estimate of the number of

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stars in the galaxy. Now we are starting to

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do an okay job on that. 20 to 30 years ago

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it would have been viewed impossible to say

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the fraction of stars that have planets, but

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now we are finding exoplanets. We are seeing

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stars wobble. We are finding we are getting

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more and more accurate instruments.

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So we can start to think about planets that are

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closer to the size of earth so we are even making

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headway there. There are other indirect

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methods to think about: You know, some of these

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exoplanets look like they're in the right zone and

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they look like they have the right chemical

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signature based on other information

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that we are getting that maybe they are

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capable of sustaining life.

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So as time goes on and as technology

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improves we might get better and better at

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this. With that said, it's not going to happen

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any time soon and the real value of all this

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is really to structure our thoughts

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about really a super interesting topic.

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Now the other thing I want to talk about is

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a slight clarification of what I talked about

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in the last video. In the last video for this L

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I said it's the civilization's lifespan, but

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what's actually relevant is the lifespan of

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the civilization while it is detectable. So detectable.

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So, it doesn't matter if the civilization

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is around a hundred thousand years,

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but it's not releasing any type of thing that

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we can detect. That's not what we care about.

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We care about the 5,000 years or the 10,000

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years or the 100,000 years when they

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are actually using some type of communications

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or some type of electromagnetic radiation

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that we can eventually detect once those things

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reach us. Now the other thing I want to make

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clear is we're talking about the number of

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detectable civilizations in the galaxy right

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now. And I will write now in quotation marks

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because we're not talking about a

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civilization that is maybe even a peer civilization

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with us that developed radio communication

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on the order of a hundred years ago because

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frankly, they would have to be no more than

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a hundred light years away for us to

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be able to detect those signals now.

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If they were on the other side of the galaxy,

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we wouldn't be able to detect their signal

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for another tens of thousands of years.

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So when I talk about now, I am saying that the

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signals are getting to us. Signals getting

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Signals recieved. The signals are being received

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right now. So you could have a civilization

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that developed radio seventy thousand

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years ago, but they are seventy thousand light

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years away and maybe they collapsed

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ten thousand years later, but we are just

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receiving their first radio signal.

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So that would be a civilization that I would count

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in this equation that we are setting up.

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So just to make sure that we understand

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it and then we can play with some numbers, let's

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remind ourselves. This is the number of

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our estimate of the number of stars

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in the galaxy. Multiplied by this, you now

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know the number of stars in the galaxy

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that have planets. You multiply

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by this N sub P (the average number

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of planets capable of sustaining life) and these

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first three terms will give you

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the total number of planets in the galaxy

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that have been capable of sustaining life

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at some point in their history. Multiply it by this.

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This is the number of planets in

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the galaxy that have sustained actual life.

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Not just capability of it. They actually had

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life on them at some point in their history.

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Multiply it by this. This is the fraction

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that have developed intelligent life on these

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planets. The number of planets with

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intelligent life at some point in their history.

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Multiply it by this fraction.

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All of these terms, you have the

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number of planets in the galaxy that have had

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intelligent life that became detectable, that

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started emitting some type of radio signature

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We don't know, some type of thing like that

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at some point in their history

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So over here, all of these first six terms

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tell us the number of detectable civilizations

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that occured at some point in the history

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of the stars, the solar systems, the planets that

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are out there right now. But, we care

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about the ones that are detectable now.

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We don't care about the ones that came and

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went and their radio signature went past us

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while we were still living in caves or we were

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hunter-gatherers. We care about the ones that

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their radio signatures are recieving us now.

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And that's why we have this little term right

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over here. So this is the length of the detectable

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civilization, so while they were actually releasing a

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radio signature divided by the life of that

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planet or that solar system or that star

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So for any given star or planet that

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meets all of these criteria. whats the

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probability that it's releasing its....

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So at some point in the history there was a

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detectable civilization or more that was

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releasing some type of a radio signature.

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But, what's the probability that it's doing it right now?

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So that's the detectable lifespan of that

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civilization divided by the life of that solar

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system or that planet because frankly,

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the star and the solar system and

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the planet are all going to essentially have

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give or take, a few hundreds of thousands

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of years or even a few millions of years

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because we are thinking in the billions here.

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They're going to have roughly the same life span.

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And so if you have let's say, and

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just to make this a little bit more

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tangible, lets say the sun has a lifespan and

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lets say that with the Earth and our solar system

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has a lifespan of approximately ten billion years.

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Ten billion years.

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And let's say that us as humans,

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let me be pretty optimistic about it.

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Let's say that we are detectable as

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a civilization for one million years. So we

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have our best days ahead of us.

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So we are detectable for one million years.

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So this term right over here will be

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1 million over 10 billion.

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So this will be 1 over 10 thousand.

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So even though we might be around

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sending out detactable signals for a million

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years, the odds relative to the entire span

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of the history of the planet and our sun,

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if someone is just randomly sampling our

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solar system at a random time in its history and a

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random part of this ten billion years, there is only

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a one in ten thousand chance that

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they will be sampling us at a time that we are

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releasing signals. Assuming that there weren't

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any other civilizations on Mars or Venus or

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that there weren't any other civilizations on Earth

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hundreds of thousands of years ago

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that were doing this, they would definitely

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only have a one in ten thousand chance of

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detecting us assuming that they are sampling

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There could have been a civilization that

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was around three million years ago and they

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did this whole search for extraterrestrial life and

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maybe they are twenty or a hundred or a thousand

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light years away and they pointed their telescopes

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at us, but a million or two million years ago they

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would have pointed it at the direction of our sun

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and they would have not gotten any radio

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signals and they are like "Man, when is this

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extraterrestrial life going to show up?"

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Even though the sun and Earth does

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eventually develop us, they weren't

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able to observe us because when they

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sampled was outside of that 1 in 10,000 window.