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# Detectable civilizations in our galaxy 3

## 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 we'll
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 10 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 stars with planet formations per year. You multiply that times
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
times this, which is the same exact fraction. The fraction of
those planets that are capable of sustaining
life, that actually, 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 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 something 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 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 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 going to make
a few assumptions. I'm going to 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 4, 5, 6 billion years
ago, I don't know how long it has to be
ago, so that now 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 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 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 this year, so this is
this year, so this is-- 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 it, I could show that this is 10
units high, or whatever. And then last year, there was
also 10, so on and so forth. Now, 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 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, there were also 10
new stars came about. And 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 to stars 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 10 billion and 1 years
ago, on average. We're talking about
on averages here. On average, that star
will not exist anymore, so that star is
not 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 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. Times the average
lifespan of the stars. And once again, this works
because the stars that were 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 average life
of the stars 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 with the
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 up here, and then
you get the exact same thing. So hopefully that reconciles
it a little bit for you.