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.

You could do an equation like that for a person finding someone compatible to spend a happy eternal marriage with XD I bet the fraction for each person is tiny!

GREAT VID KHAN

CAN U PLEASE EXPLAIN THE BIG CRUNCH TOO!!!

UR THE BEST BRO

I don't know if I am getting this explanation right, but, what's the point of all that measures and assumptions if they are only assumptions with no proves ata all, anyway?

I mean, the probability of a single protein exists by accident is less then a man fly by himself…

@marcelobetel theory comes before practice, so with the assumptions of these stars are made so that in future it will be disproven by new evidence made by observation and that will be disproved by other evidence and that will be the basis for a new theory and it'll go on until we can prove it by heading in space ships ðŸ˜‰

@MoOtJeMan Translating: While relying on human science, you will never know.

I see…

astrobiology

The Drake Equation seems to me a bit like a Dating Site.

So i don't agree to not take into account all life that was created before 10B years ago, because if they lived long enough, they would have been able to move to a solar system that is still in the currect 10B lifetime range.