If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:8:09

LeBron: If the history of the
earth was a basketball game, at what point in the game
will the humans show up? Voiceover: Let's first think about how
long a basketball game is in the NBA. We have 4 quarters that
each lasts 12 minutes, so we're talking about 48 minutes. 48 minutes of regulation play. I'm not considering half
time and the time outs and the commercial breaks
and potential overtime. I am just taking about regulation play. We could think about how the numbers
might change if you think about the total duration of the game,
including time outs and commercial breaks and everything that might get
you closer to 2 or 2 1/2 hours. But 48 minutes we can
actually convert to seconds because we know that there
are 60 seconds per minute, times 60 seconds, 60 seconds per minute and this is pretty straight
forward multiplication. We can just say 48 times 60
gives us, so we got this 0 here and then 6 times 48, 6 times 8 is 48 and then 6 times 4 is 24 plus 4 is 28. So there's 2,880 seconds
during regulation play. Now let's think about
the actual age of earth. We estimate that the earth, and
actually the entire solar system, which was all formed roughly at the
same time, is 4.54 billion years old. So let me draw that here. We're going to make a comparison, so I am going to draw
it as the same length. So 4.54 billion years old
and just to give a sense of how large of a number that
is, a billion is a 1,000 million. So we could also write this
as 4,540 million years. or we could write it as 4,540,000
thousand years, or millennia, or we could just write out the
number as 4,540,000,000 years which seems kind of old but let's
think about how long anatomically, modern humans have been roaming
the surface of the earth and here we estimate that
anatomically modern humans have been on the surface of the earth
for about 200,000 years, which seems like a
reasonable amount of time but we'll see it's a very small fraction when you compare it to 4.54 billion years. So let's say that that's that little there and I am actually overdoing it
when I'm drawing the diagram. So that right over there is the amount
of time humans have been 200,000 years and I am actually
drawing this way too big. But what we want to figure out
is what is that equivalent length in seconds on a basketball game or another way to think
about it, 200,000 years is to 4.54 billion years as
the number of seconds. Let's call this thing
right over here x as x is to the total number of seconds in a game. So 2,880 seconds, 2,880 seconds just like that. And one way that we can
do this, to solve for x and this is kind of a more basic algebra, but just as a reminder if
we want to solve for x here, the easiest way is to multiply by 2,880 and that will cancel with
this right over here. but we can't just do it to the right
hand side, we also have to do it to the left hand side and so if
you multiply both sides by 2,880, so multiply both sides
by 2,880, you get that x, the number of the equivalent number
of seconds in a basketball game. If the history of the earth
was a basketball game, when the humans would show up is equal
to the fraction of earth's history that humans have been around. That's this part right over here,
times the number of seconds in a game. So let's think about what we get there. We are going to have the
fraction of earth's history, so 200,000 divided by 4.45 billion. There's a couple of ways I could write it. I could write it 4.54e9, which
literally means 4.54 times 10 to the 9th or 4.54 times
1 followed with 9 zeros or 4.54 times a billion,
which is exactly 4.54 billion. So I could write it like that or I could just write it out. I could write 4, 5 so 4
billion, we'll be careful, 4, 540,000,000 and now
I am doing the thousands 2, 3 and now I am just doing the 1, 2, 3. So this is 4 billion and then I
should have 9 places after that 1,2,3,4,5,6,7,8,9. So this expression right here
is a fraction of earth's history that anatomically modern
humans have been around and then I am going to multiply that, I am going to multiply that, times I am going to multiply that
times the number of seconds of regulation play,
2,880 and now drum roll, we get .12, we could round up .13 seconds. So we get x is equal to, or I could
say maybe approximately equal to 0.13 seconds and so, just to imagine if the history of earth were
regulation play of an NBA game and let's say this game is kind of, at the end of this game there is a
buzzer beater shot that wins the game, the humans don't show up in the
game until the ball has left that final shot taker's hands and it
has just about to enter the basket that's when the first humans,
200,000 years ago will show up. A little over a tenth of a
second before the end of the game and since we already have
our brains in this mindset, I will throw out another
interesting question. Okay, humans are you know, just a flash that they've actually shown up. Just as the ball is about
to go into the basket, we have a little over a tenth
of a second left in the game. Think about when the
dinosaurs went extinct. I will give you a hint here. The dinosaurs went extinct. So we believe an asteroid hit the earth. So, this kind of a meteorite. This is a current theory,
meteorite hit the earth, mass extinction event
65.5 million years ago. So if we think of that 65.5
million years ago relative to the history of the earth and if the history of the earth were just
regulation play of a basketball game, when did that happen? Well, once again let's
get our calculator out. What fraction of the earth's
history ago was this? 65.5 million, I could write this
as 65.5 times 10 to the 6th, which is that and then I'll just
divide that by 4.54 billion years. So times 10 to the 9th and so this
is the fraction of earth's history that has happened since the
extinction of the dinosaurs. So a little more, about a percent and
a half of earth's history has happened since the extinction of the
dinosaurs 65.5 million years ago and if we are talking
about a basketball game, let's just multiply that times the
number of seconds in a basketball game, 2,880 and we get about 41 seconds. So with less than a minute
left in the 4th quarter is when the meteorite hits the earth