Scale of the galaxy

WEBVTT
Kind: captions
Language: en

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In the last video, I hinted that
things were about to get wacky.

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And they are.

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So if we start where we
left off in the last video,

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we started right over here,
looking at the distance

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to the nearest star.

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And just as a reminder,
in this drawing

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right here, this
depiction right here,

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this circle right here,
this solar system circle,

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it's not the size of the Sun.

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It's not the size of the
orbits of the Earth, or Pluto,

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or the Kuiper Belt.

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This is close to the
size of the Oort Cloud.

00:00:31.120 --> 00:00:35.280
And the actual orbit of
Earth is about-- well,

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the diameter of the orbit
of Earth is about 1/50,000

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of this.

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So you wouldn't
even see it on this.

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It would not even make
up a pixel on this screen

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right here, much
less the actual size

00:00:46.760 --> 00:00:48.470
of the Sun or
something much smaller.

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And just remember that
orbit of the Earth,

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that was at a huge distance.

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It takes eight minutes for
light to get from the Sun

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to the Earth, this
super long distance.

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If you shot a bullet
at the Sun from Earth,

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it would take you that 17 years
to actually get to the Sun.

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So one thing, this huge
distance wouldn't even

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show up on this picture.

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Now, what we saw
in the last video

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is that if you travel at
unimaginably fast speeds,

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if you travel at 60,000
kilometers per hour--

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and I picked that
speed because that's

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how fast Voyager 1
actually is traveling.

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That's I think
the fastest object

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we have out there
in space right here.

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And it's actually kind of
leaving the solar system

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as we speak.

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But even if you were
able to get that fast,

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it would still take 80,000
years, 75,000 or 80,000 years,

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to travel the 4.2 light
years to the Alpha Centauri

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cluster of stars.

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To the nearest star, it
would take 80,000 years.

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And that scale of time is
already an amount of time

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that I have trouble
comprehending.

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As you can imagine, all
of modern civilization

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has occurred, well, definitely
in the last 10,000 years.

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But most of recorded history
is in the last 4,000 or 5,000

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years.

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So this is 80,000 years to
travel to the nearest star.

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So it's a huge distance.

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Another way to think about
it is if the Sun were

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the size of a basketball and you
put that basketball in London,

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if you wanted to do it in scale,
the next closest star, which

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is actually a
smaller basketball,

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right over here, Proxima
Centauri, that smaller

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basketball you would have
to put in Kiev, Ukraine

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in order to have
a similar scale.

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So these are basketballs
sitting in these cities.

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And you would have to
travel about 1,200 miles

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to place the next basketball.

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And these basketballs
are representing

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these super huge things that
we saw in the first video.

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The Sun, if you actually
made the Earth relative

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to these basketballs, these
would be little grains of sand.

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So there are any little
small planets over here,

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they would have to
be grains of sand

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in Kiev, Ukraine versus the
grain of sand in London.

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So this is a massive,
massive distance,

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already, at least in
my mind, unimaginable.

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And when it gets
really wacky is when

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you start really
looking at this.

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Even this is a super,
super small distance

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relative to the galactic scale.

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So this whole depiction of kind
of our neighborhood of stars,

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this thing over here is
about, give or take--

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and we're doing rough
estimates right here--

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it's about 30 light years.

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I'll just do LY for short.

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So that's about 30 light years,

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And once again, you can
take pictures of our galaxy

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from our point of view.

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But you actually can't take
a picture of the whole galaxy

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from above it.

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So these are going to
be artists' depictions.

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But if this is 30 light years,
this drawing right here of kind

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of our local neighborhood
of the galaxy,

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this right here is roughly-- and
these are all approximations.

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Let me do this in
a darker color.

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This is about 1,000 light years.

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And this is the
1,000 light years

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of our Sun's neighborhood,
if you can even

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call it a neighborhood anymore.

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Even this isn't really a
neighborhood if it takes you

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80,000 years to get to
your nearest neighbor.

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But this whole
drawing over here--

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now, it would take forever
to get anywhere over here--

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it would be 1/30 of this.

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So it would be about that
big, this whole drawing.

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And what's really
going to blow your mind

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is this would be roughly
a little bit more

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than a pixel on this
drawing right here, that

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spans a 1,000 light years.

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But then when you
start to really

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put it into
perspective-- so now,

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let's zoom out a little bit--
so this drawing right here,

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this 1,000 light years is
now this 1,000 light years

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over here.

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So this is the local
vicinity of the Sun.

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And once again,
the word "local" is

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used in a very liberal
way at this point.

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So this right here
is 1,000 light years.

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If you're sitting
here and you're

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looking at an object
that's sitting--

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let me do this in
a darker color--

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if we're sitting here on Earth
and we're looking at an object

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out here that's 500
light years away,

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we're looking at it as it was
500 years ago because the light

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that is reaching our
eyeballs right now,

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or our telescopes
right now, left

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this guy over here
500 years ago.

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In fact, he's not going
to even be there anymore.

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He probably has moved
around a little bit.

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So just even on
this scale, we're

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talking about these
unimaginably huge distances.

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And then when we
zoom out, this is

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kind of our local part of
the galaxy right over here.

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This piece right here, this
is called the Orion Spur.

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And people are still
trying to work out

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exactly the details
of the actual shape

00:05:55.480 --> 00:05:58.800
the Milky Way Galaxy,
the galaxy that we're in.

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But we're pretty
sure-- actually,

00:06:00.470 --> 00:06:02.541
we're very sure-- we
have these spiral arms

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and we have these
spurs off of them.

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But it's actually very hard to
come up with the actual shape,

00:06:06.380 --> 00:06:08.620
especially because you can't
see a lot of the galaxy,

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because it's kind of
on the other side,

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on the other side of the center.

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But really just to get
a sense of something

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that at least-- I mean it blows
my mind if you really think

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about what it's saying--
these unbelievable distances

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show up as a little dot here.

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This whole drawing
shows up as a dot here.

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Now when we zoom out,
over here that dot

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would no longer even show up.

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It wouldn't even
register a pixel

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on this drawing right over here.

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And then this whole drawing,
this whole thing right

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over here, this whole picture
is this grid right over here.

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It is this right over here.

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So hopefully, that gives you
a sense of how small even

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our local neighborhood
is relative to the galaxy

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as a whole.

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And the galaxy as a whole,
just to give you a sense,

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has 200 to 400 billion stars.

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Or maybe I should say
solar systems just

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to give you a sense that
when we saw the solar system,

00:07:11.490 --> 00:07:12.500
it's not just the Sun.

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There's all this
neat, dynamic stuff.

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And there are planets, and
asteroids, and solar winds.

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And so there's 200
to 400 billion stars

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and for the most part, 200
and 400 billion solar systems.

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So it's an unimaginably, I
guess, complex or huge place.

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And just to make
it clear, even when

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we zoom in to this
picture right here,

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and I think it was obvious
based on telling you about this,

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that these little white
pockets right here,

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this isn't one star.

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This isn't two stars.

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These are thousands
of stars here.

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So when you go over here,
each little blotch of white

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that you see, that's not a star,
that's not a thousand stars.

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We're starting to talk
in the millions of stars

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when you look at certain
blotches here and there.

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I mean, maybe it might be
one star that's closer to you

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or might be a million
stars that are far apart

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and that are just
relatively close together.

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And everything has to be used
in kind of loose terms here.

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And we'll talk more
about other galaxies.

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But even this isn't the
upper bound of galaxies.

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People believe the
Andromeda Galaxy

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has a trillion stars in it,
a trillion solar systems.

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We're talking about these
huge, huge, immense distances.

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And so just to give you a sense
of where we fit in the picture,

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this is a rough
location of our Sun.

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And remember, that little
dot I drew just now

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is including millions of stars,
millions of solar systems,

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already unimaginable
the distances.

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But if you really want
to get at the sense

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relative to the whole galaxy,
this is an artist's depiction.

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Once again, we could
never obviously get

00:08:42.620 --> 00:08:44.075
this perspective on the galaxy.

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It would take us
forever to travel this

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far so that you could see
the galaxy from above.

00:08:48.590 --> 00:08:50.110
But this is our
best guess looking

00:08:50.110 --> 00:08:52.020
at things from
our vantage point.

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And we actually can't even
see this whole area over here

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because it's on the other side
of the center of the galaxy,

00:08:58.150 --> 00:09:01.030
which is super, super
dense and super bright.

00:09:01.030 --> 00:09:03.280
And so it's very hard to see
things on the other side.

00:09:03.280 --> 00:09:07.300
We think-- or actually there's
a super massive black hole

00:09:07.300 --> 00:09:08.630
at the center of the galaxy.

00:09:08.630 --> 00:09:12.010
And we think that they're at the
center of all or most galaxies.

00:09:12.010 --> 00:09:14.350
But you know the whole point
of this video, actually

00:09:14.350 --> 00:09:16.760
this whole series of videos,
this is just kind of-- I

00:09:16.760 --> 00:09:21.311
don't know-- to put you in awe
a little bit of just how huge

00:09:21.311 --> 00:09:21.810
this is.

00:09:21.810 --> 00:09:23.940
Because when you really
think about the scale--

00:09:23.940 --> 00:09:27.040
I don't know-- no words
can really describe it.

00:09:27.040 --> 00:09:31.950
But just to give
you a sense, we're

00:09:31.950 --> 00:09:39.870
about 25,000 light years from
the center of the galaxy.

00:09:39.870 --> 00:09:43.330
So even when we look at things
in the center of the galaxy,

00:09:43.330 --> 00:09:46.120
that's as they were
25,000 years ago.

00:09:46.120 --> 00:09:49.580
It took 25,000 years for
that light to get to us.

00:09:49.580 --> 00:09:52.030
I mean when that light left
the center of the galaxy,

00:09:52.030 --> 00:09:56.390
I won't even guess to
think what humanity

00:09:56.390 --> 00:09:58.170
was like at that point in time.

00:09:58.170 --> 00:10:02.120
So it's these huge distances
in the whole galaxy over here.

00:10:02.120 --> 00:10:04.106
And once again,
like solar systems,

00:10:04.106 --> 00:10:06.730
it's hard to say the edge of the
galaxy, because there's always

00:10:06.730 --> 00:10:09.584
going to be a few more stars
and other things orbiting

00:10:09.584 --> 00:10:11.750
around the galaxy as you
go further and further out,

00:10:11.750 --> 00:10:13.460
but it gets less
dense with stars.

00:10:13.460 --> 00:10:15.650
But the main density,
the main disk,

00:10:15.650 --> 00:10:19.756
is about 100,000 light years.

00:10:19.756 --> 00:10:24.560
100,000 light years is
the diameter roughly

00:10:24.560 --> 00:10:26.490
of the main part of the galaxy.

00:10:26.490 --> 00:10:28.460
And it's about 1,000
light years thick.

00:10:28.460 --> 00:10:30.290
So you can kind of
imagine it as this disk,

00:10:30.290 --> 00:10:31.540
this thing that's fairly flat.

00:10:31.540 --> 00:10:33.790
But it's 1,000
light years thick.

00:10:33.790 --> 00:10:39.340
It's 1,000 light years thick.

00:10:39.340 --> 00:10:42.010
You would have to do this
distance 250 times just

00:10:42.010 --> 00:10:45.450
to go from the top part of
the galaxy to the bottom part,

00:10:45.450 --> 00:10:47.320
much less going
across the galaxy.

00:10:47.320 --> 00:10:49.560
So it might seem
relatively flat.

00:10:49.560 --> 00:10:52.050
But it's still immensely,
immensely thick.

00:10:52.050 --> 00:10:54.360
And just as another
way to visualize it,

00:10:54.360 --> 00:10:57.270
if this thing right over here
that includes the Oort Cloud,

00:10:57.270 --> 00:11:05.800
roughly a light year in
diameter, is a grain of sand,

00:11:05.800 --> 00:11:09.610
a millimeter in
diameter grain of sand,

00:11:09.610 --> 00:11:11.170
then the universe
as a whole is going

00:11:11.170 --> 00:11:13.580
to be the diameter
of a football field.

00:11:13.580 --> 00:11:17.240
And that might tell you, OK,
those are two tractable things.

00:11:17.240 --> 00:11:21.770
I can imagine a grain of sand,
a millimeter wide grain of sand

00:11:21.770 --> 00:11:22.750
in a football field.

00:11:22.750 --> 00:11:29.580
But remember, that
grain of sand is still

00:11:29.580 --> 00:11:34.380
50,000 or 60,000 times the
diameter of Earth's orbit.

00:11:34.380 --> 00:11:36.450
And Earth's orbit,
it would still

00:11:36.450 --> 00:11:38.900
take a bullet or something
traveling as fast as a jet

00:11:38.900 --> 00:11:42.630
plane 15 hours to just go
half of that-- or sorry,

00:11:42.630 --> 00:11:46.540
not-- 15 years or 17 years,
I forgot the exact number.

00:11:46.540 --> 00:11:49.500
But it was 15, 16, 17
years to even cover

00:11:49.500 --> 00:11:50.660
half of that distance.

00:11:54.200 --> 00:11:56.960
So 30 years just to cover the
diameter of Earth's orbit.

00:11:56.960 --> 00:12:02.450
That's 1/60,000 of our little
grain of sand in the football

00:12:02.450 --> 00:12:03.160
field.

00:12:03.160 --> 00:12:05.950
And just to kind
of really, I don't

00:12:05.950 --> 00:12:11.430
know, have an appreciation
for how mind-blowing

00:12:11.430 --> 00:12:14.210
this really is, this is actually
a picture of the Milky Way

00:12:14.210 --> 00:12:17.360
Galaxy, our galaxy,
from our vantage point.

00:12:17.360 --> 00:12:19.330
As you can see,
we're in the galaxy

00:12:19.330 --> 00:12:21.690
and this is looking
towards the center.

00:12:21.690 --> 00:12:24.830
And even this picture, you start
to appreciate the complexity

00:12:24.830 --> 00:12:27.760
of what 100 billion stars are.

00:12:27.760 --> 00:12:29.341
But what I really
want to point out

00:12:29.341 --> 00:12:30.840
is even in this
picture, when you're

00:12:30.840 --> 00:12:32.715
looking at these things,
some of these things

00:12:32.715 --> 00:12:35.340
that look like stars,
those aren't stars.

00:12:35.340 --> 00:12:38.660
those are thousands of
stars or millions of stars.

00:12:38.660 --> 00:12:40.630
Maybe it could be
one star closer up.

00:12:40.630 --> 00:12:41.630
But when we're
starting to approach

00:12:41.630 --> 00:12:43.088
the center of the
galaxy, these are

00:12:43.088 --> 00:12:44.680
thousands and
thousands and millions

00:12:44.680 --> 00:12:47.580
of stars or solar systems that
we're actually looking at.

00:12:47.580 --> 00:12:50.810
So really, it starts
to boggle the mind

00:12:50.810 --> 00:12:54.930
to imagine what might actually
be going on over there.


Scale of earth and sun

WEBVTT
Kind: captions
Language: en

00:00:00.720 --> 00:00:02.630
My goal in this video
and the next video

00:00:02.630 --> 00:00:06.210
is to start giving
a sense of the scale

00:00:06.210 --> 00:00:08.529
of the earth and
the solar system.

00:00:08.529 --> 00:00:09.945
And as we see, as
we start getting

00:00:09.945 --> 00:00:11.444
into to the galaxy
and the universe,

00:00:11.444 --> 00:00:13.860
it just becomes almost
impossible to imagine.

00:00:13.860 --> 00:00:16.050
But we'll at least
give our best shot.

00:00:16.050 --> 00:00:18.220
So I think most of us
watching this video

00:00:18.220 --> 00:00:20.295
know that this
right here is earth.

00:00:22.800 --> 00:00:24.400
And just to get a
sense of scale here,

00:00:24.400 --> 00:00:27.380
I think probably
the largest distance

00:00:27.380 --> 00:00:29.760
that we can somehow relate
to is about 100 miles.

00:00:29.760 --> 00:00:32.537
You can get into a car for
an hour, hour and a half,

00:00:32.537 --> 00:00:33.495
and go about 100 miles.

00:00:33.495 --> 00:00:36.560
And on the earth that
would be about this far.

00:00:36.560 --> 00:00:40.480
It would be a speck that would
look something like that.

00:00:40.480 --> 00:00:42.690
That is 100 miles.

00:00:42.690 --> 00:00:44.660
And also to get
us a bit of scale,

00:00:44.660 --> 00:00:46.600
let's think about a
speed that at least we

00:00:46.600 --> 00:00:47.940
can kind of comprehend.

00:00:47.940 --> 00:00:56.797
And that would be, maybe,
the speed of a bullet.

00:00:56.797 --> 00:00:58.380
Maybe we can't
comprehend it, but I'll

00:00:58.380 --> 00:01:01.970
say this is the fastest thing
that we could maybe comprehend.

00:01:01.970 --> 00:01:05.129
It goes about-- and there are
different types of bullets

00:01:05.129 --> 00:01:09.110
depending on the type of gun and
all of that-- about 280 meters

00:01:09.110 --> 00:01:18.030
per second, which is about
1,000 kilometers per hour.

00:01:18.030 --> 00:01:24.360
And this is also roughly
the speed of a jet.

00:01:27.430 --> 00:01:29.170
So just to give a
sense of scale here,

00:01:29.170 --> 00:01:33.310
the earth's
circumference-- so if you

00:01:33.310 --> 00:01:47.750
were to go around the planet--
is about 40,000 kilometers.

00:01:47.750 --> 00:01:51.070
So if you were to travel
at the speed of a bullet

00:01:51.070 --> 00:01:55.570
or the speed of a jetliner,
at 1,000 kilometers an hour,

00:01:55.570 --> 00:01:58.950
it would take you 40 hours
to circumnavigate the earth.

00:02:06.260 --> 00:02:09.289
And I think none of this
information is too surprising.

00:02:09.289 --> 00:02:12.296
You might have taken a
12- or 15-hour flight that

00:02:12.296 --> 00:02:14.170
gets you-- not all the
way around the earth--

00:02:14.170 --> 00:02:15.210
but gets you pretty far.

00:02:15.210 --> 00:02:18.540
San Francisco to Australia,
or something like that.

00:02:18.540 --> 00:02:21.710
So right now these aren't
scales that are too crazy.

00:02:21.710 --> 00:02:24.000
Although, even for
me, the earth itself

00:02:24.000 --> 00:02:27.510
is a pretty mind-blowingly
large object.

00:02:27.510 --> 00:02:30.270
Now, with that out of the way
let's think about the sun.

00:02:30.270 --> 00:02:34.020
Because the sun starts to
approach something far huger.

00:02:34.020 --> 00:02:36.810
So this obviously
here is the sun.

00:02:36.810 --> 00:02:38.660
And I think most
people appreciate

00:02:38.660 --> 00:02:42.150
that the sun is much
larger than the earth,

00:02:42.150 --> 00:02:44.970
and that it's pretty
far away from the earth.

00:02:44.970 --> 00:02:47.110
But I don't think most
people, including myself,

00:02:47.110 --> 00:02:50.170
fully appreciate
how large the sun is

00:02:50.170 --> 00:02:53.930
or how far it is
away from the earth.

00:02:53.930 --> 00:02:58.180
So just to give you
a sense, the sun

00:02:58.180 --> 00:03:07.040
is 109 times the
circumference of the earth.

00:03:10.400 --> 00:03:13.180
So if we do that same
thought exercise there--

00:03:13.180 --> 00:03:16.300
if we said, OK, if I'm traveling
at the speed of a bullet

00:03:16.300 --> 00:03:19.330
or the speed of a jetliner,
it would take me 40 hours

00:03:19.330 --> 00:03:20.480
to go around the earth.

00:03:20.480 --> 00:03:23.190
Well, how long would it
take to go around the sun?

00:03:23.190 --> 00:03:26.020
So if you were to
get on a jet plane

00:03:26.020 --> 00:03:27.770
and try to go around
the sun, or if you

00:03:27.770 --> 00:03:30.200
were to somehow ride a
bullet and try to go around

00:03:30.200 --> 00:03:34.130
the sun-- do a complete
circumnavigation of the sun--

00:03:34.130 --> 00:03:36.350
it's going to take
you 109 times as long

00:03:36.350 --> 00:03:38.930
as it would have taken
you to do the earth.

00:03:38.930 --> 00:03:42.300
So it would be 100
times-- I could do 109,

00:03:42.300 --> 00:03:44.360
but just for approximate--
it's roughly 100

00:03:44.360 --> 00:03:46.140
times the circumference
of the earth.

00:03:46.140 --> 00:03:53.840
So 109 times 40 is
equal to 4,000 hours.

00:03:53.840 --> 00:03:56.580
And just to get a sense of
what 4,000 is-- actually,

00:03:56.580 --> 00:03:59.430
since I have the calculator out,
let's do the exact calculation.

00:03:59.430 --> 00:04:06.516
It's 109 times the circumference
of the earth times 40 hours.

00:04:06.516 --> 00:04:09.140
That's what it would take to do
the circumference of the Earth.

00:04:09.140 --> 00:04:15.080
So it's 4,360 hours to
circumnavigate the sun, going

00:04:15.080 --> 00:04:17.980
at the speed of a
bullet or a jetliner.

00:04:17.980 --> 00:04:23.100
And so that is-- 24 hours in
the day-- that is 181 days.

00:04:23.100 --> 00:04:27.100
It would take you
roughly half a year

00:04:27.100 --> 00:04:30.530
to go around the sun at
the speed of a jetliner.

00:04:30.530 --> 00:04:31.870
Let me write this down.

00:04:31.870 --> 00:04:32.610
Half a year.

00:04:37.240 --> 00:04:38.420
The sun is huge.

00:04:41.627 --> 00:04:44.210
Now, that by itself may or may
not be surprising--and actually

00:04:44.210 --> 00:04:45.350
let me give you a
sense of scale here,

00:04:45.350 --> 00:04:47.550
because I have this
other diagram of a sun.

00:04:49.824 --> 00:04:51.240
And we'll talk
more about the rest

00:04:51.240 --> 00:04:52.823
of the solar system
in the next video.

00:04:52.823 --> 00:04:56.379
But over here, at
this scale, the sun,

00:04:56.379 --> 00:04:58.420
at least on my screen--
if I were to complete it,

00:04:58.420 --> 00:05:01.220
it would probably be about
20 inches in diameter.

00:05:01.220 --> 00:05:04.069
The earth is just this little
thing over here, smaller

00:05:04.069 --> 00:05:04.735
than a raindrop.

00:05:09.145 --> 00:05:11.520
If I were to draw it on this
scale, where the sun is even

00:05:11.520 --> 00:05:17.990
smaller, the earth
would be about that big.

00:05:17.990 --> 00:05:21.400
Now, what isn't obvious, because
we've all done our science

00:05:21.400 --> 00:05:24.060
projects in third and fourth
grade--or we always see these

00:05:24.060 --> 00:05:27.420
diagrams of the solar system
that look something like this--

00:05:27.420 --> 00:05:29.950
is that these planets
are way further away.

00:05:29.950 --> 00:05:33.650
Even though these are
depicted to scale,

00:05:33.650 --> 00:05:35.840
they're way further
away from the sun

00:05:35.840 --> 00:05:38.660
than this makes it look.

00:05:38.660 --> 00:05:44.350
So the earth is 150 million
kilometers from the sun.

00:05:48.800 --> 00:05:55.110
So if this is the sun
right here, at this scale

00:05:55.110 --> 00:05:57.920
you wouldn't even be
able to see the earth.

00:05:57.920 --> 00:05:59.850
It wouldn't even be a pixel.

00:05:59.850 --> 00:06:13.269
But it would be 150 million
kilometers from the earth.

00:06:13.269 --> 00:06:15.810
And this distance right here is
called an astronomical unit--

00:06:15.810 --> 00:06:18.480
and we'll be using that
term in the next few videos

00:06:18.480 --> 00:06:21.120
just because it's an easier
way to think about distance--

00:06:21.120 --> 00:06:24.080
sometimes abbreviated
AU, astronomical unit.

00:06:30.430 --> 00:06:34.350
And just to give a sense of
how far this is, light, which

00:06:34.350 --> 00:06:36.620
is something that we think
is almost infinitely fast

00:06:36.620 --> 00:06:38.760
and that is something
that looks instantaneous,

00:06:38.760 --> 00:06:41.840
that takes eight minutes
to travel from the sun

00:06:41.840 --> 00:06:42.400
to the earth.

00:06:42.400 --> 00:06:47.000
If the sun were to disappear, it
would take eight minutes for us

00:06:47.000 --> 00:06:49.540
to know that it
disappeared on earth.

00:06:49.540 --> 00:06:53.630
Or another way, just to put
it in the sense of this jet

00:06:53.630 --> 00:06:56.750
airplane-- let's get
the calculator back out.

00:06:56.750 --> 00:07:07.080
So we're talking about
150 million kilometers.

00:07:07.080 --> 00:07:11.910
So if we're going at
1,000 kilometers an hour,

00:07:11.910 --> 00:07:15.990
it would take us 150,000
hours at the speed of a bullet

00:07:15.990 --> 00:07:18.170
or at the speed of a jet
plane to get to the sun.

00:07:18.170 --> 00:07:20.630
And just to put
that in perspective,

00:07:20.630 --> 00:07:25.690
if we want it in days,
there's 24 hours per day.

00:07:25.690 --> 00:07:28.610
So this would be 6,250 days.

00:07:28.610 --> 00:07:33.410
Or, if we divided by
365, roughly 17 years.

00:07:33.410 --> 00:07:35.530
If you were to shoot a
bullet straight at the sun

00:07:35.530 --> 00:07:38.130
it would take 17
years to get there,

00:07:38.130 --> 00:07:40.430
if it could maintain
its velocity somehow.

00:07:40.430 --> 00:07:42.680
So this would take a
bullet or a jet plane

00:07:42.680 --> 00:07:45.060
17 years to get to the sun.

00:07:49.260 --> 00:07:52.620
Or another way to visualize
it-- this sun right over here,

00:07:52.620 --> 00:07:56.420
on my screen it has about a
five- or six-inch diameter.

00:07:56.420 --> 00:07:59.430
If I were to actually do it
at scale, this little dot

00:07:59.430 --> 00:08:02.400
right here, which
is the earth, this

00:08:02.400 --> 00:08:09.590
speck-- I would have to
put this back about 50 feet

00:08:09.590 --> 00:08:10.520
away from the sun.

00:08:10.520 --> 00:08:12.610
50 or 60 feet away from the sun.

00:08:12.610 --> 00:08:14.540
If you were to look
at the solar system--

00:08:14.540 --> 00:08:16.305
and obviously there's other
things in the solar system,

00:08:16.305 --> 00:08:18.430
and we'll talk more about
them in the next video--

00:08:18.430 --> 00:08:19.930
you wouldn't even
notice this speck.

00:08:19.930 --> 00:08:23.010
This is a little dust thing
flying around this sun.

00:08:23.010 --> 00:08:25.696
And as we go further and further
out of this solar system,

00:08:25.696 --> 00:08:27.570
you're going to see even
this distance starts

00:08:27.570 --> 00:08:29.640
to become ridiculously small.

00:08:29.640 --> 00:08:31.790
Or another way to
think about it--

00:08:31.790 --> 00:08:39.770
if the sun was about this size,
then the earth at this scale

00:08:39.770 --> 00:08:42.620
would be about 200
feet away from it.

00:08:42.620 --> 00:08:47.510
So you could imagine, if you
had a football field-- let

00:08:47.510 --> 00:08:49.600
me draw a football field.

00:08:49.600 --> 00:08:52.200
These are the end zones-- one
end zone, another end zone.

00:08:52.200 --> 00:08:53.770
And if you were to
stick something--

00:08:53.770 --> 00:08:55.480
maybe the size of
a medicine ball,

00:08:55.480 --> 00:08:58.240
a little bit bigger than a
basketball, at one end zone--

00:08:58.240 --> 00:09:03.260
this little speck would
be about 60 yards away,

00:09:03.260 --> 00:09:04.287
roughly 60 meters away.

00:09:04.287 --> 00:09:05.370
So it's this little speck.

00:09:05.370 --> 00:09:07.619
You wouldn't even notice it
on the scale of a football

00:09:07.619 --> 00:09:09.179
field, something this size.

00:09:09.179 --> 00:09:10.720
Anyway, I'm going
to leave you there.

00:09:10.720 --> 00:09:13.820
Hopefully that just
starts to blow your mind

00:09:13.820 --> 00:09:17.510
when you think about the
scale of the sun, the earth,

00:09:17.510 --> 00:09:19.911
and how far the earth
is away from the sun.

00:09:19.911 --> 00:09:22.160
And then we're going to see
even those distances, even

00:09:22.160 --> 00:09:24.520
those scales, are super
small when you start thinking

00:09:24.520 --> 00:09:27.120
about the rest of
the solar system.

00:09:27.120 --> 00:09:31.100
And especially when we start
going beyond the solar system.


Scale of distance to closest stars

WEBVTT
Kind: captions
Language: en

00:00:00.640 --> 00:00:03.350
Before we start going
off into things outside

00:00:03.350 --> 00:00:06.780
of our solar system, I want
to take a few steps back

00:00:06.780 --> 00:00:09.774
because I found this neat
picture of the Sun over here.

00:00:09.774 --> 00:00:11.440
And the reason why,
at least in my mind,

00:00:11.440 --> 00:00:14.730
it's kind of mind blowing
is because at this scale,

00:00:14.730 --> 00:00:18.410
the Sun is obviously still
a huge object at this scale.

00:00:18.410 --> 00:00:20.580
The Earth would be
roughly-- and this

00:00:20.580 --> 00:00:24.640
is an approximation--
roughly that big.

00:00:24.640 --> 00:00:27.290
And so for me at least,
this is mind blowing.

00:00:27.290 --> 00:00:29.600
Because it's this idea
that our whole planet,

00:00:29.600 --> 00:00:33.700
everything could fit into one
of these kind of plasma flares

00:00:33.700 --> 00:00:34.974
coming off of the Sun.

00:00:34.974 --> 00:00:36.140
And you can only imagine it.

00:00:36.140 --> 00:00:37.590
We can't realistically be there.

00:00:37.590 --> 00:00:39.673
But if you were in some
type of protected capsule,

00:00:39.673 --> 00:00:43.100
what it would be like to be in
this type of an environment.

00:00:43.100 --> 00:00:46.365
So I just thought this was
kind of a fascinating concept.

00:00:46.365 --> 00:00:47.990
Well, anyway, with
that out of the way,

00:00:47.990 --> 00:00:49.860
let's think about
what it means to be

00:00:49.860 --> 00:00:51.380
at the boundary of
the solar system.

00:00:51.380 --> 00:00:55.660
In the last video, we
explored the Ort Belt.

00:00:55.660 --> 00:00:59.454
It started a little under one
light year away from the Sun.

00:00:59.454 --> 00:01:01.370
But depending on what
you view as the boundary

00:01:01.370 --> 00:01:03.745
of the solar system, it could
be something way farther in

00:01:03.745 --> 00:01:07.280
or could be something as far
out of something like the Oort

00:01:07.280 --> 00:01:08.450
Cloud.

00:01:08.450 --> 00:01:11.850
So the Sun, we see these
things being ejected.

00:01:11.850 --> 00:01:15.470
But even in unseen ways,
or unseen particles,

00:01:15.470 --> 00:01:21.060
super high energy electrons,
electrons and protons,

00:01:21.060 --> 00:01:23.430
are also being
ejected from the Sun

00:01:23.430 --> 00:01:27.830
at super high velocities,
400 kilometers per second.

00:01:27.830 --> 00:01:32.870
Let me write that down,
400 kilometers per second.

00:01:32.870 --> 00:01:36.120
And on Earth, we're protected
from these highly energetic

00:01:36.120 --> 00:01:40.610
particles because of
Earth's magnetic field.

00:01:40.610 --> 00:01:42.970
But if you're on the
surface of the Moon

00:01:42.970 --> 00:01:45.450
when the Sun is on
top, and you're not

00:01:45.450 --> 00:01:47.500
on the dark side
of the Moon, you'll

00:01:47.500 --> 00:01:49.030
have direct contact with these.

00:01:49.030 --> 00:01:51.620
And as you can imagine,
it's not the best thing

00:01:51.620 --> 00:01:53.650
to hang around in too along.

00:01:53.650 --> 00:01:56.910
But the whole reason why I'm
even talking about these, these

00:01:56.910 --> 00:01:59.389
charged particles that are
coming out at huge velocities

00:01:59.389 --> 00:02:00.805
from the surface
of the Sun, these

00:02:00.805 --> 00:02:03.280
are considered the solar wind.

00:02:03.280 --> 00:02:06.640
These are the solar wind.

00:02:06.640 --> 00:02:08.414
And I'll put "wind' in quotes.

00:02:08.414 --> 00:02:09.830
Because it's really
very different

00:02:09.830 --> 00:02:12.580
than our traditional
association of a nice breeze.

00:02:12.580 --> 00:02:14.720
These are just
charged particles that

00:02:14.720 --> 00:02:17.370
are going out at super high
velocities from the Sun.

00:02:17.370 --> 00:02:20.100
And I'm even going into
the idea of the solar wind

00:02:20.100 --> 00:02:24.120
because to some degree,
they can help us

00:02:24.120 --> 00:02:27.250
with one definition of maybe
the limits of the solar system.

00:02:27.250 --> 00:02:30.830
And that's the limits of how
far the solar wind is getting

00:02:30.830 --> 00:02:33.100
before it kind of
comes in confrontation

00:02:33.100 --> 00:02:35.540
with the interstellar medium.

00:02:35.540 --> 00:02:39.370
And this right here shows
a depiction of that.

00:02:39.370 --> 00:02:41.900
So the Ort Cloud, it
was way-- at least

00:02:41.900 --> 00:02:45.410
the edges of the dense part
of it is way outside of this.

00:02:45.410 --> 00:02:48.120
As we saw, this is just
where Voyager 1, Voyager 2.

00:02:48.120 --> 00:02:55.100
If we wanted the orbit
of Sedna, the close part

00:02:55.100 --> 00:02:57.350
would be something over here
and then it would go out.

00:02:57.350 --> 00:02:59.730
But the Ort Cloud is
much, much further out.

00:02:59.730 --> 00:03:02.900
So if you look at this kind
of view of the solar system

00:03:02.900 --> 00:03:05.880
as the extent of the solar wind,
its much smaller than the Ort

00:03:05.880 --> 00:03:06.380
Cloud.

00:03:06.380 --> 00:03:08.130
But it's still fairly large.

00:03:08.130 --> 00:03:09.180
So this is right here.

00:03:09.180 --> 00:03:13.420
This heliopause right here--
and I got this from Wikipedia--

00:03:13.420 --> 00:03:18.400
this is essentially where
the velocity and the forces

00:03:18.400 --> 00:03:21.240
of the solar wind
are counteracted.

00:03:21.240 --> 00:03:24.730
That the pressure is so
diluted at this point

00:03:24.730 --> 00:03:28.440
that it's counteracted by mainly
the hydrogen and the helium

00:03:28.440 --> 00:03:32.380
that's in the interstellar
kind of medium,

00:03:32.380 --> 00:03:33.680
that's just kind of out there.

00:03:33.680 --> 00:03:36.590
So after this point,
it's not really

00:03:36.590 --> 00:03:39.030
being injected out anymore.

00:03:39.030 --> 00:03:42.040
There's this kind of pause,
I guess you could say.

00:03:42.040 --> 00:03:43.690
And Voyager 1 and
Voyager 2, as I said,

00:03:43.690 --> 00:03:46.430
have essentially gotten pretty
close to, people believe,

00:03:46.430 --> 00:03:48.540
that pause over there.

00:03:48.540 --> 00:03:51.350
And so that's one view of the
edges of the solar system.

00:03:51.350 --> 00:03:53.510
There's never going to
be any hard edge to it.

00:03:53.510 --> 00:03:57.500
Another view would be something
like the Oort Cloud, the area

00:03:57.500 --> 00:04:01.450
where you have the
still objects out there.

00:04:01.450 --> 00:04:04.160
And actually we haven't
directly observed

00:04:04.160 --> 00:04:05.400
objects in the Ort Cloud.

00:04:05.400 --> 00:04:08.120
We think that they
are out there.

00:04:08.120 --> 00:04:10.170
And then maybe the most
abstract definition

00:04:10.170 --> 00:04:14.750
would be a significant
influence from the Sun's

00:04:14.750 --> 00:04:15.990
gravitational pull.

00:04:15.990 --> 00:04:18.420
So all of those
ways are to imagine

00:04:18.420 --> 00:04:20.000
the extent of the solar system.

00:04:20.000 --> 00:04:22.510
But they all kind of leave a
grey area for what is and what

00:04:22.510 --> 00:04:24.111
is not in the solar system.

00:04:24.111 --> 00:04:25.860
But my whole point
here, what I want to do

00:04:25.860 --> 00:04:28.330
is start exploring a little
bit outside of the solar system

00:04:28.330 --> 00:04:30.530
and just give you a
sense of the scale

00:04:30.530 --> 00:04:33.560
as we just go to
the closest star.

00:04:33.560 --> 00:04:36.030
So if we go right
over here, this

00:04:36.030 --> 00:04:40.471
shows our local neighborhood
from a stellar point of view.

00:04:40.471 --> 00:04:42.970
And even though these stars
look pretty big, if you actually

00:04:42.970 --> 00:04:48.260
were to draw-- this is our
solar system right here.

00:04:48.260 --> 00:04:50.400
And you might be saying,
oh, maybe that's the Sun.

00:04:50.400 --> 00:04:50.480
No.

00:04:50.480 --> 00:04:52.142
The Sun, if you were
to draw it here,

00:04:52.142 --> 00:04:53.600
it wouldn't even
make up one pixel.

00:04:53.600 --> 00:04:58.010
In fact, the entire orbit of
Pluto, everything inside of it,

00:04:58.010 --> 00:05:03.980
still would not make up one
pixel on the screen right here.

00:05:03.980 --> 00:05:08.210
What we see right here,
which is a radius-- it's

00:05:08.210 --> 00:05:12.360
roughly a radius of about
give or take a light year--

00:05:12.360 --> 00:05:17.170
this is roughly maybe the
radius of the Oort Cloud.

00:05:17.170 --> 00:05:18.750
And we saw in the
last video, how

00:05:18.750 --> 00:05:27.220
huge that was, especially
relative to the radius of

00:05:27.220 --> 00:05:30.820
say Pluto's orbit, which
is roughly like that.

00:05:30.820 --> 00:05:36.000
And that itself is a huge, huge
diameter or a huge distance

00:05:36.000 --> 00:05:37.420
away from the Sun.

00:05:37.420 --> 00:05:39.360
And that wouldn't
even make a pixel.

00:05:39.360 --> 00:05:42.220
That wouldn't even make
a pixel on this diagram

00:05:42.220 --> 00:05:43.670
right over here.

00:05:43.670 --> 00:05:48.810
But just to give you an
idea of how far we are-- so

00:05:48.810 --> 00:05:52.290
we're a speck of a speck
of a speck inside here,

00:05:52.290 --> 00:05:54.380
of a pixel of a
pixel in the center

00:05:54.380 --> 00:05:56.920
here-- to make it
from our solar system,

00:05:56.920 --> 00:05:59.190
or in particular
from Earth maybe,

00:05:59.190 --> 00:06:02.315
to the nearest star or
maybe the nearest cluster

00:06:02.315 --> 00:06:04.310
of stars, the Alpha Centauri.

00:06:04.310 --> 00:06:06.770
They're the nearest
cluster of stars.

00:06:06.770 --> 00:06:09.200
There's three stars,
Alpha Centauri A,

00:06:09.200 --> 00:06:11.330
which is the largest;
Alpha Centauri B;

00:06:11.330 --> 00:06:13.300
and then, there's one
that you can't observe

00:06:13.300 --> 00:06:15.820
with the naked eye,
Alpha Proximus.

00:06:15.820 --> 00:06:17.850
Or I think it's
Proximus Centauri,

00:06:17.850 --> 00:06:20.310
I think is what it's called,
not Alpha Proximus, Proximus

00:06:20.310 --> 00:06:20.810
Centauri.

00:06:20.810 --> 00:06:22.820
But that's a much smaller star.

00:06:22.820 --> 00:06:25.770
But that's the
closest star-- well,

00:06:25.770 --> 00:06:29.490
you could view it as this whole
cluster of stars right here.

00:06:29.490 --> 00:06:36.400
And they're the closest-- is
about 4.2 light years away.

00:06:36.400 --> 00:06:37.920
Or another way to
think about it,

00:06:37.920 --> 00:06:40.680
if someone were to shine a
light on one of these planets,

00:06:40.680 --> 00:06:42.780
and assuming that
light could get to us,

00:06:42.780 --> 00:06:44.900
it would take 4.2
years to get to us.

00:06:44.900 --> 00:06:46.990
Or if these guys just
disappeared or blew up,

00:06:46.990 --> 00:06:49.419
we wouldn't know
it for 4.2 years.

00:06:49.419 --> 00:06:51.210
And you might say, hey,
that's not too bad.

00:06:51.210 --> 00:06:54.010
We should take a trip over
there and check them out,

00:06:54.010 --> 00:06:55.968
see if there are any
other people there that we

00:06:55.968 --> 00:07:00.380
can meet and exchange
technologies with, or whatnot.

00:07:00.380 --> 00:07:02.200
But this is a huge distance.

00:07:02.200 --> 00:07:06.320
Just this 4.2 light years is
an unbelievably ridiculous

00:07:06.320 --> 00:07:06.820
distance.

00:07:06.820 --> 00:07:10.424
And just to give you a
sense, the Voyager 1 and 2,

00:07:10.424 --> 00:07:11.840
we talked about
in the last video,

00:07:11.840 --> 00:07:13.730
and we can even see
how far they've gotten.

00:07:13.730 --> 00:07:17.210
They've gotten to pretty
much to the heliopause.

00:07:17.210 --> 00:07:26.030
These guys are traveling at
60,000 kilometers an hour,

00:07:26.030 --> 00:07:29.165
which is the same thing as
17 kilometers per second.

00:07:31.980 --> 00:07:34.260
If we were able to get up
to those type of velocities,

00:07:34.260 --> 00:07:36.460
and these guys got up to
those type of velocities

00:07:36.460 --> 00:07:40.170
by leveraging the gravitational
pull of some of the larger

00:07:40.170 --> 00:07:42.250
planets to accelerate
and keep accelerating.

00:07:42.250 --> 00:07:45.330
So this is a pretty hard
velocity to actually reach.

00:07:45.330 --> 00:07:48.420
But if you were able
to reach that velocity

00:07:48.420 --> 00:07:53.670
and go straight in the direction
of the direction of the Alpha

00:07:53.670 --> 00:07:59.550
Centauri system, the
closest stars to Earth,

00:07:59.550 --> 00:08:05.060
it would take you
80,000 years traveling

00:08:05.060 --> 00:08:07.990
at the same velocity
as Voyager 1,

00:08:07.990 --> 00:08:09.870
which is the fastest
of the Voyagers.

00:08:09.870 --> 00:08:12.080
So it's a ridiculously
long time.

00:08:12.080 --> 00:08:16.591
So we're going to figure out
some better way to do that.


Scale of solar system

WEBVTT
Kind: captions
Language: en

00:00:00.660 --> 00:00:02.170
Where we left off
in the last video,

00:00:02.170 --> 00:00:04.420
I think we were getting a
reasonably good appreciation

00:00:04.420 --> 00:00:07.910
for how huge the
sun is, especially

00:00:07.910 --> 00:00:12.110
relative to the Earth, and
how far the Earth is away

00:00:12.110 --> 00:00:12.750
from the sun.

00:00:12.750 --> 00:00:16.180
That most of these diagrams that
we see in science textbooks--

00:00:16.180 --> 00:00:17.590
they don't give justice.

00:00:17.590 --> 00:00:20.550
In fact, when I showed
this sun over here

00:00:20.550 --> 00:00:22.650
that was about five
or six inches across,

00:00:22.650 --> 00:00:27.242
I said Earth would be just this
little speck, about 40 feet.

00:00:27.242 --> 00:00:28.450
It wouldn't be this distance.

00:00:28.450 --> 00:00:30.574
It would be about 40 feet
to the left or the right.

00:00:30.574 --> 00:00:35.119
Or its orbit would have a
radius of about 40 feet.

00:00:35.119 --> 00:00:36.535
You wouldn't even
notice it if you

00:00:36.535 --> 00:00:38.070
were looking at this
thing over here.

00:00:38.070 --> 00:00:39.653
It would be this
little speck orbiting

00:00:39.653 --> 00:00:42.030
at this huge, huge distance.

00:00:42.030 --> 00:00:44.682
If you look at
this sun over here,

00:00:44.682 --> 00:00:46.140
if I were to draw
the whole sun, it

00:00:46.140 --> 00:00:49.490
looks like it would have a
diameter of about 20 inches.

00:00:49.490 --> 00:00:53.330
So in this situation, this
Earth right here-- and this

00:00:53.330 --> 00:00:55.530
is drawn to scale--
this Earth would not

00:00:55.530 --> 00:00:56.960
be anywhere near this close.

00:00:56.960 --> 00:01:02.690
It would be about 200
feet that way, or about 60

00:01:02.690 --> 00:01:06.040
or 70 meters, 60 meters.

00:01:06.040 --> 00:01:08.700
So you can imagine if the
sun was this size, sitting

00:01:08.700 --> 00:01:10.460
on something like
a football field,

00:01:10.460 --> 00:01:13.880
this little speck of an Earth,
this little thing right here,

00:01:13.880 --> 00:01:19.440
would be sitting on the other
40-yard line, 60 meters away.

00:01:19.440 --> 00:01:21.350
So you wouldn't even notice it.

00:01:21.350 --> 00:01:23.050
You might notice
this from a distance,

00:01:23.050 --> 00:01:25.030
but you wouldn't even
see this thing over here.

00:01:25.030 --> 00:01:26.830
And the other planets
are even further.

00:01:26.830 --> 00:01:27.850
Well, not all of
the other planets.

00:01:27.850 --> 00:01:29.016
Obviously, you have Mercury.

00:01:31.850 --> 00:01:33.779
I think most of us are
familiar with these.

00:01:33.779 --> 00:01:35.570
But I'll just list them
here, just in case.

00:01:35.570 --> 00:01:37.080
That's Mercury.

00:01:37.080 --> 00:01:38.160
This is Venus.

00:01:38.160 --> 00:01:40.550
Mercury is the smallest of
the planets where it's not

00:01:40.550 --> 00:01:41.850
debated whether it's a planet.

00:01:41.850 --> 00:01:44.390
Pluto is the smallest,
but some people

00:01:44.390 --> 00:01:46.720
debate whether it's
really a planet or just

00:01:46.720 --> 00:01:48.969
a large solar body
or a dwarf planet

00:01:48.969 --> 00:01:50.260
or any of those type of things.

00:01:50.260 --> 00:01:53.719
But then you have Venus,
probably the closest in size

00:01:53.719 --> 00:01:54.260
to the Earth.

00:01:54.260 --> 00:01:56.430
Or it is the closest
in size to the Earth.

00:01:56.430 --> 00:01:59.590
And then you have Mars.

00:01:59.590 --> 00:02:00.870
And then you have Jupiter.

00:02:00.870 --> 00:02:02.600
And just to give a
sense of, once again,

00:02:02.600 --> 00:02:05.550
how far these things
are, if I were to go back

00:02:05.550 --> 00:02:08.720
to the analogy of this
being the size of the sun,

00:02:08.720 --> 00:02:11.360
then Jupiter is five
times further than Earth.

00:02:11.360 --> 00:02:15.340
So this would be-- If I were to
actually do the scale distance,

00:02:15.340 --> 00:02:19.730
this would be 300 meters away.

00:02:19.730 --> 00:02:23.760
So if I had a nice, big,
maybe medicine-balled-size sun

00:02:23.760 --> 00:02:25.567
right over here, maybe
basketball-sized.

00:02:25.567 --> 00:02:27.150
A little bit bigger
than a basketball,

00:02:27.150 --> 00:02:31.240
this looks on my screen--
then this little thing

00:02:31.240 --> 00:02:33.260
that's smaller than
a ping pong ball,

00:02:33.260 --> 00:02:36.600
I would put this three
football fields away.

00:02:36.600 --> 00:02:38.670
That's how far Jupiter is.

00:02:38.670 --> 00:02:40.990
And then Saturn's about
twice as far as that.

00:02:40.990 --> 00:02:42.980
Saturn is about nine
times the distance.

00:02:42.980 --> 00:02:45.180
So let me make it clear.

00:02:45.180 --> 00:02:48.220
The Earth is one astronomical
unit away from the sun,

00:02:48.220 --> 00:02:48.720
roughly.

00:02:48.720 --> 00:02:49.880
Its distance changes.

00:02:49.880 --> 00:02:53.030
It's not a perfectly
circular orbit.

00:02:53.030 --> 00:02:55.950
Jupiter is approximately
a little bit--

00:02:55.950 --> 00:02:58.830
5 plus astronomical
units-- a little bit

00:02:58.830 --> 00:03:00.560
more than five
times the distance

00:03:00.560 --> 00:03:02.140
of the sun to the Earth.

00:03:02.140 --> 00:03:07.210
And Saturn is approximately
nine astronomical units,

00:03:07.210 --> 00:03:11.440
or nine times the distance
from the sun to the Earth.

00:03:11.440 --> 00:03:13.732
So once again, this would be
nine football fields away.

00:03:13.732 --> 00:03:16.023
Or another way to think about
it would be, essentially,

00:03:16.023 --> 00:03:16.840
a kilometer away.

00:03:16.840 --> 00:03:20.380
If we had kind of a
medicine-ball-size sun,

00:03:20.380 --> 00:03:22.720
this little smaller
than a ping pong

00:03:22.720 --> 00:03:26.277
balled Saturn would
be a kilometer away.

00:03:26.277 --> 00:03:27.735
And I just want to
really reiterate

00:03:27.735 --> 00:03:30.090
that because you never
visualize it that way.

00:03:30.090 --> 00:03:31.554
Because just for
the sake of being

00:03:31.554 --> 00:03:32.970
able to draw it
on a page, you see

00:03:32.970 --> 00:03:35.990
diagrams that look like this.

00:03:35.990 --> 00:03:38.880
And they really don't give
you a sense of how small

00:03:38.880 --> 00:03:40.850
these planets are
relative to the sun,

00:03:40.850 --> 00:03:45.460
and especially relative to
their distance from the sun.

00:03:45.460 --> 00:03:52.340
And then after Saturn, you
have Uranus and then Neptune.

00:03:58.000 --> 00:03:59.850
And obviously, these
guys are even further.

00:03:59.850 --> 00:04:01.550
And just to give
you a sense, it's

00:04:01.550 --> 00:04:05.960
very easy to start talking about
galaxies and universes and all

00:04:05.960 --> 00:04:07.750
of the-- or the universe.

00:04:07.750 --> 00:04:09.870
But I really just
want to get-- already,

00:04:09.870 --> 00:04:12.720
what we've talked about, we're
talking about huge distances,

00:04:12.720 --> 00:04:14.720
huge scale.

00:04:14.720 --> 00:04:17.410
We already talked about that it
would take a jet plane 17 years

00:04:17.410 --> 00:04:19.850
to travel from the
Earth to the sun.

00:04:19.850 --> 00:04:22.150
Multiply that by
five, about 100 years

00:04:22.150 --> 00:04:24.940
to go from Jupiter
to the sun, 200 years

00:04:24.940 --> 00:04:27.140
to go from Saturn to the sun.

00:04:27.140 --> 00:04:31.140
So you could have had Abraham
Lincoln get into a jet plane,

00:04:31.140 --> 00:04:34.270
and if he left from
Saturn, he still

00:04:34.270 --> 00:04:36.050
would not have
gotten to the sun.

00:04:36.050 --> 00:04:37.931
So these are huge,
huge distances.

00:04:37.931 --> 00:04:39.930
But we're not done with
the solar system, there.

00:04:39.930 --> 00:04:44.590
Just to give a sense of
scale-- so this right here,

00:04:44.590 --> 00:04:45.430
that's the sun.

00:04:45.430 --> 00:04:47.220
And each of these
planets are actually

00:04:47.220 --> 00:04:48.520
narrower than these orbits.

00:04:48.520 --> 00:04:50.020
So they just draw
these orbits here,

00:04:50.020 --> 00:04:52.460
but you wouldn't actually
even see the actual planets

00:04:52.460 --> 00:04:54.160
here at this type of a scale.

00:04:54.160 --> 00:04:56.670
But this is one astronomical
unit right over here,

00:04:56.670 --> 00:04:59.260
the distance from
the sun to the Earth.

00:04:59.260 --> 00:05:00.240
Then you have Mars.

00:05:00.240 --> 00:05:02.790
Then you have the asteroid belt.

00:05:02.790 --> 00:05:06.644
There you have
the asteroid belt,

00:05:06.644 --> 00:05:08.810
which also has some pretty
big things in it, itself.

00:05:08.810 --> 00:05:11.570
And it has these things that
are kind of considered almost

00:05:11.570 --> 00:05:13.040
dwarf planets,
things like Ceres.

00:05:13.040 --> 00:05:14.540
You could look those
type things up.

00:05:14.540 --> 00:05:16.582
And then you have
Jupiter out here.

00:05:16.582 --> 00:05:19.040
And once again, we said it
would take 100 years, or roughly

00:05:19.040 --> 00:05:23.720
100 years, for a jet plane to
get from Jupiter to the sun.

00:05:23.720 --> 00:05:25.340
But even if you
take this whole box

00:05:25.340 --> 00:05:28.410
here-- which is a huge amount
of distance, of roughly about

00:05:28.410 --> 00:05:33.230
five astronomical units-- it
would take about 40 minutes

00:05:33.230 --> 00:05:37.230
for light to get from
the sun to Jupiter.

00:05:37.230 --> 00:05:40.150
So this is a huge,
huge distance.

00:05:40.150 --> 00:05:42.140
But even this huge
distance-- we can put it

00:05:42.140 --> 00:05:44.050
into this little
box right over here.

00:05:46.670 --> 00:05:55.104
So this whole box right over
there can be fit into this box.

00:05:55.104 --> 00:05:57.020
And you need to do that
in order to appreciate

00:05:57.020 --> 00:05:59.140
the orbits of the outer planets.

00:05:59.140 --> 00:06:03.494
And so on this scale, Earth
and Venus and Mercury and Mars,

00:06:03.494 --> 00:06:05.410
their orbits look pretty
much-- you can't even

00:06:05.410 --> 00:06:07.420
differentiate them from the sun.

00:06:07.420 --> 00:06:08.284
They look so close.

00:06:08.284 --> 00:06:09.700
They almost look
like they're part

00:06:09.700 --> 00:06:11.574
of the sun when you look
at it on this scale.

00:06:11.574 --> 00:06:13.710
And then you have you
have the outer planets--

00:06:13.710 --> 00:06:15.950
Saturn, Uranus, Neptune.

00:06:15.950 --> 00:06:17.830
And they we have a Kuiper belt.

00:06:17.830 --> 00:06:21.967
And this is more asteroids, but
these are kind of more frozen.

00:06:21.967 --> 00:06:24.300
And when we think of ice, you
always think of water ice.

00:06:24.300 --> 00:06:25.890
But out here, it's so cold.

00:06:25.890 --> 00:06:27.980
And it's relatively
getting dark, now,

00:06:27.980 --> 00:06:29.620
because we're pretty
far from the sun

00:06:29.620 --> 00:06:31.994
that things that we normally
associate as gases are going

00:06:31.994 --> 00:06:33.600
to be in their
solid form out here.

00:06:33.600 --> 00:06:36.280
So this isn't just
rocky elements.

00:06:36.280 --> 00:06:39.150
This will also be things that
we normally associate as gases,

00:06:39.150 --> 00:06:41.370
like methane, frozen methane.

00:06:41.370 --> 00:06:42.700
But even here, we're not done.

00:06:42.700 --> 00:06:46.270
We're not even out of
the solar system yet.

00:06:46.270 --> 00:06:49.820
And actually, just to give
you a sense of the scale we're

00:06:49.820 --> 00:06:52.040
operating right here, I
have this chart right here

00:06:52.040 --> 00:06:53.310
from the Voyager mission.

00:06:53.310 --> 00:06:55.880
So the Voyager missions--
Voyager 1 and 2-- actually,

00:06:55.880 --> 00:06:58.600
Voyager 2 left a little bit
earlier, a month earlier.

00:06:58.600 --> 00:07:00.700
Voyager 1 is just
traveling faster.

00:07:00.700 --> 00:07:04.977
They left about a
year after I was born

00:07:04.977 --> 00:07:06.810
And their current
velocity, just to give you

00:07:06.810 --> 00:07:12.480
a sense of how fast--
Voyager 1 right here is right

00:07:12.480 --> 00:07:19.340
now traveling at 61,000
kilometers per hour.

00:07:19.340 --> 00:07:23.105
That's about 17
kilometers per second.

00:07:23.105 --> 00:07:25.950
The size of a city every
second-- it's going that fast.

00:07:25.950 --> 00:07:31.060
That's, at least in my mind,
an unfathomably fast velocity.

00:07:31.060 --> 00:07:33.120
This thing has been
traveling roughly that fast.

00:07:33.120 --> 00:07:36.209
It's been going around planets
and gaining acceleration

00:07:36.209 --> 00:07:37.250
as it went around orbits.

00:07:37.250 --> 00:07:38.540
But for most of
the time, it's been

00:07:38.540 --> 00:07:39.910
going at a pretty fast speed.

00:07:39.910 --> 00:07:42.057
And just to translate
it to people

00:07:42.057 --> 00:07:43.640
who don't relate to
kilometers, that's

00:07:43.640 --> 00:07:50.390
about 38,000 miles per hour,
so this huge, huge unfathomably

00:07:50.390 --> 00:07:51.640
fast speed.

00:07:51.640 --> 00:07:55.570
And it's been doing
it since 1977.

00:07:55.570 --> 00:07:57.342
I was learning to walk.

00:07:57.342 --> 00:07:58.800
And when I was
learning to walk, it

00:07:58.800 --> 00:08:00.920
was traveling at this
super fast speed.

00:08:00.920 --> 00:08:04.174
And then when I was learning
to talk-- our whole lives,

00:08:04.174 --> 00:08:06.090
when we're sleeping,
everything, we're eating,

00:08:06.090 --> 00:08:09.190
I'm in elementary school--
it's still rocketing out

00:08:09.190 --> 00:08:11.592
of the solar system
at roughly this speed.

00:08:11.592 --> 00:08:13.300
Its velocity has
changed, but especially,

00:08:13.300 --> 00:08:15.150
once it got outside
of the planets,

00:08:15.150 --> 00:08:17.750
it's been roughly
at this velocity.

00:08:17.750 --> 00:08:19.370
So it's just been rocketing out.

00:08:19.370 --> 00:08:24.111
And I don't want to say only,
but it's gotten this far.

00:08:24.111 --> 00:08:25.610
If we look at it
on this scale, it's

00:08:25.610 --> 00:08:28.160
gotten about that
far right there.

00:08:28.160 --> 00:08:32.011
It's about 115, 116
astronomical units.

00:08:32.011 --> 00:08:34.510
And to give a sense-- so there's
two ways to think about it.

00:08:34.510 --> 00:08:36.770
One says, like, wow,
that's really far.

00:08:36.770 --> 00:08:39.000
Because we know that
even on this scale,

00:08:39.000 --> 00:08:40.650
you can't even
see Earth's orbit.

00:08:40.650 --> 00:08:43.309
So this looks like it's a
pretty, pretty far distance.

00:08:43.309 --> 00:08:47.200
And just to give you a sense of
how far 116 astronomical units

00:08:47.200 --> 00:08:52.140
are, if 2,000 years ago,
Jesus got on a plane--

00:08:52.140 --> 00:08:54.210
I actually cut and
pasted a copy of Jesus,

00:08:54.210 --> 00:08:56.000
just for visualization
purposes--

00:08:56.000 --> 00:08:59.880
but if he'd got on a jet liner
at 1,000 kilometers per hour

00:08:59.880 --> 00:09:01.580
and went straight
in that direction,

00:09:01.580 --> 00:09:05.110
in the direction that Voyager,
Voyager would only just now be

00:09:05.110 --> 00:09:06.900
catching up to Jesus.

00:09:06.900 --> 00:09:09.877
So this is a huge, huge,
huge, huge distance.

00:09:09.877 --> 00:09:11.460
But at the same time,
even though it's

00:09:11.460 --> 00:09:13.640
a huge distance, especially
relative to everything

00:09:13.640 --> 00:09:15.890
else we've talked about,
relative to just even

00:09:15.890 --> 00:09:18.030
the outer reaches
of the solar system,

00:09:18.030 --> 00:09:21.770
we're still talking in
terms of a small scale.

00:09:21.770 --> 00:09:24.250
So that's how far Voyager is.

00:09:24.250 --> 00:09:27.020
And just to give a sense, on
this scale-- so this whole box

00:09:27.020 --> 00:09:32.534
over here can be
contained in this box.

00:09:32.534 --> 00:09:34.200
And when you look at
this box, Voyager's

00:09:34.200 --> 00:09:39.850
only gotten about that
far after traveling

00:09:39.850 --> 00:09:44.440
at this unbelievable
velocity for over 30 years,

00:09:44.440 --> 00:09:45.464
for about 33 years.

00:09:45.464 --> 00:09:47.880
And just to give you an idea
of these other things, Sedna,

00:09:47.880 --> 00:09:53.730
right here, is a reasonably
large-sized outer solar system

00:09:53.730 --> 00:09:54.440
object.

00:09:54.440 --> 00:09:56.710
It's one of the
furthest objects that we

00:09:56.710 --> 00:09:58.310
know of in the solar system.

00:09:58.310 --> 00:10:00.190
And it has this very
eccentric orbit.

00:10:00.190 --> 00:10:02.900
So it gets-- I don't want to
say relatively close, but not

00:10:02.900 --> 00:10:05.280
unreasonably far away.

00:10:05.280 --> 00:10:09.140
And then it gets really
far away from the sun.

00:10:09.140 --> 00:10:11.970
But even Sedna's orbit-- so
if I were to look at this,

00:10:11.970 --> 00:10:17.180
so this whole box over here can
be contained right over here.

00:10:17.180 --> 00:10:19.212
So in this diagram
right here, you

00:10:19.212 --> 00:10:20.420
wouldn't even be able to see.

00:10:20.420 --> 00:10:22.630
It would be like a
speck how far Voyager

00:10:22.630 --> 00:10:27.950
has traveled in 33 years
at 38,000 miles per hour.

00:10:27.950 --> 00:10:30.770
You would not even
be able to notice.

00:10:30.770 --> 00:10:33.380
You wouldn't even
notice that distance.

00:10:33.380 --> 00:10:35.640
And even though you can't
even notice that distance,

00:10:35.640 --> 00:10:39.010
we still have the
sun's influence.

00:10:39.010 --> 00:10:42.360
The gravitational pull is
still attracting things to it.

00:10:42.360 --> 00:10:45.470
And this right
here, we speculate

00:10:45.470 --> 00:10:46.740
that there is the Oort cloud.

00:10:46.740 --> 00:10:48.573
And this is where the
comets originate from.

00:10:48.573 --> 00:10:51.670
And this is just a
bunch of frozen gases

00:10:51.670 --> 00:10:54.650
and ice particles
and things like that.

00:10:54.650 --> 00:10:57.840
But we're starting to
get to the outer reaches

00:10:57.840 --> 00:10:58.960
of the solar system.

00:10:58.960 --> 00:11:04.960
And this distance right here
is about 50,000 astronomical

00:11:04.960 --> 00:11:05.460
units.

00:11:07.807 --> 00:11:09.390
And just to give a
scale-- because you

00:11:09.390 --> 00:11:11.900
hear a lot about light years
and all of that-- light years

00:11:11.900 --> 00:11:14.800
are about 63,000
astronomical units.

00:11:14.800 --> 00:11:19.320
So if you go a light
year out from the sun,

00:11:19.320 --> 00:11:24.670
you'll end up in the Oort cloud,
the hypothesized Oort cloud.

00:11:24.670 --> 00:11:26.910
And just to give a
sense, another scale,

00:11:26.910 --> 00:11:30.210
the Oort cloud is actually--
most of the planets' orbits

00:11:30.210 --> 00:11:32.130
are roughly in the same plane.

00:11:32.130 --> 00:11:34.560
But this right here is
the orbit of the planets.

00:11:34.560 --> 00:11:36.610
And once again, these
lines are drawn too thick.

00:11:36.610 --> 00:11:38.200
They're just drawn the
thinnest possible so

00:11:38.200 --> 00:11:40.575
that you can see them, but
they're still drawn too thick.

00:11:40.575 --> 00:11:42.820
And this gets us all the
way to the Kuiper belt.

00:11:42.820 --> 00:11:45.030
But all of this over
here, so all the way

00:11:45.030 --> 00:11:46.840
out to the Kuiper
belt, all the way out

00:11:46.840 --> 00:11:48.850
to all of the major
planets-- this

00:11:48.850 --> 00:11:52.760
is Pluto's orbit
right over here.

00:11:52.760 --> 00:11:56.750
This whole diagram is only
sitting in right over there.

00:11:56.750 --> 00:11:57.900
You can barely see it.

00:11:57.900 --> 00:12:00.720
This whole diagram is
just that dot in this.

00:12:00.720 --> 00:12:02.922
And then you can see the
Oort cloud all around it.

00:12:02.922 --> 00:12:04.380
And it's more of
a spherical cloud.

00:12:04.380 --> 00:12:05.338
And we think it exists.

00:12:05.338 --> 00:12:08.430
Obviously, it's hard to observe
things at that distance.

00:12:08.430 --> 00:12:11.180
So hopefully, that gives
you a beginning sense

00:12:11.180 --> 00:12:12.555
of the scale of
the solar system.

00:12:12.555 --> 00:12:14.971
And what's really going to
blow your mind-- if this hasn't

00:12:14.971 --> 00:12:17.320
blown your mind already--
is that this whole thing's

00:12:17.320 --> 00:12:19.040
going to start
looking like a speck.

00:12:19.040 --> 00:12:21.950
When you even just look at the
local area around our galaxy,

00:12:21.950 --> 00:12:25.220
much less the galaxy, much
less the universe as a whole.

00:12:25.220 --> 00:12:27.530
Anyway, I don't want
to get-- well, anyway.

00:12:27.530 --> 00:12:30.540
This is starting to get crazy.


ANOVA 3: Hypothesis test with F-statistic

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:06.400
In the last couple of videos we first figured out the TOTAL variation in these 9 data points right here

00:00:06.400 --> 00:00:11.533
and we got 30, that's our Total Sum of Squares. Then we asked ourselves,

00:00:11.533 --> 00:00:19.533
how much of that variation is due to variation WITHIN each of these groups, versus variation BETWEEN the groups themselves?

00:00:19.533 --> 00:00:24.933
So, for the variation within the groups we have our Sum of Squares within.

00:00:24.933 --> 00:00:26.933
And there we got 6.

00:00:26.933 --> 00:00:32.533
And then the balance of this, 30, the balance of this variation,

00:00:32.533 --> 00:00:36.333
came from variation between the groups, and we calculated it,

00:00:36.333 --> 00:00:39.867
We got 24.

00:00:39.867 --> 00:00:43.600
What I want to do in this video, is actually use this type of information,

00:00:43.600 --> 00:00:49.267
essentially these statistics we've calculated, to do some inferential statistics,

00:00:49.267 --> 00:00:53.200
to come to some time of conclusion, or maybe not to come to some type of conclusion.

00:00:53.200 --> 00:00:56.867
What I want to do is to put some context around these groups.

00:00:56.867 --> 00:01:00.267
We've been dealing with them abstractly right now, but you can imagine

00:01:00.267 --> 00:01:03.133
these are the results of some type of experiment.

00:01:03.133 --> 00:01:11.867
Let's say that I gave 3 different types of pills or 3 different types of food to people taking a test.

00:01:11.867 --> 00:01:13.933
And these are the scores on the test.

00:01:13.933 --> 00:01:25.333
So this is food 1, food 2, and then this over here is food 3.

00:01:25.333 --> 00:01:33.400
And I want to figure out if the type of food people take going into the test really affect their scores?

00:01:33.400 --> 00:01:40.267
If you look at these means, it looks like they perform best in group 3, than in group 2 or 1.

00:01:40.267 --> 00:01:44.733
But is that difference purely random? Random chance?

00:01:44.733 --> 00:01:50.600
Or can I be pretty confident that it's due to actual differences

00:01:50.600 --> 00:01:56.867
in the population means, of all of the people who would ever take food 3 vs food 2 vs food 1?

00:01:56.867 --> 00:02:03.733
So, my question here is, are the means and the true population means the same?

00:02:03.733 --> 00:02:10.333
This is a sample mean based on 3 samples. But if I knew the true population means--

00:02:10.333 --> 00:02:17.800
So my question is: Is the mean of the population of people taking Food 1 equal to the mean of Food 2?

00:02:17.800 --> 00:02:22.000
Obviously I'll never be able to give that food to every human being that could

00:02:22.000 --> 00:02:25.667
ever live and then make them all take an exam.

00:02:25.667 --> 00:02:30.000
But there is some true mean there, it's just not really measurable.

00:02:30.000 --> 00:02:35.667
So my question is "this" equal to "this" equal to the mean 3, the true population of mean 3.

00:02:35.667 --> 00:02:38.933
And my question is, are these equal?

00:02:38.933 --> 00:02:47.800
Because if they're not equal, that means that the type of food given does have some type of impact

00:02:47.800 --> 00:02:50.067
on how people perform on a test.

00:02:50.067 --> 00:02:55.000
So let's do a little hypothesis test here. Let's say that my null hypothesis

00:02:55.000 --> 00:03:01.267
is that the means are the same. Food doesn't make a difference.

00:03:01.267 --> 00:03:07.200
"food doesn't make a difference"

00:03:07.200 --> 00:03:17.000
and that my Alternate hypothesis is that it does. "It does."

00:03:17.000 --> 00:03:19.000
and the way of thinking about this quantitatively

00:03:19.000 --> 00:03:20.933
is that if it doesn't make a difference,

00:03:20.933 --> 00:03:24.000
the true population means of the groups will be the same.

00:03:24.000 --> 00:03:28.733
The true population mean of the group that took food 1 will be the same

00:03:28.733 --> 00:03:35.400
as the group that took food 2, which will be the same as the group that took food 3.

00:03:35.400 --> 00:03:40.867
If our alternate hypothesis is correct, then these means will not be all the same.

00:03:40.867 --> 00:03:43.067
How can we test this hypothesis?

00:03:43.067 --> 00:03:47.200
So we're going to assume the null hypothesis, which is

00:03:47.200 --> 00:03:49.800
what we always do when we are hypothesis testing,

00:03:49.800 --> 00:03:52.600
we're going to assume our null hypothesis.

00:03:52.600 --> 00:03:56.267
And then essentially figure out, what are the chances

00:03:56.267 --> 00:03:59.267
of getting a certain statistic this extreme?

00:03:59.267 --> 00:04:01.200
And I haven't even defined what that statistic is.

00:04:01.200 --> 00:04:05.267
So we're going to define--we're going to assume our null hypothesis,

00:04:05.267 --> 00:04:08.667
and then we're going to come up with a statistic called the F statistic.

00:04:08.667 --> 00:04:11.933
So our F statistic

00:04:11.933 --> 00:04:16.600
which has an F distribution--and we won't go real deep into the details of

00:04:16.600 --> 00:04:19.067
the F distribution. But you can already start to think of it

00:04:19.067 --> 00:04:23.800
as the ratio of two Chi-squared distributions that may or may not have different degrees of freedom.

00:04:23.800 --> 00:04:31.933
Our F statistic is going to be the ratio of our Sum of Squares between the samples--

00:04:31.933 --> 00:04:37.067
Sum of Squares between

00:04:37.067 --> 00:04:41.733
divided by, our degrees of freedom between

00:04:41.733 --> 00:04:46.333
and this is sometimes called the mean squares between, MSB,

00:04:46.333 --> 00:04:52.333
that, divided by the Sum of Squares within,

00:04:52.333 --> 00:04:56.533
so that's what I had done up here, the SSW in blue,

00:04:56.533 --> 00:05:01.133
divided by the SSW

00:05:01.133 --> 00:05:07.800
divided by the degrees of freedom of the SSwithin, and that was

00:05:07.800 --> 00:05:12.267
m (n-1). Now let's just think about what this is doing right here.

00:05:12.267 --> 00:05:18.333
If this number, the numerator, is much larger than the denominator,

00:05:18.333 --> 00:05:27.333
then that tells us that the variation in this data is due mostly

00:05:27.333 --> 00:05:31.600
to the differences between the actual means

00:05:31.600 --> 00:05:35.933
and its due less to the variation within the means.

00:05:35.933 --> 00:05:40.867
That's if this numerator is much bigger than this denominator over here.

00:05:40.867 --> 00:05:45.733
So that should make us believe that there is a difference

00:05:45.733 --> 00:05:47.200
in the true population mean.

00:05:47.200 --> 00:05:48.733
So if this number is really big,

00:05:48.733 --> 00:05:51.333
it should tell us that there is a lower probability

00:05:51.333 --> 00:05:53.600
that our null hypothesis is correct.

00:05:53.600 --> 00:05:58.533
If this number is really small and our denominator is larger,

00:05:58.533 --> 00:06:02.067
that means that our variation within each sample,

00:06:02.067 --> 00:06:05.467
makes up more of the total variation than our variation between

00:06:05.467 --> 00:06:07.333
the samples. So that means that our variation

00:06:07.333 --> 00:06:12.733
within each of these samples is a bigger percentage of the total variation

00:06:12.733 --> 00:06:15.200
versus the variation between the samples.

00:06:15.200 --> 00:06:17.800
So that would make us believe that "hey! ya know... any difference

00:06:17.800 --> 00:06:21.000
we see between the means is probably just random."

00:06:21.000 --> 00:06:24.400
And that would make it a little harder to reject the null.

00:06:24.400 --> 00:06:26.867
So let's actually calculate it.

00:06:26.867 --> 00:06:34.200
So in this case, our SSbetween, we calculated over here, was 24.

00:06:34.200 --> 00:06:37.933
and we had 2 degrees of freedom.

00:06:37.933 --> 00:06:49.800
And our SSwithin was 6 and we had how many degrees of freedom?

00:06:49.800 --> 00:06:52.667
Also, 6. 6 degrees of freedom.

00:06:52.667 --> 00:06:58.600
So this is going to be 24/2 which is 12, divided by 1.

00:06:58.600 --> 00:07:05.867
Our F statistic that we've calculated is going to be 12.

00:07:05.867 --> 00:07:10.867
F stands for Fischer who is the biologist and statistician who came up with this.

00:07:10.867 --> 00:07:15.267
So our F statistic is going to be 12.

00:07:15.267 --> 00:07:18.067
We're going to see that this is a pretty high number.

00:07:18.067 --> 00:07:19.800
Now, one thing I forgot to mention, with any hypothesis test,

00:07:19.800 --> 00:07:22.267
we're going to need some type of significance level.

00:07:22.267 --> 00:07:24.733
So let's say the significance level that we care about,

00:07:24.733 --> 00:07:28.333
for our hypothesis test, is 10%.

00:07:28.333 --> 00:07:32.267
0.10 -- which means

00:07:32.267 --> 00:07:36.200
that if we assume the null hypothesis, there is

00:07:36.200 --> 00:07:40.067
less than a 10% chance of getting the result we got,

00:07:40.067 --> 00:07:41.667
of getting this F statistic,

00:07:41.667 --> 00:07:44.800
then we will reject the null hypothesis.

00:07:44.800 --> 00:07:48.667
So what we want to do is figure out a critical F statistic value,

00:07:48.667 --> 00:07:54.000
that getting that extreme of a value or greater, is 10%

00:07:54.000 --> 00:07:57.133
and if this is bigger than our critical F statistic value,

00:07:57.133 --> 00:07:59.533
then we're going to reject the null hypothesis,

00:07:59.533 --> 00:08:01.400
if it's less, we can't reject the null.

00:08:01.400 --> 00:08:06.267
So I'm not going to go into a lot of the guts of the F statistic,

00:08:06.267 --> 00:08:09.067
but we can already appreciate that each of these Sum of squares

00:08:09.067 --> 00:08:12.533
has a Chi-squared distribution. "This" has a Chi-squared distribution,

00:08:12.533 --> 00:08:15.200
and "this" has a different Chi-squared distribution

00:08:15.200 --> 00:08:17.533
This is a Chi-squared distribution with 2 degrees of freedom,

00:08:17.533 --> 00:08:21.333
this is a Chi-squared distribution with--And we haven't normalized it and all of that--

00:08:21.333 --> 00:08:24.067
but roughly a Chi squared distribution with 6 degrees of freedom.

00:08:24.067 --> 00:08:29.800
So the F distribution is actually the ratio of two Chi-squared distributions

00:08:29.800 --> 00:08:34.933
And I got this--this is a screenshot from a professor's course at UCLA,

00:08:34.933 --> 00:08:38.533
I hope they don't mind, I need to find us an F table for us to look into.

00:08:38.533 --> 00:08:41.800
But this is what an F distribution looks like.

00:08:41.800 --> 00:08:43.267
And obviously it's going to look different

00:08:43.267 --> 00:08:46.600
depending on the df of the numerator and the denominator.

00:08:46.600 --> 00:08:49.200
There's two df to think about,

00:08:49.200 --> 00:08:52.533
the numerator degrees of freedom and the denominator degrees of freedom

00:08:52.533 --> 00:08:56.933
With that said, let's calculate the critical F statistic,

00:08:56.933 --> 00:09:02.867
for alpha is equal to 0.10,

00:09:02.867 --> 00:09:06.533
and you're actually going to see different F tables for each different alpha,

00:09:06.533 --> 00:09:11.933
where our numerator df is 2, and our denominator df is 6.

00:09:11.933 --> 00:09:17.400
So this table that I got, this whole table is for an alpha of 10%

00:09:17.400 --> 00:09:23.733
or 0.10, and our numerator df was 2 and our denominator

00:09:23.733 --> 00:09:30.133
was 6. So our critical F value is 3.46.

00:09:30.133 --> 00:09:40.000
So our critical F value is 3.46--this value right over here is 3.46

00:09:40.000 --> 00:09:43.533
The value that we got based on our data is much larger than this,

00:09:43.533 --> 00:09:46.267
WAY above it. It's going to have a very, very small p value.

00:09:46.267 --> 00:09:48.000
The probability of getting something this extreme,

00:09:48.000 --> 00:09:50.667
just by chance, assuming the null hypothesis,

00:09:50.667 --> 00:09:54.733
is very low. It's way bigger than our critical F statistic with

00:09:54.733 --> 00:09:56.933
a 10% significance level.

00:09:56.933 --> 00:10:01.733
So because of that we can reject the null hypothesis.

00:10:01.733 --> 00:10:04.400
Which leads us to believe, "you know what, there probably

00:10:04.400 --> 00:10:06.600
IS a difference in the population means."

00:10:06.600 --> 00:10:09.600
Which tells us there probably is a difference in performance

00:10:09.600 --> 00:10:13.467
on an exam if you give them the different foods.


ANOVA 1: Calculating SST (total sum of squares)

WEBVTT
Kind: captions
Language: en

00:00:00.680 --> 00:00:02.400
In this video and
the next few videos,

00:00:02.400 --> 00:00:05.120
we're just really going to be
doing a bunch of calculations

00:00:05.120 --> 00:00:07.640
about this data set
right over here.

00:00:07.640 --> 00:00:09.850
And hopefully, just going
through those calculations

00:00:09.850 --> 00:00:11.730
will give you an
intuitive sense of what

00:00:11.730 --> 00:00:14.540
the analysis of
variance is all about.

00:00:14.540 --> 00:00:17.060
Now, the first thing I
want to do in this video

00:00:17.060 --> 00:00:19.940
is calculate the
total sum of squares.

00:00:19.940 --> 00:00:22.740
So I'll call that SST.

00:00:22.740 --> 00:00:24.830
SS-- sum of squares total.

00:00:24.830 --> 00:00:27.170
And you could view it
as really the numerator

00:00:27.170 --> 00:00:28.450
when you calculate variance.

00:00:28.450 --> 00:00:30.700
So you're just going to take
the distance between each

00:00:30.700 --> 00:00:33.427
of these data points and the
mean of all of these data

00:00:33.427 --> 00:00:35.260
points, square them,
and just take that sum.

00:00:35.260 --> 00:00:37.660
We're not going to divide by
the degree of freedom, which

00:00:37.660 --> 00:00:39.535
you would normally do
if you were calculating

00:00:39.535 --> 00:00:40.920
sample variance.

00:00:40.920 --> 00:00:42.180
Now, what is this going to be?

00:00:42.180 --> 00:00:43.680
Well, the first
thing we need to do,

00:00:43.680 --> 00:00:46.920
we have to figure out the mean
of all of this stuff over here.

00:00:46.920 --> 00:00:50.449
And I'm actually going to
call that the grand mean.

00:00:50.449 --> 00:00:51.990
And I'm going to
show you in a second

00:00:51.990 --> 00:00:55.140
that it's the same thing as
the mean of the means of each

00:00:55.140 --> 00:00:56.750
of these data sets.

00:00:56.750 --> 00:00:58.920
So let's calculate
the grand mean.

00:00:58.920 --> 00:01:09.990
So it's going to be 3 plus 2
plus 1 plus 5 plus 3 plus 4

00:01:09.990 --> 00:01:11.620
plus 5 plus 6 plus 7.

00:01:16.010 --> 00:01:20.430
And then we have
nine data points here

00:01:20.430 --> 00:01:21.540
so we'll divide by 9.

00:01:21.540 --> 00:01:23.410
And what is this
going to be equal to?

00:01:23.410 --> 00:01:26.460
3 plus 2 plus 1 is 6.

00:01:26.460 --> 00:01:28.160
6 plus-- let me just add.

00:01:28.160 --> 00:01:30.040
So these are 6.

00:01:30.040 --> 00:01:36.010
5 plus 3 plus 4 is 12.

00:01:36.010 --> 00:01:40.550
And then 5 plus 6 plus 7 is 18.

00:01:40.550 --> 00:01:44.860
And then 6 plus 12 is 18 plus
another 18 is 36, divided by 9

00:01:44.860 --> 00:01:45.994
is equal to 4.

00:01:45.994 --> 00:01:48.160
And let me show you that
that's the exact same thing

00:01:48.160 --> 00:01:49.940
as the mean of the means.

00:01:49.940 --> 00:01:52.580
So the mean of this
group 1 over here--

00:01:52.580 --> 00:01:54.580
let me do it in
that same green--

00:01:54.580 --> 00:01:58.350
the mean of group 1 over
here is 3 plus 2 plus 1.

00:01:58.350 --> 00:02:00.970
That's that 6 right over
here, divided by 3 data

00:02:00.970 --> 00:02:03.600
points so that
will be equal to 2.

00:02:03.600 --> 00:02:08.574
The mean of group 2,
the sum here is 12.

00:02:08.574 --> 00:02:09.740
We saw that right over here.

00:02:09.740 --> 00:02:13.250
5 plus 3 plus 4 is
12, divided by 3

00:02:13.250 --> 00:02:15.820
is 4 because we have
three data points.

00:02:15.820 --> 00:02:21.000
And then the mean
of group 3, 5 plus 6

00:02:21.000 --> 00:02:24.790
plus 7 is 18 divided by 3 is 6.

00:02:24.790 --> 00:02:27.100
So if you were to take the
mean of the means, which

00:02:27.100 --> 00:02:30.120
is another way of viewing this
grand mean, you have 2 plus 4

00:02:30.120 --> 00:02:34.040
plus 6, which is 12,
divided by 3 means here.

00:02:34.040 --> 00:02:35.530
And once again, you would get 4.

00:02:35.530 --> 00:02:36.946
So you could view
this as the mean

00:02:36.946 --> 00:02:38.830
of all of the data
in all of the groups

00:02:38.830 --> 00:02:41.505
or the mean of the means
of each of these groups.

00:02:41.505 --> 00:02:43.380
But either way, now that
we've calculated it,

00:02:43.380 --> 00:02:46.780
we can actually figure out
the total sum of squares.

00:02:46.780 --> 00:02:48.590
So let's do that.

00:02:48.590 --> 00:02:53.950
So it's going to be
equal to 3 minus 4--

00:02:53.950 --> 00:02:59.730
the 4 is this 4 right over
here-- squared plus 2 minus 4

00:02:59.730 --> 00:03:03.280
squared plus 1 minus 4 squared.

00:03:03.280 --> 00:03:05.490
Now, I'll do these guys
over here in purple.

00:03:05.490 --> 00:03:15.270
Plus 5 minus 4 squared plus 3
minus 4 squared plus 4 minus 4

00:03:15.270 --> 00:03:15.770
squared.

00:03:15.770 --> 00:03:19.320
Let me scroll over a little bit.

00:03:19.320 --> 00:03:25.330
Now, we only have three
left, plus 5 minus 4 squared

00:03:25.330 --> 00:03:31.210
plus 6 minus 4 squared
plus 7 minus 4 squared.

00:03:31.210 --> 00:03:32.770
And what does this give us?

00:03:32.770 --> 00:03:36.620
So up here, this is going
to be equal to 3 minus 4.

00:03:36.620 --> 00:03:37.490
Difference is 1.

00:03:37.490 --> 00:03:38.730
You square it.

00:03:38.730 --> 00:03:41.810
It's actually negative 1,
but you square it, you get 1,

00:03:41.810 --> 00:03:48.320
plus you get negative 2 squared
is 4, plus negative 3 squared.

00:03:48.320 --> 00:03:50.700
Negative 3 squared is 9.

00:03:50.700 --> 00:03:53.570
And then we have here
in the magenta 5 minus 4

00:03:53.570 --> 00:03:55.640
is 1 squared is still 1.

00:03:55.640 --> 00:03:57.420
3 minus 4 squared is 1.

00:03:57.420 --> 00:03:59.320
You square it again,
you still get 1.

00:03:59.320 --> 00:04:00.964
And then 4 minus 4 is just 0.

00:04:00.964 --> 00:04:03.130
So we could-- well, I'll
just write the 0 there just

00:04:03.130 --> 00:04:05.344
to show you that we
actually calculated that.

00:04:05.344 --> 00:04:07.260
And then we have these
last three data points.

00:04:07.260 --> 00:04:09.180
5 minus 4 squared.

00:04:09.180 --> 00:04:09.760
That's 1.

00:04:09.760 --> 00:04:11.800
6 minus 4 squared.

00:04:11.800 --> 00:04:13.330
That is 4, right?

00:04:13.330 --> 00:04:14.850
That's 2 squared.

00:04:14.850 --> 00:04:19.370
And then plus 7 minus
4 is 3 squared is 9.

00:04:19.370 --> 00:04:22.230
So what's this going
to be equal to?

00:04:22.230 --> 00:04:27.760
So I have 1 plus 4
plus 9 right over here.

00:04:27.760 --> 00:04:29.110
That's 5 plus 9.

00:04:29.110 --> 00:04:33.360
This right over
here is 14, right?

00:04:33.360 --> 00:04:35.110
5 plus-- yup, 14.

00:04:35.110 --> 00:04:37.290
And then we also have
another 14 right over here

00:04:37.290 --> 00:04:39.270
because we have a
1 plus 4 plus 9.

00:04:39.270 --> 00:04:41.940
So that right over
there is also 14.

00:04:41.940 --> 00:04:43.190
And then we have 2 over here.

00:04:43.190 --> 00:04:46.720
So it's going to be
28-- 14 times 2, 14

00:04:46.720 --> 00:04:50.738
plus 14 is 28-- plus 2 is 30.

00:04:50.738 --> 00:04:53.380
Is equal to 30.

00:04:53.380 --> 00:04:55.770
So our total sum of
squares-- and actually,

00:04:55.770 --> 00:04:57.450
if we wanted the
variance here, we

00:04:57.450 --> 00:04:59.760
would divide this by
the degrees of freedom.

00:04:59.760 --> 00:05:02.300
And we've learned multiple
times the degrees of freedom

00:05:02.300 --> 00:05:06.840
here so let's say
that we have-- so we

00:05:06.840 --> 00:05:08.710
know that we have
m groups over here.

00:05:08.710 --> 00:05:10.800
So let me just write
it as m and I'm not

00:05:10.800 --> 00:05:12.540
going to prove things
rigorously here,

00:05:12.540 --> 00:05:14.510
but I want to show
you where some

00:05:14.510 --> 00:05:17.730
of these strange formulas that
show up in statistics books

00:05:17.730 --> 00:05:21.440
actually come from without
proving it rigorously.

00:05:21.440 --> 00:05:22.780
More to give you the intuition.

00:05:22.780 --> 00:05:25.460
So we have m groups here.

00:05:25.460 --> 00:05:32.120
And each group
here has n members.

00:05:32.120 --> 00:05:34.180
So how many total
members do we have here?

00:05:34.180 --> 00:05:36.800
Well, we had m
times n or 9, right?

00:05:36.800 --> 00:05:38.490
3 times 3 total members.

00:05:38.490 --> 00:05:41.510
So our degrees of
freedom-- and remember,

00:05:41.510 --> 00:05:43.930
you have however
many data points

00:05:43.930 --> 00:05:46.310
you had minus 1
degrees of freedom

00:05:46.310 --> 00:05:51.070
because if you know
the mean of means,

00:05:51.070 --> 00:05:57.885
if you assume you knew
that, then only 9 minus 1,

00:05:57.885 --> 00:06:00.260
only eight of these are going
to give you new information

00:06:00.260 --> 00:06:03.005
because if you know that, you
could calculate the last one.

00:06:03.005 --> 00:06:04.880
Or it really doesn't
have to be the last one.

00:06:04.880 --> 00:06:07.629
If you have the other eight,
you could calculate this one.

00:06:07.629 --> 00:06:09.420
If you have eight of
them, you could always

00:06:09.420 --> 00:06:13.897
calculate the ninth one
using the mean of means.

00:06:13.897 --> 00:06:15.730
So one way to think
about it is that there's

00:06:15.730 --> 00:06:17.710
only eight independent
measurements here.

00:06:17.710 --> 00:06:22.470
Or if we want to
talk generally, there

00:06:22.470 --> 00:06:27.810
are m times n-- so that tells
us the total number of samples--

00:06:27.810 --> 00:06:30.210
minus 1 degrees of freedom.

00:06:33.840 --> 00:06:37.920
And if we were actually
calculating the variance here,

00:06:37.920 --> 00:06:41.640
we would just divide
30 by m times n minus 1

00:06:41.640 --> 00:06:44.960
or this is another way of
saying eight degrees of freedom

00:06:44.960 --> 00:06:46.065
for this exact example.

00:06:46.065 --> 00:06:48.190
We would take 30 divided
by 8 and we would actually

00:06:48.190 --> 00:06:50.110
have the variance for
this entire group,

00:06:50.110 --> 00:06:52.964
for the group of nine
when you combine them.

00:06:52.964 --> 00:06:54.380
I'll leave you
here in this video.

00:06:54.380 --> 00:06:57.090
In the next video, we're
going to try to figure out

00:06:57.090 --> 00:07:02.970
how much of this total
variance, how much of this total

00:07:02.970 --> 00:07:06.400
squared sum, total
variation comes

00:07:06.400 --> 00:07:09.850
from the variation within
each of these groups

00:07:09.850 --> 00:07:13.790
versus the variation
between the groups.

00:07:13.790 --> 00:07:15.290
And I think you get
a sense of where

00:07:15.290 --> 00:07:17.354
this whole analysis of
variance is coming from.

00:07:17.354 --> 00:07:18.770
It's the sense
that, look, there's

00:07:18.770 --> 00:07:20.890
a variance of this
entire sample of nine,

00:07:20.890 --> 00:07:23.430
but some of that variance--
if these groups are

00:07:23.430 --> 00:07:27.390
different in some way--
might come from the variation

00:07:27.390 --> 00:07:30.710
from being in different groups
versus the variation from being

00:07:30.710 --> 00:07:31.350
within a group.

00:07:31.350 --> 00:07:33.070
And we're going to
calculate those two things

00:07:33.070 --> 00:07:34.528
and we're going to
see that they're

00:07:34.528 --> 00:07:38.000
going to add up to the
total squared sum variation.