Computing a tangent plane

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:01.566
- [Voiceover] Hey guys,
so in the last video

00:00:01.566 --> 00:00:03.842
I was talking about how
you can define a function

00:00:03.842 --> 00:00:05.350
whose graph is a plane,

00:00:05.350 --> 00:00:08.230
and moreover a plane that
passes through a specified point

00:00:08.230 --> 00:00:11.077
and whose orientation
you can somehow specify.

00:00:11.077 --> 00:00:13.758
And we ended up seeing how
specifying that orientation

00:00:13.758 --> 00:00:16.938
comes down to certain partial
derivative information.

00:00:16.938 --> 00:00:19.654
And first let me just kind of
repeat what the conclusion was

00:00:19.654 --> 00:00:22.186
but I'll put it in more abstract terms

00:00:22.186 --> 00:00:24.994
since I did it in a very
specific example last time.

00:00:24.994 --> 00:00:27.270
So basically if you want
some kind of function

00:00:27.270 --> 00:00:29.222
which gives you a plane that

00:00:29.222 --> 00:00:30.706
passes through a certain point.

00:00:30.706 --> 00:00:32.218
Well first let's see
what that point is right.

00:00:32.218 --> 00:00:36.200
Let's say the point was x
nought, y nought, and z nought.

00:00:36.200 --> 00:00:37.963
So these are constant values

00:00:37.963 --> 00:00:39.891
and this is my way of
abstractly describing

00:00:39.891 --> 00:00:41.563
a single point in space using

00:00:41.563 --> 00:00:43.979
x nought to represent a constant x value,

00:00:43.979 --> 00:00:47.067
y nought to represent constant
y value, that kind of thing.

00:00:47.067 --> 00:00:49.899
So what it is, is it's gonna
be some sort of other constant

00:00:49.899 --> 00:00:52.982
a multiplied by x minus x nought.

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So this white x here is the variable

00:00:57.703 --> 00:00:59.651
and then x nought is just a constant.

00:00:59.651 --> 00:01:04.111
Now let me go ahead and
make that parentheses there.

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Then we add to that b multiplied by

00:01:08.219 --> 00:01:09.775
and then b is just some other constant

00:01:09.775 --> 00:01:11.423
just like a is some other constant

00:01:11.423 --> 00:01:13.756
multiplied by y minus y nought

00:01:15.419 --> 00:01:18.419
and then all of that you add z nought.

00:01:19.275 --> 00:01:21.295
And now if you were just
presented this as it is

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it's kind of a lot right,

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there's five different constants going on.

00:01:24.267 --> 00:01:26.055
But really what this is saying is

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you want something where
the partial derivative

00:01:29.163 --> 00:01:31.139
with respect to x is just some constant

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and you want to be able to
specify what that constant is.

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And similarly, the partial derivative

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with respect to y is another constant.

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And you just want to ensure that this

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passes through this point
x nought, y nought, z nought.

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And if you imagine plugging in
x the variable equals x nought

00:01:44.585 --> 00:01:46.745
the constant this part goes to zero.

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Similarly plugging in y nought the constant

00:01:48.697 --> 00:01:50.181
makes this part go to zero.

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So this is a way of
specifying that when you

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evaluate the function x
nought y nought equals z nought,

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and that's what makes sure that the graph

00:01:57.313 --> 00:01:58.937
passes through that point.

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So with that said let's
start thinking about

00:02:01.097 --> 00:02:03.905
how you can find the
tangent plane to a graph.

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And first of all let's think
about what that point is,

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how you specify such a point.

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Instead of specifying any
three numbers in space,

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because you have to make sure the point

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is somewhere on the graph,

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you instead only specify two.

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You're basically gonna say
what's the x coordinate

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and in this case let's say
the x coordinate was one,

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and then the y coordinate which

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looks about like negative two.

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To make it easier I'm just
gonna say it is negative two.

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Then the z coordinate is specified

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because this is a graph.

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Z coordinate is forced
to be whatever the output

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of the function is at one negative two.

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So this is gonna be whatever
the output of our function is

00:02:39.245 --> 00:02:40.912
at one negative two.

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And f here, f is going to be whatever

00:02:44.101 --> 00:02:45.725
function gives us this graph.

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So maybe I should write
down the actual function

00:02:48.533 --> 00:02:50.089
that I'm using for this graph.

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In this case f which is
a function of x and y

00:02:55.569 --> 00:02:58.319
is equal to three minus one third

00:02:59.821 --> 00:03:03.257
of x squared minus y squared.

00:03:03.257 --> 00:03:05.253
So this is the function that we're using

00:03:05.253 --> 00:03:06.761
and you evaluate it at that point

00:03:06.761 --> 00:03:09.337
and this will give you your
point in three dimensional space

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that our linear function,

00:03:10.965 --> 00:03:13.589
that our tangent plane
has to pass through.

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So we can start writing
out our linear function.

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We can say okay so our linear function

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has a function of x and y.

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It's gotta make sure it goes through

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that one and that negative two,

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so this is gonna be some constant a

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that we'll fill in in a moment,

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multiplied by x minus that one,

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plus and then b also a constant
we'll specify in a moment,

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times y minus that negative two,

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so it's minus a negative two

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and then the thing that we add to it

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is f of one negative two.

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Now let's just go ahead and evaluate that.

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Let's say we plug in one to negative two.

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So if we go up here and we plug
in three minus one third of

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if x equals one, one third of one squared,

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so that's one third one squared,

00:03:58.850 --> 00:04:01.262
and then y is negative two.

00:04:01.262 --> 00:04:04.929
So that would be minus
negative two squared.

00:04:05.862 --> 00:04:09.195
So that's three minus a third minus four

00:04:11.250 --> 00:04:12.874
so the whole thing is equal to

00:04:12.874 --> 00:04:15.614
three minus four is negative
one minus another third

00:04:15.614 --> 00:04:17.614
is negative four thirds.

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So that's what we add
to this entire thing.

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We add negative four thirds

00:04:25.250 --> 00:04:26.458
or maybe I should just kind of

00:04:26.458 --> 00:04:28.802
make clear the separation here.

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So this is our function but we
don't know what a and b are.

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Those are things that we need to plug in.

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Now the whole idea of the tangent plane

00:04:35.814 --> 00:04:38.554
is that the partial
derivative with respect to x

00:04:38.554 --> 00:04:41.038
should match that of
the original function.

00:04:41.038 --> 00:04:42.410
So if we go over to the graph here

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and start thinking about
partial derivative information.

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If we want the partial
derivative with respect to x

00:04:47.446 --> 00:04:50.234
then you imagine moving purely
in the x direction here.

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This intersects the graph
along some kind of curve

00:04:54.114 --> 00:04:56.134
and what the partial
derivative with respect to x

00:04:56.134 --> 00:05:00.301
at this point tells you, is
the slope of the tangent line,

00:05:06.240 --> 00:05:08.020
in that direction of that point.

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So that's what the partial
derivative with respect to x

00:05:10.320 --> 00:05:12.804
is telling you and what
you want when you look

00:05:12.804 --> 00:05:15.984
at the tangent plane is
that the tangent plane

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also has that same slope.

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If I lined things up here,

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you'd want it also to
have that same slope.

00:05:21.580 --> 00:05:24.436
So you can specify over here and say a.

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You want a to be equal
to the partial derivative

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of the function with respect to x

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evaluated at this one negative two.

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Evaluated at that special
point, one negative two.

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And similarly b for pretty
much the same reasons

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and I'll draw it out here
so let's erase this line.

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So instead of intersecting
it with that slice

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let's see what movement in
the y direction looks like.

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So in this case it looks
like a very steep slope right

00:05:58.362 --> 00:06:01.589
because in this case the
tangent line in that direction

00:06:01.589 --> 00:06:05.349
is a pretty steep slope
and now when we bring in

00:06:05.349 --> 00:06:09.229
the tangent plane it
should intersect with that

00:06:09.229 --> 00:06:13.709
constant x value plane
along that same slope.

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Made it kind of messy there

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but you can see the line formed

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by intersecting these two planes

00:06:20.001 --> 00:06:22.185
should be that desired tangent,

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and what that corresponds to in formulas

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is that this b which represents
the partial derivative of l,

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l is the tangent plane function,

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that should be the same as if
we took the partial derivative

00:06:33.933 --> 00:06:37.137
of f with respect to y at that point,

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at this point one negative two.

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And this is stuff that we can compute

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and that we can figure out.

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So let's start plugging that in.

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First let me just copy this function

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because we're gonna need it.

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Now let's go on down here.

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I'm just gonna, let's paste it down here

00:07:01.475 --> 00:07:03.423
in the bottom because
that's what we'll need.

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So let's compute the
partial derivative of f

00:07:05.071 --> 00:07:06.723
with respect to x.

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So we look down here, the
only place where x shows up

00:07:09.415 --> 00:07:12.991
is in this negative one
third of x squared context

00:07:12.991 --> 00:07:16.379
so the partial derivative
of f with respect to x

00:07:16.379 --> 00:07:19.027
is gonna be just the
derivative of this little guy

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which is negative, we bring down the two,

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negative two thirds of x.

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So when we go ahead and
plug in x equals one

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to see what it looks like
when we evaluate at this point

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that's just gonna be equal
to negative two thirds.

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So that tells us that a is gonna

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have to be negative two thirds.

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Now for similar reasons,

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let's go ahead and compute the

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partial derivative with respect to y.

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We look down here, the
only place that y shows up

00:07:46.011 --> 00:07:49.051
in the entire expression
is this negative y squared.

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So the partial derivative
of f with respect to y

00:07:53.555 --> 00:07:57.138
is equal to negative
two y, negative two y.

00:07:58.131 --> 00:08:01.170
And now when we plug in
y equals negative two

00:08:01.170 --> 00:08:04.494
what we get is negative two
multiplied coincidentally

00:08:04.494 --> 00:08:06.612
by negative two, didn't
have to be the case

00:08:06.612 --> 00:08:10.541
that those were the same, and
that whole thing equals four.

00:08:10.541 --> 00:08:14.469
So the partial derivative
of f with respect to y

00:08:14.469 --> 00:08:16.033
evaluated at this point one negative two

00:08:16.033 --> 00:08:17.357
is equal to four.

00:08:17.357 --> 00:08:18.865
So if we were to plug
this information back up

00:08:18.865 --> 00:08:20.653
into our formula we would replace

00:08:20.653 --> 00:08:22.257
a with negative two thirds.

00:08:22.257 --> 00:08:24.650
It would say negative two thirds.

00:08:24.650 --> 00:08:29.293
And we would replace b with
four, replace b with four.

00:08:29.293 --> 00:08:33.221
And that would give us the full formula,

00:08:33.221 --> 00:08:36.580
the full formula for the tangent plane.

00:08:36.580 --> 00:08:38.232
And this can be kind of
a lot to look at at first

00:08:38.232 --> 00:08:42.248
because we have to specify the
input point one negative two.

00:08:42.248 --> 00:08:43.456
And then we had to figure out where

00:08:43.456 --> 00:08:45.544
the function evaluates at that point.

00:08:45.544 --> 00:08:46.984
And then we had to figure out both of the

00:08:46.984 --> 00:08:50.328
partial derivatives with respect
to x and with respect to y.

00:08:50.328 --> 00:08:51.976
But all in all, there's not actually

00:08:51.976 --> 00:08:54.672
a lot to remember from how
you go about computing this.

00:08:54.672 --> 00:08:55.808
Looking at the graph actually makes

00:08:55.808 --> 00:08:57.620
things seem a lot more reasonable

00:08:57.620 --> 00:08:59.896
because each of those terms
has an actual meaning.

00:08:59.896 --> 00:09:03.168
If we look at the one and negative two,

00:09:03.168 --> 00:09:04.632
that's just telling us the input,

00:09:04.632 --> 00:09:06.444
the kind of x and y
coordindates of the input

00:09:06.444 --> 00:09:07.952
and of course we have to evaluate that

00:09:07.952 --> 00:09:10.180
because that tells us the z coordinate

00:09:10.180 --> 00:09:13.548
that will put us on the graph
corresponding to that point

00:09:13.548 --> 00:09:15.872
and then to get a tangent plane

00:09:15.872 --> 00:09:17.079
you just need to specify the two bits of

00:09:17.079 --> 00:09:19.027
partial differential information

00:09:19.027 --> 00:09:20.839
and that will tell you how this graph

00:09:20.839 --> 00:09:22.231
needs to be oriented,

00:09:22.231 --> 00:09:23.903
and once you start thinking
of things in that way,

00:09:23.903 --> 00:09:26.227
geometrically, even though
there's a lot going on here,

00:09:26.227 --> 00:09:28.291
there's five different
numbers you have to put in,

00:09:28.291 --> 00:09:31.335
each one of them feels like
of course you need that number

00:09:31.335 --> 00:09:33.539
otherwise you couldn't
specify a tangent plane.

00:09:33.539 --> 00:09:35.327
There's kind of a lot
of information required

00:09:35.327 --> 00:09:37.883
to put it on the appropriate spot.

00:09:37.883 --> 00:09:39.938
So with that I will see you next video.


Controlling a plane in space

WEBVTT
Kind: captions
Language: en

00:00:00.865 --> 00:00:01.706
- [Voiceover] Hello everyone.

00:00:01.706 --> 00:00:03.524
So I'm talking about how
to find the tangent plane

00:00:03.524 --> 00:00:04.457
to a graph.

00:00:04.457 --> 00:00:05.290
And I think the first step
of that is to just figure

00:00:05.290 --> 00:00:09.189
out how we control planes
in three dimensions

00:00:09.189 --> 00:00:10.224
in the first place.

00:00:10.224 --> 00:00:13.071
So what I have pictured here
is a red dot representing

00:00:13.071 --> 00:00:15.102
a point in three dimensions,

00:00:15.102 --> 00:00:16.735
and the coordinates of that point,

00:00:16.735 --> 00:00:18.152
easily enough are

00:00:20.699 --> 00:00:21.866
one two three.

00:00:22.760 --> 00:00:24.549
So the x coordinate is
one, the y coordinate's two

00:00:24.549 --> 00:00:26.293
and the z coordinate is three.

00:00:26.293 --> 00:00:28.285
And then I have a plane
that passes through it.

00:00:28.285 --> 00:00:29.831
And the goal of the video is going to be

00:00:29.831 --> 00:00:31.051
to find a function,

00:00:31.051 --> 00:00:32.715
a function that I'll call l,

00:00:32.715 --> 00:00:35.868
that takes in a two dimensional input

00:00:35.868 --> 00:00:37.051
x and y

00:00:37.051 --> 00:00:41.768
and this function l should
have this plane as it's graph.

00:00:41.768 --> 00:00:42.825
Now the first thing to notice

00:00:42.825 --> 00:00:44.289
is that there's lots of different planes

00:00:44.289 --> 00:00:45.879
that could be passing
through this point, right?

00:00:45.879 --> 00:00:47.996
At the moment it's one that's
got a certain kind of angle,

00:00:47.996 --> 00:00:50.394
you could think of it
going up in one direction,

00:00:50.394 --> 00:00:52.098
but you could give this a
lot of different directions,

00:00:52.098 --> 00:00:53.678
and get a lot of different planes,

00:00:53.678 --> 00:00:55.629
that all pass through that one point.

00:00:55.629 --> 00:00:56.767
So we're going to need to find

00:00:56.767 --> 00:00:58.109
some way of distinguishing

00:00:58.109 --> 00:00:59.858
the specific one that we're looking at,

00:00:59.858 --> 00:01:01.366
which is this one right here,

00:01:01.366 --> 00:01:03.726
from other possible planes
that can pass through it.

00:01:03.726 --> 00:01:05.661
And as we work through you'll see

00:01:05.661 --> 00:01:08.603
how this is done in terms
of partial derivatives.

00:01:08.603 --> 00:01:10.351
But as we are getting our head around

00:01:10.351 --> 00:01:12.503
what the formula for this graph can be,

00:01:12.503 --> 00:01:14.373
let's just start observing properties

00:01:14.373 --> 00:01:15.386
that it has.

00:01:15.386 --> 00:01:16.566
The first property

00:01:16.566 --> 00:01:18.679
is that the graph actually
passes through this point,

00:01:18.679 --> 00:01:19.817
one, two, three.

00:01:19.817 --> 00:01:22.825
And what that means in terms
of functions over here,

00:01:22.825 --> 00:01:26.683
is that if you evaluated
at the point one two,

00:01:26.683 --> 00:01:29.163
the input pair where both
x is one and y is two,

00:01:29.163 --> 00:01:31.560
then it should equal three.

00:01:31.560 --> 00:01:33.839
It should equal three
because that's telling you

00:01:33.839 --> 00:01:37.249
that when you go x equals
one and y equals two

00:01:37.249 --> 00:01:39.362
and then you say what's
the height of the graph

00:01:39.362 --> 00:01:40.195
above that point,

00:01:40.195 --> 00:01:41.764
it should be the z coordinate

00:01:41.764 --> 00:01:43.186
at the end of the desired point.

00:01:43.186 --> 00:01:45.057
So this right here is the fact number one,

00:01:45.057 --> 00:01:46.559
that we can take into consideration.

00:01:46.559 --> 00:01:47.494
And beyond that,

00:01:47.494 --> 00:01:49.889
let's start thinking
about what makes planes,

00:01:49.889 --> 00:01:51.516
what makes these kind of flat graphs,

00:01:51.516 --> 00:01:52.980
different from the sort of curvy graphs

00:01:52.980 --> 00:01:56.721
that you might be used to in
other multi-variable function.

00:01:56.721 --> 00:01:58.065
The main idea is that if you intersect

00:01:58.065 --> 00:01:59.406
it with another plane,

00:01:59.406 --> 00:02:00.992
so here I'm going to intersect it with

00:02:00.992 --> 00:02:04.283
y equals two, this kind of constant plane,

00:02:04.283 --> 00:02:06.808
and so I'll go ahead and write that down.

00:02:06.808 --> 00:02:07.948
That plane that you're looking at,

00:02:07.948 --> 00:02:09.281
is y equals two.

00:02:10.470 --> 00:02:12.017
And you can think of this as representing,

00:02:12.017 --> 00:02:14.538
what is movement in the
x direction look like.

00:02:14.538 --> 00:02:16.441
As we move along the x direction,

00:02:16.441 --> 00:02:17.904
this kind of has a slope.

00:02:17.904 --> 00:02:20.955
The two planes intersect along a line,

00:02:20.955 --> 00:02:22.825
and that's one of the
crucial features of a plane,

00:02:22.825 --> 00:02:24.735
is that if you intersect
it with another plane,

00:02:24.735 --> 00:02:26.482
you just get a straight line,

00:02:26.482 --> 00:02:28.109
meaning the slope is constant,

00:02:28.109 --> 00:02:29.815
as you move in the x direction.

00:02:29.815 --> 00:02:31.398
But it's also constant, that same slope,

00:02:31.398 --> 00:02:32.415
if you move in the y direction.

00:02:32.415 --> 00:02:33.799
If I had chosen a different plane.

00:02:33.799 --> 00:02:36.810
If instead I had chosen y equals one,

00:02:36.810 --> 00:02:39.045
which looks like this,

00:02:39.045 --> 00:02:41.275
then you get a line with the same slope.

00:02:41.275 --> 00:02:43.788
And no matter what constant
value of y you choose,

00:02:43.788 --> 00:02:45.699
it's always intersecting that plane,

00:02:45.699 --> 00:02:48.506
with a line that has the same slope.

00:02:48.506 --> 00:02:49.400
And now if you look back

00:02:49.400 --> 00:02:51.305
to the videos on partial derivatives,

00:02:51.305 --> 00:02:52.160
and in particular

00:02:52.160 --> 00:02:55.251
on how you interpret the partial
derivative of a function,

00:02:55.251 --> 00:02:56.835
with respect to it's graph,

00:02:56.835 --> 00:02:59.032
what this is telling
you is that when we take

00:02:59.032 --> 00:03:02.933
the partial derivative
of l with respect to x,

00:03:02.933 --> 00:03:06.427
because constant y means you
are moving in the x direction,

00:03:06.427 --> 00:03:08.133
this should just be some kind of constant.

00:03:08.133 --> 00:03:09.754
Some kind of constant a.

00:03:09.754 --> 00:03:13.921
I'll kind of emphasize that
that is a constant value here.

00:03:14.916 --> 00:03:16.785
And the same goes in the
other direction, right.

00:03:16.785 --> 00:03:18.533
Let's say instead of intersecting it with

00:03:18.533 --> 00:03:19.875
constant values of y,

00:03:19.875 --> 00:03:21.663
we say well what if
you intersected it with

00:03:21.663 --> 00:03:24.507
a constant value of x, like x equals one.

00:03:24.507 --> 00:03:25.970
Well in that case what you should get,

00:03:25.970 --> 00:03:27.189
'cos you're intersecting it with a plane,

00:03:27.189 --> 00:03:29.101
is another straight line,

00:03:29.101 --> 00:03:31.425
so these two planes are
intersecting along a straight line,

00:03:31.425 --> 00:03:33.582
which means as you move
in the y direction,

00:03:33.582 --> 00:03:35.537
this slope won't change.

00:03:35.537 --> 00:03:37.245
But also as you move in the x direction,

00:03:37.245 --> 00:03:38.789
if you imaginee slicing it with
a bunch of different planes,

00:03:38.789 --> 00:03:42.298
all representing different
constant values of x,

00:03:42.298 --> 00:03:45.214
you would be getting a
line with that same slope.

00:03:45.214 --> 00:03:47.048
And that's telling you
another powerful fact.

00:03:47.048 --> 00:03:49.079
The partial derivative
of l, with respect to y,

00:03:49.079 --> 00:03:50.704
now if you're moving in the y direction,

00:03:50.704 --> 00:03:52.004
that's equal to some other constant,

00:03:52.004 --> 00:03:53.589
that I'm going to call b.

00:03:53.589 --> 00:03:54.686
And now, keep in mind,

00:03:54.686 --> 00:03:56.387
these are very powerful statements,

00:03:56.387 --> 00:03:58.661
because the partial derivative
of l with respect to x

00:03:58.661 --> 00:04:00.205
is a function,

00:04:00.205 --> 00:04:01.665
this is a function of x and y,

00:04:01.665 --> 00:04:03.860
and that might actually
be worth emphasizing here,

00:04:03.860 --> 00:04:05.935
that the partial derivative
of x with respect to y

00:04:05.935 --> 00:04:08.980
is something that you evaluate at

00:04:08.980 --> 00:04:12.156
a point in two dimensional space.

00:04:12.156 --> 00:04:13.738
And we're saying that
that's equal to some kind

00:04:13.738 --> 00:04:14.958
of constant value.

00:04:14.958 --> 00:04:16.177
Now that's a pretty powerful thing right?

00:04:16.177 --> 00:04:18.048
Because it's telling you,
it's giving you control over

00:04:18.048 --> 00:04:20.080
the function at all possible input points,

00:04:20.080 --> 00:04:22.556
for movement in a specified direction.

00:04:22.556 --> 00:04:23.694
And the same goes over here.

00:04:23.694 --> 00:04:26.051
This is telling you that. A
function is constantly equal

00:04:26.051 --> 00:04:30.218
to some value b, and we're
not sure what this value b is.

00:04:31.585 --> 00:04:33.356
But just geometrically

00:04:33.356 --> 00:04:35.492
we can estimate what
these things should be.

00:04:35.492 --> 00:04:36.999
So if I take back the plane representing

00:04:36.999 --> 00:04:39.761
a constant y value, and
we say what's the slope,

00:04:39.761 --> 00:04:42.197
you're moving in the x direction,

00:04:42.197 --> 00:04:43.703
we've got a constant y value,

00:04:43.703 --> 00:04:46.817
what is the slope at which this
plane intersects our graph?

00:04:46.817 --> 00:04:49.353
I would estimate this as
about the slope of two.

00:04:49.353 --> 00:04:52.075
You know you go over
one and it goes up two.

00:04:52.075 --> 00:04:53.334
So what that would tell you is that,

00:04:53.334 --> 00:04:55.445
at least in the specific
graph we're looking at,

00:04:55.445 --> 00:04:58.621
this is at least
approximately equal to two.

00:04:58.621 --> 00:05:02.524
And then similarly if we
look at constant x value,

00:05:02.524 --> 00:05:06.419
and we say that represents
movement in the y direction,

00:05:06.419 --> 00:05:08.573
what is the slope there.

00:05:08.573 --> 00:05:10.646
This looks to me like about one,

00:05:10.646 --> 00:05:11.498
as a slope.

00:05:11.498 --> 00:05:13.533
You kind of move over one
unit you go up one unit.

00:05:13.533 --> 00:05:15.931
So I'd say down here
that the constant value

00:05:15.931 --> 00:05:18.328
of the partial derivative
with respect to y

00:05:18.328 --> 00:05:20.198
is about equal to one.

00:05:20.198 --> 00:05:22.030
So we have three different facts here,

00:05:22.030 --> 00:05:25.161
the value of the function
at the point of one two,

00:05:25.161 --> 00:05:28.415
the value of its partial
derivative with respect to x

00:05:28.415 --> 00:05:29.472
everywhere,

00:05:29.472 --> 00:05:32.317
and the partial derivative
with respect to y, everywhere.

00:05:32.317 --> 00:05:34.148
And this information
is actually going to be

00:05:34.148 --> 00:05:37.293
enough to tell us what the
function as a whole should equal.

00:05:37.293 --> 00:05:40.846
Now specifically, this idea
that the partial derivative

00:05:40.846 --> 00:05:42.563
with respect to x is constant,

00:05:42.563 --> 00:05:45.396
tells us that the function l of xy

00:05:47.033 --> 00:05:48.175
is going to equal

00:05:48.175 --> 00:05:51.873
two times x plus something that
doesn't have any x's in it,

00:05:51.873 --> 00:05:54.427
something that as far as x
is concerned is constant,

00:05:54.427 --> 00:05:57.028
because the only thing whose
derivative, with respect to x,

00:05:57.028 --> 00:06:00.573
is the constant two is two x
plus something that's constant,

00:06:00.573 --> 00:06:02.432
as far as x is concerned.

00:06:02.432 --> 00:06:04.098
And then similarly over here,

00:06:04.098 --> 00:06:07.309
if the partial with respect
to y is the constant one,

00:06:07.309 --> 00:06:10.722
then that tells you that the
whole function looks like

00:06:10.722 --> 00:06:13.403
this looks like a constant
as far as y is concerned.

00:06:13.403 --> 00:06:17.570
So once we bring in y, it's
going to be one times y

00:06:18.889 --> 00:06:21.857
plus something that's constant,
as far as y is concerned.

00:06:21.857 --> 00:06:23.238
You know this part is already constant,

00:06:23.238 --> 00:06:24.538
as far as y is concerned,

00:06:24.538 --> 00:06:27.423
so anything that I add beyond
here has to be constant

00:06:27.423 --> 00:06:29.538
as far as both x and y is concerned.

00:06:29.538 --> 00:06:32.218
So that part has to actually
literally be a constant.

00:06:32.218 --> 00:06:35.672
So I'm just going to put in c for that,

00:06:35.672 --> 00:06:38.271
to represent constant.

00:06:38.271 --> 00:06:39.816
So, you can see this is a very

00:06:39.816 --> 00:06:41.324
restricted property on our function,

00:06:41.324 --> 00:06:42.947
because the only place x can show up

00:06:42.947 --> 00:06:45.381
is this linear term and the
only place y can show up

00:06:45.381 --> 00:06:47.415
is as this linear term.

00:06:47.415 --> 00:06:48.797
And when I use the word linear,

00:06:48.797 --> 00:06:52.169
you can pretty much interpret
as saying the term x shows up

00:06:52.169 --> 00:06:54.404
without an exponent or without
anything fancy happening

00:06:54.404 --> 00:06:55.237
to it.

00:06:55.237 --> 00:06:56.599
It's just x times a constant,

00:06:56.599 --> 00:06:58.179
that's pretty much what I mean by linear.

00:06:58.179 --> 00:07:00.537
It's got more precise
formulations in other contexts,

00:07:00.537 --> 00:07:02.125
but as far as we're concerned here,

00:07:02.125 --> 00:07:03.386
you can just think of it as meaning

00:07:03.386 --> 00:07:05.744
variable times a constant.

00:07:05.744 --> 00:07:08.350
So the question is what should this c be.

00:07:08.350 --> 00:07:09.901
And you can imagine that we can,

00:07:09.901 --> 00:07:10.958
based on this property,

00:07:10.958 --> 00:07:12.703
based on the value at the point one two,

00:07:12.703 --> 00:07:14.936
we can uniquely determine c.

00:07:14.936 --> 00:07:17.738
And you can plug in, x
equals one, y equals two,

00:07:17.738 --> 00:07:21.390
know that this has to equal
three and solve for c.

00:07:21.390 --> 00:07:23.378
Which we could do but
I'm going to actually

00:07:23.378 --> 00:07:25.043
do something a little bit more convenient.

00:07:25.043 --> 00:07:27.238
I'm going to kind of shift around where

00:07:27.238 --> 00:07:28.456
the constants show up,
and I'm going to say

00:07:28.456 --> 00:07:30.529
that the whole function should equal

00:07:30.529 --> 00:07:32.929
two times and then I'm
going to put a constant

00:07:32.929 --> 00:07:33.783
in with the x,

00:07:33.783 --> 00:07:36.995
I'm going to say x minus one,

00:07:36.995 --> 00:07:38.544
and then I'm going to do
the same thing with y,

00:07:38.544 --> 00:07:40.128
and I'm going to say plus one,

00:07:40.128 --> 00:07:43.423
here is the partial
derivative with respect to y,

00:07:43.423 --> 00:07:46.759
y minus and then I'm going to say two.

00:07:46.759 --> 00:07:48.102
And the reason I'm doing this,

00:07:48.102 --> 00:07:49.525
notice this doesn't change

00:07:49.525 --> 00:07:50.948
the partial derivative information,

00:07:50.948 --> 00:07:52.822
it's just if we take
the partial derivative

00:07:52.822 --> 00:07:55.145
with respect to x, this will still be two,

00:07:55.145 --> 00:07:56.570
and when we take it with respect to y,

00:07:56.570 --> 00:07:58.034
this will still be one.

00:07:58.034 --> 00:07:59.617
But the reason I'm putting these in here,

00:07:59.617 --> 00:08:03.518
is because we're gonna evaluate
it at the point one two

00:08:03.518 --> 00:08:05.186
so I want to make it
look as easy as possible

00:08:05.186 --> 00:08:07.703
to evaluate at the point one two.

00:08:07.703 --> 00:08:09.291
And then from here I'm
just going to add another

00:08:09.291 --> 00:08:11.693
constant, so instead of saying c

00:08:11.693 --> 00:08:13.642
because this is going to be
slightly different from c,

00:08:13.642 --> 00:08:14.781
I'll call it k.

00:08:14.781 --> 00:08:16.527
But the idea is that I'm
just moving around constants.

00:08:16.527 --> 00:08:19.250
If you imagined distributing
the multiplication here,

00:08:19.250 --> 00:08:21.606
and having two times that negative one,

00:08:21.606 --> 00:08:23.396
and one times that negative two,

00:08:23.396 --> 00:08:25.102
you're just changing what
the value of the constant

00:08:25.102 --> 00:08:26.567
stuck on the end here is.

00:08:26.567 --> 00:08:27.749
Now the important part,

00:08:27.749 --> 00:08:29.495
the reason that I'm writing it this way,

00:08:29.495 --> 00:08:30.919
which is only slightly different,

00:08:30.919 --> 00:08:34.380
is because then when I evaluate this,

00:08:34.380 --> 00:08:37.837
at l of one two, this whole first part,

00:08:37.837 --> 00:08:40.602
cancels out because
plugging in x equals one

00:08:40.602 --> 00:08:42.717
means this whole part goes to zero.

00:08:42.717 --> 00:08:43.896
Same with the second part,

00:08:43.896 --> 00:08:45.242
because when I plug in y equals two,

00:08:45.242 --> 00:08:46.624
this part goes to zero.

00:08:46.624 --> 00:08:49.712
So k this other constant,
that I'm tagging on the end,

00:08:49.712 --> 00:08:52.313
is going to completely
specify what happens

00:08:52.313 --> 00:08:53.856
when I evaluate this at the point one two.

00:08:53.856 --> 00:08:56.055
And of course I want it to be the case,

00:08:56.055 --> 00:08:58.664
when I evaluate at one two I get three.

00:08:58.664 --> 00:09:00.533
I want it to be the case
when I evaluate at one two,

00:09:00.533 --> 00:09:01.961
I get three.

00:09:01.961 --> 00:09:04.902
So that tells me, that this constant

00:09:04.902 --> 00:09:07.159
k here should just equal 3.

00:09:07.159 --> 00:09:09.843
So notice the way that I've
written the function here,

00:09:09.843 --> 00:09:10.778
is actually quite powerful.

00:09:10.778 --> 00:09:11.955
We have a lot of control.

00:09:11.955 --> 00:09:14.842
This term two was telling us the slope

00:09:14.842 --> 00:09:16.264
with respect to x.

00:09:16.264 --> 00:09:18.421
So when you moved purely
in the x direction,

00:09:18.421 --> 00:09:20.044
and that was kind of illustrated here,

00:09:20.044 --> 00:09:21.264
purely in the x direction,

00:09:21.264 --> 00:09:23.541
that's telling us the
slope with respect to x,

00:09:23.541 --> 00:09:25.082
and then this term one here,

00:09:25.082 --> 00:09:27.477
was telling us the
slope with respect to y.

00:09:27.477 --> 00:09:29.630
So when we moved purely
in the y direction,

00:09:29.630 --> 00:09:31.135
that's telling us the slope there.

00:09:31.135 --> 00:09:32.926
And we could just turn those knobs if we

00:09:32.926 --> 00:09:34.833
change the two and we change the one,

00:09:34.833 --> 00:09:36.583
that's what's going to allow us to

00:09:36.583 --> 00:09:39.920
basically change what the
slopes of the plane are.

00:09:39.920 --> 00:09:41.180
I'm going to say slopes plural

00:09:41.180 --> 00:09:43.823
because it's with respect to
the x and the y direction.

00:09:43.823 --> 00:09:46.103
And that will give us control
of various different planes

00:09:46.103 --> 00:09:46.956
that pass through.

00:09:46.956 --> 00:09:50.327
If I'm looking at the one right here,

00:09:50.327 --> 00:09:54.230
then the movement in the y
direction is very shallow,

00:09:54.230 --> 00:09:56.142
so that would be turning this knob lower,

00:09:56.142 --> 00:09:58.503
and instead of one it
might be point zero one.

00:09:58.503 --> 00:10:00.662
And if I were looking at
movement in the x direction,

00:10:00.662 --> 00:10:02.165
you know this looks actually negative.

00:10:02.165 --> 00:10:03.794
So this would tell you
that it's going to be

00:10:03.794 --> 00:10:05.054
some kind of negative number.

00:10:05.054 --> 00:10:06.922
So you can kind of dial
these knobs and that changes

00:10:06.922 --> 00:10:10.053
the different planes that
pass through that same point.

00:10:10.053 --> 00:10:13.141
And then, plugging in
this one two and three,

00:10:13.141 --> 00:10:14.807
tells us what point we're specifying.

00:10:14.807 --> 00:10:17.082
We're basically saying when
you input x equals one,

00:10:17.082 --> 00:10:18.629
and you input y equals 2,

00:10:18.629 --> 00:10:20.340
the whole thing should equal three.

00:10:20.340 --> 00:10:22.497
So this form right here's
is powerful enough that

00:10:22.497 --> 00:10:25.258
I want you to remember
it for the next video.

00:10:25.258 --> 00:10:26.847
I want you to remember the
idea of writing things down

00:10:26.847 --> 00:10:28.636
in this way where you specify

00:10:28.636 --> 00:10:29.816
the point its passing through

00:10:29.816 --> 00:10:32.787
with it's x coordinate y
coordinate and z coordinate,

00:10:32.787 --> 00:10:33.683
placed where they are,

00:10:33.683 --> 00:10:36.363
and then you tweak the slopes,
using these coefficients

00:10:36.363 --> 00:10:37.802
out front.

00:10:37.802 --> 00:10:39.264
So with that, I will see you next video.


Circuit Terminology

WEBVTT
Kind: captions
Language: en

00:00:00.505 --> 00:00:01.447
- [Voiceover] In this
video, we're gonna talk

00:00:01.447 --> 00:00:04.499
about some terminology
that we use to talk about,

00:00:04.499 --> 00:00:06.703
how circuits are put together.

00:00:06.703 --> 00:00:08.537
In previous videos, we've talked

00:00:08.537 --> 00:00:10.101
about the components, or the elements,

00:00:10.101 --> 00:00:11.794
that are used to make up circuits.

00:00:11.794 --> 00:00:15.127
So, for an example, resistor, capacitor,

00:00:16.684 --> 00:00:19.913
and inductor, are circuit components.

00:00:19.913 --> 00:00:22.059
We also call those elements.

00:00:22.059 --> 00:00:24.892
In addition, we have some sources,

00:00:26.825 --> 00:00:31.229
like a voltage source, or for
example, a current source.

00:00:31.229 --> 00:00:33.896
Those would be the components...

00:00:38.941 --> 00:00:41.024
Or elements of a circuit.

00:00:48.251 --> 00:00:49.787
Now, we're going to start
assembling these things

00:00:49.787 --> 00:00:53.533
into circuits, and we need a
few more words to talk about.

00:00:53.533 --> 00:00:55.586
Here's some circuit components,

00:00:55.586 --> 00:00:57.765
that are laying out on the tabletop,

00:00:57.765 --> 00:01:01.605
and we're gonna connect
those up with a wire.

00:01:01.605 --> 00:01:05.789
For example, I could connect
this one to this one,

00:01:05.789 --> 00:01:08.319
with this yellow, ideal wire.

00:01:08.319 --> 00:01:10.874
An ideal wire has zero resistance,

00:01:10.874 --> 00:01:13.890
and it's perfect everywhere.

00:01:13.890 --> 00:01:17.887
This forms a junction,
between these two components.

00:01:17.887 --> 00:01:19.720
That is called a node.

00:01:21.586 --> 00:01:25.753
Node is the word for
junction, mean the same thing.

00:01:30.042 --> 00:01:31.081
That's what a node is.

00:01:31.081 --> 00:01:34.664
If I connect up these
two other components,

00:01:35.658 --> 00:01:38.918
I still have one node,
because I have one junction,

00:01:38.918 --> 00:01:41.457
that's the same voltage everywhere.

00:01:41.457 --> 00:01:43.290
That's what a node is.

00:01:44.795 --> 00:01:46.128
We're gonna go over to this circuit here,

00:01:46.128 --> 00:01:47.429
and we'll identify the nodes.

00:01:47.429 --> 00:01:50.736
This is a little more normal
looking, tidy circuit.

00:01:50.736 --> 00:01:53.620
Here's a junction, right here,

00:01:53.620 --> 00:01:57.789
between a resistor, and
this voltage source.

00:01:57.789 --> 00:01:59.544
So that's one node.

00:01:59.544 --> 00:02:03.087
If I move over here, I see
resistors connected together

00:02:03.087 --> 00:02:08.055
by ideal wires, so that forms
one single node, like that.

00:02:08.055 --> 00:02:10.453
That's our second node.

00:02:10.453 --> 00:02:12.350
Down below, same sort of thing.

00:02:12.350 --> 00:02:16.065
I see an ideal wire,
connecting the resistors,

00:02:16.065 --> 00:02:19.309
and the source, so I can color that in.

00:02:19.309 --> 00:02:21.392
That's node number three.

00:02:23.416 --> 00:02:25.833
This circuit has three nodes.

00:02:29.889 --> 00:02:31.143
Now what's connecting the nodes?

00:02:31.143 --> 00:02:32.600
The thing that's connecting the nodes,

00:02:32.600 --> 00:02:34.183
is called a branch.

00:02:36.660 --> 00:02:39.622
A branch is the same things as an element.

00:02:39.622 --> 00:02:43.415
We'll count the branches,
or elements, in this thing.

00:02:43.415 --> 00:02:46.219
This voltage source,
connects the third node

00:02:46.219 --> 00:02:50.324
to the first node, so that's one element.

00:02:50.324 --> 00:02:53.130
This resistor connects
node one and node two,

00:02:53.130 --> 00:02:56.014
so that's the second branch.

00:02:56.014 --> 00:02:58.867
This resister connects
node two and node three,

00:02:58.867 --> 00:03:00.873
so there's the third branch.

00:03:00.873 --> 00:03:03.757
And this resistor, with
a separate current,

00:03:03.757 --> 00:03:05.387
also connects those two nodes,

00:03:05.387 --> 00:03:08.205
so that's the fourth branch.

00:03:08.205 --> 00:03:12.372
This circuit has one, two,
three, four elements in it,

00:03:14.368 --> 00:03:17.659
and it also means, it has four branches.

00:03:17.659 --> 00:03:19.086
Four branches.

00:03:19.086 --> 00:03:22.565
That's what a branch and a node are.

00:03:22.565 --> 00:03:24.054
I'm gonna move the
picture over a little bit,

00:03:24.054 --> 00:03:26.484
so that we can do this again,

00:03:26.484 --> 00:03:29.067
on a little more fancy circuit.

00:03:29.963 --> 00:03:31.546
First thing we're gonna do, again,

00:03:31.546 --> 00:03:34.289
just to repeat the process,
we're gonna count the nodes.

00:03:34.289 --> 00:03:38.456
Here's a junction between
a resistor and a source,

00:03:39.979 --> 00:03:44.148
here's three resistors,
connected by a perfect wire,

00:03:44.148 --> 00:03:45.935
so that's the second node.

00:03:45.935 --> 00:03:48.768
Here we find three more resistors,

00:03:50.371 --> 00:03:53.302
connected by a perfect
wire, there's the third.

00:03:53.302 --> 00:03:55.559
Down here, we have, there's a junction,

00:03:55.559 --> 00:03:59.493
between two resistors, so
that's our fourth node.

00:03:59.493 --> 00:04:02.486
Finally, we have this node here,

00:04:02.486 --> 00:04:06.319
connecting these four
elements, with one node.

00:04:09.634 --> 00:04:12.596
This is sometimes called a distributed,

00:04:12.596 --> 00:04:14.524
a distributed node,
when it's all spread out

00:04:14.524 --> 00:04:17.580
on the page like that, but
it's still just one node.

00:04:17.580 --> 00:04:20.163
So this circuit has five nodes.

00:04:25.449 --> 00:04:26.765
If we count up the elements,

00:04:26.765 --> 00:04:28.865
that will tell us how
many branches there are.

00:04:28.865 --> 00:04:32.865
One element, two, three,
four, five, six, seven?

00:04:38.129 --> 00:04:39.379
Seven elements.

00:04:46.859 --> 00:04:48.991
Alright, there's our two key words.

00:04:48.991 --> 00:04:50.574
Elements and nodes.

00:04:55.887 --> 00:04:59.288
Now, I'm gonna quickly move again, down.

00:04:59.288 --> 00:05:01.749
Bring in another circuit here.

00:05:01.749 --> 00:05:05.249
We're gonna talk about the idea of a mesh.

00:05:08.614 --> 00:05:12.781
The other thing we're gonna
about is the word, loop.

00:05:14.962 --> 00:05:17.533
The word mesh comes from screen doors,

00:05:17.533 --> 00:05:20.117
or screens that you put on your windows,

00:05:20.117 --> 00:05:21.112
to keep the bugs out.

00:05:21.112 --> 00:05:23.761
If I draw a screen, like this,

00:05:23.761 --> 00:05:26.269
this is what it looks like.

00:05:26.269 --> 00:05:27.351
A bunch of crossing wires.

00:05:27.351 --> 00:05:28.605
This little space right here,

00:05:28.605 --> 00:05:30.909
that little gap, is called a mesh.

00:05:30.909 --> 00:05:34.075
That's what that word comes from.

00:05:34.075 --> 00:05:36.097
We're gonna find the
meshes of our circuit.

00:05:36.097 --> 00:05:38.837
What we look for, here's the branches,

00:05:38.837 --> 00:05:41.920
and the mesh, it is a kind of a loop,

00:05:42.839 --> 00:05:45.339
that fills up this open space.

00:05:46.397 --> 00:05:50.564
This circuit has one mesh,
two mesh, three meshes.

00:05:55.253 --> 00:05:56.256
That's how that looks.

00:05:56.256 --> 00:05:58.780
To draw a mesh, you start on a node,

00:05:58.780 --> 00:06:01.005
you go through elements, until you

00:06:01.005 --> 00:06:02.933
come back to where you started.

00:06:02.933 --> 00:06:04.312
That's how we did those three,

00:06:04.312 --> 00:06:07.212
and they fill the open
windows of the circuit.

00:06:07.212 --> 00:06:09.712
This circuit has three meshes.

00:06:12.116 --> 00:06:16.513
A mesh is a loop, and we can
have other kinds of loops, too.

00:06:16.513 --> 00:06:19.773
They don't have to be just the
ones that fill the windows.

00:06:19.773 --> 00:06:22.563
In general, this circuit has other loops,

00:06:22.563 --> 00:06:24.364
and we'll identify some of those.

00:06:24.364 --> 00:06:26.895
Let's just start at one
of these nodes here,

00:06:26.895 --> 00:06:29.669
and go around like that.

00:06:29.669 --> 00:06:30.919
This is a loop.

00:06:32.600 --> 00:06:34.152
I could draw other loops in here,

00:06:34.152 --> 00:06:35.751
we'll make them all different colors.

00:06:35.751 --> 00:06:38.918
There's a loop, if I start right here,

00:06:40.093 --> 00:06:43.510
I can draw a loop through these elements.

00:06:46.738 --> 00:06:48.635
Finally, if I have a sharp eye,

00:06:48.635 --> 00:06:51.783
there's one more loop in this circuit.

00:06:51.783 --> 00:06:53.045
Let's just start right here,

00:06:53.045 --> 00:06:57.212
and it actually goes all
the way around the outside.

00:06:59.080 --> 00:07:01.682
This circuit has three, actually,

00:07:01.682 --> 00:07:04.549
if I add them together,
this has three loops,

00:07:04.549 --> 00:07:08.312
that I drew here, plus the three
loops that were the meshes.

00:07:08.312 --> 00:07:10.562
This circuit has six loops.

00:07:12.998 --> 00:07:14.487
Circuits always have a lot of loops,

00:07:14.487 --> 00:07:17.434
and so, usually, we
don't talk about these.

00:07:17.434 --> 00:07:19.926
More often, it's more
organized and straightforward

00:07:19.926 --> 00:07:23.249
to talk about how many
meshes are in a circuit.

00:07:23.249 --> 00:07:24.082
Alright.

00:07:25.004 --> 00:07:26.148
That does it for this video.

00:07:26.148 --> 00:07:27.981
We got mesh and loop,

00:07:29.252 --> 00:07:32.752
we talked about components and elements...

00:07:41.618 --> 00:07:43.609
And we finished up, with the idea,

00:07:43.609 --> 00:07:45.942
also, of nodes and branches.

00:07:58.076 --> 00:07:58.909
That'll do it.

00:07:58.909 --> 00:08:01.879
There's our new vocabulary,
for talkin' about circuits.


Apostrophes and plurals

WEBVTT
Kind: captions
Language: en

00:00:00.435 --> 00:00:01.923
- [Paige] Hello Grammarians, Hello David.

00:00:01.923 --> 00:00:02.883
- [David] Hello Paige.

00:00:02.883 --> 00:00:04.035
- [Paige] So today, we're gonna talk about

00:00:04.035 --> 00:00:06.723
apostrophes and plurals.

00:00:06.723 --> 00:00:08.312
We talked about this a little bit in our

00:00:08.312 --> 00:00:10.729
Introduction to the Apostrophe video.

00:00:10.729 --> 00:00:15.400
This is a very, very rare case,
where we use an apostrophe

00:00:15.400 --> 00:00:17.429
to show that something is plural,

00:00:17.429 --> 00:00:19.051
and it almost never happens,

00:00:19.051 --> 00:00:20.538
but we will explain when it does.

00:00:20.538 --> 00:00:22.896
- [David] Paige, when is the one time

00:00:22.896 --> 00:00:25.488
in this immense and
wonderful galaxy of English

00:00:25.488 --> 00:00:28.097
when the stars align
for it to be permissible

00:00:28.097 --> 00:00:31.521
to pluralize something with an apostrophe?

00:00:31.521 --> 00:00:34.688
- [Paige] That one time is
when you are pluralizing

00:00:34.688 --> 00:00:36.355
a lower case letter.

00:00:37.312 --> 00:00:39.824
If you're saying something
like, "You need to remember

00:00:39.824 --> 00:00:43.106
" to always dot your i's,"
where you're talking about

00:00:43.106 --> 00:00:47.168
the letter I, and there
are several of them,

00:00:47.168 --> 00:00:49.744
you're gonna put an
apostrophe before the S.

00:00:49.744 --> 00:00:53.584
- [David] OK, so that's to
prevent it from looking like is,

00:00:53.584 --> 00:00:56.224
right, 'cause if we didn't
have that apostrophe in there,

00:00:56.224 --> 00:00:59.329
it would just be the word is.

00:00:59.329 --> 00:01:03.441
There's no way to tell I's
from the word is in that case.

00:01:03.441 --> 00:01:05.234
- [Paige] Right, and
you need to remember to

00:01:05.234 --> 00:01:08.065
always dot your is,
doesn't make any sense.

00:01:08.065 --> 00:01:09.398
- [David] Right.

00:01:10.903 --> 00:01:12.981
- [Paige] This apostrophe can look like

00:01:12.981 --> 00:01:16.149
it's making the letter I possessive,

00:01:16.149 --> 00:01:18.725
but it's really just there
to make it clear that

00:01:18.725 --> 00:01:20.225
this is a plural I

00:01:21.289 --> 00:01:22.206
and not is.

00:01:23.881 --> 00:01:26.299
- [David] So this is the only case.

00:01:26.299 --> 00:01:29.574
If it were upper case letters,

00:01:29.574 --> 00:01:32.642
you wouldn't do this, right.

00:01:32.642 --> 00:01:36.003
If you were saying David's capital As

00:01:36.003 --> 00:01:37.336
look like trees.

00:01:40.099 --> 00:01:42.482
It's less likely that
you're gonna gonna confuse

00:01:42.482 --> 00:01:45.282
capital A, lower case S in
the middle of a sentence

00:01:45.282 --> 00:01:47.314
for the word as.

00:01:47.314 --> 00:01:48.930
- [Paige] Right, 'cause you
wouldn't just capitalize

00:01:48.930 --> 00:01:50.801
the word as in the middle of a sentence.

00:01:50.801 --> 00:01:52.151
- [David] Right.

00:01:52.151 --> 00:01:56.072
So this is for only lower case letters,

00:01:56.072 --> 00:01:58.696
the little ones, the inside voice.

00:01:58.696 --> 00:02:00.215
(laughing)

00:02:00.215 --> 00:02:03.016
Paige, that's it, right?
- [Paige] Yeah.

00:02:03.016 --> 00:02:04.329
- [David] That's the only exception,

00:02:04.329 --> 00:02:06.760
that's the only time you use apostrophes

00:02:06.760 --> 00:02:09.498
to form the plural, no other time.

00:02:09.498 --> 00:02:11.738
So if you're talking
about, doesn't matter,

00:02:11.738 --> 00:02:14.888
if you're talking about CDs,

00:02:14.888 --> 00:02:15.721
or DVDs,

00:02:16.676 --> 00:02:17.509
or MP3s,

00:02:19.220 --> 00:02:21.687
or whatever you kids are
listening to these days,

00:02:21.687 --> 00:02:24.340
it doesn't matter, there's no need for an

00:02:24.340 --> 00:02:26.676
apostrophe in any of these places.

00:02:26.676 --> 00:02:27.893
- [Paige] Right, 'cause
that's pretty clear.

00:02:27.893 --> 00:02:30.484
- [David] You just use a lower case S,

00:02:30.484 --> 00:02:31.588
but if you're trying to talk about

00:02:31.588 --> 00:02:36.533
multiple lower case letters,
then you use an apostrophe.

00:02:36.533 --> 00:02:39.032
- [Paige] Yeah, so if
you're trying to figure out

00:02:39.032 --> 00:02:41.719
how to make something
plural, and you're like,

00:02:41.719 --> 00:02:43.142
"Do I use an apostrophe?"

00:02:43.142 --> 00:02:46.142
No, unless it's a lower case letter.

00:02:47.126 --> 00:02:48.439
You can learn anything.

00:02:48.439 --> 00:02:49.272
- [David] David out.

00:02:49.272 --> 00:02:50.198
- [Paige] Paige out.


Choosing between its and it’s

WEBVTT
Kind: captions
Language: en

00:00:00.279 --> 00:00:01.112
- [Voiceover] Hello, grammarians,

00:00:01.112 --> 00:00:02.026
and, hello, Paige.

00:00:02.026 --> 00:00:02.859
- [Voiceover] Hi, David.

00:00:02.859 --> 00:00:05.117
- [Voiceover] So, what
are we working on today?

00:00:05.117 --> 00:00:06.469
- [Voiceover] So, today
we're gonna talk about

00:00:06.469 --> 00:00:09.487
the difference between it's and its.

00:00:09.487 --> 00:00:12.274
- [Voiceover] Oh, oh,
that sounds real tricky.

00:00:12.274 --> 00:00:14.473
- [Voiceover] Yeah, but we'll be okay.

00:00:14.473 --> 00:00:15.450
- [Voiceover] Okay.

00:00:15.450 --> 00:00:16.955
So, it's, with an apos--

00:00:16.955 --> 00:00:18.854
So, we have these two forms in English

00:00:18.854 --> 00:00:21.399
and they mean very different things.

00:00:21.399 --> 00:00:24.125
So, let's go though them really quick.

00:00:24.125 --> 00:00:28.392
So, it's with an apostrophe
is a contraction, right?

00:00:28.392 --> 00:00:30.090
What is it a contraction of?

00:00:30.090 --> 00:00:33.059
- [Voiceover] It is or it has.

00:00:33.059 --> 00:00:35.730
- [Voiceover] As in, it's
a lovely day outside.

00:00:35.730 --> 00:00:38.950
Or, for it has, like it's been,

00:00:38.950 --> 00:00:42.410
it has been one week since
you looked at cheese.

00:00:42.410 --> 00:00:44.199
- [Voiceover] (laughing)
Sad, it's been a sad week.

00:00:44.199 --> 00:00:45.668
- [Voiceover] It's been a sad week.

00:00:45.668 --> 00:00:46.915
As opposed to its.

00:00:46.915 --> 00:00:48.291
Can you walk me through its.

00:00:48.291 --> 00:00:52.282
- [Voiceover] So, its
is a possessive pronoun.

00:00:52.282 --> 00:00:54.178
And it's a little
confusing 'cause possessive

00:00:54.178 --> 00:00:56.816
usually uses an apostrophe, too.

00:00:56.816 --> 00:01:00.649
But possessive pronouns
don't use apostrophes.

00:01:02.551 --> 00:01:04.034
So, you would say something like,

00:01:04.034 --> 00:01:07.431
I like rib-eye steak
because of its rich flavor.

00:01:07.431 --> 00:01:09.731
- [Voiceover] That's a
pretty grody-looking steak.

00:01:09.731 --> 00:01:12.038
- [Voiceover] (laughs) I
know, pink and green is

00:01:12.038 --> 00:01:15.271
not how you want your steak to look.

00:01:15.271 --> 00:01:17.490
- [Voiceover] So, we frankly just used

00:01:17.490 --> 00:01:21.657
its where we would use his
or her or their or our.

00:01:22.730 --> 00:01:24.203
You would use its.

00:01:24.203 --> 00:01:27.103
- [Voiceover] Right, it's just
that it's not a person, so.

00:01:27.103 --> 00:01:27.936
- [Voiceover] So, if I were asking you,

00:01:27.936 --> 00:01:29.983
can I borrow your book?

00:01:29.983 --> 00:01:32.109
That's kinda the same thing as

00:01:32.109 --> 00:01:35.944
I like rib-eye steak
because of its flavor.

00:01:35.944 --> 00:01:37.719
- [Voiceover] Right, it's showing that

00:01:37.719 --> 00:01:39.742
the flavor belongs to the steak

00:01:39.742 --> 00:01:41.788
just like the book belongs to me.

00:01:41.788 --> 00:01:42.857
- [Voiceover] Right.

00:01:42.857 --> 00:01:45.138
So, flavor belongs to it,

00:01:45.138 --> 00:01:46.805
book belongs to you.

00:01:49.840 --> 00:01:52.590
So, this is the core distinction,

00:01:53.589 --> 00:01:56.057
is if you're talking about anything

00:01:56.057 --> 00:01:59.640
that would be about
possession you use its.

00:02:00.627 --> 00:02:03.036
I-T-S, no apostrophe.

00:02:03.036 --> 00:02:05.477
If you're trying to contract something,

00:02:05.477 --> 00:02:08.673
it is or it has, like
it's a lovely day outside

00:02:08.673 --> 00:02:11.140
or it's been one week
since you looked at cheese.

00:02:11.140 --> 00:02:13.980
Then you would use I-T apostrophe S

00:02:13.980 --> 00:02:15.496
'cause it's a contraction,
you're trying to

00:02:15.496 --> 00:02:18.599
cram more information into
this one little phrase.

00:02:18.599 --> 00:02:20.163
- [Voiceover] Precisely.

00:02:20.163 --> 00:02:21.645
- [Voiceover] Sweet.

00:02:21.645 --> 00:02:24.378
That's how you choose
between I-T apostrophe S

00:02:24.378 --> 00:02:26.378
and I-T no apostrophe S.

00:02:27.371 --> 00:02:28.413
You can learn anything.

00:02:28.413 --> 00:02:29.246
David out.

00:02:29.246 --> 00:02:30.183
- [Voiceover] Paige out.


BONUS: History of the possessive apostrophe

WEBVTT
Kind: captions
Language: en

00:00:00.322 --> 00:00:02.412
- [Voiceover] Hello
grammarians and historians

00:00:02.412 --> 00:00:04.386
and linguists and friends.

00:00:04.386 --> 00:00:06.286
David here along with Jake.

00:00:06.286 --> 00:00:07.119
- [Jake] Hey.

00:00:07.119 --> 00:00:08.576
- [David] And Paige.
- [Paige] Hello.

00:00:08.576 --> 00:00:11.224
- [David] And I want to
continue our discussion

00:00:11.224 --> 00:00:15.195
of the history of the
apostrophe, in English,

00:00:15.195 --> 00:00:17.633
and what I'm having Jake
draw for me right now

00:00:17.633 --> 00:00:20.675
is an old English King because what's...

00:00:20.675 --> 00:00:24.320
The story of the possessive
apostrophe, in English,

00:00:24.320 --> 00:00:27.237
is really the story of old English.

00:00:28.554 --> 00:00:32.878
Like, how did we get this
like Paige's and Jake's?

00:00:32.878 --> 00:00:36.171
How did we get that ending
up as our possessive form,

00:00:36.171 --> 00:00:38.186
in English, with that apostrophe s.

00:00:38.186 --> 00:00:41.015
Because it didn't always
used to be that way.

00:00:41.015 --> 00:00:43.802
It didn't always used to be apostrophe s.

00:00:43.802 --> 00:00:46.038
Oh, that's very nice, Jake.

00:00:46.038 --> 00:00:47.788
- [Jake] Well, I try.

00:00:51.337 --> 00:00:52.695
- [David] So, that's King Ethelred.

00:00:52.695 --> 00:00:56.445
So, okay, when we're
talking about, you know,

00:00:59.217 --> 00:01:02.064
the possessive in English is very strange

00:01:02.064 --> 00:01:05.222
because it's this relic from history

00:01:05.222 --> 00:01:08.722
of these forms left over from old English.

00:01:10.064 --> 00:01:13.477
So, here's this table, this
vastly simplified table.

00:01:13.477 --> 00:01:17.784
English used to have these
things called case endings.

00:01:17.784 --> 00:01:19.909
And this is not a very, this is like

00:01:19.909 --> 00:01:21.639
a super-simplified version.

00:01:21.639 --> 00:01:25.064
These are all, what are called,
the strong case endings.

00:01:25.064 --> 00:01:28.187
They were strong and weak
case endings for each gender,

00:01:28.187 --> 00:01:31.914
and, in English, we have
masculine, feminine, and neuter.

00:01:31.914 --> 00:01:34.153
But the important thing to remember, is

00:01:34.153 --> 00:01:37.126
that the singular form of the neuter

00:01:37.126 --> 00:01:38.961
and the masculine was es,

00:01:38.961 --> 00:01:41.286
and that just sounds like
gobbledyook right now, I get it.

00:01:41.286 --> 00:01:44.777
So, let's take our king,
which in old English

00:01:44.777 --> 00:01:47.277
would have been cyning, right,

00:01:48.864 --> 00:01:51.500
and so if we're gonna look this crown.

00:01:51.500 --> 00:01:54.123
Well, in old English, they
would have just used the Latin,

00:01:54.123 --> 00:01:56.941
corona, so we're just gonna
refer to this as a hat.

00:01:56.941 --> 00:01:59.099
So, if we want to talk
about the king's hat,

00:01:59.099 --> 00:02:01.865
in old English, we would use

00:02:01.865 --> 00:02:04.365
the special possessive ending,

00:02:06.627 --> 00:02:08.973
the masculine possessive ending, right,

00:02:08.973 --> 00:02:11.306
because English had a
million of these endings.

00:02:11.306 --> 00:02:13.651
There was one where if you
were the subject of a sentence,

00:02:13.651 --> 00:02:14.601
you would use that ending.

00:02:14.601 --> 00:02:16.021
If you were the object of a sentence,

00:02:16.021 --> 00:02:17.134
you would use that ending.

00:02:17.134 --> 00:02:19.352
The Norman Invasion lopped all those off

00:02:19.352 --> 00:02:20.838
along with a bunch English heads,

00:02:20.838 --> 00:02:22.893
and now we have a much
more simplified language

00:02:22.893 --> 00:02:24.367
for better or worse.

00:02:24.367 --> 00:02:27.595
If we're talking about the king, here,

00:02:27.595 --> 00:02:30.095
we can refer to this guy's hat

00:02:32.065 --> 00:02:33.565
as secyninges haet

00:02:35.113 --> 00:02:37.463
which might not be the most accurate,

00:02:37.463 --> 00:02:40.587
but, you know, Beowulf
isn't around to correct me.

00:02:40.587 --> 00:02:43.895
So, if we're looking at
this cyning, here, right,

00:02:43.895 --> 00:02:46.066
the possessive ending is this es.

00:02:46.066 --> 00:02:47.041
If, for example, we had,

00:02:47.041 --> 00:02:50.482
and I'm gonna draw a queen
that's not gonna be as nice,

00:02:50.482 --> 00:02:52.638
Queen Pun Hilda.

00:02:52.638 --> 00:02:54.791
So the difference between...

00:02:54.791 --> 00:02:56.864
So, okay, so the old English word

00:02:56.864 --> 00:03:00.531
for queen was, perhaps
unsurprisingly, cwen,

00:03:02.060 --> 00:03:04.944
and if we're gonna talk
about the queen's hat,

00:03:04.944 --> 00:03:09.310
we would use this singular,
strong, feminine genitive ending

00:03:09.310 --> 00:03:12.060
which is cwene, right, with an e.

00:03:13.071 --> 00:03:14.488
So, secwene haet,

00:03:15.431 --> 00:03:17.889
and that's where all of this started.

00:03:17.889 --> 00:03:22.069
Okay, so we have this really
ludicrously complicated system.

00:03:22.069 --> 00:03:24.298
Even this table is simplified, right?

00:03:24.298 --> 00:03:27.412
Like I've left out half of it,

00:03:27.412 --> 00:03:29.267
but, ultimately, what it boils down to

00:03:29.267 --> 00:03:32.239
is secyninges haet, secwene haet.

00:03:32.239 --> 00:03:34.341
And as we move through history,

00:03:34.341 --> 00:03:35.874
what happens is the French invade,

00:03:35.874 --> 00:03:38.427
and they say, "Uh, this
system is very complicated.

00:03:38.427 --> 00:03:40.982
"Let us get rid of it," and they do,

00:03:40.982 --> 00:03:42.340
and it basically leaves us with,

00:03:42.340 --> 00:03:44.395
by the time we get to middle English,

00:03:44.395 --> 00:03:45.765
the following.

00:03:45.765 --> 00:03:46.787
So, by the time we get to middle English,

00:03:46.787 --> 00:03:48.870
we have the kinges hatte,

00:03:51.431 --> 00:03:54.507
and we have the quenes hatte.

00:03:54.507 --> 00:03:57.816
And what's happened is this old English

00:03:57.816 --> 00:04:00.191
masculine and neuter genitive,

00:04:00.191 --> 00:04:03.349
this possessive form, has just become

00:04:03.349 --> 00:04:05.436
the norm for everything.

00:04:05.436 --> 00:04:08.294
Everything is now masculine-ized.

00:04:08.294 --> 00:04:09.808
For better or worse, that's like,

00:04:09.808 --> 00:04:13.745
everything has been
simplified in that direction.

00:04:13.745 --> 00:04:15.266
That's part one.

00:04:15.266 --> 00:04:17.286
Okay, so hold that in your head.

00:04:17.286 --> 00:04:18.119
Okay.

00:04:19.039 --> 00:04:22.116
Then, so (laughs) that's middle English,

00:04:22.116 --> 00:04:25.699
And then, the printing
press gets invented.

00:04:27.120 --> 00:04:29.535
Now, all of the sudden,
people are writing texts

00:04:29.535 --> 00:04:31.148
in English all over the place,

00:04:31.148 --> 00:04:33.900
but nobody knows how to spell yet, right?

00:04:33.900 --> 00:04:36.187
So, we've got that possessive form,

00:04:36.187 --> 00:04:40.158
and then we have, what's
called, the his possessive.

00:04:40.158 --> 00:04:42.282
So, at this point, we're
in modern English, right,

00:04:42.282 --> 00:04:45.185
and so some bit of middle
English and old English

00:04:45.185 --> 00:04:47.092
have fallen away.

00:04:47.092 --> 00:04:48.759
But so, for example,

00:04:50.234 --> 00:04:54.484
we're still looking at something
like, "The kinges hat,"

00:04:54.484 --> 00:04:57.271
but what we're starting
to see in this one weird

00:04:57.271 --> 00:05:00.638
little period between like the late-16th

00:05:00.638 --> 00:05:02.867
and early-17th centuries.

00:05:02.867 --> 00:05:04.887
This brief fad for this thing,

00:05:04.887 --> 00:05:07.220
where people went, "the king

00:05:08.823 --> 00:05:09.656
"his hat."

00:05:11.168 --> 00:05:13.668
And, if you can imagine, like,

00:05:14.812 --> 00:05:17.867
post-Elizabethan era Londoner saying this,

00:05:17.867 --> 00:05:21.153
it kind of sounds the same, to my mind,

00:05:21.153 --> 00:05:23.521
"The kinges hat," "the king his hat,"

00:05:23.521 --> 00:05:25.239
right, like you're losing...

00:05:25.239 --> 00:05:27.434
This 'h' is kind of swallowed.

00:05:27.434 --> 00:05:28.583
- [Jake] So, nobody knew how to spell

00:05:28.583 --> 00:05:30.402
because there was no way to spell.

00:05:30.402 --> 00:05:32.898
- [David] Right, like, Samuel
Johnson had not yet written

00:05:32.898 --> 00:05:35.378
the first dictionary,
and that's like 1720.

00:05:35.378 --> 00:05:37.658
- [Jake] Uh-huh.
[David] I'm pretty sure.

00:05:37.658 --> 00:05:40.932
There were no standards,
not because people were dumb

00:05:40.932 --> 00:05:42.337
or anything, certainly not.

00:05:42.337 --> 00:05:45.367
It's just that these
standards didn't exist.

00:05:45.367 --> 00:05:48.699
Like, in the great scheme of history,

00:05:48.699 --> 00:05:50.824
there's stuff that we do now, you know,

00:05:50.824 --> 00:05:53.482
that 400 years from now
people are gonna look back

00:05:53.482 --> 00:05:56.791
at us and be like, "Phh, you
used words to communicate?"

00:05:56.791 --> 00:05:59.740
You know, like we have no idea.

00:05:59.740 --> 00:06:01.823
So, what starts to happen

00:06:02.731 --> 00:06:04.407
is this thing,

00:06:04.407 --> 00:06:07.424
the king his hat, becomes
more and more common

00:06:07.424 --> 00:06:09.980
to the point where people
just sort of understand it

00:06:09.980 --> 00:06:14.147
as a given, and it starts to
get collapsed to save space.

00:06:15.089 --> 00:06:17.315
So, the king his hat

00:06:17.315 --> 00:06:19.982
becomes the king's hat, like so.

00:06:21.300 --> 00:06:24.604
And just this one weird, fad usage,

00:06:24.604 --> 00:06:27.685
which you could even argue
is like a folk entomology,

00:06:27.685 --> 00:06:28.707
or something made up.

00:06:28.707 --> 00:06:29.540
It doesn't matter.

00:06:29.540 --> 00:06:30.669
It happened.

00:06:30.669 --> 00:06:34.216
It's attested in print, and
this is how it was collapsed,

00:06:34.216 --> 00:06:36.590
and, what happened as
a result of this usage,

00:06:36.590 --> 00:06:38.982
is the same thing happened to this.

00:06:38.982 --> 00:06:41.273
So, the kinges hat became

00:06:41.273 --> 00:06:44.857
the king's hat, and it
was just well, frankly,

00:06:44.857 --> 00:06:48.119
because if you were talking
about the queen's hat,

00:06:48.119 --> 00:06:51.358
in this his possessive context, it just...

00:06:51.358 --> 00:06:54.858
You'd either have to do the Queen her hat,

00:06:56.176 --> 00:06:57.558
which is fine, I suppose,

00:06:57.558 --> 00:06:59.324
or the Queen his hat,

00:06:59.324 --> 00:07:02.539
which doesn't make a ton of sense.

00:07:02.539 --> 00:07:04.141
- [Jake] And if you're
wondering how there can be just

00:07:04.141 --> 00:07:07.995
this random change in sound in a language

00:07:07.995 --> 00:07:09.957
without anybody orchestrating it,

00:07:09.957 --> 00:07:11.885
think of a time where say something like,

00:07:11.885 --> 00:07:13.986
"I'm gonna go to the store."

00:07:13.986 --> 00:07:15.135
"I'm gonna..."

00:07:15.135 --> 00:07:16.494
What are you really saying there?

00:07:16.494 --> 00:07:19.002
It's a contraction of, I am going to.

00:07:19.002 --> 00:07:22.612
Nobody actually says, "I
am going to go right now."

00:07:22.612 --> 00:07:24.133
They say, "I'm gonna go."

00:07:24.133 --> 00:07:26.316
So, words are always kind of mashing

00:07:26.316 --> 00:07:27.674
into each other.

00:07:27.674 --> 00:07:29.439
- [David] If you remember
from an earlier video

00:07:29.439 --> 00:07:31.831
when Paige and I were
discussing the principle

00:07:31.831 --> 00:07:34.431
of least effort, that's
what Jake is getting at.

00:07:34.431 --> 00:07:35.952
Is, "the tongue is lazy."

00:07:35.952 --> 00:07:38.611
Don't feel bad, but "the tongue is lazy."

00:07:38.611 --> 00:07:41.432
Yeah, so what happened was, you know,

00:07:41.432 --> 00:07:43.099
this thing became...

00:07:46.436 --> 00:07:50.113
And pretty soon,
everything became this way.

00:07:50.113 --> 00:07:52.529
So, because of this
one strange little fad,

00:07:52.529 --> 00:07:54.255
what we call the Saxon possessive,

00:07:54.255 --> 00:07:56.392
this thing, the kinges, the cwenes,

00:07:56.392 --> 00:07:58.729
eventually just became king's

00:07:58.729 --> 00:08:01.063
and queen's, like so.

00:08:01.063 --> 00:08:03.290
- [Jake] How elegant.
- [David] Thank you.

00:08:03.290 --> 00:08:05.520
Jake, Paige, does this square with how...

00:08:05.520 --> 00:08:08.221
I mean, this is how apostrophes
are used in English,

00:08:08.221 --> 00:08:09.637
but Jake and Paige,
you all were telling me

00:08:09.637 --> 00:08:13.121
about all the many ways
that apostrophes are used

00:08:13.121 --> 00:08:15.737
in other languages around the world.

00:08:15.737 --> 00:08:17.436
- [Jake] Right, well I think, you know,

00:08:17.436 --> 00:08:20.302
punctuation marks are tools
just like any other tools

00:08:20.302 --> 00:08:21.376
that human beings use.

00:08:21.376 --> 00:08:22.467
- [David] Uh-huh.
- [Jake] And they can be used

00:08:22.467 --> 00:08:23.658
different ways in different languages.

00:08:23.658 --> 00:08:26.491
So, in Dutch, apostrophes are used

00:08:27.591 --> 00:08:28.659
to make plurals.

00:08:28.659 --> 00:08:29.492
- [David] What?!?!

00:08:29.492 --> 00:08:31.053
- [Jake] For words that end in a vowel.

00:08:31.053 --> 00:08:32.361
- [Jake] So.
- [David] Okay.

00:08:32.361 --> 00:08:34.571
- [Jake] Photo in Dutch, is f-o-t-o,

00:08:34.571 --> 00:08:36.252
and if you want to have
multiple photos, well,

00:08:36.252 --> 00:08:37.085
you have to throw in an apostrophe.

00:08:37.085 --> 00:08:38.974
You have to throw in an apostrophe

00:08:38.974 --> 00:08:40.057
before the s.

00:08:41.057 --> 00:08:42.442
No good reason why that's the case.

00:08:42.442 --> 00:08:44.868
That's just how they do it.

00:08:44.868 --> 00:08:48.607
Conversely, Dutch does
not put an apostrophe

00:08:48.607 --> 00:08:50.001
for possession.

00:08:50.001 --> 00:08:52.671
So, if you wanted to say, Jan's book,

00:08:52.671 --> 00:08:55.109
you would just say J-a-n-s.

00:08:55.109 --> 00:08:58.685
- [David] Oh, so it kind
of retains this genitive.

00:08:58.685 --> 00:09:00.879
It retains this possessive form.

00:09:00.879 --> 00:09:01.712
- [Jake] Right.

00:09:01.712 --> 00:09:02.922
Same thing with German.

00:09:02.922 --> 00:09:05.999
- [David] So how do we say, "Jan's book?"

00:09:05.999 --> 00:09:08.460
Jans book, like that?

00:09:08.460 --> 00:09:10.126
- [Jake] Uh-hum.
- [David] Okay.

00:09:10.126 --> 00:09:11.166
- [Jake] Same thing with German.

00:09:11.166 --> 00:09:13.186
German is a little bit more conservative,

00:09:13.186 --> 00:09:14.649
and that it retains the es.

00:09:14.649 --> 00:09:17.470
So, "Das Buch" might mean the book,

00:09:17.470 --> 00:09:20.263
in German, and if you want
to say, "Of the book,"

00:09:20.263 --> 00:09:22.122
or if you want to say, "The book's,"

00:09:22.122 --> 00:09:25.807
you'd say "Des Buches" with that es ending

00:09:25.807 --> 00:09:29.293
tagged onto "Buch".

00:09:29.293 --> 00:09:33.387
- [David] Oh, the same
one as in old English.

00:09:33.387 --> 00:09:35.129
- [Jake] Right, so
since English is kind of

00:09:35.129 --> 00:09:36.510
a cousin language to German.

00:09:36.510 --> 00:09:37.343
- [David] Uh-huh.

00:09:37.343 --> 00:09:40.179
- [Jake] You can see
which way the ball fell

00:09:40.179 --> 00:09:41.328
on these two languages.

00:09:41.328 --> 00:09:44.730
- [David] Wow! That's super cool.

00:09:44.730 --> 00:09:46.611
Paige, any insights from Danish?

00:09:46.611 --> 00:09:48.358
- [Paige] Yeah, so from my limited,

00:09:48.358 --> 00:09:51.529
you know, expertise in Danish,

00:09:51.529 --> 00:09:52.761
people who speak Danish tend

00:09:52.761 --> 00:09:55.794
to abbreviate like all their words.

00:09:55.794 --> 00:09:58.000
Like, everything gets
shortened all the time.

00:09:58.000 --> 00:09:59.366
- [David] Sure.

00:09:59.366 --> 00:10:02.165
- [Paige] So, the
apostrophe is sometimes used

00:10:02.165 --> 00:10:04.513
in a similar way to how it is here

00:10:04.513 --> 00:10:06.638
to sort of show what's being shortened.

00:10:06.638 --> 00:10:07.471
- [David] Okay.

00:10:07.471 --> 00:10:09.053
- [Paige] So in Danish,
to say something like,

00:10:09.053 --> 00:10:09.970
"Take me with you."

00:10:09.970 --> 00:10:10.803
- [David] Uh-huh.

00:10:10.803 --> 00:10:12.838
- [Paige] You would say,
"tag mig med"

00:10:12.838 --> 00:10:14.440
- [David] Tag mig med

00:10:14.440 --> 00:10:17.698
- [Paige] So then, you can
shorten that first word,

00:10:17.698 --> 00:10:20.499
in writing, by getting rid of the g

00:10:20.499 --> 00:10:22.079
and adding an apostrophe.

00:10:22.079 --> 00:10:22.912
- [David] Okay.

00:10:22.912 --> 00:10:23.867
- [Paige] This actually
doesn't happen much.

00:10:23.867 --> 00:10:25.260
It kind of has limited use,

00:10:25.260 --> 00:10:28.092
but it's similar to how we use it

00:10:28.092 --> 00:10:29.746
for contractions in English.

00:10:29.746 --> 00:10:30.601
- [David] Sure.

00:10:30.601 --> 00:10:33.515
- [Paige] And like, how
this possessive was formed.

00:10:33.515 --> 00:10:34.885
It's interesting that the possessive,

00:10:34.885 --> 00:10:36.543
the modern possessive in English,

00:10:36.543 --> 00:10:38.616
is just a form of contraction.

00:10:38.616 --> 00:10:39.657
- [David] Yeah.

00:10:39.657 --> 00:10:40.841
- [Paige] It's bizarre.

00:10:40.841 --> 00:10:41.944
- [David] Well, folks, thank you so much

00:10:41.944 --> 00:10:43.093
for joining me on this journey

00:10:43.093 --> 00:10:45.997
through the wacky history of
the apostrophe, in English.

00:10:45.997 --> 00:10:47.238
- [Jake] Thanks for taking us.

00:10:47.238 --> 00:10:48.306
- [Paige] Yeah, it was fun.

00:10:48.306 --> 00:10:49.665
- [David] Anytime.

00:10:49.665 --> 00:10:52.869
And remember, folks, you can learn anything.

00:10:52.869 --> 00:10:54.094
David out.

00:10:54.094 --> 00:10:55.458
- [Paige] Paige out.

00:10:55.458 --> 00:10:56.470
- [Jake] Jake out.


BONUS: History of the apostrophe

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:02.638
- [Voiceover] Hello grammarians,
historians, and linguists.

00:00:02.638 --> 00:00:03.666
David here with Paige.

00:00:03.666 --> 00:00:04.499
- [Voiceover] Hi.

00:00:04.499 --> 00:00:05.665
- [Voiceover] And Jake.
- [Voiceover] Hey.

00:00:05.665 --> 00:00:06.589
- [Voiceover] And we're gonna talk about

00:00:06.589 --> 00:00:09.069
the history of the apostrophe.

00:00:09.069 --> 00:00:12.402
The apostrophe isn't
just a punctuation mark.

00:00:12.402 --> 00:00:16.569
In fact, the word apostrophe
comes to us from Greek,

00:00:17.463 --> 00:00:19.504
from two different compounds.

00:00:19.504 --> 00:00:23.786
"Apo," meaning "away," and
"stroph," meaning "to turn."

00:00:23.786 --> 00:00:26.079
So it's a turning of strophe.

00:00:26.079 --> 00:00:27.068
We need to turn away.

00:00:27.068 --> 00:00:29.004
So it's a turning away.

00:00:29.004 --> 00:00:31.593
And in rhetoric, in classical rhetoric,

00:00:31.593 --> 00:00:34.093
when we talk about apostrophe,

00:00:36.131 --> 00:00:38.945
it's turning away from
your actual audience

00:00:38.945 --> 00:00:41.888
to deliver a message to absent people

00:00:41.888 --> 00:00:45.638
or inanimate objects or
just non-personified,

00:00:48.029 --> 00:00:51.236
you're trying to personify
an inhuman concept.

00:00:51.236 --> 00:00:52.604
- [Voiceover] So before
it was a punctuation mark,

00:00:52.604 --> 00:00:54.057
it was a literary technique.

00:00:54.057 --> 00:00:54.985
- [Voiceover] Yes, it was a turn,

00:00:54.985 --> 00:00:57.220
it was a figure of speech.

00:00:57.220 --> 00:00:59.829
You know, so if you think
about examples from literature,

00:00:59.829 --> 00:01:02.998
this can be, the two things that my mind

00:01:02.998 --> 00:01:04.850
immediately leaps to, being me,

00:01:04.850 --> 00:01:06.875
are "O, happy dagger,"

00:01:06.875 --> 00:01:10.446
the speech from the end of
Romeo and Juliet in act five.

00:01:10.446 --> 00:01:12.464
Boom, sorry, y'all didn't see.

00:01:12.464 --> 00:01:15.040
I plunged the stylus into my breast.

00:01:15.040 --> 00:01:17.227
(giggles)

00:01:17.227 --> 00:01:19.237
"O, happy dagger, this is thy sheath."

00:01:19.237 --> 00:01:21.444
"There rust and let me die."

00:01:21.444 --> 00:01:22.277
Boom.

00:01:22.277 --> 00:01:23.707
So, like in that, like, you know,

00:01:23.707 --> 00:01:25.240
we're addressing the dagger.

00:01:25.240 --> 00:01:27.101
The dagger is not alive.

00:01:27.101 --> 00:01:27.934
It is a knife.

00:01:27.934 --> 00:01:28.930
It cannot respond.

00:01:28.930 --> 00:01:31.513
Or, on a lighter note perhaps,

00:01:33.336 --> 00:01:35.718
from H.M.S. Pinafore, there's a song,

00:01:35.718 --> 00:01:39.334
"Fair moon, to thee I sing,
bright regent of the heavens."

00:01:39.334 --> 00:01:40.167
It's the moon.

00:01:40.167 --> 00:01:41.000
The moon can't talk back.

00:01:41.000 --> 00:01:42.551
It's the moon.

00:01:42.551 --> 00:01:44.658
And from this figure of speech,

00:01:44.658 --> 00:01:46.510
this is where we get the idea

00:01:46.510 --> 00:01:50.790
that an apostrophe represents
something that is missing.

00:01:50.790 --> 00:01:54.630
That's how we come to get its main use,

00:01:54.630 --> 00:01:56.241
to represent that something,

00:01:56.241 --> 00:01:59.658
that it's standing in for absent letters,

00:02:00.895 --> 00:02:02.870
just like an apostrophe in rhetoric

00:02:02.870 --> 00:02:05.857
would be delivered to absent friends.

00:02:05.857 --> 00:02:07.193
Follow me over to the next screen.

00:02:07.193 --> 00:02:09.310
Let's do a little bit of history.

00:02:09.310 --> 00:02:13.660
So the apostrophe was introduced
to the French language

00:02:13.660 --> 00:02:16.752
by an engraver and humanist
named Geoffroy Tory,

00:02:16.752 --> 00:02:18.224
I think, is how you would say his name.

00:02:18.224 --> 00:02:19.399
That's a guess.

00:02:19.399 --> 00:02:21.889
And around the late 16th century,

00:02:21.889 --> 00:02:24.406
I think it's around the 1580s,

00:02:24.406 --> 00:02:26.446
Tory is the man who also introduced

00:02:26.446 --> 00:02:30.549
a lot of diacritic or
accent marks into French.

00:02:30.549 --> 00:02:33.698
So, you know, instead of
like, "aime" meaning "loved,"

00:02:33.698 --> 00:02:35.822
it would be "aime" like that.

00:02:35.822 --> 00:02:39.004
And he's the person that
used it originally in French

00:02:39.004 --> 00:02:42.421
to start representing eliminated letters.

00:02:44.015 --> 00:02:47.107
So if you have an
expression like "la heure,"

00:02:47.107 --> 00:02:49.204
meaning "the hour,"

00:02:49.204 --> 00:02:52.303
Tory would have it "l'heure," like that.

00:02:52.303 --> 00:02:54.268
You know, and this
apostrophe in there, boom,

00:02:54.268 --> 00:02:58.016
represents this missing vowel sound.

00:02:58.016 --> 00:03:02.183
So, okay, so it's around this
time that this apostrophe

00:03:03.692 --> 00:03:05.476
starts making its way into English,

00:03:05.476 --> 00:03:09.376
because remember, England
has been under French rule

00:03:09.376 --> 00:03:11.678
for centuries at this point.

00:03:11.678 --> 00:03:13.954
The French invaded in the 11th century.

00:03:13.954 --> 00:03:16.671
We're talking about the
Norman Conquest of 1066.

00:03:16.671 --> 00:03:18.352
And since then, French culture has had

00:03:18.352 --> 00:03:23.063
a very profound impact on
the island of Great Britain.

00:03:23.063 --> 00:03:25.811
You know, so everyone
in a position of power

00:03:25.811 --> 00:03:28.512
speaks French or understands
and reads French.

00:03:28.512 --> 00:03:30.906
So the nobility speaks and reads French.

00:03:30.906 --> 00:03:33.968
Anyone that's literate
speaks and reads French.

00:03:33.968 --> 00:03:35.755
And so you're gonna be, you know,

00:03:35.755 --> 00:03:38.550
this intelligentsia is going
to be coming into contact

00:03:38.550 --> 00:03:39.596
with a lot of French,

00:03:39.596 --> 00:03:42.258
see the apostrophe being
used this way and say,

00:03:42.258 --> 00:03:44.434
"Oh, that's awfully convenient."

00:03:44.434 --> 00:03:46.851
And so it's around this time,

00:03:47.836 --> 00:03:51.836
around the early 17th
century, late 16th century

00:03:53.080 --> 00:03:57.024
that we're starting to see this
apostrophe usage in English.

00:03:57.024 --> 00:03:58.811
This is around the time when you first see

00:03:58.811 --> 00:04:00.978
the contraction of "I am,"

00:04:03.345 --> 00:04:05.107
"I'm," show up,

00:04:05.107 --> 00:04:07.455
is around this period.

00:04:07.455 --> 00:04:10.103
Jake, does this square with
how apostrophes are used

00:04:10.103 --> 00:04:11.590
in other languages too?

00:04:11.590 --> 00:04:13.272
- [Voiceover] Yeah, it's
the same in pretty much

00:04:13.272 --> 00:04:14.474
all the Romance languages.

00:04:14.474 --> 00:04:16.243
So anything derived from Latin,

00:04:16.243 --> 00:04:20.076
you have in Latin these
long definite articles

00:04:21.615 --> 00:04:23.365
like "ille," i l l e,

00:04:26.318 --> 00:04:27.901
or "illa," i l l a.

00:04:30.317 --> 00:04:32.539
And all the definite articles
that come out of this

00:04:32.539 --> 00:04:34.025
in all the Romance languages

00:04:34.025 --> 00:04:37.176
take some fraction of
the original from Latin

00:04:37.176 --> 00:04:40.059
and omit some part with an apostrophe.

00:04:40.059 --> 00:04:41.892
So "amico" in Italian,

00:04:43.804 --> 00:04:46.453
to add a definite article
to make it "the friend,"

00:04:46.453 --> 00:04:47.968
you can add just l apostrophe.

00:04:47.968 --> 00:04:48.810
"L'amico."

00:04:48.810 --> 00:04:51.209
- [Voiceover] Cool.

00:04:51.209 --> 00:04:53.419
So yeah, so during this time

00:04:53.419 --> 00:04:57.720
of apostrophe expansion
across the continent,

00:04:57.720 --> 00:04:59.349
people are just going nuts, right?

00:04:59.349 --> 00:05:02.478
There's no standardization
of usage for apostrophes.

00:05:02.478 --> 00:05:05.703
People are using it every
which way, but loose, you know.

00:05:05.703 --> 00:05:07.287
So they're using it like this.

00:05:07.287 --> 00:05:08.588
They're using it for contractions.

00:05:08.588 --> 00:05:10.609
They're using it for multiples of stuff,

00:05:10.609 --> 00:05:13.740
like stuff that we would
consider incorrect today.

00:05:13.740 --> 00:05:15.341
Like "book's," like that.

00:05:15.341 --> 00:05:17.247
Wah, that looks terrible to me.

00:05:17.247 --> 00:05:21.414
And crucially, they're
using it for the possessive.

00:05:22.692 --> 00:05:24.192
So like, "Jake's."

00:05:26.088 --> 00:05:29.508
And the history of that usage
is another story entirely.

00:05:29.508 --> 00:05:31.731
But this, for now, is the history

00:05:31.731 --> 00:05:36.244
of the introduction of the
apostrophe into English.

00:05:36.244 --> 00:05:37.938
You can learn anything.

00:05:37.938 --> 00:05:39.588
David and company out.


Introduction to the possessive

WEBVTT
Kind: captions
Language: en

00:00:00.191 --> 00:00:01.945
- [Voiceover] Hello
grammarians, hello Paige.

00:00:01.945 --> 00:00:03.172
- [Voiceover] Hi David.

00:00:03.172 --> 00:00:04.765
- [Voiceover] In the driver's seat.

00:00:04.765 --> 00:00:07.216
- [Voiceover] So, Paige,
today, it is my understanding

00:00:07.216 --> 00:00:09.881
that we are gonna talk
about the possessive.

00:00:09.881 --> 00:00:11.602
- [Voiceover] That's right.

00:00:11.602 --> 00:00:14.437
- [Voiceover] What even is
the possessive in English?

00:00:14.437 --> 00:00:17.309
What does that mean when we say that?

00:00:17.309 --> 00:00:19.515
What does it mean to possess something?

00:00:19.515 --> 00:00:21.399
- [Voiceover] Right, so that means to own

00:00:21.399 --> 00:00:23.116
something or to have something.

00:00:23.116 --> 00:00:25.525
- [Voiceover] Okay, so this
relates to the apostrophe,

00:00:25.525 --> 00:00:28.092
in that we use the
apostrophe in many cases,

00:00:28.092 --> 00:00:31.779
we use the apostrophe s in
many cases to show possession.

00:00:31.779 --> 00:00:33.825
Right, so if I were
talking about, there are

00:00:33.825 --> 00:00:35.179
a couple of ways to show that something

00:00:35.179 --> 00:00:38.699
belongs to someone or
something in English,

00:00:38.699 --> 00:00:42.220
like I could say, the carrot that

00:00:42.220 --> 00:00:45.007
belonged to that rabbit was delicious.

00:00:45.007 --> 00:00:47.136
- [Voiceover] Yeah, but
that's pretty complicated,

00:00:47.136 --> 00:00:50.696
and can make sentences much
longer than they need to be.

00:00:50.696 --> 00:00:53.284
- [Voiceover] So what's
a simpler way of saying

00:00:53.284 --> 00:00:56.466
the carrot that belonged to
the rabbit was delicious.

00:00:56.466 --> 00:00:57.407
- [Voiceover] You can say something like

00:00:57.407 --> 00:00:59.982
the rabbit's carrot was delicious.

00:00:59.982 --> 00:01:02.190
- [Voiceover] Oh, interesting,
so you're actually

00:01:02.190 --> 00:01:04.067
containing, there's like
a lot of information

00:01:04.067 --> 00:01:08.294
that's contained within the
rabbit's, that little thing.

00:01:08.294 --> 00:01:09.782
'Cause you're expressing the relationship

00:01:09.782 --> 00:01:12.062
between the rabbit and the carrot,

00:01:12.062 --> 00:01:13.660
just with that little apostrophe s,

00:01:13.660 --> 00:01:15.512
that contains so much information in it.

00:01:15.512 --> 00:01:18.509
- [Voiceover] Yeah, the
whole idea of the rabbit

00:01:18.509 --> 00:01:21.609
owning the carrot comes
from that apostrophe s.

00:01:21.609 --> 00:01:22.796
- [Voiceover] That's super cool.

00:01:22.796 --> 00:01:24.594
- [Voiceover] Yeah,
it's a pretty big deal.

00:01:24.594 --> 00:01:26.035
- [Voiceover] So this
doesn't just apply to

00:01:26.035 --> 00:01:27.807
common nouns, like rabbits, this can also

00:01:27.807 --> 00:01:30.061
apply to proper nouns, like people,

00:01:30.061 --> 00:01:32.274
or countries, or businesses, or whatever.

00:01:32.274 --> 00:01:34.900
- [Voiceover] Totally.
- [Voiceover] Or movies.

00:01:34.900 --> 00:01:36.701
- [Voiceover] Yeah, anything, I think

00:01:36.701 --> 00:01:40.873
- [Voiceover] Okay, so
to pull a completely

00:01:40.873 --> 00:01:43.093
random figure from American history,

00:01:43.093 --> 00:01:46.166
let's say Alexander
Hamilton had a surfboard.

00:01:46.166 --> 00:01:47.512
- [Voiceover] Okay.

00:01:47.512 --> 00:01:48.990
- [Voiceover] So, we could say, using the

00:01:48.990 --> 00:01:51.238
apostrophe s construction,
we could refer to

00:01:51.238 --> 00:01:54.831
Alexander Hamilton's surfboard, right?

00:01:54.831 --> 00:01:56.186
- [Voiceover] Right, the surfboard that

00:01:56.186 --> 00:01:58.161
belongs to Alexander Hamilton.

00:01:58.161 --> 00:02:00.572
- [Voiceover] Alright, so that
seems pretty straightforward.

00:02:00.572 --> 00:02:04.057
If we wanna show possession,
we just add an apostrophe s.

00:02:04.057 --> 00:02:06.303
Is that true in all cases though?

00:02:06.303 --> 00:02:07.814
- [Voiceover] Well, okay, not always.

00:02:07.814 --> 00:02:09.756
- [Voiceover] Okay, so there's a wrinkle.

00:02:09.756 --> 00:02:11.433
- [Voiceover] Of course,
there's always a wrinkle.

00:02:11.433 --> 00:02:13.823
- [Voiceover] Introduce
for us this wrinkle, Paige.

00:02:13.823 --> 00:02:15.225
- [Voiceover] So, there's an exception

00:02:15.225 --> 00:02:17.565
to this rule of using apostrophe s

00:02:17.565 --> 00:02:20.177
for possession when
you're using a pronoun.

00:02:20.177 --> 00:02:21.942
- [Voiceover] Ah!
- [Voiceover] Right.

00:02:21.942 --> 00:02:25.912
- [Voiceover] So, rabbit
and Alexander Hamilton

00:02:25.912 --> 00:02:28.318
are both nouns, but there are pronouns

00:02:28.318 --> 00:02:32.292
like it, or he, or she, where you don't

00:02:32.292 --> 00:02:34.580
use an apostrophe to show possessive.

00:02:34.580 --> 00:02:36.016
- [Voiceover] So if I wanted to say,

00:02:36.016 --> 00:02:38.998
that surfboard is his, there's

00:02:38.998 --> 00:02:40.390
no apostrophe in there, right?

00:02:40.390 --> 00:02:42.057
- [Voiceover] Right.

00:02:43.007 --> 00:02:44.773
- [Voiceover] Or, we
could just as easily say

00:02:44.773 --> 00:02:47.728
his surfboard, and I think
that's the same as saying

00:02:47.728 --> 00:02:51.492
that surfboard is Alexander Hamilton's.

00:02:51.492 --> 00:02:55.624
And you can see that there's
this real, it makes sense

00:02:55.624 --> 00:02:59.791
to want to put a possessive
apostrophe s in there,

00:03:01.136 --> 00:03:03.739
right, but that's not what you do.

00:03:03.739 --> 00:03:04.805
- [Voiceover] Right.

00:03:04.805 --> 00:03:06.255
- [Voiceover] This is this one kind of

00:03:06.255 --> 00:03:08.214
obnoxious exception to the rule.

00:03:08.214 --> 00:03:11.200
So, for possessive pronouns, they don't,

00:03:11.200 --> 00:03:14.061
they just, they never take apostrophes.

00:03:14.061 --> 00:03:15.378
- [Voiceover] That's right.

00:03:15.378 --> 00:03:17.019
- [Voiceover] Okay, so
the possessive in English

00:03:17.019 --> 00:03:19.194
usually formed with apostrophe s,

00:03:19.194 --> 00:03:21.532
The rabbit's carrot was delicious,

00:03:21.532 --> 00:03:23.865
Alexander Hamilton's surfboard,

00:03:23.865 --> 00:03:25.505
but when we're talking
about possessive pronouns

00:03:25.505 --> 00:03:29.098
like his, or hers, or ours, or theirs,

00:03:29.098 --> 00:03:32.515
or my, or its, no apostrophes are needed.

00:03:34.550 --> 00:03:37.099
Possessive pronouns
never take apostrophes.

00:03:37.099 --> 00:03:37.999
- [Voiceover] You got it.

00:03:37.999 --> 00:03:39.433
- [Voiceover] Sweet, thanks Paige.

00:03:39.433 --> 00:03:40.572
- [Voiceover] Thank you.

00:03:40.572 --> 00:03:42.255
- [Voiceover] You can
learn anything, David out.

00:03:42.255 --> 00:03:44.022
- [Voiceover] Paige out.


Possession for words ending in “s”

WEBVTT
Kind: captions
Language: en

00:00:00.327 --> 00:00:01.847
- [Voiceover] Hello
Grammarians, hello Paige.

00:00:01.847 --> 00:00:02.680
- [Paige] Hi David.

00:00:02.680 --> 00:00:04.745
- [David] We're talking about possession

00:00:04.745 --> 00:00:08.200
for names or words ending in the letter S.

00:00:08.200 --> 00:00:09.896
There's some confusion, I think,

00:00:09.896 --> 00:00:13.191
about what to do if you've got to make

00:00:13.191 --> 00:00:16.809
someone's name possessive
if their name ends in an S,

00:00:16.809 --> 00:00:19.142
for example, my friend Jess.

00:00:20.215 --> 00:00:21.048
If we're talking about Jess,

00:00:21.048 --> 00:00:23.015
and we're talking about
something that belongs to her,

00:00:23.015 --> 00:00:24.348
like Jess's hat.

00:00:25.271 --> 00:00:28.153
We know that there should
be an apostrophe in there,

00:00:28.153 --> 00:00:29.703
but should there also be an S?

00:00:29.703 --> 00:00:31.351
The answer is, yes.

00:00:31.351 --> 00:00:33.111
There had been some debate
over this for some time,

00:00:33.111 --> 00:00:37.639
but now, let me tell you, the
answer is yes, Jess's hat.

00:00:37.639 --> 00:00:39.482
- [Paige] Right, it seems
like a lot of Esses in a row,

00:00:39.482 --> 00:00:42.506
but it's important for understanding

00:00:42.506 --> 00:00:43.652
what someone's trying to say.

00:00:43.652 --> 00:00:47.796
- [David] Mm-hm, the same
thing happens regardless,

00:00:47.796 --> 00:00:50.795
it can be for words ending in S,

00:00:50.795 --> 00:00:52.204
like bus.

00:00:52.204 --> 00:00:56.827
So if we said, "The air
conditioning on this bus is broken,"

00:00:56.827 --> 00:00:59.864
We could say instead to make
it a little bit shorter,

00:00:59.864 --> 00:01:03.650
"The bus's air conditioning is broken."

00:01:03.650 --> 00:01:06.589
Again, we're just taking all
of that information about

00:01:06.589 --> 00:01:09.966
the air conditioning
that belongs to the bus,

00:01:09.966 --> 00:01:12.622
all of that is just sort of
being bundled up into this

00:01:12.622 --> 00:01:14.334
apostrophe S.

00:01:14.334 --> 00:01:17.999
It doesn't matter that bus
already ends with an S,

00:01:17.999 --> 00:01:20.287
this works the same as any other word,

00:01:20.287 --> 00:01:21.990
we're just gonna say, "bus's."

00:01:21.990 --> 00:01:23.816
If we wanted to talk
about the chili culture

00:01:23.816 --> 00:01:26.199
of the state of Texas, for example,

00:01:26.199 --> 00:01:29.798
we would say, "Texas's chili culture."

00:01:29.798 --> 00:01:31.672
- [Paige] Yeah, so it's
exactly the same as any other

00:01:31.672 --> 00:01:33.992
singular word even though it ends in S,

00:01:33.992 --> 00:01:36.487
you still need another S.

00:01:36.487 --> 00:01:39.654
- [David] So just add an apostrophe S,

00:01:41.030 --> 00:01:43.328
and if you didn't know, now you know.

00:01:43.328 --> 00:01:44.783
That's how you form the possessive for

00:01:44.783 --> 00:01:47.167
names or words ending in S.

00:01:47.167 --> 00:01:49.110
You can learn anything, David out,

00:01:49.110 --> 00:01:49.943
- [Paige] Paige out.