Vector fields, introduction

WEBVTT
Kind: captions
Language: en

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- [Voiceover] Hello
everyone, so in this video

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I'm gonna introduce vector fields.

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Now these are a concept
that come up all the time

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in multi variable calculus,
and that's probably because

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they come up all the time in physics.

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It comes up with fluid
flow, with electrodynamics,

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you see them all over the place.

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And what a vector field is,
is its pretty much a way

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of visualizing functions
that have the same number

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of dimensions in their
input as in their output.

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So here I'm gonna write a function

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that's got a two dimensional input

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X and Y, and then its output

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is going to be a two dimensional vector

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and each of the components
will somehow depend on X and Y.

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I'll make the first one
Y cubed minus nine Y

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and then the second component,
the Y component of the output

00:00:42.853 --> 00:00:45.738
will be X cubed minus nine X.

00:00:45.738 --> 00:00:48.237
I made them symmetric here,
looking kind of similar

00:00:48.237 --> 00:00:52.077
they don't have to be, I'm
just a sucker for symmetry.

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So if you imagine trying to
visualize a function like this

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with a graph it would be really hard

00:00:58.680 --> 00:01:01.084
because you have two
dimensions in the input

00:01:01.084 --> 00:01:02.646
two dimensions in the output

00:01:02.646 --> 00:01:03.891
so you'd have to somehow

00:01:03.891 --> 00:01:06.441
visualize this thing in four dimensions.

00:01:06.441 --> 00:01:09.022
So instead what we do, we
look only in the input space.

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So that means we look
only in the X,Y plane.

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So I'll draw these coordinate axes

00:01:13.207 --> 00:01:16.356
and just mark it up,
this here's our X axis

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this here's our Y axis

00:01:17.880 --> 00:01:21.188
and for each individual input point

00:01:21.188 --> 00:01:22.938
like lets say one,two

00:01:23.975 --> 00:01:26.308
so lets say we go to one,two

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I'm gonna consider the
vector that it outputs

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and attach that vector to the point.

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So lets walk through an
example of what I mean by that

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so if we actually evaluate F at one,two

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X is equal to one Y is equal to two

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so we plug in two cubed

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whoops, two cubed

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minus nine times two

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up here in the X component

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and then one cubed minus nine times Y

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nine times one, excuse me

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down in the Y component.

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Two cubed is eight nine times two is 18

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so eight minus 18 is negative 10

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negative 10

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and then one cubed is one,
nine times one is nine

00:02:13.509 --> 00:02:16.509
so one minus nine is negative eight.

00:02:18.446 --> 00:02:21.128
Now first imagine that this was

00:02:21.128 --> 00:02:22.896
if we just drew this vector where we count

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starting from the origin,
negative one, two,

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three, four, five, six,
seven, eight, nine, 10,

00:02:29.316 --> 00:02:31.226
so its going to have
this as its X component

00:02:31.226 --> 00:02:33.055
and then negative eight,
one, two, three, four,

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five, six, seven, we're gonna
actually go off the screen

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its a very very large vector

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so its gonna be something here

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and it ends up having
to go off the screen.

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But the nice thing about vectors

00:02:42.380 --> 00:02:44.229
it doesn't matter where they start

00:02:44.229 --> 00:02:46.688
so instead we can start it
here and we still want it

00:02:46.688 --> 00:02:49.573
to have that negative ten X component

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and the negative eight, negative one, two,

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three, four, five, six, seven, eight,

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negative eight

00:02:58.457 --> 00:03:00.457
as its Y component there

00:03:03.287 --> 00:03:04.770
and a plan with the vector field

00:03:04.770 --> 00:03:07.086
is to do this at not just one,two

00:03:07.086 --> 00:03:08.732
but at a whole bunch of different points

00:03:08.732 --> 00:03:10.825
and see what vectors attach to them

00:03:10.825 --> 00:03:12.674
and if we drew them all
according to their size

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this would be a real mess.

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There'd be markings all over the place

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and this one might have some
huge vector attached to it

00:03:19.744 --> 00:03:22.182
and this one would have some
huge vector attached to it

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and it would get really really messy.

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But instead what we do, just
gonna clear up the board here

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we scale them down, this is common

00:03:32.077 --> 00:03:34.820
you'll scale them down and
so that you're kind of lying

00:03:34.820 --> 00:03:37.705
about what the vectors themselves are

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but you get a much better feel for

00:03:39.493 --> 00:03:42.073
what each thing corresponds to.

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And another thing about this drawing

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that's not entirely faithful

00:03:45.222 --> 00:03:47.620
to the original function that we have

00:03:47.620 --> 00:03:50.139
is that all of these
vectors are the same length.

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I made this one just kind of the same unit

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this one the same unit, and over here

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they all just have the same length

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even though in reality
the length of the vectors'

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output by this function
can be wildly different.

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This is kind of common practice
when vector fields are drawn

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or when some kind of software
is drawing them for you

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so there are ways of getting around this

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one way is to just use
colors with your vectors

00:04:11.472 --> 00:04:15.272
so I'll switch over to a
different vector field here

00:04:15.272 --> 00:04:17.994
and here color is used to
kind of give a hint of length

00:04:17.994 --> 00:04:19.721
so it still looks organized
because all of them

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have the same length but the difference

00:04:23.541 --> 00:04:27.239
is that red and warmer
colors are supposed to

00:04:27.239 --> 00:04:29.799
indicate this is a very
long vector somehow

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and then blue would indicate
that its very short.

00:04:32.176 --> 00:04:34.655
Another thing you can
do is scale them to be

00:04:34.655 --> 00:04:37.235
roughly proportional
to what they should be

00:04:37.235 --> 00:04:38.515
so notice all the blue vectors

00:04:38.515 --> 00:04:40.384
scaled way down to basically be zero

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red vectors kind of stay the same size

00:04:42.700 --> 00:04:44.834
even though in reality this
might be representing a function

00:04:44.834 --> 00:04:47.353
where the true vector
here should be really long

00:04:47.353 --> 00:04:49.933
or the true vector should
be kind of medium length

00:04:49.933 --> 00:04:51.742
its still common for people
to just shrink them down

00:04:51.742 --> 00:04:54.139
so its a reasonable thing to view.

00:04:54.139 --> 00:04:56.638
So in the next video I'm
gonna talk about fluid flow

00:04:56.638 --> 00:04:58.365
a context in which vector
fields come up all the time

00:04:58.365 --> 00:05:01.169
and its also a pretty
good way to get a feel for

00:05:01.169 --> 00:05:02.693
a random vector field that you look at

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to understand what its all about.


Parametric surfaces

WEBVTT
Kind: captions
Language: en

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- So I have here

00:00:01.538 --> 00:00:03.314
a very complicated function.

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It's got a two-dimensional input,

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two different coordinates to its input,

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and then a three-dimensional output.

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Specifically, it's a
three-dimensional vector,

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and each one of these is some expression,

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its a bunch of cosines and sines

00:00:15.957 --> 00:00:18.171
that depends on the two input coordinates.

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And in the last video, we talked about how

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to visualize functions
that have a single input,

00:00:22.668 --> 00:00:24.553
a single parameter

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like T,

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and then, a two-dimensional vector output.

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So some kind of expression of T

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and another expression of T.

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And this is sort of the
three-dimensional analog of that.

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So what we're going to do,

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we're just going to visualize
things in the output space,

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and we're gonna try to think of all

00:00:39.897 --> 00:00:42.601
the possible points that could be outputs.

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So, for example, let's
just start off simple,

00:00:44.553 --> 00:00:46.991
let's get a feel for this function

00:00:46.991 --> 00:00:51.429
by evaluating it at a
simple pair of points.

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So, let's say

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we evaluate this function F,

00:00:55.958 --> 00:01:00.125
at T equals zero, I think will
probably be pretty simple,

00:01:01.276 --> 00:01:03.443
and then S is equal to pi.

00:01:08.402 --> 00:01:09.970
So let's think about what this would be.

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We go up and we say,

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okay, T of zero, cosine of zero is one,

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so this whole thing is gonna be one,

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same with this one.

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And sine of zero is zero.

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So this over here's gonna be zero,

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and this is also gonna be zero.

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Now cosine of pi is negative one.

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So this here's gonna be negative one.

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This one here's also
gonna be negative one.

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And then sine of pi,
just like sine of zero,

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is zero.

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So this whole thing actually
ends up simplifying quite a bit

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so that the top is three
times one plus negative one,

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one times negative one is negative one,

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and we get two.

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Then we have three times zero plus zero,

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so the Y component is just zero,

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and then the Z component is also zero.

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So what that would mean

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is that this output is gonna be the point

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that's two along the x-axis,

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and, there's nothing else to it,

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it's just two along the x-axis.

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So go ahead and--whoop,

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move the graph about,

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add that point there.

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So that's what would correspond

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to this one particular input, zero and pi.

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And, you know you can do
this with a whole bunch,

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and you might add a couple of other points

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based on other inputs that you find.

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But this would take forever,

00:02:29.567 --> 00:02:31.669
to start to get a feel for
the function as a whole.

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And another thing you can do, is say,

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okay, maybe rather than thinking of

00:02:35.959 --> 00:02:37.799
evaluating at a particular point,

00:02:37.799 --> 00:02:41.252
imagine one of the inputs was constant.

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So let's imagine that S
stayed constant at pi.

00:02:45.514 --> 00:02:47.110
But then we let T range freely.

00:02:47.110 --> 00:02:48.944
So, that means we're gonna have some kind

00:02:48.944 --> 00:02:51.027
of different output here.

00:02:52.485 --> 00:02:54.318
And, we're gonna let T

00:02:57.563 --> 00:03:00.579
just be some kind of variable
while the output is pi.

00:03:00.579 --> 00:03:03.378
So what that means is
we keep all of these,

00:03:03.378 --> 00:03:05.026
these negative one, negative one, and zero

00:03:05.026 --> 00:03:06.949
for what sine of pi is.

00:03:06.949 --> 00:03:09.250
But the output now

00:03:09.250 --> 00:03:11.750
is gonna be three cosine of T,

00:03:13.487 --> 00:03:14.487
cosine of T,

00:03:15.886 --> 00:03:19.010
plus negative one times the cosine of T,

00:03:19.010 --> 00:03:21.927
so it's gonna be minus cosine of T.

00:03:25.028 --> 00:03:28.429
The next part is gonna
still be three sine of T,

00:03:28.429 --> 00:03:30.264
this is no longer zero.

00:03:30.264 --> 00:03:34.822
I should probably erase
those guys actually so...

00:03:34.822 --> 00:03:37.401
We're no longer evaluating

00:03:37.401 --> 00:03:41.899
(inaudible) when T was zero.

00:03:41.899 --> 00:03:43.969
So, three times sine of T,

00:03:43.969 --> 00:03:47.504
that's just still the function
that we're dealing with.

00:03:47.504 --> 00:03:48.337
Three,

00:03:50.219 --> 00:03:51.052
sine of T,

00:03:54.994 --> 00:03:57.960
and then minus one times sine of T.

00:03:57.960 --> 00:03:59.043
So minus sine

00:04:00.444 --> 00:04:01.277
of T.

00:04:02.160 --> 00:04:06.077
Keep drawing it in green
just to be consistent.

00:04:07.068 --> 00:04:09.749
And then the bottom stays at zero.

00:04:09.749 --> 00:04:11.189
And this whole thing actually simplifies,

00:04:11.189 --> 00:04:12.803
three cosine T minus cosine T,

00:04:12.803 --> 00:04:14.886
that's just two cosine T.

00:04:16.482 --> 00:04:18.570
And then the same deal for the other one.

00:04:18.570 --> 00:04:20.163
It's gonna be two sine of T.

00:04:20.163 --> 00:04:21.830
So this whole thing,

00:04:23.554 --> 00:04:25.554
actually simplifies down

00:04:28.147 --> 00:04:29.297
to this.
So this is again

00:04:29.297 --> 00:04:30.647
when we're letting S stay constant

00:04:30.647 --> 00:04:32.845
and T ranges freely.

00:04:32.845 --> 00:04:34.595
And when you do that,

00:04:35.442 --> 00:04:36.357
what you're gonna end up getting

00:04:36.357 --> 00:04:37.361
is a circle that you draw.

00:04:37.361 --> 00:04:38.849
And you can maybe see why it's a circle

00:04:38.849 --> 00:04:41.452
'cause you have this cosine/sine pattern.

00:04:41.452 --> 00:04:42.780
It's a circle with radius two,

00:04:42.780 --> 00:04:43.613
and it should make sense that

00:04:43.613 --> 00:04:46.302
it runs through that first
point that we evaluated.

00:04:46.302 --> 00:04:47.177
So that's what happens if you let

00:04:47.177 --> 00:04:49.003
just one of the variables run.

00:04:49.003 --> 00:04:50.791
But now let's do the same thing,

00:04:50.791 --> 00:04:51.952
but think instead of what happens

00:04:51.952 --> 00:04:54.702
is S varies and T stays constant.

00:04:56.400 --> 00:04:58.105
I encourage you to work
it out for yourself,

00:04:58.105 --> 00:05:00.311
I'll go ahead and just kind of draw it,

00:05:00.311 --> 00:05:04.144
because I kinda wanna
give the intuition here.

00:05:05.644 --> 00:05:06.958
So in that case you're gonna get a circle

00:05:06.958 --> 00:05:08.708
that looks like this.

00:05:09.747 --> 00:05:10.875
So again I encourage you to try

00:05:10.875 --> 00:05:12.108
to think through for the same reasons.

00:05:12.108 --> 00:05:14.263
Imagine that you let S run freely,

00:05:14.263 --> 00:05:16.375
keep T constant at zero.

00:05:16.375 --> 00:05:18.028
Why is that you would get a circle

00:05:18.028 --> 00:05:19.328
that looks like this?

00:05:19.328 --> 00:05:23.328
And in fact, if you let
both T and S run freely,

00:05:24.831 --> 00:05:26.747
a very nice way to visualize that

00:05:26.747 --> 00:05:28.303
is to imagine that this circle,

00:05:28.303 --> 00:05:30.032
which represents S running freely,

00:05:30.032 --> 00:05:33.321
sweeps throughout space
as you let T run freely.

00:05:33.321 --> 00:05:38.310
And what you're gonna end
up getting when you do that,

00:05:38.310 --> 00:05:40.930
is a shape that goes like this.

00:05:40.930 --> 00:05:43.482
This is a doughnut. We have a fancy word

00:05:43.482 --> 00:05:47.136
for this in mathematics
we call it a torus.

00:05:47.136 --> 00:05:49.027
But it turns out the function here

00:05:49.027 --> 00:05:51.546
is a fancy way of drawing the torus.

00:05:51.546 --> 00:05:54.332
And in another video I'm gonna
go through in more detail

00:05:54.332 --> 00:05:55.481
if you were just given the torus,

00:05:55.481 --> 00:05:57.049
how you can find this function,

00:05:57.049 --> 00:05:59.272
how you can kind of get the
intuitive feel for that.

00:05:59.272 --> 00:06:01.069
And in that it'll involve going through,

00:06:01.069 --> 00:06:02.235
in a bit more detail,

00:06:02.235 --> 00:06:03.917
why when you sweep the circle out

00:06:03.917 --> 00:06:06.136
it gets the torus just so.

00:06:06.136 --> 00:06:07.209
And what the relationship between

00:06:07.209 --> 00:06:09.061
this red circle and the blue circle is.

00:06:09.061 --> 00:06:10.122
But here I just kind of want to give

00:06:10.122 --> 00:06:13.136
an intuition for what parametric
surfaces are all about,

00:06:13.136 --> 00:06:14.648
how it's a way of visualizing something

00:06:14.648 --> 00:06:17.468
that has a two-dimensional input

00:06:17.468 --> 00:06:20.135
and a three-dimensional output.


Introduction to 3d graphs

WEBVTT
Kind: captions
Language: en

00:00:00.526 --> 00:00:01.573
- [Voiceover] Hello everyone.

00:00:01.573 --> 00:00:03.683
So what I'd like to do here is to describe

00:00:03.683 --> 00:00:06.220
how we think about
three-dimensional graphs.

00:00:06.220 --> 00:00:08.858
Three-dimensional graphs
are a way that we represent

00:00:08.858 --> 00:00:10.255
certain kind of multi-variable function

00:00:10.255 --> 00:00:12.156
that kind of has two inputs,

00:00:12.156 --> 00:00:14.539
or rather a two-dimensional input,

00:00:14.539 --> 00:00:17.003
and then one-dimensional
of output of some kind.

00:00:17.003 --> 00:00:19.302
So the one that I have pictured here

00:00:19.302 --> 00:00:23.733
is f of (x, y) equals x
squared plus y squared.

00:00:23.733 --> 00:00:26.618
And before talking
exactly about this graph,

00:00:26.618 --> 00:00:28.463
I think it would be helpful, by analogy,

00:00:28.463 --> 00:00:30.380
we take a look at the
two-dimensional graphs and

00:00:30.380 --> 00:00:32.580
kinda remind ourselves how those work,

00:00:32.580 --> 00:00:36.562
what it is that we do,
because, it's pretty much

00:00:36.562 --> 00:00:38.876
the same thing in three-dimensions,

00:00:38.876 --> 00:00:41.148
but it takes a little bit
more of visualization.

00:00:41.148 --> 00:00:43.365
So the two-dimensional graphs,

00:00:43.365 --> 00:00:45.559
they have some kind of function, you know,

00:00:45.559 --> 00:00:49.726
let's see you have f of
x is equal to x squared,

00:00:51.086 --> 00:00:54.000
and anytime you visualizing
a function, you trying to

00:00:54.000 --> 00:00:55.554
understand the relationship between

00:00:55.554 --> 00:00:57.154
the inputs and the outputs.

00:00:57.154 --> 00:00:59.032
And here those are both just numbers,

00:00:59.032 --> 00:01:00.873
so you know you input a number like two,

00:01:00.873 --> 00:01:03.646
and it's gonna output four,

00:01:03.646 --> 00:01:07.351
you know you input negative
one it's gonna output one.

00:01:07.351 --> 00:01:09.638
And you're trying to
understand all the possible

00:01:09.638 --> 00:01:11.506
input-output pairs.

00:01:11.506 --> 00:01:13.089
And the fact that we can do this,

00:01:13.089 --> 00:01:17.571
that we can get a pretty
good intuitive feel for

00:01:17.571 --> 00:01:21.376
every possible input-output
pair is pretty incredible,

00:01:21.376 --> 00:01:24.476
the way we go about this
with graphs is you think

00:01:24.476 --> 00:01:26.492
we just plotting these
actual pairs, right?

00:01:26.492 --> 00:01:30.189
So you're gonna plot the
point, let's say we are gonna

00:01:30.189 --> 00:01:34.306
plot the point (2,4), so we
may kind of mark our graph,

00:01:34.306 --> 00:01:36.973
two here, one, two, three, four,

00:01:39.221 --> 00:01:43.261
so you wanna mark somewhere here (2,4),

00:01:43.261 --> 00:01:45.862
and that represents an input-output pair.

00:01:45.862 --> 00:01:48.300
And if you do that with,
you know, negative one, one,

00:01:48.300 --> 00:01:50.383
you go negative one, one.

00:01:51.586 --> 00:01:55.302
And when you do this for every
possible input-output pair,

00:01:55.302 --> 00:01:59.159
what you end up getting, I
might not draw this super well,

00:01:59.159 --> 00:02:01.491
is some kind of smooth curve.

00:02:01.491 --> 00:02:04.232
The implication for doing this
is that we typically think of

00:02:04.232 --> 00:02:07.406
what is on the x-axis as
being where the inputs live,

00:02:07.406 --> 00:02:09.813
you know, this would be, we
think of as the input one,

00:02:09.813 --> 00:02:13.018
and this is the input two, and so on,

00:02:13.018 --> 00:02:17.185
and then you think of the
output as being the height

00:02:18.828 --> 00:02:21.554
of the graph above each point.

00:02:21.554 --> 00:02:23.272
But this is kind of a
consequence of the fact

00:02:23.272 --> 00:02:26.078
where we just listing
all of the pairs here.

00:02:26.078 --> 00:02:29.149
Now if we go to the world
of multi-variable functions,

00:02:29.149 --> 00:02:31.905
you know, not gonna show
the graph right now,

00:02:31.905 --> 00:02:34.122
let's just think we've got
three-dimensional space

00:02:34.122 --> 00:02:37.106
at out disposal to do with what we will.

00:02:37.106 --> 00:02:39.010
We still want to understand
the relationship between

00:02:39.010 --> 00:02:42.653
inputs and outputs of
this guy, but this case,

00:02:42.653 --> 00:02:46.820
inputs are something that we
think of as pair of points,

00:02:47.914 --> 00:02:51.391
we might have a pair of points like (1,2),

00:02:51.391 --> 00:02:53.654
and the output there is gonna be

00:02:53.654 --> 00:02:57.821
one squared plus two squared,
and that equals is five.

00:03:02.573 --> 00:03:05.328
So how do we visualize that?

00:03:05.328 --> 00:03:08.053
Well if we wanna pair these
things together, the natural way

00:03:08.053 --> 00:03:10.813
to do that is to think of
a triplet of some kind.

00:03:10.813 --> 00:03:14.980
So in this case, you wanna
plug the triplet (1, 2, 5),

00:03:17.268 --> 00:03:19.932
and to do that in three-dimensions,

00:03:19.932 --> 00:03:23.157
we'll take a look over
here, we think of going one

00:03:23.157 --> 00:03:25.938
in the x direction, this
axis here is the x-axis,

00:03:25.938 --> 00:03:28.276
so we want to move distance one there,

00:03:28.276 --> 00:03:31.700
and we want to go two in the y direction,

00:03:31.700 --> 00:03:34.610
so we kinda think of
going distance two there,

00:03:34.610 --> 00:03:37.442
and then five up, and then

00:03:37.442 --> 00:03:40.120
that's gonna give us some
kind of point, right?

00:03:40.120 --> 00:03:41.489
So we think this point in space

00:03:41.489 --> 00:03:44.043
and that's a given input-output pair.

00:03:44.043 --> 00:03:45.807
But we could do this for a lot, right,

00:03:45.807 --> 00:03:48.571
a couple different
points that you might get

00:03:48.571 --> 00:03:51.183
if you start plotting
various different ones,

00:03:51.183 --> 00:03:54.014
look something like this,
and of course there is

00:03:54.014 --> 00:03:56.244
infinitely many that you can
do and it'll take forever

00:03:56.244 --> 00:03:58.926
if you try to just draw each
one in three-dimensions,

00:03:58.926 --> 00:04:02.042
but what's really nice here
is that you know get rid of

00:04:02.042 --> 00:04:04.567
those lines, if you imagine doing this

00:04:04.567 --> 00:04:07.289
for all of the infinite
many pairs of inputs

00:04:07.289 --> 00:04:11.892
that you could possibly have,
you end up drawing a surface.

00:04:11.892 --> 00:04:14.952
So in this case the surface
kind of looks like a

00:04:14.952 --> 00:04:17.215
three-dimensional parabola,
that's no coincidence,

00:04:17.215 --> 00:04:19.038
it has to do with the
fact that we are using

00:04:19.038 --> 00:04:21.331
x squared and y squared here.

00:04:21.331 --> 00:04:25.498
And now the inputs like (1,
2), we think of as being

00:04:27.177 --> 00:04:29.301
on the xy-plane, right?

00:04:29.301 --> 00:04:31.658
So you think of the inputs living here,

00:04:31.658 --> 00:04:33.818
and then what corresponds
to the output is that

00:04:33.818 --> 00:04:37.463
height of a giving point
above the graph, right?

00:04:37.463 --> 00:04:39.564
So it's very similar to
two-dimensions, you think,

00:04:39.564 --> 00:04:42.084
you know, we think of the
inputs as being on one axis,

00:04:42.084 --> 00:04:44.417
and the height gives the output there.

00:04:44.417 --> 00:04:45.936
So just to give an example of

00:04:45.936 --> 00:04:49.283
what the consequence of this
is, I want you to think about

00:04:49.283 --> 00:04:52.522
what might happen if we change
our multi-variable function

00:04:52.522 --> 00:04:56.690
a little bit, and we multiply
everything by half, right?

00:04:56.690 --> 00:05:00.857
So I'll draw in red here, let's
see that we have a function,

00:05:02.178 --> 00:05:06.452
but I'm gonna change it so
that it outputs one half

00:05:06.452 --> 00:05:09.227
of x squared plus y squared.

00:05:09.227 --> 00:05:13.394
What's gonna be the shape of
the graph for that function?

00:05:14.286 --> 00:05:15.919
And what it means is the
height of every point

00:05:15.919 --> 00:05:19.645
above this xy-plane is gonna
have to get cut in half.

00:05:19.645 --> 00:05:21.392
So it's actually just the modification

00:05:21.392 --> 00:05:23.420
of what we already have,
but everything kind of

00:05:23.420 --> 00:05:27.181
sloops on down to be
about half of what it was.

00:05:27.181 --> 00:05:29.386
So in this case instead
of that height being five,

00:05:29.386 --> 00:05:31.531
it'll be two-point-five.

00:05:31.531 --> 00:05:33.442
You could imagine, let's
say we did this, you know,

00:05:33.442 --> 00:05:35.823
is even more extreme,
instead of saying one-half,

00:05:35.823 --> 00:05:38.725
you cut it down by like one-twelfth,

00:05:38.725 --> 00:05:42.558
maybe I'll use the same
color, by one-twelfth,

00:05:43.440 --> 00:05:45.017
that would mean that everything, you know,

00:05:45.017 --> 00:05:49.259
sloops very flat, very flat
and close to the xy-plane.

00:05:49.259 --> 00:05:51.443
So the graph being very
close to xy-plane like this

00:05:51.443 --> 00:05:54.909
corresponds to very small outputs.

00:05:54.909 --> 00:05:57.287
And one thing that I'd like
to caution you against,

00:05:57.287 --> 00:05:59.563
it's very tempting to try to think of

00:05:59.563 --> 00:06:01.520
every multi-variable function as a graph,

00:06:01.520 --> 00:06:03.687
cause we are so used to
graphs in two-dimensions

00:06:03.687 --> 00:06:06.726
and we are so used to
trying to find analogies

00:06:06.726 --> 00:06:09.781
between two-dimensions and
three-dimensions directly,

00:06:09.781 --> 00:06:12.734
but the only reason that
this works is because

00:06:12.734 --> 00:06:15.376
if you take the number of
dimension in the input,

00:06:15.376 --> 00:06:17.515
two-dimensions, and then
the number of dimensions

00:06:17.515 --> 00:06:19.926
in the output, one-dimension,
it was reasonable

00:06:19.926 --> 00:06:23.281
to fit all of that into
three, which we could do.

00:06:23.281 --> 00:06:25.104
But imagine if you have
a multi-variable function

00:06:25.104 --> 00:06:27.044
with, you know, a three-dimensional input,

00:06:27.044 --> 00:06:29.156
and a two-dimensional
output, that would require

00:06:29.156 --> 00:06:31.420
a five-dimensional graph,
but we are not very good

00:06:31.420 --> 00:06:33.899
at visualizing things like that.

00:06:33.899 --> 00:06:35.586
So there's lots of other
methods, and I think

00:06:35.586 --> 00:06:37.883
it's very important to
kinda of open you mind

00:06:37.883 --> 00:06:39.752
to what those might be.

00:06:39.752 --> 00:06:42.940
In particular, another one
that I'm gonna go through soon,

00:06:42.940 --> 00:06:44.613
lets us think about 3-D graphs but kind of

00:06:44.613 --> 00:06:46.709
in a two-dimensional setting,
and we are just gonna

00:06:46.709 --> 00:06:50.093
look at the input space,
that's called a contour map.

00:06:50.093 --> 00:06:52.194
Couple of other ones,
like parametric functions,

00:06:52.194 --> 00:06:54.216
you just look in the output space;

00:06:54.216 --> 00:06:55.616
things like vector space,

00:06:55.616 --> 00:06:59.210
you kind of look at the input
space but get all the outputs.

00:06:59.210 --> 00:07:00.770
There's lots of different
ways, I'll go over those

00:07:00.770 --> 00:07:03.301
in the next few videos.

00:07:03.301 --> 00:07:05.409
And that's three-dimensional graphs.


BONUS VIDEO

WEBVTT
Kind: captions
Language: en

00:00:00.776 --> 00:00:02.361
- [Voiceover] So you may have
been hearing a lot of talk

00:00:02.361 --> 00:00:04.962
about this thing called
singular they recently

00:00:04.962 --> 00:00:08.294
not knowing entirely what
it is or whether or not

00:00:08.294 --> 00:00:11.835
it's okay to use in a
sentence or in formal writing.

00:00:11.835 --> 00:00:15.097
Um, it's been in the news
a lot lately, you know

00:00:15.097 --> 00:00:17.721
we're seeing publications
like The Washington Post

00:00:17.721 --> 00:00:21.680
and The Economist putting
it into their style guides.

00:00:21.680 --> 00:00:23.434
It was the American Dialect Society's

00:00:23.434 --> 00:00:27.052
Word of the Year in 2015

00:00:27.052 --> 00:00:31.572
but like what is it,
and is it okay to use?

00:00:31.572 --> 00:00:33.661
I know that I got dinged all the time

00:00:33.661 --> 00:00:35.937
for using "they" as a singular pronoun

00:00:35.937 --> 00:00:38.921
in papers in high school, along with "is,"

00:00:38.921 --> 00:00:40.373
I got in a lot of trouble for using "is,"

00:00:40.373 --> 00:00:41.754
which would always be circled.

00:00:41.754 --> 00:00:43.716
Some teachers of mine
just really hated "is."

00:00:43.716 --> 00:00:46.958
I get it now, it's kind of weak but

00:00:46.958 --> 00:00:49.590
anyway we're not talking about that today,

00:00:49.590 --> 00:00:52.511
we're talking about they, singular they.

00:00:52.511 --> 00:00:54.976
So they is more commonly known as

00:00:54.976 --> 00:00:58.193
the plural third person pronoun in English

00:00:58.193 --> 00:01:00.124
so if we say, you know,

00:01:00.124 --> 00:01:05.044
Rolando and Phil

00:01:06.434 --> 00:01:10.796
go to the park we can switch out

00:01:10.796 --> 00:01:13.379
Rolando and Phil and say

00:01:13.379 --> 00:01:16.479
they go to the park,

00:01:16.479 --> 00:01:18.255
and that's one usage of they but you may

00:01:18.255 --> 00:01:21.233
have also seen sentences
that look like this.

00:01:21.233 --> 00:01:23.958
Like, "When a journalist files
a story they should always

00:01:23.958 --> 00:01:26.212
"make sure their sources check out,"

00:01:30.052 --> 00:01:31.978
or "Anyone will tell you the truth if you

00:01:31.978 --> 00:01:34.333
"ask them the right questions,"

00:01:34.333 --> 00:01:36.437
and you may have noticed
that these sentences

00:01:36.437 --> 00:01:40.338
use the word "they" to
agree with a singular

00:01:40.338 --> 00:01:42.753
antecedent like journalist or anyone.

00:01:42.753 --> 00:01:44.378
Now for some of you, you
might not have noticed

00:01:44.378 --> 00:01:46.016
and for some of you, you
might have, your immediate

00:01:46.016 --> 00:01:48.477
reaction might have been, oh
wait, eh, let me get my red pen

00:01:48.477 --> 00:01:52.913
but before you do, in order to explain

00:01:52.913 --> 00:01:55.943
the context and the history

00:01:55.943 --> 00:01:58.694
around this usage, around singular they,

00:01:58.694 --> 00:02:02.412
I would like for a moment
to talk about "you."

00:02:04.452 --> 00:02:06.519
Not you the person, you the person

00:02:06.519 --> 00:02:10.591
are a vast unknowable ocean
but I mean you the pronoun

00:02:13.401 --> 00:02:16.422
and how weird and transgressive

00:02:16.422 --> 00:02:19.835
and transformative it is.

00:02:19.835 --> 00:02:21.518
In many languages today there are

00:02:21.518 --> 00:02:23.341
second person pronouns for both

00:02:23.341 --> 00:02:26.058
singular and plural usage.

00:02:26.058 --> 00:02:29.541
In French, for example,
we'd say tu for singular you

00:02:29.541 --> 00:02:31.840
and vous for plural you.

00:02:31.840 --> 00:02:34.615
Tu to one person, vous to many.

00:02:34.615 --> 00:02:36.693
There's also a social distinction here

00:02:36.693 --> 00:02:38.515
that was once more pronounced,

00:02:38.515 --> 00:02:41.511
where you'd say vous to social superiors

00:02:41.511 --> 00:02:43.636
and tu to close friends.

00:02:43.636 --> 00:02:48.093
Now in those languages
the vous form is formal

00:02:48.093 --> 00:02:50.470
and the tu form is informal.

00:02:53.620 --> 00:02:55.280
You're addressing someone you don't know

00:02:55.280 --> 00:02:56.650
very well, you use vous.

00:02:56.650 --> 00:02:59.112
You're addressing your
best buddy, you use tu.

00:02:59.112 --> 00:03:03.071
All of this is to say
that English used to have

00:03:03.071 --> 00:03:06.194
the same distinction so this kind of

00:03:06.194 --> 00:03:10.141
lines up with tu and vous.

00:03:10.141 --> 00:03:12.556
Once upon a time the
singular second person

00:03:12.556 --> 00:03:16.155
subject form was thou, the object form

00:03:16.155 --> 00:03:19.232
of the singular was thee.

00:03:19.232 --> 00:03:22.358
The plural second person subject form

00:03:22.358 --> 00:03:27.254
was ye or ye and the object form was you.

00:03:27.254 --> 00:03:28.972
This is where you comes in, all right,

00:03:28.972 --> 00:03:32.038
and so we, it's funny because we think

00:03:32.038 --> 00:03:34.499
of thee and thou as being more fancy

00:03:34.499 --> 00:03:37.740
and formal but really
it was the opposite way,

00:03:37.740 --> 00:03:41.114
this was the informal

00:03:41.114 --> 00:03:43.854
and ye and you was the formal.

00:03:45.704 --> 00:03:47.467
Now you may recall from our video on

00:03:47.467 --> 00:03:50.498
who versus whom that I said whom

00:03:50.498 --> 00:03:54.027
was on its way out of the language.

00:03:54.027 --> 00:03:57.928
Its usage is being overtaken by who,

00:03:57.928 --> 00:04:01.306
it is now usually permissible
to use who as an object,

00:04:01.306 --> 00:04:04.417
as in the song Who Do
You Love by Bo Diddley.

00:04:04.417 --> 00:04:07.308
Well the same thing
that's happening to whom

00:04:07.308 --> 00:04:10.280
happened to ye.

00:04:10.280 --> 00:04:13.585
Over the years its
function decreased as "you"

00:04:13.585 --> 00:04:16.585
took over, it took on a
subject and object role

00:04:16.585 --> 00:04:19.244
as well as singular and plural functions

00:04:19.244 --> 00:04:22.808
but it was still reserved
for the highborn,

00:04:22.808 --> 00:04:24.386
it was the polite form of address

00:04:24.386 --> 00:04:26.639
used for addressing social superiors.

00:04:26.639 --> 00:04:28.381
So even though there's only one king

00:04:28.381 --> 00:04:30.958
you would refer to that king as "you"

00:04:30.958 --> 00:04:33.362
because apparently he was better than you.

00:04:33.362 --> 00:04:35.498
He wasn't, but we'll get to that.

00:04:35.498 --> 00:04:37.820
But something marvelous
happened in English,

00:04:37.820 --> 00:04:40.839
the social distinction
between you and thou

00:04:40.839 --> 00:04:44.367
fell away and you overtook thou and its

00:04:44.367 --> 00:04:47.862
subject form thee so now
for both the singular

00:04:47.862 --> 00:04:51.740
and the plural, for the
informal and the formal,

00:04:51.740 --> 00:04:54.283
for the subject and the
object, all we have here

00:04:54.283 --> 00:04:57.801
is you, you, you and you.

00:04:57.801 --> 00:05:01.980
It would be as if I, me
and we were all replaced

00:05:01.980 --> 00:05:05.603
by us, I cannot emphasize
how revolutionary this is!

00:05:05.603 --> 00:05:08.005
In English you address
a king and a peasant

00:05:08.005 --> 00:05:12.545
with the same address, under
the language they are equal.

00:05:12.545 --> 00:05:15.540
Mind you the existence of a single form

00:05:15.540 --> 00:05:17.757
of direct address did not annihilate class

00:05:17.757 --> 00:05:21.287
distinctions or prejudice in
the English-speaking world

00:05:21.287 --> 00:05:23.841
but it is no longer possible to encode

00:05:23.841 --> 00:05:26.047
a power relationship in English

00:05:26.047 --> 00:05:29.948
in the very specific way it once was.

00:05:29.948 --> 00:05:32.026
I cheer this development, I think it's

00:05:32.026 --> 00:05:33.617
awfully democratic and affirming

00:05:33.617 --> 00:05:36.264
of the principle that all human beings

00:05:36.264 --> 00:05:41.048
are worthy of respect,
which brings us to "they."

00:05:41.048 --> 00:05:42.770
This didn't really used to be a problem

00:05:42.770 --> 00:05:45.018
in English composition,
people were writing

00:05:45.018 --> 00:05:48.223
sentences like, "Everybody
has their failing,

00:05:48.223 --> 00:05:50.324
"you know, and everybody has a right to do

00:05:50.324 --> 00:05:52.739
what they like with their own money,"

00:05:52.739 --> 00:05:54.747
which is a Jane Austen quote by the way

00:05:54.747 --> 00:05:56.514
from Northanger Abbey.

00:05:56.514 --> 00:05:58.637
Austen used this construction, Chaucer

00:05:58.637 --> 00:06:01.505
used this construction,
Shakespeare used this construction,

00:06:01.505 --> 00:06:04.024
C.S. Lewis used this
construction, these are the people

00:06:04.024 --> 00:06:08.342
that we look to as paragons of correctness

00:06:08.342 --> 00:06:10.723
and of style in English literature,

00:06:10.723 --> 00:06:14.937
and they used this form
without any compunctions.

00:06:14.937 --> 00:06:17.723
There is a class of
grammarians who thought

00:06:17.723 --> 00:06:20.881
it would be a great idea
to make English adhere

00:06:20.881 --> 00:06:23.226
to Latin grammar rules, which is where

00:06:23.226 --> 00:06:25.723
we get silly language superstitions like

00:06:25.723 --> 00:06:27.964
the prohibition on ending sentences

00:06:27.964 --> 00:06:31.319
with prepositions, making it ungrammatical

00:06:31.319 --> 00:06:35.045
to say a sentence like,
"He's a guy you can rely on,"

00:06:35.045 --> 00:06:37.182
or spreading the spurious rumor

00:06:37.182 --> 00:06:39.643
that you couldn't split
an English infinitive,

00:06:39.643 --> 00:06:43.161
as in, you know, to boldly go.

00:06:43.161 --> 00:06:46.284
These are falsehoods
and they are confusing

00:06:46.284 --> 00:06:49.186
and they are needless,
pompous class markers

00:06:49.186 --> 00:06:51.067
and defeating them, and making you feel

00:06:51.067 --> 00:06:52.809
more comfortable with English is why

00:06:52.809 --> 00:06:55.782
I got into this profession
in the first place.

00:06:55.782 --> 00:06:59.229
Anyway, that group of
grammarians, that group

00:06:59.229 --> 00:07:02.073
decided that when speaking
of a generic person

00:07:02.073 --> 00:07:05.371
we should say "he," a
hypothetical person in

00:07:05.371 --> 00:07:07.657
a sentence was always
"he" on the grounds that

00:07:07.657 --> 00:07:11.678
according to 16th century
grammarian William Lily,

00:07:11.678 --> 00:07:15.390
"The masculine gender is more
worthy than the feminine,"

00:07:15.390 --> 00:07:17.735
so you'd be, you'd get
sentences that began

00:07:17.735 --> 00:07:19.530
"Any judge worth his salt,"

00:07:19.530 --> 00:07:22.832
or "Anyone that would say
that is out of his mind,"

00:07:22.832 --> 00:07:25.897
which presumably was
supposed to refer to anyone.

00:07:25.897 --> 00:07:28.056
Now for centuries arguments raged over

00:07:28.056 --> 00:07:30.193
whether or not the generic "he" erased

00:07:30.193 --> 00:07:32.515
women from consideration and now with

00:07:32.515 --> 00:07:34.477
the benefit of hindsight we can say

00:07:34.477 --> 00:07:37.658
of course it did!

00:07:37.658 --> 00:07:40.503
The generic "he" isn't generic.

00:07:43.483 --> 00:07:45.611
When referring to a person whose gender

00:07:45.611 --> 00:07:48.618
is unknown or undefined by he or she,

00:07:48.618 --> 00:07:53.594
it is elegant to call
such a person "they,"

00:07:53.594 --> 00:07:57.134
as opposed to the ungainly "he or she"

00:07:58.614 --> 00:08:03.601
or she, like s/he,

00:08:03.601 --> 00:08:05.440
which on their own look alright

00:08:05.440 --> 00:08:07.564
but in context and especially when they're

00:08:07.564 --> 00:08:11.559
repeated tend to get a little
clunky and distracting.

00:08:11.559 --> 00:08:14.844
What happened to the word "you"

00:08:14.844 --> 00:08:16.818
is happening to "they," the plural

00:08:16.818 --> 00:08:20.115
is expanding into the realm
of the singular again.

00:08:20.115 --> 00:08:21.879
The language is changing because that's

00:08:21.879 --> 00:08:24.155
what languages do, and
now this is something

00:08:24.155 --> 00:08:26.519
that's already done unconsciously,

00:08:26.519 --> 00:08:28.579
you see it in literature,
you see it in the Bible,

00:08:28.579 --> 00:08:31.702
in formal as well as informal speech.

00:08:31.702 --> 00:08:33.859
But formalizing this understanding is what

00:08:33.859 --> 00:08:35.986
undergirds the decisions of The Economist

00:08:35.986 --> 00:08:37.182
and The Washington Post

00:08:37.182 --> 00:08:40.700
to start using singular they formally.

00:08:40.700 --> 00:08:42.139
Like if you had to ask me right now,

00:08:42.139 --> 00:08:44.380
"David, is singular they grammatical?"

00:08:44.380 --> 00:08:47.643
I'd say it's as grammatical as "you"

00:08:47.643 --> 00:08:50.854
but yeah, this is some of
the context of singular they.

00:08:50.854 --> 00:08:52.727
This is where it comes from, this is why

00:08:52.727 --> 00:08:54.945
it's used, this is what it's replacing,

00:08:54.945 --> 00:08:57.429
it's replacing this generic "he" and this

00:08:57.429 --> 00:09:00.123
kind of a clunky "she or he."

00:09:00.123 --> 00:09:02.790
You can learn anything, David out.


Tomorrow: AP US History Office Hours with Sal

WEBVTT
Kind: captions
Language: en

00:00:00.251 --> 00:00:02.422
- Hi, this is Sal, founder
of the Khan Academy.

00:00:02.422 --> 00:00:05.889
- And I am Kim, the US
History Content fellow.

00:00:05.889 --> 00:00:09.244
- And tomorrow, Wednesday, May 4th,

00:00:09.244 --> 00:00:12.309
we're going to have a
live stream of Kim and I

00:00:12.309 --> 00:00:14.910
doing a review session for this Friday's

00:00:14.910 --> 00:00:16.674
AP American History exam.

00:00:16.674 --> 00:00:18.753
- So we're going to
hit the major points of

00:00:18.753 --> 00:00:21.412
American History themes and strategies

00:00:21.412 --> 00:00:22.828
for tackling the exam.

00:00:22.828 --> 00:00:23.995
- So join us.


Intro to adjectives

WEBVTT
Kind: captions
Language: en

00:00:00.075 --> 00:00:01.108
- [Voiceover] So,
grammarians, we have this

00:00:01.108 --> 00:00:04.081
class of words called adjectives,

00:00:04.081 --> 00:00:06.820
and what they do is they change stuff.

00:00:06.820 --> 00:00:09.443
Adjectives...

00:00:10.292 --> 00:00:12.751
change stuff.

00:00:14.010 --> 00:00:16.007
Adjectives change stuff.

00:00:16.007 --> 00:00:18.538
They're part of this
larger category of words

00:00:18.538 --> 00:00:21.606
that we call modifiers.

00:00:23.031 --> 00:00:24.941
Because that's what they do, they modify,

00:00:24.941 --> 00:00:26.410
they change things.

00:00:26.410 --> 00:00:28.413
So let's say I were to draw you a bear,

00:00:28.413 --> 00:00:31.640
a kinda human-looking,
standing on two legs

00:00:31.640 --> 00:00:35.243
kinda bear, sure.

00:00:35.243 --> 00:00:39.488
I could refer to this bear
and I could say, the bear.

00:00:40.667 --> 00:00:42.374
But I could also refer to this bear

00:00:42.374 --> 00:00:47.374
with a description,
like, the friendly bear.

00:00:49.236 --> 00:00:51.767
But if that bear were blue, for instance,

00:00:51.767 --> 00:00:56.658
I could describe the
bear as the blue bear.

00:00:57.639 --> 00:01:02.639
And in the blue bear the
word blue modifies bear.

00:01:02.945 --> 00:01:06.950
Blue is an adjective that describes bear.

00:01:06.950 --> 00:01:11.950
So adjectives change stuff
and they describe stuff.

00:01:16.226 --> 00:01:18.351
And if that bear were a
different color it would be,

00:01:18.351 --> 00:01:21.624
you know, the red bear.

00:01:24.082 --> 00:01:26.326
And now that bear is red.

00:01:26.326 --> 00:01:29.507
Actually more of a salmon color, frankly.

00:01:29.507 --> 00:01:32.885
Let's put this into action
with some sentences.

00:01:32.885 --> 00:01:37.458
Steven is Connie's best friend.

00:01:37.458 --> 00:01:40.409
Now what is the word that describes

00:01:40.409 --> 00:01:44.542
or changes another word in this sentence?

00:01:44.542 --> 00:01:46.829
If you guessed best, you were correct.

00:01:46.829 --> 00:01:49.232
Best modifies friend.

00:01:49.232 --> 00:01:51.159
So Steven is Connie's best friend.

00:01:51.159 --> 00:01:52.750
What is Steven? A friend.

00:01:52.750 --> 00:01:54.100
What kind of friend is he?

00:01:54.100 --> 00:01:56.643
The best friend.

00:01:56.643 --> 00:02:00.336
The enormous pie is not for sale.

00:02:01.588 --> 00:02:06.034
Now what's the adjective in that sentence?

00:02:06.034 --> 00:02:08.286
If you guessed enormous
you would be correct.

00:02:08.286 --> 00:02:10.365
Enormous, which means very big,

00:02:10.365 --> 00:02:13.592
is modifying or changing the word pie.

00:02:13.592 --> 00:02:15.636
And I thought a little bit of word origins

00:02:15.636 --> 00:02:17.888
might be kind of useful here if we go

00:02:17.888 --> 00:02:19.026
back to the Latin.

00:02:19.026 --> 00:02:20.428
Now you don't, obviously you don't need to

00:02:20.428 --> 00:02:23.082
speak Latin in order to
make sense of English,

00:02:23.082 --> 00:02:25.462
but I thought it would
be cool to look at what

00:02:25.462 --> 00:02:27.865
adjective literally means.

00:02:27.865 --> 00:02:30.884
The word part, ad-, comes from the Latin

00:02:30.884 --> 00:02:35.423
meaning to or toward or on.

00:02:35.423 --> 00:02:40.423
And the -jective part comes
from a Latin word, jacere.

00:02:40.694 --> 00:02:43.799
It means to throw.

00:02:45.781 --> 00:02:48.567
So, an adjective is
something that's kind of

00:02:48.567 --> 00:02:51.748
thrown on or thrown on top of something,

00:02:51.748 --> 00:02:54.035
because you don't necessarily need

00:02:54.035 --> 00:02:58.285
adjectives in order for
a sentence to make sense

00:02:58.285 --> 00:02:59.597
the way that you need to have a verb

00:02:59.597 --> 00:03:02.242
or the way that you need to have a noun.

00:03:02.242 --> 00:03:04.196
Adjectives are a little bit extra,

00:03:04.196 --> 00:03:07.319
they're thrown on top.

00:03:07.319 --> 00:03:08.773
These sentences would work on their own

00:03:08.773 --> 00:03:09.992
without the adjectives in them.

00:03:09.992 --> 00:03:11.629
Steven is Connie's friend.

00:03:11.629 --> 00:03:13.301
The pie is not for sale.

00:03:13.301 --> 00:03:15.217
You know, they would work.

00:03:15.217 --> 00:03:18.392
But what's nice about adjectives,

00:03:18.392 --> 00:03:20.517
and modifiers of all
kinds, is that they add

00:03:20.517 --> 00:03:23.629
something extra, they add more detail.

00:03:23.629 --> 00:03:26.566
They change and describe stuff.

00:03:26.566 --> 00:03:28.412
That's what adjectives do.

00:03:28.412 --> 00:03:29.759
You can learn anything.

00:03:29.759 --> 00:03:31.232
David out.


Intro to the comparative and the superlative

WEBVTT
Kind: captions
Language: en

00:00:00.342 --> 00:00:03.202
- [Voiceover] SO we've got these
three penguins, grammarians

00:00:03.202 --> 00:00:06.137
we've got Raúl, who
you may remember from

00:00:06.137 --> 00:00:10.812
his sweet mohawk, we've got
Cesar and we've got Gabriela.

00:00:14.410 --> 00:00:18.280
Three magellanic penguins from Argentina.

00:00:18.280 --> 00:00:23.088
And they are all different
amounts of happy.

00:00:23.088 --> 00:00:28.088
Cesar is a medium amount of
happy, Raúl is more happy,

00:00:28.613 --> 00:00:31.993
and Gabriela is the most happy.

00:00:31.993 --> 00:00:35.014
And in English, we have
a way to compare these.

00:00:35.014 --> 00:00:37.047
To compare Raúl to Cesar.

00:00:37.047 --> 00:00:41.468
To compare Raúl to Gabriela,
or any combination thereof.

00:00:41.468 --> 00:00:44.881
We call these comparative
and superlative adjectives.

00:00:44.881 --> 00:00:47.330
And before I get too into
the weeds on that, let me

00:00:47.330 --> 00:00:48.989
just show you what that looks like.

00:00:48.989 --> 00:00:53.989
So we can say Raúl, let
me put in the accent,

00:00:54.691 --> 00:00:58.868
Raúl is a happy penguin.

00:01:00.099 --> 00:01:04.598
He's go all the fish
he wants, life is good.

00:01:04.598 --> 00:01:09.598
Raúl is happier than Cesar.

00:01:16.362 --> 00:01:19.580
This is what we call a comparative,
because we're comparing

00:01:19.580 --> 00:01:24.001
Raúl to Cesar, and we're
comparing their happiness levels.

00:01:24.001 --> 00:01:28.643
And Raúl has more happiness
in him than Cesar does.

00:01:28.643 --> 00:01:31.267
Poor Cesar.

00:01:31.267 --> 00:01:36.267
However, Gabriela is the happiest penguin.

00:01:41.531 --> 00:01:43.978
Ta-da.

00:01:43.978 --> 00:01:46.247
The happiest is something that we call

00:01:46.247 --> 00:01:48.735
superlative in English.

00:01:48.735 --> 00:01:53.156
So it's not just a comparison.

00:01:53.156 --> 00:01:55.840
It's not Raúl is happier than Cesar.

00:01:55.840 --> 00:01:59.274
Gabriela is happier than
all the other penguins.

00:01:59.274 --> 00:02:02.036
She is the happy-est, she is the happiest,

00:02:02.036 --> 00:02:03.557
she is the most happy.

00:02:03.557 --> 00:02:05.807
So one way to think about
this is that Raúls happiness

00:02:05.807 --> 00:02:09.517
is slightly larger than Cesars happiness,

00:02:09.517 --> 00:02:12.735
but Gabriela's happiness is double plus,

00:02:12.735 --> 00:02:16.622
is unbeatably more than both of them.

00:02:16.622 --> 00:02:18.833
I'm gonna use a made up math symbol.

00:02:18.833 --> 00:02:21.517
Boom boom boom, like super greater than

00:02:21.517 --> 00:02:26.517
undisputed, she is the happiest penguin.

00:02:26.926 --> 00:02:31.926
Because the comparative is
the same thing as saying more.

00:02:33.617 --> 00:02:37.741
The comparative equals
more, and the superlative

00:02:37.741 --> 00:02:40.857
equals most.

00:02:40.857 --> 00:02:45.617
So this is slightly more,
this is super much more.

00:02:45.617 --> 00:02:46.989
And something that's neat
about English is that

00:02:46.989 --> 00:02:49.772
you can use the comparative
and superlative for both

00:02:49.772 --> 00:02:53.522
positive relationships and
also negative relationships.

00:02:53.522 --> 00:02:57.667
So we could say Raúl is a
happy penguin, and we can say

00:02:57.667 --> 00:03:00.588
Raúl is happier than Cesar.

00:03:00.588 --> 00:03:05.588
We can also say Cesar
is less happy than Raúl.

00:03:09.568 --> 00:03:12.960
So this is comparative but
it's going the other way.

00:03:12.960 --> 00:03:14.182
Right.

00:03:14.182 --> 00:03:16.828
Cesar is less happy than Raúl.

00:03:16.828 --> 00:03:18.940
So then we use the less than symbol.

00:03:18.940 --> 00:03:21.426
Gabriela is the happiest
penguin, and so for this group

00:03:21.426 --> 00:03:26.197
of three, Cesar is the least happy.

00:03:28.116 --> 00:03:30.662
So you can use the comparative
and the superlative forms

00:03:30.662 --> 00:03:34.427
of adjectives to compare
relationships where one thing is

00:03:34.427 --> 00:03:39.427
more or most than another
or others, or relationships

00:03:39.460 --> 00:03:44.050
where one thing is less
or least than others.

00:03:44.050 --> 00:03:46.926
That's how the comparative and
superlative work, but if you

00:03:46.926 --> 00:03:50.023
stick around for the next video,
I'm gonna talk about how to

00:03:50.023 --> 00:03:53.755
figure out, how to form the
comparative and superlative

00:03:53.755 --> 00:03:56.754
when you're looking at a word
you've never seen before,

00:03:56.754 --> 00:04:00.188
like, what if we made up a word, like

00:04:00.188 --> 00:04:03.209
like blarfy.

00:04:03.209 --> 00:04:04.492
What do you do with that?

00:04:04.492 --> 00:04:06.169
Well, you'll find out next time.

00:04:06.169 --> 00:04:08.775
In the meantime, you can learn anything.

00:04:08.775 --> 00:04:10.242
David out.


Intro to adverbs

WEBVTT
Kind: captions
Language: en

00:00:00.693 --> 00:00:01.951
- [Voiceover] Hello grammarians.

00:00:01.951 --> 00:00:03.317
Today we are going to talk,

00:00:03.317 --> 00:00:04.944
skillfully and patiently,

00:00:04.944 --> 00:00:06.104
about adverbs.

00:00:06.104 --> 00:00:08.844
And what it is that adverbs do.

00:00:08.844 --> 00:00:11.305
And in order to do that,
I think it might be

00:00:11.305 --> 00:00:15.138
useful to talk about
what adjectives do first.

00:00:17.365 --> 00:00:19.948
So adjectives can modify stuff.

00:00:21.269 --> 00:00:22.613
And I should have been clearer

00:00:22.613 --> 00:00:23.889
in the last video,

00:00:23.889 --> 00:00:28.349
and said that the stuff
they modify is nouns.

00:00:28.349 --> 00:00:31.089
But, I didn't wanna
introduce too many rules

00:00:31.089 --> 00:00:33.017
and strictures.

00:00:33.017 --> 00:00:35.684
What adjectives modify is nouns,

00:00:37.828 --> 00:00:39.078
and only nouns.

00:00:39.966 --> 00:00:42.549
Adverbs modify everything else.

00:00:44.542 --> 00:00:46.875
So adverbs modify everything

00:00:48.929 --> 00:00:50.429
that's not a noun.

00:00:51.622 --> 00:00:55.058
And the way we usually see
this applied, is with verbs,

00:00:55.058 --> 00:00:56.710
and it's right there in the name too.

00:00:56.710 --> 00:00:57.917
Ad-Verbs.

00:00:57.917 --> 00:00:59.105
And this comes from

00:00:59.105 --> 00:01:01.272
the Latin meaning on or to

00:01:03.793 --> 00:01:05.460
verbs, action words.

00:01:07.034 --> 00:01:10.701
Adverbs are words that
you slap on to verbs,

00:01:11.897 --> 00:01:13.081
basically.

00:01:13.081 --> 00:01:15.428
What I imagine when I think of adverbs,

00:01:15.428 --> 00:01:18.095
is I kind of see like a sticker.

00:01:18.956 --> 00:01:21.533
Here's the sticker we've got we can say

00:01:21.533 --> 00:01:22.366
"slowly".

00:01:24.854 --> 00:01:26.922
So we can take this thing

00:01:26.922 --> 00:01:29.498
and turn it into a sticker.

00:01:29.498 --> 00:01:32.122
Move it around, do what we like.

00:01:32.122 --> 00:01:34.419
So, we can write a sentence like

00:01:34.419 --> 00:01:35.336
Greyson ran

00:01:39.093 --> 00:01:39.926
slowly.

00:01:43.293 --> 00:01:46.293
And slowly here, refers back to ran.

00:01:47.276 --> 00:01:48.972
It's how he ran.

00:01:48.972 --> 00:01:50.180
It's not really describing

00:01:50.180 --> 00:01:51.017
Greyson.

00:01:51.017 --> 00:01:54.056
It's modifying or describing

00:01:54.056 --> 00:01:55.889
the action of running.

00:01:56.772 --> 00:01:59.105
Pearl arranged the furniture

00:02:02.878 --> 00:02:03.711
slowly.

00:02:06.015 --> 00:02:09.218
Little sticker that we
just, poof, put on there.

00:02:09.218 --> 00:02:11.403
But a word is also considered an adverb,

00:02:11.403 --> 00:02:14.490
if it modifies an adjective.

00:02:14.490 --> 00:02:16.675
So let's say adverbs

00:02:16.675 --> 00:02:17.675
modify verbs

00:02:21.898 --> 00:02:23.148
and adjectives.

00:02:27.794 --> 00:02:30.998
So we could say something like,

00:02:30.998 --> 00:02:31.831
"Vanessa

00:02:34.623 --> 00:02:35.456
was

00:02:36.570 --> 00:02:37.653
very hungry".

00:02:40.219 --> 00:02:43.259
Right, because hungry is an adjective,

00:02:43.259 --> 00:02:45.303
and very, is doing this thing,

00:02:45.303 --> 00:02:47.636
where it's modifying hungry.

00:02:48.506 --> 00:02:50.691
It's not Vanessa wasn't very.

00:02:50.691 --> 00:02:54.476
You can't be very; very
is not an adjective.

00:02:54.476 --> 00:02:57.611
But it is a modifier, and
the word that it's modifying,

00:02:57.611 --> 00:02:58.655
is hungry.

00:02:58.655 --> 00:03:00.023
How hungry was Vanessa?

00:03:00.023 --> 00:03:02.299
Vanessa was very hungry.

00:03:02.299 --> 00:03:05.549
Vanessa could also be, slightly hungry.

00:03:07.711 --> 00:03:09.776
And this leads me to one of the most

00:03:09.776 --> 00:03:11.868
important things about adverbs.

00:03:11.868 --> 00:03:13.236
Which is that generally,

00:03:13.236 --> 00:03:14.903
they tend to have ly

00:03:16.488 --> 00:03:17.648
on them.

00:03:17.648 --> 00:03:20.504
So generally the way to make an adverb,

00:03:20.504 --> 00:03:22.921
is to just take an adjective,

00:03:23.780 --> 00:03:25.197
and add ly to it.

00:03:26.100 --> 00:03:27.980
So you take the word slow,

00:03:27.980 --> 00:03:28.816
you add ly

00:03:28.816 --> 00:03:30.584
you get the adverb slowly.

00:03:30.584 --> 00:03:32.116
You take the word nice,

00:03:32.116 --> 00:03:33.020
you add ly,

00:03:33.020 --> 00:03:35.621
you get the adverb nicely.

00:03:35.621 --> 00:03:38.712
If you take the adjective cheerful,

00:03:38.712 --> 00:03:39.916
add an ly,

00:03:39.916 --> 00:03:43.192
you get the adverb cheerfully.

00:03:43.192 --> 00:03:45.768
So adverbs modify everything
that isn't a noun.

00:03:45.768 --> 00:03:47.649
And that means that they modify verbs,

00:03:47.649 --> 00:03:48.996
and adjectives.

00:03:48.996 --> 00:03:51.736
The way you make an
adverb most of the time,

00:03:51.736 --> 00:03:55.545
is by taking an adjective
and tacking on ly

00:03:55.545 --> 00:03:57.077
to the end of it.

00:03:57.077 --> 00:03:58.889
It's like a sticker, that you, poof,

00:03:58.889 --> 00:04:01.972
put on top of a verb or an adjective.

00:04:02.929 --> 00:04:06.065
That's what adverbs are,
and that's what they do.

00:04:06.065 --> 00:04:07.153
And what you can do,

00:04:07.153 --> 00:04:08.849
is learn anything.

00:04:08.849 --> 00:04:09.682
David out.


Definite and indefinite articles

WEBVTT
Kind: captions
Language: en

00:00:00.633 --> 00:00:01.889
laz- [Voiceover] So we've covered the

00:00:01.889 --> 00:00:04.372
basic idea that divides the usage

00:00:04.372 --> 00:00:06.967
of "the" from "a" and "an".

00:00:06.967 --> 00:00:09.843
"The" is the definite article,

00:00:11.265 --> 00:00:14.492
and "a" or "an" is the indefinite.

00:00:14.492 --> 00:00:16.093
So when you're being non-specific

00:00:16.093 --> 00:00:17.069
in language,

00:00:17.069 --> 00:00:18.068
you would use

00:00:18.068 --> 00:00:19.393
the indefinite article

00:00:19.393 --> 00:00:20.504
as in,

00:00:20.504 --> 00:00:22.640
"May I have

00:00:26.040 --> 00:00:27.664
an orange?"

00:00:30.947 --> 00:00:32.363
Cause it doesn't matter

00:00:32.363 --> 00:00:35.079
which orange you're asking for,

00:00:35.079 --> 00:00:35.798
you don't care,

00:00:35.798 --> 00:00:36.799
it's any orange,

00:00:36.799 --> 00:00:38.282
as opposed to if you wanted

00:00:38.282 --> 00:00:41.436
the orange.

00:00:43.598 --> 00:00:45.410
This usage is much more specific,

00:00:45.410 --> 00:00:47.686
and it seems to indicate
that there is only

00:00:47.686 --> 00:00:49.168
one orange.

00:00:50.682 --> 00:00:53.214
You see the orange in
particular that you want,

00:00:53.214 --> 00:00:54.326
you're identifying it,

00:00:54.326 --> 00:00:55.392
you're asking for it.

00:00:55.392 --> 00:00:57.754
That's what this definite usage is.

00:00:58.921 --> 00:01:00.592
Something that's interesting about

00:01:00.592 --> 00:01:01.453
the word "the"

00:01:01.453 --> 00:01:03.907
is that it can be used for both singular

00:01:03.907 --> 00:01:06.176
and plural nouns.

00:01:09.366 --> 00:01:12.222
So it's both singular and plural.

00:01:12.222 --> 00:01:13.034
So you could say

00:01:13.034 --> 00:01:13.754
"May I have the orange?"

00:01:13.754 --> 00:01:14.358
You could also say

00:01:14.358 --> 00:01:16.604
"May I have the oranges?"

00:01:17.954 --> 00:01:19.973
And "a" and "an" does not really allow this,

00:01:19.973 --> 00:01:21.479
it is only singular.

00:01:23.249 --> 00:01:24.689
So you can't say

00:01:24.689 --> 00:01:28.801
"May I have an oranges?"

00:01:28.801 --> 00:01:30.356
This is not standard.

00:01:30.356 --> 00:01:32.024
What you'd probably say instead is

00:01:32.024 --> 00:01:36.508
"May I have some oranges?"

00:01:36.508 --> 00:01:39.015
So this is not standard,

00:01:39.015 --> 00:01:41.193
does not work in standard
American English.

00:01:43.078 --> 00:01:44.703
The other thing about "a" or "an"

00:01:44.703 --> 00:01:47.906
is that it's "a" or "an".

00:01:47.906 --> 00:01:50.018
The indefinite article changes

00:01:50.018 --> 00:01:51.598
depending on the vowel sound

00:01:51.598 --> 00:01:53.758
that comes after it.

00:01:53.758 --> 00:01:58.758
So changes for vowel sounds.

00:01:59.633 --> 00:02:00.630
Now what does that mean?

00:02:02.700 --> 00:02:04.371
Well it means that if you know

00:02:04.371 --> 00:02:07.507
that word that you're going to say next

00:02:07.507 --> 00:02:12.507
like ah or ooh or eh or uh or ee,

00:02:14.287 --> 00:02:16.865
then you're gonna change it to "an".

00:02:16.865 --> 00:02:18.537
So it's the difference between saying

00:02:18.537 --> 00:02:19.929
"A box,"

00:02:22.189 --> 00:02:22.807
and

00:02:22.807 --> 00:02:24.637
"An apple."

00:02:26.547 --> 00:02:27.591
What we don't say

00:02:27.591 --> 00:02:28.823
in standard American English

00:02:28.823 --> 00:02:30.257
is "a apple."

00:02:32.190 --> 00:02:34.442
It's not as easy on the mouth, frankly,

00:02:34.442 --> 00:02:36.042
it takes a little bit more effort.

00:02:36.042 --> 00:02:37.506
And any linguist will tell you

00:02:37.506 --> 00:02:39.482
that the way languages develop

00:02:39.482 --> 00:02:42.382
is that they reward laziness.

00:02:42.382 --> 00:02:43.797
So we say "a box"

00:02:43.797 --> 00:02:45.280
but we say "an apple."

00:02:46.213 --> 00:02:48.373
Something a little weird though,

00:02:48.373 --> 00:02:49.138
you want to make sure

00:02:49.138 --> 00:02:50.718
that you're looking for vowel sounds

00:02:50.718 --> 00:02:52.475
not just for vowels.

00:02:53.665 --> 00:02:55.641
Because some vowels,

00:02:55.641 --> 00:02:56.753
for example,

00:02:56.753 --> 00:02:57.869
the letter U

00:02:57.869 --> 00:03:00.517
don't always produce "ooh" sounds.

00:03:00.517 --> 00:03:02.097
Sometimes if they're at
the beginning of a word,

00:03:02.097 --> 00:03:03.416
like in word union,

00:03:03.416 --> 00:03:06.392
so if you say "a union,"

00:03:06.392 --> 00:03:09.432
that produces a "yuh" sound,

00:03:09.432 --> 00:03:12.344
and "yuh" is technically
a consonant sound.

00:03:12.344 --> 00:03:14.784
That's not a vowel.

00:03:14.784 --> 00:03:17.220
But there are certainly cases like

00:03:17.220 --> 00:03:19.659
"An underwater boat,"

00:03:19.659 --> 00:03:22.004
where the letter U does produce

00:03:22.004 --> 00:03:24.584
an "ooh" or an "uh" sound,

00:03:24.584 --> 00:03:25.671
and that's a vowel.

00:03:25.671 --> 00:03:26.812
So if you're gonna start the word

00:03:26.812 --> 00:03:28.019
with a vowel sound,

00:03:28.019 --> 00:03:29.527
what you wanna do is choose

00:03:29.527 --> 00:03:31.756
"an" instead of "a"

00:03:31.756 --> 00:03:35.447
but just be careful of
the letter U for example.

00:03:35.447 --> 00:03:36.727
So to recap,

00:03:36.727 --> 00:03:38.768
"the" is the definite article.

00:03:38.768 --> 00:03:41.952
You can use it for both
singular and plural usage.

00:03:41.952 --> 00:03:43.460
"May I have the orange?"

00:03:43.460 --> 00:03:45.664
"May I have the oranges?"

00:03:45.664 --> 00:03:47.384
"A" or "an" is indefinite

00:03:47.384 --> 00:03:48.823
and it's only singular,

00:03:48.823 --> 00:03:49.820
so you can say

00:03:49.820 --> 00:03:50.911
"May I have an orange?"

00:03:50.911 --> 00:03:51.723
or

00:03:51.723 --> 00:03:54.365
"May I have some oranges?"

00:03:55.323 --> 00:03:56.855
Before a vowel sound,

00:03:56.855 --> 00:03:58.875
"a" changes to "an"

00:03:58.875 --> 00:04:01.479
so you say "a box,"

00:04:01.479 --> 00:04:03.091
but "an apple".

00:04:03.091 --> 00:04:05.732
Not "a apple."

00:04:05.732 --> 00:04:07.171
You say "a union,"

00:04:07.171 --> 00:04:09.393
but "an underwater boat."

00:04:10.931 --> 00:04:11.931
You can learn anything.

00:04:11.931 --> 00:04:12.969
David out.


Forming comparative and superlative modifiers

WEBVTT
Kind: captions
Language: en

00:00:01.191 --> 00:00:02.198
- [Voiceover] Hey grammarians.

00:00:02.198 --> 00:00:04.664
So last time we talked
about Raúl the penguin,

00:00:04.664 --> 00:00:09.497
and how he was happier than
another penguin, Cesar.

00:00:09.497 --> 00:00:14.051
But I wanna talk today about
how to form the comparative

00:00:14.051 --> 00:00:15.482
and the superlative.

00:00:15.482 --> 00:00:18.947
How to compare, how to
say something is more than

00:00:18.947 --> 00:00:23.513
or most in an unfamiliar
situation, if you're looking

00:00:23.513 --> 00:00:27.358
at a word for the first time
or you're trying to figure out

00:00:27.358 --> 00:00:31.195
how to make a word
comparative or superlative.

00:00:31.195 --> 00:00:36.195
To be like, oh well
I've got this word cute,

00:00:36.715 --> 00:00:39.752
like that's a cute little
baby penguin, but how do I say

00:00:39.752 --> 00:00:43.015
that it is more cute than another animal.

00:00:43.015 --> 00:00:44.733
Well, there's a shorthand for that.

00:00:44.733 --> 00:00:47.783
Sometimes you can say
more cute, certainly.

00:00:47.783 --> 00:00:51.182
But you can also say cuter.

00:00:51.182 --> 00:00:54.827
And you can furthermore say cutest.

00:00:54.827 --> 00:00:58.739
And it turns out that there
are a series of sound rules

00:00:58.739 --> 00:01:03.228
in English that govern the
way that we choose to make

00:01:03.228 --> 00:01:04.972
these words go.

00:01:04.972 --> 00:01:07.994
So I'll show you each of them in turn.

00:01:07.994 --> 00:01:11.555
So we've got this little
table that I'm building here,

00:01:11.555 --> 00:01:14.922
and we've got the description,
how it looks in the

00:01:14.922 --> 00:01:18.956
comparative, and how it
looks in the superlative.

00:01:20.921 --> 00:01:23.956
So if you take a word like cute,

00:01:26.986 --> 00:01:29.989
So if you take a word like cute,

00:01:29.989 --> 00:01:34.989
words like cute have one
syllable, one word sound.

00:01:37.955 --> 00:01:38.933
Cute.

00:01:38.933 --> 00:01:43.933
So a word like cute, that is
one syllable and ends in an E.

00:01:48.549 --> 00:01:50.901
All we have to do to make it comparative

00:01:50.901 --> 00:01:53.734
is add an R.

00:01:53.734 --> 00:01:58.734
So, add R, and that gives us cuter.

00:02:01.999 --> 00:02:06.850
For the comparative, all
you have to do is add ST,

00:02:08.434 --> 00:02:11.959
and you get the word cutest.

00:02:11.959 --> 00:02:15.767
But what if you have a word like big?

00:02:15.767 --> 00:02:19.633
If you try to add just R to
that, it would just look like

00:02:19.633 --> 00:02:24.633
bigr, or ST to that, it would
look like bigst, and that's

00:02:27.142 --> 00:02:30.642
not really how we would
form these words in standard

00:02:30.642 --> 00:02:33.780
English, that doesn't go because they're

00:02:33.780 --> 00:02:37.808
inconvenient to say, we like
to have vowels in between

00:02:37.808 --> 00:02:42.373
some of those consonant
sounds, between the b and the g

00:02:42.373 --> 00:02:46.590
and the st, so what you
do, if it's one syllable

00:02:46.590 --> 00:02:51.590
and if it's got one vowel in
the middle like I, like that,

00:02:51.924 --> 00:02:56.924
one vowel, and it ends in
a consonant like a G, then

00:02:57.529 --> 00:03:02.529
what you do is double
the consonant and add ER.

00:03:03.680 --> 00:03:06.590
So this word big ends in a
G, so what I'm gonna do is

00:03:06.590 --> 00:03:09.680
I'm gonna, for the
comparative, I'm gonna say big,

00:03:09.680 --> 00:03:12.221
and then I'm gonna double that
G, I'm gonna use it twice.

00:03:12.221 --> 00:03:14.203
Bigger.

00:03:14.203 --> 00:03:17.225
Like that, and then add the ER.

00:03:17.225 --> 00:03:20.409
Likewise for the superlative, same thing.

00:03:20.409 --> 00:03:25.253
So you double the consonant
at the end of the word,

00:03:25.253 --> 00:03:30.253
and then you add EST, so
it becomes BIG and then

00:03:30.390 --> 00:03:35.390
I double this consonant
sound, so BIGGEST, biggest.

00:03:37.640 --> 00:03:41.840
And for words like short and sweet,

00:03:41.840 --> 00:03:43.556
oh I should clarify.

00:03:43.556 --> 00:03:47.759
For this one, for big, this
should end in one consonant.

00:03:47.759 --> 00:03:51.983
So BIG, there's only one
consonant there, because

00:03:51.983 --> 00:03:54.924
for words like short and
sweet that have one syllable,

00:03:54.924 --> 00:03:59.924
but either have two vowels like
sweet does, so it's E and E

00:04:02.316 --> 00:04:07.316
or two consonants at the end,
what you do is you just add ER

00:04:10.982 --> 00:04:15.866
so shorter or sweeter.

00:04:17.482 --> 00:04:22.315
And for the superlative form, add EST.

00:04:23.558 --> 00:04:26.236
So shortest or sweetest.

00:04:27.698 --> 00:04:29.480
And now we're getting
into the weird stuff.

00:04:29.480 --> 00:04:33.388
So if you take a word like
shiny, which is two syllables,

00:04:33.388 --> 00:04:38.316
and it ends in Y, then what you have to do

00:04:38.316 --> 00:04:43.316
is you change Y into an I, and you add ER.

00:04:44.915 --> 00:04:48.875
So shiny becomes shinier.

00:04:48.875 --> 00:04:51.689
See how this Y becomes and I here?

00:04:51.689 --> 00:04:54.523
Same thing for superlative,
the Y becomes an I,

00:04:54.523 --> 00:04:59.073
and then you add EST, so shiniest.

00:05:03.207 --> 00:05:08.074
Now, if you've got a
word like magnificent,

00:05:11.957 --> 00:05:16.023
magnificent, this is a four syllable word,

00:05:16.023 --> 00:05:19.174
it means like super huge,
super great, super wonderful,

00:05:19.174 --> 00:05:22.473
you've got a word like that,
you take a word like that,

00:05:22.473 --> 00:05:26.346
it's a little bit too big
to be adding more parts to

00:05:26.346 --> 00:05:28.647
the way that standard
American English works.

00:05:28.647 --> 00:05:32.387
So you wouldn't say
magnificenter, or magnificentest.

00:05:32.387 --> 00:05:35.145
It just sounds unwieldy,
'cause the word's already

00:05:35.145 --> 00:05:39.688
pretty long, so if you've got
a two or more syllable word,

00:05:39.688 --> 00:05:44.688
that doesn't end in Y, then
you just have to add the word

00:05:46.622 --> 00:05:51.605
more to the beginning,
so more magnificent, and

00:05:51.605 --> 00:05:54.639
most magnificent.

00:05:55.606 --> 00:05:57.888
So let's say that you're
encountering a word you've

00:05:57.888 --> 00:06:00.172
never seen before.

00:06:00.172 --> 00:06:05.172
And in a sentence you have to
compare, let's say the word

00:06:05.172 --> 00:06:07.788
is blarfy, I don't know what it means,

00:06:07.788 --> 00:06:09.639
probably something gross.

00:06:09.639 --> 00:06:13.873
So if we wanna compare
two really gross meals,

00:06:13.873 --> 00:06:18.873
like a steaming pile of
dog food covered in flies,

00:06:25.056 --> 00:06:29.961
or a plate of ancient
cheese that 3000 years old.

00:06:31.128 --> 00:06:33.226
You gotta eat it, gross.

00:06:33.226 --> 00:06:35.680
Which one is grosser?

00:06:35.680 --> 00:06:39.211
But you have to describe
them using the word blarfy,

00:06:39.211 --> 00:06:40.681
this word we've never seen before.

00:06:40.681 --> 00:06:43.861
Well, what do we know about blarfy?

00:06:43.861 --> 00:06:47.846
Well, it's got two syllables, blarfy,

00:06:47.846 --> 00:06:51.513
so that automatically crosses
out any of this stuff,

00:06:52.703 --> 00:06:56.087
it does end in a Y, blarfy,
so we know that it's

00:06:56.087 --> 00:07:00.790
probably going to behave like
shiny, like the word shiny,

00:07:00.790 --> 00:07:05.192
because it's got two
syllables and it ends in Y.

00:07:05.192 --> 00:07:10.192
So, I'm gonna say that the
dog food is less blarfy,

00:07:13.239 --> 00:07:18.239
and the cheese is blarfier,
in fact this cheese

00:07:21.456 --> 00:07:24.924
is the blarfiest food on the planet.

00:07:24.924 --> 00:07:27.555
Now don't get me wrong, I
love a good stinky cheese,

00:07:27.555 --> 00:07:31.505
but this one in particular,
this 3000 year old cheese,

00:07:31.505 --> 00:07:35.121
super blarfy, in fact, I'm
just gonna go so far as to say

00:07:35.121 --> 00:07:37.077
it is the blarfiest.

00:07:37.077 --> 00:07:38.223
You can blarf anything.

00:07:38.223 --> 00:07:39.842
David out.


Adjective order

WEBVTT
Kind: captions
Language: en

00:00:00.392 --> 00:00:01.892
- [Voiceover] So, grammarians,
if you're a native

00:00:01.892 --> 00:00:06.385
English speaker, the phrase
French old white house

00:00:06.385 --> 00:00:09.781
might seem a little weird to
you, if you're not a native

00:00:09.781 --> 00:00:12.641
English speaker it might
not, and this is something

00:00:12.641 --> 00:00:15.584
that I didn't really know about
before I started preparing

00:00:15.584 --> 00:00:19.958
to teach this course, is that
there is a specific order

00:00:19.958 --> 00:00:22.049
that adjectives go in in English.

00:00:22.049 --> 00:00:24.747
This is something that
I think we just pick up

00:00:24.747 --> 00:00:27.115
as English speakers but if
you didn't grow up speaking

00:00:27.115 --> 00:00:30.965
English it gets a little tricky sometimes.

00:00:30.965 --> 00:00:33.995
So the question is, in order
to make this seem right,

00:00:33.995 --> 00:00:37.496
what order do you put these adjectives in?

00:00:42.546 --> 00:00:44.326
That's near about as I can reckon it.

00:00:44.326 --> 00:00:49.326
Making this into old white French house.

00:00:57.946 --> 00:01:02.025
Because there is an order
and it goes like this.

00:01:02.025 --> 00:01:07.025
Determiner, opinion, size,
age, shape, color, origin,

00:01:14.335 --> 00:01:19.335
material, purpose, or
for short dosa scomp.

00:01:22.330 --> 00:01:23.782
Dosa scomp. Aw.

00:01:23.782 --> 00:01:25.557
Okay, that's actually kind of a thing.

00:01:25.557 --> 00:01:30.557
So a dosa is a South Indian
flat bread, and a scomp,

00:01:33.237 --> 00:01:37.103
I'm gonna say is a word for eating.

00:01:37.103 --> 00:01:40.274
It's not a word, it's a made
up word, but dosa scomp.

00:01:40.274 --> 00:01:44.494
Sounds like scarf to me.

00:01:45.829 --> 00:01:47.664
Or chomp.

00:01:48.684 --> 00:01:51.743
Both of those are verbs that denote
eating, as well as scarf

00:01:51.743 --> 00:01:54.616
being a garment, so dosa scomp.

00:01:54.616 --> 00:01:57.263
I just want you to imagine
sitting down to a delicious

00:01:57.263 --> 00:02:00.346
South Indian meal and
scomping on some dosas.

00:02:00.346 --> 00:02:01.407
So dosa scomp.

00:02:01.407 --> 00:02:06.407
Determiner, and that's
words like the or an.

00:02:07.364 --> 00:02:10.464
Opinion, this is when you're
describing something there are

00:02:10.464 --> 00:02:15.464
certain descriptors that not
everyone would agree with.

00:02:16.264 --> 00:02:20.653
So if you're looking at a
piece of black metal, everyone

00:02:20.653 --> 00:02:22.481
would be able to agree that it is black.

00:02:22.481 --> 00:02:26.347
But if you think it's cool
looking or ugly looking,

00:02:26.347 --> 00:02:28.455
you know, everything that anyone
could conceivably disagree

00:02:28.455 --> 00:02:31.083
about, that's an opinion.

00:02:31.083 --> 00:02:35.176
So, cool for example,
that would be an opinion.

00:02:35.176 --> 00:02:40.176
Size, so the cool, big,
old, square, black,.

00:02:46.809 --> 00:02:51.129
And origin usually can be where it's from.

00:02:51.129 --> 00:02:54.943
So let's say Texan.

00:02:54.943 --> 00:02:57.662
And then we have materials,
let's say leather, cause leather

00:02:57.662 --> 00:02:59.525
can be black, and the purpose.

00:02:59.525 --> 00:03:02.259
This is where we would use
what's called a participle

00:03:02.259 --> 00:03:06.298
or a gerundive to determine
what the thing is for.

00:03:06.298 --> 00:03:09.939
So if we were talking
about a lawnmower that you

00:03:09.939 --> 00:03:14.939
ride around on, that's
called a riding mower.

00:03:17.672 --> 00:03:22.113
And the last thing here
is the thing itself.

00:03:22.113 --> 00:03:24.984
So we're looking at, so this
thing is cool, big, old,

00:03:24.984 --> 00:03:29.793
square, black, Texan, leather,
riding mower, but frankly

00:03:29.793 --> 00:03:33.309
in most normal English
sentences you'll probably never

00:03:33.309 --> 00:03:38.309
going to use more than
three adjectives to describe

00:03:38.377 --> 00:03:40.677
a given thing.

00:03:40.677 --> 00:03:43.480
Like old white French house.

00:03:43.480 --> 00:03:47.379
Now sometimes, you might
find yourself using more than

00:03:47.379 --> 00:03:50.516
one adjective that fits
into the same category.

00:03:50.516 --> 00:03:55.309
So you might say the exciting,
unparalleled green dragon.

00:03:58.318 --> 00:04:01.870
And you'll notice I put a comma
there, because when you use

00:04:01.870 --> 00:04:06.870
two adjectives from the same
category, so two opinions,

00:04:07.810 --> 00:04:11.014
exciting and unparalleled,
you wanna separate them with

00:04:11.014 --> 00:04:15.071
a comma, but generally if
you're just scooting down the

00:04:15.071 --> 00:04:18.572
dosa scomp, old white French
house, you don't need to

00:04:18.572 --> 00:04:23.135
separate these non-coordinate
adjectives from each other.

00:04:23.135 --> 00:04:25.956
And we'll get more into
commas in punctuation section,

00:04:25.956 --> 00:04:30.159
but for now, all you need
to remember is dosa scomp.

00:04:31.145 --> 00:04:34.227
And if you've never had a
dosa, I strongly urge you to

00:04:34.227 --> 00:04:36.874
look up recipes online or go
to a South Indian restaurant

00:04:36.874 --> 00:04:40.027
and make and eat this delicious food.

00:04:40.027 --> 00:04:41.994
And then, you're just
gonna scomp on some dosas.

00:04:41.994 --> 00:04:44.920
So determiner, opinion, size, age, dosa.

00:04:44.920 --> 00:04:49.920
Shape, color, origin, material,
purpose, and then the thing.

00:04:50.127 --> 00:04:53.731
That's the order that
adjectives go in in English.

00:04:53.731 --> 00:04:55.837
Why is this? I have no idea.

00:04:55.837 --> 00:04:58.636
You know sometimes language can be really,

00:04:58.636 --> 00:05:00.681
the word I tend to use is arbitrary.

00:05:00.681 --> 00:05:02.841
You can call it random, if you like.

00:05:02.841 --> 00:05:06.951
This is just the way that
we arrived at this order,

00:05:06.951 --> 00:05:10.521
it's just basically through
random chance of convention.

00:05:10.521 --> 00:05:12.852
And what seems to sound right.

00:05:12.852 --> 00:05:14.874
And what sounds right for
English isn't always what sounds

00:05:14.874 --> 00:05:16.161
right for other languages.

00:05:16.161 --> 00:05:18.235
For example, the way we're
using adjectives here,

00:05:18.235 --> 00:05:21.353
we're always putting them
to the left of whatever they

00:05:21.353 --> 00:05:23.982
modify, the exciting,
unparalleled green dragon.

00:05:23.982 --> 00:05:27.587
It's all to the left, it's
all old white French house.

00:05:27.587 --> 00:05:30.564
It's all on this one side of it.

00:05:30.564 --> 00:05:34.013
And other languages don't
do that necessarily.

00:05:34.013 --> 00:05:36.922
So when you're trying to just
throw a bunch of adjectives

00:05:36.922 --> 00:05:40.875
together on the left side of
the noun, this is the order.

00:05:40.875 --> 00:05:43.120
Just remember dosa scomp.

00:05:43.120 --> 00:05:46.764
And that's how adjective
order works in English.

00:05:46.764 --> 00:05:47.944
You can learn anything.

00:05:47.944 --> 00:05:49.944
David out.


Relative adverbs

WEBVTT
Kind: captions
Language: en

00:00:00.583 --> 00:00:01.486
- [Voiceover] Hey grammarians.

00:00:01.486 --> 00:00:03.352
Today we're gonna talk about three of

00:00:03.352 --> 00:00:05.774
the relative adverbs in English.

00:00:05.774 --> 00:00:07.982
Which is where, when, and why.

00:00:07.982 --> 00:00:11.565
And this over here is Peggy the dragon.

00:00:11.565 --> 00:00:13.916
And we're gonna use the story
of Peggy the dragon in order

00:00:13.916 --> 00:00:16.932
to figure out how to use
these relative adverbs.

00:00:16.932 --> 00:00:19.166
You may be looking at
these words and thinking

00:00:19.166 --> 00:00:22.093
that they look an awful
lot like question words.

00:00:22.093 --> 00:00:23.754
And you're right they are.

00:00:23.754 --> 00:00:25.907
These are questions words.

00:00:25.907 --> 00:00:26.996
But you can also--

00:00:26.996 --> 00:00:29.198
so you can use them to
ask a question like,

00:00:29.198 --> 00:00:30.781
where are you from?

00:00:32.159 --> 00:00:33.337
Because we use the word,

00:00:33.337 --> 00:00:36.642
where to figure out
where stuff is in space.

00:00:36.642 --> 00:00:40.259
So you know, where figures out place.

00:00:40.259 --> 00:00:41.601
So Peggy could respond and say

00:00:41.601 --> 00:00:44.351
that is the cave where I grew up.

00:00:45.295 --> 00:00:46.731
And you can see that where,

00:00:46.731 --> 00:00:49.273
here is not being used in a question way.

00:00:49.273 --> 00:00:51.521
It's actually connecting

00:00:51.521 --> 00:00:53.271
the clause I grew up,

00:00:54.180 --> 00:00:55.013
to cave.

00:00:56.439 --> 00:00:59.936
And this is why we call
this a relative adverb.

00:00:59.936 --> 00:01:03.725
Because the word, where,
modifies the word grew.

00:01:03.725 --> 00:01:05.231
It's I grew up, where.

00:01:05.231 --> 00:01:09.619
And it also connects
this whole thing to cave.

00:01:09.619 --> 00:01:11.571
Because where did peggy grow up?

00:01:11.571 --> 00:01:12.596
A cave.

00:01:12.596 --> 00:01:14.762
And it connects this whole chunk

00:01:14.762 --> 00:01:17.420
to the rest of the sentence.

00:01:17.420 --> 00:01:20.095
To the sentence being, that is the cave.

00:01:20.095 --> 00:01:24.262
We use the word, when, to
ask questions about time.

00:01:25.117 --> 00:01:27.299
So if I ask Peggy you
know, you're a dragon

00:01:27.299 --> 00:01:30.216
when did you learn to breathe fire?

00:01:31.245 --> 00:01:32.879
Because all dragons can breathe fire

00:01:32.879 --> 00:01:34.181
(whooshing)

00:01:34.181 --> 00:01:35.348
She would say,

00:01:36.866 --> 00:01:41.033
I learned to breathe fire
when I was 10 years old.

00:01:41.950 --> 00:01:43.812
So again we're using this word, when,

00:01:43.812 --> 00:01:46.062
to connect these two ideas.

00:01:47.534 --> 00:01:48.949
When did she learn to breathe fire?

00:01:48.949 --> 00:01:51.550
When she was 10 years old.

00:01:51.550 --> 00:01:55.717
And technically, when is an
adverb that modifies was.

00:01:58.195 --> 00:02:00.314
Finally, we use the word why

00:02:00.314 --> 00:02:03.481
to figure out reasons for doing stuff.

00:02:05.189 --> 00:02:07.597
So if something strange were happening

00:02:07.597 --> 00:02:11.597
in the countryside and I
asked Peggy, oh mighty dragon

00:02:11.597 --> 00:02:14.514
do you know why it is raining fish?

00:02:15.761 --> 00:02:17.094
Peggy could say,

00:02:18.007 --> 00:02:20.840
I don't know why that's happening.

00:02:22.978 --> 00:02:24.804
So again we've go these two clauses

00:02:24.804 --> 00:02:26.829
that is happening, and I don't know.

00:02:26.829 --> 00:02:29.829
And, why, connects and relates them.

00:02:32.084 --> 00:02:35.334
And why is modifying is happening here.

00:02:36.646 --> 00:02:39.393
And there are other relative adverbs like

00:02:39.393 --> 00:02:42.422
while, is another way to say when.

00:02:42.422 --> 00:02:46.391
And whence, which is
archaic and nobody really

00:02:46.391 --> 00:02:49.664
uses it but it's another way to say where.

00:02:49.664 --> 00:02:51.977
And if you're familiar
with Romeo and Juliet

00:02:51.977 --> 00:02:53.875
from Shakespeare, you've probably

00:02:53.875 --> 00:02:55.958
heard the word wherefore.

00:02:57.273 --> 00:02:58.132
You know as in,

00:02:58.132 --> 00:03:00.300
"Romeo, Romeo, wherefore art thou Romeo?

00:03:00.300 --> 00:03:02.117
Deny thy father refuse thy name."

00:03:02.117 --> 00:03:02.950
Etcetera.

00:03:02.950 --> 00:03:05.650
And that's an old fashioned
way of saying why.

00:03:05.650 --> 00:03:07.276
So we don't really say wherefore anymore.

00:03:07.276 --> 00:03:09.384
We don't really say whence anymore.

00:03:09.384 --> 00:03:11.785
But while, is another way to say when.

00:03:11.785 --> 00:03:13.303
Where, you ask about place.

00:03:13.303 --> 00:03:14.616
When, you ask about time.

00:03:14.616 --> 00:03:16.730
Why, is for reasons.

00:03:16.730 --> 00:03:20.124
These are the relative adverbs of English.

00:03:20.124 --> 00:03:21.106
You can learn anything.

00:03:21.106 --> 00:03:21.939
David out.


Intro to articles

WEBVTT
Kind: captions
Language: en

00:00:00.931 --> 00:00:02.424
- [Voiceover] Grammarians,
I would like to tell you

00:00:02.424 --> 00:00:04.118
a tale of two elephants.

00:00:04.118 --> 00:00:06.247
In order to get at the idea

00:00:06.247 --> 00:00:08.039
of this thing called the article.

00:00:08.039 --> 00:00:11.464
We'll explain what that
is after I tell you about

00:00:11.464 --> 00:00:15.412
the elephant and an elephant.

00:00:18.308 --> 00:00:22.378
Now articles are words
like "a" or "an" or "the".

00:00:23.695 --> 00:00:25.965
Articles are a kind of adjective,

00:00:25.965 --> 00:00:27.858
some people would call them a determiner,

00:00:27.858 --> 00:00:32.449
that help you figure out
how important something is.

00:00:32.449 --> 00:00:35.724
Or how specific something is.

00:00:35.724 --> 00:00:37.325
So, articles.

00:00:37.325 --> 00:00:39.735
What articles do is they tell you whether

00:00:39.735 --> 00:00:42.510
or not something is specific.

00:00:45.840 --> 00:00:48.256
Are you thinking about any old elephant

00:00:48.256 --> 00:00:49.650
when you talk about an elephant,

00:00:49.650 --> 00:00:52.424
or are you thinking about
one elephant in particular?

00:00:52.424 --> 00:00:54.364
The elephant.

00:00:54.364 --> 00:00:56.702
And this is the difference.

00:00:56.702 --> 00:00:58.385
When we're talking about the elephant

00:00:58.385 --> 00:01:00.483
we're talking about a specific elephant.

00:01:00.483 --> 00:01:02.597
We have particular one in mind.

00:01:02.597 --> 00:01:05.221
This what's called the definite.

00:01:05.221 --> 00:01:09.052
Because it defines what
we're talking about.

00:01:11.171 --> 00:01:15.175
You know, this elephant could
be the queen of the elephants.

00:01:15.175 --> 00:01:16.511
Sometimes, when we make sentences

00:01:16.511 --> 00:01:18.427
we want to aim for that kind of precision.

00:01:18.427 --> 00:01:20.516
We want to be precise.

00:01:20.516 --> 00:01:22.896
We want to know exactly what we're talking

00:01:22.896 --> 00:01:25.172
and who we're talking about and why.

00:01:25.172 --> 00:01:28.383
That's a case where you
would use the word "the".

00:01:29.606 --> 00:01:32.109
Now if you're not being specific.

00:01:32.109 --> 00:01:35.092
If you're talking about any old elephant.

00:01:35.092 --> 00:01:37.322
An elephant that you're not
especially familiar with.

00:01:37.322 --> 00:01:39.993
An elephant you haven't introduced before.

00:01:39.993 --> 00:01:43.486
You would say "an" elephant,

00:01:43.486 --> 00:01:46.343
because it's not specific...

00:01:48.903 --> 00:01:50.999
and it's undefined.

00:01:50.999 --> 00:01:54.807
So, grammarians call that
an indefinite article.

00:01:59.427 --> 00:02:02.156
When you know who and
what you are talking about

00:02:02.156 --> 00:02:03.764
for sure you say "the".

00:02:03.764 --> 00:02:07.555
And when you're not sure,
you say "a" or "an".

00:02:07.555 --> 00:02:11.542
So if you knew you were talking
about a specific elephant.

00:02:12.512 --> 00:02:15.786
Say for example the
queen of the elephants.

00:02:15.786 --> 00:02:17.806
The queen.

00:02:21.386 --> 00:02:25.148
As indicated by her royal
crown, you would say "the".

00:02:25.148 --> 00:02:28.070
And if you were talking
about any old elephant?

00:02:28.070 --> 00:02:33.070
You'd say "an". You'd use
the indefinite article.

00:02:33.671 --> 00:02:35.442
We'll cover this more later.

00:02:35.442 --> 00:02:37.149
I just wanted to give you an introduction

00:02:37.149 --> 00:02:39.494
to the idea of what an article is.

00:02:39.494 --> 00:02:44.352
So "the" for specific, "a"
or "an" for nonspecific.

00:02:44.352 --> 00:02:46.634
You can learn anything, David out.


Intensifiers and adverbs of degree

WEBVTT
Kind: captions
Language: en

00:00:00.226 --> 00:00:01.573
- [Voiceover] Hey,
grammarians, so we've already

00:00:01.573 --> 00:00:05.207
talked about the idea of the comparative

00:00:05.207 --> 00:00:07.645
modifiers, right, so you
know the difference between

00:00:07.645 --> 00:00:10.954
saying something is cute
and then saying that

00:00:10.954 --> 00:00:13.659
something is cuter than
that thing, and then

00:00:13.659 --> 00:00:15.690
looking at, like, I don't know,
let's say we're looking at

00:00:15.690 --> 00:00:17.978
a puppy or a mushroom, a little mushroom

00:00:17.978 --> 00:00:19.406
with a smiley face and you'd say,

00:00:19.406 --> 00:00:22.877
"Oh, that's the world's cutest mushroom."

00:00:22.877 --> 00:00:24.920
Right, that's the comparative,
we've already covered that.

00:00:24.920 --> 00:00:27.289
I would like to talk
about something I think is

00:00:27.289 --> 00:00:29.541
a really interesting topic.

00:00:29.541 --> 00:00:30.273
"What's that," you say?

00:00:30.273 --> 00:00:34.394
A really interesting topic.

00:00:34.394 --> 00:00:38.063
Now, what's that really doing there

00:00:38.063 --> 00:00:40.397
in this little phrase?

00:00:40.397 --> 00:00:42.475
A really interesting topic.

00:00:42.475 --> 00:00:44.228
Well, it's modifying interesting.

00:00:44.228 --> 00:00:47.246
We recognize that this
is an adverb, right?

00:00:47.246 --> 00:00:51.623
Really is modifying interesting,
which is an adjective.

00:00:51.623 --> 00:00:54.967
Interesting, in turn, is modifying topic.

00:00:54.967 --> 00:00:59.967
But, the question is,
what does really mean?

00:01:01.155 --> 00:01:03.242
What is it's function?

00:01:03.242 --> 00:01:05.123
And the answer is that it's a type of word

00:01:05.123 --> 00:01:06.713
we call an intensifier.

00:01:06.713 --> 00:01:10.231
So the function of really
is to just double down

00:01:10.231 --> 00:01:11.729
on the idea of interesting.

00:01:11.729 --> 00:01:13.528
So it's not just an interesting topic,

00:01:13.528 --> 00:01:15.691
it's a really interesting topic.

00:01:15.691 --> 00:01:18.928
You could also say it's
a very interesting topic.

00:01:18.928 --> 00:01:23.297
Or even, an extremely interesting topic.

00:01:23.297 --> 00:01:26.136
And that kind of gets us
into this other category

00:01:26.136 --> 00:01:28.540
which is called adverbs of degree.

00:01:28.540 --> 00:01:30.908
So an intensifier, let me
just step back a little bit,

00:01:30.908 --> 00:01:34.101
an intensifier is a type of adverb that

00:01:34.101 --> 00:01:37.119
modifies an adjective or
another adverb in a way

00:01:37.119 --> 00:01:41.496
that doubles down on the
modified thing's meaning.

00:01:41.496 --> 00:01:43.656
So it's not just an interesting topic,

00:01:43.656 --> 00:01:47.441
it's a really interesting topic,
so it's like extra special,

00:01:47.441 --> 00:01:48.415
extra interesting.

00:01:48.415 --> 00:01:53.257
It makes, it intensifies,
it really accentuates

00:01:53.257 --> 00:01:55.928
or makes clear the fact
that you're trying to

00:01:55.928 --> 00:02:00.830
drive home the
interesting-ness of this topic.

00:02:01.943 --> 00:02:03.961
But frankly talking about
how interesting a topic is

00:02:03.961 --> 00:02:06.091
is a pretty good shortcut for boring,

00:02:06.091 --> 00:02:08.843
so in order to talk
about adverbs of degree

00:02:08.843 --> 00:02:11.292
I'm going to talk instead about the

00:02:11.292 --> 00:02:14.555
Incredibly Deadly Viper,

00:02:14.555 --> 00:02:17.695
which is a creature from

00:02:17.695 --> 00:02:19.988
A Series of Unfortunate
Events by Lemony Snicket,

00:02:19.988 --> 00:02:24.111
so the Incredibly Deadly

00:02:24.111 --> 00:02:26.693
Viper.

00:02:29.925 --> 00:02:34.154
There it is, there's your
terrifying, horned viper, yonder.

00:02:34.154 --> 00:02:36.871
And what the word incredibly is doing here

00:02:36.871 --> 00:02:41.770
is, it is serving as
an intensifier, right.

00:02:41.770 --> 00:02:46.770
But it is also what we like
to call an adverb of degree

00:02:47.079 --> 00:02:50.086
because it's saying the extent to which

00:02:50.086 --> 00:02:52.117
this viper is so very deadly.

00:02:52.117 --> 00:02:56.553
However, if this viper had a cousin

00:02:56.553 --> 00:03:00.845
that was the somewhat deadly viper,

00:03:02.487 --> 00:03:05.634
maybe we can blunt its teeth somewhat,

00:03:05.634 --> 00:03:09.196
maybe it's got square teeth.

00:03:09.196 --> 00:03:12.383
That's the somewhat deadly viper.

00:03:12.383 --> 00:03:14.940
We can see that somewhat, this word here

00:03:14.940 --> 00:03:18.005
is changing the meaning of the phrase.

00:03:18.005 --> 00:03:20.257
It's not just the deadly viper,

00:03:20.257 --> 00:03:22.533
it's the somewhat deadly viper.

00:03:22.533 --> 00:03:27.200
It's import has been blunted
slightly as have its teeth.

00:03:27.200 --> 00:03:29.475
And you could also say, what if he didn't

00:03:29.475 --> 00:03:32.866
have any teeth at all, this
ostensibly deadly viper?

00:03:32.866 --> 00:03:35.605
What if he just had little gums?

00:03:35.605 --> 00:03:40.388
Well then he's the barely deadly viper,

00:03:44.259 --> 00:03:45.938
instead.

00:03:45.938 --> 00:03:48.260
And these words like
incredibly and somewhat

00:03:48.260 --> 00:03:51.732
and barely, these are adverbs of degree,

00:03:51.732 --> 00:03:53.998
so they illustrate the degree to which

00:03:53.998 --> 00:03:57.795
the viper is deadly dangerous.

00:03:57.795 --> 00:04:00.453
So that's basically what intensifiers

00:04:00.453 --> 00:04:04.354
and adverbs of degree do.

00:04:04.354 --> 00:04:06.804
So, whenever you think of an intensifier

00:04:06.804 --> 00:04:10.844
just think of the word very,

00:04:10.844 --> 00:04:12.435
and when you're trying to figure out

00:04:12.435 --> 00:04:13.974
what an adverb of degree is, well that

00:04:13.974 --> 00:04:17.863
kind of answers the question, how much?

00:04:17.863 --> 00:04:19.709
So if you want to double down on the

00:04:19.709 --> 00:04:21.300
meaning of something
you use an intensifier

00:04:21.300 --> 00:04:24.237
like very or extremely, and if you want to

00:04:24.237 --> 00:04:27.423
express a degree of something

00:04:27.423 --> 00:04:32.283
you could say, let's say we're
talking about a cup of tea

00:04:32.283 --> 00:04:34.978
or something and you want
to express how warm it is.

00:04:34.978 --> 00:04:37.254
You could say it's too hot.

00:04:37.254 --> 00:04:41.178
You could say it's slightly hot.

00:04:41.178 --> 00:04:44.722
You could say somewhat,

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or almost hot.

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There are a lot of
different adverbs of degree.

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But that's basically the distinction.

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An intensifier is powerful but

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it has a very narrow usage.

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And adverbs of degree, you can use for

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a wide range of uses to express

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a variety of different meanings.

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That's intensifiers and adverbs of degree.

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You can learn anything.

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David out.