Dipole–dipole forces

WEBVTT
Kind: captions
Language: en

00:00:00.840 --> 00:00:02.560
- [Instructor] So I have
these two molecules here,

00:00:02.560 --> 00:00:06.140
propane on the left and
acetaldehyde here on the right.

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And we've already calculated
their molar masses for you,

00:00:09.540 --> 00:00:13.370
and you see that they have
very close molar masses.

00:00:13.370 --> 00:00:16.710
And so based on what
you see in front of you,

00:00:16.710 --> 00:00:18.160
which of these, you think,

00:00:18.160 --> 00:00:20.520
would have a higher boiling point,

00:00:20.520 --> 00:00:22.810
a sample of pure propane

00:00:22.810 --> 00:00:26.210
or a sample of pure acetaldehyde?

00:00:26.210 --> 00:00:28.160
Pause this video, and think about that.

00:00:29.520 --> 00:00:32.080
All right, well, in previous videos,

00:00:32.080 --> 00:00:33.740
when we talked about boiling points

00:00:33.740 --> 00:00:34.930
and why they might be different,

00:00:34.930 --> 00:00:37.530
we talked about intermolecular forces.

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Because you could imagine, if
you have a bunch of molecules,

00:00:40.500 --> 00:00:42.780
let's say, in a liquid state,

00:00:42.780 --> 00:00:45.390
the boiling point is going to be dependent

00:00:45.390 --> 00:00:48.630
on how much energy you
need to put into the system

00:00:48.630 --> 00:00:53.630
in order for the intermolecular
forces between the molecules

00:00:53.660 --> 00:00:57.140
to be overcome so that
molecules could break free

00:00:57.140 --> 00:01:00.430
and enter into a gaseous state.

00:01:00.430 --> 00:01:02.380
And so when we're thinking about

00:01:02.380 --> 00:01:04.800
which might have a higher boiling point,

00:01:04.800 --> 00:01:06.310
we really just need to think about

00:01:06.310 --> 00:01:11.160
which one would have higher
intermolecular forces.

00:01:11.160 --> 00:01:12.110
Now, in a previous video,

00:01:12.110 --> 00:01:14.580
we talked about London dispersion forces,

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which you can view as
random dipoles forming

00:01:18.170 --> 00:01:21.010
in one molecule, and then
that can induce dipoles

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in a neighboring molecule.

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And then the positive end,
even temporarily positive end,

00:01:25.630 --> 00:01:28.000
of one could be attracted
to the temporarily

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negative end of another and vice versa,

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and that whole phenomenon can domino.

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And we said that you're going to have more

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of those London dispersion forces

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the more polarizable your molecule is,

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which is related to how large
of an electron cloud it has,

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which is related to its molar mass.

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And when we look at these two molecules,

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they have near identical molar masses.

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So you might expect them

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to have near identical boiling points,

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but it turns out that
that is not the case.

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The boiling point of propane

00:02:02.440 --> 00:02:06.440
is negative 42.1 degrees Celsius,

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while the boiling point of acetaldehyde

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is 20.1 degrees Celsius.

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So what makes the difference?

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Why does acetaldehyde have
such a higher boiling point?

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Why does it take more energy

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for the molecules in liquid acetaldehyde

00:02:24.430 --> 00:02:26.250
to be able to break free of each other

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to overcome their intermolecular forces?

00:02:29.620 --> 00:02:32.850
Well, the answer, you might
imagine, is other things are

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at play on top of the
London dispersion forces.

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And what we're going to
talk about in this video is

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dipole-dipole forces.

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So you might already
imagine where this is going.

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In the video on London dispersion forces,

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we talked about a temporary dipole

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inducing a dipole in
a neighboring molecule

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and then them being
attracted to each other.

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Now we're going to talk
about permanent dipoles.

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So when you look at
both of these molecules,

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which one would you think has
a stronger permanent dipole?

00:03:07.440 --> 00:03:08.910
Or another way of thinking about it is

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which one has a larger dipole moment?

00:03:12.900 --> 00:03:17.460
Remember, molecular dipole
moments are just the vector sum

00:03:17.460 --> 00:03:20.290
of all of the dipole moments
of the individual bonds,

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and the dipole moments
are all proportional

00:03:23.100 --> 00:03:26.010
to the differences in electronegativity.

00:03:26.010 --> 00:03:28.490
When we look at propane here on the left,

00:03:28.490 --> 00:03:31.720
carbon is a little bit more
electronegative than hydrogen

00:03:31.720 --> 00:03:33.680
but not a lot more electronegative.

00:03:33.680 --> 00:03:37.690
So you will have these dipole
moments on each of the bonds

00:03:37.690 --> 00:03:40.200
that might look something like this.

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So you would have these
things that look like that.

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If that is looking unfamiliar to you,

00:03:44.790 --> 00:03:49.790
I encourage you to review
the videos on dipole moments.

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But as you can see, there's a
symmetry to propane as well.

00:03:53.610 --> 00:03:57.250
So if you were to take all of
these arrows that I'm drawing,

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if you were to take all of these arrows

00:03:59.240 --> 00:04:01.220
that I'm drawing and net them together,

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you're not going to get much
of a molecular dipole moment.

00:04:05.090 --> 00:04:06.280
You will get a little bit of one,

00:04:06.280 --> 00:04:08.383
but they, for the most part, cancel out.

00:04:09.270 --> 00:04:11.968
Now what about acetaldehyde?

00:04:11.968 --> 00:04:15.030
Well, acetaldehyde, there's
a few giveaways here.

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One is it's an asymmetric molecule.

00:04:18.640 --> 00:04:21.230
So asymmetric molecules are good suspects

00:04:21.230 --> 00:04:24.530
for having a higher dipole moment.

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Another good indicator is
you have some character here

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that's quite electronegative.

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In this case, oxygen is
quite electronegative.

00:04:32.410 --> 00:04:33.540
And even more important,

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it's a good bit more
electronegative than carbon.

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So right over here, this
carbon-oxygen double bond,

00:04:40.470 --> 00:04:43.310
you're going to have a pretty
significant dipole moment

00:04:43.310 --> 00:04:44.830
just on this double bond.

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It might look like that.

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And all of the other dipole moments

00:04:48.950 --> 00:04:50.800
for all of the other bonds aren't going

00:04:50.800 --> 00:04:53.130
to cancel this large one out.

00:04:53.130 --> 00:04:55.480
In fact, they might add to it a little bit

00:04:55.480 --> 00:04:58.260
because of the molecule's asymmetry.

00:04:58.260 --> 00:05:01.100
And so net-net, your whole molecule

00:05:01.100 --> 00:05:04.380
is going to have a pretty
significant dipole moment.

00:05:04.380 --> 00:05:06.160
It'll look something like this,

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and I'm just going to approximate it.

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But we're going to point
towards the more negative end,

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so it might look something like this,

00:05:14.260 --> 00:05:16.330
pointing towards the more negative end.

00:05:16.330 --> 00:05:17.920
And I'll put this little cross here

00:05:17.920 --> 00:05:19.200
at the more positive end.

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And so you would expect
a partial negative charge

00:05:22.230 --> 00:05:26.550
at that end and a partial
positive charge at this end.

00:05:26.550 --> 00:05:28.200
And so what's going to happen

00:05:28.200 --> 00:05:30.350
if it's next to another acetaldehyde?

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Well, the partially negative
end of one acetaldehyde

00:05:33.310 --> 00:05:36.440
is going to be attracted to
the partially positive end

00:05:36.440 --> 00:05:38.320
of another acetaldehyde.

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And so this is what
people are talking about

00:05:40.220 --> 00:05:42.970
when they say dipole-dipole forces.

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We are talking about a permanent dipole

00:05:46.010 --> 00:05:48.980
being attracted to
another permanent dipole.

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And so acetaldehyde is experiencing that

00:05:51.570 --> 00:05:54.030
on top of the London dispersion forces,

00:05:54.030 --> 00:05:57.280
which is why it has a
higher boiling point.

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Now some of you might be wondering,

00:05:58.900 --> 00:06:01.770
hey, can a permanent dipole

00:06:01.770 --> 00:06:05.010
induce a dipole in a neighboring molecule

00:06:05.010 --> 00:06:07.940
and then those get
attracted to each other?

00:06:07.940 --> 00:06:10.950
And the simple answer is
yes, it makes a lot of sense.

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You can absolutely have a dipole

00:06:14.330 --> 00:06:15.710
and then induced

00:06:17.837 --> 00:06:20.240
dipole interaction.

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And we might cover that in a
few examples in the future,

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but this can also occur.

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You can have a temporary dipole

00:06:26.930 --> 00:06:28.620
inducing a dipole in the neighbor,

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and then they get attracted to each other.

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And you could have a
bit of a domino effect.

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You can have a permanent
dipole interacting

00:06:35.340 --> 00:06:36.930
with another permanent dipole.

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They get attracted to each other.

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And you could have a permanent
dipole inducing a dipole

00:06:42.280 --> 00:06:43.593
in a neighboring molecule.


Guided meditation for procrastination

WEBVTT
Kind: captions
Language: en

00:00:00.930 --> 00:00:04.840
- [Instructor] Welcome to the
meditation on procrastination

00:00:04.840 --> 00:00:07.730
and somewhat ironically,
I've been procrastinating

00:00:07.730 --> 00:00:09.530
making this meditation,

00:00:09.530 --> 00:00:12.463
so we're all in the same boat together.

00:00:13.470 --> 00:00:16.220
So, as with all meditations,

00:00:16.220 --> 00:00:18.390
posture and breathing
makes a big difference.

00:00:18.390 --> 00:00:22.460
So, I really encourage you find
a nice firm seat to sit on.

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If your legs don't fall asleep,

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you could sit on the ground as well.

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But try to sit with your back
upright, really good posture.

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Breathe in, breathe out,

00:00:33.550 --> 00:00:37.123
a little bit slower a little
bit deeper every time,

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you could lay your hands on your lap,

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I like to leave them face up,

00:00:43.220 --> 00:00:46.290
and when you're ready,
you can soften your gaze

00:00:46.290 --> 00:00:49.853
and slowly close your eyes.

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Breathing in, breathing out.

00:01:00.090 --> 00:01:03.110
Now, procrastination is
an interesting thing.

00:01:03.110 --> 00:01:07.410
I'm not sure whether we human
beings are the only animals

00:01:07.410 --> 00:01:09.390
we know of that procrastinate,

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it's may be worth some
research for somebody

00:01:12.070 --> 00:01:14.713
to figure that out, but we clearly do it.

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And a lot of meditation is about

00:01:18.900 --> 00:01:22.680
becoming aware of our thoughts
and observing our thoughts

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and realizing that we
are not our thoughts,

00:01:26.400 --> 00:01:29.240
even though many times our
thoughts seem to control us

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or even overwhelm us.

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And so let's do that, let's
try to observe those thoughts

00:01:39.350 --> 00:01:42.010
that are making us put off something,

00:01:42.010 --> 00:01:43.793
that we know we need to do.

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Why do you think you are
putting that thing off?

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I'll tell you what happens to be usually

00:01:55.530 --> 00:01:58.360
from my experience, it usually is

00:01:58.360 --> 00:02:01.820
I'm afraid to start
because I might realize

00:02:01.820 --> 00:02:04.140
it's harder than I expected

00:02:05.180 --> 00:02:08.380
or I might not do as well as I expected

00:02:09.580 --> 00:02:12.750
or I might make a mistake,

00:02:12.750 --> 00:02:15.713
maybe I don't think I'm
prepared enough to start.

00:02:17.360 --> 00:02:20.170
Another way to think about it
is we're getting too caught up

00:02:20.170 --> 00:02:24.370
in the outcome versus enjoying the journey

00:02:24.370 --> 00:02:27.040
or enjoying whatever the thing
is that you're putting off,

00:02:27.040 --> 00:02:29.853
'cause that's just a part
of this fun experience.

00:02:31.940 --> 00:02:34.893
And so I find that when I tell myself,

00:02:36.039 --> 00:02:40.763
define yourself by the
action not the outcome,

00:02:41.990 --> 00:02:45.783
don't define yourself by
whether you succeed or fail,

00:02:46.730 --> 00:02:51.710
define yourself as making the effort,

00:02:51.710 --> 00:02:56.710
showing up and enjoying
it, laughing at yourself,

00:02:57.120 --> 00:03:00.530
laughing at this mystery that we call life

00:03:00.530 --> 00:03:03.750
and just putting one foot
in front of the other

00:03:03.750 --> 00:03:06.530
and realizing it's not so bad,

00:03:06.530 --> 00:03:08.560
and then you can put the other
foot in front of that one

00:03:08.560 --> 00:03:09.713
and keep going.

00:03:12.290 --> 00:03:14.440
And slowly but surely you realize

00:03:14.440 --> 00:03:17.320
that you're making a lot of progress.

00:03:17.320 --> 00:03:20.010
And the more you make that progress,

00:03:20.010 --> 00:03:22.210
the more that you actually enjoy it,

00:03:22.210 --> 00:03:25.130
especially if you're not
going it the last minute.

00:03:25.130 --> 00:03:27.310
And I will give you about a minute

00:03:27.310 --> 00:03:31.380
for you to repeat something in your mind

00:03:31.380 --> 00:03:35.250
that can hopefully short-circuit
any of those thoughts

00:03:35.250 --> 00:03:37.550
that have been keeping
you from taking action.

00:03:39.200 --> 00:03:42.360
For the next minute or
so repeat to yourself

00:03:43.230 --> 00:03:45.903
that you really enjoy taking action,

00:03:47.090 --> 00:03:48.640
you're lucky that you're in a position

00:03:48.640 --> 00:03:51.103
to be able to take action.

00:03:53.020 --> 00:03:56.023
The outcome, it is what it is.

00:03:57.900 --> 00:04:02.853
You enjoy action, you are lucky
to be able to take action,

00:04:04.480 --> 00:04:07.773
the outcome is what it is.

00:04:09.510 --> 00:04:11.730
Keep thinking that for
the next minute or so

00:04:11.730 --> 00:04:14.093
and I'll be back, don't worry.

00:05:17.430 --> 00:05:22.430
All right, so when you're
ready, really at your own time,

00:05:24.990 --> 00:05:28.600
just become a little bit more
aware of your surroundings,

00:05:28.600 --> 00:05:30.450
a little bit more aware of your body,

00:05:31.980 --> 00:05:34.093
a little bit more aware
of your every breath,

00:05:35.780 --> 00:05:38.723
and slowly open your eyes.

00:05:40.690 --> 00:05:42.873
And so, I'll finished with one last tip:

00:05:44.050 --> 00:05:45.730
sometimes we put something off

00:05:45.730 --> 00:05:49.433
because it just feels big or overwhelming.

00:05:50.740 --> 00:05:52.320
What I like to do is say,

00:05:52.320 --> 00:05:56.910
Hey, let me just put 20 minutes towards it

00:05:56.910 --> 00:06:00.010
and see where I am at
the end of 20 minutes.

00:06:00.010 --> 00:06:03.280
If I didn't make any
progress, no big deal,

00:06:03.280 --> 00:06:04.653
it was just 20 minutes,

00:06:05.490 --> 00:06:07.900
but if I did make some progress, great!

00:06:07.900 --> 00:06:10.523
I did the 20 minutes, I deserve a break.

00:06:11.370 --> 00:06:13.130
If after a five or 10 minute break

00:06:13.130 --> 00:06:16.150
I'm ready to put another
20 minutes, awesome.

00:06:16.150 --> 00:06:18.670
If at the end of the 20
minutes I wanna keep going,

00:06:18.670 --> 00:06:21.373
I shouldn't stop myself,
I should keep going.

00:06:22.390 --> 00:06:24.430
For when you view things as, hey,

00:06:24.430 --> 00:06:27.530
I'm just committing 20
minutes to something,

00:06:27.530 --> 00:06:29.443
it doesn't feel as intimidating.

00:06:30.470 --> 00:06:31.770
You just own it, you say,

00:06:31.770 --> 00:06:34.570
Hey, I can do anything for 20 minutes,

00:06:34.570 --> 00:06:38.250
and I can enjoy anything for 20 minutes

00:06:38.250 --> 00:06:40.980
and then you'll wanna do
it, put a smile on your face

00:06:40.980 --> 00:06:43.063
and own that action.

00:06:44.150 --> 00:06:45.730
And not only will you make progress,

00:06:45.730 --> 00:06:47.940
but you're gonna have a good time.

00:06:47.940 --> 00:06:52.940
And so take it with that
playful mindset, enjoy it, smile

00:06:53.460 --> 00:06:54.853
and just get started.

00:06:55.750 --> 00:06:57.160
And I think you'll find

00:06:57.160 --> 00:06:59.353
you'll be procrastinating a lot less.


Guided meditation visualizing thoughts as the surface of an ocean

WEBVTT
Kind: captions
Language: en

00:00:00.330 --> 00:00:02.940
- [Instructor] Welcome and
thanks for taking out the time

00:00:02.940 --> 00:00:04.060
for yourself

00:00:04.060 --> 00:00:08.530
for what will hopefully
be a nice inward journey.

00:00:08.530 --> 00:00:12.240
So just start off sitting upright

00:00:12.240 --> 00:00:14.080
feet planted on the ground

00:00:14.080 --> 00:00:17.730
if you're ideally on
some type of a firm chair

00:00:17.730 --> 00:00:21.030
and start to soften your gaze.

00:00:21.030 --> 00:00:25.200
If your eyes are still
open, gently close them.

00:00:25.200 --> 00:00:30.200
I like to leave my hands on
my lap, palms up to the sky

00:00:31.130 --> 00:00:33.370
but whatever feels comfortable for you

00:00:34.890 --> 00:00:36.940
and then with your eyes closed,

00:00:36.940 --> 00:00:40.343
gently become a little bit
more aware of your breaths.

00:00:41.460 --> 00:00:45.233
Make them a little bit deeper
and a little bit slower.

00:00:47.030 --> 00:00:50.083
At your own time, breathe in.

00:00:52.850 --> 00:00:54.920
Breathe out.

00:00:54.920 --> 00:00:58.793
Just a little bit deeper
and a little bit slower.

00:01:01.810 --> 00:01:05.060
So the whole idea behind meditation

00:01:05.060 --> 00:01:10.060
is trying to ease all the chatter
that exists in our brains,

00:01:10.510 --> 00:01:12.780
trying to still our thoughts

00:01:13.730 --> 00:01:16.490
and so as we do that and every meditation

00:01:16.490 --> 00:01:19.270
I'm going to try to
introduce some frameworks,

00:01:19.270 --> 00:01:21.950
ways of thinking about your mind

00:01:21.950 --> 00:01:25.220
but as you try to quiet the mind,

00:01:25.220 --> 00:01:28.070
it will inevitably get distracted.

00:01:28.070 --> 00:01:31.590
It might get distracted
by some noise in the room

00:01:31.590 --> 00:01:35.330
or some noise outside or more likely,

00:01:35.330 --> 00:01:37.570
it'll get distracted by thoughts

00:01:37.570 --> 00:01:40.400
that are just surfacing
into your consciousness

00:01:40.400 --> 00:01:43.730
and if that happens, don't
let it make you anxious.

00:01:43.730 --> 00:01:45.640
A lot of folks when they meditate,

00:01:45.640 --> 00:01:47.270
they worry that they're doing it wrong

00:01:47.270 --> 00:01:48.720
and then if they get distracted,

00:01:48.720 --> 00:01:50.580
it actually makes things worse.

00:01:50.580 --> 00:01:52.590
They say I'm never going to be able

00:01:52.590 --> 00:01:54.890
to do this meditation thing.

00:01:54.890 --> 00:01:57.610
The important thing is to
approach the meditation

00:01:57.610 --> 00:02:00.940
with a spirit of fun,
a spirit of curiosity,

00:02:00.940 --> 00:02:02.440
have a sense of humor about it.

00:02:02.440 --> 00:02:06.280
We are all literally human
and we do very human things

00:02:06.280 --> 00:02:09.190
and so when you find your
mind wandering a bit,

00:02:09.190 --> 00:02:12.150
just laugh it off and say,
oh, there you go, mind.

00:02:12.150 --> 00:02:13.920
Just come back to the stillness.

00:02:13.920 --> 00:02:17.070
Not a big deal, don't beat
up on yourself over it

00:02:17.070 --> 00:02:19.420
and as part of that as we
go through this meditation,

00:02:19.420 --> 00:02:20.910
as much as possible,

00:02:20.910 --> 00:02:24.810
try to keep a little bit
of a smile on your face.

00:02:24.810 --> 00:02:27.450
Your eyes are closed but you
can still smile a little bit

00:02:27.450 --> 00:02:29.760
or at least smile with your mind.

00:02:29.760 --> 00:02:34.363
Reminds you that this should
be fun, this is relaxing.

00:02:36.230 --> 00:02:40.790
So with that said, let's keep
breathing in, breathing out

00:02:41.660 --> 00:02:44.180
a little bit deeper, a little bit slower

00:02:48.760 --> 00:02:51.150
and the framework that
I'm going to introduce

00:02:51.150 --> 00:02:54.960
for how you can still your
mind is one that I use a lot

00:02:54.960 --> 00:02:59.060
which is imagining all the
thoughts in your subconscious

00:02:59.060 --> 00:03:04.060
as the ocean and the surface
of the ocean is the interface

00:03:04.140 --> 00:03:08.070
between your subconscious
and your consciousness

00:03:08.070 --> 00:03:11.480
and most of us have a
pretty choppy surface.

00:03:11.480 --> 00:03:14.360
There's a lot of thoughts
that are jumping up and down

00:03:14.360 --> 00:03:15.900
out of our subconscious

00:03:15.900 --> 00:03:18.990
and sometimes we're
drowning in those thoughts

00:03:19.990 --> 00:03:24.640
and one way to think about it
is we can elevate ourselves.

00:03:24.640 --> 00:03:29.640
We can elevate ourselves above
the surface of that water

00:03:29.660 --> 00:03:32.110
and when you start to elevate yourself,

00:03:32.110 --> 00:03:34.970
you're not suppressing the thoughts

00:03:34.970 --> 00:03:37.620
but you're just looking down on them.

00:03:37.620 --> 00:03:39.200
You see that they're still there,

00:03:39.200 --> 00:03:42.520
the surface is still
choppy, there's still waves

00:03:42.520 --> 00:03:44.860
but as you rise and you look down on it,

00:03:44.860 --> 00:03:47.420
you realize that you
are not those thoughts,

00:03:47.420 --> 00:03:50.330
you are not the surface of the water.

00:03:50.330 --> 00:03:52.780
So whether the thing that's bothering you

00:03:52.780 --> 00:03:54.560
is an assignment you have to do

00:03:54.560 --> 00:03:58.140
or some interpersonal relations

00:03:58.140 --> 00:03:59.570
or just something in your life

00:03:59.570 --> 00:04:02.570
not working out the way
that you would like it to,

00:04:02.570 --> 00:04:04.870
remind yourself that that is not you.

00:04:04.870 --> 00:04:08.330
You are not defined by the
outcome of that situation.

00:04:08.330 --> 00:04:11.140
Those are just waves on that ocean

00:04:14.690 --> 00:04:16.730
and the more that you surface above them

00:04:16.730 --> 00:04:20.580
and you look at them and analyze them,

00:04:20.580 --> 00:04:23.080
you realize that they
have no control over you

00:04:23.930 --> 00:04:28.180
and once that happens,
things start to slow down.

00:04:28.180 --> 00:04:31.450
The surface of that water
begins to get calmer

00:04:31.450 --> 00:04:33.440
and calmer and calmer

00:04:35.080 --> 00:04:38.800
and there you are floating
above that surface.

00:04:38.800 --> 00:04:40.680
Just pure awareness

00:04:41.900 --> 00:04:44.540
and you realize that you're a lot more

00:04:44.540 --> 00:04:45.883
than you thought you were.

00:04:46.900 --> 00:04:50.063
You aren't just your physical body.

00:04:50.910 --> 00:04:53.400
You aren't just those thoughts

00:04:53.400 --> 00:04:56.423
that you see as waves on
the surface of that ocean.

00:04:57.870 --> 00:05:00.460
You aren't even just that identity

00:05:00.460 --> 00:05:02.510
that you associate yourself with,

00:05:02.510 --> 00:05:05.530
your name, your position
in the world, your status,

00:05:05.530 --> 00:05:07.743
what people think of you, your relations.

00:05:08.970 --> 00:05:12.053
Those are aspects of
you but they aren't you.

00:05:13.150 --> 00:05:16.523
You are something much
bigger than all of them.

00:05:17.370 --> 00:05:22.160
You are the space in which they
occur, in which they happen

00:05:22.160 --> 00:05:23.680
but they aren't you

00:05:24.530 --> 00:05:27.800
and now let's just try to
sit in that pure awareness

00:05:27.800 --> 00:05:29.530
for the next minute or so and once again,

00:05:29.530 --> 00:05:31.940
if your thoughts wander, not a big deal.

00:05:31.940 --> 00:05:34.410
That's just the choppiness
on the surface of that water

00:05:34.410 --> 00:05:38.010
and you need to elevate yourself
back to that pure awareness

00:05:38.010 --> 00:05:40.370
and if the quiet bothers you, don't worry,

00:05:40.370 --> 00:05:42.963
I will be back in about a minute.

00:06:42.830 --> 00:06:47.040
All right, so that was a
relatively short amount of time

00:06:47.040 --> 00:06:49.870
for you to be on your
own and as you'll see

00:06:49.870 --> 00:06:53.340
as we do more and more
advanced meditations,

00:06:53.340 --> 00:06:55.710
give yourself more and more time

00:06:55.710 --> 00:06:58.510
and over time, you won't need me talking.

00:06:58.510 --> 00:07:00.620
In fact, that will probably annoy you.

00:07:00.620 --> 00:07:04.210
You'll just be able to sit
down and still your mind

00:07:04.210 --> 00:07:06.890
and realize that you are not your thoughts

00:07:06.890 --> 00:07:08.880
and these things that are bothering you,

00:07:08.880 --> 00:07:10.290
they're only going to bother you

00:07:10.290 --> 00:07:12.223
as much as you let them bother you.

00:07:13.237 --> 00:07:17.600
In the whole scheme of things,
in all of time and space,

00:07:17.600 --> 00:07:21.480
none of them are really
what should define you

00:07:21.480 --> 00:07:23.890
or are anywhere near as important

00:07:23.890 --> 00:07:26.840
as we sometimes make them out to be.

00:07:26.840 --> 00:07:28.640
I'll see you in the next meditation.


Guided meditation for high school students

WEBVTT
Kind: captions
Language: en

00:00:00.600 --> 00:00:03.700
- [Instructor] Welcome, and
thanks for joining me on this,

00:00:03.700 --> 00:00:06.750
let's call it a voyage of the mind.

00:00:06.750 --> 00:00:10.970
So before we begin, posture and breathing

00:00:10.970 --> 00:00:13.960
make a big difference in meditation.

00:00:13.960 --> 00:00:17.860
So if you're not already
on a nice firm chair

00:00:17.860 --> 00:00:21.220
with your back straight,
pause this recording

00:00:21.220 --> 00:00:24.500
and go find a nice firm chair
with your back straight,

00:00:24.500 --> 00:00:28.313
ideally in a place that's
kind of quiet and peaceful.

00:00:29.750 --> 00:00:33.870
So now that you're there,
sit with your back straight,

00:00:33.870 --> 00:00:37.000
try to put your feet firmly on the floor.

00:00:37.000 --> 00:00:40.520
When I do this, I like to
rest my hands on my lap,

00:00:40.520 --> 00:00:43.513
palms up gently curled,
so really no effort.

00:00:44.790 --> 00:00:49.400
And now start to slowly
breathe a bit deeper

00:00:49.400 --> 00:00:52.263
than you were just now and a bit slower.

00:00:53.420 --> 00:00:58.420
In and out, at your own time
but just a little bit deeper,

00:00:58.720 --> 00:01:00.143
a little bit slower.

00:01:01.240 --> 00:01:03.870
If you like, a lot of
folks like to breathe

00:01:03.870 --> 00:01:06.190
in through their nose,

00:01:06.190 --> 00:01:08.060
out through their mouth,

00:01:08.060 --> 00:01:12.090
but the key, once again,
a little bit deeper,

00:01:12.090 --> 00:01:13.353
a little bit slower.

00:01:14.930 --> 00:01:18.770
And as you do so, start
to soften your gaze

00:01:18.770 --> 00:01:21.180
if your eyes are still open,

00:01:21.180 --> 00:01:26.163
and when you feel comfortable,
gently close your eyes.

00:01:29.210 --> 00:01:32.510
Now, before we get into the
heart of the meditation,

00:01:32.510 --> 00:01:35.030
I'm going to give you a few reminders.

00:01:35.030 --> 00:01:40.030
This whole exercise is about
exploring your inner being.

00:01:41.120 --> 00:01:42.580
It's about curiosity.

00:01:42.580 --> 00:01:44.500
It's about relaxation.

00:01:44.500 --> 00:01:47.180
There's no perfect way to meditate.

00:01:47.180 --> 00:01:50.010
Sometimes folks think that
they're not doing it right

00:01:50.010 --> 00:01:52.120
or their mind is wandering too much.

00:01:52.120 --> 00:01:53.580
And then it causes stress.

00:01:53.580 --> 00:01:55.130
And that's the exact opposite

00:01:55.130 --> 00:01:57.350
of what you want meditation to be.

00:01:57.350 --> 00:02:00.460
It should be fun, it could
even be funny at moments.

00:02:00.460 --> 00:02:01.970
You should be curious.

00:02:01.970 --> 00:02:03.883
You should be enjoying it.

00:02:04.830 --> 00:02:07.040
If there are some random distractions,

00:02:07.040 --> 00:02:08.600
and there inevitably will be,

00:02:08.600 --> 00:02:10.720
it could be sounds around you,

00:02:10.720 --> 00:02:15.210
it might be part of your
body that itches or tingles.

00:02:15.210 --> 00:02:18.580
Don't let it stress you
out, just accept it.

00:02:18.580 --> 00:02:20.670
It's part of the universe.

00:02:20.670 --> 00:02:23.120
It's just atoms doing what they do.

00:02:23.120 --> 00:02:25.840
It's the universe doing its thing.

00:02:25.840 --> 00:02:28.390
And no worries if you need to scratch

00:02:28.390 --> 00:02:32.403
or adjust part of your
body, no reason to stress.

00:02:33.900 --> 00:02:36.080
Now to add to the idea

00:02:36.080 --> 00:02:38.220
that this shouldn't be
a stressful experience,

00:02:38.220 --> 00:02:39.750
I'm going to ask you to do something

00:02:39.750 --> 00:02:43.420
that may or may not
feel completely natural.

00:02:43.420 --> 00:02:45.080
I want you to smile right now.

00:02:45.080 --> 00:02:46.580
Give yourself a good smile

00:02:46.580 --> 00:02:49.430
with your eyes closed, just smile.

00:02:49.430 --> 00:02:51.160
Obviously, we smile when we're happy.

00:02:51.160 --> 00:02:53.350
But sometimes, making a smile

00:02:53.350 --> 00:02:55.430
can actually make us a little bit happier.

00:02:55.430 --> 00:02:57.870
It can make us a little bit less stressed.

00:02:57.870 --> 00:03:00.550
So even if you need to force it, smile.

00:03:00.550 --> 00:03:03.410
And as much as possible, as
we go through this meditation,

00:03:03.410 --> 00:03:05.440
as long as you don't have
to force it too much,

00:03:05.440 --> 00:03:08.303
try to keep a gentle smile
on your face the whole time.

00:03:10.820 --> 00:03:13.133
All right, now let's get into it.

00:03:14.110 --> 00:03:16.790
So, one thing to keep in mind

00:03:16.790 --> 00:03:19.950
as we start trying to still our minds,

00:03:19.950 --> 00:03:23.730
is to just appreciate that you're alive.

00:03:23.730 --> 00:03:27.640
You're in this vast mystery we call life

00:03:27.640 --> 00:03:28.990
and that you're taking pause

00:03:28.990 --> 00:03:31.550
to appreciate who you really are.

00:03:31.550 --> 00:03:32.980
And the beauty of this mystery,

00:03:32.980 --> 00:03:36.670
this existence, this
universe that we share.

00:03:36.670 --> 00:03:41.670
So as you breathe deeper and
slower, your eyes are closed.

00:03:43.590 --> 00:03:46.250
Try to become aware of your thoughts.

00:03:46.250 --> 00:03:47.650
What are you thinking about?

00:03:49.870 --> 00:03:53.660
Are they random thoughts,
something you saw on TV?

00:03:53.660 --> 00:03:55.563
Is it something going on at school?

00:03:56.840 --> 00:04:01.150
Are you thinking about some
tests you might have coming up?

00:04:01.150 --> 00:04:05.550
Or someone at your school,
you tend to think about a lot?

00:04:05.550 --> 00:04:06.820
Just observe your thoughts.

00:04:06.820 --> 00:04:09.223
Don't try to fight
them, just observe them.

00:04:12.350 --> 00:04:14.680
And as you observe your thoughts,

00:04:14.680 --> 00:04:19.250
start to appreciate that
you are not your thoughts.

00:04:19.250 --> 00:04:22.600
You are something different
than your thoughts.

00:04:22.600 --> 00:04:25.320
They're all in there
in your head with you.

00:04:25.320 --> 00:04:26.950
But clearly, you can observe them.

00:04:26.950 --> 00:04:29.560
You can see them go by.

00:04:29.560 --> 00:04:32.200
Sometimes we can get lost in them.

00:04:32.200 --> 00:04:33.350
But I think you're seeing right now

00:04:33.350 --> 00:04:34.630
that you are not your thoughts,

00:04:34.630 --> 00:04:36.843
you can actually observe your thoughts.

00:04:39.660 --> 00:04:42.480
One metaphor that folks sometimes use

00:04:42.480 --> 00:04:44.560
is that your thoughts are cars on a road

00:04:44.560 --> 00:04:46.080
or cars on a highway.

00:04:46.080 --> 00:04:48.160
And oftentimes, we're in
the middle of the highway

00:04:48.160 --> 00:04:50.600
and those cars are bombarding us.

00:04:50.600 --> 00:04:52.820
They're hitting us, or we
have to dodge them in some way

00:04:52.820 --> 00:04:54.240
or they're overwhelming us.

00:04:54.240 --> 00:04:55.900
And one thing to do to observe them

00:04:55.900 --> 00:04:57.670
is just get out of the highway.

00:04:57.670 --> 00:04:58.960
You don't have to fight the thoughts,

00:04:58.960 --> 00:05:01.290
those cars will keep on going by.

00:05:01.290 --> 00:05:03.170
But now that you're on the median,

00:05:03.170 --> 00:05:06.333
you're no longer on the
highway, you can see them go by.

00:05:07.700 --> 00:05:09.240
And what you'll often find is

00:05:09.240 --> 00:05:11.210
when you're observing your thoughts,

00:05:11.210 --> 00:05:12.853
they start to slow down.

00:05:14.560 --> 00:05:17.080
And so if your thoughts
start to slow down, great,

00:05:17.080 --> 00:05:19.850
really embrace that, start to
realize what that feels like

00:05:19.850 --> 00:05:21.910
when your thoughts slow down.

00:05:21.910 --> 00:05:23.910
And then there's even going to be moments

00:05:23.910 --> 00:05:25.653
when you have no thoughts.

00:05:26.730 --> 00:05:29.280
For the next few breaths, try that.

00:05:29.280 --> 00:05:31.600
Try to have no thoughts.

00:05:31.600 --> 00:05:34.173
Just breathe in, breathe out.

00:05:35.320 --> 00:05:36.860
No thoughts.

00:05:36.860 --> 00:05:38.650
Just stillness.

00:05:38.650 --> 00:05:42.020
Just your consciousness
here in this universe.

00:05:42.020 --> 00:05:46.990
No time, no space, it's all in your mind.

00:05:46.990 --> 00:05:49.263
No thoughts, stillness.

00:05:56.870 --> 00:05:59.060
Now as you try to keep that state,

00:05:59.060 --> 00:06:01.760
your mind will inevitably wander.

00:06:01.760 --> 00:06:03.940
You're going to start
thinking about an assignment

00:06:03.940 --> 00:06:05.750
that you have due soon,

00:06:05.750 --> 00:06:07.750
you're going to think about something

00:06:07.750 --> 00:06:09.200
that you have to do this weekend

00:06:09.200 --> 00:06:14.200
or someone that you think
a lot about, that's okay.

00:06:14.860 --> 00:06:17.210
Don't beat yourself up,
if your mind wanders,

00:06:17.210 --> 00:06:19.910
just remind yourself,
just gently nudge it back.

00:06:19.910 --> 00:06:21.340
Try to get back to the stillness.

00:06:21.340 --> 00:06:23.830
Say, oh, look, I got a
little bit distracted,

00:06:23.830 --> 00:06:25.550
I started thinking about something.

00:06:25.550 --> 00:06:26.640
That's funny.

00:06:26.640 --> 00:06:29.580
I'm going to get my mind
back to the stillness.

00:06:29.580 --> 00:06:31.630
I'm going to try to slow down those cars.

00:06:35.450 --> 00:06:38.730
And so gently breathe in and breathe out.

00:06:38.730 --> 00:06:40.270
And I'm going to give you a few minutes

00:06:40.270 --> 00:06:42.980
to just sit there, still.

00:06:42.980 --> 00:06:46.120
Breathing in, breathing out.

00:06:46.120 --> 00:06:48.280
Being still with your thoughts.

00:06:48.280 --> 00:06:51.140
If your mind wanders, no big deal.

00:06:51.140 --> 00:06:53.510
Just try to nudge it back when you can.

00:06:53.510 --> 00:06:55.610
And if the silence starts
to get to you a little bit,

00:06:55.610 --> 00:06:59.860
don't worry, I will be back
for sure in a few minutes.

00:08:06.840 --> 00:08:09.030
Now that you've had a little
bit of time on your own,

00:08:09.030 --> 00:08:10.880
I'm going to give you some ideas

00:08:10.880 --> 00:08:14.323
that just might help
appreciate who you really are.

00:08:15.650 --> 00:08:18.580
A lot of times we get
caught up in the day to day,

00:08:18.580 --> 00:08:20.740
we start worrying about test scores

00:08:20.740 --> 00:08:24.493
or things we have due or
what people think about us.

00:08:25.400 --> 00:08:28.053
But remind yourself that you are not that.

00:08:29.340 --> 00:08:32.650
You are not defined by your test scores.

00:08:32.650 --> 00:08:35.063
You are not defined by your grades.

00:08:36.440 --> 00:08:39.603
And you are not defined by
what people think of you.

00:08:42.080 --> 00:08:43.923
You are pure consciousness.

00:08:45.610 --> 00:08:49.563
You associate yourself with
your body with your thoughts.

00:08:50.790 --> 00:08:54.293
But they're part of you, they aren't you.

00:08:55.490 --> 00:08:59.053
You're something deeper and
you're something far larger.

00:09:01.330 --> 00:09:05.210
Like the whole universe, if
you really think about it,

00:09:05.210 --> 00:09:06.860
it's a construction of your mind.

00:09:07.840 --> 00:09:11.193
Your mind has set up the
simulation for you to enjoy.

00:09:12.080 --> 00:09:15.410
In theory, there's a universe out there,

00:09:15.410 --> 00:09:18.590
sound waves stimulating your ear.

00:09:18.590 --> 00:09:21.610
Photons stimulate your eye,

00:09:21.610 --> 00:09:23.843
air particles bouncing into your skin.

00:09:25.650 --> 00:09:26.963
But from that input,

00:09:28.120 --> 00:09:30.893
your mind creates the
reality that you're in.

00:09:32.120 --> 00:09:33.870
When you realize that,

00:09:33.870 --> 00:09:36.883
that everything you see is a construct.

00:09:37.890 --> 00:09:40.740
It's a construct of your mind

00:09:40.740 --> 00:09:42.853
to make sense of all of that information.

00:09:44.170 --> 00:09:47.130
You realize that you're a lot more central

00:09:47.130 --> 00:09:49.453
than you might have appreciated before.

00:09:50.330 --> 00:09:52.600
And you also realize

00:09:52.600 --> 00:09:55.560
that the things that you
might have been thinking about

00:09:55.560 --> 00:09:57.710
things at school, what
people think of you,

00:09:57.710 --> 00:10:00.950
your test scores, those are nice,

00:10:00.950 --> 00:10:03.020
you should try to do what you can.

00:10:03.020 --> 00:10:05.500
But they don't define who you are.

00:10:05.500 --> 00:10:07.453
They don't define your reality.

00:10:08.690 --> 00:10:10.963
Think about how vast the universe is,

00:10:11.810 --> 00:10:14.723
not just vast in space, but vast in time.

00:10:15.860 --> 00:10:18.820
Let put some of our
problems in perspective.

00:10:18.820 --> 00:10:23.020
100 years from now, 1,000 years from now,

00:10:23.020 --> 00:10:25.513
will these problems really
be that significant?

00:10:27.300 --> 00:10:32.190
When you think about where
you are, on this planet,

00:10:32.190 --> 00:10:33.683
part of the cosmos,

00:10:34.770 --> 00:10:37.283
are these issues really that significant?

00:10:38.900 --> 00:10:40.450
So I'll give you a few more moments

00:10:40.450 --> 00:10:42.180
to just think about those ideas,

00:10:42.180 --> 00:10:45.160
to just think about the
vastness of the universe

00:10:45.160 --> 00:10:48.180
and what a privilege it is to
be able to participate in it,

00:10:48.180 --> 00:10:49.890
to see the beauty of it.

00:10:49.890 --> 00:10:51.710
And how small some of the things

00:10:51.710 --> 00:10:55.173
that we often define
ourselves by really are.

00:10:58.240 --> 00:11:00.110
And so now when you get a chance

00:11:01.830 --> 00:11:03.530
gently with your eyes closed,

00:11:03.530 --> 00:11:07.110
start to feel and hear the
room around you a little bit,

00:11:07.110 --> 00:11:09.410
get a little bit more
in touch with your body.

00:11:10.810 --> 00:11:13.123
And when you're ready, open your eyes.

00:11:15.960 --> 00:11:17.250
And take these ideas,

00:11:17.250 --> 00:11:20.150
take that stillness with you
through the rest of your day.

00:11:21.680 --> 00:11:23.630
And you should thank yourself

00:11:23.630 --> 00:11:26.760
for taking the time out
for doing this today.

00:11:26.760 --> 00:11:29.240
And I encourage you to make it a practice.

00:11:29.240 --> 00:11:30.940
Some of you might be skeptical,

00:11:30.940 --> 00:11:33.523
what would a few minute
meditation do for me?

00:11:34.550 --> 00:11:37.060
But I can guarantee you if
you do it day in day out,

00:11:37.060 --> 00:11:40.253
if you make a practice
of it, do it regularly.

00:11:41.180 --> 00:11:43.260
Over a few weeks, a few months,

00:11:43.260 --> 00:11:45.580
you're going to notice some changes.

00:11:45.580 --> 00:11:48.640
You're going to see yourself
be more open to experience,

00:11:48.640 --> 00:11:52.180
you're going to see more
beauty in more things.

00:11:52.180 --> 00:11:54.410
You're going to just
have a positive energy

00:11:54.410 --> 00:11:57.090
that people are going
to want to connect with,

00:11:57.090 --> 00:11:59.590
that people are going to be drawn to.

00:11:59.590 --> 00:12:02.150
And you'll also see
that you're doing better

00:12:02.150 --> 00:12:04.240
at some of those things
we talked about before,

00:12:04.240 --> 00:12:06.010
because you're not stressed
about them anymore.

00:12:06.010 --> 00:12:07.410
You're enjoying them.

00:12:07.410 --> 00:12:09.500
You're doing what you can,

00:12:09.500 --> 00:12:13.360
but you're not attached to the outcome.

00:12:13.360 --> 00:12:17.573
You do your best, wherever
the chips fall, that's okay.

00:12:18.710 --> 00:12:21.780
If things don't turn out the
way you want it, that's okay.

00:12:21.780 --> 00:12:23.803
You just accept where things are.

00:12:24.770 --> 00:12:28.210
And then you decide what
other actions can you take.

00:12:28.210 --> 00:12:30.670
Assemble your actions piece by piece,

00:12:30.670 --> 00:12:33.010
so that you can get to another outcome.

00:12:33.010 --> 00:12:36.090
But once again, if the outcome
is what you want, awesome,

00:12:36.090 --> 00:12:39.323
if it isn't, accept it
and move on from there.

00:12:40.830 --> 00:12:42.920
So I'll leave you in this meditation.

00:12:42.920 --> 00:12:44.580
Thank you for joining.

00:12:44.580 --> 00:12:47.883
And once again, thanks for
taking time out for yourself.


The development of an American culture

WEBVTT
Kind: captions
Language: en

00:00:00.450 --> 00:00:02.530
- [Instructor] In this video
I'm gonna take some time

00:00:02.530 --> 00:00:05.860
to talk about the culture
of the young United States

00:00:05.860 --> 00:00:08.740
that developed in the early 19th century.

00:00:08.740 --> 00:00:10.270
At the beginning of this period,

00:00:10.270 --> 00:00:13.550
most of the dominant artistic
and cultural productions

00:00:13.550 --> 00:00:16.670
in the United States, the
paintings, architecture,

00:00:16.670 --> 00:00:19.110
literature, and even philosophy,

00:00:19.110 --> 00:00:21.709
were either borrowed from or imitations

00:00:21.709 --> 00:00:24.890
of what was being produced in Europe.

00:00:24.890 --> 00:00:27.080
The United States itself was born

00:00:27.080 --> 00:00:29.730
in the midst of an intellectual movement

00:00:29.730 --> 00:00:33.180
that crossed the Atlantic from
Europe, the Enlightenment.

00:00:33.180 --> 00:00:35.570
And if you read the
Declaration of Independence,

00:00:35.570 --> 00:00:38.467
you can hear the echoes
of the Enlightenment:

00:00:38.467 --> 00:00:41.477
"We hold these truths to be self-evident,

00:00:41.477 --> 00:00:43.067
"that all men are created equal,

00:00:43.067 --> 00:00:45.087
"that they are endowed by their Creator

00:00:45.087 --> 00:00:47.037
"with certain unalienable Rights,

00:00:47.037 --> 00:00:49.127
"that among these are Life, Liberty,

00:00:49.127 --> 00:00:50.767
"and the pursuit of Happiness.

00:00:50.767 --> 00:00:52.327
"That to secure these rights,

00:00:52.327 --> 00:00:54.487
"Governments are instituted among Men,

00:00:54.487 --> 00:00:56.847
"deriving their just
powers from the consent

00:00:56.847 --> 00:00:57.700
"of the governed..."

00:00:57.700 --> 00:00:59.910
Jefferson looks at the evidence,

00:00:59.910 --> 00:01:02.710
the rational reasons for self-government.

00:01:02.710 --> 00:01:05.443
Now contrast that with a piece of writing

00:01:05.443 --> 00:01:08.870
from an American at
the end of this period.

00:01:08.870 --> 00:01:12.280
Here's the last stanza
from Edgar Allan Poe's

00:01:12.280 --> 00:01:16.787
poem The Raven, first published in 1845:

00:01:16.787 --> 00:01:19.097
"...And the Raven, never flitting,

00:01:19.097 --> 00:01:21.882
"still is sitting, still is sitting

00:01:21.882 --> 00:01:26.287
"On the pallid bust of Pallas
just above my chamber door;

00:01:26.287 --> 00:01:29.467
"And his eyes have all
the seeming of a demon's

00:01:29.467 --> 00:01:30.417
"that is dreaming.

00:01:30.417 --> 00:01:32.827
"And the lamp-light o'er him streaming

00:01:32.827 --> 00:01:34.827
"throws his shadow on the floor;

00:01:34.827 --> 00:01:38.007
"And my soul from out that
shadow that lies floating

00:01:38.007 --> 00:01:38.840
"on the floor

00:01:38.840 --> 00:01:41.810
"Shall be lifted, nevermore!"

00:01:41.810 --> 00:01:43.330
What is going on here?

00:01:43.330 --> 00:01:46.570
Poe's talking about demons,
and souls, and shadows.

00:01:46.570 --> 00:01:49.840
He's clearly not interested
in reason or logic.

00:01:49.840 --> 00:01:52.350
Where Jefferson is cold, Poe is hot,

00:01:52.350 --> 00:01:55.680
emotional, imaginative, concentrating

00:01:55.680 --> 00:01:59.310
on the unseen world instead
of the observable world

00:01:59.310 --> 00:02:00.820
that Jefferson prizes.

00:02:00.820 --> 00:02:04.470
This is because Poe, writing
nearly 70 years later,

00:02:04.470 --> 00:02:07.130
was a product of the Romantic era.

00:02:07.130 --> 00:02:10.340
The Romantics rebelled against
the Enlightenment ideas

00:02:10.340 --> 00:02:13.300
of pure reason and the scientific method,

00:02:13.300 --> 00:02:16.186
arguing instead that individual experience

00:02:16.186 --> 00:02:18.620
and emotion mattered more.

00:02:18.620 --> 00:02:21.180
So why do we care about this transition

00:02:21.180 --> 00:02:24.150
from the Enlightenment to the Romantic era

00:02:24.150 --> 00:02:25.970
in the history of the United States?

00:02:25.970 --> 00:02:27.690
Well, for one thing, because it helps

00:02:27.690 --> 00:02:29.950
us explain the Second Great Awakening,

00:02:29.950 --> 00:02:32.930
that period of intense religious devotion

00:02:32.930 --> 00:02:35.780
that emerged in the first
half of the 19th century,

00:02:35.780 --> 00:02:37.270
and drove not only the creation

00:02:37.270 --> 00:02:39.480
of new religious moments
in the United States,

00:02:39.480 --> 00:02:41.927
but also major reform movements.

00:02:41.927 --> 00:02:45.000
But we also care because
it was during this time

00:02:45.000 --> 00:02:48.640
of transition that the
first truly American art

00:02:48.640 --> 00:02:51.000
and literary movements emerged.

00:02:51.000 --> 00:02:54.830
Artists and writers
stopped merely imitating

00:02:54.830 --> 00:02:57.330
European styles, although
they were certainly

00:02:57.330 --> 00:02:58.870
still influenced by them,

00:02:58.870 --> 00:03:01.590
and began trying to capture a unique

00:03:01.590 --> 00:03:04.100
and different American culture.

00:03:04.100 --> 00:03:06.190
What they produced not only tells us a lot

00:03:06.190 --> 00:03:10.040
about their time period, but
also created the foundation

00:03:10.040 --> 00:03:12.300
of what's considered American art

00:03:12.300 --> 00:03:15.030
or American literature today.

00:03:15.030 --> 00:03:17.160
One of the ways that Americans began

00:03:17.160 --> 00:03:20.440
to distinguish their culture
was through architecture.

00:03:20.440 --> 00:03:23.490
In the late 1700s, American
architecture started

00:03:23.490 --> 00:03:26.060
to move away from the Georgian style

00:03:26.060 --> 00:03:27.460
it had borrowed from Britain,

00:03:27.460 --> 00:03:29.570
the very symmetrical brick homes

00:03:29.570 --> 00:03:31.610
that were built during the era

00:03:31.610 --> 00:03:33.800
when kings named George were in power,

00:03:33.800 --> 00:03:36.236
and they started to draw
more from the models

00:03:36.236 --> 00:03:39.270
of Roman and Greek architecture.

00:03:39.270 --> 00:03:43.160
Americans saw themselves as
carrying on the traditions

00:03:43.160 --> 00:03:45.830
of the Roman Republic and Greek democracy,

00:03:45.830 --> 00:03:47.550
so they started employing some

00:03:47.550 --> 00:03:49.990
of the same architectural language.

00:03:49.990 --> 00:03:53.620
The Federal style started
incorporating Roman elements

00:03:53.620 --> 00:03:56.780
into Georgian buildings,
like Roman arches.

00:03:56.780 --> 00:03:59.470
Here you can see a bit of the transition

00:03:59.470 --> 00:04:01.987
from this Georgian building
on Harvard's campus

00:04:01.987 --> 00:04:05.720
to this Federal building
in Salem, Massachusetts.

00:04:05.720 --> 00:04:08.090
You go from square windows and doors

00:04:08.090 --> 00:04:09.830
to Roman arches.

00:04:09.830 --> 00:04:13.790
And this transition continued
as the U.S. Capitol was built

00:04:13.790 --> 00:04:15.320
in Washington D.C.

00:04:15.320 --> 00:04:19.002
Starting in the 1820s,
the Greek Revival style

00:04:19.002 --> 00:04:22.028
became prominent for monumental buildings,

00:04:22.028 --> 00:04:25.130
incorporating triangular pediments

00:04:25.130 --> 00:04:26.920
and Greek columns.

00:04:26.920 --> 00:04:28.730
Here you can see the original design

00:04:28.730 --> 00:04:31.840
of the U.S. Capitol building,
which houses Congress.

00:04:31.840 --> 00:04:35.200
It has a central dome
like the Pantheon in Rome,

00:04:35.200 --> 00:04:38.060
and then a full-on Greek
temple pasted to its face.

00:04:38.060 --> 00:04:39.174
By adopting these elements,

00:04:39.174 --> 00:04:41.820
American architects sent the message

00:04:41.820 --> 00:04:45.270
that the United States wasn't
just imitating British styles.

00:04:45.270 --> 00:04:48.300
Instead they were crafting
an architectural form

00:04:48.300 --> 00:04:50.720
that was suitable for a republic.

00:04:50.720 --> 00:04:53.340
American art also began to diverge

00:04:53.340 --> 00:04:57.140
from its European forbears
during the early 19th century.

00:04:57.140 --> 00:05:00.190
American-born painters
in the Revolutionary era,

00:05:00.190 --> 00:05:02.230
like Gilbert Stuart, went to Europe

00:05:02.230 --> 00:05:04.240
to study and start their careers

00:05:04.240 --> 00:05:06.630
before heading back to the United States.

00:05:06.630 --> 00:05:09.470
Stuart's portraits of
important American figures

00:05:09.470 --> 00:05:12.370
like George Washington
followed the conventions

00:05:12.370 --> 00:05:14.330
of classical portraiture.

00:05:14.330 --> 00:05:17.300
It wasn't until the 1820s
that American art began

00:05:17.300 --> 00:05:20.290
to come into its own with
the Hudson River School.

00:05:20.290 --> 00:05:22.900
This was started by a
group of painters working

00:05:22.900 --> 00:05:26.512
in Upstate New York who
captured the majestic nature

00:05:26.512 --> 00:05:28.750
of the American landscape.

00:05:28.750 --> 00:05:32.010
They were influenced by the
Romantic movement's emphasis

00:05:32.010 --> 00:05:34.590
on emotion and the sublime,

00:05:34.590 --> 00:05:38.380
which is the awe-inspiring, untamed aspect

00:05:38.380 --> 00:05:40.550
of nature that you find in mountains,

00:05:40.550 --> 00:05:42.420
and storms, and wilderness.

00:05:42.420 --> 00:05:45.610
The painters of the Hudson
River School explored

00:05:45.610 --> 00:05:49.000
the relationship between
the American environment

00:05:49.000 --> 00:05:50.940
and the march of settlement.

00:05:50.940 --> 00:05:54.270
Let's take a look at one
Hudson River School painting,

00:05:54.270 --> 00:05:59.190
The Oxbow, which was painted
in 1836 by Thomas Cole.

00:05:59.190 --> 00:06:02.900
The painting depicts a bend
in the Connecticut River

00:06:02.900 --> 00:06:04.830
in Western Massachusetts.

00:06:04.830 --> 00:06:07.340
You can see that a thunderstorm is passing

00:06:07.340 --> 00:06:09.810
with dark clouds here on the left.

00:06:09.810 --> 00:06:13.040
And there's this twisted
tree and downed limbs,

00:06:13.040 --> 00:06:16.070
which show how violent the
storm was up on the mountain.

00:06:16.070 --> 00:06:18.870
It feels dangerous and unpredictable.

00:06:18.870 --> 00:06:20.570
That's the sublime right there.

00:06:20.570 --> 00:06:24.110
Then, on the right side,
you have this river valley

00:06:24.110 --> 00:06:27.660
with farms and little
plumes of smoke from houses.

00:06:27.660 --> 00:06:28.773
There's a boat on the river

00:06:28.773 --> 00:06:31.200
and some sheep grazing down here,

00:06:31.200 --> 00:06:33.760
and just barely visible in the foreground

00:06:33.760 --> 00:06:36.440
is a little self-portrait of Thomas Cole

00:06:36.440 --> 00:06:37.470
out with his easel.

00:06:37.470 --> 00:06:39.087
He's kind of saying, "Yeah, that's right.

00:06:39.087 --> 00:06:40.857
"I'm out here dodging
lightning to show you

00:06:40.857 --> 00:06:42.420
"how the real deal looks."

00:06:42.420 --> 00:06:43.810
So you can see in this painting

00:06:43.810 --> 00:06:45.340
that there's kind of a tension

00:06:45.340 --> 00:06:48.320
between the settled
society on the right side

00:06:48.320 --> 00:06:50.550
and the wilderness on the left side.

00:06:50.550 --> 00:06:52.932
The vastness of the American West

00:06:52.932 --> 00:06:55.790
and the march of the first wave

00:06:55.790 --> 00:06:58.040
of industrialization gave painters

00:06:58.040 --> 00:07:01.650
a unique American subject for their art.

00:07:01.650 --> 00:07:06.250
Lastly, the first American
writers and thinkers came

00:07:06.250 --> 00:07:08.080
on the scene during this era.

00:07:08.080 --> 00:07:11.483
Remember the Romantics
glorified the experience

00:07:11.483 --> 00:07:14.730
of the individual and their emotions.

00:07:14.730 --> 00:07:16.950
The first American fiction writers

00:07:16.950 --> 00:07:20.380
to gain traction for an
international audience described

00:07:20.380 --> 00:07:23.370
unique aspects of American society.

00:07:23.370 --> 00:07:26.290
Washington Irving, who we remember today

00:07:26.290 --> 00:07:29.300
for the Headless Horseman in
"The Legend of Sleepy Hollow,"

00:07:29.300 --> 00:07:33.270
another romantic ghost
story like Poe's The Raven,

00:07:33.270 --> 00:07:36.430
achieved renown by telling folk tales

00:07:36.430 --> 00:07:40.310
about the lingering Dutch
culture in Upstate New York.

00:07:40.310 --> 00:07:42.700
James Fenimore Cooper's protagonist

00:07:42.700 --> 00:07:45.660
in his "Leatherstocking
Tales," Natty Bumppo,

00:07:45.660 --> 00:07:48.520
was a white frontiersman who grew up

00:07:48.520 --> 00:07:50.850
among the indigenous Delaware People.

00:07:50.850 --> 00:07:52.700
His nickname was Hawkeye,

00:07:52.700 --> 00:07:55.310
and yes, the Marvel
character is named after him,

00:07:55.310 --> 00:07:56.760
which gives you a sense of how

00:07:56.760 --> 00:07:59.820
these first American
characters have continued

00:07:59.820 --> 00:08:02.940
to live on in our contemporary culture.

00:08:02.940 --> 00:08:05.970
In New England, particularly Boston

00:08:05.970 --> 00:08:07.540
and the surrounding areas,

00:08:07.540 --> 00:08:11.190
American intellectuals
embraced Romanticism

00:08:11.190 --> 00:08:14.510
in the philosophy of Transcendentalism.

00:08:14.510 --> 00:08:17.390
The Transcendentalists
were a group of writers,

00:08:17.390 --> 00:08:20.410
poets, and philosophers who believed

00:08:20.410 --> 00:08:23.736
that truth transcended
the observable world

00:08:23.736 --> 00:08:26.970
of the Enlightenment, and
that spiritual meaning

00:08:26.970 --> 00:08:28.810
could be found in nature.

00:08:28.810 --> 00:08:30.870
Henry David Thoreau is probably

00:08:30.870 --> 00:08:32.790
the most famous Transcendentalist.

00:08:32.790 --> 00:08:35.117
He wrote a book about his
two years living simply

00:08:35.117 --> 00:08:38.059
in a cabin he built on
the edge of Walden Pond,

00:08:38.059 --> 00:08:42.380
on fellow Transcendentalist
Ralph Waldo Emerson's property.

00:08:42.380 --> 00:08:45.861
The Transcendentalists also
emphasized the individual

00:08:45.861 --> 00:08:47.850
and freedom of thought.

00:08:47.850 --> 00:08:50.332
Emerson, who's generally
considered the founder

00:08:50.332 --> 00:08:52.570
of the Transcendentalist movement,

00:08:52.570 --> 00:08:54.950
wrote essays encouraging Americans

00:08:54.950 --> 00:08:57.530
to think for themselves, not just go along

00:08:57.530 --> 00:08:58.500
with the crowd.

00:08:58.500 --> 00:09:01.800
Some of the most influential
Transcendentalists were women,

00:09:01.800 --> 00:09:04.180
like Margaret Fuller,
who wrote about the state

00:09:04.180 --> 00:09:05.990
of women in the 19th century

00:09:05.990 --> 00:09:09.183
and edited the Transcendentalist
magazine The Dial.

00:09:09.183 --> 00:09:12.270
Poet Emily Dickinson has
sometimes been classed

00:09:12.270 --> 00:09:13.860
among the Transcendentalists,

00:09:13.860 --> 00:09:17.520
as has Louisa May Alcott,
the author of "Little Women."

00:09:17.520 --> 00:09:20.013
The freedom of thought
that the Transcendentalists

00:09:20.013 --> 00:09:22.173
espoused also led them to become some

00:09:22.173 --> 00:09:26.370
of the strongest opponents of
the institution of slavery.

00:09:26.370 --> 00:09:29.370
Thoreau refused to pay his taxes

00:09:29.370 --> 00:09:31.960
in protest of the Mexican American War,

00:09:31.960 --> 00:09:33.760
which he and many Northerners saw

00:09:33.760 --> 00:09:37.610
as an unjust land-grab to
extend southern territory

00:09:37.610 --> 00:09:39.310
and spread slavery west.

00:09:39.310 --> 00:09:41.807
He wrote an essay about
his experience called

00:09:41.807 --> 00:09:43.970
"Resistance to Civil Government,"

00:09:43.970 --> 00:09:46.871
sometimes shortened to
"Civil Disobedience,"

00:09:46.871 --> 00:09:49.110
which encouraged individuals not

00:09:49.110 --> 00:09:51.350
to obey unjust laws.

00:09:51.350 --> 00:09:54.420
His ideas would go on to
influence Mahatma Gandhi

00:09:54.420 --> 00:09:56.653
and later Martin Luther King, Junior.


Showing segment congruence equivalent to having same length

WEBVTT
Kind: captions
Language: en

00:00:00.280 --> 00:00:01.113
- [Instructor] In this video,

00:00:01.113 --> 00:00:05.590
we're gonna talk a little
bit about segment congruence.

00:00:05.590 --> 00:00:09.340
And what we have here, let's
call this statement one,

00:00:09.340 --> 00:00:12.590
this is the definition of
line segment congruence,

00:00:12.590 --> 00:00:14.770
or at least the one that we will use.

00:00:14.770 --> 00:00:17.900
Two segments are congruent,
that means that we can map

00:00:17.900 --> 00:00:22.900
one segment onto the other
using rigid transformations.

00:00:23.180 --> 00:00:25.720
And examples of rigid
transformations are reflections,

00:00:25.720 --> 00:00:29.470
rotations, translations,
and combinations of them.

00:00:29.470 --> 00:00:31.180
Now what we're going to see in this video

00:00:31.180 --> 00:00:32.820
is that statement one

00:00:32.820 --> 00:00:37.100
is actually equivalent to statement two.

00:00:37.100 --> 00:00:40.970
Or another way of saying it
is if statement one is true,

00:00:40.970 --> 00:00:42.720
then statement two is true,

00:00:42.720 --> 00:00:46.200
and if statement two is true,
then statement one is true.

00:00:46.200 --> 00:00:47.750
Or we can write it like this,

00:00:47.750 --> 00:00:49.820
we can map one segment onto another

00:00:49.820 --> 00:00:54.820
using rigid transformations
if and only, only if,

00:00:56.950 --> 00:00:59.280
the two segments have the same length.

00:00:59.280 --> 00:01:01.140
So how do we go about proving it?

00:01:01.140 --> 00:01:04.700
Well the first thing that
we'd want to prove is

00:01:04.700 --> 00:01:09.700
that if statement one is true, then,

00:01:11.500 --> 00:01:16.050
then statement two is true.

00:01:16.050 --> 00:01:17.600
So how would we go about doing this?

00:01:17.600 --> 00:01:18.580
And like always, I encourage you

00:01:18.580 --> 00:01:20.623
to pause the video and have a go at it.

00:01:21.670 --> 00:01:23.600
All right, now let's
work through it together.

00:01:23.600 --> 00:01:25.660
Some proofs like this might be difficult

00:01:25.660 --> 00:01:28.090
because they feel so intuitive.

00:01:28.090 --> 00:01:33.060
But one way to prove this is
to first say that by definition

00:01:33.060 --> 00:01:36.400
rigid transformations preserve length.

00:01:36.400 --> 00:01:41.400
So by definition, by
definition, definition,

00:01:42.850 --> 00:01:47.850
rigid transformations,
that's what makes them rigid,

00:01:48.040 --> 00:01:52.297
rigid transformations preserve length.

00:01:59.709 --> 00:02:01.409
So if one segment, if one segment,

00:02:06.190 --> 00:02:10.130
can be mapped onto,

00:02:12.530 --> 00:02:17.110
onto a second segment

00:02:18.960 --> 00:02:23.960
with rigid transformations,
with rigid transformations,

00:02:27.770 --> 00:02:31.020
they must have had the original,
the same original length,

00:02:31.020 --> 00:02:35.620
they must have had the
same original length,

00:02:35.620 --> 00:02:40.620
they must have had same original length.

00:02:43.420 --> 00:02:46.400
Or another way to say
it is, then two is true.

00:02:46.400 --> 00:02:50.570
Then we can try to do
it the other way around.

00:02:50.570 --> 00:02:54.710
So let's see if we can prove that if two,

00:02:54.710 --> 00:02:58.890
if statement two is true,
then statement one is true,

00:02:58.890 --> 00:03:03.000
then statement one, and why
don't you pause this video

00:03:03.000 --> 00:03:05.083
and have a go at that as well.

00:03:06.700 --> 00:03:11.700
So let's assume, assume, I have segment AB

00:03:13.220 --> 00:03:16.600
and then I have another
segment, let's call it CD,

00:03:16.600 --> 00:03:20.773
have the same length, have same length.

00:03:21.680 --> 00:03:25.263
So they meet the number two
statement right over there.

00:03:26.620 --> 00:03:30.370
To map, to map AB onto CD,

00:03:37.100 --> 00:03:41.350
all I have to do, I can do this
in two rotations every time,

00:03:41.350 --> 00:03:46.350
I first will, I will translate
so that A is on top of C,

00:03:48.550 --> 00:03:53.550
so I will translate, translate AB,

00:03:53.760 --> 00:03:58.760
so that point A is on top of point C.

00:04:06.520 --> 00:04:10.630
And then the next thing
I would do is rotate,

00:04:10.630 --> 00:04:15.630
rotate AB so that point B,

00:04:17.350 --> 00:04:22.350
point B, is on top of point D.

00:04:25.860 --> 00:04:27.000
And there you have it.

00:04:27.000 --> 00:04:29.440
For any two segments with the same length,

00:04:29.440 --> 00:04:31.380
I can always translate it

00:04:31.380 --> 00:04:33.770
so that I have one set of points overlap,

00:04:33.770 --> 00:04:35.770
and then to get the
other points to overlap

00:04:35.770 --> 00:04:36.700
I just have to rotate it.

00:04:36.700 --> 00:04:37.810
I know that's going to work

00:04:37.810 --> 00:04:39.980
because they have the same length.

00:04:39.980 --> 00:04:43.890
So I've just shown you,
if we can map one segment

00:04:43.890 --> 00:04:45.840
onto another using rigid transformations,

00:04:45.840 --> 00:04:47.620
then we know they have the same length,

00:04:47.620 --> 00:04:49.830
and if two segments have the same length,

00:04:49.830 --> 00:04:52.060
then we know that we can map one segment

00:04:52.060 --> 00:04:54.953
onto the other using
rigid transformations.


Idea behind hypothesis testing

WEBVTT
Kind: captions
Language: en

00:00:00.300 --> 00:00:01.630
- [Instructor] What we're
going to do in this video

00:00:01.630 --> 00:00:04.930
is talk about hypothesis testing,

00:00:04.930 --> 00:00:07.640
which is the heart of all
of inferential statistics,

00:00:07.640 --> 00:00:10.840
statistics that allow us to
make inferences about the world.

00:00:10.840 --> 00:00:12.560
So, to give us the gist of this,

00:00:12.560 --> 00:00:14.890
let's start with a tangible example.

00:00:14.890 --> 00:00:16.950
Let's say, hypothetically,

00:00:16.950 --> 00:00:20.350
you run a website that has the mission

00:00:20.350 --> 00:00:24.200
of giving everyone on the
planet a free education,

00:00:24.200 --> 00:00:27.330
and you wanna think about
how you might change

00:00:27.330 --> 00:00:29.090
the amount of time
people spend on the site.

00:00:29.090 --> 00:00:30.830
Ideally, you wanna
increase the amount of time

00:00:30.830 --> 00:00:31.663
people spend on the site

00:00:31.663 --> 00:00:33.940
so there's more learning on the planet.

00:00:33.940 --> 00:00:38.380
Well, currently the website has
a white background like this

00:00:38.380 --> 00:00:42.050
and the mean amount of time people spend

00:00:42.050 --> 00:00:44.540
when you have a white background,

00:00:44.540 --> 00:00:46.610
the mean amount of time when
you have a white background

00:00:46.610 --> 00:00:48.400
is 20 minutes.

00:00:48.400 --> 00:00:50.160
And you or someone on your team,

00:00:50.160 --> 00:00:52.680
maybe you read some
type of study that says

00:00:52.680 --> 00:00:54.800
people like to spend more
time on yellow backgrounds.

00:00:54.800 --> 00:00:56.360
I don't actually think that's true,

00:00:56.360 --> 00:00:58.680
but let's just go with that
for the sake of this video.

00:00:58.680 --> 00:01:00.820
And so you have a hypothesis

00:01:00.820 --> 00:01:02.790
that if you actually
have a yellow background,

00:01:02.790 --> 00:01:05.420
if you change your background to yellow,

00:01:05.420 --> 00:01:08.240
that the mean amount of
time that people spend

00:01:08.240 --> 00:01:11.540
on a yellow background, on yellow,

00:01:11.540 --> 00:01:15.690
is going to be different,
is not going to be equal to

00:01:15.690 --> 00:01:20.690
the mean amount of time people
spend on a white background.

00:01:21.450 --> 00:01:23.700
So, the question is how do you test this,

00:01:23.700 --> 00:01:25.710
and how do you feel good
about your inferences

00:01:25.710 --> 00:01:27.110
that you make from your test?

00:01:27.110 --> 00:01:30.060
And that is the heart
of hypothesis testing.

00:01:30.060 --> 00:01:33.440
And medical research,
actually almost all research

00:01:33.440 --> 00:01:36.800
involves some form of hypothesis testing.

00:01:36.800 --> 00:01:38.410
So, how would you do this?

00:01:38.410 --> 00:01:40.120
Well, the standard why to do this

00:01:40.120 --> 00:01:42.640
is to set up a couple of hypothesis.

00:01:42.640 --> 00:01:44.630
Hypotheses, I should say.

00:01:44.630 --> 00:01:48.350
The first one is known
as your null hypothesis,

00:01:48.350 --> 00:01:50.910
and I often think about this
as the skeptic's hypothesis.

00:01:50.910 --> 00:01:52.310
Skeptics think that,

00:01:52.310 --> 00:01:54.430
hey, it's hard to make a
difference in this world,

00:01:54.430 --> 00:01:55.750
or cynics feel like it's hard

00:01:55.750 --> 00:01:57.040
to make a difference in the world

00:01:57.040 --> 00:01:59.550
and so they always have
this null hypothesis

00:01:59.550 --> 00:02:01.597
that's saying, "Hey, you think
you're making a difference,

00:02:01.597 --> 00:02:02.720
"but you aren't."

00:02:02.720 --> 00:02:05.850
So, the null hypothesis is that

00:02:05.850 --> 00:02:09.260
the mean amount of time people
spend on the yellow site,

00:02:09.260 --> 00:02:11.490
or on a yellow site,

00:02:11.490 --> 00:02:15.450
is going to be equal to
the mean amount of time

00:02:15.450 --> 00:02:16.840
that people spend on the current site

00:02:16.840 --> 00:02:20.280
or the existing site or on a white site,

00:02:20.280 --> 00:02:22.267
while the people who are thinking about,

00:02:22.267 --> 00:02:23.387
"Hey, how do I make change?

00:02:23.387 --> 00:02:24.860
"How do I make improvements in the world?"

00:02:24.860 --> 00:02:26.560
they had some type of hypothesis

00:02:26.560 --> 00:02:30.630
and we call that the
alternative hypothesis.

00:02:30.630 --> 00:02:35.460
And so the alternative
hypothesis, A for alternative,

00:02:35.460 --> 00:02:39.770
is that the mean time on the yellow site,

00:02:39.770 --> 00:02:41.300
on the yellow site,

00:02:41.300 --> 00:02:42.930
is actually different.

00:02:42.930 --> 00:02:43.900
Is actually different.

00:02:43.900 --> 00:02:47.570
It is not equal to the mean amount of time

00:02:47.570 --> 00:02:49.610
on the white site.

00:02:49.610 --> 00:02:50.820
So, how do we think about this

00:02:50.820 --> 00:02:53.040
now that we set up these hypotheses?

00:02:53.040 --> 00:02:55.100
Well, what we're going to do is

00:02:55.100 --> 00:02:57.460
we are going to assume,

00:02:57.460 --> 00:03:00.023
we assume the null hypothesis.

00:03:00.970 --> 00:03:04.630
Then we build this yellow site

00:03:04.630 --> 00:03:06.240
and then we take a sample

00:03:06.240 --> 00:03:09.100
of the people using the yellow site,

00:03:09.100 --> 00:03:11.127
and we say, "What is the probability

00:03:11.127 --> 00:03:13.010
"of getting that sample mean,"

00:03:13.010 --> 00:03:16.007
which is an approximation of
the parameter of the true mean,

00:03:16.007 --> 00:03:19.307
"what is the probability
of getting that sample mean

00:03:19.307 --> 00:03:22.040
"if we assume the null hypothesis?"

00:03:22.040 --> 00:03:25.300
And if the probability of
getting that sample mean

00:03:25.300 --> 00:03:26.340
on the yellow site,

00:03:26.340 --> 00:03:29.620
assuming the null
hypothesis, is really low,

00:03:29.620 --> 00:03:32.170
then we reject the null hypothesis,

00:03:32.170 --> 00:03:34.330
which suggests the alternative.

00:03:34.330 --> 00:03:37.360
On the other hand, if we get a sample mean

00:03:37.360 --> 00:03:39.380
that seems pretty reasonable to get

00:03:39.380 --> 00:03:41.670
if you assume the null hypothesis,

00:03:41.670 --> 00:03:44.150
then we fail to reject the null hypothesis

00:03:44.150 --> 00:03:47.310
and then that would not
suggest the alternative.

00:03:47.310 --> 00:03:49.450
Now, to make this a
little bit more tangible,

00:03:49.450 --> 00:03:52.360
and we'll go over this
into a lot of videos,

00:03:52.360 --> 00:03:54.620
if you assume the null hypothesis,

00:03:54.620 --> 00:03:57.440
then there's a few things
you can think about.

00:03:57.440 --> 00:03:59.980
You can think about just
the general distribution

00:03:59.980 --> 00:04:02.640
of the amount of time
people spend on the site.

00:04:02.640 --> 00:04:03.930
It would look something like this.

00:04:03.930 --> 00:04:05.550
We will, for this sake,

00:04:05.550 --> 00:04:07.290
assume that it's a normal distribution,

00:04:07.290 --> 00:04:09.750
and normal distributions
are very important,

00:04:09.750 --> 00:04:11.910
and/or things that are close
to normal distributions,

00:04:11.910 --> 00:04:13.500
for hypothesis testing.

00:04:13.500 --> 00:04:15.260
But let's say that it's
a normal distribution

00:04:15.260 --> 00:04:17.200
of the amount of time
people spend on the site

00:04:17.200 --> 00:04:19.410
and so there is some mean.

00:04:19.410 --> 00:04:20.530
We know that mean,

00:04:20.530 --> 00:04:23.740
so the mean that people
spend on that white site

00:04:23.740 --> 00:04:27.790
is equal to 20 minutes.

00:04:27.790 --> 00:04:30.090
And, remember, we're
assuming the null hypothesis,

00:04:30.090 --> 00:04:33.020
so we're assuming that this
is also the amount of time

00:04:33.020 --> 00:04:35.150
that people would spend
on the yellow site.

00:04:35.150 --> 00:04:39.660
We've assumed, assuming,
the null hypothesis,

00:04:39.660 --> 00:04:43.380
and you could view this
as time or distribution

00:04:44.470 --> 00:04:47.023
of time spent.

00:04:48.520 --> 00:04:50.330
Now, one of the things
we're going to talk about

00:04:50.330 --> 00:04:53.340
in future videos is if you
have this distribution,

00:04:53.340 --> 00:04:56.210
you can actually come up
with another distribution

00:04:56.210 --> 00:04:59.550
of the means of samples you might get.

00:04:59.550 --> 00:05:03.720
So, there's something else
called the sampling distribution,

00:05:03.720 --> 00:05:05.390
and I know it's very confusing at first.

00:05:05.390 --> 00:05:10.390
Sampling distribution of the sample

00:05:10.670 --> 00:05:14.210
of the sample mean,

00:05:14.210 --> 00:05:16.150
and it'll be for a given sample size,

00:05:16.150 --> 00:05:20.980
for sample size, sample size.

00:05:20.980 --> 00:05:24.760
Let's say this is sample size 1,000.

00:05:24.760 --> 00:05:25.720
I'm just making things up.

00:05:25.720 --> 00:05:26.780
I could've said N,

00:05:26.780 --> 00:05:30.150
but I'm just gonna make this
a little bit more tangible.

00:05:30.150 --> 00:05:31.920
Well, we're going to
get statistical methods

00:05:31.920 --> 00:05:33.770
for how you can think
about this distribution

00:05:33.770 --> 00:05:36.060
assuming this distribution
we have on the left.

00:05:36.060 --> 00:05:38.290
And it turns out this distribution

00:05:38.290 --> 00:05:40.530
is going to look like the one on the left,

00:05:40.530 --> 00:05:44.120
but it's going to be
narrower around that mean.

00:05:44.120 --> 00:05:46.670
It's going to look something like this.

00:05:46.670 --> 00:05:49.700
And, actually, the larger your
sample sizes are going to be,

00:05:49.700 --> 00:05:51.740
the narrower it's going to get.

00:05:51.740 --> 00:05:53.700
Now, remember, this isn't
just the distribution

00:05:53.700 --> 00:05:56.310
of the amount of time
people spend on the site.

00:05:56.310 --> 00:06:01.220
This is the distribution that
if I were to take a sample

00:06:01.220 --> 00:06:03.440
of the amount of time
people spend on the site

00:06:03.440 --> 00:06:05.210
and calculate the means,

00:06:05.210 --> 00:06:08.600
this is the distribution of
those sample means I might get.

00:06:08.600 --> 00:06:11.550
Now, the center of this
distribution is still

00:06:11.550 --> 00:06:15.550
our mean for white which is
equal to the mean for yellow.

00:06:15.550 --> 00:06:18.270
Remember, we're assuming
the null hypothesis.

00:06:18.270 --> 00:06:21.380
The mean for yellow.

00:06:21.380 --> 00:06:23.480
But each of these points,

00:06:23.480 --> 00:06:25.010
for example, if I think about this,

00:06:25.010 --> 00:06:27.200
this is amount of time
that someone might spend

00:06:27.200 --> 00:06:29.760
and you can see that there's
a low probability about it.

00:06:29.760 --> 00:06:33.740
This over here, this would be
a sample mean you might get

00:06:33.740 --> 00:06:36.830
for a time that you sampled 1,000 people

00:06:36.830 --> 00:06:38.350
and you calculated the mean,

00:06:38.350 --> 00:06:40.720
and you see that there's
a low probability for it.

00:06:40.720 --> 00:06:42.560
So, then what you would do is,

00:06:42.560 --> 00:06:45.350
if you were able to statistically
generate these things

00:06:45.350 --> 00:06:47.210
assuming the null hypothesis,

00:06:47.210 --> 00:06:48.320
and don't worry too much,

00:06:48.320 --> 00:06:50.550
we'll find out the
techniques for doing this

00:06:50.550 --> 00:06:52.713
and the assumptions we need
to make for doing this,

00:06:52.713 --> 00:06:56.020
what we do is then take a sample of 1,000.

00:06:56.020 --> 00:06:58.834
So, you take your sample of 1,000,

00:06:58.834 --> 00:07:00.167
so sample 1,000,

00:07:02.560 --> 00:07:07.560
and then from that you are able
to calculate a sample mean.

00:07:07.740 --> 00:07:09.360
You are able to calculate that.

00:07:09.360 --> 00:07:13.713
And let's say you get a
sample mean of 30 minutes.

00:07:14.590 --> 00:07:17.470
And let's say, actually,
that that is right over here,

00:07:17.470 --> 00:07:19.170
that this is 30 minutes right over here.

00:07:19.170 --> 00:07:21.260
The center was 20 minutes.

00:07:21.260 --> 00:07:23.657
The next thing, what you do is you say,

00:07:23.657 --> 00:07:25.247
"What's the probability
of getting a result

00:07:25.247 --> 00:07:28.880
"at least that extreme
assuming the null hypothesis?"

00:07:28.880 --> 00:07:31.350
And that high probability on these curves,

00:07:31.350 --> 00:07:33.330
it would be this right tail here

00:07:33.330 --> 00:07:34.620
and it would be the left tail

00:07:34.620 --> 00:07:36.270
that is equally far on the left side,

00:07:36.270 --> 00:07:37.560
so it'd be like that.

00:07:37.560 --> 00:07:38.850
And what you do is you look.

00:07:38.850 --> 00:07:40.290
You look at this probability,

00:07:40.290 --> 00:07:43.370
which would be these yellow areas there,

00:07:43.370 --> 00:07:47.650
and then we think about the probability

00:07:47.650 --> 00:07:52.430
of getting a result at least
as extreme as 30 minutes.

00:07:52.430 --> 00:07:55.060
So, probability of getting,

00:07:55.060 --> 00:07:58.950
getting a sample mean at least

00:08:00.160 --> 00:08:02.080
as extreme

00:08:04.110 --> 00:08:08.790
as the sample mean equaling 30 minutes,

00:08:08.790 --> 00:08:11.550
assuming, assuming

00:08:13.330 --> 00:08:14.960
your null hypothesis,

00:08:14.960 --> 00:08:19.470
and that's exactly what those
yellow areas are all about.

00:08:19.470 --> 00:08:24.270
And you compare that to some
pre-specified threshold.

00:08:24.270 --> 00:08:27.510
So, that threshold is oftentimes 5%.

00:08:27.510 --> 00:08:29.220
Sometimes it's 1%.

00:08:29.220 --> 00:08:34.220
But if this probability
is less than or equal to,

00:08:35.010 --> 00:08:37.723
if it's less than or
equal to your threshold,

00:08:38.760 --> 00:08:41.060
and the threshold is oftentimes denoted

00:08:41.060 --> 00:08:42.980
by the Greek letter alpha,

00:08:42.980 --> 00:08:46.237
well, we say, "Hey, that
was a very low probability

00:08:46.237 --> 00:08:48.967
"of getting a result at least this extreme

00:08:48.967 --> 00:08:51.080
"if we assume the null hypothesis,"

00:08:51.080 --> 00:08:54.670
and so that will allow us to reject,

00:08:54.670 --> 00:08:57.480
reject the null hypothesis,

00:08:57.480 --> 00:09:01.890
which would suggest,
suggest the alternative.

00:09:01.890 --> 00:09:04.250
Notice we haven't proven the alternative.

00:09:04.250 --> 00:09:06.710
We also haven't proven
the the null hypothesis

00:09:06.710 --> 00:09:08.560
is for sure false.

00:09:08.560 --> 00:09:11.440
We've just said if we
assume the null hypothesis,

00:09:11.440 --> 00:09:13.990
there's a very low probability
of getting a result

00:09:13.990 --> 00:09:16.870
at least as extreme as what we just got,

00:09:16.870 --> 00:09:19.280
so we will reject the null.

00:09:19.280 --> 00:09:21.920
Now, if it's the other way around,

00:09:21.920 --> 00:09:25.120
if the probability of
getting a sample mean

00:09:25.120 --> 00:09:28.220
at least as extreme as
this is still reasonable,

00:09:28.220 --> 00:09:33.190
if it's greater than your
pre-specified threshold,

00:09:33.190 --> 00:09:35.970
then you fail to reject the null.

00:09:35.970 --> 00:09:39.040
You fail to reject

00:09:39.990 --> 00:09:42.570
your null hypothesis.

00:09:42.570 --> 00:09:43.550
So, I'll leave you there.

00:09:43.550 --> 00:09:44.400
In future videos,

00:09:44.400 --> 00:09:46.620
we'll go into much more
depth into all of this,

00:09:46.620 --> 00:09:50.950
but this is to give you a
sense of how hypothesis testing

00:09:50.950 --> 00:09:54.340
allows science or all of us in the world

00:09:54.340 --> 00:09:57.743
to start making inferences
that we can feel good about.


Conclusion for a two sample t test using a P value

WEBVTT
Kind: captions
Language: en

00:00:00.810 --> 00:00:03.210
- [Instructor] We're told a
sociologist studying fertility

00:00:03.210 --> 00:00:05.830
in Argentina and Bolivia wanted to test

00:00:05.830 --> 00:00:08.100
if there was a difference
in the average number

00:00:08.100 --> 00:00:10.300
of babies women in each country have.

00:00:10.300 --> 00:00:12.820
The sociologist obtained a random sample

00:00:12.820 --> 00:00:14.490
of women from each country.

00:00:14.490 --> 00:00:16.910
Here are the results of their test.

00:00:16.910 --> 00:00:21.910
So they take a sample of
75 women in Argentina,

00:00:22.220 --> 00:00:26.740
and these women had a
mean of 2.4 babies each,

00:00:26.740 --> 00:00:29.063
with a standard deviation of 1.5.

00:00:30.490 --> 00:00:34.260
And then the standard
error of the mean was 0.17.

00:00:34.260 --> 00:00:38.500
And then they calculated
similar statistics for Bolivia.

00:00:38.500 --> 00:00:41.010
And then they give us the t test

00:00:41.010 --> 00:00:43.690
for the means being different,

00:00:43.690 --> 00:00:46.750
and we were able to
calculate these statistics.

00:00:46.750 --> 00:00:49.410
And they say assume that all conditions

00:00:49.410 --> 00:00:51.890
for inference have been met.

00:00:51.890 --> 00:00:56.580
At the alpha equals 0.05
level of significance,

00:00:56.580 --> 00:00:59.410
is there sufficient evidence to conclude

00:00:59.410 --> 00:01:02.700
that there is a difference
in the average number

00:01:02.700 --> 00:01:05.980
of babies women in each country have?

00:01:05.980 --> 00:01:08.923
So pause this video, and
see if you can answer that.

00:01:10.340 --> 00:01:13.450
All right, now let's work
through this together.

00:01:13.450 --> 00:01:17.020
So this is classic hypothesis
testing right over here,

00:01:17.020 --> 00:01:20.010
where your null hypothesis
is actually going to be

00:01:20.010 --> 00:01:21.770
that your means are the same,

00:01:21.770 --> 00:01:24.530
so that the mean in Argentina is equal

00:01:24.530 --> 00:01:27.020
to the mean in Bolivia.

00:01:27.020 --> 00:01:30.590
And then your alternative hypothesis is

00:01:30.590 --> 00:01:34.600
that your means are different.

00:01:34.600 --> 00:01:36.700
And what you do is you say, all right,

00:01:36.700 --> 00:01:41.700
if we assume the null hypothesis,
what is the probability

00:01:41.700 --> 00:01:45.320
that we would have gotten
means this far apart?

00:01:45.320 --> 00:01:49.040
And that's what our p-value tells us,

00:01:49.040 --> 00:01:52.720
that we have a 0.31 probability,

00:01:52.720 --> 00:01:57.480
or a 31% probability, of
getting means this far apart.

00:01:57.480 --> 00:02:00.720
Now, if your probability,
assuming the null hypothesis,

00:02:00.720 --> 00:02:03.350
is below your level of significance,

00:02:03.350 --> 00:02:05.190
your alpha right over here,

00:02:05.190 --> 00:02:06.550
then you would say, all right,

00:02:06.550 --> 00:02:08.380
that seems like such a low probability.

00:02:08.380 --> 00:02:10.530
I'll reject the null hypothesis,

00:02:10.530 --> 00:02:13.530
which suggests the alternative hypothesis.

00:02:13.530 --> 00:02:15.440
But in this situation here,

00:02:15.440 --> 00:02:18.730
if we compare our p to our alpha,

00:02:18.730 --> 00:02:23.730
we see that our p-value is for
sure greater than our alpha.

00:02:23.830 --> 00:02:25.180
So in this situation,

00:02:25.180 --> 00:02:26.290
I mean you could see it right over here,

00:02:26.290 --> 00:02:31.290
0.31 is for sure greater than 0.05.

00:02:31.620 --> 00:02:35.150
So in this situation, we cannot
reject the null hypothesis,

00:02:35.150 --> 00:02:38.100
cannot reject

00:02:38.100 --> 00:02:39.850
our null hypothesis.

00:02:39.850 --> 00:02:42.530
And so there is not sufficient evidence

00:02:42.530 --> 00:02:44.530
to conclude that there is a difference

00:02:44.530 --> 00:02:47.953
in the average number of babies
women in each country have.


Dilating shapes: shrinking

WEBVTT
Kind: captions
Language: en

00:00:00.720 --> 00:00:02.930
- [Instructor] We're told draw the image

00:00:02.930 --> 00:00:06.630
of triangle ABC under a dilation

00:00:06.630 --> 00:00:11.630
whose center is P and scale factor is 1/4.

00:00:12.640 --> 00:00:17.010
And what we see here is
the widget on Khan Academy

00:00:17.010 --> 00:00:19.400
where we can do that.

00:00:19.400 --> 00:00:22.617
So we have this figure, this triangle ABC,

00:00:23.558 --> 00:00:27.270
A, B, C, right over here,

00:00:27.270 --> 00:00:29.620
and what we wanna do is dilate it,

00:00:29.620 --> 00:00:32.020
so that means scaling it up or down,

00:00:32.020 --> 00:00:36.170
and the center of that
dilation is this point P.

00:00:36.170 --> 00:00:38.480
So one way to think
about it is let's think

00:00:38.480 --> 00:00:40.470
about the distance between point P

00:00:40.470 --> 00:00:41.840
and each of these points,

00:00:41.840 --> 00:00:44.350
and we wanna scale it by 1/4.

00:00:44.350 --> 00:00:46.160
So the distance is going to be 1/4

00:00:46.160 --> 00:00:47.910
of what it was before.

00:00:47.910 --> 00:00:50.100
So, for example, this
point right over here,

00:00:50.100 --> 00:00:53.010
if we just even look
diagonally from P to A,

00:00:53.010 --> 00:00:55.450
we can see that we are
crossing one square,

00:00:55.450 --> 00:00:58.560
two squares, three squares, four squares.

00:00:58.560 --> 00:01:00.900
So if we have a scale factor of 1/4,

00:01:00.900 --> 00:01:03.590
instead of crossing
four squares diagonally,

00:01:03.590 --> 00:01:05.880
we would only cross one square diagonally.

00:01:05.880 --> 00:01:09.470
So I'll put the corresponding
point to A right over there.

00:01:09.470 --> 00:01:10.970
Now, what about for point C?

00:01:10.970 --> 00:01:13.570
It's not quite as obvious,

00:01:13.570 --> 00:01:15.230
but one way we could think about it

00:01:15.230 --> 00:01:18.080
is we can think about how
far are we going horizontally

00:01:18.080 --> 00:01:21.760
from P to C, and then how
far do we go vertically?

00:01:21.760 --> 00:01:24.100
So horizontally, we're going one, two,

00:01:24.100 --> 00:01:29.100
three, four, five, six,
seven, eight of these units,

00:01:29.160 --> 00:01:33.610
and then vertically we're
going one, two, three, four.

00:01:33.610 --> 00:01:36.290
So we're going to the
left eight and up four.

00:01:36.290 --> 00:01:38.300
Now, if we have a scale factor of 1/4,

00:01:38.300 --> 00:01:40.580
we just multiply each of those by 1/4.

00:01:40.580 --> 00:01:42.410
So instead of going to the left eight,

00:01:42.410 --> 00:01:44.100
we would go to the left two.

00:01:44.100 --> 00:01:45.930
Eight times 1/4 is two.

00:01:45.930 --> 00:01:49.250
Instead of going up
four, we would go up one.

00:01:49.250 --> 00:01:51.970
So this would be the
corresponding point to point C.

00:01:51.970 --> 00:01:54.480
And then we'll do the
same thing for point B.

00:01:54.480 --> 00:01:57.680
When we go from P to B,
we're going one, two,

00:01:57.680 --> 00:02:02.570
three, four, five, six, seven, eight up,

00:02:02.570 --> 00:02:04.630
and we're going four to the left.

00:02:04.630 --> 00:02:06.300
So if we have a scale factor of 1/4,

00:02:06.300 --> 00:02:08.320
instead of going eight
up, we'll go two up,

00:02:08.320 --> 00:02:09.540
and instead of going four to the left,

00:02:09.540 --> 00:02:11.600
we'll go one to the left.

00:02:11.600 --> 00:02:12.960
So there you have it.

00:02:12.960 --> 00:02:16.450
We have just dilated triangle ABC

00:02:16.450 --> 00:02:21.450
around point P with a scale factor of 1/4,

00:02:23.410 --> 00:02:25.083
and we are done.