Guided visualization to calm your mind

WEBVTT
Kind: captions
Language: en

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- [Instructor] Welcome, and
thanks for taking out the time

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for yourself for what will hopefully be

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a nice inward journey.

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So just start off sitting upright,

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feet planted on the ground

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if you're ideally on some
type of a firm chair.

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And start to soften your gaze
if your eyes are still open.

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Gently close them.

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I like to leave my hands on my lap,

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palms up to the sky,

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but whatever feels comfortable for you.

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And then with your eyes closed,

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gently become a little bit
more aware of your breaths.

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Make them a little bit deeper
and a little bit slower.

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At your own time breathe in,

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breathe out, just a little bit deeper

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and a little bit slower.

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So the whole idea behind meditation

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is trying to ease all the chatter

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that exists in our brains,

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trying to still our thoughts.

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And so as we do that,

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and every meditation I'm
going to try to introduce

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some frameworks, ways of
thinking about your mind.

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But as you try to quiet the mind,

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it will inevitably get distracted.

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It might get distracted
by some noise in the room

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or some noise outside, or more likely,

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it'll get distracted by thoughts

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that are just surfacing
into your consciousness.

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And if that happens, don't
let it make you anxious.

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A lot of folks, when they meditate,

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they worry that they're doing it wrong,

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and then if they get distracted,

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it actually makes things worse.

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They say, "I'm never going to be able

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"to do this meditation thing."

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The important thing is to
approach the meditation

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with a spirit of fun,
a spirit of curiosity.

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Have a sense of humor about it.

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We are all literally human,

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and we do very human things.

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And so when you find your
mind wandering a bit,

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just laugh it off and say,
"Oh, there you go, mind."

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Just come back to the
stillness, not a big deal.

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Don't beat up on yourself over it.

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And as part of that, as we
go over to this meditation,

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as much as possible try
to keep a little bit

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of a smile on your face.

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Your eyes are closed,

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but you can still smile a little bit

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or at least smile with your mind.

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Reminds you that this should be fun.

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This is relaxing.

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So with that said, let's keep
breathing in, breathing out,

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a little bit deeper, a little bit slower.

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In the framework that
I'm going to introduce

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for how you can still your mind

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is one that I use a lot,

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which is imagining all the thoughts

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in your subconscious as the ocean.

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And the surface of the
ocean is the interface

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between your subconscious
and your consciousness.

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And most of us have a
pretty choppy surface.

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There's a lot of thoughts

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that are jumping up and down
out of our subconscious.

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And sometimes we're
drowning in those thoughts.

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And one way to think about it

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is we can elevate ourselves.

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We can elevate ourselves above
the surface of that water.

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And when you start to elevate yourself,

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you're not suppressing the thoughts,

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but you're just looking down on them.

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You see that they're still there.

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The surface is still choppy.

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There's still waves.

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But as you rise and you look down on it,

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you realize that you
are not those thoughts.

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You are not the surface of the water.

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So whether the thing that's bothering you

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is an assignment you have to do

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or some interpersonal relations

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or just something in your life

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not working out the way
that you would like it to,

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remind yourself that that is not you.

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You are not defined by the
outcome of that situation.

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Those are just waves on that ocean.

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And the more that you surface above them

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and you look at them and analyze them,

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you realize that they
have no control over you.

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And once that happens,
things start to slow down.

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The surface of that water begins

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to get calmer and calmer and calmer.

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And there you are floating
above that surface,

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just pure awareness.

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And you realize that you're a lot more

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than you thought you were.

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You aren't just your physical body.

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You aren't just those thoughts

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that you see as waves on
the surface of that ocean.

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You aren't even just that identity

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that you associate yourself with,

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your name, your position in the world,

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your status, what people
think of you, your relations.

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Those are aspects of
you, but they aren't you.

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You are something much
bigger than all of them.

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You are the space in which they occur,

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in which they happen, but they aren't you.

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And now let's just try to
sit in that pure awareness

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for the next minute or so.

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And once again, if your
thoughts wander, not a big deal.

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That's just the choppiness
on the surface of that water,

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and you need to elevate yourself back

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to that pure awareness.

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And if the quiet bothers you, don't worry.

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I will be back in about a minute.

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All right, so that was a
relatively short amount of time

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for you to be on your own.

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And as you'll see,

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as we do more and more
advanced meditations,

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give yourself more and more time.

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And over time you won't need me talking.

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In fact, that will probably annoy you.

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You'll just be able to sit
down and still your mind

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and realize that you are not your thoughts

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and that these things
that are bothering you,

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they're only going to bother you

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as much as you let them bother you.

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In the whole scheme of things,

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in all of time and space,

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none of them are really
what should define you

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or are anywhere near as important

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as we sometimes make them out to be.

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I'll see you in the next meditation.


Guided meditation to help with test anxiety

WEBVTT
Kind: captions
Language: en

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- [Instructor] Welcome to this meditation

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and I'll assume that if you are listening

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that you have some type of
major test or exam coming up

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because that's what the title
of this meditation is about.

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Now the word meditation can
conjure up different ideas

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to different folks, but
all it is is a way for us

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to observe our thoughts and
maybe quiet our thoughts down,

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especially in a way that makes us feel

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just a little bit lighter,
a little bit more peaceful,

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a little bit happier, and
less stressed or anxious.

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Oftentimes by doing that,
it helps us do better

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on the thing that we were
stressed about in the first place.

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Let's get started.

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The first thing that I always emphasize,

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this is true whenever I meditate,

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is posture and breathing and
environment can matter a lot.

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Find someplace nice that you can sit down,

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ideally a little bit quiet
or at least where the sound

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doesn't bother you, and sit
upright as well as you can.

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If there is a little bit of ambient sound,

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don't let it bother you or irritate you.

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Just accept that's the
universe making its noises,

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just something to observe.

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It's almost a little bit funny.

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As you accept your environment,

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whether it's your external environment

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or even sensations that
you have from your body,

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start to breathe a little bit
deeper and a little bit slower

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than you were before
this meditation began.

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Breathe in.

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Pause.

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Breathe out.

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You can set your own pace for breathing in

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and breathing out, but just
try to go a little bit deeper

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and a little bit slower.

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Now when I do this, I like to sit upright,

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usually on a chair, and keep
my hands on my lap face up,

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but you can do whatever feels
comfortable for yourself.

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The other thing that I'll ask you to do,

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it might feel a little unnatural,

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is force a smile.

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Try to make it as real as possible,

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but if you have to, force it.

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What I find is, obviously
when we're happy,

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we tend to smile, but you
can actually make the wiring

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go the other way.

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That by forcing a smile,
it can actually make you

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feel a little bit better,
a little bit more positive.

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Try to keep that smile on your face

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throughout the meditation

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and ideally well beyond the meditation.

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It doesn't have to be a fake smile,

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it could just be a very slight,
gentle smirk, if you like.

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But something that makes you
feel a little bit better.

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With that, continue to
breathe in, breathe out.

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If you haven't closed your eyes already,

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you can gently close your eyes.

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Before I give you a chance to
just be with yourself quietly

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and observe and maybe still your thoughts,

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I'll give you some ideas to think about.

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A lot of the stress of an exam

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comes from identifying with the outcome.

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We get caught up with,
"What if I don't do well?"

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Or "I need to do well."

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Or "I am going to do so
awesome that when I do awesome,

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"all these amazing things are
going to happen in my life."

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The problem with getting
attached to the outcome

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is the outcome may or may not happen.

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All those fears that you
have may or may not happen.

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All those hopes you have
may or may not happen.

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When you identify with those,
and if they don't happen,

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well that might create a
little bit of a disconnect

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between yourself and
reality and that's one

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of the number one reasons
why people get unhappy.

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Reality isn't working out
the way they want it to.

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Instead, you could identify
a bit more with the process,

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the adventure.

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Saying, "Look, I have this thing coming up

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"and I'm going to put
my best foot forward.

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"I am going to put in the work to prepare

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"and I'm going to enjoy that work.

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"I am the sentient being on this planet,

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"in this mystery that we call life

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"and I get to engage on this
challenge called this test.

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"Let me enjoy these moments."

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Before you know it, you're
going to be a lot older

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and you're going to
reminisce about this moment

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in your life right now.

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You're going to laugh at yourself,

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"Why didn't I enjoy it more?"

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Now with that notion of
focusing on the adventure

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of preparation, I'll give
you another visualization

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that I find really useful.

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Imagine that your subconscious
is a massive ocean

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and your consciousness, the
part that thinks to itself,

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"Here I am!

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"I'm some type of pure
awareness trying to observe

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"and make sense of the universe."

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That's a sky that's clear
and full of sunlight.

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Most of us are operating on
the surface of that ocean

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most of the time.

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There are all these random thoughts

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that are just bubbling up from that ocean,

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waves that are crashing
into our consciousness.

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For many of you, it might
be thoughts, ruminations

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about how you're doing on that test

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or thinking about consequences
of doing well or not well.

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It could be other things.

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It could be things going
on in your social life,

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assignments that you have due,

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things in the broader world
that are troubling you.

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But one of the ideas behind
meditation is to realize

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that those thoughts that are surfacing

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from your subconscious, they aren't you

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and you can actually rise
above those thoughts,

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rise above the surface of that ocean.

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Imagine yourself as just a
pure awareness rising above

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that surface and you're
realizing all of those thoughts

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that were thrashing around,

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that were splashing against
your pure awareness,

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your consciousness, they don't have to.

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Now you're above them and
there's just a few drops

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that every now and then you
can giggle and wipe off a bit.

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You can look down on the
surface of that ocean

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and from a distance, those
thoughts really don't seem

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like that big of a deal.

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As you look down on those
thoughts, you begin to appreciate

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that they're starting to slow down.

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The ocean is starting to
become a little more still.

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As you continue to breathe
in and breathe out,

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there you are, just in
that sun-drenched sky

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above the ocean.

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You are that sun-drenched
sky above that ocean

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that is your subconsciousness.

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You are that pure sunlight.

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With that idea in mind, I'll
give you a minute of silence

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where you can just breathe in, breathe out

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and experience joy in that
sunlight that you are in.

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Experience joy in not getting
caught up in those thoughts.

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If your brain wanders off, if
your consciousness goes back

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to the surface of that
ocean and that starts

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to get a little bit choppier,
no reason to worry about that.

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Just remind yourself, giggle a little bit,

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and say, "Oh! I got
lost in the ocean again

00:07:22.077 --> 00:07:23.687
"on the surface with those waves.

00:07:23.687 --> 00:07:26.030
"Let me just rise up again."

00:07:26.030 --> 00:07:27.653
I'll be back in about a minute.

00:07:53.920 --> 00:07:56.383
All right so we are back.

00:07:57.900 --> 00:08:01.700
Continue to breathe in, breathe out.

00:08:01.700 --> 00:08:04.360
Hopefully you experienced just
a little bit of stillness,

00:08:04.360 --> 00:08:06.310
even if it was for five or 10 seconds,

00:08:06.310 --> 00:08:10.460
the experience of knowing
that you aren't your thoughts,

00:08:10.460 --> 00:08:12.560
knowing that you can
observe your thoughts,

00:08:12.560 --> 00:08:15.040
knowing that there can
be moments in your life

00:08:15.040 --> 00:08:17.183
where you are free of your thoughts.

00:08:18.540 --> 00:08:22.630
Now as we are winding
down this meditation,

00:08:22.630 --> 00:08:25.760
keep a couple of big ideas in your head.

00:08:25.760 --> 00:08:28.770
Remind yourself not to
focus on the outcome,

00:08:28.770 --> 00:08:32.240
but to focus on the
process and to enjoy it.

00:08:32.240 --> 00:08:35.210
That smile that hopefully
you still have on your face,

00:08:35.210 --> 00:08:38.310
have that smile the whole
time that you're preparing.

00:08:38.310 --> 00:08:41.500
Have that smile as you go
into whatever type of test

00:08:41.500 --> 00:08:43.963
or exam you are about to take on.

00:08:44.910 --> 00:08:48.400
If you can, try to take a little
bit of time out every day,

00:08:48.400 --> 00:08:50.470
even if you can do it for
a minute, two minutes,

00:08:50.470 --> 00:08:54.610
three minutes, where you can
sit silently with good posture,

00:08:54.610 --> 00:08:58.920
breathe slowly, deeply,
put a smile on your face,

00:08:58.920 --> 00:09:01.400
and rise above your thoughts.

00:09:01.400 --> 00:09:03.300
I feel confident that
not only are you going

00:09:03.300 --> 00:09:05.740
to enjoy this experience,

00:09:05.740 --> 00:09:08.680
but you're going to put your
best foot forward on that test

00:09:08.680 --> 00:09:11.110
and you're also going to realize over time

00:09:11.110 --> 00:09:14.240
that this test isn't that big of a deal.

00:09:14.240 --> 00:09:15.520
Many things in our life

00:09:15.520 --> 00:09:18.150
that in the moment seem like a big deal,

00:09:18.150 --> 00:09:20.670
with a little bit of
distance of time and space,

00:09:20.670 --> 00:09:22.173
aren't that big of a deal.

00:09:23.390 --> 00:09:25.930
If you haven't already, I encourage you

00:09:25.930 --> 00:09:28.160
at your own time and pace,
while you're continuing

00:09:28.160 --> 00:09:30.710
to smile and continuing to breathe in

00:09:30.710 --> 00:09:35.710
and breathe out deeply,
gently open up your eyes

00:09:36.070 --> 00:09:38.010
and take joy in this adventure,

00:09:38.010 --> 00:09:40.423
this mystery that we call life.


Guided meditation to help you stop procrastinating

WEBVTT
Kind: captions
Language: en

00:00:00.631 --> 00:00:04.880
- [Instructor] Welcome to the
meditation on procrastination.

00:00:04.880 --> 00:00:06.510
And somewhat ironically,

00:00:06.510 --> 00:00:09.600
I've been procrastinating
making this meditation.

00:00:09.600 --> 00:00:12.513
So we're all in the same boat together.

00:00:13.510 --> 00:00:16.250
So as with all meditations,

00:00:16.250 --> 00:00:18.450
posture and breathing
makes a big difference.

00:00:18.450 --> 00:00:19.770
So I really encourage you

00:00:19.770 --> 00:00:22.510
to find a nice, firm seat to sit on.

00:00:22.510 --> 00:00:23.810
If your legs don't fall asleep,

00:00:23.810 --> 00:00:25.510
you can sit on the ground as well.

00:00:25.510 --> 00:00:29.523
But try to sit with your back
upright, really good posture.

00:00:30.450 --> 00:00:33.590
Breathe in, breathe out,

00:00:33.590 --> 00:00:37.910
a little bit slower, a
little bit deeper every time.

00:00:37.910 --> 00:00:40.650
You can lay your hands on your lap.

00:00:40.650 --> 00:00:42.193
I like to leave them face up.

00:00:43.260 --> 00:00:44.215
And when you're ready,

00:00:44.215 --> 00:00:49.215
you can soften your gaze,
and slowly close your eyes,

00:00:53.650 --> 00:00:56.563
breathing in, breathing out.

00:01:00.140 --> 00:01:03.150
Now procrastination is
an interesting thing.

00:01:03.150 --> 00:01:05.930
I'm not sure whether we human beings

00:01:05.930 --> 00:01:09.430
are the only animals we
know of that procrastinate.

00:01:09.430 --> 00:01:12.110
It's maybe worth some
research for somebody

00:01:12.110 --> 00:01:13.530
to figure that out.

00:01:13.530 --> 00:01:14.763
But we clearly do it.

00:01:15.730 --> 00:01:16.977
And a lot of meditation

00:01:16.977 --> 00:01:21.110
is about becoming aware of our thoughts,

00:01:21.110 --> 00:01:22.730
and observing our thoughts,

00:01:22.730 --> 00:01:26.450
and realizing that we
are not our thoughts,

00:01:26.450 --> 00:01:29.290
even though many times, our
thoughts seem to control us,

00:01:29.290 --> 00:01:30.913
or even overwhelm us.

00:01:33.720 --> 00:01:34.931
And so let's do that.

00:01:34.931 --> 00:01:38.629
Let's try to observe those thoughts

00:01:38.629 --> 00:01:42.060
that are making us put off something

00:01:42.060 --> 00:01:43.823
that we know we need to do.

00:01:47.303 --> 00:01:51.073
Why do you think you are
putting that thing off?

00:01:53.271 --> 00:01:55.570
I'll tell you what happens to be usually

00:01:55.570 --> 00:01:56.650
for my experience.

00:01:56.650 --> 00:01:59.926
It usually is, I'm afraid to start,

00:01:59.926 --> 00:02:04.110
because I might realize that
it's harder than I expected,

00:02:04.110 --> 00:02:08.503
or I might not do as well as I expected,

00:02:09.640 --> 00:02:12.800
or I might make a mistake.

00:02:12.800 --> 00:02:15.743
Maybe I don't think I'm
prepared enough to start.

00:02:17.400 --> 00:02:18.840
Another way to think about it is,

00:02:18.840 --> 00:02:20.939
we're getting too caught up in the outcome

00:02:20.939 --> 00:02:24.410
versus enjoying the journey,

00:02:24.410 --> 00:02:26.210
or enjoying whatever the thing is

00:02:26.210 --> 00:02:27.080
that you're putting off,

00:02:27.080 --> 00:02:29.903
'cause that's just a part
of this fun experience.

00:02:30.936 --> 00:02:35.101
And so I find that when I tell myself,

00:02:35.101 --> 00:02:40.101
self, define yourself by
the action, not the outcome.

00:02:42.040 --> 00:02:45.823
Don't define yourself by
whether you succeed or fail.

00:02:46.780 --> 00:02:51.780
Define yourself as making
the effort, showing up,

00:02:53.130 --> 00:02:57.170
and enjoying it, laughing at yourself,

00:02:57.170 --> 00:03:00.100
laughing at this mystery
that we call life,

00:03:00.100 --> 00:03:03.800
and just putting one foot
in front of the other,

00:03:03.800 --> 00:03:06.570
and realizing it's not so bad.

00:03:06.570 --> 00:03:07.620
And then you can put the other foot

00:03:07.620 --> 00:03:09.763
in front of that one, and keep going.

00:03:12.340 --> 00:03:13.630
And slowly but surely,

00:03:13.630 --> 00:03:17.370
you realize that you're
making a lot of progress.

00:03:17.370 --> 00:03:20.050
And the more you make that progress,

00:03:20.050 --> 00:03:22.250
the more that you actually enjoy it,

00:03:22.250 --> 00:03:25.180
especially if you're not
doing it at the last minute.

00:03:25.180 --> 00:03:27.360
And now, I'll give you about a minute

00:03:27.360 --> 00:03:30.348
for you to repeat something in your mind

00:03:30.348 --> 00:03:35.300
that can hopefully short-circuit
any of those thoughts

00:03:35.300 --> 00:03:38.059
that have been keeping
you from taking action.

00:03:38.059 --> 00:03:42.909
For the next minute or
so, repeat to yourself,

00:03:42.909 --> 00:03:45.963
that you really enjoy taking action.

00:03:47.140 --> 00:03:48.680
You're lucky that you're in a position

00:03:48.680 --> 00:03:51.143
to be able to take action.

00:03:52.346 --> 00:03:53.959
The outcome?

00:03:53.959 --> 00:03:56.053
It is what it is.

00:03:57.950 --> 00:03:59.613
You enjoy action.

00:04:00.700 --> 00:04:02.913
You're lucky to be able to take action.

00:04:04.520 --> 00:04:07.823
The outcome is what it is.

00:04:08.975 --> 00:04:11.780
Keep thinking that for
the next minute or so,

00:04:11.780 --> 00:04:14.143
and I'll be back, don't worry.

00:05:16.921 --> 00:05:18.223
All right.

00:05:20.270 --> 00:05:22.793
So when you're ready,
really at your own time,

00:05:25.050 --> 00:05:28.640
just become a little bit more
aware of your surroundings,

00:05:28.640 --> 00:05:30.490
a little bit more aware of your body,

00:05:32.020 --> 00:05:34.020
a little bit more aware of your breaths,

00:05:35.840 --> 00:05:38.763
and slowly open your eyes.

00:05:40.810 --> 00:05:42.923
And so I'll finish with one last tip:

00:05:44.100 --> 00:05:45.760
Sometimes we put something off

00:05:45.760 --> 00:05:49.483
because it just feels
big, or overwhelming.

00:05:50.405 --> 00:05:53.570
What I like to do then is say hey,

00:05:53.570 --> 00:05:56.960
let me just put 20 minutes towards it,

00:05:56.960 --> 00:06:00.060
and see where I am at
the end of 20 minutes.

00:06:00.060 --> 00:06:03.330
If I didn't make any
progress, no big deal.

00:06:03.330 --> 00:06:04.693
It was juts 20 minutes.

00:06:05.540 --> 00:06:07.940
But if I did make some progress, great.

00:06:07.940 --> 00:06:10.945
I did the 20 minutes, I deserve a break.

00:06:10.945 --> 00:06:13.190
If after a five or 10-minute break

00:06:13.190 --> 00:06:15.531
I'm ready to put in another
20 minutes, awesome.

00:06:15.531 --> 00:06:18.242
If at the end of the 20
minutes, I wanna keep going,

00:06:18.242 --> 00:06:20.150
I shouldn't stop myself.

00:06:20.150 --> 00:06:21.129
I should keep going.

00:06:21.129 --> 00:06:21.962
(laughs)

00:06:21.962 --> 00:06:24.172
But when you view things as hey,

00:06:24.172 --> 00:06:27.570
I'm just committing 20
minutes to something,

00:06:27.570 --> 00:06:29.483
it doesn't feel as intimidating.

00:06:30.520 --> 00:06:31.353
You just own it.

00:06:31.353 --> 00:06:34.610
You say hey, I can do
anything for 20 minutes.

00:06:34.610 --> 00:06:38.270
And I can enjoy anything for 20 minutes.

00:06:38.270 --> 00:06:39.690
And then you'll wanna do it.

00:06:39.690 --> 00:06:43.113
Put a smile on your face
and own that action.

00:06:44.180 --> 00:06:45.800
And not only will you make progress,

00:06:45.800 --> 00:06:48.020
but you're gonna have a good time.

00:06:48.020 --> 00:06:51.400
And so take it wit that playful mindset.

00:06:51.400 --> 00:06:52.270
Enjoy it.

00:06:52.270 --> 00:06:53.510
Smile.

00:06:53.510 --> 00:06:55.275
And just get started.

00:06:55.275 --> 00:06:57.200
And I think you'll find

00:06:57.200 --> 00:06:59.533
you'll be procrastinating a lot, lot less.


Guided meditation for students

WEBVTT
Kind: captions
Language: en

00:00:00.630 --> 00:00:02.900
- [Instructor] Welcome,
and thanks for joining me

00:00:02.900 --> 00:00:06.790
on this, let's call it
a voyage of the mind.

00:00:06.790 --> 00:00:11.020
So before we begin, posture and breathing

00:00:11.020 --> 00:00:14.010
make a big difference in meditation.

00:00:14.010 --> 00:00:17.920
So if you're not already
on a nice, firm chair

00:00:17.920 --> 00:00:21.270
with your back straight,
pause this recording

00:00:21.270 --> 00:00:24.550
and go find a nice, firm
chair with your back straight,

00:00:24.550 --> 00:00:28.363
ideally in a place that's
kind of quiet and peaceful.

00:00:29.800 --> 00:00:33.920
So now that you're there,
sit with your back straight.

00:00:33.920 --> 00:00:37.040
Try to put your feet firmly on the floor.

00:00:37.040 --> 00:00:40.570
When I do this, I like to
rest my hands on my lap,

00:00:40.570 --> 00:00:43.563
palms up, gently curled,
so really no effort.

00:00:44.840 --> 00:00:48.220
And now start to slowly breathe,

00:00:48.220 --> 00:00:52.313
a bit deeper than you were
just now and a bit slower.

00:00:53.460 --> 00:00:55.770
In, and out.

00:00:55.770 --> 00:00:58.770
At your own time, but
just a little bit deeper,

00:00:58.770 --> 00:01:00.173
a little bit slower.

00:01:01.290 --> 00:01:04.250
If you like, a lot of
folks like to breathe in

00:01:04.250 --> 00:01:08.100
through their nose, out
through their mouth,

00:01:08.100 --> 00:01:12.130
but the key, once again,
a little bit deeper,

00:01:12.130 --> 00:01:13.393
a little bit slower.

00:01:15.050 --> 00:01:18.810
And as you do so, start
to soften your gaze

00:01:18.810 --> 00:01:21.230
if your eyes are still open.

00:01:21.230 --> 00:01:26.223
And when you feel comfortable,
gently close your eyes.

00:01:29.250 --> 00:01:32.550
Now, before we get into the
heart of the meditation,

00:01:32.550 --> 00:01:35.080
I'm gonna give you a few reminders.

00:01:35.080 --> 00:01:40.080
This whole exercise is about
exploring your inner being,

00:01:41.150 --> 00:01:44.550
it's about curiosity,
it's about relaxation.

00:01:44.550 --> 00:01:47.230
There's no perfect way to meditate.

00:01:47.230 --> 00:01:50.070
Sometimes folks think that
they're not doing it right

00:01:50.070 --> 00:01:52.180
or their mind is wandering too much

00:01:52.180 --> 00:01:53.610
and then it causes stress.

00:01:53.610 --> 00:01:56.600
And that's the exact opposite
of what you want meditation

00:01:56.600 --> 00:02:00.510
to be, it should be fun, it
could even by funny at moments.

00:02:00.510 --> 00:02:02.010
You should be curious.

00:02:02.010 --> 00:02:03.943
You should be enjoying it.

00:02:04.870 --> 00:02:07.080
If there are some random distractions,

00:02:07.080 --> 00:02:08.640
and there inevitably will be.

00:02:08.640 --> 00:02:10.770
It could be sounds around you,

00:02:10.770 --> 00:02:15.260
it might be part of your
body that itches or tingles.

00:02:15.260 --> 00:02:18.630
Don't let it stress you
out, just accept it.

00:02:18.630 --> 00:02:20.720
It's part of the universe,

00:02:20.720 --> 00:02:23.160
it's just atoms doing what they do,

00:02:23.160 --> 00:02:25.890
it's the universe doing its thing.

00:02:25.890 --> 00:02:28.420
And no worries if you need to scratch

00:02:28.420 --> 00:02:32.473
or adjust part of your
body, no reason to stress.

00:02:33.940 --> 00:02:36.650
Now to add to the idea that this shouldn't

00:02:36.650 --> 00:02:38.970
be a stressful experience,
I'm gonna ask you

00:02:38.970 --> 00:02:43.470
to do something that may or may
not feel completely natural.

00:02:43.470 --> 00:02:45.130
I want you to smile right now.

00:02:45.130 --> 00:02:46.630
Give yourself a good smile.

00:02:46.630 --> 00:02:49.470
With your eyes closed, just smile.

00:02:49.470 --> 00:02:51.210
Obviously we smile when we're happy,

00:02:51.210 --> 00:02:53.400
but sometimes making us smile

00:02:53.400 --> 00:02:55.480
can actually make us a little bit happier.

00:02:55.480 --> 00:02:57.910
It can make us a little bit less stressed.

00:02:57.910 --> 00:03:00.570
So even if you need to force it, smile.

00:03:00.570 --> 00:03:03.440
And as much as possible as we
go through this meditation,

00:03:03.440 --> 00:03:05.490
as long as you don't have
to force it too much,

00:03:05.490 --> 00:03:08.363
try to keep a gentle smile
on your face the whole time.

00:03:10.860 --> 00:03:13.183
All right, now let's get into it.

00:03:14.150 --> 00:03:17.900
So one thing to keep in mind as we start

00:03:17.900 --> 00:03:21.720
trying to still our minds
is to just appreciate

00:03:21.720 --> 00:03:26.720
that you're alive, you're in
this vast mystery we call life,

00:03:27.710 --> 00:03:29.860
and that you're taking pause to appreciate

00:03:29.860 --> 00:03:31.600
who you really are,

00:03:31.600 --> 00:03:33.980
and the beauty of this
mystery, this existence,

00:03:33.980 --> 00:03:36.710
this universe that we share.

00:03:36.710 --> 00:03:40.900
So as you breathe deeper and slower,

00:03:40.900 --> 00:03:45.900
your eyes are closed, try to
become aware of your thoughts.

00:03:46.280 --> 00:03:47.680
What are you thinking about?

00:03:49.920 --> 00:03:51.800
Are they random thoughts?

00:03:51.800 --> 00:03:53.700
Something you saw on TV?

00:03:53.700 --> 00:03:55.623
Is it something going on at school?

00:03:56.870 --> 00:03:58.990
Are you thinking about some test

00:03:58.990 --> 00:04:01.180
you might have coming up?

00:04:01.180 --> 00:04:05.590
Or is someone at your school
you tend to think about a lot?

00:04:05.590 --> 00:04:08.220
Just observe your thoughts,
don't try to fight them,

00:04:08.220 --> 00:04:09.273
just observe them.

00:04:12.420 --> 00:04:14.720
And as you observe your thoughts,

00:04:14.720 --> 00:04:19.290
start to appreciate that
you are not your thoughts.

00:04:19.290 --> 00:04:22.640
You are something different
than your thoughts.

00:04:22.640 --> 00:04:25.370
They're all in there
in your head with you,

00:04:25.370 --> 00:04:27.010
but clearly you can observe them.

00:04:27.010 --> 00:04:29.620
You can see them go by.

00:04:29.620 --> 00:04:32.240
Sometimes we can get lost in them,

00:04:32.240 --> 00:04:33.380
but I think you're seeing right now

00:04:33.380 --> 00:04:34.690
that you are not your thoughts.

00:04:34.690 --> 00:04:36.893
You can actually observe your thoughts.

00:04:39.710 --> 00:04:42.530
One metaphor that folks sometimes use

00:04:42.530 --> 00:04:44.620
is that your thoughts are cars on a road

00:04:44.620 --> 00:04:47.140
or cars on a highway, and oftentimes

00:04:47.140 --> 00:04:48.200
we're in the middle of the highway

00:04:48.200 --> 00:04:50.640
and those cars are bombarding us,

00:04:50.640 --> 00:04:52.860
they're hitting us, or we
have to dodge them in some way

00:04:52.860 --> 00:04:54.410
or they're overwhelming us.

00:04:54.410 --> 00:04:55.940
And one thing to do to observe them

00:04:55.940 --> 00:04:57.710
is just get out of the highway.

00:04:57.710 --> 00:04:59.000
You don't have to fight the thoughts,

00:04:59.000 --> 00:05:01.330
those cars will keep on going by.

00:05:01.330 --> 00:05:03.200
But now that you're on the median,

00:05:03.200 --> 00:05:06.423
you're no longer on the
highway, you can see them go by.

00:05:07.730 --> 00:05:10.530
And what you'll often find
is when you're observing

00:05:10.530 --> 00:05:12.893
your thoughts, they start to slow down.

00:05:14.610 --> 00:05:17.130
And so if your thoughts
start to slow down, great,

00:05:17.130 --> 00:05:18.980
really embrace that, start to realize

00:05:18.980 --> 00:05:21.940
what that feels like when
your thoughts slow down.

00:05:21.940 --> 00:05:23.960
And then there's even going to be moments

00:05:23.960 --> 00:05:25.703
when you have no thoughts.

00:05:26.780 --> 00:05:29.330
For the next few breaths, try that.

00:05:29.330 --> 00:05:31.650
Try to have no thoughts.

00:05:31.650 --> 00:05:34.213
Just breathe in, breathe out.

00:05:35.360 --> 00:05:38.710
No thoughts, just stillness.

00:05:38.710 --> 00:05:42.060
Just your consciousness
here in this universe.

00:05:42.060 --> 00:05:47.030
No time, no space, it's all in your mind,

00:05:47.030 --> 00:05:49.313
no thoughts, stillness.

00:05:56.920 --> 00:05:59.100
Now as you try to keep that state,

00:05:59.100 --> 00:06:01.810
your mind will inevitably wander,

00:06:01.810 --> 00:06:02.910
you're going to start thinking

00:06:02.910 --> 00:06:05.790
about an assignment
that you have due soon.

00:06:05.790 --> 00:06:07.800
You're going to think about something

00:06:07.800 --> 00:06:09.260
that you have to do this weekend,

00:06:09.260 --> 00:06:13.530
or someone that you think a lot about.

00:06:13.530 --> 00:06:17.250
That's okay, don't beat yourself
up if your mind wanders.

00:06:17.250 --> 00:06:19.970
Just remind yourself,
just gently nudge it back.

00:06:19.970 --> 00:06:21.380
Try to get back to the stillness.

00:06:21.380 --> 00:06:23.880
Say, oh, look, I got a
little bit distracted,

00:06:23.880 --> 00:06:25.600
I started thinking about something.

00:06:25.600 --> 00:06:29.640
That's funny, I'm gonna get
my mind back to the stillness.

00:06:29.640 --> 00:06:31.623
I'm gonna try to slow down those cars.

00:06:35.500 --> 00:06:38.770
And so gently breathe in and breathe out,

00:06:38.770 --> 00:06:40.320
and I'm gonna give you a few minutes

00:06:40.320 --> 00:06:45.320
to just sit there, still,
breathing in, breathing out,

00:06:46.160 --> 00:06:48.290
being still with your thoughts.

00:06:48.290 --> 00:06:51.180
If your mind wanders, no big deal,

00:06:51.180 --> 00:06:53.540
just try to nudge it back when you can.

00:06:53.540 --> 00:06:55.660
And if the silence starts
to get to you a little bit,

00:06:55.660 --> 00:06:59.910
don't worry, I will be back
for sure in a few minutes.

00:08:06.890 --> 00:08:09.070
Now that you've had a little
bit of time on your own,

00:08:09.070 --> 00:08:10.920
I'm gonna give you some ideas

00:08:10.920 --> 00:08:14.373
that just might help
appreciate who you really are.

00:08:15.690 --> 00:08:18.620
A lot of times we get
caught up in the day-to-day,

00:08:18.620 --> 00:08:20.780
we start worrying about test scores

00:08:20.780 --> 00:08:24.563
or things we have due or
what people think about us,

00:08:25.440 --> 00:08:28.113
but remind yourself that you are not that.

00:08:29.400 --> 00:08:32.700
You are not defined by your test scores.

00:08:32.700 --> 00:08:35.113
You are not defined by your grades.

00:08:36.480 --> 00:08:39.653
And you are not defined by
what people think of you.

00:08:42.130 --> 00:08:43.983
You are pure consciousness.

00:08:45.660 --> 00:08:48.520
You associate yourself with your body,

00:08:48.520 --> 00:08:53.000
with your thoughts, but
they're part of you.

00:08:53.000 --> 00:08:54.333
They aren't you.

00:08:55.400 --> 00:08:59.103
You're something deeper, and
you're something far larger.

00:09:00.810 --> 00:09:03.083
Think about how vast the universe is.

00:09:03.930 --> 00:09:06.853
Not just vast in space, but vast in time.

00:09:07.760 --> 00:09:10.940
That puts some of our
problems in perspective.

00:09:10.940 --> 00:09:15.140
A hundred years from now,
a thousand years from now,

00:09:15.140 --> 00:09:17.623
will these problems really
be that significant?

00:09:19.410 --> 00:09:24.300
When you think about where
you are on this planet,

00:09:24.300 --> 00:09:27.930
part of the cosmos, are these issues

00:09:27.930 --> 00:09:29.393
really that significant?

00:09:31.000 --> 00:09:32.550
So I'll give you a few more moments

00:09:32.550 --> 00:09:34.300
to just think about those ideas,

00:09:34.300 --> 00:09:37.270
to just think about the
vastness of the universe

00:09:37.270 --> 00:09:39.210
and what a privilege it is to be able

00:09:39.210 --> 00:09:41.990
to participate in it,
to see the beauty of it,

00:09:41.990 --> 00:09:43.830
and how small some of the things

00:09:43.830 --> 00:09:47.283
that we often define
ourselves by really are.

00:09:50.350 --> 00:09:52.323
And so now when you get a chance,

00:09:53.940 --> 00:09:55.620
gently, with your eyes closed,

00:09:55.620 --> 00:09:59.230
start to feel and hear the
room around you a little bit.

00:09:59.230 --> 00:10:01.530
Get a little bit more
in touch with your body.

00:10:02.920 --> 00:10:05.253
And when you're ready, open your eyes.

00:10:08.070 --> 00:10:10.710
And take these ideas, take
that stillness with you

00:10:10.710 --> 00:10:11.913
to the rest of your day.

00:10:13.800 --> 00:10:16.910
And you should thank yourself
for taking the time out

00:10:16.910 --> 00:10:18.870
for doing this today.

00:10:18.870 --> 00:10:21.370
And I encourage you to make it a practice.

00:10:21.370 --> 00:10:23.070
Some of you might be skeptical.

00:10:23.070 --> 00:10:25.633
What would a few minute
meditation do for me?

00:10:26.660 --> 00:10:29.170
But I can guarantee you if
you do it day in, day out,

00:10:29.170 --> 00:10:32.353
if you make a practice
of it, do it regularly,

00:10:33.290 --> 00:10:35.360
over a few weeks, a few months,

00:10:35.360 --> 00:10:37.690
you're gonna notice some changes.

00:10:37.690 --> 00:10:40.750
You're gonna see yourself
be more open to experience.

00:10:40.750 --> 00:10:44.290
You're going to see more
beauty in more things.

00:10:44.290 --> 00:10:46.520
You're going to just
have a positive energy

00:10:46.520 --> 00:10:49.210
that people are going
to want to connect with,

00:10:49.210 --> 00:10:51.700
that people are going to be drawn to.

00:10:51.700 --> 00:10:54.260
And you'll also see
that you're doing better

00:10:54.260 --> 00:10:56.340
at some of those things
we talked about before

00:10:56.340 --> 00:10:58.120
because you're not stressed
about them anymore,

00:10:58.120 --> 00:10:59.510
you're enjoying them.

00:10:59.510 --> 00:11:01.620
You're doing what you can,

00:11:01.620 --> 00:11:05.470
but you're not attached to the outcome.

00:11:05.470 --> 00:11:09.683
You do your best, wherever
the chips fall, that's okay.

00:11:10.830 --> 00:11:13.880
If things don't turn out the
way you wanted, that's okay.

00:11:13.880 --> 00:11:15.913
You just accept where things are,

00:11:16.890 --> 00:11:20.320
and then you decide, what
other actions can you take?

00:11:20.320 --> 00:11:22.790
Assemble your actions piece by piece

00:11:22.790 --> 00:11:25.130
so that you can get to another outcome.

00:11:25.130 --> 00:11:28.210
But once again, if the outcome
is what you want, awesome.

00:11:28.210 --> 00:11:31.433
If it isn't, accept it
and move on from there.

00:11:32.940 --> 00:11:35.040
So I'll leave you in this meditation.

00:11:35.040 --> 00:11:38.170
Thank you for joining,
and once again thanks

00:11:38.170 --> 00:11:40.013
for taking time out for yourself.


Influence of political events on ideology

WEBVTT
Kind: captions
Language: en

00:00:00.140 --> 00:00:02.260
- [Instructor] In discussing
political socialization,

00:00:02.260 --> 00:00:06.380
we've talked a lot about
factors that go into how people

00:00:06.380 --> 00:00:10.210
develop their opinions on
government and politics.

00:00:10.210 --> 00:00:14.220
Your family, your friends, your
demographic characteristics,

00:00:14.220 --> 00:00:15.940
like your race, your gender,

00:00:15.940 --> 00:00:18.080
they all contribute to your views.

00:00:18.080 --> 00:00:21.210
In this video, I wanna talk
about another set of factors

00:00:21.210 --> 00:00:24.230
that influence a person's political views,

00:00:24.230 --> 00:00:26.760
and that's political events.

00:00:26.760 --> 00:00:30.960
And political events include
not just elections or debates

00:00:30.960 --> 00:00:34.225
or laws, but things
like terrorist attacks,

00:00:34.225 --> 00:00:38.840
or international incidents,
or economic recessions.

00:00:38.840 --> 00:00:43.840
These are external events
that shape a person's beliefs,

00:00:46.490 --> 00:00:49.050
either in the short-term or maybe even

00:00:49.050 --> 00:00:50.773
for the rest of their lives.

00:00:52.740 --> 00:00:54.431
So what are some examples

00:00:54.431 --> 00:00:58.570
of how political events
influence ideology?

00:00:58.570 --> 00:01:02.880
Some events can change a
person's party identification

00:01:04.860 --> 00:01:08.530
or how strongly they
identify with a party.

00:01:08.530 --> 00:01:11.940
For example, researchers
have found that people

00:01:11.940 --> 00:01:14.950
who lost family members
in the September 11th

00:01:14.950 --> 00:01:18.660
terrorist attacks became
more politically active

00:01:18.660 --> 00:01:21.160
and have identified more strongly

00:01:21.160 --> 00:01:23.810
with the Republican party since then.

00:01:23.810 --> 00:01:27.340
Sometimes events can
influence a person's attitudes

00:01:27.340 --> 00:01:31.100
toward government and the
political process as a whole.

00:01:31.100 --> 00:01:34.300
And here we're not talking
about which party a person

00:01:34.300 --> 00:01:38.750
favors, but rather their
ideas about government itself,

00:01:38.750 --> 00:01:41.450
like is the government trustworthy?

00:01:41.450 --> 00:01:43.530
Does my vote really count?

00:01:43.530 --> 00:01:46.694
One example of this is
the lasting influence

00:01:46.694 --> 00:01:50.450
of the Vietnam War and Watergate scandal

00:01:50.450 --> 00:01:53.120
on public trust in government.

00:01:53.120 --> 00:01:56.470
You can see in this graph
by the Pew Research Center

00:01:56.470 --> 00:02:01.470
that since polls started asking
Americans whether they trust

00:02:01.840 --> 00:02:06.840
Washington to do what is right
always or most of the time,

00:02:06.960 --> 00:02:11.563
trust peaked in the early
Johnson administration,

00:02:12.710 --> 00:02:17.710
then crashed in the mid-1960s and 1970s

00:02:18.880 --> 00:02:22.290
and has never really recovered since.

00:02:22.290 --> 00:02:26.820
So events that happened more
than 50 years ago have left

00:02:26.820 --> 00:02:30.440
a mark on public trust in
government that hasn't gone away.

00:02:30.440 --> 00:02:33.230
But not all political events have

00:02:33.230 --> 00:02:36.140
such a lasting effect on beliefs.

00:02:36.140 --> 00:02:40.040
Some events influence opinions
for just a short term,

00:02:40.040 --> 00:02:42.950
like international events that influence

00:02:42.950 --> 00:02:46.150
Americans' attitudes
towards other countries.

00:02:46.150 --> 00:02:50.600
For example, you can see in
this poll data done by Gallup,

00:02:50.600 --> 00:02:55.279
that the public's favorable
opinion about Russia has changed

00:02:55.279 --> 00:02:58.600
a great deal over the last 20 years,

00:02:58.600 --> 00:03:03.300
with revelations about
Russian hacking coming in 2015

00:03:03.300 --> 00:03:07.557
leading to a sharp decline
in favorable opinions.

00:03:07.557 --> 00:03:10.930
The last thing I wanna note
here is that researchers

00:03:10.930 --> 00:03:13.380
have discovered that
political events that happen

00:03:13.380 --> 00:03:17.650
when someone is in their
formative age, or the age

00:03:17.650 --> 00:03:21.800
from about 18 to 24, when
people are just getting out

00:03:21.800 --> 00:03:25.460
on their own and starting to
form an independent identity.

00:03:25.460 --> 00:03:29.270
Events that happen then are
more likely to have long lasting

00:03:29.270 --> 00:03:33.510
effects on a person's political
beliefs and behaviors.

00:03:33.510 --> 00:03:38.510
The great recession in 2008
had a strong effect on people

00:03:38.570 --> 00:03:42.100
in the millennial generation,
many of whom were just getting

00:03:42.100 --> 00:03:43.950
out into the workforce when it hit.

00:03:43.950 --> 00:03:46.940
Studies have shown that
this had an especially

00:03:46.940 --> 00:03:50.670
strong influence on their
ideas about government

00:03:50.670 --> 00:03:53.690
and money compared to other generations.

00:03:53.690 --> 00:03:57.610
So events can have both
short and long-term effects

00:03:57.610 --> 00:04:00.890
on people's political beliefs,
not just about whether

00:04:00.890 --> 00:04:03.300
they lean more liberal or conservative,

00:04:03.300 --> 00:04:06.120
but also about how they think
about government itself.

00:04:06.120 --> 00:04:10.160
And those effects may be
felt more strongly depending

00:04:10.160 --> 00:04:12.990
on what stage a person is in their life

00:04:12.990 --> 00:04:16.673
or how deeply an event
impacts them personally.


Segment congruence equivalent to having same length

WEBVTT
Kind: captions
Language: en

00:00:00.560 --> 00:00:02.310
- [Instructor] So, what I have
here are a few definitions

00:00:02.310 --> 00:00:05.020
that will be useful for
a proof we're going to do

00:00:05.020 --> 00:00:08.840
that connects the worlds of
congruence of line segments

00:00:08.840 --> 00:00:11.930
to the idea of them
having the same length.

00:00:11.930 --> 00:00:13.390
So, first of all, there's this idea

00:00:13.390 --> 00:00:15.930
of rigid transformations,
which we've talked about

00:00:15.930 --> 00:00:18.480
in other videos, but just as a refresher,

00:00:18.480 --> 00:00:19.970
these are transformations

00:00:19.970 --> 00:00:23.440
that preserve distance between points.

00:00:23.440 --> 00:00:27.920
So, for example, if I have points A and B,

00:00:27.920 --> 00:00:31.610
a rigid transformation could
be something like a translation

00:00:31.610 --> 00:00:34.840
because after I've translated
them, notice the distance

00:00:34.840 --> 00:00:38.010
between the points is still the same.

00:00:38.010 --> 00:00:40.300
It could be like that.

00:00:40.300 --> 00:00:41.440
It includes rotation.

00:00:41.440 --> 00:00:44.660
Let's say I rotated about point
A as the center of rotation.

00:00:44.660 --> 00:00:49.070
That still would not change,
that still would not change

00:00:49.070 --> 00:00:51.410
my distance between points A and B.

00:00:51.410 --> 00:00:54.620
It could even be things like
taking the mirror image.

00:00:54.620 --> 00:00:56.690
Once again, that's not
going to change the distance

00:00:56.690 --> 00:00:57.860
between A and B.

00:00:57.860 --> 00:00:59.790
What's not a rigid transformation?

00:00:59.790 --> 00:01:02.470
Well, one thing you might
imagine is dilating,

00:01:02.470 --> 00:01:03.970
scaling it up or down.

00:01:03.970 --> 00:01:06.310
That is going to change the distance,

00:01:06.310 --> 00:01:09.080
so rigid transformation
are any transformations

00:01:09.080 --> 00:01:11.850
that preserve the distance between points.

00:01:11.850 --> 00:01:14.470
Now, another idea is congruence,

00:01:14.470 --> 00:01:18.060
and in the context of this
video, we're going to be viewing

00:01:18.060 --> 00:01:21.630
the definition of congruence
as two figures are congruent

00:01:21.630 --> 00:01:24.910
if and only if there exists a series

00:01:24.910 --> 00:01:28.530
of rigid transformations
which will map one figure

00:01:28.530 --> 00:01:30.710
onto the other.

00:01:30.710 --> 00:01:33.520
You might see other definitions
of congruence in your life,

00:01:33.520 --> 00:01:36.160
but this is the rigid
transformation definition

00:01:36.160 --> 00:01:38.990
of congruence that we will
use, and we're going to use

00:01:38.990 --> 00:01:42.900
these two definitions
to prove the following,

00:01:42.900 --> 00:01:46.240
to prove that saying two
segments are congruent

00:01:46.240 --> 00:01:50.323
is equivalent to saying that
they have the same length.

00:01:52.040 --> 00:01:54.760
So, let me get some
space here to do that in.

00:01:54.760 --> 00:01:59.760
So first, let me prove that if segment AB

00:01:59.760 --> 00:02:04.570
is congruent to segment CD,

00:02:04.570 --> 00:02:08.060
then the length of segment AB,

00:02:08.060 --> 00:02:11.110
which we'll just denote as
AB without the line over it,

00:02:11.110 --> 00:02:15.840
is equal to the length of segment CD.

00:02:15.840 --> 00:02:18.700
How do we do that?

00:02:18.700 --> 00:02:23.700
Well, the first thing to realize is if AB,

00:02:24.010 --> 00:02:27.130
if AB is

00:02:27.130 --> 00:02:29.990
congruent to CD,

00:02:29.990 --> 00:02:34.840
then AB can

00:02:34.840 --> 00:02:39.330
be mapped onto CD

00:02:42.010 --> 00:02:47.010
with rigid transformations,
rigid transformations.

00:02:47.260 --> 00:02:51.880
That comes out of the
definition of congruence.

00:02:51.880 --> 00:02:53.980
And then we could say, "Since

00:02:55.187 --> 00:03:00.163
"the transformations are rigid,

00:03:02.137 --> 00:03:06.533
"distance is preserved,

00:03:07.627 --> 00:03:10.860
"preserved," and so, that would imply

00:03:10.860 --> 00:03:12.490
that the distance between the points

00:03:12.490 --> 00:03:14.180
are going to be the same.

00:03:14.180 --> 00:03:17.360
AB, the distance between
points AB, or the length

00:03:17.360 --> 00:03:21.890
of segment AB, is equal to
the length of segment CD.

00:03:21.890 --> 00:03:24.330
That might almost seem
too intuitive for you,

00:03:24.330 --> 00:03:26.230
but that's all we're talking about.

00:03:26.230 --> 00:03:28.430
So, now, let's see if we
can prove the other way.

00:03:28.430 --> 00:03:32.830
Let's see if we can prove that
if the length of segment AB

00:03:32.830 --> 00:03:37.507
is equal to the length of
segment CD, then segment AB

00:03:39.770 --> 00:03:44.643
is congruent to segment
CD, and let me draw them

00:03:46.410 --> 00:03:50.150
right over here, just to, so,
let's say I have segment AB

00:03:51.800 --> 00:03:53.330
right over there, and
I'll draw another segment

00:03:53.330 --> 00:03:56.900
that has the same length,
so maybe it looks something

00:03:56.900 --> 00:03:59.970
like this, and this is
obviously hand-drawn.

00:03:59.970 --> 00:04:02.313
So, then, let's call this CD.

00:04:03.870 --> 00:04:05.697
So, in order to prove
this, I have to show,

00:04:05.697 --> 00:04:08.597
"Hey, if I have two segments
with the same length,

00:04:08.597 --> 00:04:11.807
"that there's always a set
of rigid transformations

00:04:11.807 --> 00:04:14.717
"that will map one segment onto the other,

00:04:14.717 --> 00:04:17.840
"which means, by definition,
they are congruent."

00:04:17.840 --> 00:04:21.130
So, let me just construct
those transformations.

00:04:21.130 --> 00:04:24.480
So, my first rigid
transformation that I could do

00:04:24.480 --> 00:04:29.480
is to translate, translate,
and I'll underline the name

00:04:29.930 --> 00:04:34.930
of the transformation,
segment AB, so that point A is

00:04:38.030 --> 00:04:43.030
on top of point C, or A is mapped onto C,

00:04:44.030 --> 00:04:46.120
and you could see that
there's always a translation

00:04:46.120 --> 00:04:46.953
to do that.

00:04:46.953 --> 00:04:50.600
It would be doing that, and
of course we would translate.

00:04:50.600 --> 00:04:55.600
B would end up like that, and
so, after this translation,

00:04:56.500 --> 00:04:59.280
it's going to be A right over there.

00:04:59.280 --> 00:05:03.180
A is going to be there,
and then B is going

00:05:03.180 --> 00:05:05.630
to be right over there.

00:05:05.630 --> 00:05:10.630
Now, the second step I
would do is then rotate AB

00:05:13.930 --> 00:05:18.720
about A, so A is the center of rotation,

00:05:18.720 --> 00:05:22.910
so I'm gonna rotate it so that

00:05:22.910 --> 00:05:27.910
point B lies on ray CD.

00:05:30.400 --> 00:05:32.170
Well, what does this transformation do?

00:05:32.170 --> 00:05:34.250
Well, since point A is
the center of rotation,

00:05:34.250 --> 00:05:37.230
A is going to stay mapped on top of C

00:05:37.230 --> 00:05:41.310
from our first translation,
but now B is rotated,

00:05:41.310 --> 00:05:44.620
so it sits on top of
the ray that starts at C

00:05:44.620 --> 00:05:48.000
and goes through D and keeps going,

00:05:48.000 --> 00:05:50.950
and where will B be on that ray?

00:05:50.950 --> 00:05:54.330
Well, since the distance
between B and A is the same

00:05:54.330 --> 00:05:57.070
as the distance between D and C,

00:05:57.070 --> 00:05:58.980
and A and C are the same point,

00:05:58.980 --> 00:06:03.700
and now B sits on that ray,
B will now sit right on top

00:06:03.700 --> 00:06:08.700
of D because AB is equal to CD.

00:06:10.110 --> 00:06:14.700
B will be mapped onto,

00:06:16.890 --> 00:06:19.500
onto D, and just like that,

00:06:19.500 --> 00:06:22.550
we've shown that if the
segment lengths are equal,

00:06:22.550 --> 00:06:26.090
there is always a set
of rigid transformations

00:06:26.090 --> 00:06:29.270
that will map one segment onto the other.

00:06:29.270 --> 00:06:33.780
Therefore, since A and B have
been mapped onto C and D,

00:06:33.780 --> 00:06:38.780
we know that A, that segment
AB is congruent to segment CD,

00:06:39.370 --> 00:06:40.540
and we are done.

00:06:40.540 --> 00:06:43.633
We have proven what we set
out to prove both ways.


Area model for multiplying polynomials with negative terms

WEBVTT
Kind: captions
Language: en

00:00:00.260 --> 00:00:01.320
- [Instructor] In previous videos,

00:00:01.320 --> 00:00:03.330
we've already looked at using area models

00:00:03.330 --> 00:00:05.590
to think about multiplying expressions,

00:00:05.590 --> 00:00:09.050
like multiplying x plus
seven times x plus three.

00:00:09.050 --> 00:00:11.850
In those videos, we saw
that we could think about it

00:00:11.850 --> 00:00:14.140
as finding the area of a rectangle,

00:00:14.140 --> 00:00:17.090
where we could break up
the length of the rectangle

00:00:17.090 --> 00:00:20.700
as part of the length has length x,

00:00:20.700 --> 00:00:23.800
and then the rest of it has length seven.

00:00:23.800 --> 00:00:26.420
So this would be seven here,
and then the total length

00:00:26.420 --> 00:00:29.020
of this side would be x plus seven.

00:00:29.020 --> 00:00:34.020
And then the total length of
this side would be x plus,

00:00:34.110 --> 00:00:36.540
and then you have three right over here.

00:00:36.540 --> 00:00:40.160
And what area models did
is they helped us visualize

00:00:40.160 --> 00:00:42.400
why we multiply the different terms

00:00:42.400 --> 00:00:44.470
or how we multiply the different terms.

00:00:44.470 --> 00:00:47.300
Because if we're looking
for the entire area,

00:00:47.300 --> 00:00:50.100
the entire area is going
to be x plus seven,

00:00:50.100 --> 00:00:53.500
x plus seven times x plus three,

00:00:53.500 --> 00:00:55.290
times x plus three.

00:00:55.290 --> 00:00:57.460
And then of course, we can break that down

00:00:57.460 --> 00:01:00.000
into these sub-rectangles.

00:01:00.000 --> 00:01:02.700
This rectangle, and this is
actually going to be a square,

00:01:02.700 --> 00:01:04.860
would have an area of x squared.

00:01:04.860 --> 00:01:07.700
This one over here will
have an area of seven x,

00:01:07.700 --> 00:01:09.670
seven times x.

00:01:09.670 --> 00:01:12.490
This one over here will
have an area of three x.

00:01:12.490 --> 00:01:14.430
And then this one over
here will have an area

00:01:14.430 --> 00:01:17.820
of three times seven, or 21.

00:01:17.820 --> 00:01:20.660
And so we can figure out that
the ultimate product here

00:01:20.660 --> 00:01:24.690
is going to be x squared plus seven x

00:01:24.690 --> 00:01:27.440
plus three x plus 21.

00:01:27.440 --> 00:01:29.790
That's going to be the area
of the entire rectangle.

00:01:29.790 --> 00:01:31.510
Of course, we could add the seven x

00:01:31.510 --> 00:01:34.140
to the three x to get to 10x.

00:01:34.140 --> 00:01:36.260
But some of you might be wondering,

00:01:36.260 --> 00:01:37.630
well, this is all nice

00:01:37.630 --> 00:01:40.690
when I have plus seven and plus three.

00:01:40.690 --> 00:01:43.250
I can think about positive lengths.

00:01:43.250 --> 00:01:45.740
I can think about positive areas.

00:01:45.740 --> 00:01:47.440
But what if it wasn't that way?

00:01:47.440 --> 00:01:50.860
What if we were dealing
with negatives instead?

00:01:50.860 --> 00:01:55.060
For example, if we now
try to do the same thing,

00:01:55.060 --> 00:01:56.680
we could say, all right,

00:01:56.680 --> 00:01:59.130
this top length right over here

00:01:59.130 --> 00:02:02.830
would be x minus seven.

00:02:02.830 --> 00:02:04.440
So let's just keep going with it,

00:02:04.440 --> 00:02:07.800
and let's call this length
negative seven up here.

00:02:07.800 --> 00:02:10.260
So it has a negative seven
length, and we're not

00:02:10.260 --> 00:02:12.060
necessarily used to thinking
about lengths as negative.

00:02:12.060 --> 00:02:13.080
Let's just go with it.

00:02:13.080 --> 00:02:15.580
And then the height right over here,

00:02:15.580 --> 00:02:17.490
it would be x minus three.

00:02:17.490 --> 00:02:20.060
So we could write an x there
for that part of the height.

00:02:20.060 --> 00:02:21.720
And for this part of the height,

00:02:21.720 --> 00:02:24.990
we could put a negative three.

00:02:24.990 --> 00:02:27.400
So let's see, if we kept going
with what we did last time,

00:02:27.400 --> 00:02:29.590
the area here would be x squared.

00:02:29.590 --> 00:02:32.580
The area here would be
negative seven times x,

00:02:32.580 --> 00:02:35.250
so that would be negative seven x.

00:02:35.250 --> 00:02:38.040
This green area would be negative three x.

00:02:38.040 --> 00:02:40.380
And then this orange area
would be negative three

00:02:40.380 --> 00:02:43.770
times negative seven,
which is positive 21.

00:02:43.770 --> 00:02:47.180
And then we would say that the
entire product is x squared

00:02:47.180 --> 00:02:51.670
minus seven x minus three x plus 21.

00:02:51.670 --> 00:02:52.570
And we can, of course,

00:02:52.570 --> 00:02:55.800
add these two together
to get negative 10x.

00:02:55.800 --> 00:02:57.810
But does this make sense?

00:02:57.810 --> 00:03:00.170
Well, one way to think about
it is that a negative area

00:03:00.170 --> 00:03:04.550
is an area that you would
take away from the total area.

00:03:04.550 --> 00:03:07.290
So if x happens to be
a positive number here,

00:03:07.290 --> 00:03:09.070
then this pink area would be negative,

00:03:09.070 --> 00:03:10.850
and so we would take
it away from the whole.

00:03:10.850 --> 00:03:14.450
And that's exactly what is
happening in this expression.

00:03:14.450 --> 00:03:16.640
And it's worth mentioning

00:03:16.640 --> 00:03:19.090
that even before when this
wasn't a negative seven,

00:03:19.090 --> 00:03:20.420
when it was a positive seven

00:03:20.420 --> 00:03:22.970
and this was a positive seven x,

00:03:22.970 --> 00:03:25.580
it's completely possible
that x is negative,

00:03:25.580 --> 00:03:29.090
in which case you would've
had a negative area anyway.

00:03:29.090 --> 00:03:32.330
But to appreciate that
this will all work out,

00:03:32.330 --> 00:03:33.870
even with negative numbers,

00:03:33.870 --> 00:03:37.640
I'll give an example,
if x were equal to 10.

00:03:37.640 --> 00:03:39.950
That will help us make sense of things.

00:03:39.950 --> 00:03:42.330
So if x were equal to 10,

00:03:42.330 --> 00:03:44.700
we would get an area model
that looks like this.

00:03:44.700 --> 00:03:48.720
We're having 10 minus seven,

00:03:48.720 --> 00:03:51.680
so I'll put minus seven right over here,

00:03:51.680 --> 00:03:56.680
times 10 minus three.

00:03:56.720 --> 00:03:58.060
Now, you can figure out in your heads

00:03:58.060 --> 00:03:58.900
what's that going to be.

00:03:58.900 --> 00:04:00.750
10 minus seven is three.

00:04:00.750 --> 00:04:02.750
10 minus three is seven.

00:04:02.750 --> 00:04:06.250
So this should all add up to positive 21.

00:04:06.250 --> 00:04:08.100
Let's make sure that's actually occurring.

00:04:08.100 --> 00:04:11.940
So this blue area is going to
be 10 times 10, which is 100.

00:04:11.940 --> 00:04:15.000
This pink area now is
10 times negative seven.

00:04:15.000 --> 00:04:16.550
So it's negative 70,

00:04:16.550 --> 00:04:19.450
so we're gonna take it
away from the total area.

00:04:19.450 --> 00:04:21.600
This green area is
negative three times 10,

00:04:21.600 --> 00:04:23.260
so that's negative 30.

00:04:23.260 --> 00:04:26.410
And then negative three
times negative seven,

00:04:26.410 --> 00:04:29.150
this orange area is positive 21.

00:04:29.150 --> 00:04:30.820
Does that all work out?

00:04:30.820 --> 00:04:35.820
Let's see, if we take this
positive area, 100 minus 70

00:04:36.430 --> 00:04:40.130
minus 30 and then add 21,

00:04:40.130 --> 00:04:43.340
100 minus 70 is going to be 30,

00:04:43.340 --> 00:04:44.820
minus 30 again is zero,

00:04:44.820 --> 00:04:46.370
and then you just have 21 left over,

00:04:46.370 --> 00:04:48.920
which is exactly what you would expect.

00:04:48.920 --> 00:04:51.170
You could actually move
this pink area over

00:04:51.170 --> 00:04:53.520
and subtract it from this blue area.

00:04:53.520 --> 00:04:55.110
And then you could take this green area

00:04:55.110 --> 00:04:56.340
and then you could turn it vertical,

00:04:56.340 --> 00:04:59.010
and then that would subtract
out the rest of the blue area.

00:04:59.010 --> 00:05:02.450
And then all you would have
left is this orange area.

00:05:02.450 --> 00:05:04.940
So hopefully this helps you appreciate

00:05:04.940 --> 00:05:09.110
that area models for multiplying
expressions also works

00:05:09.110 --> 00:05:10.970
if the terms are negative.

00:05:10.970 --> 00:05:13.600
And also, reminder, when
we just had x's here,

00:05:13.600 --> 00:05:15.700
they could've been negative to begin with.


Hydrogen bonding

WEBVTT
Kind: captions
Language: en

00:00:00.320 --> 00:00:02.850
- [Instructor] Let's talk
about hydrogen bonds.

00:00:02.850 --> 00:00:05.790
Depicted here, I have three
different types of molecules.

00:00:05.790 --> 00:00:07.470
On the left, I have ammonia.

00:00:07.470 --> 00:00:11.060
Each ammonia molecule
has one nitrogen bonded

00:00:11.060 --> 00:00:12.440
to three hydrogens.

00:00:12.440 --> 00:00:13.273
In the middle,

00:00:13.273 --> 00:00:15.980
I have something you're
probably very familiar with,

00:00:15.980 --> 00:00:18.910
in fact, you're made up
of it, which is water.

00:00:18.910 --> 00:00:22.330
Each oxygen is bonded to two hydrogens.

00:00:22.330 --> 00:00:25.500
And then here on the right,
I have hydrogen fluoride.

00:00:25.500 --> 00:00:28.900
Each fluorine is bonded to one hydrogen.

00:00:28.900 --> 00:00:32.720
Now, why are these types
of molecules interesting?

00:00:32.720 --> 00:00:35.020
And what does that have
to do with hydrogen bonds?

00:00:35.020 --> 00:00:38.220
And the simple answer is,
in each of these cases,

00:00:38.220 --> 00:00:40.010
you have hydrogen bonded

00:00:40.010 --> 00:00:43.480
to a much more electronegative atom.

00:00:43.480 --> 00:00:45.660
Even though these are covalent bonds,

00:00:45.660 --> 00:00:47.980
they're going to be polar covalent bonds.

00:00:47.980 --> 00:00:51.740
You are going to have a
bond dipole moment that goes

00:00:51.740 --> 00:00:55.630
from the hydrogen to the
more electronegative atom,

00:00:55.630 --> 00:00:58.650
from the hydrogen to the
more electronegative atom,

00:00:58.650 --> 00:01:02.530
from the hydrogen to the
more electronegative atom.

00:01:02.530 --> 00:01:05.320
The more electronegative atom
is going to hog the electrons.

00:01:05.320 --> 00:01:07.390
The electrons are gonna
spend more time around that.

00:01:07.390 --> 00:01:09.610
So that end of the molecule is going

00:01:09.610 --> 00:01:11.320
to have a partial negative charge.

00:01:11.320 --> 00:01:13.200
And then the ends with the hydrogens,

00:01:13.200 --> 00:01:17.000
those are gonna have
partial positive charges.

00:01:17.000 --> 00:01:18.170
Another way to think about it is,

00:01:18.170 --> 00:01:20.410
if you added these dipole moments,

00:01:20.410 --> 00:01:24.440
you would have a net dipole
for the entire molecule

00:01:26.812 --> 00:01:27.653
that would look something like that.

00:01:28.900 --> 00:01:31.320
So we are dealing with polar molecules.

00:01:31.320 --> 00:01:34.680
And the polarity comes
from both the asymmetry,

00:01:34.680 --> 00:01:39.680
and you have a very electronegative
atom bonded to hydrogen,

00:01:40.090 --> 00:01:43.740
oxygen, very electronegative
atom, bonded to hydrogen.

00:01:43.740 --> 00:01:46.720
So this end of the molecule
is partially negative.

00:01:46.720 --> 00:01:47.890
This end of the molecule

00:01:47.890 --> 00:01:50.250
or these ends of the molecule
are partially positive.

00:01:50.250 --> 00:01:53.500
For hydrogen fluoride, this
end is partially positive.

00:01:53.500 --> 00:01:55.280
This end is partially negative.

00:01:55.280 --> 00:01:56.540
And so what do you think could happen

00:01:56.540 --> 00:01:59.090
when these molecules
interact with each other?

00:01:59.090 --> 00:02:01.950
The nitrogen end right
over here, of this ammonia,

00:02:01.950 --> 00:02:04.370
could be attracted to
one of these hydrogens

00:02:04.370 --> 00:02:07.220
that has a partially positive
charge right over there.

00:02:07.220 --> 00:02:11.670
Or this hydrogen, the
partial positive charge,

00:02:11.670 --> 00:02:13.690
might be attracted to that nitrogen

00:02:13.690 --> 00:02:15.870
that has a partial negative charge.

00:02:15.870 --> 00:02:16.970
And this attraction

00:02:16.970 --> 00:02:19.460
between the partial positive hydrogen end

00:02:19.460 --> 00:02:23.470
and the partially negative
end of another molecule,

00:02:23.470 --> 00:02:26.210
those are hydrogen bonds.

00:02:26.210 --> 00:02:30.260
And they are an intermolecular
force that will be additive

00:02:30.260 --> 00:02:31.990
to the total intermolecular force

00:02:31.990 --> 00:02:35.320
from, say, things like
London dispersion forces,

00:02:35.320 --> 00:02:37.570
which makes you have
a higher boiling point

00:02:37.570 --> 00:02:39.170
than you would have if you just thought

00:02:39.170 --> 00:02:41.070
about London dispersion forces.

00:02:41.070 --> 00:02:44.350
And to make that clear,
you can look at this chart.

00:02:44.350 --> 00:02:47.810
You can see all of these
molecules are formed

00:02:47.810 --> 00:02:50.990
between period two elements and hydrogen.

00:02:50.990 --> 00:02:55.300
In fact, all of these molecules
have similar molar masses,

00:02:55.300 --> 00:02:58.690
methane, ammonia, hydrogen
fluoride, and water.

00:02:58.690 --> 00:03:01.350
If we were just thinking about
London dispersion forces,

00:03:01.350 --> 00:03:03.540
London dispersion forces are proportional

00:03:03.540 --> 00:03:07.030
to the polarizability of a molecule,

00:03:07.030 --> 00:03:10.760
which is proportional to
the electron cloud size,

00:03:10.760 --> 00:03:13.100
which is proportional to the molar mass.

00:03:13.100 --> 00:03:15.590
And generally speaking, as
you go from molecules formed

00:03:15.590 --> 00:03:18.150
with period two elements
to period three elements

00:03:18.150 --> 00:03:21.100
to period four elements
to period five elements,

00:03:21.100 --> 00:03:23.620
you do see that as the molar mass

00:03:23.620 --> 00:03:25.390
of those molecules increase,

00:03:25.390 --> 00:03:29.780
there is that general upward
trend of the boiling point,

00:03:29.780 --> 00:03:32.810
and that's due to the
London dispersion forces.

00:03:32.810 --> 00:03:36.400
But for any given period,
you do see the separation.

00:03:36.400 --> 00:03:37.233
And in particular,

00:03:37.233 --> 00:03:39.500
you see a lot of separation
for the molecules formed

00:03:39.500 --> 00:03:41.830
with oxygen, fluorine, and nitrogen.

00:03:41.830 --> 00:03:45.190
These molecules, despite
having similar molar masses,

00:03:45.190 --> 00:03:47.750
have very different boiling points.

00:03:47.750 --> 00:03:51.470
So there must be some other
type of intermolecular forces

00:03:51.470 --> 00:03:55.260
at play above and beyond
London dispersion forces.

00:03:55.260 --> 00:03:58.130
And the simple answer is yes.

00:03:58.130 --> 00:04:02.200
What you have at play
are the hydrogen bonds.

00:04:02.200 --> 00:04:03.500
Now, some of you might be wondering,

00:04:03.500 --> 00:04:04.900
well, look at these molecules formed

00:04:04.900 --> 00:04:06.900
with period three elements and hydrogen

00:04:06.900 --> 00:04:09.070
or period four elements and hydrogen,

00:04:09.070 --> 00:04:11.980
they also don't have
the same boiling point,

00:04:11.980 --> 00:04:13.310
even though you would expect

00:04:13.310 --> 00:04:15.360
similar London dispersion forces

00:04:15.360 --> 00:04:17.650
because they have similar molar masses.

00:04:17.650 --> 00:04:20.470
And the separation that you
see here in boiling points,

00:04:20.470 --> 00:04:22.970
this, too, would be due to other things,

00:04:22.970 --> 00:04:24.920
other than London dispersion forces.

00:04:24.920 --> 00:04:29.370
In particular, dipole-dipole
forces would be at play.

00:04:29.370 --> 00:04:31.490
But what you can see is
the spread is much higher

00:04:31.490 --> 00:04:34.870
for these molecules formed
with nitrogen and hydrogen,

00:04:34.870 --> 00:04:37.830
fluorine and hydrogen,
and oxygen and hydrogen.

00:04:37.830 --> 00:04:40.870
And that's because hydrogen
bonds can be viewed

00:04:40.870 --> 00:04:45.870
as the strongest form
of dipole-dipole forces.

00:04:46.440 --> 00:04:51.440
Hydrogen bonds are a special
case of dipole-dipole forces.

00:04:52.120 --> 00:04:54.240
When we're talking about hydrogen bonds,

00:04:54.240 --> 00:04:58.110
we're usually talking about
a specific bond dipole,

00:04:58.110 --> 00:05:01.880
the bond between hydrogen and
a more electronegative atom

00:05:01.880 --> 00:05:04.440
like nitrogen, oxygen, and fluorine.

00:05:04.440 --> 00:05:05.860
And so we're specifically talking

00:05:05.860 --> 00:05:07.630
about that part of the molecule,

00:05:07.630 --> 00:05:10.890
that hydrogen part that has
a partially positive charge

00:05:10.890 --> 00:05:13.220
being attracted to the
partially negative end

00:05:13.220 --> 00:05:14.670
of another molecule.

00:05:14.670 --> 00:05:18.130
So it's really about a bond
dipole with hydrogen bonds

00:05:18.130 --> 00:05:20.580
versus a total molecular dipole

00:05:20.580 --> 00:05:23.870
when we talk about dipole-dipole
interactions in general.

00:05:23.870 --> 00:05:25.200
And so you could imagine,

00:05:25.200 --> 00:05:27.170
it doesn't even just
have to be hydrogen bonds

00:05:27.170 --> 00:05:29.170
between a like molecule.

00:05:29.170 --> 00:05:31.750
You could have hydrogen bonds
between an ammonia molecule

00:05:31.750 --> 00:05:34.110
and a water molecule or
between a water molecule

00:05:34.110 --> 00:05:36.430
and a hydrogen fluoride molecule.

00:05:36.430 --> 00:05:40.630
And I mentioned that these are
really important in biology.

00:05:40.630 --> 00:05:43.890
This right over here is a closeup of DNA.

00:05:43.890 --> 00:05:46.700
You can see that the base pairs in DNA,

00:05:46.700 --> 00:05:48.550
you can imagine the rungs of the ladder,

00:05:48.550 --> 00:05:52.940
those are formed by hydrogen
bonds between base pairs.

00:05:52.940 --> 00:05:54.930
So those hydrogen bonds are strong enough

00:05:54.930 --> 00:05:57.170
to keep that double helix together,

00:05:57.170 --> 00:05:58.750
but then they're not so strong

00:05:58.750 --> 00:06:00.690
that they can't be pulled apart

00:06:00.690 --> 00:06:04.870
when it's time to replicate
or transcribe the DNA.

00:06:04.870 --> 00:06:07.830
Hydrogen bonds are also
a big deal in proteins.

00:06:07.830 --> 00:06:10.370
You learn in biology class
that proteins are made up

00:06:10.370 --> 00:06:12.290
of chains of amino acids,

00:06:12.290 --> 00:06:13.910
and the function is heavily influenced

00:06:13.910 --> 00:06:15.620
by the shape of that protein.

00:06:15.620 --> 00:06:19.280
And that shape is
influenced by hydrogen bonds

00:06:19.280 --> 00:06:22.300
that might form between the amino acids

00:06:22.300 --> 00:06:24.720
that make up the protein.

00:06:24.720 --> 00:06:27.040
So hydrogen bonds are everywhere.

00:06:27.040 --> 00:06:30.130
There are many hydrogen bonds
in your body right now mainly,

00:06:30.130 --> 00:06:31.290
not just because of the DNA,

00:06:31.290 --> 00:06:33.360
mainly because you're mostly water.

00:06:33.360 --> 00:06:36.450
So life, as we know it, would not exist

00:06:36.450 --> 00:06:38.353
without hydrogen bonds.


Intermolecular forces and vapor pressure

WEBVTT
Kind: captions
Language: en

00:00:00.630 --> 00:00:03.270
- [Instructor] So we have
four different molecules here.

00:00:03.270 --> 00:00:04.350
And what I want you to think about,

00:00:04.350 --> 00:00:05.860
if you had a pure sample of each,

00:00:05.860 --> 00:00:07.280
which of those pure samples would have

00:00:07.280 --> 00:00:09.460
the highest boiling point, second highest,

00:00:09.460 --> 00:00:11.400
third highest, and fourth highest?

00:00:11.400 --> 00:00:14.180
Pause this video, and
try to figure that out.

00:00:14.180 --> 00:00:16.380
All right, now to figure that out,

00:00:16.380 --> 00:00:17.780
it really just boils down to

00:00:17.780 --> 00:00:20.450
which of these has the
highest intermolecular forces

00:00:20.450 --> 00:00:21.910
when they're in a liquid state?

00:00:21.910 --> 00:00:24.160
Because if you have high
intermolecular forces,

00:00:24.160 --> 00:00:27.480
it would take a lot of energy
or a higher boiling point

00:00:27.480 --> 00:00:30.120
to really overcome those
intermolecular forces

00:00:30.120 --> 00:00:32.420
and get to a gas state.

00:00:32.420 --> 00:00:34.790
So let's think about the
intermolecular forces

00:00:34.790 --> 00:00:35.950
that we have studied.

00:00:35.950 --> 00:00:38.800
So I will start with hydrogen bonds,

00:00:38.800 --> 00:00:41.630
hydrogen bonds.

00:00:41.630 --> 00:00:42.850
'Cause you could really view those,

00:00:42.850 --> 00:00:46.620
those are the strongest of the
dipole-dipole interactions,

00:00:46.620 --> 00:00:48.040
and they're going to be stronger

00:00:48.040 --> 00:00:50.340
than your London dispersion forces.

00:00:50.340 --> 00:00:53.370
We can see that diethyl ether
won't form hydrogen bonds.

00:00:53.370 --> 00:00:56.040
We don't see any bonds between hydrogen

00:00:56.040 --> 00:00:59.130
and an oxygen, a nitrogen, or a fluorine.

00:00:59.130 --> 00:01:02.440
Ethanol has one oxygen-hydrogen bond.

00:01:02.440 --> 00:01:05.850
Methanol also has one
oxygen-hydrogen bond.

00:01:05.850 --> 00:01:09.900
Water has two oxygen-hydrogen bonds.

00:01:09.900 --> 00:01:12.340
So if I had to rank the
hydrogen bond contribution

00:01:12.340 --> 00:01:13.730
to the intermolecular forces,

00:01:13.730 --> 00:01:15.570
I would put water as number one

00:01:15.570 --> 00:01:18.210
'cause it can form the
most hydrogen bonds.

00:01:18.210 --> 00:01:22.090
I would put methanol and
ethanol as a tie for second.

00:01:22.090 --> 00:01:24.530
And then I would put diethyl ether last

00:01:24.530 --> 00:01:26.330
'cause it can't form hydrogen bonds.

00:01:26.330 --> 00:01:28.240
So just looking at this,

00:01:28.240 --> 00:01:30.800
I know that water's going to
have the highest boiling point.

00:01:30.800 --> 00:01:33.480
Diethyl ether is going to
have the lowest boiling point.

00:01:33.480 --> 00:01:37.080
But what about the difference
between methanol and ethanol?

00:01:37.080 --> 00:01:40.530
And we could think about
other types of dipole forces,

00:01:40.530 --> 00:01:43.740
but not a lot that you could
intuit just by eyeballing them.

00:01:43.740 --> 00:01:45.890
They might actually have
similar dipole moments

00:01:45.890 --> 00:01:47.310
on a molecular basis.

00:01:47.310 --> 00:01:50.170
But we can think about
London dispersion forces.

00:01:50.170 --> 00:01:51.270
I'll do this in a different color.

00:01:51.270 --> 00:01:54.130
So London dispersion forces.

00:01:54.130 --> 00:01:55.740
And if we're just trying to,

00:01:55.740 --> 00:01:57.740
actually I'll rank all of them.

00:01:57.740 --> 00:02:00.747
So London dispersion
forces are proportional to

00:02:00.747 --> 00:02:03.430
how polarizable a molecule is,

00:02:03.430 --> 00:02:05.850
which is proportional to how
large its electron cloud is,

00:02:05.850 --> 00:02:07.630
which is proportional to its molar mass.

00:02:07.630 --> 00:02:09.440
And it's clear that diethyl ether

00:02:09.440 --> 00:02:11.190
has the highest molar mass,

00:02:11.190 --> 00:02:12.810
followed by ethanol,

00:02:12.810 --> 00:02:15.310
followed by methanol,

00:02:15.310 --> 00:02:16.500
followed by water.

00:02:16.500 --> 00:02:17.660
How did I know that?

00:02:17.660 --> 00:02:19.710
Well, you literally can take atoms away

00:02:19.710 --> 00:02:23.630
from the diethyl ether
to get to an ethanol.

00:02:23.630 --> 00:02:25.040
And you can literally take atoms away

00:02:25.040 --> 00:02:26.670
from that to get to a methanol.

00:02:26.670 --> 00:02:28.020
And you can literally take atoms away

00:02:28.020 --> 00:02:29.610
from that to get to a water.

00:02:29.610 --> 00:02:33.630
So we know that this is
the order of molar mass.

00:02:33.630 --> 00:02:35.900
And so London dispersion forces,

00:02:35.900 --> 00:02:37.750
I wouldn't make that change the ranking

00:02:37.750 --> 00:02:40.260
between water or diethyl
ether because these are going

00:02:40.260 --> 00:02:42.530
to be a lot weaker than
those hydrogen bonds.

00:02:42.530 --> 00:02:44.530
But they can be useful for the tiebreaker

00:02:44.530 --> 00:02:46.790
between ethanol and methanol.

00:02:46.790 --> 00:02:49.790
And so my overall ranking
on boiling points,

00:02:49.790 --> 00:02:52.980
the highest boiling point
I would put would be water,

00:02:52.980 --> 00:02:56.630
followed by, since ethanol
won the tiebreaker,

00:02:56.630 --> 00:02:58.510
followed by ethanol,

00:02:58.510 --> 00:03:01.320
followed by methanol,

00:03:01.320 --> 00:03:04.650
and then the lowest boiling
point would be diethyl ether.

00:03:04.650 --> 00:03:06.660
And if we look at the actual data,

00:03:06.660 --> 00:03:10.060
it's consistent with what
we just talked about.

00:03:10.060 --> 00:03:11.430
We can see very clearly

00:03:11.430 --> 00:03:13.520
that water has the highest boiling point,

00:03:13.520 --> 00:03:14.920
ethanol is second,

00:03:14.920 --> 00:03:16.270
methanol is third,

00:03:16.270 --> 00:03:18.570
and diethyl ether was fourth,

00:03:18.570 --> 00:03:21.550
completely consistent with our intuition.

00:03:21.550 --> 00:03:23.160
Now, what's also interesting here,

00:03:23.160 --> 00:03:25.980
you might have noticed, is this
thing called vapor pressure.

00:03:25.980 --> 00:03:29.960
And you might have also noticed
that vapor pressure seems

00:03:29.960 --> 00:03:32.430
to trend the opposite
way as boiling point.

00:03:32.430 --> 00:03:34.110
The things that have
the high boiling point

00:03:34.110 --> 00:03:35.500
have the low vapor pressure,

00:03:35.500 --> 00:03:37.510
and the things that have
the low boiling point

00:03:37.510 --> 00:03:39.520
have a high vapor pressure.

00:03:39.520 --> 00:03:41.130
So what are we talking about, why,

00:03:41.130 --> 00:03:44.870
about vapor pressure, and why
do we see this relationship?

00:03:44.870 --> 00:03:47.040
And I'm not going to go
deep into vapor pressure.

00:03:47.040 --> 00:03:49.260
There'll be other videos
on that on Khan Academy.

00:03:49.260 --> 00:03:51.290
But just to get you a sense,

00:03:51.290 --> 00:03:54.670
imagine a closed container here.

00:03:54.670 --> 00:03:56.990
And I put one of these,

00:03:56.990 --> 00:03:59.370
a sample of one of these
molecules in a liquid state,

00:03:59.370 --> 00:04:00.820
and I'm gonna just draw the molecules,

00:04:00.820 --> 00:04:04.890
clearly not drawn to scale,
as these little circles.

00:04:04.890 --> 00:04:06.850
And the temperature matters,

00:04:06.850 --> 00:04:10.000
so let's say that this
is at 20 degrees Celsius.

00:04:10.000 --> 00:04:11.880
Now, you might notice,
at 20 degrees Celsius,

00:04:11.880 --> 00:04:13.460
it's lower than the boiling point

00:04:13.460 --> 00:04:15.820
of all of these characters.

00:04:15.820 --> 00:04:18.770
So for the most part, they're
going to be in a liquid state,

00:04:18.770 --> 00:04:22.870
but we know that not every one
of these molecules is moving

00:04:22.870 --> 00:04:25.050
with the exact same kinetic energy.

00:04:25.050 --> 00:04:26.840
The temperature, you
could view as a measure

00:04:26.840 --> 00:04:29.400
of the average kinetic
energy of the molecules,

00:04:29.400 --> 00:04:31.690
but they're all bumping
around into each other,

00:04:31.690 --> 00:04:34.930
in different positions, with
different amounts of velocities

00:04:34.930 --> 00:04:36.710
and therefore different kinetic energies.

00:04:36.710 --> 00:04:40.490
And so every now and then,
you're going to have a molecule

00:04:40.490 --> 00:04:43.320
that has the right position
and the right kinetic energy

00:04:43.320 --> 00:04:47.190
to escape and get into the vapor state,

00:04:47.190 --> 00:04:48.940
into a gaseous state.

00:04:48.940 --> 00:04:51.120
And so that's going to keep happening.

00:04:51.120 --> 00:04:53.270
But then the things that
are in the gaseous state,

00:04:53.270 --> 00:04:55.020
every now and then they're
bumping into each other,

00:04:55.020 --> 00:04:57.200
and they're bumping into
the sides of the container.

00:04:57.200 --> 00:04:58.280
And every now and then,

00:04:58.280 --> 00:05:00.660
they might approach the surface

00:05:00.660 --> 00:05:03.730
with the right kinetic energy,
with the right position,

00:05:03.730 --> 00:05:06.430
so that they get recaptured
by the intermolecular forces

00:05:06.430 --> 00:05:07.720
and enter a liquid state.

00:05:07.720 --> 00:05:09.840
And so you can imagine,
this will keep happening

00:05:09.840 --> 00:05:13.130
where things go from liquid,
and then they go to vapor.

00:05:13.130 --> 00:05:15.710
But then when that vapor gets high enough

00:05:15.710 --> 00:05:17.900
or when you could say the vapor
pressure gets high enough,

00:05:17.900 --> 00:05:19.260
remember, that pressure's just from

00:05:19.260 --> 00:05:21.210
the vapor molecules bouncing around,

00:05:21.210 --> 00:05:24.320
then you will get to some
form of an equilibrium.

00:05:24.320 --> 00:05:25.620
And you could imagine,

00:05:25.620 --> 00:05:28.220
the things that have
a lower boiling point,

00:05:28.220 --> 00:05:30.840
that means they have lower
intermolecular forces,

00:05:30.840 --> 00:05:33.280
more of the vapor is going to form,

00:05:33.280 --> 00:05:35.630
and so you're going to have
a higher vapor pressure

00:05:35.630 --> 00:05:37.470
before you get to equilibrium.

00:05:37.470 --> 00:05:40.730
On the other hand, things with
high intermolecular forces,

00:05:40.730 --> 00:05:43.750
fewer of those molecules
are going to break away,

00:05:43.750 --> 00:05:46.100
and so you're going to
have a lower vapor pressure

00:05:46.100 --> 00:05:48.550
when you get to that equilibrium.

00:05:48.550 --> 00:05:51.220
And you can see that very clearly here.

00:05:51.220 --> 00:05:52.820
So I will leave you there.

00:05:52.820 --> 00:05:54.330
We got a little bit of practice,

00:05:54.330 --> 00:05:56.010
seeing everything we've seen so far,

00:05:56.010 --> 00:05:58.700
and we learned a little
bit about vapor pressure

00:05:58.700 --> 00:06:01.940
and how that relates to
intermolecular forces

00:06:01.940 --> 00:06:02.843
and boiling point.


Ion–dipole forces

WEBVTT
Kind: captions
Language: en

00:00:00.450 --> 00:00:01.283
- [Instructor] Let's talk a little bit

00:00:01.283 --> 00:00:03.950
about ion-dipole forces.

00:00:03.950 --> 00:00:05.697
And before we think about how ions

00:00:05.697 --> 00:00:07.480
and dipoles might interact,

00:00:07.480 --> 00:00:09.190
let's just remind ourselves

00:00:09.190 --> 00:00:12.610
what the difference is
between ions and dipoles.

00:00:12.610 --> 00:00:14.020
And I encourage you to pause this video

00:00:14.020 --> 00:00:15.580
and try to refresh your own memory

00:00:15.580 --> 00:00:17.580
before we refresh our memories together.

00:00:18.710 --> 00:00:21.920
All right, now let's
first think about ions.

00:00:21.920 --> 00:00:26.920
Ions are atoms or molecules
that have a net charge.

00:00:27.250 --> 00:00:32.250
So for example, when
chlorine gains an electron

00:00:32.430 --> 00:00:35.060
and becomes the chloride ion,

00:00:35.060 --> 00:00:39.320
it's an ion because it now
has a net negative charge.

00:00:39.320 --> 00:00:42.910
Similarly, when sodium loses an electron,

00:00:42.910 --> 00:00:45.070
it now has a net positive charge.

00:00:45.070 --> 00:00:48.310
So this is the sodium ion.

00:00:48.310 --> 00:00:50.930
Now what's the difference
between that and a dipole?

00:00:50.930 --> 00:00:53.900
Well, generally speaking when
we're talking about dipoles,

00:00:53.900 --> 00:00:55.420
we're not talking about something

00:00:55.420 --> 00:00:57.910
that has necessarily a net charge,

00:00:57.910 --> 00:01:01.587
we're talking about something
where the charge is separated

00:01:01.587 --> 00:01:04.030
on different ends of the molecule,

00:01:04.030 --> 00:01:05.660
that you have a partially positive end

00:01:05.660 --> 00:01:08.000
and you have a partial negative end,

00:01:08.000 --> 00:01:12.220
that there is a molecular dipole moment.

00:01:12.220 --> 00:01:16.400
And a good example of a
molecule that is a dipole

00:01:16.400 --> 00:01:20.980
or has a dipole moment at
a molecular level is water.

00:01:20.980 --> 00:01:24.030
Water is a very polar molecule.

00:01:24.030 --> 00:01:26.320
We've talked about this many times.

00:01:26.320 --> 00:01:30.510
You have your oxygen which
is quite electronegative,

00:01:30.510 --> 00:01:32.770
covalently bonded to two hydrogens,

00:01:32.770 --> 00:01:34.740
and those are really polar covalent bonds

00:01:34.740 --> 00:01:37.090
because the oxygen's so
much more electronegative

00:01:37.090 --> 00:01:40.200
that it hogs the electrons,
it's selfish of the electrons.

00:01:40.200 --> 00:01:43.470
And since the electrons spend
more time around the oxygen

00:01:43.470 --> 00:01:45.880
than around the hydrogen,

00:01:45.880 --> 00:01:47.460
you have a partial negative charge

00:01:47.460 --> 00:01:48.730
at this end of the molecule

00:01:48.730 --> 00:01:50.960
and you have partial positive charges

00:01:50.960 --> 00:01:53.060
at the other end of the molecules.

00:01:53.060 --> 00:01:54.310
And we describe this

00:01:54.310 --> 00:01:56.210
when we talked about hydrogen bonding

00:01:56.210 --> 00:01:59.670
where the partial negative
end of one water molecule

00:01:59.670 --> 00:02:02.330
would be attracted to
the partial positive end

00:02:02.330 --> 00:02:04.160
of another water molecule.

00:02:04.160 --> 00:02:06.670
But, as we've talked
about, hydrogen bonds,

00:02:06.670 --> 00:02:08.550
which are an intermolecular force

00:02:08.550 --> 00:02:12.570
are just a special case of dipole forces.

00:02:12.570 --> 00:02:14.600
Things that are able
to form hydrogen bonds

00:02:14.600 --> 00:02:16.820
just have a very strong dipole moment,

00:02:16.820 --> 00:02:19.950
because you have hydrogen
bonded to an oxygen,

00:02:19.950 --> 00:02:23.840
a nitrogen, and a fluorine,
that is quite electronegative.

00:02:23.840 --> 00:02:26.760
So now that we know the difference
between ions and dipoles,

00:02:26.760 --> 00:02:28.690
how might they interact?

00:02:28.690 --> 00:02:31.730
Well you might guess
Coulomb forces are at play.

00:02:31.730 --> 00:02:36.290
The partial negative end of
a dipole would be attracted

00:02:36.290 --> 00:02:38.450
to a positively charged ion.

00:02:38.450 --> 00:02:41.430
And I have prearranged
these water molecules

00:02:41.430 --> 00:02:43.750
so that you have the partial negative end

00:02:43.750 --> 00:02:48.127
is facing towards this
sodium positive ion.

00:02:48.127 --> 00:02:50.490
And so what I'm drawing right over here,

00:02:50.490 --> 00:02:54.200
these are ion-dipole forces.

00:02:54.200 --> 00:02:59.060
Similarly, if you have a chloride
anion, or a negative ion,

00:02:59.060 --> 00:03:02.260
well then the partially
positive ends of the dipoles

00:03:02.260 --> 00:03:04.010
are going to be attracted,

00:03:04.010 --> 00:03:07.740
and so water might
arrange itself in this way

00:03:07.740 --> 00:03:11.350
where the partial positive ends,
the ends with the hydrogen,

00:03:11.350 --> 00:03:13.530
are facing the chlorine.

00:03:13.530 --> 00:03:15.070
And this is one of the reasons

00:03:15.070 --> 00:03:19.010
why it's so easy to
dissolve sodium chloride,

00:03:19.010 --> 00:03:22.120
to dissolve table salt in water.

00:03:22.120 --> 00:03:24.760
Those ions are able to separate

00:03:24.760 --> 00:03:27.800
and be attracted to the water
molecules which are polar,

00:03:27.800 --> 00:03:30.933
which have molecular dipoles.

00:03:30.933 --> 00:03:34.610
Now, if I were to ask you what's
gonna dictate the strength

00:03:34.610 --> 00:03:38.780
of the ion-dipole
forces, think about that.

00:03:38.780 --> 00:03:42.160
Pause this video, and what do
you think is going to matter?

00:03:42.160 --> 00:03:44.950
Well, as you can imagine,
these are Coulomb forces.

00:03:44.950 --> 00:03:47.420
So the strength of the charges matter.

00:03:47.420 --> 00:03:50.260
So you're gonna have a
stronger ion-dipole force

00:03:50.260 --> 00:03:53.570
if you have stronger charges on the ions.

00:03:53.570 --> 00:03:56.710
So instead of a sodium
with a positive one charge,

00:03:56.710 --> 00:04:00.410
if you had a calcium ion that
had a positive two charge,

00:04:00.410 --> 00:04:03.070
then the partially negative
ends of the water molecules

00:04:03.070 --> 00:04:05.000
would be even more strongly attracted.

00:04:05.000 --> 00:04:08.160
You would have stronger ion-dipole forces.

00:04:08.160 --> 00:04:10.660
Similarly if you have
stronger dipole moments,

00:04:10.660 --> 00:04:13.890
that will also make the
ion-dipole forces stronger,

00:04:13.890 --> 00:04:14.890
or vice versa.

00:04:14.890 --> 00:04:17.200
If you had a molecule that
had a weaker dipole moment,

00:04:17.200 --> 00:04:21.180
you're not going to have as
strong ion-dipole forces.

00:04:21.180 --> 00:04:22.990
Coulomb forces are inversely proportional

00:04:22.990 --> 00:04:24.940
to the distance between the charges.

00:04:24.940 --> 00:04:28.490
So you're also going to have
stronger ion-dipole forces

00:04:28.490 --> 00:04:31.730
the closer that these
things get to each other.

00:04:31.730 --> 00:04:33.400
But to some degree that's true of a lot

00:04:33.400 --> 00:04:36.060
of the intermolecular
forces we've talked about,

00:04:36.060 --> 00:04:38.933
because on some level they
are all Coulomb forces.