HTTP and HTML

WEBVTT
Kind: captions
Language: en

00:00:07.826 --> 00:00:08.894
- I'm Jasmine Lawrence

00:00:08.894 --> 00:00:10.291
and I'm a Program Manager

00:00:10.291 --> 00:00:12.675
on the Xbox One engineering team.

00:00:13.863 --> 00:00:16.956
One of our biggest features
is called Xbox Live.

00:00:16.956 --> 00:00:19.260
It's an online service
that connects gamers

00:00:19.260 --> 00:00:20.991
from all around the world,

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and we rely on the internet
to make that happen.

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This is no easy task and there are a lot

00:00:26.591 --> 00:00:29.939
of things happening behind the scenes.

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The internet is totally changing

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how people interact and connect.

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But how does it work?

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How do the computers all across the world

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actually communicate with each other?

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Let's look at web browsing.

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First, you open a web browser.

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It's the app you use to
access the web pages.

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Next, you type in the web address, or URL,

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which stands for Uniform Resource Locator,

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of a website you want to
visit like Tumblr.com.

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(upbeat electronic music)

00:01:04.354 --> 00:01:06.537
- Hi, I'm David Karp,
the founder of Tumblr,

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and we're here today to talk about

00:01:07.725 --> 00:01:09.987
how those web browsers we use every day

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actually work.

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So you've probably wondered what

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actually happens when you type an address

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into your web browser and then hit enter,

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and it really is about as
crazy as you can imagine.

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So in that moment,

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your computer starts
talking to another computer

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called a server

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that's usually thousands of miles away,

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and in milliseconds your computer

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asks that server for a website,

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and that server starts to talk back

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to your computer in a
language called HTTP.

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HTTP stands for Hypertext
Transfer Protocol.

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You can kind of think of it

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as the language that one computer uses

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to ask another computer for a document.

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It's actually really
pretty straightforward.

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If you were to intercept

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the conversation between your computer

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and a web server on the internet,

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it's mainly made up of something

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called "GET" requests.

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And those are really very
simply the word "GET"

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and then the name of the document

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that you're requesting.

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So if you're trying to log into Tumblr

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and load our login page,

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all you're doing is sending a GET request

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to Tumblr's server

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that says "GET /login"

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and that tells Tumblr's server that

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you want all of the HTML code

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for the Tumblr login page.

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HTML stands for HyperText Markup Language

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and you can think of that
as the language you use

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to tell a web browser
how to make a page look.

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So if you think about
something like Wikipedia,

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which is really just
a big simple document,

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and HTML is the language that you use

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to make that title big and bold,

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to make the font the right font,

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to link certain text
to certain other pages,

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to make some text bold,

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to make some text italic,

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to put an image in the middle of the page,

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to align the image to the right,

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to align the image to the left.

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- The text of a web page is included

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directly in the HTML,

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but other parts, images or videos,

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are separate files with their own URLs

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that need to be requested.

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The browser sends separate HTTP requests

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for each of these and
displays them as they arrive.

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If a web page has a lot
of different images,

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each of them causes a
separate HTTP request

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and the page loads slower.

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Now sometimes when you browse the web,

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you're not just requesting pages

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with GET requests.

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Sometimes you send information,

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like when you fill out a
form or type a search query.

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Your browser sends this information

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in plain text to the web server

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using an HTTP post request.

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- So let's say you log in to Tumblr.

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The first thing you do
is make a "POST" request

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That is, a "POST" to Tumblr's login page

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that has some data attached to it.

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It has your email address,
it has your password.

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That goes to Tumblr's server.

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Tumblr's server figures out
that, okay, you're David.

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It sends a web page back to your browser

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that says, "Success! Logged in as David."

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But along with that web page,

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it also attaches a little
bit of invisible cookie data

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that your browser sees and knows to save,

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and that's really important because

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it's really the only way that a website

00:04:09.746 --> 00:04:12.056
can remember who you are.

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All that cookie data really is

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is an ID card for Tumblr.

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It's a number that
identifies you as David.

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Your web browser holds onto that number,

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and then the next time you refresh Tumblr,

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the next time you go to Tumblr.com,

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your web browser knows to automatically

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attach that ID number with the request

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that it sends over to Tumblr's server,

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so now Tumblr's server sees the request

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coming from your browser,
sees the ID number,

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and knows, okay, this
is a request from David.

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- Now, the internet is completely open,

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all of its connections are shared,

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and information is sent in plain text.

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This makes it possible for hackers

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to snoop on any personal information

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that you send over the internet,

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but safe websites prevent this

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by asking your web browser

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to communicate on a secure channel

00:05:01.045 --> 00:05:03.962
using something called
Secure Sockets Layer

00:05:03.962 --> 00:05:07.510
and its successor
Transport Layer Security.

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You can think of SSL and
TLS as a layer of security

00:05:11.949 --> 00:05:14.219
wrapped around your communications

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to protect them from
snooping or tampering.

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SSL and TLS are active when
you see the little lock

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that appears in your browser address bar

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next to the HTTPS.

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The HTTPS protocols ensure that your

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HTTP requests are secure and protected.

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When a website asks your browser

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to engage in a secure connection,

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it first provides a digital certificate,

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which is like an official ID card

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proving that it's the
website it claims to be.

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Digital certificates are published

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by certificate authorities,

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which are trusted entities
that verify the identities

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of websites and issue
certificates for them,

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just like a government can
issue IDs or passports.

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Now, if a website tries to
start a secure connection

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without a properly issued
digital certificate,

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your browser will warn you.

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That's the basics of web browsing,

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the part of the internet
we see day to day.

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To summarize, HTTP and DNS manage

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the sending and receiving of HTML,

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media files, or anything on the web.

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What makes this possible under the hood

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are TCP/IP and router networks

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that break down and transport information

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in small packets.

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Those packets themselves
are made up of binary,

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sequences of ones and zeros

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that are physically sent
through electric wires,

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fiber optic cables, and wireless networks.

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Fortunately, once you've
learned how one layer

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of the internet works, you can rely on it

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without remembering all the details.

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We can trust that all those
layers will work together

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to successfully deliver information

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at scale and with reliability.


Wires, cables, and WiFi

WEBVTT
Kind: captions
Language: en

00:00:02.235 --> 00:00:07.235
(upbeat music)

00:00:10.172 --> 00:00:11.448
- My name is Tess Winlock.

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I'm a software engineer at Google.

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Here's a question.

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How does a picture, text message, or email

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get sent from one device to another?

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It isn't magic.

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It's the Internet, a
tangible, physical system

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that was made to move information.

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The Internet is a lot
like the postal service,

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but the physical stuff that gets sent

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is a little bit different.

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Instead of boxes and envelopes,

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the Internet ships binary information.

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Information is made of bits.

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A bit can be described
as any pair of opposites,

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on or off, yes or no.

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We typically use a one, meaning on,

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or a zero, meaning off.

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Because a bit has two possible states,

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we call it binary code.

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Eight bits strung together makes one byte.

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One thousand bytes all
together is a kilobyte.

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One thousand kilobytes is a megabyte.

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A song is typically encoded using about

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three to four megabytes.

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It doesn't matter if it's a
picture, a video, or a song.

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Everything on the Internet is represented

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and sent around as bits.

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These are the atoms of information,

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but it's not like we're physically sending

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ones and zeroes from one place to another

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one person to another.

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So, what is the physical
stuff that actually gets sent

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over the wires and the airwaves?

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Well, let's look at a small
example here of how humans

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can physically communicate
to send a single bit

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of information from one place to another.

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So say that we could
turn on a light for a one

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or off for zero or use beeps

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or similar sort of things
of like Morse code.

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These methods work, but
they're really slow, error prone,

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and totally dependent upon humans.

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What we really need is a machine.

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Throughout history, we've
built many systems that can

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actually send this binary information

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through different types
of physical mediums.

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Today, we physically send bits

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by electricity, light, and radio waves.

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(electricity humming)

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To send a bit via electricity,

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imagine that you have two light bulbs

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connected by a copper wire.

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If one device operator
turns on the electricity,

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then the light bulb lights up.

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No electricity, no light.

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If the operators on both ends
agree that light on means one

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and light off means zero,

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then we have a system for
sending bits of information

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from one person to
another using electricity.

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They have kind of a small problem.

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If you need to send a
zero five times in a row,

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well, how can you do that in such a way

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that either person can actually
count the number of zeroes?

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Well, the solution is to
introduce a clock or a timer.

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The operators can agree that
the sender will send one bit

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per second, and the receiver
will sit down and record

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every single second and
see what's on the line.

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To send five zeros in a row,

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you just turn off the
light, wait five seconds.

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The person on the other end
of the line will write down

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all five seconds, fives ones in a row.

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Switch it on.

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Five seconds, write down every second.

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Obviously, we'd like to send
things a little bit faster than

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one bit per second, so we need
to increase our bandwidth,

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the maximum transmission
capacity of a device.

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Bandwidth is measured by bitrate,

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which is the number of bits
that we can actually send

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over a given period of time,
usually measured in seconds.

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A different measure of
speed is the latency,

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or the amount of time it
takes for one bit to travel

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from one place to another,

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from the source to the requesting device.

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In our human analogy, one bit
per second was pretty fast,

00:03:25.054 --> 00:03:27.051
but kind of hard for a
human to keep up with.

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So let's say that you
wanna actually download

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a three megabyte song in three seconds.

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At 8,000,0000 bits per megabyte,

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that means a bitrate of about
8,000,000 bits per second.

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Obviously, humans can't send or receive

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8,000,000 bits per second,

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but a machine can do that just fine,

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but now there's also a
question of what sort of cable

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to send these messages over

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and how far the signals can go.

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With an Ethernet wire,

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the kind that you find in
your home or office or school,

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you see measurable signal
loss or interference

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over just a few hundred feet.

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For the Internet to work
all around the world,

00:04:00.012 --> 00:04:02.654
we need to have an alternative
method to send bits

00:04:02.654 --> 00:04:04.473
really long distances.

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We're talking across oceans.

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So what else can we use?

00:04:07.818 --> 00:04:09.894
Well, what do we know
that moves a lot faster

00:04:09.894 --> 00:04:12.574
than just electricity through a wire?

00:04:12.574 --> 00:04:13.716
Light.

00:04:14.771 --> 00:04:16.284
We can actually send bits as light beams

00:04:16.284 --> 00:04:19.302
from one place to another
using a fiber optic cable.

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A fiber optic cable is a thread of glass

00:04:21.047 --> 00:04:23.249
engineered to reflect light.

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When you send a beam of
light down the cable,

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light bounces up and down
the length of the cable

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until it is received on the other end.

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Depending on the bounce angle,

00:04:30.842 --> 00:04:33.430
we can actually send
multiple bits simultaneously,

00:04:33.430 --> 00:04:35.683
all of them traveling
at the speed of light,

00:04:35.683 --> 00:04:39.102
so fiber is really, really
fast, but, more importantly,

00:04:39.102 --> 00:04:41.446
the signal doesn't really
degrade over long distances.

00:04:41.446 --> 00:04:43.369
This is how you can go hundreds of miles

00:04:43.369 --> 00:04:44.354
without signal loss.

00:04:44.354 --> 00:04:46.602
This is why we use fiber optic cables

00:04:46.602 --> 00:04:50.467
across the ocean floors to
connect one continent to another.

00:04:51.180 --> 00:04:53.387
In 2008, there was a cable
that was actually cut near

00:04:53.387 --> 00:04:56.362
Alexandria, Egypt, which
really interrupted the Internet

00:04:56.362 --> 00:04:59.098
for most of the Middle East and India.

00:04:59.098 --> 00:05:00.596
So we take this Internet
thing for granted,

00:05:00.596 --> 00:05:03.777
but it's really a pretty
fragile physical system,

00:05:03.777 --> 00:05:05.983
and fiber is awesome, but
it's also really expensive

00:05:05.983 --> 00:05:07.282
and hard to work with.

00:05:07.282 --> 00:05:10.134
Form most purposes, you're
gonna find copper cable.

00:05:11.225 --> 00:05:12.909
But how do we move things without wires?

00:05:12.909 --> 00:05:15.080
How do we send things wirelessly?

00:05:16.072 --> 00:05:19.364
Wireless bit sending machines
typically use radio signal

00:05:19.364 --> 00:05:21.980
to send bits from one place to another.

00:05:21.980 --> 00:05:25.884
The machines have to actually
translate the ones and zeroes

00:05:25.884 --> 00:05:28.649
into radio waves of different frequencies.

00:05:28.649 --> 00:05:30.925
The receiving machines reverse the process

00:05:30.925 --> 00:05:33.682
and convert back into
binary on your computer.

00:05:33.682 --> 00:05:35.951
So wireless has made our Internet mobile,

00:05:35.951 --> 00:05:38.273
but a radio signal doesn't
travel all that far

00:05:38.273 --> 00:05:40.630
before it completely gets garbled.

00:05:40.630 --> 00:05:42.392
This is why you can't
really pick up a Los Angeles

00:05:42.392 --> 00:05:44.506
radio station in Chicago.

00:05:45.669 --> 00:05:46.865
As great as wireless is,

00:05:46.865 --> 00:05:48.870
today it still relies
on the wired Internet.

00:05:48.870 --> 00:05:50.432
If you're in a coffee shop using Wi-Fi,

00:05:50.432 --> 00:05:53.127
then the bits get sent
through this wireless router

00:05:53.127 --> 00:05:54.966
and then are transferred
to the physical wire

00:05:54.966 --> 00:05:58.236
to travel the really long
distances of the Internet.

00:05:58.236 --> 00:06:00.302
The physical method for
sending bits may change

00:06:00.302 --> 00:06:03.006
in the future, whether it's
laser sent between satellites

00:06:03.006 --> 00:06:05.624
or radio waves from balloons or drones,

00:06:05.624 --> 00:06:08.333
but the underlying binary
representation of information

00:06:08.333 --> 00:06:10.627
and the protocols for
sending that information

00:06:10.627 --> 00:06:12.589
and receiving that
information have pretty much

00:06:12.589 --> 00:06:13.831
stayed the same.

00:06:13.831 --> 00:06:15.991
Everything on the Internet,
whether its words, emails,

00:06:15.991 --> 00:06:18.371
images, cat videos, puppy videos,

00:06:18.371 --> 00:06:20.873
all come down to these ones
and zeroes being delivered

00:06:20.873 --> 00:06:24.158
by electronic pulses,
light beams, radio waves,

00:06:24.158 --> 00:06:26.535
and lots and lots of love.

00:06:26.535 --> 00:06:31.535
(upbeat music)


Area of a circle

WEBVTT
Kind: captions
Language: en

00:00:00.830 --> 00:00:03.620
- [Teacher] A candy machine
creates small chocolate wafers

00:00:03.620 --> 00:00:06.130
in the shape of circular discs.

00:00:06.130 --> 00:00:11.130
The diameter, the diameter of
each wafer is 16 millimeters.

00:00:11.130 --> 00:00:13.660
What is the area of each candy?

00:00:13.660 --> 00:00:17.570
So, the candy, they say it's
the shape of circular discs.

00:00:17.570 --> 00:00:19.250
And they tell us that the diameter

00:00:19.250 --> 00:00:20.890
of each wafer is 16 millimeters.

00:00:20.890 --> 00:00:23.330
So if I draw a line across the circle

00:00:23.330 --> 00:00:26.830
that goes through the center,
the length of that line

00:00:26.830 --> 00:00:28.230
all the way across the circle

00:00:28.230 --> 00:00:30.800
through the center is 16 millimeters.

00:00:30.800 --> 00:00:34.130
So let me write that, so
diameter, the diameter

00:00:34.130 --> 00:00:39.130
here is 16 millimeters and
they want us to figure out

00:00:39.690 --> 00:00:42.770
the area, the area of the
surface of this candy.

00:00:42.770 --> 00:00:45.990
Or essentially the area of this circle.

00:00:45.990 --> 00:00:47.700
And so when we think about area,

00:00:47.700 --> 00:00:51.170
we know that the area of a
circle, the area of a circle

00:00:51.170 --> 00:00:55.730
is equal to pi times the
radius of the circle squared.

00:00:55.730 --> 00:00:57.700
Times the radius of the circle squared,

00:00:57.700 --> 00:00:59.690
and you say, well they
gave us the diameter,

00:00:59.690 --> 00:01:01.240
what is the radius?

00:01:01.240 --> 00:01:03.120
Well, you might remember the radius

00:01:03.120 --> 00:01:05.440
is half of diameter, so
distance from the center

00:01:05.440 --> 00:01:09.270
of the circle to the outside,
to the boundary of the circle.

00:01:09.270 --> 00:01:11.750
So it would be this
distance right over here,

00:01:11.750 --> 00:01:13.920
which is exactly half of the diameter.

00:01:13.920 --> 00:01:16.730
So, it would be eight millimeters.

00:01:16.730 --> 00:01:21.690
So, where we see the radius,
we could put eight millimeters.

00:01:21.690 --> 00:01:24.200
So the area is going to be equal

00:01:24.200 --> 00:01:27.650
to pi times eight millimeters squared,

00:01:27.650 --> 00:01:32.650
which would be 64, 64 square,
64 square millimeters.

00:01:33.720 --> 00:01:37.070
And typically, this is
written with pi after the 64,

00:01:37.070 --> 00:01:40.510
so you might often see it as this is equal

00:01:40.510 --> 00:01:45.510
to 64 pi, 64 pi millimeters squared,

00:01:48.840 --> 00:01:52.480
millimeters squared, millimeters squared.

00:01:52.480 --> 00:01:55.920
Now, this is the answer,
64 pi millimeters squared,

00:01:55.920 --> 00:01:57.730
but sometimes it's not so satisfying

00:01:57.730 --> 00:01:58.947
to just leave this pi, you might say,

00:01:58.947 --> 00:02:01.837
"Well, I wanna get a
estimate of what number

00:02:01.837 --> 00:02:05.750
"this is close to, I wanna
decimal representation of this."

00:02:05.750 --> 00:02:09.300
And so we can start to use
approximate values of pi.

00:02:09.300 --> 00:02:11.937
So, the most rough
approximate value that tends

00:02:11.937 --> 00:02:14.540
to be used is saying that pi,

00:02:14.540 --> 00:02:17.073
a very rough approximation
is equal to 3.14.

00:02:18.920 --> 00:02:20.720
So in that case, we could
say that this is going

00:02:20.720 --> 00:02:25.720
to be equal to 64, 64
times 3.14 millimeters,

00:02:29.970 --> 00:02:33.220
millimeters squared and
we can get our calculator

00:02:33.220 --> 00:02:36.423
to figure out what this
will be in decimal form.

00:02:37.530 --> 00:02:42.530
So we have 64 times 3.14 gives us 200.96.

00:02:48.000 --> 00:02:51.680
So we could say that the area
is approximately equal to,

00:02:51.680 --> 00:02:56.680
approximately equal to
200.96 square millimeters.

00:02:57.560 --> 00:03:00.690
Now, if we wanna get a more
accurate representation

00:03:00.690 --> 00:03:02.470
of this, pi actually just keeps going on

00:03:02.470 --> 00:03:05.600
and on and on forever, we
could use the calculator's

00:03:05.600 --> 00:03:07.880
internal representation of pi.

00:03:07.880 --> 00:03:12.040
In which case we'll say 64 times

00:03:12.040 --> 00:03:14.200
and then we have to look for
the pi in the calculator,

00:03:14.200 --> 00:03:15.730
it's up here in this yellow so I'll do

00:03:15.730 --> 00:03:18.250
this little second
function, get the pi there,

00:03:18.250 --> 00:03:19.570
every calculator will
be a little different.

00:03:19.570 --> 00:03:21.350
But 64 times pi, now we're going to use

00:03:21.350 --> 00:03:24.420
the calculator's internal
approximation of pi,

00:03:24.420 --> 00:03:26.450
which is going to be
more precise than what

00:03:26.450 --> 00:03:29.090
I had in the last one and you get

00:03:29.090 --> 00:03:32.890
201, so let me put it over
here so I can write it down,

00:03:32.890 --> 00:03:36.791
so a more precise is 201,
and I'll round, I'll round

00:03:36.791 --> 00:03:40.000
to the nearest, I'll round
to the nearest hundredth

00:03:40.000 --> 00:03:45.000
so you get 201.06, so 201, so more precise

00:03:47.240 --> 00:03:52.240
is 201.06 square millimeters.

00:03:52.550 --> 00:03:54.410
So this is closer to the actual answer

00:03:54.410 --> 00:03:57.180
'cause a calculator's
representation is more precise

00:03:57.180 --> 00:04:00.893
than this very rough
approximation of what pi is.


Graphs of indefinite integrals

WEBVTT
Kind: captions
Language: en

00:00:00.570 --> 00:00:03.850
- [Instructor] Find the
general indefinite integral.

00:00:03.850 --> 00:00:06.670
And so we have the integral of two x dx.

00:00:06.670 --> 00:00:09.760
Which of the graphs shown below,

00:00:09.760 --> 00:00:11.970
which of the graphs below shows

00:00:11.970 --> 00:00:14.750
several members of the family?

00:00:14.750 --> 00:00:16.140
So if we're talking about,

00:00:16.140 --> 00:00:21.140
so if we're taking the
integral of two x dx,

00:00:21.260 --> 00:00:24.020
we're talking about the
antiderivative of two x.

00:00:24.020 --> 00:00:25.800
And what's that going to be?

00:00:25.800 --> 00:00:30.070
Well, it's going to be two x

00:00:30.070 --> 00:00:32.090
to the second power.

00:00:32.090 --> 00:00:33.690
'Cause this was two x to the first power,

00:00:33.690 --> 00:00:36.590
so we increment the exponent to two.

00:00:36.590 --> 00:00:39.680
And then we divide by that
newly incremented exponent,

00:00:39.680 --> 00:00:42.720
so this is going to be x squared.

00:00:42.720 --> 00:00:44.440
And you might have done that
on your own, you said, okay,

00:00:44.440 --> 00:00:46.060
I know that the derivative
of x squared is two x,

00:00:46.060 --> 00:00:48.800
so the antiderivative
of two x is x squared.

00:00:48.800 --> 00:00:51.670
But we aren't quite done yet.

00:00:51.670 --> 00:00:52.960
Because remember,

00:00:52.960 --> 00:00:55.340
this isn't the only
antiderivative of this.

00:00:55.340 --> 00:00:57.450
We could add any constant here.

00:00:57.450 --> 00:00:59.180
If we add some constant here

00:00:59.180 --> 00:01:02.860
and we take the derivative
of it, we still get two x.

00:01:02.860 --> 00:01:05.670
Because the derivative of a
constant with respect to x,

00:01:05.670 --> 00:01:07.530
it's not changing with respect to x,

00:01:07.530 --> 00:01:10.600
so its derivative is zero.

00:01:10.600 --> 00:01:13.500
So the antiderivatives, I
guess you could say here,

00:01:13.500 --> 00:01:15.440
take this form,

00:01:15.440 --> 00:01:18.090
take the form of x squared plus C.

00:01:18.090 --> 00:01:20.430
Now what does that mean visually?

00:01:20.430 --> 00:01:22.730
So,

00:01:22.730 --> 00:01:26.060
let me draw, I can draw
a neater version of that.

00:01:26.060 --> 00:01:28.780
So slightly better.

00:01:28.780 --> 00:01:30.630
So if that's my y-axis

00:01:31.480 --> 00:01:34.483
and this is my x-axis,

00:01:36.180 --> 00:01:39.370
we know what y equals
x squared looks like.

00:01:39.370 --> 00:01:42.550
Y equals x squared looks like,

00:01:42.550 --> 00:01:44.693
I'll just draw the general shape.

00:01:45.580 --> 00:01:49.483
So y equals x squared looks like this.

00:01:50.520 --> 00:01:51.810
Now, what happens

00:01:54.030 --> 00:01:55.660
if I add a C?

00:01:55.660 --> 00:01:56.890
Let's say if I add,

00:01:56.890 --> 00:01:59.590
let's say y is equal
to x squared plus two.

00:01:59.590 --> 00:02:02.120
And two is a valid C, so we could say,

00:02:02.120 --> 00:02:03.970
so let me write this down.

00:02:03.970 --> 00:02:07.450
This right over here is
y is equal to x squared.

00:02:07.450 --> 00:02:09.240
But remember, and I
guess you could say that,

00:02:09.240 --> 00:02:12.510
in this case, our C is zero.

00:02:12.510 --> 00:02:14.680
But what if our C was some positive value?

00:02:14.680 --> 00:02:17.330
So let's say it is y

00:02:17.330 --> 00:02:20.200
is equal to x squared

00:02:20.200 --> 00:02:24.370
plus, I don't know, y is
equal to x squared plus five.

00:02:24.370 --> 00:02:27.710
Well, then we're going to have
a y-intercept here at five,

00:02:27.710 --> 00:02:30.870
so essentially we're just
gonna shift up the graph

00:02:30.870 --> 00:02:33.520
by our constant right over
here, which is positive five.

00:02:33.520 --> 00:02:36.420
So we shift up by positive five,

00:02:36.420 --> 00:02:40.150
and we will get something
that looks like this.

00:02:40.150 --> 00:02:41.980
We just shifted it up.

00:02:41.980 --> 00:02:43.690
Now, you might be saying, okay,

00:02:43.690 --> 00:02:46.720
well, that kind of looks like
this choice right over here.

00:02:46.720 --> 00:02:49.410
But this choice also,

00:02:49.410 --> 00:02:52.150
also has some choices

00:02:52.150 --> 00:02:55.180
that start down here, that
we're adding a constant.

00:02:55.180 --> 00:02:57.660
But you remember, this
constant can be any constant.

00:02:57.660 --> 00:02:59.500
It could be a negative value.

00:02:59.500 --> 00:03:01.340
So in this case, C is five.

00:03:01.340 --> 00:03:02.430
In this case, C is zero.

00:03:02.430 --> 00:03:04.770
But C could also be negative five.

00:03:04.770 --> 00:03:06.840
So C could also be negative five.

00:03:06.840 --> 00:03:08.710
So if we wanted to do y is equal

00:03:08.710 --> 00:03:11.680
to x squared plus negative five,

00:03:11.680 --> 00:03:13.530
which is really x squared minus five,

00:03:14.900 --> 00:03:17.090
then the graph would look like this.

00:03:17.090 --> 00:03:20.240
It would shift x squared down,

00:03:20.240 --> 00:03:22.130
down by five.

00:03:22.130 --> 00:03:24.160
So this one is shifted up by five.

00:03:24.160 --> 00:03:26.180
This one is shifted down by five.

00:03:26.180 --> 00:03:27.850
So you would shift by the constant.

00:03:27.850 --> 00:03:29.600
If it's a positive
constant, you're going up.

00:03:29.600 --> 00:03:32.200
If it's a negative constant,
you are going down.

00:03:32.200 --> 00:03:34.380
So B is definitely

00:03:35.302 --> 00:03:38.440
the class of solutions to
this indefinite integral.

00:03:38.440 --> 00:03:40.530
You take any, any of the functions

00:03:40.530 --> 00:03:42.910
that are represented by these graphs,

00:03:42.910 --> 00:03:45.450
you take their derivative,
you're going to get two x.

00:03:45.450 --> 00:03:46.610
Or another way to think about it,

00:03:46.610 --> 00:03:49.350
the antiderivative of
this or the integral,

00:03:49.350 --> 00:03:51.220
the indefinite integral of two x dx

00:03:51.220 --> 00:03:52.720
is gonna be x squared plus C,

00:03:52.720 --> 00:03:56.020
which would be represented
by things that look like,

00:03:56.020 --> 00:03:57.880
so essentially things,

00:03:57.880 --> 00:04:01.330
essentially y equals x
squared shifted up or down.

00:04:01.330 --> 00:04:03.530
So I could keep drawing
over and over again.


Solving proportions 2 exercise examples

WEBVTT
Kind: captions
Language: en

00:00:00.560 --> 00:00:03.600
- [Instructor] We have the
proportion x minus nine over 12

00:00:03.600 --> 00:00:06.180
is equal to two over three,

00:00:06.180 --> 00:00:10.790
and we wanna solve for the x
that satisfies this proportion.

00:00:10.790 --> 00:00:12.640
Now, there's a bunch of
ways that you could do it.

00:00:12.640 --> 00:00:14.870
A lot of people, as soon as
they see a proportion like this,

00:00:14.870 --> 00:00:16.100
they wanna cross-multiply.

00:00:16.100 --> 00:00:18.470
They wanna say, hey,
three times x minus nine

00:00:18.470 --> 00:00:20.320
is going to be equal to two times 12.

00:00:20.320 --> 00:00:21.680
And that's completely legitimate.

00:00:21.680 --> 00:00:23.000
You would get, let me write that down.

00:00:23.000 --> 00:00:25.330
So three times x minus nine,

00:00:25.330 --> 00:00:30.040
three times x minus nine
is equal to two times 12.

00:00:30.040 --> 00:00:32.810
So it would be equal to two times 12.

00:00:32.810 --> 00:00:34.450
And then you can distribute the three.

00:00:34.450 --> 00:00:37.090
You'd get three x minus 27

00:00:37.090 --> 00:00:39.340
is equal to 24.

00:00:39.340 --> 00:00:42.480
And then you could add 27 to both sides,

00:00:42.480 --> 00:00:44.100
and you would get, let
me actually do that.

00:00:44.100 --> 00:00:47.440
So let me add 27 to both sides,

00:00:47.440 --> 00:00:48.680
and we are left with

00:00:49.650 --> 00:00:53.050
three x is equal to,

00:00:53.050 --> 00:00:56.510
is equal to, let's see, 51.

00:00:56.510 --> 00:00:59.030
And then x would be equal to 17.

00:00:59.030 --> 00:01:01.490
X would be equal to 17.

00:01:01.490 --> 00:01:03.130
And you can verify that this works.

00:01:03.130 --> 00:01:05.060
17 minus nine is eight.

00:01:05.060 --> 00:01:07.520
8/12 is the same thing as 2/3.

00:01:07.520 --> 00:01:09.260
So this checks out.

00:01:09.260 --> 00:01:10.290
Another way you could do that,

00:01:10.290 --> 00:01:13.000
instead of just straight up
doing the cross-multiplication,

00:01:13.000 --> 00:01:14.680
you could say look, I
wanna get rid of this 12

00:01:14.680 --> 00:01:15.870
in the denominator right over here,

00:01:15.870 --> 00:01:19.680
let's multiply both sides by 12.

00:01:19.680 --> 00:01:21.900
So if you multiply both sides by 12,

00:01:21.900 --> 00:01:26.370
on your left-hand side, you are
just left with x minus nine.

00:01:26.370 --> 00:01:29.830
And on your right-hand side, 2/3 times 12,

00:01:29.830 --> 00:01:32.880
well, 2/3 of 12 is just eight.

00:01:32.880 --> 00:01:34.500
And you could do the
actual multiplication,

00:01:34.500 --> 00:01:37.020
2/3 times 12 over one.

00:01:37.020 --> 00:01:38.390
12,

00:01:38.390 --> 00:01:41.680
12 and three, so 12
divided by three is four.

00:01:41.680 --> 00:01:43.430
Three divided by three is one.

00:01:43.430 --> 00:01:47.380
So it becomes two times four
over one, which is just eight.

00:01:47.380 --> 00:01:49.890
And then you add nine to both sides.

00:01:49.890 --> 00:01:52.550
So the fun of algebra is that
as long as you do something

00:01:52.550 --> 00:01:55.610
that's logically consistent,
you will get the right answer.

00:01:55.610 --> 00:01:57.410
There's no one way of doing it.

00:01:57.410 --> 00:02:01.630
So here you get x is equal to 17 again.

00:02:01.630 --> 00:02:04.562
And you can also, you can
multiply both sides by 12

00:02:04.562 --> 00:02:07.560
and both sides by three,
and then that would be

00:02:07.560 --> 00:02:10.070
functionally equivalent
to cross-multiplying.

00:02:10.070 --> 00:02:11.900
Let's do one more.

00:02:11.900 --> 00:02:13.500
So here, another proportion,

00:02:13.500 --> 00:02:16.050
and this time the x is in the denominator.

00:02:16.050 --> 00:02:19.200
But just like before, if we
want, we can cross-multiply.

00:02:19.200 --> 00:02:21.450
And just to see where
cross-multiplying comes from,

00:02:21.450 --> 00:02:22.480
that it's not some voodoo,

00:02:22.480 --> 00:02:24.910
that you still are doing logical algebra,

00:02:24.910 --> 00:02:25.910
that you're doing the same thing

00:02:25.910 --> 00:02:28.960
to both sides of the equation,
you just need to appreciate

00:02:28.960 --> 00:02:31.870
that we're just multiplying
both sides by both denominators.

00:02:31.870 --> 00:02:35.340
So we have this eight right
over here on the left-hand side.

00:02:35.340 --> 00:02:36.900
If we wanna get rid of this eight

00:02:36.900 --> 00:02:38.500
on the left-hand side in the denominator,

00:02:38.500 --> 00:02:40.900
we can multiply the
left-hand side by eight.

00:02:40.900 --> 00:02:42.500
But in order for the
equality to hold true,

00:02:42.500 --> 00:02:44.150
I can't do something to just one side.

00:02:44.150 --> 00:02:46.780
I have to do it to both sides.

00:02:46.780 --> 00:02:50.763
Similarly, similar-larly, if (laughs) I,

00:02:51.845 --> 00:02:54.960
if I wanna get this x plus
one out of the denominator,

00:02:54.960 --> 00:02:58.620
I could multiply by x
plus one right over here.

00:02:58.620 --> 00:03:00.220
But I have to do that on both sides

00:03:00.220 --> 00:03:03.250
if I want my equality to hold true.

00:03:03.250 --> 00:03:05.550
And notice, when you do what we just did,

00:03:05.550 --> 00:03:08.410
this is going to be equivalent
to cross-multiplying.

00:03:08.410 --> 00:03:10.860
Because these eights cancel out,

00:03:10.860 --> 00:03:13.680
and this x plus one cancels

00:03:13.680 --> 00:03:15.940
with that x plus one right over there.

00:03:15.940 --> 00:03:17.730
And you are left with,

00:03:17.730 --> 00:03:20.670
you are left with x plus one,

00:03:20.670 --> 00:03:23.410
x plus one times seven,

00:03:23.410 --> 00:03:26.410
and I could write it as
seven times x plus one,

00:03:26.410 --> 00:03:29.040
is equal to five times eight,

00:03:29.040 --> 00:03:33.000
is equal to five times eight.

00:03:33.000 --> 00:03:34.700
Notice, this is exactly what you have done

00:03:34.700 --> 00:03:36.400
if you would've cross-multiplied.

00:03:36.400 --> 00:03:38.440
Cross-multiplication is just a shortcut

00:03:38.440 --> 00:03:41.280
of multiplying both sides
by both the denominators.

00:03:41.280 --> 00:03:45.600
We have seven times x plus one
is equal to five times eight.

00:03:45.600 --> 00:03:48.230
And now we can go and solve the algebra.

00:03:48.230 --> 00:03:49.620
So distributing the seven,

00:03:49.620 --> 00:03:52.350
we get seven x plus seven

00:03:52.350 --> 00:03:54.330
is equal to 40.

00:03:54.330 --> 00:03:57.940
And then subtracting
seven from both sides,

00:03:57.940 --> 00:04:00.910
so let's subtract seven from both sides,

00:04:00.910 --> 00:04:03.690
we are left with seven x

00:04:03.690 --> 00:04:06.330
is equal to 33.

00:04:06.330 --> 00:04:08.800
Dividing both sides by seven,

00:04:08.800 --> 00:04:13.100
we are left with x is
equal to 33 over seven.

00:04:13.100 --> 00:04:15.960
And if we wanna write
that as a mixed number,

00:04:15.960 --> 00:04:17.160
this is the same thing, let's see,

00:04:17.160 --> 00:04:18.993
this is the same thing as 4 5/7,

00:04:20.965 --> 00:04:21.863
And we're done.


Limits at infinity using algebra

WEBVTT
Kind: captions
Language: en

00:00:00.760 --> 00:00:02.465
- Let's think about the
limit of the square root

00:00:02.465 --> 00:00:05.430
of 100 + x - the square root of x,

00:00:05.430 --> 00:00:07.890
as x approaches infinity and I encourage

00:00:07.890 --> 00:00:09.120
you to pause this video and try to

00:00:09.120 --> 00:00:10.886
figure this out on your own.

00:00:10.886 --> 00:00:13.450
So I'm assuming you've had a go at it.

00:00:13.450 --> 00:00:14.970
So first let's just try to think about it,

00:00:14.970 --> 00:00:17.360
before we try to manipulate
this algebraically,

00:00:17.360 --> 00:00:18.670
in some way.

00:00:18.670 --> 00:00:19.960
So what happens is x

00:00:19.960 --> 00:00:22.080
gets really really really really large,

00:00:22.080 --> 00:00:23.770
as x approaches,

00:00:23.770 --> 00:00:25.800
as x approaches infinity.

00:00:25.800 --> 00:00:27.090
While even though this 100

00:00:27.090 --> 00:00:28.480
is a reasonably

00:00:28.480 --> 00:00:30.090
a reasonably large number,

00:00:30.090 --> 00:00:31.280
as x gets really large,

00:00:31.280 --> 00:00:33.720
Billion, trillion, trillion trillions.

00:00:33.720 --> 00:00:34.730
Even larger than that.

00:00:34.730 --> 00:00:36.530
Trillion trillion trillion trillions.

00:00:36.530 --> 00:00:38.650
You could imagine that the 100,

00:00:38.650 --> 00:00:39.680
under the radical sign,

00:00:39.680 --> 00:00:41.600
starts to matter a lot less.

00:00:41.600 --> 00:00:44.041
As x approaches really
really large numbers,

00:00:44.041 --> 00:00:46.910
the square root of 100 + x is going to be

00:00:46.910 --> 00:00:49.247
approximately the same thing as the

00:00:49.247 --> 00:00:50.980
square root of x.

00:00:50.980 --> 00:00:52.190
So for

00:00:53.724 --> 00:00:55.570
really really

00:00:55.570 --> 00:00:59.440
large large x's,

00:00:59.440 --> 00:01:01.440
we can reason that the square root

00:01:01.440 --> 00:01:03.980
of 100 + x is going to be

00:01:03.980 --> 00:01:05.840
approximately equal to

00:01:05.840 --> 00:01:07.900
the square root of x

00:01:07.900 --> 00:01:08.940
and so in that reality,

00:01:08.940 --> 00:01:10.335
we are going to

00:01:10.335 --> 00:01:11.230
really really really large x's.

00:01:11.230 --> 00:01:12.290
In fact,

00:01:12.290 --> 00:01:13.123
there's nothing larger,

00:01:13.123 --> 00:01:15.048
where you can keep increasing x's,

00:01:15.048 --> 00:01:17.270
then these two things are going to be

00:01:17.270 --> 00:01:19.360
roughly equal to each other.

00:01:19.360 --> 00:01:21.311
So it's reasonable to believe,

00:01:21.311 --> 00:01:23.019
that the limit as x approaches

00:01:23.019 --> 00:01:24.550
infinity here,

00:01:24.550 --> 00:01:25.740
is going to be zero.

00:01:25.740 --> 00:01:27.480
You're subtracting this,

00:01:27.480 --> 00:01:28.350
from something that is

00:01:28.350 --> 00:01:30.020
pretty similar to that,

00:01:30.020 --> 00:01:30.920
but let's actually do

00:01:30.920 --> 00:01:32.170
some algrebraic manipulation

00:01:32.170 --> 00:01:33.680
to feel better about that,

00:01:33.680 --> 00:01:34.513
instead of this kind of

00:01:34.513 --> 00:01:36.010
hand-wavy argument about

00:01:36.010 --> 00:01:37.560
the 100 not mattering as much,

00:01:37.560 --> 00:01:39.970
when x gets really really really large

00:01:39.970 --> 00:01:42.360
and so let me re-write this expression.

00:01:42.360 --> 00:01:43.610
See if we can

00:01:43.610 --> 00:01:45.910
manipulate it in interesting ways.

00:01:45.910 --> 00:01:47.030
So this is

00:01:49.252 --> 00:01:50.627
100 + x - x.

00:01:54.240 --> 00:01:55.890
So one thing that might jump out at you

00:01:55.890 --> 00:01:58.670
whenever you see one radical,

00:01:58.670 --> 00:02:01.130
minus another radical like this.

00:02:01.130 --> 00:02:02.540
Well maybe we can multiply

00:02:02.540 --> 00:02:03.900
by its conjugate and somehow

00:02:03.900 --> 00:02:05.130
get rid of the radicals,

00:02:05.130 --> 00:02:07.000
or at least transform the

00:02:07.000 --> 00:02:07.890
expression in some way,

00:02:07.890 --> 00:02:09.190
that might be a little more useful

00:02:09.190 --> 00:02:10.500
when we try to find the limit,

00:02:10.500 --> 00:02:12.350
as x approaches infinity.

00:02:12.350 --> 00:02:13.480
So let's just and obviously

00:02:13.480 --> 00:02:14.450
we can't just multiply it

00:02:14.450 --> 00:02:15.770
by anything arbitrary,

00:02:15.770 --> 00:02:17.020
in order to not change the value

00:02:17.020 --> 00:02:17.853
of this expression,

00:02:17.853 --> 00:02:19.730
we can only multiply it by one.

00:02:19.730 --> 00:02:21.690
So let's multiply it by a form of one,

00:02:21.690 --> 00:02:23.440
but a form of one that helps us,

00:02:23.440 --> 00:02:25.890
that is essentially made
up of its conjugate.

00:02:25.890 --> 00:02:27.700
So let's multiply this

00:02:27.700 --> 00:02:28.970
let's multiply this

00:02:30.532 --> 00:02:32.970
times the square root

00:02:32.970 --> 00:02:36.516
of 100 + x

00:02:36.516 --> 00:02:39.370
+ the square root of x,

00:02:39.370 --> 00:02:40.620
over the same thing.

00:02:40.620 --> 00:02:42.860
The square root of

00:02:42.860 --> 00:02:45.327
100 + x

00:02:45.327 --> 00:02:48.130
+ the square root of x.

00:02:48.130 --> 00:02:48.963
Now notice this,

00:02:48.963 --> 00:02:51.550
of course is exactly equal to one

00:02:51.550 --> 00:02:52.630
and the reason why we like

00:02:52.630 --> 00:02:53.553
to multiply by conjugates,

00:02:53.553 --> 00:02:55.120
is that we can take advantage

00:02:55.120 --> 00:02:56.740
of differences of squares.

00:02:56.740 --> 00:02:58.230
So this is going to be equal to

00:02:58.230 --> 00:02:59.280
and our denominator,

00:02:59.280 --> 00:03:00.970
we're just going to have

00:03:00.970 --> 00:03:02.675
we're just going to have the

00:03:02.675 --> 00:03:04.700
square root of 100.

00:03:04.700 --> 00:03:06.530
Let me write it this way actually.

00:03:06.530 --> 00:03:08.970
100 + x

00:03:10.037 --> 00:03:12.770
+ the square root of x

00:03:12.770 --> 00:03:14.400
and our then our numberator,

00:03:14.400 --> 00:03:17.460
we have the square root

00:03:17.460 --> 00:03:19.870
of 100 + x,

00:03:19.870 --> 00:03:22.060
minus the square root of x

00:03:22.060 --> 00:03:24.780
times this thing.

00:03:24.780 --> 00:03:27.470
Times square root of

00:03:27.470 --> 00:03:30.170
100 + x +

00:03:30.170 --> 00:03:32.130
the square root of x.

00:03:32.130 --> 00:03:33.300
Now right over here,

00:03:33.300 --> 00:03:34.350
we're essentially multiplying

00:03:34.350 --> 00:03:37.180
A + B times A - B,

00:03:37.180 --> 00:03:39.720
will produce a difference of squares.

00:03:39.720 --> 00:03:41.791
So this is going to be equal to

00:03:41.791 --> 00:03:44.180
this top part right over here,

00:03:44.180 --> 00:03:46.040
is going to be equal to

00:03:46.040 --> 00:03:47.460
is going to be equal to

00:03:48.853 --> 00:03:49.686
this,

00:03:49.686 --> 00:03:50.902
let me do this in a different color.

00:03:50.902 --> 00:03:52.740
It's going to be equal to

00:03:53.660 --> 00:03:55.230
this thing squared

00:03:55.230 --> 00:03:56.700
minus,

00:03:56.700 --> 00:03:58.140
minus,

00:03:58.140 --> 00:03:59.420
this thing,

00:03:59.420 --> 00:04:01.350
minus that thing squared.

00:04:01.350 --> 00:04:03.290
So what's 100 + x squared?

00:04:03.290 --> 00:04:05.583
Well that's just 100 + x,

00:04:05.583 --> 00:04:07.850
100 + x

00:04:07.850 --> 00:04:09.050
and then what square root

00:04:09.050 --> 00:04:10.180
of x squared?

00:04:10.180 --> 00:04:12.100
Well that's just going to be x.

00:04:12.100 --> 00:04:14.190
So minus x

00:04:14.190 --> 00:04:15.230
and we do see that this

00:04:15.230 --> 00:04:17.160
is starting to simplify nicely.

00:04:17.160 --> 00:04:18.290
All of that,

00:04:18.290 --> 00:04:21.190
over the square root

00:04:21.190 --> 00:04:23.747
of 100 + x

00:04:23.747 --> 00:04:25.880
+ the square root of x

00:04:25.880 --> 00:04:27.050
and these x's

00:04:27.050 --> 00:04:29.640
x - x will just be nothing

00:04:29.640 --> 00:04:31.530
and so we are left with 100 over

00:04:31.530 --> 00:04:33.790
the square root of 100 + x +

00:04:33.790 --> 00:04:35.220
the square root of x.

00:04:35.220 --> 00:04:37.220
So we could re-write the original limit,

00:04:37.220 --> 00:04:39.010
as the limit,

00:04:39.010 --> 00:04:41.540
the limit as x approaches infinity.

00:04:41.540 --> 00:04:42.720
Instead of this,

00:04:42.720 --> 00:04:44.400
we just algebraically manipulated it,

00:04:44.400 --> 00:04:45.690
to be this.

00:04:45.690 --> 00:04:47.400
So the limit as x approaches infinity

00:04:47.400 --> 00:04:50.240
of 100 over

00:04:50.240 --> 00:04:51.580
the square root of

00:04:51.580 --> 00:04:54.577
100 + x

00:04:54.577 --> 00:04:56.560
+ the square root of x

00:04:56.560 --> 00:04:58.170
and now it becomes much clearer.

00:04:58.170 --> 00:04:59.980
We have a fixed numerator.

00:04:59.980 --> 00:05:02.060
This numerator just stays at 100,

00:05:02.060 --> 00:05:03.770
but our denominator right over here,

00:05:03.770 --> 00:05:04.603
is just going to be,

00:05:04.603 --> 00:05:06.060
it's just going to keep increasing.

00:05:06.060 --> 00:05:07.780
It's going to be unbounded.

00:05:07.780 --> 00:05:09.900
So if you're just
increasing this denominator,

00:05:09.900 --> 00:05:12.089
while you keep the numerator fixed,

00:05:12.089 --> 00:05:14.210
you essentially have a fixed numerator,

00:05:14.210 --> 00:05:15.730
with an ever-increasing,

00:05:15.730 --> 00:05:16.590
or a super large,

00:05:16.590 --> 00:05:18.120
or an infinitely large denominator.

00:05:18.120 --> 00:05:20.200
So that is going to approach,

00:05:20.200 --> 00:05:22.010
that is going to approach zero,

00:05:22.010 --> 00:05:23.080
which is consistent with

00:05:23.080 --> 00:05:24.793
our original intuition.


Vertical asymptote of natural log

WEBVTT
Kind: captions
Language: en

00:00:00.680 --> 00:00:02.890
- [Narrator] Right over
here, we've defined y

00:00:02.890 --> 00:00:03.990
as a function of x,

00:00:03.990 --> 00:00:07.600
where y is equal to the
natural log of x minus three.

00:00:07.600 --> 00:00:11.170
What I encourage you to do
right now is to pause this video

00:00:11.170 --> 00:00:13.780
and think about for what x values

00:00:13.780 --> 00:00:15.380
is this function actually defined?

00:00:15.380 --> 00:00:16.250
Or another way of thinking about it,

00:00:16.250 --> 00:00:18.910
what is the domain of this function,

00:00:18.910 --> 00:00:21.210
and then try to plot this
function on your own,

00:00:21.210 --> 00:00:22.400
on maybe some scratch paper

00:00:22.400 --> 00:00:23.870
that you might have in front of you,

00:00:23.870 --> 00:00:26.030
and then we'll talk about,
and also think about,

00:00:26.030 --> 00:00:29.313
does this have any vertical
asymptotes, and if so, where?

00:00:30.210 --> 00:00:31.850
So, I'm assuming you've given a go at it,

00:00:31.850 --> 00:00:35.010
so first, let's think about
where is this function defined?

00:00:35.010 --> 00:00:37.810
So, the important realization
is this is only defined

00:00:37.810 --> 00:00:40.980
if you're taking the natural
log of a positive value.

00:00:40.980 --> 00:00:43.820
So, this thing right over here must be,

00:00:43.820 --> 00:00:47.120
this thing right over
here, must be positive,

00:00:47.120 --> 00:00:48.780
or, another way we could think about it,

00:00:48.780 --> 00:00:52.620
it's only going to be
defined for any x, such that,

00:00:52.620 --> 00:00:55.680
x minus three is strictly positive.

00:00:55.680 --> 00:00:58.760
Not greater than or equal
to zero, greater than zero.

00:00:58.760 --> 00:01:02.140
We haven't defined what
the natural log of zero is,

00:01:02.140 --> 00:01:05.030
so x minus three has
to be greater than zero

00:01:05.030 --> 00:01:06.660
in order to give a positive,

00:01:06.660 --> 00:01:09.170
in order to take the natural
log of a positive something,

00:01:09.170 --> 00:01:10.950
or if we add three to both sides,

00:01:10.950 --> 00:01:13.750
we get x is greater than three.

00:01:13.750 --> 00:01:18.750
So, it defined, defined
four, x greater than three.

00:01:19.740 --> 00:01:22.490
You could do this as the domain,

00:01:22.490 --> 00:01:27.120
the set of all real numbers
that are greater than three.

00:01:27.120 --> 00:01:28.390
Now, that out of the way,

00:01:28.390 --> 00:01:33.313
let's actually try to plot
natural log of x minus three.

00:01:34.230 --> 00:01:38.600
So, let me put some of this
graph paper right over here,

00:01:38.600 --> 00:01:41.180
and the first thing I
wanna think about is,

00:01:41.180 --> 00:01:45.760
well, let's just try to plot
some interesting points here,

00:01:45.760 --> 00:01:49.860
and the most obvious one is
what makes this natural log,

00:01:49.860 --> 00:01:52.620
what makes this entire
function equal to zero?

00:01:52.620 --> 00:01:56.830
When are we going to intersect the x-axis?

00:01:56.830 --> 00:01:59.089
So, let's just think about
that for a little bit.

00:01:59.089 --> 00:02:04.089
So, when is the natural
log of x minus three

00:02:04.680 --> 00:02:08.100
going to be equal to zero?

00:02:08.100 --> 00:02:09.380
Well, one way to think about this

00:02:09.380 --> 00:02:11.000
is to view these both as exponents

00:02:11.000 --> 00:02:13.860
and raise e to both of these powers.

00:02:13.860 --> 00:02:16.910
So, you could say that e to the
natural log of x minus three

00:02:16.910 --> 00:02:19.030
is the same thing as e to the zero,

00:02:19.030 --> 00:02:20.600
and, of course, if you raise e

00:02:20.600 --> 00:02:23.380
to whatever exponent you need
to get you to x minus three,

00:02:23.380 --> 00:02:25.680
that's just going to get
you to x minus three,

00:02:26.650 --> 00:02:28.120
and if you raise e to the zero,

00:02:28.120 --> 00:02:29.729
well, anything to the zeroth power,

00:02:29.729 --> 00:02:32.560
except possibly zero, that
one's under contention,

00:02:32.560 --> 00:02:36.100
or maybe not defined, e to
the zero is equal to one.

00:02:36.100 --> 00:02:37.667
This is just another way of saying,

00:02:37.667 --> 00:02:40.727
"Hey, look, if I wanna know what exponent

00:02:40.727 --> 00:02:43.270
"do I need to raise e to to get to zero,"

00:02:43.270 --> 00:02:45.800
we know e to the zeroth
power is equal to one,

00:02:45.800 --> 00:02:50.560
so x minus three is equal to one.

00:02:50.560 --> 00:02:52.960
So, if I'm taking the natural
log of one, it'll be zero.

00:02:52.960 --> 00:02:54.980
So, x minus three is equal to one,

00:02:54.980 --> 00:02:56.660
add three to both sides,

00:02:56.660 --> 00:02:58.120
you get x equals four.

00:02:58.120 --> 00:03:01.390
So, we know that the .4,
zero is on this graph,

00:03:01.390 --> 00:03:02.980
so let me graph that.

00:03:02.980 --> 00:03:07.980
One, two, three, and four.

00:03:08.850 --> 00:03:11.150
So, that right over there is the point.

00:03:11.150 --> 00:03:14.480
X is four, and y is zero.

00:03:14.480 --> 00:03:16.980
Four minus one, four minus three is one,

00:03:16.980 --> 00:03:20.270
natural log of one is zero.

00:03:20.270 --> 00:03:21.947
We also know that this is only defined

00:03:21.947 --> 00:03:23.720
for x being greater than three,

00:03:23.720 --> 00:03:25.850
so let's just put a little dotted line

00:03:25.850 --> 00:03:28.120
right over here at x equals three.

00:03:28.120 --> 00:03:30.567
And we know that our
function isn't even defined,

00:03:30.567 --> 00:03:35.370
for x equals three, and in
any value, to the left of it.

00:03:35.370 --> 00:03:36.470
Well, let's think about what happens

00:03:36.470 --> 00:03:40.830
as we approach x equals three
from the right-hand side,

00:03:40.830 --> 00:03:43.230
and to do that, I'll
make a little table here.

00:03:43.230 --> 00:03:45.800
So, let me make a little table here,

00:03:45.800 --> 00:03:48.730
and put some x values here,

00:03:48.730 --> 00:03:49.810
and then let's just think about

00:03:49.810 --> 00:03:52.170
what our corresponding y value is.

00:03:52.170 --> 00:03:53.630
So, we could put in,

00:03:53.630 --> 00:03:57.040
so we already know that we get four, zero.

00:03:57.040 --> 00:04:01.723
Let's try out 3.1, 3.01,

00:04:02.750 --> 00:04:06.760
and 3.001 and see what you get.

00:04:06.760 --> 00:04:08.900
And you can imagine, from each of these,

00:04:08.900 --> 00:04:11.330
you're gonna subtract
three, so then the input

00:04:11.330 --> 00:04:15.570
into the natural log function
is gonna be .1, .01, .001,

00:04:15.570 --> 00:04:19.900
and so you're gonna have more
and more negative exponents,

00:04:19.900 --> 00:04:21.600
or powers, that you have to raise e to

00:04:21.600 --> 00:04:22.780
to get to those values,

00:04:22.780 --> 00:04:24.280
but to just verify that,

00:04:24.280 --> 00:04:26.770
let's actually get our calculator out.

00:04:26.770 --> 00:04:28.050
Let's get our calculator out,

00:04:28.050 --> 00:04:30.880
and let me go to the main screen.

00:04:30.880 --> 00:04:35.010
And so, let's take the natural log

00:04:35.010 --> 00:04:38.751
of three, of 3.1 minus three.

00:04:38.751 --> 00:04:42.380
3.1 minus three.

00:04:42.380 --> 00:04:47.380
We get negative 2.3, and
I'll just round to the tenth.

00:04:47.920 --> 00:04:50.643
So, this right over here is negative 2.3.

00:04:52.040 --> 00:04:56.130
If we raise, if we take the natural log,

00:04:56.130 --> 00:04:58.903
natural log of 3.01,

00:05:00.250 --> 00:05:05.250
3.01 minus three, we get to

00:05:05.640 --> 00:05:10.640
negative 4.6, once again,
just rounding, negative 4.6,

00:05:11.660 --> 00:05:15.033
and if we take the natural log,

00:05:15.973 --> 00:05:19.480
the natural log of 3.001,

00:05:19.480 --> 00:05:24.480
zero, one, minus three,
we get to negative 6.9.

00:05:25.910 --> 00:05:29.190
Negative 6.9, and just for fun,

00:05:29.190 --> 00:05:31.380
let's do one that's way more dramatic.

00:05:31.380 --> 00:05:34.490
So, let's take the natural log of 3.,

00:05:34.490 --> 00:05:38.180
let's do one, two,
three, four, five, zeros,

00:05:38.180 --> 00:05:41.480
followed by one, minus three,

00:05:41.480 --> 00:05:46.480
and we get a fairly more
negative value right over here.

00:05:46.480 --> 00:05:49.100
So, as you see, as we're getting
closer and closer to three,

00:05:49.100 --> 00:05:52.580
we're getting more, and more,
and more negative values.

00:05:52.580 --> 00:05:54.590
Let me just plot this right over here,

00:05:54.590 --> 00:05:58.370
so this is negative one,
this is negative two,

00:05:58.370 --> 00:06:02.960
this is negative three,
this is negative four.

00:06:02.960 --> 00:06:05.700
So, when x is equal to 3.1,

00:06:05.700 --> 00:06:08.200
which is right about there,
we're at negative 2.3,

00:06:09.160 --> 00:06:10.990
which is right around there.

00:06:10.990 --> 00:06:14.500
When x is 3.01, which is really
hard to see right over here,

00:06:14.500 --> 00:06:17.320
we get to negative 4.6,
so it's way down here.

00:06:17.320 --> 00:06:19.750
So, our graph is gonna
look something like,

00:06:19.750 --> 00:06:21.570
our graph is gonna look something like,

00:06:21.570 --> 00:06:24.270
and my best attempt is
to draw it freehand,

00:06:24.270 --> 00:06:26.000
is gonna look something,

00:06:26.000 --> 00:06:29.530
something like, something like that.

00:06:29.530 --> 00:06:31.480
So, do we have a vertical asymptote?

00:06:31.480 --> 00:06:32.690
Absolutely.

00:06:32.690 --> 00:06:35.640
As we approach three from
values larger than three,

00:06:35.640 --> 00:06:40.640
from the right-hand side, our
function is plummeting down.

00:06:41.030 --> 00:06:41.930
It's unbounded.

00:06:41.930 --> 00:06:42.850
It's going down.

00:06:42.850 --> 00:06:43.820
Our value of our function

00:06:43.820 --> 00:06:46.790
is quickly approaching negative infinity.

00:06:46.790 --> 00:06:49.780
So, we clearly have a vertical asymptote.

00:06:49.780 --> 00:06:53.023
We have a vertical asymptote at,

00:06:53.879 --> 00:06:58.683
asymptote, at x equals three.


Education as a force of convergence

WEBVTT
Kind: captions
Language: en

00:00:00.570 --> 00:00:02.090
- [Instructor] We talked
about the dissemination

00:00:02.090 --> 00:00:05.030
of information being
a force of convergence

00:00:05.030 --> 00:00:06.470
on the global scale.

00:00:06.470 --> 00:00:10.003
But what about on the individual scale?

00:00:11.234 --> 00:00:12.950
When we're talking about
knowledge dissemination

00:00:12.950 --> 00:00:14.090
on an individual scale,

00:00:14.090 --> 00:00:16.210
we're really talking about
education on some level.

00:00:16.210 --> 00:00:19.740
So once again, this is a
topic very close to my heart.

00:00:19.740 --> 00:00:22.750
So let's just go through a
few thought experiments here.

00:00:22.750 --> 00:00:24.863
So in general, you have income.

00:00:27.050 --> 00:00:28.940
Income, and that income,

00:00:28.940 --> 00:00:31.540
in order to produce it, you need capital.

00:00:31.540 --> 00:00:33.260
You need capital.

00:00:33.260 --> 00:00:34.660
And you need,

00:00:34.660 --> 00:00:35.750
you need labor.

00:00:35.750 --> 00:00:37.370
For example, if you're running a farm,

00:00:37.370 --> 00:00:39.580
you need land and you need animals

00:00:39.580 --> 00:00:43.710
and you need some equipment,
but you also need people to

00:00:43.710 --> 00:00:46.580
run the equipment and manage the farm.

00:00:46.580 --> 00:00:49.080
If you're running a software company,

00:00:49.080 --> 00:00:52.220
you need a building, you need computers,

00:00:52.220 --> 00:00:54.380
you need servers.

00:00:54.380 --> 00:00:56.290
I guess that's computers as well.

00:00:56.290 --> 00:00:59.960
But you need people to
program the computers

00:01:01.402 --> 00:01:03.140
and to sell the software

00:01:03.140 --> 00:01:05.180
and to develop it and whatever else.

00:01:05.180 --> 00:01:07.100
So these are the two things that you need

00:01:07.100 --> 00:01:09.180
in order to produce output,

00:01:09.180 --> 00:01:12.100
which you would recognize
in terms of income.

00:01:12.100 --> 00:01:15.290
But then the question is how
does that income get split?

00:01:15.290 --> 00:01:17.350
How much of it goes to the capital,

00:01:17.350 --> 00:01:19.690
and how much goes to labor?

00:01:19.690 --> 00:01:22.870
And the idea here is, is that
if you have dissemination

00:01:22.870 --> 00:01:25.180
of knowledge and if knowledge work

00:01:25.180 --> 00:01:27.930
becomes more and more and more valuable,

00:01:27.930 --> 00:01:29.690
so if knowledge work,

00:01:29.690 --> 00:01:33.480
so let me put a little,
little aura around this.

00:01:33.480 --> 00:01:36.290
So this is the aura of knowledge.

00:01:36.290 --> 00:01:37.670
If this is knowledge work

00:01:37.670 --> 00:01:40.090
and it's less and less of a commodity,

00:01:40.090 --> 00:01:42.470
then maybe labor has more leverage here.

00:01:42.470 --> 00:01:43.303
On the other hand,

00:01:43.303 --> 00:01:46.730
if you have these hugely
capital-intensive industries

00:01:46.730 --> 00:01:50.150
where labor is kind of this
monotonous, unskilled work,

00:01:50.150 --> 00:01:53.870
then maybe capital has
more of the leverage.

00:01:53.870 --> 00:01:55.140
Now let's just think about,

00:01:55.140 --> 00:01:57.710
and Piketty tends to
be a little dismissive

00:01:57.710 --> 00:02:00.100
of this happening on a large scale.

00:02:00.100 --> 00:02:02.140
He says it might be happening in pockets.

00:02:02.140 --> 00:02:04.730
It might be happening
in pockets in terms of,

00:02:04.730 --> 00:02:07.560
you know, managers in finance

00:02:07.560 --> 00:02:10.580
or maybe in certain industries
like the software industry.

00:02:10.580 --> 00:02:12.510
But in his mind, this isn't,

00:02:12.510 --> 00:02:15.230
this knowledge dissemination
isn't going to make

00:02:15.230 --> 00:02:19.730
labor important enough in
order to offset this whole,

00:02:19.730 --> 00:02:22.860
in more and more income going to capital,

00:02:22.860 --> 00:02:25.100
especially after
generation and generation,

00:02:25.100 --> 00:02:28.190
potentially leading to dynastic wealth.

00:02:28.190 --> 00:02:30.090
But the one thought
experiment, once again,

00:02:30.090 --> 00:02:32.170
my goal here isn't to
give my point of view,

00:02:32.170 --> 00:02:33.990
it's really to just give
you things to think about

00:02:33.990 --> 00:02:36.200
and for you to come to
your own point of view,

00:02:36.200 --> 00:02:39.370
is to think about the comparison
between the present day

00:02:39.370 --> 00:02:41.870
and the Gilded Age, which the book makes.

00:02:41.870 --> 00:02:45.130
If we look at the Gilded Age,
so let me write this here.

00:02:45.130 --> 00:02:46.240
So the Gilded Age,

00:02:46.240 --> 00:02:50.350
so this is the end of the
19th century, the late 1800s.

00:02:50.350 --> 00:02:51.513
The Gilded Age,

00:02:52.672 --> 00:02:55.680
what were the forces of
growth in the Gilded Age?

00:02:55.680 --> 00:02:58.970
Where was a lot of the
income being generated from?

00:02:58.970 --> 00:03:01.920
Well, this was really the peak
of the Industrial Revolution.

00:03:01.920 --> 00:03:04.430
You have things like railroads,

00:03:04.430 --> 00:03:06.120
railroads.

00:03:06.120 --> 00:03:10.880
You have oil, I guess you could
say, you know, energy, oil.

00:03:10.880 --> 00:03:13.493
You have manufacturing,

00:03:14.470 --> 00:03:16.920
manufacturing.

00:03:16.920 --> 00:03:20.780
All of these industries are
incredibly capital-intensive.

00:03:20.780 --> 00:03:21.820
Capital is very important.

00:03:21.820 --> 00:03:24.630
You can't even do these
things without capital.

00:03:24.630 --> 00:03:27.790
And in all of these, labor
is a bit of a commodity,

00:03:27.790 --> 00:03:30.470
that, hey, you just need
people to kind of, you know,

00:03:30.470 --> 00:03:33.410
nail the railroad ties
in and things like that.

00:03:33.410 --> 00:03:35.440
You need people to just,
you know, work on the rig.

00:03:35.440 --> 00:03:37.610
You need people to work
on the assembly line.

00:03:37.610 --> 00:03:40.340
And the Industrial Revolution
was really a process

00:03:40.340 --> 00:03:43.570
of taking these crafts and
turning them into more and more,

00:03:43.570 --> 00:03:47.200
you know, one-off, almost you
could call it commodity labor.

00:03:47.200 --> 00:03:48.860
Now let's think about the present day,

00:03:48.860 --> 00:03:50.170
and we could probably,

00:03:50.170 --> 00:03:52.620
I think it's fair to call
it the Information Age,

00:03:55.370 --> 00:03:56.820
Information Age.

00:03:56.820 --> 00:04:01.460
And what are the growth industries

00:04:01.460 --> 00:04:03.370
in the Information Age?

00:04:03.370 --> 00:04:05.740
Well, one that's close to my heart,

00:04:05.740 --> 00:04:09.000
I'm making this video in the
middle of Silicon Valley,

00:04:09.000 --> 00:04:11.555
is software.

00:04:11.555 --> 00:04:12.750
Actually, that's probably the one

00:04:12.750 --> 00:04:15.410
that really stands out to
me as a major growth area,

00:04:15.410 --> 00:04:18.300
but there's, you know, kind of biotech,

00:04:18.300 --> 00:04:20.530
biotech, we could go on and on and on.

00:04:20.530 --> 00:04:23.000
And what's common about all of these?

00:04:23.000 --> 00:04:24.610
Well, they're not necessarily

00:04:24.610 --> 00:04:26.700
as capital-intensive as what we see here.

00:04:26.700 --> 00:04:30.610
In particular, if we're
talking about software,

00:04:30.610 --> 00:04:32.640
it's not very capital-intensive at all.

00:04:32.640 --> 00:04:35.640
You just need some computers
and a place to program,

00:04:35.640 --> 00:04:37.870
and you can, in theory, do
it inside someone's house.

00:04:37.870 --> 00:04:40.080
And this is really more about highly,

00:04:40.080 --> 00:04:42.500
highly, highly skilled labor.

00:04:42.500 --> 00:04:45.050
Same thing with biotech,
it does need capital,

00:04:45.050 --> 00:04:47.450
but that capital isn't for railroads

00:04:47.450 --> 00:04:49.990
or isn't for, you know, hugely,

00:04:49.990 --> 00:04:52.840
I mean, there is some equipment,
but it's mainly for people.

00:04:52.840 --> 00:04:54.420
It's mainly for researchers

00:04:54.420 --> 00:04:58.310
and people to run the clinical
trials and for whatever else.

00:04:58.310 --> 00:05:01.120
And so we are, it seems
like we are in an age

00:05:01.120 --> 00:05:04.980
where labor is going to become
more and more invaluable,

00:05:04.980 --> 00:05:07.480
more valuable, but not
just commodity labor,

00:05:07.480 --> 00:05:09.000
not just to someone to kind of, you know,

00:05:09.000 --> 00:05:10.770
work one shift at the factory,

00:05:10.770 --> 00:05:13.490
but highly, highly, highly skilled labor.

00:05:13.490 --> 00:05:16.300
Now, just because this is happening, this,

00:05:16.300 --> 00:05:20.160
or because this is happening,
this could be a driver

00:05:20.160 --> 00:05:22.630
of more and more income going to labor.

00:05:22.630 --> 00:05:25.830
But that by itself wouldn't necessarily

00:05:25.830 --> 00:05:27.140
drive off inequality.

00:05:27.140 --> 00:05:29.390
For example, you might have a situation,

00:05:29.390 --> 00:05:32.610
and there's some date signs
that maybe this is happening,

00:05:32.610 --> 00:05:34.990
where if you look at, if
this is the pool of folks,

00:05:34.990 --> 00:05:37.380
that the people who are
able to participate in this,

00:05:37.380 --> 00:05:39.750
these high-growth sectors

00:05:39.750 --> 00:05:42.700
where labor adds a
significant amount of value,

00:05:42.700 --> 00:05:45.720
that that's actually a small
percentage of this population.

00:05:45.720 --> 00:05:48.080
So a small percentage of the population

00:05:48.080 --> 00:05:49.260
is going to take advantage,

00:05:49.260 --> 00:05:51.640
could potentially take
advantage of these, and if,

00:05:51.640 --> 00:05:53.130
of these dynamics.

00:05:53.130 --> 00:05:54.520
But if the rest of the population

00:05:54.520 --> 00:05:56.880
doesn't have the skills necessary,

00:05:56.880 --> 00:05:59.600
then they're going to
essentially be left out

00:05:59.600 --> 00:06:02.470
of this growth, and so that
could still drive inequality.

00:06:02.470 --> 00:06:03.830
It won't be driving inequality

00:06:03.830 --> 00:06:07.710
because of income going
more and more to capital,

00:06:07.710 --> 00:06:09.540
because of R being greater than G,

00:06:09.540 --> 00:06:11.510
because returns of capital
are greater than growth.

00:06:11.510 --> 00:06:12.890
It wouldn't be because of that.

00:06:12.890 --> 00:06:16.100
It would be because of this
differentiation in labor

00:06:16.100 --> 00:06:18.210
where highly, highly skilled labor

00:06:18.210 --> 00:06:20.640
is getting a disproportionate
share of the income

00:06:20.640 --> 00:06:23.540
relative to other labor.

00:06:23.540 --> 00:06:24.840
So the question is,

00:06:24.840 --> 00:06:27.640
is can we get more people
to participate this?

00:06:27.640 --> 00:06:30.000
And once again, this is
an issue of education.

00:06:30.000 --> 00:06:33.720
Can we get this pool, as a
percentage of the population,

00:06:33.720 --> 00:06:36.470
to become a much larger
pool of the population

00:06:36.470 --> 00:06:38.080
so more and more,

00:06:38.080 --> 00:06:40.360
so more and more of the world,

00:06:40.360 --> 00:06:44.550
more and more of the world
can participate in that?

00:06:44.550 --> 00:06:47.330
So once again, this is just
something to think about.

00:06:47.330 --> 00:06:49.000
I don't know the answer to this,

00:06:49.000 --> 00:06:50.280
but there are some dynamics in play.

00:06:50.280 --> 00:06:52.700
And we're definitely in
a different type of world

00:06:52.700 --> 00:06:54.930
than we were in the Gilded Age.

00:06:54.930 --> 00:06:56.500
Another way that you could think about it,

00:06:56.500 --> 00:06:57.530
and this isn't from the book,

00:06:57.530 --> 00:07:00.860
but this is just a way that
I sometimes think about it.

00:07:00.860 --> 00:07:03.250
If you think, in the
Industrial Revolution,

00:07:03.250 --> 00:07:04.860
you have the world was kind of a,

00:07:04.860 --> 00:07:06.870
the world was kind of a pyramid,

00:07:06.870 --> 00:07:09.443
that down here you have your labor,

00:07:10.740 --> 00:07:13.210
then, and you needed a lot of folks there,

00:07:13.210 --> 00:07:15.120
but it was relatively unskilled.

00:07:15.120 --> 00:07:16.440
And then in the middle,

00:07:16.440 --> 00:07:19.010
you kind of have your white-collar jobs.

00:07:19.010 --> 00:07:22.420
You could, white-collar jobs,
you know, this is the folks

00:07:22.420 --> 00:07:25.450
who are kind of manipulating
information, filing papers,

00:07:25.450 --> 00:07:27.400
et cetera, et cetera, the office jobs.

00:07:27.400 --> 00:07:29.953
And then at the top of the pyramid

00:07:29.953 --> 00:07:31.370
during the Industrial Revolution

00:07:31.370 --> 00:07:34.300
and really going into the
20th century, you had,

00:07:34.300 --> 00:07:38.700
you could, I guess you could
say your capital owners,

00:07:38.700 --> 00:07:40.290
your owners of capital.

00:07:40.290 --> 00:07:42.860
And then you had also a very small,

00:07:42.860 --> 00:07:45.680
you had a very small, I
would say, creative class.

00:07:45.680 --> 00:07:48.740
So this is creative,

00:07:48.740 --> 00:07:49.843
creative,

00:07:50.930 --> 00:07:52.000
creative class.

00:07:52.000 --> 00:07:56.180
And so this would be folks like engineers

00:07:56.180 --> 00:07:58.840
and artists and people doing research.

00:07:58.840 --> 00:08:01.610
And so, this is essentially
the dynamic you had.

00:08:01.610 --> 00:08:03.750
But now when we go into
the Information Age,

00:08:03.750 --> 00:08:06.620
automation is making labor,

00:08:06.620 --> 00:08:08.370
is making labor less important

00:08:08.370 --> 00:08:10.950
in even white-collar jobs,
information processing.

00:08:10.950 --> 00:08:13.840
And so there's two different realities

00:08:13.840 --> 00:08:15.490
that we could potentially go to.

00:08:15.490 --> 00:08:17.030
There's one where essentially

00:08:18.109 --> 00:08:21.630
you still have a relatively small

00:08:21.630 --> 00:08:23.550
class of people who own capital

00:08:23.550 --> 00:08:27.220
or own most of the capital
or, and a creative class.

00:08:27.220 --> 00:08:29.890
And then you have a small,

00:08:29.890 --> 00:08:32.410
you have a, actually, let me just,

00:08:32.410 --> 00:08:34.380
so if I just take that triangle,

00:08:34.380 --> 00:08:36.263
that same triangle right over there,

00:08:39.618 --> 00:08:42.580
so you still have a small group of people

00:08:42.580 --> 00:08:44.380
who fall into the top of the triangle.

00:08:44.380 --> 00:08:47.580
And because automation is
taking care of these middle two,

00:08:47.580 --> 00:08:49.980
you only need a small sliver of people

00:08:49.980 --> 00:08:51.690
who are participating in here.

00:08:51.690 --> 00:08:53.560
And so everyone else here

00:08:53.560 --> 00:08:56.070
is essentially going to be left out.

00:08:56.070 --> 00:08:58.770
So these folks are going to be left out,

00:08:58.770 --> 00:09:01.350
which isn't a good recipe for anyone.

00:09:01.350 --> 00:09:04.050
But there's another reality where,

00:09:04.050 --> 00:09:06.710
well, what if we could
expand this top triangle

00:09:06.710 --> 00:09:08.930
where we can have a larger
and larger creative class?

00:09:08.930 --> 00:09:13.430
And if these people can
participate in the high-value labor

00:09:14.650 --> 00:09:16.260
jobs, I guess you can say,

00:09:16.260 --> 00:09:17.760
then they are going to be in a position

00:09:17.760 --> 00:09:19.550
to capture more and more of the income,

00:09:19.550 --> 00:09:21.080
and then they will also be in a position

00:09:21.080 --> 00:09:22.540
to have more and more capital.

00:09:22.540 --> 00:09:24.890
You see that happening in Silicon Valley.

00:09:24.890 --> 00:09:26.790
People who get a neat software job

00:09:26.790 --> 00:09:30.230
at Google or Facebook or Apple,

00:09:30.230 --> 00:09:31.850
not only, you know, they're getting that

00:09:31.850 --> 00:09:33.260
through their labor,

00:09:33.260 --> 00:09:36.840
but because that income is
larger than their expenses,

00:09:36.840 --> 00:09:39.930
they're able to start
to accumulate capital

00:09:39.930 --> 00:09:42.040
and also become capital owners.

00:09:42.040 --> 00:09:43.310
So there's a reality that,

00:09:43.310 --> 00:09:45.780
if we play our cards right in education,

00:09:45.780 --> 00:09:47.860
and once again, this is close to my heart,

00:09:47.860 --> 00:09:49.250
maybe instead of going to this world

00:09:49.250 --> 00:09:51.200
where we leave all of these people out,

00:09:52.374 --> 00:09:56.590
we can go to a world
that looks more like this

00:09:56.590 --> 00:10:00.300
where we don't need a lot of labor

00:10:00.300 --> 00:10:02.900
because of automation, more kind of,

00:10:02.900 --> 00:10:04.640
I guess you could say commodity labor.

00:10:04.640 --> 00:10:07.270
We don't need a lot of
kind of the traditional

00:10:07.270 --> 00:10:09.920
white-collar jobs in
information processing.

00:10:09.920 --> 00:10:11.100
And then most people,

00:10:11.100 --> 00:10:13.450
if we can get education to be good enough,

00:10:13.450 --> 00:10:17.510
can now participate in
these really high-value jobs

00:10:17.510 --> 00:10:20.030
where labor has a lot more leverage,

00:10:20.030 --> 00:10:22.380
where the returns to labor are larger

00:10:22.380 --> 00:10:23.470
than the returns to capital.

00:10:23.470 --> 00:10:25.630
And because the returns
to labor are larger,

00:10:25.630 --> 00:10:27.500
you're going to have those people also,

00:10:27.500 --> 00:10:29.020
they're gonna get more share of income,

00:10:29.020 --> 00:10:30.960
and they're also going to be able to start

00:10:30.960 --> 00:10:32.820
to accumulate capital.

00:10:32.820 --> 00:10:34.370
So getting to this reality

00:10:34.370 --> 00:10:36.110
where you're having a
larger and larger percentage

00:10:36.110 --> 00:10:39.700
of people who are
essentially capital owners,

00:10:39.700 --> 00:10:43.460
capital owners and software
engineers and artists

00:10:43.460 --> 00:10:45.530
and people doing R and D,

00:10:45.530 --> 00:10:47.340
in my mind, this is predicated

00:10:48.800 --> 00:10:50.600
on improving education.

00:10:50.600 --> 00:10:52.590
So to get from here to here

00:10:52.590 --> 00:10:54.460
and to avoid going to this top one,

00:10:54.460 --> 00:10:58.270
it really is about having

00:10:58.270 --> 00:11:00.330
a more talented labor pool,

00:11:00.330 --> 00:11:02.400
a more educated labor pool.

00:11:02.400 --> 00:11:04.280
And if we pull this off, then we get into

00:11:04.280 --> 00:11:06.650
what could be considered
kind of a Star Trek reality.

00:11:06.650 --> 00:11:08.920
A Star Trek reality, people
don't really view Star Trek

00:11:08.920 --> 00:11:11.210
from economic point of
view, but in Star Trek,

00:11:11.210 --> 00:11:13.130
you might realize that
there aren't a lot of people

00:11:13.130 --> 00:11:14.970
kind of tilling the fields here.

00:11:14.970 --> 00:11:16.090
There aren't a lot of people

00:11:16.090 --> 00:11:17.870
just kind of doing desk jobs at Star Trek.

00:11:17.870 --> 00:11:21.730
Everyone at Star Trek
is either doing R and D,

00:11:21.730 --> 00:11:23.473
they are Explorers,

00:11:25.225 --> 00:11:27.600
or they are artists.

00:11:27.600 --> 00:11:30.900
So once again, just
something to think about,

00:11:30.900 --> 00:11:33.650
that education, that
knowledge dissemination

00:11:33.650 --> 00:11:37.820
could be a very, very
powerful force of convergence

00:11:37.820 --> 00:11:41.163
and keep us from going
into another Gilded Age.


r greater than g but less inequality

WEBVTT
Kind: captions
Language: en

00:00:00.600 --> 00:00:01.750
- [Instructor] One of the core ideas

00:00:01.750 --> 00:00:04.480
of Thomas Piketty's book
is if the return on capital

00:00:04.480 --> 00:00:06.870
is greater than the growth in economy,

00:00:06.870 --> 00:00:09.410
then that could drive inequality.

00:00:09.410 --> 00:00:12.183
That could drive inequality.

00:00:13.460 --> 00:00:14.410
Inequality.

00:00:14.410 --> 00:00:17.490
And inequality is a natural
byproduct of a market

00:00:17.490 --> 00:00:19.987
capitalist economy and
one could argue that,

00:00:19.987 --> 00:00:23.462
"Hey, look, some inequality
is going to happen

00:00:23.462 --> 00:00:25.047
"as you grow your economy
and you let people

00:00:25.047 --> 00:00:27.217
"be entrepreneurial, and
some people get lucky,

00:00:27.217 --> 00:00:29.247
"some people less lucky,
some people work harder,

00:00:29.247 --> 00:00:31.687
"some people work less
hard, some people are able

00:00:31.687 --> 00:00:33.850
"to allocate capital
well, some people aren't."

00:00:33.850 --> 00:00:36.550
So it all comes into
it, but in extreme forms

00:00:36.550 --> 00:00:37.630
maybe this is bad.

00:00:37.630 --> 00:00:40.660
And in particular, maybe
this is bad for democracy.

00:00:40.660 --> 00:00:44.170
So bad for democracy right over here.

00:00:44.170 --> 00:00:47.300
Maybe too much power starts
to accrue in some ways.

00:00:47.300 --> 00:00:48.930
And maybe that and in the worst case

00:00:48.930 --> 00:00:52.370
because that kind of starts
to drive in on itself.

00:00:52.370 --> 00:00:54.390
It actually might even
hurt economic growth

00:00:54.390 --> 00:00:57.120
if you don't have enough
consumers or people

00:00:57.120 --> 00:00:59.490
with enough purchasing
power, discretionary income.

00:00:59.490 --> 00:01:01.420
Or whatever else.

00:01:01.420 --> 00:01:03.540
But what I really wanna focus on here

00:01:03.540 --> 00:01:06.880
is not so much whether these causalities

00:01:06.880 --> 00:01:09.210
are actually there or how much
we should worry about them.

00:01:09.210 --> 00:01:11.770
Once again, my point
isn't to give an opinion

00:01:11.770 --> 00:01:15.410
on whether I agree or disagree
with some or all of the book.

00:01:15.410 --> 00:01:16.740
It's really just to give you a framework

00:01:16.740 --> 00:01:18.760
because I think the book at least raises

00:01:18.760 --> 00:01:20.576
an interesting conversation
and it gives us

00:01:20.576 --> 00:01:23.290
a lot of I would say
fodder for interesting

00:01:23.290 --> 00:01:24.980
analysis and critical thinking.

00:01:24.980 --> 00:01:26.790
And that's really what I
want you to walk away with.

00:01:26.790 --> 00:01:28.210
How do you think about these things?

00:01:28.210 --> 00:01:31.100
And you just need to
make your own judgment.

00:01:31.100 --> 00:01:33.230
So what I wanna do here is at least show

00:01:33.230 --> 00:01:35.660
a circumstance that this might be

00:01:35.660 --> 00:01:39.140
returns on capital being
greater than economic growth.

00:01:39.140 --> 00:01:43.770
Can be a reasonable proxy
for rising inequality.

00:01:43.770 --> 00:01:46.120
And of course we, you know,
this connection over here

00:01:46.120 --> 00:01:48.010
is even kind of a harder thing

00:01:48.010 --> 00:01:50.420
to necessarily draw the connection.

00:01:50.420 --> 00:01:55.293
But even this one isn't
always going to be the case.

00:01:56.630 --> 00:01:59.950
And to think about
that, let's just imagine

00:01:59.950 --> 00:02:04.070
an economy where the whole
economy just produces.

00:02:04.070 --> 00:02:06.450
It just produces apples.

00:02:06.450 --> 00:02:10.430
So let's say the whole
economy right over here,

00:02:10.430 --> 00:02:12.730
this is our whole, our entire economy.

00:02:12.730 --> 00:02:14.283
And let me copy and paste it.

00:02:15.160 --> 00:02:17.930
So copy and paste it.

00:02:17.930 --> 00:02:20.130
I'm gonna paste it to show
the growth in the economy.

00:02:20.130 --> 00:02:24.060
So let's say in year
one, so this is year one

00:02:24.060 --> 00:02:25.103
right over here.

00:02:27.076 --> 00:02:29.893
Year one, it produced 1000 apples.

00:02:32.520 --> 00:02:35.393
1000 apples.

00:02:36.347 --> 00:02:38.430
And let's say in year two.

00:02:38.430 --> 00:02:43.430
Year two, we have economic growth.

00:02:43.460 --> 00:02:44.930
So let me draw that.

00:02:44.930 --> 00:02:49.160
So G going from year one
to year two, let's say

00:02:49.160 --> 00:02:51.403
that this is equal to 2%.

00:02:52.360 --> 00:02:55.590
So 2% of 1000 would be 20 more apples.

00:02:55.590 --> 00:03:00.023
So in year two the economy produces 1020.

00:03:01.108 --> 00:03:04.780
1020 apples, right over there.

00:03:04.780 --> 00:03:08.130
Now let's say that in year one.

00:03:08.130 --> 00:03:12.410
In year one, of the 1000
apples that were produced.

00:03:12.410 --> 00:03:16.870
Let's say that 500 of them,
I'll just split it half.

00:03:16.870 --> 00:03:21.100
Let's say 500 of them go
to the owners of capital.

00:03:21.100 --> 00:03:25.830
500 to the owners of capital.

00:03:25.830 --> 00:03:27.240
Now, what's the owners of capital?

00:03:27.240 --> 00:03:28.470
What do they own and
what's 'cause it's a very

00:03:28.470 --> 00:03:30.570
simple economy that only has one industry

00:03:30.570 --> 00:03:32.088
right over here.

00:03:32.088 --> 00:03:33.400
But the owners of capital
are the people who would

00:03:33.400 --> 00:03:35.550
own the orchard, who own the trees,

00:03:35.550 --> 00:03:37.560
who own the machinery, whatever they need

00:03:37.560 --> 00:03:39.520
to pick the apples.

00:03:39.520 --> 00:03:42.663
And let's say that the
other 500 goes to labor.

00:03:45.870 --> 00:03:47.463
500 to labor.

00:03:48.420 --> 00:03:52.840
And let's say that the
value of the capital here.

00:03:52.840 --> 00:03:54.383
So the value.

00:03:56.040 --> 00:03:59.537
Of capital in apples.

00:03:59.537 --> 00:04:01.440
we're just assuming everything
going on here, is apples.

00:04:01.440 --> 00:04:04.380
I guess to buy this apple
orchard, the owner of it

00:04:04.380 --> 00:04:08.130
had to give, let's say 4000 apples.

00:04:08.130 --> 00:04:10.720
4000 apples.

00:04:10.720 --> 00:04:14.620
So given this, what is the
return on capital in year one?

00:04:14.620 --> 00:04:17.670
Well, the return on
capital, I'll just write.

00:04:17.670 --> 00:04:22.190
Return on capital.

00:04:22.190 --> 00:04:25.620
Capital in year one is going to be.

00:04:25.620 --> 00:04:28.230
well, the return is 500 apples.

00:04:28.230 --> 00:04:30.290
500 apples.

00:04:30.290 --> 00:04:32.390
Divided by the cost,
or I guess we could say

00:04:32.390 --> 00:04:34.410
the value of the capital.

00:04:34.410 --> 00:04:36.433
So divided by 4000.

00:04:37.680 --> 00:04:39.440
4000 apples.

00:04:39.440 --> 00:04:42.260
So that's going to give us five.

00:04:42.260 --> 00:04:46.910
Five divided by, assuming
it's five divided by 40.

00:04:46.910 --> 00:04:48.860
Which is one-eighth.

00:04:48.860 --> 00:04:50.600
So that's going to 12.5%.

00:04:52.388 --> 00:04:54.070
12.5%.

00:04:54.070 --> 00:04:56.240
So the return on capital,
at least in year one.

00:04:56.240 --> 00:04:58.620
Is greater than.

00:04:58.620 --> 00:05:00.070
Well, let's go to year two.

00:05:00.070 --> 00:05:01.960
So we can look at the return
on capital in year two.

00:05:01.960 --> 00:05:03.653
And compare it.

00:05:03.653 --> 00:05:05.800
And compare it to the
growth right over here.

00:05:05.800 --> 00:05:10.090
And so let's just say that
the value of the capital.

00:05:10.090 --> 00:05:11.860
That all of it was reinvested.

00:05:11.860 --> 00:05:13.930
So now the value of the capital.

00:05:13.930 --> 00:05:17.653
Value of capital.

00:05:19.040 --> 00:05:22.623
Is now 4000 plus 500 more apples.

00:05:23.700 --> 00:05:27.590
So 4500 apples, they
reinvested it in the business.

00:05:27.590 --> 00:05:30.180
And they didn't necessarily
use the apples as capital.

00:05:30.180 --> 00:05:32.520
But they use those extra
500 apples to go buy

00:05:32.520 --> 00:05:33.600
some more machinery.

00:05:33.600 --> 00:05:34.960
Or buy some more land.

00:05:34.960 --> 00:05:36.253
Whatever it might be.

00:05:37.110 --> 00:05:38.750
And let's say though, that the laborer had

00:05:38.750 --> 00:05:40.520
a little bit of leverage this year.

00:05:40.520 --> 00:05:42.970
So in this year, because
the laborer had leverage.

00:05:42.970 --> 00:05:45.660
Only 500 still goes to
the owners of capital.

00:05:45.660 --> 00:05:47.290
Now this isn't necessarily
going to be the case.

00:05:47.290 --> 00:05:49.360
If the owners of the
capital have leverage,

00:05:49.360 --> 00:05:51.460
maybe they can negotiate the other way.

00:05:51.460 --> 00:05:53.980
But let's say in this situation, still 500

00:05:54.926 --> 00:05:56.573
goes to labor.

00:05:58.414 --> 00:05:59.903
Sorry, 500 goes to capital.

00:06:01.090 --> 00:06:02.730
Capital.

00:06:02.730 --> 00:06:04.820
And here, 520.

00:06:06.350 --> 00:06:07.653
520 would go to labor.

00:06:09.070 --> 00:06:13.480
520 to labor.

00:06:13.480 --> 00:06:15.320
So now what's the return on capital?

00:06:15.320 --> 00:06:17.890
The return on capital now is going to be.

00:06:17.890 --> 00:06:19.803
Still 500 apples.

00:06:20.908 --> 00:06:21.823
500 apples.

00:06:23.690 --> 00:06:24.523
Divided by 4500.

00:06:26.700 --> 00:06:28.833
4500 apples.

00:06:30.290 --> 00:06:34.590
Which is going to be equal to one-ninth.

00:06:34.590 --> 00:06:37.676
Which is the same thing as, what is that?

00:06:37.676 --> 00:06:38.509
0.99.

00:06:38.509 --> 00:06:39.970
So let's see, oh actually 0.1111.

00:06:39.970 --> 00:06:42.592
Let me just, one divided by nine.

00:06:42.592 --> 00:06:43.425
Yep, it's 0.11111.

00:06:43.425 --> 00:06:45.810
So it's going to be approximately 11%.

00:06:45.810 --> 00:06:47.740
Or let's say 11.1%.

00:06:47.740 --> 00:06:50.690
Approximately 11.1%.

00:06:50.690 --> 00:06:53.110
Now the whole reason why
I wanted to show that.

00:06:53.110 --> 00:06:54.260
Why I did this diagram.

00:06:54.260 --> 00:06:55.720
Is that this is a situation where

00:06:55.720 --> 00:06:57.800
R is greater than G.

00:06:57.800 --> 00:07:02.800
Our return on capital,
is 12.5% going to 11.1%.

00:07:02.950 --> 00:07:05.430
Both of these numbers
are much larger than our

00:07:05.430 --> 00:07:07.640
growth of the entire economy.

00:07:07.640 --> 00:07:09.870
But even though that's
happening, you actually

00:07:09.870 --> 00:07:12.317
don't have rising in equality over here.

00:07:12.317 --> 00:07:13.210
In this situation, of course.

00:07:13.210 --> 00:07:14.770
I worked the numbers to make this happen.

00:07:14.770 --> 00:07:16.480
I could have worked them the other way.

00:07:16.480 --> 00:07:19.540
But in this situation it's
not necessarily the case

00:07:19.540 --> 00:07:24.010
that R being greater than
G lead to more inequality.

00:07:24.010 --> 00:07:25.730
Now in future videos
I'll do some spreadsheets

00:07:25.730 --> 00:07:29.350
where you see, if R stays
constant at a constant value

00:07:29.350 --> 00:07:30.600
higher than G.

00:07:30.600 --> 00:07:31.970
That will lead to inequality.

00:07:31.970 --> 00:07:34.010
But the whole reason why I
did this one is to show you.

00:07:34.010 --> 00:07:37.160
That just in a given period of
time, R being greater than G.

00:07:37.160 --> 00:07:39.330
Doesn't necessarily mean more inequality.

00:07:39.330 --> 00:07:44.330
In this case, labor got more of a fraction

00:07:44.380 --> 00:07:46.630
of the total national income.

00:07:46.630 --> 00:07:49.150
And once again, the
connection being capital

00:07:50.149 --> 00:07:51.310
and labor and income inequality.

00:07:51.310 --> 00:07:55.780
Is that, in general the
income that goes to labor

00:07:55.780 --> 00:07:59.830
is more indicative of the
income that might go to the

00:07:59.830 --> 00:08:03.010
lower quartiles of a population.

00:08:03.010 --> 00:08:04.920
And the income that goes to capital,

00:08:04.920 --> 00:08:08.160
is more indicative of the income

00:08:08.160 --> 00:08:11.345
that might go to the top
percentile or decile.

00:08:11.345 --> 00:08:13.090
Because capital tends to be concentrated

00:08:13.090 --> 00:08:15.763
in the top few sections.