The Gates Notes: Administrators in Los Altos

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JEFFREY BAIER: When I
first saw Khan Academy,

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what was attractive
to me was the ability

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for students to learn concepts
at their own pace, when

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they were ready for them.

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And it brings that learning to
students both in the classroom

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and at home with a seamless
transition from one location

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to the next.

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ALYSSA GALLAGHER:
What caught our eye

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in using it to
differentiate instruction

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is the interface that
the students have,

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and really on the back end,
all of the complex data

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that's provided to the teachers.

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It would take them hours to
get that same kind of data.

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SANDRA McGONAGLE: It
was easy to roll out.

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Thankfully, I have some teachers
who are just great risk takers

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and saw the potential of how
it would help their students.

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Cost wise is great.

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I know there are other math
programs out there that you

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can purchase, but it is a
cost and it's not real time.

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JEFFREY BAIER: The data sets
the Khan Academy provides

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allows principals at
the school site level

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to have conversations
with their teachers about

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progress students are making;
to recognize very quickly which

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students are grasping
skills and moving ahead,

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which students are struggling
with a particular concept,

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and which students
are stuck and need

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some additional intervention.

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ALYSSA GALLAGHER: Khan
Academy is directly

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helping because every
day, every child

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has the opportunity
to have individualized

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learning opportunities, where
they are specifically working

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at their level, being provided
with instantaneous feedback.

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Which is not something
that they would

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get in the traditional
teacher lecture model.

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SANDRA McGONAGLE:
I see every student

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utterly engaged in
what they're doing.

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And they are talking about math.

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They are excited about math.

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They're appropriately
challenged.

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And those kids who are
really math superstars

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are able to push themselves
to where they want to be.

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JEFFREY BAIER: The
parent involvement aspect

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is important, as well,
because they can actually

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see the teaching, the
instruction, as the student

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hears the instruction in class,
as well, because they, too,

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can watch the videos.

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It brings an opportunity
into the home for parents

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to have conversations
with their children

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about math, about
learning, and about what

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they're doing in school.

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SANDRA McGONAGLE: I am most
excited that our kids are

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happy and excited about
learning, and especially

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learning math, because it
seems to be the older you get

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in grades, you either have
determined for yourself

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that you love math, or
you're not good at math.

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And so if kids can have
success at their level,

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to build that mental
math capability,

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I think that's amazing.

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JEFFREY BAIER: When both
teachers and students

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are excited about the
teaching and learning going on

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in the classroom, it has
limitless possibilities.


The Gates Notes:  Insights into students' progress

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Shantanu: We tell teachers that you
shouldn't be the sage on the stage

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but you should actually
be the guide on the side.

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But they really don't have the tools

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that are necessary to really
make that possible today.

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One of the big differences
with Khan Academy

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is that we're not trying to just replicate
the existing systems using technology

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to augment the way existing
instruction is done.

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We're fundamentally thinking
about reinventing instruction.

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Sal: We've gotten letters
from teachers who said,

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"Hey, you've already given the lecture
on L'Hopitals rule or the unit circle."

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Instead of me giving the
basic lecture on that

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and then assigning
homework, we flip the model.

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I'm assigning the lecture
for them to watch at home

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and then they can watch what I assign.

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But then if they have some
questions they can re-mediate

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and watch stuff that was
taught in previous sections.

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Or if they're bored they can move
ahead and go as advance as they want.

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Then when they go into the classroom
they can actually do problems,

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they should do their
homework in the classroom.

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We have this teacher dash board right now

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where it shows all of the
students and all of the concepts.

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Within a glance a teacher
can see whose mastered what,

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who's struggling with what,

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where each student is in their
development and learning.

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They can see in real time where
all the students are in aggregate.

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The coach will be able to see who's stuck.

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They can click on any one of the concepts

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and see exactly what the
students have been up to.

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By problem, they can see how
long they spent on each problem.

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Did they get it right or wrong?

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Did they watch the video before
or after working on that problem.

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If they saw that they got a problem wrong
they can actually click on that part

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and see the exact problem
that they got wrong,

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so they can really diagnose and
do very focused interventions

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to kind of make sure that all
of the students are progressing.

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In every other industry, if you want to
diagnose why something is not working,

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you try to get as much
data on it as possible,

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so that you can really say, "Okay,"

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"I need to just tighten
that part right over there."

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What we're trying to do is give
teachers that level of data.

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Shantanu: We can just try to
impact individuals directly

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without having to change the
entire educational system.

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Sal: To roll out it's actually super
simple, it's all web based, it's all free,

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so literally if a school has internet
connectivity and has computers,

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any type of computer, they're ready
to start 1 + 1 and get to Calculus.


The Gates Notes: Sal on Khan Academy

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In 2004, my cousin Nadia was
having trouble with math.

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She was in New Orleans,
I was in Boston.

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I decided to
virtually tutor her.

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It worked out, so I said, oh,
let me tutor some other family

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members.

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It became pretty
obvious pretty quick

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that it was hard to
scale that, and it

00:00:26.210 --> 00:00:27.590
was hard to schedule
it all the time.

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So essentially, I just started
putting videos on YouTube.

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In 2009, I started doing
Khan Academy full-time.

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In the fall of
2010, we got funding

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from the Bill and Melinda Gates
Foundation, and from Google,

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and now we're a
real organization.

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Right now in a
traditional classroom,

00:00:41.760 --> 00:00:44.093
a teacher has to deliver
essentially a one-size fits all

00:00:44.093 --> 00:00:45.580
lecture, pretty
much guaranteeing

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that some of the students
are going to be lost

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or some are bored.

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Students have to do
problems in a vacuum.

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They come back.

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You kind of repeat that process.

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Then you get a snapshot exam.

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And then on that exam, whether
you get 70%, 90%, or 95%,

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you're moved onto
the next concept.

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And it's almost guaranteed to
leave gaps in your knowledge.

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At some point,
your foundation is

00:01:04.340 --> 00:01:06.548
going to be so weak that it
will essentially crumble.

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There's got to be a
better way to do this.

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Going through the high
school experience, when

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we would train for
math competitions,

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we had a completely different
way of teaching each other.

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Everyone was learning math
a lot better in this kind

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of extracurricular
setting where the peers

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were teaching each other.

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Everyone was learning
at their own pace.

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It was really interactive,
really social.

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People were starting to make the
connections across subject area

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because you had to have a
holistic understanding when

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you went to a competition.

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The ideal interaction is
one-on-one, you have a tutor,

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you have a student,
and the tutor

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can kind of adapt
to the student.

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And the reason why that doesn't
exist in the school system

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is that that's not economic.

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How do you reduce that?

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How do we give
them more resources

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so it's a lower
student-teacher ratio?

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In my mind, the
relevant metric is

00:01:45.850 --> 00:01:50.177
student to actual productive
time with the teacher ratio.

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We see the Khan
Academy as essentially

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the world's free virtual school.

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We have the videos,
literally covering everything

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from basic arithmetic all the
way through college-level math

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and science and economics.

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The lecturer frees
up the teacher,

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so that all of their
time is now spent

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on these focused interventions.

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We have the software platform.

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And we have a way for students
and teachers and parents

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to get data on what's happening.

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And for our students and
teachers and parents actually

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communicate with each other,
and maybe actually even

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teach each other.

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So we actually see it as a real,
virtual school for the world.


Answers to Questions from the Independent

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Voiceover: These are questions
from the Independent in the UK.

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The first question is how does
he, I'm assuming that's me Sal,

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how does he see the development
in video conferencing?

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Particularly new services
like Google Hangouts

00:00:14.664 --> 00:00:17.598
as affecting the provision
of distance learning.

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Is that something that he sees
the Khan Academy using and
in what kind of time frame?

00:00:22.650 --> 00:00:25.452
Interesting question, so
there's a couple of layers here.

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First of all, just kind of
the idea of distance learning

00:00:28.922 --> 00:00:31.999
and this is where I think right now
everything that's online learning

00:00:31.999 --> 00:00:35.448
kind of gets grouped to into
distance learning and online learning

00:00:35.448 --> 00:00:36.719
and all the same.

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Most people kind of don't really
differentiate between what they are.

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Right now, what's happening
with distance learning

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is that they are for the most part

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very similar what happens
in physical classes.

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It's just the people
aren't in the same room.

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Distance learning fundamentally,
they still involve

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when someone is participating in the
learning there is a live professor

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or teacher on the other side of that,

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and they still are kind
of signing up for courses.

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They still meet at a certain
time to do their courses

00:01:05.949 --> 00:01:07.324
or to do their interactions.

00:01:07.324 --> 00:01:10.657
I would call it much more in the
domain a synchronous learning

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which means that all the parties
have to be there at the same time

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and that all the students are also
kind of moving along at the same pace.

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It really is exactly
as the physical model,

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it's just they've taken the idea that
you have to be in the same place.

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Khan Academy isn't the
only version of this

00:01:26.256 --> 00:01:29.284
but Khan Academy, we kind of view
it as more of asynchronous model.

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Asynchronous which really just means

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that things aren't necessarily
happening at the same place.

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Which is the idea that I can
record this video right now

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and you don't have to be
listening to it right now.

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You might listen to this video an hour
later or a day later, or a year later.

00:01:43.336 --> 00:01:46.001
You can really go through
things at your own pace.

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We don't view video conferencing as
maybe our main delivery mechanism

00:01:53.308 --> 00:01:57.315
although distance learning,
vendors or companies or schools

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might view video conferencing as
their main way to get to people.

00:02:00.533 --> 00:02:04.671
We think, we can record videos, people
can consume those at their own pace

00:02:04.671 --> 00:02:07.068
and we can give people
exercises and feedbacks

00:02:07.068 --> 00:02:08.934
that they can do at their own pace.

00:02:08.934 --> 00:02:11.538
Where we do think video
conferencing could be

00:02:11.538 --> 00:02:16.365
really, really, really interesting, this
is something that we have not done yet.

00:02:16.365 --> 00:02:17.946
We've kind of thrown around the idea

00:02:17.946 --> 00:02:20.029
and we just really have to get
the bandwidth to address it,

00:02:20.029 --> 00:02:26.192
is I think video conferencing
is an amazing way to have
peer to peer interactions.

00:02:26.192 --> 00:02:30.697
Peer to peer, I'll just do the
acronym, peer to peer interactions.

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Right now in a lot of the classrooms
that are piloting Khan Academy

00:02:34.860 --> 00:02:38.409
or even the ones doing it on their own,
and this is what we really advocate

00:02:38.409 --> 00:02:40.402
is every student works at their own pace

00:02:40.402 --> 00:02:42.469
but when they're stuck either
this teacher intervenes

00:02:42.469 --> 00:02:44.135
based on the data the teacher sees

00:02:44.135 --> 00:02:46.870
or even better a student
intervenes and helps their peer.

00:02:46.870 --> 00:02:51.533
There's no reason why that has to
be sit just in a physical classroom

00:02:51.533 --> 00:02:53.462
but you can actually
transcend a physical classroom

00:02:53.462 --> 00:02:56.529
and that's where something like video
conferencing could be really valuable.

00:02:56.529 --> 00:02:59.796
If two people could share a blackboard
that looks very similar like this

00:02:59.796 --> 00:03:03.686
and they have either a
tablet device or a pen tablet

00:03:03.686 --> 00:03:07.352
like what I'm using right now, they can
run a tutoring session with each other.

00:03:07.352 --> 00:03:09.730
Would even be cool if they could
record it and they could be archived

00:03:09.730 --> 00:03:12.599
for other people to use it in the future.

00:03:12.599 --> 00:03:16.594
That is really powerful and that's
mainly in the tutoring space,

00:03:16.594 --> 00:03:19.197
so that you can have
peer to peer tutoring.

00:03:20.182 --> 00:03:22.812
Tutoring or really
teaching or mentoring even.

00:03:22.812 --> 00:03:26.118
The other interesting place where peer
to peer actions could be interesting,

00:03:26.118 --> 00:03:30.011
I think this is completely untapped,
is the whole idea of assessment.

00:03:30.011 --> 00:03:34.069
Right now, Khan Academy the
assessment piece happens,

00:03:34.069 --> 00:03:36.484
you're doing exercises, it
keeps track of how you're doing.

00:03:36.484 --> 00:03:40.938
In a traditional classroom assessments
are some form of paper exam.

00:03:40.938 --> 00:03:43.905
It could be multiple choice, it could
be free answer, it could be essay exam

00:03:43.905 --> 00:03:48.627
but I think what most of us have
always realized is that the most,

00:03:48.627 --> 00:03:51.800
the highest form of assessment is
either the practical assessment

00:03:51.800 --> 00:03:53.353
or the oral assessment.

00:03:53.353 --> 00:03:57.278
Practical would literally mean
if you're studying to be a nurse

00:03:57.278 --> 00:04:03.132
someone observes you while you're trying
to insert an IV into someones arm.

00:04:03.132 --> 00:04:06.111
Oral examination, and this
is really the goal standard

00:04:06.111 --> 00:04:07.533
for what we see in the academia.

00:04:07.533 --> 00:04:09.693
Is when you're going to your qualifiers,

00:04:09.693 --> 00:04:11.771
there's an oral part of that examination

00:04:11.771 --> 00:04:15.532
and then essentially you'll sit in
front of a room full of faculty members

00:04:15.532 --> 00:04:19.027
and they'll grill you on and make sure
you really, really, really do understand

00:04:19.027 --> 00:04:20.726
a concept deeply.

00:04:20.726 --> 00:04:24.961
What we think we could do, we're on the
peer to peer side is eventually have -

00:04:24.961 --> 00:04:28.261
not only just a kind of assessment that
we already have in place of Khan Academy

00:04:28.261 --> 00:04:29.963
but maybe an oral assessment.

00:04:29.963 --> 00:04:33.876
Where right now maybe you are a,
we don't have the proper words for,

00:04:33.876 --> 00:04:39.460
but maybe you are a level one in
Trigonometry or level one in Algebra

00:04:39.460 --> 00:04:43.665
and you want to become
level two in Trigonometry.

00:04:43.665 --> 00:04:46.091
You want to get into this,
like a smaller circle,

00:04:46.091 --> 00:04:47.466
there's more a lead circle of people

00:04:47.466 --> 00:04:49.335
who've gotten to this deep
level of trigonometry.

00:04:49.335 --> 00:04:51.963
To do that, maybe at a
baseline you have to do some,

00:04:51.963 --> 00:04:55.949
you have to show that you've
done something kind of
the traditional exercises

00:04:55.949 --> 00:04:59.601
on Khan Academy at your own
pace and you've been able
to prove competency there.

00:04:59.601 --> 00:05:02.615
But to really make it, then you
would have an oral examination

00:05:02.615 --> 00:05:05.487
with maybe five people from level two.

00:05:08.241 --> 00:05:11.741
If maybe four of the five say
that you are ready for level two

00:05:11.741 --> 00:05:13.591
then you will be bumped up to level two.

00:05:13.591 --> 00:05:15.929
Then one of your responsibilities
as someone in level two

00:05:15.929 --> 00:05:20.944
is assess future people from
level one, coming from level one.

00:05:20.944 --> 00:05:24.204
Then of course your next
aspiration is to go to level three

00:05:24.204 --> 00:05:26.608
or going to become a
master of all of the Math

00:05:26.608 --> 00:05:27.997
or whatever you might want to say.

00:05:27.997 --> 00:05:30.609
I think peer to peer interactions
could be really, really powerful

00:05:30.609 --> 00:05:33.062
when it comes to the assessment part.

00:05:33.062 --> 00:05:37.039
I'd be hard pressed to see
how this isn't more rigorous

00:05:37.039 --> 00:05:38.783
than really all the
assessment that has in place.

00:05:38.783 --> 00:05:42.086
Because you're not just being
assessed by arbitrary peers,

00:05:42.086 --> 00:05:45.672
you're being assessed by peers who've
already really proven themselves

00:05:45.672 --> 00:05:48.073
to really deeply understand the concept.

00:05:48.780 --> 00:05:51.882
The other things when you say,

00:05:51.882 --> 00:05:56.492
is that something he sees the Khan
Academy using and what kind of time frame?

00:05:56.492 --> 00:05:59.725
Once again we do see ourselves using
it but we don't know the time frame,

00:05:59.725 --> 00:06:00.864
it's just a bandwidth issue.

00:06:00.864 --> 00:06:03.388
That reminds me, so the other
area I think video conferencing

00:06:03.388 --> 00:06:06.280
could be really powerful is in
the idea of foreign language.

00:06:06.280 --> 00:06:10.135
Once again the goal standard in
foreign language is really immersion

00:06:10.135 --> 00:06:15.239
but that's obviously not always
possible or economically possible.

00:06:15.239 --> 00:06:18.770
The second best thing to immersion
is actually having live interactions

00:06:18.770 --> 00:06:20.459
with people on the other side of the world

00:06:20.459 --> 00:06:22.482
or maybe even not on the
other side of the world.

00:06:22.482 --> 00:06:24.786
One thing I want to do with
my two and a half year old

00:06:24.786 --> 00:06:28.367
is maybe get him a Skype or maybe
a Google+ buddy or whatever it is

00:06:28.367 --> 00:06:31.382
in different countries so that
he can start chatting with kids

00:06:31.382 --> 00:06:33.119
maybe his own age or little
older, little younger.

00:06:33.119 --> 00:06:36.278
They can just start to at least get
the basics of each others languages

00:06:36.278 --> 00:06:37.928
and start to teach each other.

00:06:37.928 --> 00:06:41.233
I think it can have a lot to
be done, not full immersion

00:06:41.233 --> 00:06:45.748
but some immersion for
foreign language learning.

00:06:45.748 --> 00:06:48.198
Then a lot of the core
for the foreign language

00:06:48.198 --> 00:06:52.574
like the vocabulary and the grammar, we
could probably do our exercise platform

00:06:52.574 --> 00:06:55.235
but this is really what gives you
that deeper understanding of it.

00:06:55.235 --> 00:06:59.163
The next question is, is
there a possibility of Khan
Academy's qualifications,

00:06:59.163 --> 00:07:01.577
achievements being externally
validated at some point

00:07:01.577 --> 00:07:03.520
such that they're
recognized internationally

00:07:03.520 --> 00:07:05.272
as a measure of academic achievement?

00:07:05.272 --> 00:07:07.587
There definitely is a possibility

00:07:07.587 --> 00:07:12.592
and we are exploring to
see how can we validate

00:07:12.592 --> 00:07:14.224
that when someone does
something on Khan Academy,

00:07:14.224 --> 00:07:15.362
that it is really coming from them.

00:07:15.362 --> 00:07:16.585
We think there are ways to do it.

00:07:16.585 --> 00:07:20.192
We could even have places where you
could go and you could show your ID

00:07:20.192 --> 00:07:21.978
or whatever and say,
"Hey look this is me."

00:07:21.978 --> 00:07:24.223
"I'm not going to do
the Khan Academy there."

00:07:24.223 --> 00:07:27.281
Then we could validate that yes this
was definitely the person who did that.

00:07:27.281 --> 00:07:32.660
Then once you do that, we could
give badges or validations

00:07:32.660 --> 00:07:34.583
that "Look this person really
does know that information."

00:07:34.583 --> 00:07:38.869
Then it's a matter of making sure
that they are accepted broadly.

00:07:38.869 --> 00:07:41.895
I think this actually touches
a generalized problem.

00:07:41.895 --> 00:07:45.235
In that right now you and I have
talked about this in other videos,

00:07:45.235 --> 00:07:46.633
in other lectures.

00:07:46.633 --> 00:07:51.140
Right now education is kind of a
mixture of you have the learning part,

00:07:52.939 --> 00:07:54.847
you have the credentialing part,

00:07:56.893 --> 00:07:59.947
and then you have a little
bit of a socialization part.

00:08:02.162 --> 00:08:03.726
You have a little bit of socialization.

00:08:03.726 --> 00:08:06.526
When you go to a university
and you pay the big tuition

00:08:06.526 --> 00:08:10.305
you're kind of getting all of these
stuff and depending who you ask,

00:08:10.305 --> 00:08:12.932
different people think they're paying
for or providing different things.

00:08:12.932 --> 00:08:15.221
If you ask most students
at most universities,

00:08:15.221 --> 00:08:17.734
they're probably most
focused on the credential.

00:08:17.734 --> 00:08:20.026
But if you ask most of the universities

00:08:20.026 --> 00:08:23.113
they'll say, "Hey no, all of our resources
are going to this right over here."

00:08:23.113 --> 00:08:26.984
"The credential is just to make sure
that people are learning the things,"

00:08:26.984 --> 00:08:29.039
"but actually spending
the resources over here."

00:08:29.039 --> 00:08:32.268
That question I think about whether
Khan Academy can get credentials,

00:08:32.268 --> 00:08:34.110
so frankly where the third
party can get credentials

00:08:34.110 --> 00:08:37.367
I think is just the whole
issue of can we decouple this?

00:08:37.367 --> 00:08:41.178
Can we separate, can we
create a line of separation

00:08:41.178 --> 00:08:44.214
between the learning side of
education and the credentialing side?

00:08:44.214 --> 00:08:47.367
I think if you do that generally
something really powerful happens.

00:08:47.367 --> 00:08:50.710
If we can create, and it doesn't
have to come from Khan Academy.

00:08:50.710 --> 00:08:52.416
It can come from a government,
it can come from NGOs,

00:08:52.416 --> 00:08:54.153
it can come from who
knows where it comes from.

00:08:54.153 --> 00:09:00.590
If there is an internationally recognized
battery of examinations, assessments

00:09:00.590 --> 00:09:03.014
and deep assessments they can
be practical, they can be oral,

00:09:03.014 --> 00:09:04.590
they can be paper based, all of the above.

00:09:04.590 --> 00:09:08.162
If you have something like this
that is internationally recognized

00:09:08.162 --> 00:09:11.789
then all of a sudden the
rest of the education world

00:09:11.789 --> 00:09:13.478
will compete right over here

00:09:13.478 --> 00:09:16.295
and then there students will just try
to get this thing right over here.

00:09:16.295 --> 00:09:18.169
What's exciting about something like that

00:09:18.169 --> 00:09:21.008
is then Khan Academy could
compete on equal footing.

00:09:21.008 --> 00:09:25.205
Because if students who choose to
go through Khan academy for free,

00:09:25.205 --> 00:09:27.738
perform just as well on that as a student

00:09:27.738 --> 00:09:30.208
who's spending tens of
thousands of dollars

00:09:30.208 --> 00:09:33.735
or maybe certain students who say, "We
know this just works better for me."

00:09:33.735 --> 00:09:36.069
Or maybe some students
will just learn on the job

00:09:36.069 --> 00:09:39.156
or they'll learn from textbooks

00:09:39.156 --> 00:09:41.190
but allows students to
learn the best way they can,

00:09:41.190 --> 00:09:44.155
the best way that fits their career
and even their economic situation.

00:09:44.155 --> 00:09:46.784
The other good thing is, this
is internationally recognized

00:09:46.784 --> 00:09:51.157
it solves the problem that right
now there are some big name schools

00:09:51.157 --> 00:09:54.134
that if you're lucky enough
to attend one of those schools

00:09:54.134 --> 00:09:55.688
you do have something on your resume

00:09:55.688 --> 00:09:57.835
that anywhere in the world
or anywhere in the country

00:09:57.835 --> 00:09:59.234
someone might recognize it.

00:09:59.234 --> 00:10:03.030
The problem is most universities
aren't internationally recognized

00:10:03.030 --> 00:10:05.466
or aren't recognized
broadly beyond one region,

00:10:05.466 --> 00:10:09.474
and so you have students who are doing
this really, really well right now.

00:10:09.474 --> 00:10:12.267
They're learning or they're
potentially learning really well

00:10:12.267 --> 00:10:15.558
maybe at their regional university
or their community college

00:10:15.558 --> 00:10:17.226
and then they get this credential.

00:10:17.226 --> 00:10:19.337
Then they get this
credential right over here

00:10:19.337 --> 00:10:22.232
but this credential is not
universally recognized.

00:10:22.232 --> 00:10:24.835
It's not the goal of the neighboring
state or the neighboring country

00:10:24.835 --> 00:10:27.072
and people don't know how
to assess that credential.

00:10:27.072 --> 00:10:30.255
This way those students who really
do learn their material well

00:10:30.255 --> 00:10:33.858
will be able to take this
external assessments and prove

00:10:33.858 --> 00:10:36.993
that they know just as well as the
student who went to Oxford or Harvard.


Carry trade basics

WEBVTT
Kind: captions
Language: en

00:00:00.610 --> 00:00:03.640
Let's say that the economy
of country A is stagnating.

00:00:03.640 --> 00:00:06.150
It may be facing a
deflationary crisis.

00:00:06.150 --> 00:00:08.240
So central bank tries
to print as much money

00:00:08.240 --> 00:00:10.440
and lower interest rates
as much as possible.

00:00:10.440 --> 00:00:12.650
And an investor can
go into country A

00:00:12.650 --> 00:00:16.950
and borrow in A's currency
at a 1% interest rate.

00:00:16.950 --> 00:00:18.990
Let's also say that in
the rest of the world,

00:00:18.990 --> 00:00:21.750
and in particular, in
country B, one can actually

00:00:21.750 --> 00:00:24.580
make relatively, or what you
perceive as safe investments

00:00:24.580 --> 00:00:29.040
at a higher interest rate
in country B's currency.

00:00:29.040 --> 00:00:31.820
So let's say that you
can get a 5% return.

00:00:31.820 --> 00:00:34.490
So you could imagine some
opportunistic investors might

00:00:34.490 --> 00:00:37.720
say, wow, I could borrow
in country A's currency.

00:00:37.720 --> 00:00:40.620
And so let's say they go into
country A. They borrow at 1%.

00:00:40.620 --> 00:00:45.160
In particular, they borrow 100--
and I won't call them dollars

00:00:45.160 --> 00:00:47.960
or yens, I'll call them--
or anything, or euros,

00:00:47.960 --> 00:00:51.190
or anything else- I'll call
them 100 A's, where the name

00:00:51.190 --> 00:00:54.730
of A's currency is an A. So they
borrow 100 A's, and let's say

00:00:54.730 --> 00:00:57.470
the conversion rate
is-- at right now,

00:00:57.470 --> 00:01:01.160
at this point in time,
one A is equal to two B's.

00:01:01.160 --> 00:01:02.887
So they go into
currency markets,

00:01:02.887 --> 00:01:03.970
and then they exchange it.

00:01:03.970 --> 00:01:06.280
For every one A,
they get two B's.

00:01:06.280 --> 00:01:08.880
So they exchange it for 200 B's.

00:01:11.550 --> 00:01:13.430
And then they go and invest it.

00:01:13.430 --> 00:01:15.710
They are investing in B's.

00:01:15.710 --> 00:01:20.500
So this is-- they're borrowing
in A's and they're investing

00:01:20.500 --> 00:01:21.400
in B's.

00:01:21.400 --> 00:01:22.750
And so what would happen?

00:01:22.750 --> 00:01:25.680
Well, they're going to get
5% on their money in B's.

00:01:25.680 --> 00:01:28.060
So 5% of 200.

00:01:28.060 --> 00:01:30.510
They're going to get 10 B's--
let's say that's per year--

00:01:30.510 --> 00:01:33.980
so they're going to get 10
B's in interest every year.

00:01:33.980 --> 00:01:35.310
And then they can convert that.

00:01:35.310 --> 00:01:37.160
They can convert
those 10 B's, if we

00:01:37.160 --> 00:01:39.240
assume the exchange
rate holds constant.

00:01:39.240 --> 00:01:40.790
And that is a big assumption.

00:01:40.790 --> 00:01:43.260
They can convert
that to five A's

00:01:43.260 --> 00:01:45.270
based on the same exchange rate.

00:01:45.270 --> 00:01:50.490
And so that will be
five A's, but they only

00:01:50.490 --> 00:01:52.430
have to pay one A in interest.

00:01:52.430 --> 00:01:54.770
So let me divert some over here.

00:01:54.770 --> 00:01:57.190
So they only have to
pay one A in interest.

00:01:57.190 --> 00:02:01.510
And so they're just going
to get four A's per year.

00:02:01.510 --> 00:02:03.780
If we assume constant
exchange rate,

00:02:03.780 --> 00:02:08.380
they're going to get four A's
a year for free-- assuming

00:02:08.380 --> 00:02:09.919
that they could
continue to do this.

00:02:09.919 --> 00:02:11.580
And then they could take those
four A's and convert them

00:02:11.580 --> 00:02:13.470
to B's, or whatever
other currency they want.

00:02:13.470 --> 00:02:14.350
So they could
just-- you could say

00:02:14.350 --> 00:02:16.250
they're getting four
A's for free every year,

00:02:16.250 --> 00:02:20.130
or they're getting eight
B's per year, every year.

00:02:20.130 --> 00:02:22.540
And this little process,
this little trade,

00:02:22.540 --> 00:02:24.500
this little perceived
arbitrage that's

00:02:24.500 --> 00:02:30.100
going on right over here, this
is called the carry trade.

00:02:30.100 --> 00:02:33.310
And you might think about well,
where would this break down?

00:02:33.310 --> 00:02:35.390
Well, the main area where
this would break down

00:02:35.390 --> 00:02:38.690
is while you are borrowing
in A and then investing

00:02:38.690 --> 00:02:44.850
in B, if A's
currency appreciates,

00:02:44.850 --> 00:02:47.400
especially relative
to B's currency.

00:02:47.400 --> 00:02:49.990
Because then what happens, even
though you have this interest

00:02:49.990 --> 00:02:51.580
rate discrepancy, and
even though you feel like

00:02:51.580 --> 00:02:53.060
you're getting a lot of 10 B's.

00:02:53.060 --> 00:02:55.490
Those 10 B's are going to
give you fewer and fewer

00:02:55.490 --> 00:02:57.910
A's if A keeps appreciating.

00:02:57.910 --> 00:02:59.680
Or another way to
think about it is,

00:02:59.680 --> 00:03:02.000
you're going to, in terms
of B's, even though you

00:03:02.000 --> 00:03:05.070
think you only owe 1% interest,
A is also going to appreciate.

00:03:05.070 --> 00:03:07.510
So in terms of B's, you're
going to owe more and more

00:03:07.510 --> 00:03:10.240
B's every year if A appreciates.

00:03:10.240 --> 00:03:11.954
Now what's worked out
in the carry trade,

00:03:11.954 --> 00:03:13.620
or at least the most
famous of the carry

00:03:13.620 --> 00:03:15.930
trades, where in starting
in the mid-90's, people

00:03:15.930 --> 00:03:18.780
started borrowing in Japan
because they had low interest,

00:03:18.780 --> 00:03:21.630
and then investing other
places like the US,

00:03:21.630 --> 00:03:24.150
and especially other
places, like Iceland,

00:03:24.150 --> 00:03:26.710
is that the more people do
this-- so you can imagine,

00:03:26.710 --> 00:03:28.730
if a lot of people
keep doing this

00:03:28.730 --> 00:03:31.520
and it becomes kind of a big
herd affect, what happens?

00:03:31.520 --> 00:03:33.780
You have a bunch of
people borrowing in A

00:03:33.780 --> 00:03:36.010
and then converting it to B.

00:03:36.010 --> 00:03:38.130
So they're taking this
currency and converting it

00:03:38.130 --> 00:03:40.070
to the magenta currency.

00:03:40.070 --> 00:03:41.980
And if that happens,
then you actually

00:03:41.980 --> 00:03:43.280
have the opposite effect.

00:03:43.280 --> 00:03:46.090
Then you get a benefit on top
of the interest rate discrepancy

00:03:46.090 --> 00:03:48.920
because that means the demand
for B's currency goes up,

00:03:48.920 --> 00:03:51.810
and demand for A's goes down.

00:03:51.810 --> 00:03:53.800
And this is essentially
what happened,

00:03:53.800 --> 00:03:56.210
relative to Japan-- and a
lot of the rest of the world

00:03:56.210 --> 00:03:58.750
when Japan had it's
lower interest rates, all

00:03:58.750 --> 00:04:02.320
the way until really about 2008.


Logarithmic scale

WEBVTT
Kind: captions
Language: en

00:00:00.530 --> 00:00:02.029
I would guess that
you're reasonably

00:00:02.029 --> 00:00:03.615
familiar with linear scales.

00:00:03.615 --> 00:00:05.490
These are the scales
that you would typically

00:00:05.490 --> 00:00:07.319
see in most of
your math classes.

00:00:07.319 --> 00:00:09.110
And so just to make
sure we know what we're

00:00:09.110 --> 00:00:11.318
talking about, and maybe
thinking about in a slightly

00:00:11.318 --> 00:00:13.830
different way, let me
draw a linear number line.

00:00:13.830 --> 00:00:14.940
Let me start with 0.

00:00:14.940 --> 00:00:16.440
And what we're going
to do is, we're

00:00:16.440 --> 00:00:19.630
going to say, look, if I move
this distance right over here,

00:00:19.630 --> 00:00:21.820
and if I move that distance
to the right, that's

00:00:21.820 --> 00:00:23.580
equivalent to adding 10.

00:00:23.580 --> 00:00:26.060
So if you start at
0 and you add 10,

00:00:26.060 --> 00:00:27.720
that would obviously
get you to 10.

00:00:27.720 --> 00:00:29.840
If you move that distance
to the right again,

00:00:29.840 --> 00:00:33.249
you're going to add 10 again,
that would get you to 20.

00:00:33.249 --> 00:00:34.790
And obviously we
could keep doing it,

00:00:34.790 --> 00:00:37.650
and get to 30, 40, 50,
so on and so forth.

00:00:37.650 --> 00:00:39.095
And also, just
looking at what we

00:00:39.095 --> 00:00:40.720
did here, if we go
the other direction.

00:00:40.720 --> 00:00:44.170
If we start here, and move
that same distance to the left,

00:00:44.170 --> 00:00:45.560
we're clearly subtracting 10.

00:00:45.560 --> 00:00:48.550
10 minus 10 is equal to 0.

00:00:48.550 --> 00:00:50.960
So if we move that
distance to the left again,

00:00:50.960 --> 00:00:53.050
we would get to negative 10.

00:00:53.050 --> 00:00:55.400
And if we did it again, we
would get to negative 20.

00:00:55.400 --> 00:00:58.000
So the general idea
is, however many times

00:00:58.000 --> 00:01:01.370
we move that distance, we
are essentially adding--

00:01:01.370 --> 00:01:04.015
or however many times you move
that distance to the right-- we

00:01:04.015 --> 00:01:06.090
are essentially adding
that multiple of 10.

00:01:06.090 --> 00:01:08.920
If we do it twice,
we're adding 2 times 10.

00:01:08.920 --> 00:01:11.490
And that not only works
for whole numbers,

00:01:11.490 --> 00:01:13.150
it would work for
fractions as well.

00:01:13.150 --> 00:01:14.450
Where would 5 be?

00:01:14.450 --> 00:01:17.710
Well to get to 5, we only
have to multiply 10--

00:01:17.710 --> 00:01:23.170
or I guess one way to think
about it is 5 is half of 10.

00:01:23.170 --> 00:01:24.910
And so if we want to
only go half of 10,

00:01:24.910 --> 00:01:27.930
we only have to go
half this distance.

00:01:27.930 --> 00:01:31.960
So if we go half
this distance, that

00:01:31.960 --> 00:01:34.150
will get us to 1/2 times 10.

00:01:34.150 --> 00:01:35.830
In this case, that would be 5.

00:01:35.830 --> 00:01:38.397
If we go to the left, that
would get us to negative 5.

00:01:38.397 --> 00:01:40.730
And there's nothing-- let me
draw that a little bit more

00:01:40.730 --> 00:01:43.580
centered, negative 5-- and
there's nothing really new

00:01:43.580 --> 00:01:44.080
here.

00:01:44.080 --> 00:01:45.579
We're just kind of
thinking about it

00:01:45.579 --> 00:01:47.720
in a slightly novel way
that's going to be useful

00:01:47.720 --> 00:01:49.010
when we start thinking
about logarithmic.

00:01:49.010 --> 00:01:51.360
But this is just the number
line that you've always known.

00:01:51.360 --> 00:01:52.776
If we want to put
1 here, we would

00:01:52.776 --> 00:01:55.640
move 1/10 of the distance,
because 1 is 1/10 of 10.

00:01:55.640 --> 00:01:58.530
So this would be 1, 2,
3, 4, I could just put,

00:01:58.530 --> 00:02:02.090
I could label frankly, any
number right over here.

00:02:02.090 --> 00:02:04.770
Now this was a situation where
we add 10 or subtract 10.

00:02:04.770 --> 00:02:07.090
But it's completely legitimate
to have an alternate way

00:02:07.090 --> 00:02:09.990
of thinking of what you do
when you move this distance.

00:02:09.990 --> 00:02:11.800
And let's think about that.

00:02:11.800 --> 00:02:13.710
So let's say I have
another line over here.

00:02:13.710 --> 00:02:15.085
And you might
guess this is going

00:02:15.085 --> 00:02:16.760
to be the logarithmic
number line.

00:02:16.760 --> 00:02:19.660
Let me give
ourselves some space.

00:02:19.660 --> 00:02:22.025
And let's start this
logarithmic number line at 1.

00:02:22.025 --> 00:02:24.150
And I'll let you think
about, after this video, why

00:02:24.150 --> 00:02:26.670
I didn't start it at 0.

00:02:26.670 --> 00:02:29.320
And if you start at 1, and
instead of moving that,

00:02:29.320 --> 00:02:31.395
so I'm still going to
define that same distance.

00:02:36.350 --> 00:02:38.870
But instead of saying that
that same distance is adding 10

00:02:38.870 --> 00:02:40.350
when I move to the
right, I'm going

00:02:40.350 --> 00:02:41.730
to say when I move
the right that

00:02:41.730 --> 00:02:44.410
distance on this new number
line that I have created,

00:02:44.410 --> 00:02:47.790
that is the same thing
as multiplying by 10.

00:02:47.790 --> 00:02:50.860
And so if I move that distance,
I start at 1, I multiply by 10.

00:02:50.860 --> 00:02:53.910
That gets me to 10.

00:02:53.910 --> 00:02:57.470
And then if I
multiply by 10 again,

00:02:57.470 --> 00:02:58.900
if I move by that
distance again,

00:02:58.900 --> 00:03:00.520
I'm multiplying by 10 again.

00:03:00.520 --> 00:03:02.210
And so that would get me to 100.

00:03:02.210 --> 00:03:04.770
I think you can already see the
difference that's happening.

00:03:04.770 --> 00:03:07.302
And what about moving to
the left that distance?

00:03:07.302 --> 00:03:09.260
Well we already have kind
of said what happens.

00:03:09.260 --> 00:03:11.610
Because if we start
here, we start at 100

00:03:11.610 --> 00:03:14.130
and move to the left of
that distance, what happens?

00:03:14.130 --> 00:03:16.990
Well I divided by 10.

00:03:16.990 --> 00:03:18.900
100 divided by 10 gets me 10.

00:03:18.900 --> 00:03:21.180
10 divided by 10 get me 1.

00:03:21.180 --> 00:03:25.080
And so if I move that
distance to the left again,

00:03:25.080 --> 00:03:26.440
I'll divide by 10 again.

00:03:26.440 --> 00:03:30.000
That would get me to 1/10.

00:03:30.000 --> 00:03:32.330
And if I move that
distance to the left again,

00:03:32.330 --> 00:03:37.700
that would get me to 1/100.

00:03:37.700 --> 00:03:40.850
And so the general idea
is, is however many times

00:03:40.850 --> 00:03:42.710
I move that distance
to the right,

00:03:42.710 --> 00:03:47.990
I'm multiplying my starting
point by 10 that many times.

00:03:47.990 --> 00:03:52.520
And so for example, when I
move that distance twice,

00:03:52.520 --> 00:03:55.090
so this whole distance
right over here,

00:03:55.090 --> 00:03:56.630
I went that distance twice.

00:03:56.630 --> 00:03:59.250
So this is times
10 times 10, which

00:03:59.250 --> 00:04:03.860
is the same thing as times
10 to the second power.

00:04:03.860 --> 00:04:07.710
And so really I'm raising 10
to what I'm multiplying it

00:04:07.710 --> 00:04:10.070
times 10 to whatever
power, however

00:04:10.070 --> 00:04:11.980
many times I'm
jumping to the right.

00:04:11.980 --> 00:04:14.880
Same thing if I go to the left.

00:04:14.880 --> 00:04:18.079
If I go to the left
that distance twice--

00:04:18.079 --> 00:04:22.750
let me do that in
a new color-- this

00:04:22.750 --> 00:04:25.760
will be the same thing
as dividing by 10 twice.

00:04:25.760 --> 00:04:28.190
Dividing by 10,
dividing by 10, which

00:04:28.190 --> 00:04:32.470
is the same thing as multiplying
by-- one way to think of it--

00:04:32.470 --> 00:04:35.160
1/10 squared.

00:04:35.160 --> 00:04:38.060
Or dividing by 10
squared is another way

00:04:38.060 --> 00:04:39.410
of thinking about it.

00:04:39.410 --> 00:04:41.170
And so that might
make a little, that

00:04:41.170 --> 00:04:42.500
might be hopefully a
little bit intuitive.

00:04:42.500 --> 00:04:44.375
And you can already see
why this is valuable.

00:04:44.375 --> 00:04:46.210
We can already on
this number line

00:04:46.210 --> 00:04:48.887
plot a much broader
spectrum of things

00:04:48.887 --> 00:04:50.220
than we can on this number line.

00:04:50.220 --> 00:04:51.960
We can go all the way
up to 100, and then

00:04:51.960 --> 00:04:53.560
we even get some
nice granularity

00:04:53.560 --> 00:04:56.380
if we go down to 1/10 and 1/100.

00:04:56.380 --> 00:04:59.150
Here we don't get the
granularity at small scales,

00:04:59.150 --> 00:05:02.012
and we also don't get to
go to really large numbers.

00:05:02.012 --> 00:05:04.220
And if we go a little distance
more, we get to 1,000,

00:05:04.220 --> 00:05:06.420
and then we get to 10,000,
so on and so forth.

00:05:06.420 --> 00:05:08.940
So we can really cover
a much broader spectrum

00:05:08.940 --> 00:05:11.250
on this line right over here.

00:05:11.250 --> 00:05:13.380
But what's also neat
about this is that when

00:05:13.380 --> 00:05:14.950
you move a fixed
distance, so when

00:05:14.950 --> 00:05:17.740
you move fixed distance on
this linear number line,

00:05:17.740 --> 00:05:19.954
you're adding or
subtracting that amount.

00:05:19.954 --> 00:05:21.370
So if you move
that fixed distance

00:05:21.370 --> 00:05:23.140
you're adding 2 to the right.

00:05:23.140 --> 00:05:25.280
If you go to the left,
you're subtracting 2.

00:05:25.280 --> 00:05:27.680
When you do the same thing
on a logarithmic number line,

00:05:27.680 --> 00:05:30.040
this is true of any
logarithmic number line,

00:05:30.040 --> 00:05:32.420
you will be scaling
by a fixed factor.

00:05:32.420 --> 00:05:35.170
And one way to think about
what that fixed factor is

00:05:35.170 --> 00:05:37.820
is this idea of exponents.

00:05:37.820 --> 00:05:42.140
So if you wanted to say, where
would 2 sit on this number

00:05:42.140 --> 00:05:43.360
line?

00:05:43.360 --> 00:05:46.027
Then you would just
think to yourself, well,

00:05:46.027 --> 00:05:48.360
if I ask myself where does
100 sit on that number line--

00:05:48.360 --> 00:05:49.910
actually, that might be
a better place to start.

00:05:49.910 --> 00:05:52.110
If I said, if I didn't already
plot it and said where does 100

00:05:52.110 --> 00:05:53.290
sit on that number line?

00:05:53.290 --> 00:05:54.790
I would say, how
many times would we

00:05:54.790 --> 00:05:57.280
have to multiply 10
by itself to get 100?

00:05:57.280 --> 00:06:00.310
And that's how many times I
need to move this distance.

00:06:00.310 --> 00:06:02.900
And so essentially I'll
be asking 10 to the what

00:06:02.900 --> 00:06:05.450
power is equal to 100?

00:06:05.450 --> 00:06:07.910
And then I would get that
question mark is equal to 2.

00:06:07.910 --> 00:06:10.710
And then I would move that
many spaces to plot my 100.

00:06:10.710 --> 00:06:13.370
Or another way of stating
this exact same thing

00:06:13.370 --> 00:06:17.900
is log base 10 of 100 is
equal to question mark.

00:06:17.900 --> 00:06:20.080
And this question mark
is clearly equal to 2.

00:06:20.080 --> 00:06:24.440
And that says, I need to plot
the 100 2 of this distance

00:06:24.440 --> 00:06:25.664
to the right.

00:06:25.664 --> 00:06:27.330
And to figure out
where do I plot the 2,

00:06:27.330 --> 00:06:29.290
I would do the exact same thing.

00:06:29.290 --> 00:06:35.410
I would say 10 to what
power is equal to 2?

00:06:35.410 --> 00:06:40.430
Or log base 10 of
2 is equal to what?

00:06:40.430 --> 00:06:43.660
And we can get the
trusty calculator out,

00:06:43.660 --> 00:06:47.100
and we can just say log--
and on most calculators

00:06:47.100 --> 00:06:49.070
if there's a log without
the base specified,

00:06:49.070 --> 00:06:52.340
they're assuming
base 10-- so log of 2

00:06:52.340 --> 00:06:55.340
is equal to roughly 0.3.

00:06:55.340 --> 00:06:56.890
0.301.

00:06:56.890 --> 00:07:01.040
So this is equal to 0.301.

00:07:01.040 --> 00:07:03.150
So what this tells
us is we need to move

00:07:03.150 --> 00:07:06.110
this fraction of this
distance to get to 2.

00:07:06.110 --> 00:07:08.780
If we move this whole distance,
it's like multiplying times 10

00:07:08.780 --> 00:07:10.250
to the first power.

00:07:10.250 --> 00:07:12.760
But since we only want to
get 10 to the 0.301 power,

00:07:12.760 --> 00:07:15.520
we only want to do
0.301 of this distance.

00:07:15.520 --> 00:07:18.490
So it's going to be
roughly a third of this.

00:07:18.490 --> 00:07:20.610
It's going to be roughly--
actually, a little less

00:07:20.610 --> 00:07:21.400
than a third.

00:07:21.400 --> 00:07:22.910
0.3, not 0.33.

00:07:22.910 --> 00:07:25.870
So 2 is going to sit-- let
me do it a little bit more

00:07:25.870 --> 00:07:29.310
to the right-- so 2 is going
to sit right over here.

00:07:29.310 --> 00:07:32.000
Now what's really cool about
it is this distance in general

00:07:32.000 --> 00:07:37.660
on this logarithmic number
line means multiplying by 2.

00:07:37.660 --> 00:07:40.080
And so if you go that
same distance again,

00:07:40.080 --> 00:07:41.780
you're going to get to 4.

00:07:41.780 --> 00:07:43.500
If you multiply that
same distance again,

00:07:43.500 --> 00:07:44.980
you're going to multiply by 4.

00:07:44.980 --> 00:07:46.510
And you go that
same distance again,

00:07:46.510 --> 00:07:49.930
you're going to get to 8.

00:07:49.930 --> 00:07:52.290
And so if you said
where would I plot 5?

00:07:52.290 --> 00:07:55.569
Where would I plot 5
on this number line?

00:07:55.569 --> 00:07:57.110
Well, there's a
couple ways to do it.

00:07:57.110 --> 00:08:00.560
You could literally figure out
what the base 10 logarithm of 5

00:08:00.560 --> 00:08:02.870
is, and figure out where
it goes on the number line.

00:08:02.870 --> 00:08:08.120
Or you could say,
look, if I start at 10

00:08:08.120 --> 00:08:09.930
and if I move this
distance to the left,

00:08:09.930 --> 00:08:12.220
I'm going to be dividing by 2.

00:08:12.220 --> 00:08:13.940
So if I move this
distance to the left

00:08:13.940 --> 00:08:15.920
I will be dividing by 2.

00:08:15.920 --> 00:08:17.790
I know it's getting a
little bit messy here.

00:08:17.790 --> 00:08:18.820
I'll maybe do
another video where

00:08:18.820 --> 00:08:20.852
we learn how to draw a
clean version of this.

00:08:20.852 --> 00:08:22.810
So if I start at 10 and
I go that same distance

00:08:22.810 --> 00:08:24.430
I'm dividing by 2.

00:08:24.430 --> 00:08:28.440
And so this right here would
be that right over there

00:08:28.440 --> 00:08:29.868
would be 5.

00:08:29.868 --> 00:08:32.159
Now the next question, you
said well where do I plot 3?

00:08:32.159 --> 00:08:34.534
Well we could do the exact
same thing that we did with 2.

00:08:34.534 --> 00:08:37.990
We ask ourselves,
what power do we

00:08:37.990 --> 00:08:41.210
have to raise 10 to to get to 3?

00:08:41.210 --> 00:08:43.640
And to get that, we once
again get our calculator out.

00:08:43.640 --> 00:08:48.010
log base 10 of 3
is equal to 0.477.

00:08:48.010 --> 00:08:50.000
So it's almost halfway.

00:08:50.000 --> 00:08:52.216
So it's almost going to
be half of this distance.

00:08:52.216 --> 00:08:53.590
So half of that
distance is going

00:08:53.590 --> 00:08:56.370
to look something
like right over there.

00:08:56.370 --> 00:08:59.789
So 3 is going to
go right over here.

00:08:59.789 --> 00:09:01.580
And you could do the
logarithm-- let's see,

00:09:01.580 --> 00:09:03.550
we're missing 6, 7, and 8.

00:09:03.550 --> 00:09:04.480
Oh, we have 8.

00:09:04.480 --> 00:09:05.550
We're missing 9.

00:09:05.550 --> 00:09:08.820
So to get 9, we just have
to multiply by 3 again.

00:09:08.820 --> 00:09:11.640
So this is 3, and if we
go that same distance,

00:09:11.640 --> 00:09:13.520
we multiply by 3
again, 9 is going

00:09:13.520 --> 00:09:16.010
to be squeezed in
right over here.

00:09:16.010 --> 00:09:18.200
9 is going to be squeezed
in right over there.

00:09:18.200 --> 00:09:21.550
And if we want to get to 6,
we just have to multiply by 2.

00:09:21.550 --> 00:09:24.450
And we already know the
distance to multiply by 2,

00:09:24.450 --> 00:09:26.360
it's this thing right over here.

00:09:26.360 --> 00:09:29.970
So you multiply that by 2,
you do that same distance,

00:09:29.970 --> 00:09:31.859
and you're going to get to 6.

00:09:31.859 --> 00:09:33.400
And if you wanted
to figure out where

00:09:33.400 --> 00:09:39.250
7 is, once again you could take
the log base-- let me do it

00:09:39.250 --> 00:09:42.670
right over here-- so
you'll take the log of 7

00:09:42.670 --> 00:09:45.680
is going to be
0.8, roughly 0.85.

00:09:45.680 --> 00:09:47.300
So 7 is just going
to be squeezed

00:09:47.300 --> 00:09:50.759
in roughly right over there.

00:09:50.759 --> 00:09:53.050
And so a couple of neat things
you already appreciated.

00:09:53.050 --> 00:09:55.530
One, we can fit more on
this logarithmic scale.

00:09:55.530 --> 00:09:59.337
And, as I did with the
video with Vi Hart,

00:09:59.337 --> 00:10:00.920
where she talked
about how we perceive

00:10:00.920 --> 00:10:02.419
many things with
logarithmic scales.

00:10:02.419 --> 00:10:05.150
So it actually is a good
way to even understand

00:10:05.150 --> 00:10:06.324
some of human perception.

00:10:06.324 --> 00:10:07.740
But the other
really cool thing is

00:10:07.740 --> 00:10:10.600
when we move a fixed distance
on this logarithmic scale,

00:10:10.600 --> 00:10:13.160
we're multiplying
by a fixed constant.

00:10:13.160 --> 00:10:15.204
Now the one kind of
strange thing about this,

00:10:15.204 --> 00:10:16.870
and you might have
already noticed here,

00:10:16.870 --> 00:10:18.990
is that we don't see
the numbers lined up

00:10:18.990 --> 00:10:20.230
the way we normally see them.

00:10:20.230 --> 00:10:22.092
There's a big jump
from 1 to 2, then

00:10:22.092 --> 00:10:24.466
a smaller jump from 3 to 4,
then a smaller jump from that

00:10:24.466 --> 00:10:27.710
from 3 to 4, then even smaller
from 4 to 5, then even smaller

00:10:27.710 --> 00:10:28.520
5 to 6 it gets.

00:10:28.520 --> 00:10:31.525
And then 7, 8, 9, you know 7's
going to be right in there.

00:10:31.525 --> 00:10:33.150
They get squeeze,
squeeze, squeezed in,

00:10:33.150 --> 00:10:34.960
tighter and tighter and
tighter, and then you get 10.

00:10:34.960 --> 00:10:36.376
And then you get
another big jump.

00:10:36.376 --> 00:10:38.650
Because once again, if
you want to get to 20,

00:10:38.650 --> 00:10:40.115
you just have to multiply by 2.

00:10:43.050 --> 00:10:45.610
So this distance
again gets us to 20.

00:10:45.610 --> 00:10:49.290
If you go this
distance over here

00:10:49.290 --> 00:10:52.630
that will get you to 30,
because you're multiplying by 3.

00:10:52.630 --> 00:10:55.450
So this right over here
is a times 3 distance.

00:10:55.450 --> 00:10:58.070
So if you do that again,
if you do that distance,

00:10:58.070 --> 00:10:59.320
then that gets you to 30.

00:10:59.320 --> 00:11:00.810
You're multiplying by 3.

00:11:00.810 --> 00:11:03.550
And then you can plot the whole
same thing over here again.

00:11:03.550 --> 00:11:05.250
But hopefully this gives you
a little bit more intuition

00:11:05.250 --> 00:11:07.690
of why logarithmic number
lines look the way they do.

00:11:07.690 --> 00:11:09.976
Or why logarithmic scale
looks the way it does.

00:11:09.976 --> 00:11:12.100
And also, it gives you a
little bit of appreciation

00:11:12.100 --> 00:11:14.680
for why it might be useful.


Firestick farming

WEBVTT
Kind: captions
Language: en

00:00:00.640 --> 00:00:03.200
Farming, as we now
associate the word,

00:00:03.200 --> 00:00:07.880
has been around for about
7,000 to 10,000 years.

00:00:07.880 --> 00:00:10.040
And when we think of
farming, we imagine a farmer

00:00:10.040 --> 00:00:12.550
planting seeds, and later
harvesting the crops.

00:00:12.550 --> 00:00:15.690
Or maybe having cattle that
they can allow to graze,

00:00:15.690 --> 00:00:19.680
and then using that cattle for
either meat, or milk, or wool.

00:00:19.680 --> 00:00:21.680
But there's actually a
different type of farming

00:00:21.680 --> 00:00:25.990
that predates this association
with I guess what we could call

00:00:25.990 --> 00:00:28.060
the traditional form of farming.

00:00:28.060 --> 00:00:31.740
And it predates it by several
tens of thousands of years.

00:00:31.740 --> 00:00:36.260
And we believe that it started
with the original inhabitants

00:00:36.260 --> 00:00:37.900
of Australia.

00:00:37.900 --> 00:00:40.387
And what they did is-- and this
is why we call it farming--

00:00:40.387 --> 00:00:41.970
and because if you
think about farming

00:00:41.970 --> 00:00:45.520
in the most general sense, it's
really humans using technology

00:00:45.520 --> 00:00:47.560
to manipulate their
environment so it

00:00:47.560 --> 00:00:49.680
becomes more
suitable for humans.

00:00:49.680 --> 00:00:51.520
So it becomes more
suitable for things

00:00:51.520 --> 00:00:57.300
that humans might want to eat,
or get milk from, or whatever.

00:00:57.300 --> 00:00:59.865
And this type of farming is
called firestick farming.

00:01:02.710 --> 00:01:05.530
And I think you can already
imagine what it might involve.

00:01:05.530 --> 00:01:09.050
It involves using fire, which
is really a form of technology--

00:01:09.050 --> 00:01:12.140
or it can be a form of
technology-- using fire

00:01:12.140 --> 00:01:16.940
to make the environment more
suitable for human activity.

00:01:16.940 --> 00:01:19.050
And so what the original
Australians did--

00:01:19.050 --> 00:01:21.700
the indigenous
Australians, or sometimes

00:01:21.700 --> 00:01:23.575
referred to as the
Aboriginal Australians.

00:01:28.629 --> 00:01:31.170
And if you're wondering where
the word Aboriginal comes from,

00:01:31.170 --> 00:01:33.320
you might recognize
some parts of it.

00:01:33.320 --> 00:01:35.200
Original-- you know
what that means.

00:01:35.200 --> 00:01:37.230
The first things.

00:01:37.230 --> 00:01:39.380
The things that were
there from the beginning.

00:01:39.380 --> 00:01:43.020
And then you have ab,
which is Latin for from.

00:01:43.020 --> 00:01:44.730
So this is literally
from the beginning.

00:01:44.730 --> 00:01:46.040
So when you say
Aboriginal Australians,

00:01:46.040 --> 00:01:47.540
you're really saying
the Australians

00:01:47.540 --> 00:01:49.750
that were there
from the beginning.

00:01:49.750 --> 00:01:54.980
And so what they would do is, is
that we believe if you go back

00:01:54.980 --> 00:01:58.260
50,000 or 60,000 years
before the first Aboriginal

00:01:58.260 --> 00:02:02.280
Australians settled Australia,
Australia had much more forest.

00:02:02.280 --> 00:02:03.290
It still has forest.

00:02:03.290 --> 00:02:05.510
This is a modern
picture, obviously,

00:02:05.510 --> 00:02:07.510
of an Australian forest.

00:02:07.510 --> 00:02:10.979
But what they did is that
they set up controlled burns.

00:02:10.979 --> 00:02:12.770
And what these
controlled burns did

00:02:12.770 --> 00:02:15.480
is that they cleared
away a lot of the forest.

00:02:15.480 --> 00:02:19.510
They cleared away a lot of
the brush that's over here,

00:02:19.510 --> 00:02:21.040
and it made it
much more suitable

00:02:21.040 --> 00:02:22.467
for grassland to develop.

00:02:22.467 --> 00:02:24.550
And the reason why they
liked grassland-- so let's

00:02:24.550 --> 00:02:26.310
make a little cycle
here of what they did.

00:02:26.310 --> 00:02:28.640
So they have controlled burns.

00:02:28.640 --> 00:02:32.380
Controlled fires.

00:02:32.380 --> 00:02:37.390
Those controlled fires
helped promote grassland.

00:02:37.390 --> 00:02:38.880
And then once you
have grassland,

00:02:38.880 --> 00:02:41.080
that made the
environment more suitable

00:02:41.080 --> 00:02:45.490
for animals that the
original human settlers

00:02:45.490 --> 00:02:46.939
could essentially live off of.

00:02:46.939 --> 00:02:48.980
That they could hunt, that
they could potentially

00:02:48.980 --> 00:02:50.000
eat their meat.

00:02:50.000 --> 00:02:55.370
And so, for example,
things like kangaroos.

00:02:55.370 --> 00:03:00.250
And these supported
the human population,

00:03:00.250 --> 00:03:03.332
which obviously, would then
do the controlled burns.

00:03:03.332 --> 00:03:05.290
And you see here-- so we
could have started off

00:03:05.290 --> 00:03:06.900
with something like this.

00:03:06.900 --> 00:03:09.070
Someone provides
a controlled burn.

00:03:09.070 --> 00:03:11.010
And they were actually
pretty scientific

00:03:11.010 --> 00:03:11.960
about how they did it.

00:03:11.960 --> 00:03:14.418
They wouldn't just go at the
end of summer, when everything

00:03:14.418 --> 00:03:17.430
was hot, and ready
to just blow up,

00:03:17.430 --> 00:03:19.700
and then start a fire that
they couldn't control.

00:03:19.700 --> 00:03:21.810
They would often do
these in seasons knowing

00:03:21.810 --> 00:03:24.890
that it had a certain level
of moisture in the air,

00:03:24.890 --> 00:03:26.340
it wasn't too hot.

00:03:26.340 --> 00:03:29.310
And to a large degree, by
doing these controlled burns,

00:03:29.310 --> 00:03:31.770
not only did it provide an
environment-- kind of do

00:03:31.770 --> 00:03:33.375
this firestick
farming-- not only did

00:03:33.375 --> 00:03:36.090
it provide an environment
that was suitable for things

00:03:36.090 --> 00:03:39.520
like kangaroos, some type of
things that humans could eat--

00:03:39.520 --> 00:03:42.050
but it also prevented
major fires.

00:03:42.050 --> 00:03:46.280
And you still see forest rangers
doing this type of thing.

00:03:46.280 --> 00:03:47.820
And there's some
reason to believe

00:03:47.820 --> 00:03:50.550
that what the original
Australians did, on some level,

00:03:50.550 --> 00:03:53.370
was more nuanced and
more fine-tuned than even

00:03:53.370 --> 00:03:56.770
what we do, in a modern
sense, in controlled burns.

00:03:56.770 --> 00:04:02.895
So these controlled fires also
prevented major uncontrollable

00:04:02.895 --> 00:04:03.395
fires.

00:04:06.080 --> 00:04:07.800
Because what happens
is if you don't

00:04:07.800 --> 00:04:09.480
have these controlled
fires, then you

00:04:09.480 --> 00:04:12.450
have brush building up,
year after year after year.

00:04:12.450 --> 00:04:14.050
You have stuff building up.

00:04:14.050 --> 00:04:19.420
And then, when the
fires do occur,

00:04:19.420 --> 00:04:22.190
the uncontrolled fires are
less likely to be started

00:04:22.190 --> 00:04:23.925
during the winter,
when the air is cool

00:04:23.925 --> 00:04:25.590
or when there might
be some moisture.

00:04:25.590 --> 00:04:27.890
They're more likely to
occur in the dry season.

00:04:27.890 --> 00:04:29.540
So you have all
this stuff build up.

00:04:29.540 --> 00:04:31.210
And then when the
fire does happen,

00:04:31.210 --> 00:04:33.394
it happens in the driest season.

00:04:33.394 --> 00:04:35.560
And then what happens with
all of the stuff built up

00:04:35.560 --> 00:04:40.320
in the dry season, it just
becomes uncontrollable.

00:04:40.320 --> 00:04:42.350
One of the byproducts--
or actually there

00:04:42.350 --> 00:04:45.930
are several byproducts of this
firestick farming-- we believe,

00:04:45.930 --> 00:04:48.950
is a lot of the
grassland in Australia

00:04:48.950 --> 00:04:52.320
now might have been
more forested before.

00:04:52.320 --> 00:04:54.080
And even when the
first European settlers

00:04:54.080 --> 00:04:58.200
came in the late 1700s,
they were kind of surprised

00:04:58.200 --> 00:05:00.700
when they went into what is now
Sydney Harbor and they said,

00:05:00.700 --> 00:05:02.200
wow, look at all
the grassland here.

00:05:02.200 --> 00:05:03.570
It almost looks like park space.

00:05:03.570 --> 00:05:06.007
And then they would let
their sheep graze there.

00:05:06.007 --> 00:05:07.590
And they were
surprised-- because they

00:05:07.590 --> 00:05:09.454
had driven out the
original inhabitants.

00:05:09.454 --> 00:05:11.370
And then they were
surprised when forests just

00:05:11.370 --> 00:05:13.496
started to grow up
in that grassland.

00:05:13.496 --> 00:05:15.870
And it was because the original
Australians were actually

00:05:15.870 --> 00:05:17.920
controlling that
forest growth to make

00:05:17.920 --> 00:05:21.370
it more inhabitable for
things like kangaroos.

00:05:21.370 --> 00:05:23.370
And then when the
English settlers came,

00:05:23.370 --> 00:05:27.440
they started to have their
sheep graze in those grasslands.

00:05:27.440 --> 00:05:30.610
And it also was responsible
for the disappearance,

00:05:30.610 --> 00:05:34.180
we think, of many
major-- I guess,

00:05:34.180 --> 00:05:35.880
for lack of a better
word-- megafauna.

00:05:35.880 --> 00:05:39.510
So really large animals
that inhabited Australia,

00:05:39.510 --> 00:05:42.851
for really millions of years,
until humans showed up.

00:05:42.851 --> 00:05:43.850
And this is one of them.

00:05:43.850 --> 00:05:45.700
It's just neat to look at them.

00:05:45.700 --> 00:05:47.590
This is called
Diprotodon optatum.

00:05:47.590 --> 00:05:50.740
Or, another way to think
of it, the giant wombat.

00:05:50.740 --> 00:05:53.240
And there's fossils of the
giant wombat around 40,000,

00:05:53.240 --> 00:05:54.620
50,000 years ago.

00:05:54.620 --> 00:05:56.464
But they disappeared
with humans showing up.

00:05:56.464 --> 00:05:57.880
And there's multiple
ways that you

00:05:57.880 --> 00:05:59.600
can think about why
they disappeared.

00:05:59.600 --> 00:06:01.190
They might have--
and this is probably

00:06:01.190 --> 00:06:04.460
the case-- they might have been
more dependent on the forest

00:06:04.460 --> 00:06:07.260
habitat.

00:06:07.260 --> 00:06:09.580
Or this was a more
favorable habitat for them

00:06:09.580 --> 00:06:11.190
than the grasslands.

00:06:11.190 --> 00:06:13.610
Maybe because they ate
leaves that were high up.

00:06:13.610 --> 00:06:16.010
Or another thing is, once
the forest habitat goes away,

00:06:16.010 --> 00:06:17.990
they were actually also
easier to hunt down.

00:06:17.990 --> 00:06:19.470
Or either way you
think about it,

00:06:19.470 --> 00:06:21.261
they might have just
been hunted by humans.

00:06:21.261 --> 00:06:22.970
But we do see that
with humans coming

00:06:22.970 --> 00:06:25.567
to the Australian
continent, you start

00:06:25.567 --> 00:06:27.900
to see the disappearance--
and this isn't the only one--

00:06:27.900 --> 00:06:32.540
but there were several
major species of megafauna,

00:06:32.540 --> 00:06:35.770
of super large animals, that
disappeared at that time

00:06:35.770 --> 00:06:37.320
period.


Vi and Sal explore how we think about scale

WEBVTT
Kind: captions
Language: en

00:00:01.990 --> 00:00:02.810
VI HART: All right.

00:00:02.810 --> 00:00:05.710
So I'm Vi Hart and I'm
here with Sal Khan and--

00:00:05.710 --> 00:00:06.600
SAL KHAN: Hello.

00:00:06.600 --> 00:00:07.390
VI HART: Yeah.

00:00:07.390 --> 00:00:11.490
We're talking about just
how we think about numbers

00:00:11.490 --> 00:00:13.890
and what is the most
natural way to think

00:00:13.890 --> 00:00:15.607
about them in our
everyday lives.

00:00:15.607 --> 00:00:18.190
SAL KHAN: And Vi said that she
was going to test me right now.

00:00:18.190 --> 00:00:18.827
VI HART: Yeah.

00:00:18.827 --> 00:00:20.160
All right, can I borrow the pen?

00:00:20.160 --> 00:00:20.490
SAL KHAN: Yes.

00:00:20.490 --> 00:00:20.840
Yes.

00:00:20.840 --> 00:00:23.200
VI HART: I get to use the
official pen and screen-- oh

00:00:23.200 --> 00:00:23.660
wait. [INAUDIBLE]

00:00:23.660 --> 00:00:24.550
SAL KHAN: No, that's all screen.

00:00:24.550 --> 00:00:25.010
Yes.

00:00:25.010 --> 00:00:25.340
VI HART: OK.

00:00:25.340 --> 00:00:25.740
OK.

00:00:25.740 --> 00:00:27.073
SAL KHAN: You need training, Vi.

00:00:27.073 --> 00:00:28.940
VI HART: I need training.

00:00:28.940 --> 00:00:29.440
Yay.

00:00:29.440 --> 00:00:31.474
SAL KHAN: It looks like a pizza.

00:00:31.474 --> 00:00:34.040
VI HART: It's a triangle.

00:00:34.040 --> 00:00:35.070
SAL KHAN: Right.

00:00:35.070 --> 00:00:36.340
Where's your test, Vi?

00:00:36.340 --> 00:00:36.840
VI HART: OK.

00:00:36.840 --> 00:00:37.980
SAL KHAN: You're diverging.

00:00:37.980 --> 00:00:39.430
VI HART: I'm sorry.

00:00:39.430 --> 00:00:42.010
All right, so here's
a number line.

00:00:42.010 --> 00:00:43.150
Regular old number line.

00:00:43.150 --> 00:00:43.650
No, wait.

00:00:43.650 --> 00:00:44.705
I want to start at one.

00:00:44.705 --> 00:00:46.330
All right, we're
going to start at one,

00:00:46.330 --> 00:00:49.630
and we're going to go
all the way to a million.

00:00:49.630 --> 00:00:52.790
And I'm going to give you the
pen now, and I'm going to ask,

00:00:52.790 --> 00:00:54.250
where is 1,000?

00:00:54.250 --> 00:00:56.520
SAL KHAN: Where is 1,000?

00:00:56.520 --> 00:00:59.120
Where is 1,000?

00:00:59.120 --> 00:01:00.021
I see.

00:01:00.021 --> 00:01:01.020
I see what you're doing.

00:01:01.020 --> 00:01:02.260
VI HART: So you can think
about this logically.

00:01:02.260 --> 00:01:02.700
SAL KHAN: Yes.

00:01:02.700 --> 00:01:03.199
Yes.

00:01:03.199 --> 00:01:07.120
So I'll tell you what
went through my brain.

00:01:07.120 --> 00:01:11.670
My first knee-jerk
reaction was to put 1,000

00:01:11.670 --> 00:01:12.820
like right over here.

00:01:12.820 --> 00:01:14.439
That's what I was tempted to do.

00:01:14.439 --> 00:01:14.980
VI HART: Mhm.

00:01:14.980 --> 00:01:16.637
SAL KHAN: And then
my brain kicked in.

00:01:16.637 --> 00:01:16.970
VI HART: Right.

00:01:16.970 --> 00:01:17.084
Yeah.

00:01:17.084 --> 00:01:17.531
You think of it--

00:01:17.531 --> 00:01:19.100
SAL KHAN: My
highly-analytical mind.

00:01:19.100 --> 00:01:19.683
VI HART: Yeah.

00:01:19.683 --> 00:01:22.500
Because you know there is a
correct answer to this problem.

00:01:22.500 --> 00:01:26.320
We can think, all
right, where is

00:01:26.320 --> 00:01:28.990
1,000 on the number line
related to a million?

00:01:28.990 --> 00:01:31.139
Well, a million
divided by 1,000.

00:01:31.139 --> 00:01:31.930
SAL KHAN: Is 1,000.

00:01:31.930 --> 00:01:33.075
VI HART: You want
one thousandth.

00:01:33.075 --> 00:01:33.660
SAL KHAN: Thousandth.

00:01:33.660 --> 00:01:34.010
Right.

00:01:34.010 --> 00:01:34.880
So it's not there.

00:01:34.880 --> 00:01:36.629
I was going to draw
it a tenth of the way.

00:01:36.629 --> 00:01:37.590
No.

00:01:37.590 --> 00:01:40.455
1,000 is like there.

00:01:40.455 --> 00:01:42.580
You barely notice the
difference between that and--

00:01:42.580 --> 00:01:42.600
VI HART: Yeah.

00:01:42.600 --> 00:01:44.087
You couldn't even see the
difference in thousandths.

00:01:44.087 --> 00:01:44.670
SAL KHAN: Yes.

00:01:47.140 --> 00:01:48.680
So this is fascinating.

00:01:48.680 --> 00:01:50.570
What is this about?

00:01:50.570 --> 00:01:51.840
Why did I do that?

00:01:51.840 --> 00:01:52.530
VI HART: Yeah.

00:01:52.530 --> 00:01:55.760
Why do we think of 1,000 as
being much closer to a million

00:01:55.760 --> 00:01:56.730
than it is?

00:01:56.730 --> 00:01:59.450
And we do this,
actually, all the time.

00:01:59.450 --> 00:02:01.409
We're not so used
to having to think

00:02:01.409 --> 00:02:03.450
about the difference
between 1,000 and a million.

00:02:03.450 --> 00:02:06.760
But when we're thinking about
the difference between 1 and 2,

00:02:06.760 --> 00:02:11.130
or the difference between
2 and 3, or 1 and 10,

00:02:11.130 --> 00:02:13.789
we think, 1 and 2.

00:02:13.789 --> 00:02:15.080
There's a big difference there.

00:02:15.080 --> 00:02:17.732
2 is twice what 1 is.

00:02:17.732 --> 00:02:18.315
SAL KHAN: Yes.

00:02:18.315 --> 00:02:18.800
It's twice 1.

00:02:18.800 --> 00:02:19.310
Right.

00:02:19.310 --> 00:02:21.200
VI HART: And the
difference between 9 and 10

00:02:21.200 --> 00:02:23.180
is the same distance
when you're looking

00:02:23.180 --> 00:02:24.640
at it at the usual scale.

00:02:24.640 --> 00:02:25.290
It's 1.

00:02:25.290 --> 00:02:25.956
SAL KHAN: Right.

00:02:25.956 --> 00:02:26.570
Right.

00:02:26.570 --> 00:02:28.750
VI HART: But when we're thinking
about real-life things, well,

00:02:28.750 --> 00:02:30.291
the difference
between 9 and 10 isn't

00:02:30.291 --> 00:02:31.729
so big in any real
life situation.

00:02:31.729 --> 00:02:32.270
SAL KHAN: No.

00:02:32.270 --> 00:02:33.860
But the difference
between 1 and 2 is huge.

00:02:33.860 --> 00:02:34.090
VI HART: Yeah.

00:02:34.090 --> 00:02:35.070
SAL KHAN: In
real-life it's double.

00:02:35.070 --> 00:02:35.611
VI HART: Yes.

00:02:35.611 --> 00:02:36.520
SAL KHAN: Right.

00:02:36.520 --> 00:02:39.097
VI HART: So now we have to
think on a logarithmic scale

00:02:39.097 --> 00:02:39.680
is what it is.

00:02:39.680 --> 00:02:40.221
SAL KHAN: Oh.

00:02:40.221 --> 00:02:41.090
Yes.

00:02:41.090 --> 00:02:42.900
The old logarithmic scale.

00:02:42.900 --> 00:02:44.920
So what you're saying
is that we, as humans,

00:02:44.920 --> 00:02:46.420
even though everything
we're taught

00:02:46.420 --> 00:02:49.400
is these linear scales, where
we want to say this is 1,

00:02:49.400 --> 00:02:51.270
and then maybe this
is 10, and then

00:02:51.270 --> 00:02:53.690
this is 20-- even though
that's what we're taught,

00:02:53.690 --> 00:02:55.540
and that's what most
of our mathematics, we

00:02:55.540 --> 00:02:56.870
plot lines and stuff like that.

00:02:56.870 --> 00:02:57.110
VI HART: Yeah.

00:02:57.110 --> 00:02:58.943
That's how we draw it
out on paper, usually.

00:02:58.943 --> 00:03:00.370
SAL KHAN: Yes.

00:03:00.370 --> 00:03:03.260
VI HART: But that doesn't
make sense, usually,

00:03:03.260 --> 00:03:04.620
for how we think about things.

00:03:04.620 --> 00:03:07.720
Because the difference
between 5 gazillion

00:03:07.720 --> 00:03:10.060
and 5 gazillion and 10 is--

00:03:10.060 --> 00:03:10.935
SAL KHAN: Is nothing.

00:03:10.935 --> 00:03:11.190
Is nothing.

00:03:11.190 --> 00:03:11.570
VI HART: Nothing.

00:03:11.570 --> 00:03:13.860
Whereas the difference
between 1 and 10 is huge.

00:03:13.860 --> 00:03:14.720
SAL KHAN: Right, right, right.

00:03:14.720 --> 00:03:16.261
And so that's why
almost the multiple

00:03:16.261 --> 00:03:19.570
matters more than the absolute
distance between the numbers.

00:03:19.570 --> 00:03:20.245
VI HART: Yeah.

00:03:20.245 --> 00:03:20.670
SAL KHAN: Absoluately.

00:03:20.670 --> 00:03:22.740
And that's what the
logarithmic scale captures.

00:03:22.740 --> 00:03:23.710
VI HART: It is.

00:03:23.710 --> 00:03:25.930
And that's why we see
the logarithmic scale

00:03:25.930 --> 00:03:28.760
in so many things in real life.

00:03:28.760 --> 00:03:31.587
As a mathemusician, on
the piano we see it.

00:03:31.587 --> 00:03:32.170
SAL KHAN: Yes.

00:03:32.170 --> 00:03:34.322
VI HART: It's actually
the logarithmic scale.

00:03:34.322 --> 00:03:35.780
So let's get our
piano picture out.

00:03:35.780 --> 00:03:36.310
SAL KHAN: Oh, look at that.

00:03:36.310 --> 00:03:36.750
There's a piano.

00:03:36.750 --> 00:03:37.197
VI HART: Yeah.

00:03:37.197 --> 00:03:37.644
OK.

00:03:37.644 --> 00:03:38.091
OK.

00:03:38.091 --> 00:03:38.780
Can I have the pen?

00:03:38.780 --> 00:03:39.010
SAL KHAN: Here you go.

00:03:39.010 --> 00:03:39.060
Yes.

00:03:39.060 --> 00:03:39.810
VI HART: All right.

00:03:39.810 --> 00:03:41.050
Let's see if I can
figure this out.

00:03:41.050 --> 00:03:41.700
All right.

00:03:41.700 --> 00:03:43.647
So here we have
this C. Let's call

00:03:43.647 --> 00:03:46.810
it middle C. And
here we have this D.

00:03:46.810 --> 00:03:50.720
And there's a certain
distance between these.

00:03:50.720 --> 00:03:52.650
And then here is
this C and this D.

00:03:52.650 --> 00:03:56.360
And when we're listening
to these notes,

00:03:56.360 --> 00:03:58.320
we think, all right,
they're one note apart.

00:03:58.320 --> 00:04:00.779
This is the same distance
here between here and here

00:04:00.779 --> 00:04:01.570
and here and there.

00:04:01.570 --> 00:04:02.250
SAL KHAN: Yes.

00:04:02.250 --> 00:04:06.940
VI HART: But if you look
at the actual frequencies,

00:04:06.940 --> 00:04:10.760
the distances are not the same.

00:04:10.760 --> 00:04:12.610
This was maybe a bad
example, because I

00:04:12.610 --> 00:04:14.110
don't know the
frequency of D, but--

00:04:14.110 --> 00:04:14.651
SAL KHAN: No.

00:04:14.651 --> 00:04:15.380
Well, we could--

00:04:15.380 --> 00:04:17.921
VI HART: Well I'll give you an
example I can give numbers to,

00:04:17.921 --> 00:04:20.196
which is maybe the difference
between this octave

00:04:20.196 --> 00:04:21.820
and the difference
between this octave.

00:04:21.820 --> 00:04:22.370
Right?

00:04:22.370 --> 00:04:23.922
If this is C--

00:04:23.922 --> 00:04:24.794
SAL KHAN: Call it x.

00:04:24.794 --> 00:04:25.230
VI HART: x.

00:04:25.230 --> 00:04:26.380
SAL KHAN: Whatever
the frequency is.

00:04:26.380 --> 00:04:26.590
VI HART: Right.

00:04:26.590 --> 00:04:27.090
Yes.

00:04:27.090 --> 00:04:27.673
This is great.

00:04:27.673 --> 00:04:29.405
SAL KHAN: It's
like 440 kilohertz.

00:04:29.405 --> 00:04:30.465
I don't know what it is.

00:04:30.465 --> 00:04:30.636
VI HART: No.

00:04:30.636 --> 00:04:31.200
A is 440.

00:04:31.200 --> 00:04:31.620
SAL KHAN: A is 440.

00:04:31.620 --> 00:04:32.435
VI HART: C is--

00:04:32.435 --> 00:04:33.726
SAL KHAN: Well we'll call it x.

00:04:33.726 --> 00:04:35.987
VI HART: More like, I
don't know, let's say 300.

00:04:35.987 --> 00:04:36.570
SAL KHAN: Yes.

00:04:36.570 --> 00:04:37.430
VI HART: All right.

00:04:37.430 --> 00:04:41.150
So if this is 300
or 300x or just x,

00:04:41.150 --> 00:04:44.687
then this frequency
would be 600.

00:04:44.687 --> 00:04:45.270
SAL KHAN: 600.

00:04:45.270 --> 00:04:45.480
Right.

00:04:45.480 --> 00:04:46.190
It doubles.

00:04:46.190 --> 00:04:49.010
VI HART: It doubles when
you go up an octave.

00:04:49.010 --> 00:04:54.280
And this would be 1,200 up here,
this C. We're in a weird scale

00:04:54.280 --> 00:04:54.780
here.

00:04:54.780 --> 00:04:58.380
But the difference
between here is 300.

00:04:58.380 --> 00:05:01.940
And the difference
between here is 600.

00:05:01.940 --> 00:05:03.440
But when we're
listening to octaves,

00:05:03.440 --> 00:05:05.398
we feel like the difference
between this octave

00:05:05.398 --> 00:05:08.290
shouldn't be half as much as
the difference between these two

00:05:08.290 --> 00:05:08.790
notes.

00:05:08.790 --> 00:05:09.290
Right?

00:05:09.290 --> 00:05:11.990
The distance from an
octave should be an octave.

00:05:11.990 --> 00:05:12.504
Right?

00:05:12.504 --> 00:05:13.170
SAL KHAN: Right.

00:05:13.170 --> 00:05:17.430
So fundamentally the way we
perceive pitch is logarithmic.

00:05:17.430 --> 00:05:19.752
VI HART: It's just
fundamentally logarithmic.

00:05:19.752 --> 00:05:21.710
If you want to have all
your notes on the piano

00:05:21.710 --> 00:05:23.210
be right next to
each other, instead

00:05:23.210 --> 00:05:26.600
of having a piano where you
have one key for C here,

00:05:26.600 --> 00:05:28.704
and one key for C
here, and the next C

00:05:28.704 --> 00:05:29.745
is going to be over here.

00:05:29.745 --> 00:05:29.850
Right?

00:05:29.850 --> 00:05:30.475
SAL KHAN: Yeah.

00:05:30.475 --> 00:05:31.040
Twice as far.

00:05:31.040 --> 00:05:31.750
Yeah.

00:05:31.750 --> 00:05:34.250
VI HART: And the next C on the
piano would have to be like--

00:05:34.250 --> 00:05:36.440
SAL KHAN: So if
piano manufacturers--

00:05:36.440 --> 00:05:39.084
they innately made it based
on a logarithmic scale,

00:05:39.084 --> 00:05:40.250
whether they knew it or not.

00:05:40.250 --> 00:05:40.298
VI HART: Yeah.

00:05:40.298 --> 00:05:41.220
Because we think about it
on a logarithmic scale.

00:05:41.220 --> 00:05:42.410
SAL KHAN: They could have
made it on a linear scale,

00:05:42.410 --> 00:05:44.510
and then the keys would
just get fatter and fatter

00:05:44.510 --> 00:05:45.560
as we went to the right.

00:05:45.560 --> 00:05:45.970
VI HART: Oh, yeah.

00:05:45.970 --> 00:05:47.030
Fatter keys instead of
making them farther apart.

00:05:47.030 --> 00:05:47.715
SAL KHAN: Someone
should make that.

00:05:47.715 --> 00:05:48.010
VI HART: A fat key piano.

00:05:48.010 --> 00:05:49.450
SAL KHAN: A linear scale piano.

00:05:49.450 --> 00:05:50.110
Yes.

00:05:50.110 --> 00:05:52.794
VI HART: That would be awesome.

00:05:52.794 --> 00:05:54.335
But that's not how
we think of pitch.

00:05:54.335 --> 00:05:54.876
SAL KHAN: No.

00:05:54.876 --> 00:05:56.320
It might be hard to play that.

00:05:56.320 --> 00:05:57.790
VI HART: It would
be [? awesome. ?]

00:05:57.790 --> 00:05:59.206
SAL KHAN: And it's
just not pitch.

00:05:59.206 --> 00:06:03.784
It also even be how we perceive
a magnitude of the frequencies.

00:06:03.784 --> 00:06:05.200
Because we have
the decibel scale,

00:06:05.200 --> 00:06:06.547
which is a logarithmic scale.

00:06:06.547 --> 00:06:07.130
VI HART: Yeah.

00:06:07.130 --> 00:06:09.982
There's a lot of natural,
intuitive, logarithmic scales.

00:06:09.982 --> 00:06:11.940
So when we're looking at
how loud something is,

00:06:11.940 --> 00:06:15.449
that's also the difference
between how I'm talking now

00:06:15.449 --> 00:06:17.240
and how I'm talking if
I'm a little louder.

00:06:17.240 --> 00:06:23.094
And we feel like distances
between loudness also--

00:06:23.094 --> 00:06:23.760
SAL KHAN: Right.

00:06:23.760 --> 00:06:24.110
VI HART: It's harder to explain.

00:06:24.110 --> 00:06:25.310
SAL KHAN: We perceive it a
lot-- it is harder to explain.

00:06:25.310 --> 00:06:26.450
But we'll leave it there.

00:06:26.450 --> 00:06:26.720
VI HART: I don't
have any pictures

00:06:26.720 --> 00:06:27.510
of how loud something is.

00:06:27.510 --> 00:06:27.774
SAL KHAN: We don't.

00:06:27.774 --> 00:06:28.140
No.

00:06:28.140 --> 00:06:29.280
And we don't want
to bother people

00:06:29.280 --> 00:06:30.260
by just getting
louder and louder.

00:06:30.260 --> 00:06:30.620
VI HART: By screaming.

00:06:30.620 --> 00:06:31.225
SAL KHAN: Yes.

00:06:31.225 --> 00:06:32.850
VI HART: I can scream
at you some more.

00:06:32.850 --> 00:06:34.404
I think that would be great.

00:06:34.404 --> 00:06:35.070
SAL KHAN: Right.

00:06:35.070 --> 00:06:35.190
No.

00:06:35.190 --> 00:06:36.148
But that's fascinating.

00:06:36.148 --> 00:06:38.137
Especially this
little game here.

00:06:38.137 --> 00:06:40.470
I'm going to start doing this
at the next party I go to.

00:06:40.470 --> 00:06:41.011
VI HART: Mhm.

00:06:41.011 --> 00:06:41.570
It's good.

00:06:41.570 --> 00:06:42.110
And it makes sense.

00:06:42.110 --> 00:06:44.620
When we're looking at things,
the difference between how

00:06:44.620 --> 00:06:47.650
much $1 million
and $10 million is.

00:06:47.650 --> 00:06:48.832
SAL KHAN: Yes.

00:06:48.832 --> 00:06:50.790
VI HART: The world follows
these kind of rules.

00:06:50.790 --> 00:06:52.350
SAL KHAN: Right, right, right.

00:06:52.350 --> 00:06:53.220
Very cool.

00:06:53.220 --> 00:06:53.980
VI HART: Yeah.

00:06:53.980 --> 00:06:55.530
SAL KHAN: Awesome.


Benford's law explanation (sequel to mysteries of Benford's law)

WEBVTT
Kind: captions
Language: en

00:00:00.270 --> 00:00:02.150
SAL: So where we left
off in the last video,

00:00:02.150 --> 00:00:05.160
Vi and myself had
posed a mystery to you.

00:00:05.160 --> 00:00:06.920
We had talked about
Benford's law.

00:00:06.920 --> 00:00:09.855
VI: And we asked, what
is up with Benford's law?

00:00:09.855 --> 00:00:13.549
SAL: This idea that, if you
took just random countries

00:00:13.549 --> 00:00:16.090
and took their population and
took the most significant digit

00:00:16.090 --> 00:00:20.022
in their population and plotted
the numbers of countries

00:00:20.022 --> 00:00:22.230
that their most significant
digit is a 1, versus a 2,

00:00:22.230 --> 00:00:24.864
versus a 3, you just
had it was much more

00:00:24.864 --> 00:00:26.030
likely that it would be a 1.

00:00:26.030 --> 00:00:29.130
Or that, if you took physical
constants of the universe,

00:00:29.130 --> 00:00:32.280
that they're most
likely to have 1

00:00:32.280 --> 00:00:35.690
as their most significant digit.

00:00:35.690 --> 00:00:38.251
VI: I wish we had more graphs,
because graphs are fun.

00:00:38.251 --> 00:00:38.750
SAL: Yes.

00:00:38.750 --> 00:00:40.180
VI: But if you
look at information

00:00:40.180 --> 00:00:42.540
from the stock market
or anything, what's up?

00:00:42.540 --> 00:00:43.217
SAL: Yes.

00:00:43.217 --> 00:00:44.800
And it seems to all
follow this curve.

00:00:44.800 --> 00:00:46.617
And what was
extremely mysterious--

00:00:46.617 --> 00:00:48.700
and this is where we
finished off the last video--

00:00:48.700 --> 00:00:51.230
was if you look at
pure, I would say,

00:00:51.230 --> 00:00:54.620
compounding phenomenon, like
for example, the Fibonacci

00:00:54.620 --> 00:00:59.850
sequence, or powers of 2,
that exactly fits the Benford

00:00:59.850 --> 00:01:00.460
distribution.

00:01:00.460 --> 00:01:01.790
It exactly fits this.

00:01:01.790 --> 00:01:06.440
If you take all the
powers of 2, a little bit

00:01:06.440 --> 00:01:10.410
over 30% of those powers of
2, all of the powers of 2

00:01:10.410 --> 00:01:13.709
have 1 as their most
significant digit.

00:01:13.709 --> 00:01:14.250
What is this?

00:01:14.250 --> 00:01:14.880
17?

00:01:14.880 --> 00:01:17.030
Roughly 17% of
all of them have 2

00:01:17.030 --> 00:01:17.490
as their most significant digit.

00:01:17.490 --> 00:01:17.960
VI: Yeah.

00:01:17.960 --> 00:01:20.001
Although in this case,
there's an infinite number

00:01:20.001 --> 00:01:21.980
in every set, so
it's harder to graph.

00:01:21.980 --> 00:01:24.050
SAL: But if you
wanted to try it out,

00:01:24.050 --> 00:01:26.082
you could take the first
million powers of 2

00:01:26.082 --> 00:01:27.290
and then find the percentage.

00:01:27.290 --> 00:01:29.020
And that will probably give
you a pretty good approximation

00:01:29.020 --> 00:01:29.385
of things.

00:01:29.385 --> 00:01:29.970
VI: Yeah.

00:01:29.970 --> 00:01:34.300
So to me, that's
like less mysterious.

00:01:34.300 --> 00:01:37.010
On the one hand, wow, this
fits exactly with mathematics.

00:01:37.010 --> 00:01:39.030
But that also gives you
a really good handle,

00:01:39.030 --> 00:01:40.870
because you realize, alright,
there's something here

00:01:40.870 --> 00:01:42.010
I can actually take a look at.

00:01:42.010 --> 00:01:43.160
SAL: You could take
a look at it and it

00:01:43.160 --> 00:01:44.530
starts to become something
you can dig deeper in.

00:01:44.530 --> 00:01:45.946
And we said, in
the last video, we

00:01:45.946 --> 00:01:48.740
wanted you to pause it and think
about why this is happening

00:01:48.740 --> 00:01:50.860
because, frankly, we had
to do the same thing.

00:01:50.860 --> 00:01:54.400
And a big clue
for us was when we

00:01:54.400 --> 00:01:56.030
looked at a logarithmic scale.

00:01:56.030 --> 00:01:57.830
And we're looking at
one right over here.

00:01:57.830 --> 00:01:59.371
And just to be clear,
what's going on

00:01:59.371 --> 00:02:02.740
in this logarithmic scale is you
see equal spaces on this scale

00:02:02.740 --> 00:02:04.250
are powers of 10.

00:02:04.250 --> 00:02:06.270
So on a linear scale,
this would be a 1.

00:02:06.270 --> 00:02:08.884
And maybe this would
be a 2 and then a 3.

00:02:08.884 --> 00:02:10.550
Or if we wanted to
say that this is a 2,

00:02:10.550 --> 00:02:13.920
you would say this is a 1, this
is a 10, this would be a 20,

00:02:13.920 --> 00:02:15.580
then would be a 30,
so on and so forth.

00:02:15.580 --> 00:02:18.540
But in a logarithmic
scale, equal distances

00:02:18.540 --> 00:02:22.060
are times 10 or, in this case,
if we're taking powers of 10.

00:02:22.060 --> 00:02:25.620
So this is 1:10, then
10:100, then 100:1,000.

00:02:25.620 --> 00:02:28.000
And you see how the numbers
in between fall out,

00:02:28.000 --> 00:02:30.200
that the space between
1 and 2 is pretty big.

00:02:30.200 --> 00:02:32.860
And then 2 and 3 is still pretty
big, but a little bit smaller.

00:02:32.860 --> 00:02:34.360
And then 3 and 4 gets smaller
and smaller and smaller,

00:02:34.360 --> 00:02:35.260
until you get to 10.

00:02:35.260 --> 00:02:37.660
And that's a pretty
big clue about what's

00:02:37.660 --> 00:02:39.460
going on with Benford's law.

00:02:39.460 --> 00:02:40.360
VI: Yeah.

00:02:40.360 --> 00:02:42.152
It seems to match up somehow.

00:02:42.152 --> 00:02:43.360
So there's a connection here.

00:02:43.360 --> 00:02:46.360
SAL: And it actually turns out--
and this actually a very big

00:02:46.360 --> 00:02:50.860
clue-- that this, if
you take this area right

00:02:50.860 --> 00:02:56.260
here as a percentage
of this entire area,

00:02:56.260 --> 00:02:58.660
it's exactly this percentage.

00:02:58.660 --> 00:03:01.060
It's exactly that
percentage there.

00:03:01.060 --> 00:03:05.110
And if you take this area as a
percentage of that entire area,

00:03:05.110 --> 00:03:08.227
it's exactly this
percentage, that roughly 17%,

00:03:08.227 --> 00:03:10.060
or whatever that number
is right over there.

00:03:10.060 --> 00:03:11.260
So that's a huge clue.

00:03:11.260 --> 00:03:14.560
VI: Yeah, or at
least for powers of 2

00:03:14.560 --> 00:03:17.977
or a Fibonacci sequence
thing-- for powers,

00:03:17.977 --> 00:03:19.060
it definitely makes sense.

00:03:19.060 --> 00:03:20.860
SAL: Yes, for any powers.

00:03:20.860 --> 00:03:23.860
And so the logic
is-- and this is now

00:03:23.860 --> 00:03:26.260
our biggest clue-- is to
actually plot the powers of 2

00:03:26.260 --> 00:03:27.635
on a logarithmic
scale like this.

00:03:27.635 --> 00:03:29.343
VI: All right, let's
see where they fall.

00:03:29.343 --> 00:03:30.760
SAL: All right,
let's try it out.

00:03:30.760 --> 00:03:33.460
So 2 to the zeroth power is 1.

00:03:33.460 --> 00:03:35.560
2 to the first power is 2.

00:03:35.560 --> 00:03:37.060
Then you get to 4.

00:03:37.060 --> 00:03:39.460
Then you get to 8.

00:03:39.460 --> 00:03:41.410
Then you get to
16, which is going

00:03:41.410 --> 00:03:43.660
to be someplace around here.

00:03:43.660 --> 00:03:45.460
Then you want to
go to 32, which is

00:03:45.460 --> 00:03:47.260
going to be someplace
around there.

00:03:47.260 --> 00:03:48.460
That's 30, so this is 32.

00:03:48.460 --> 00:03:49.960
Then you want to go to 64.

00:03:49.960 --> 00:03:52.960
And so this is 40, 50, 60.

00:03:52.960 --> 00:03:56.560
64 is going to be
right over there.

00:03:56.560 --> 00:03:58.960
And so what you see is, when
you plot the powers of 2

00:03:58.960 --> 00:04:01.660
on this logarithmic scale,
they're equal distance apart.

00:04:01.660 --> 00:04:04.277
So you keep stepping along.

00:04:04.277 --> 00:04:05.860
If you were to plot
on a linear scale,

00:04:05.860 --> 00:04:07.060
they'd get farther
and farther apart.

00:04:07.060 --> 00:04:07.586
VI: Yeah.

00:04:07.586 --> 00:04:09.460
SAL: Actually, twice as
far apart every time.

00:04:09.460 --> 00:04:13.660
But on this scale right over
here they are equally spaced.

00:04:13.660 --> 00:04:15.594
So what's happening
is you have something

00:04:15.594 --> 00:04:17.260
that's just equally
stepping along here.

00:04:17.260 --> 00:04:19.360
You can imagine even just
like walking along this.

00:04:19.360 --> 00:04:23.860
And if your sidewalk is shaped
like this logarithmic scale,

00:04:23.860 --> 00:04:26.260
the probability on
any given step, as you

00:04:26.260 --> 00:04:28.660
do many, many steps, or as
you count all the steps,

00:04:28.660 --> 00:04:30.618
you're going to have
many, many more steps that

00:04:30.618 --> 00:04:32.560
fall into the block
that's between 1 and 2,

00:04:32.560 --> 00:04:34.360
or between 10 and
20, than you will,

00:04:34.360 --> 00:04:36.318
for example, the block
that's between 9 and 10.

00:04:36.318 --> 00:04:39.760
VI: Yeah, if you just take
a random point along here,

00:04:39.760 --> 00:04:43.060
you're more likely to fall
in a area starting with 1.

00:04:43.060 --> 00:04:45.160
SAL: Right, one of these areas.

00:04:45.160 --> 00:04:48.160
Exactly, starting with 1, so
between 1 and 2, or 10 and 20,

00:04:48.160 --> 00:04:49.960
or 100 and-- and
that's exactly--

00:04:49.960 --> 00:04:52.660
VI: So taking equal steps
is going to give you

00:04:52.660 --> 00:04:54.719
that distribution, unless
your steps happen to--

00:04:54.719 --> 00:04:56.260
because there's
special cases, right?

00:04:56.260 --> 00:04:56.860
So if you're getting--

00:04:56.860 --> 00:04:58.360
SAL: Or people walk
logarithmically.

00:04:58.360 --> 00:04:59.560
[LAUGHS]

00:04:59.560 --> 00:05:04.060
VI: Yeah, if you walk from 1 to
10, if your steps are 10 long--

00:05:04.060 --> 00:05:04.810
SAL: Yeah.

00:05:04.810 --> 00:05:05.860
In special cases, yes.

00:05:05.860 --> 00:05:06.760
VI: So that's what
happens there.

00:05:06.760 --> 00:05:07.960
SAL: If your steps are 10 long--

00:05:07.960 --> 00:05:09.160
VI: You happen to
exactly on [INAUDIBLE].

00:05:09.160 --> 00:05:09.686
SAL: Right.

00:05:09.686 --> 00:05:11.560
But if you're anything--
any slight variation

00:05:11.560 --> 00:05:12.935
away from that exact
thing, and then you

00:05:12.935 --> 00:05:13.060
will get the distribution.

00:05:13.060 --> 00:05:13.285
VI: Yeah.

00:05:13.285 --> 00:05:14.860
You're going to end up
stepping all over the place.

00:05:14.860 --> 00:05:16.193
SAL: The Benford's distribution.

00:05:16.193 --> 00:05:18.760
VI: Benford's distribution.

00:05:18.760 --> 00:05:20.802
SAL: Even though I think
we now understand why,

00:05:20.802 --> 00:05:21.760
it's still fascinating.

00:05:21.760 --> 00:05:22.360
VI: Yeah.

00:05:22.360 --> 00:05:25.660
Well, this explains it
for these number series.

00:05:25.660 --> 00:05:26.894
SAL: Yes.

00:05:26.894 --> 00:05:28.560
VI: So now we have
to somehow figure out

00:05:28.560 --> 00:05:32.260
how to connect that to the
real world information.

00:05:32.260 --> 00:05:34.260
SAL: The general idea,
well, so for populations.

00:05:34.260 --> 00:05:35.634
And we read up a
little about it.

00:05:35.634 --> 00:05:37.360
And Benford's
distribution tends to work

00:05:37.360 --> 00:05:38.860
for things that
grow exponentially.

00:05:38.860 --> 00:05:39.460
VI: Yes.

00:05:39.460 --> 00:05:40.060
SAL: Like powers of 2.

00:05:40.060 --> 00:05:40.935
VI: Like powers of 2.

00:05:40.935 --> 00:05:41.860
SAL: Like powers of 2.

00:05:41.860 --> 00:05:43.318
And populations
grow exponentially.

00:05:43.318 --> 00:05:43.960
VI: Yeah.

00:05:43.960 --> 00:05:46.960
And in finance, a lot of
things also grow exponentially.

00:05:46.960 --> 00:05:47.860
SAL: Yes.

00:05:47.860 --> 00:05:49.060
Or decline exponentially.

00:05:49.060 --> 00:05:49.660
Either way.

00:05:49.660 --> 00:05:50.260
[LAUGHTER]

00:05:50.260 --> 00:05:52.051
SAL: But it tends to
operate exponentially.

00:05:52.051 --> 00:05:53.560
You keep growing
by 10% every year.

00:05:53.560 --> 00:05:55.752
That's an exponential path.

00:05:55.752 --> 00:05:57.460
What's fascinating is
physical constants.

00:05:57.460 --> 00:05:59.860
And we actually aren't 100%
sure why this is happening.

00:05:59.860 --> 00:06:00.460
VI: No.

00:06:00.460 --> 00:06:02.260
This is still crazy to me.

00:06:02.260 --> 00:06:04.060
SAL: We only have theories here.

00:06:04.060 --> 00:06:06.019
And the general idea--
because, you know,

00:06:06.019 --> 00:06:08.185
physical constants is sort
of dependent on the units

00:06:08.185 --> 00:06:09.160
you're dealing with.

00:06:09.160 --> 00:06:11.260
They're depending on a
whole bunch of things.

00:06:14.560 --> 00:06:17.860
Actually, I have a few
very loose theories.

00:06:17.860 --> 00:06:21.160
But I'll let you all
think about that more.

00:06:21.160 --> 00:06:21.760
VI: OK.

00:06:21.760 --> 00:06:23.560
SAL: All right?

00:06:23.560 --> 00:06:26.433
And so, hopefully,
you all enjoyed this.