Sal Khan (with a severe cold!) on Future Talk

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Language: en

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(lively music)

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Martin: Welcome to Future Talk, the show

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that examines the global
impact of technology

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both for good and for bad.

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Our society is heavily
dependent on technology,

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but maintaining that technology requires

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people who are very well-educated

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especially in math and science.

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Our methods of teaching math have

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hardly changed in the
past several centuries.

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That may be about to change.

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I have three guests to discuss

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some of the new approaches

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to teaching mathematics.

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Peter Friess is president and CEO

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of the Tech Museum of Innovation

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which is the underwriter for this program,

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and he's also an experienced clockmaker.

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Keith Devlin is a mathematician,

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and executive director

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of Stanford University's H-Star Institute

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which studies the relationship

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between people and technology.

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He won the 2007 Carl Sagan Award

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for science outreach activities,

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and is known to NPR listeners

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as the Math Guy on Weekend Edition.

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He's written 28 books and
is now working on a project

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to use video game technology

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to help middle school
students learn mathematics.

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Salman Kahn is the founder

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of the Kahn Academy which is a

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one-man internet venture that aims

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to provide free, world-class education

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to anyone anywhere in the world.

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His 1400 plus videos on YouTube have

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garnered over 16 million views,

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and have received glowing testimonials

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from all over the world.

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Kahn Academy is now the most popular

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open education K through 12

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education resource on the internet.

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It's recently been profiled

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on CNN, NPR, and the PBS NewsHour.

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Salman received the 2009
Microsoft Education Award

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at the Tech Museum in San
Jose for using technology

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to benefit humanity.

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I'd like to welcome all of
you to the program tonight.

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Peter, let me start with you.

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What is the Tech Museum doing

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to advance new math education?

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Peter: First of all if you go to a museum

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especially to a science museum

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like the Tech Museum is, then
there is math everywhere.

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In every object you have math somehow.

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What is the difference to
the normal school industry?

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When you come to a museum, you have

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to explore the space for yourself.

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You have to be very active and
it's up to you what you learn.

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Parallel to this, the Tech Museum offers

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some very interesting programs.

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One, especially, is
where we bring teachers,

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kids and parents together in one classroom

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because as we always know, kids go home

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and say, "I have a problem to understand,"

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and you have to have education

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from your parents so sometimes parents

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don't even have learned themselves

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what's now going on at school;

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therefore, building this triangle

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between teacher, kids, and parents is a

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very, very helpful thing and

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that happens at the Tech Museum.

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Martin: Is this sort of an experimental

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prototype where you're experimenting

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with different ways of learning

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the role of the parent,
the role of the teacher,

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the role of the student himself?

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Peter: Exactly. The
Tech Museum would not be

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in Silicon Valley if we would not do

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these kind of experiments all the time.

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We are looking for new ways of how

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to bring these difficult subjects closer

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to the people that people
really can make use

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of what they've learned in the museum

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in becoming a global
citizen, a well-informed

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citizen about science that problems
like we have them right now

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down in Florida, cannot
happen or are going

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to be treated in a much different way.

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Martin: Does this approach, does it get

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outside the museum so where, for example,

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school districts are
watching your experiments

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and what you're doing,
and seeing how they could

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apply it to their own teaching?

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Peter: Yeah. We are working
together with teachers.

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We're working together with the kids,

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and we let them participate
in building the museum.

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For instance, we have a program right now

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where kids are in front
of teachers getting

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educated on a science
subject for about 20 minutes.

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Then they have to repeat
what they've learned in front

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of a camera and these videos
are really, really good.

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They show us what people
can learn in 20 minutes,

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and how they explain what
they've learned to the audience.

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Those videos finally end
up in the museum itself

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in front of the science experiment

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so the video basically
with the kid on the video

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explains the science experiment.

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There are no labels anywhere.

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Martin: Well, I gather
that there is a need

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to upgrade teaching
because it hasn't really

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changed much lately, and
the needs have changed.

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Keith, how long has it
been since there has been

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a major upgrade to the
way mathematics is taught?

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Keith: Well, the three
images that I brought along

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to show to the audience
are from a book that was

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written in 1202. It's by Leonardo of Pisa.

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It was written in Latin.

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It's called Liber Abaci. It
means the book of calculation.

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Martin: Yeah, can we see those pictures?

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I think we have those images.

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Let's go ahead and show those pictures.

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Keith: This book appears in 1202.

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It was the first arithmetic book that ever

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appeared in Western Europe.

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It looks very little different from an

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arithmetic book today except
that the language is changed.

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We don't write our books in Latin anymore.

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They've got a little bit thinner.

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That was about 600 pages, but essentially

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arithmetic teaching hasn't changed

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in the West in 800 years.

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Martin: Now one might say
if a system has worked

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for 800 years, why does
it need to change now?

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Keith: I think many people in our audience

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will say that it hasn't worked very well.

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We've been using it, we've used textbooks

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because for 800 years
that was the only way

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we could capture mathematical knowledge

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on any kind of device
that we could distribute

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to a large number of
people. It had to be text,

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but mathematics isn't about facts.

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Mathematics is a way of thinking

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about the world, problems in the world.

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it's something you do.

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What's the best way to learn
something you do? You do it.

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If you want to learn to play chess,

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you can learn the rules from a book,

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but you won't learn to play
chess until you play the game.

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If you want to learn to play tennis,

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the book will tell you something,

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but you've got to go out and play tennis.

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You can't always learn by going out

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and doing the real thing,
for example, if you want

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to learn how to fly an airplane,

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you learn in a simulator.

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If you want to learn how
to be a brain surgeon,

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you will be trained in a simulator.

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The U. S. Army uses
simulators to train troops

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before they go to Iraq.

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Martin: How does this
apply to mathematics?

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Keith: Mathematics learning is more like

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learning to be a soldier because there's

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a danger element that
people will get scared.

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The best way to learn
mathematics is either

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in a real-world environment
where you're using

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mathematics, and those are difficult

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to come across especially with classes

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full of students, or you
learn it in a simulator.

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The modern word for a
simulator is a video game.

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That's why I've spent the last five years

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looking at how you can use video games,

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massively, multiplayer, online games

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to provide environments in which students

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can learn mathematics
in a real environment.

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Martin: When you talk
about teaching people

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how to think mathematically,
what does that look like?

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How does a person who
thinks mathematically differ

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from a person who does
not think mathematically?

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Keith: In almost every respect.

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For example, we don't
get nervous when numbers

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are bounded around. We
know what the numbers mean.

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We know that if the
prices go up 10% this week

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and come down 10% next
week, they don't go back

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to where they were. We
just have this sense

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of what the numbers mean,
and what video games

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are ideal for, you can use
them for doing all kinds

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of mathematics, but what they're ideal for

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is getting people to that familiarity

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with numbers and
quantities that are really

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part and parcel of being a
citizen in the 21st Century

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in a country like the United States.

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Martin: We're getting
away from the traditional

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rote learning where you
just memorize everything

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whether you really understand it or not.

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Keith: Mathematics today
more than at any time

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in history, it's important to be able

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to think like a mathematician.

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You actually no longer need to do a lot

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of the detailed mathematics.

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We have machines like this device

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that Peter's got next to me that will

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do mathematics for us.

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We have computers to do that.

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We have check-out machines
at the supermarket

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doing the calculations.

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It's not as important as
it was when I was a child.

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Thinking mathematically, that's the kind

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of the realm in the 21st Century.

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Martin: I think the students of the future

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will be very happy to
learn that they'll be able

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to spend their math class
playing video games.

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Keith: I would hope they
would because learning

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math should be fun, and by
golly, we can make it fun.

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Martin: Now you're
working on this project.

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Where is this project?

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Is this game ready to
roll off the shelves?

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Keith: Absolutely not. We
started off five years ago

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thinking that this might cost
$30, $40, $50 million dollars.

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My current estimate is this is a

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$500 million dollar operation at least.

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I'm now calling this the Apollo Program

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in mathematics education.

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It's the educational equivalent of putting

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some person on the moon.

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We want to put some
person into a mathematical

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mind and just keep them
alive, if you would.

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It's got to be a big national program.

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This is not something that even a large

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video game company can do.

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This has to be a national
initiative because

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that's the only way to do
something on this scale.

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Martin: That's very interesting because

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you're talking about a $500 million dollar

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expenditure to build this video program.

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Now Sal, you've created Khan Academy

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which essentially provides free education

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which costs next to nothing to produce,

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and you've had 16 million viewers already.

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What is Khan Academy actually?

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And how does it really work?

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Sal: Yes, so most people know it as

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this library of 1400 videos on YouTube.

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As you mentioned, it's
gotten 16 million views.

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It's now the most viewed open
education library, more than

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especially on YouTube,
more than MIT and Stanford.

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All of the videos have been made by me.

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I'm the faculty of the Khan Academy.

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The goal is to, I'm going
to keep making videos,

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but we're supplementing
that with a software piece,

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and eventually build a
community around the site

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so that students can
start teaching each other.

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The goal is really to
be a free virtual school

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for the world, a place where anyone can go

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to the site and learn at their own pace,

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get feedback, get data
on what they're doing

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and start at any point
and get to any point.

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If you go to the site right now,

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you'll see there's a video
literally on 1 + 1 = 2.

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That's the very first arithmetic video.

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The videos, 1400 videos
is a lot of material,

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and it goes all the way up to the last

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calculus video I did
was a surface integral

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and you can go into
differential equations,

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and physics, and there's even stuff

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on the financial crisis and all of that.

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The goal is to start at a basic level

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and go as far as you need to go.

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Martin: Before we discuss
Khan Academy further,

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we're actually going to view some excerpts

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from some of your videos.

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What are we going to
see in these excerpts?

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Sal: The one thing that I think stands out

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to a lot of people is that the form factor

00:11:31.257 --> 00:11:33.420
for the Khan Academy is fairly different

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than what you would
expect as online video.

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You're not going to see the instructor.

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You're not going to see
someone at a whiteboard

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kind of teaching away from you.

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All you see is a black background,

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some writing in different
colors that look nice,

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and a voice, and I like to
end the voice as this voice.

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I like to think that it's
more of an experience

00:11:54.075 --> 00:11:56.295
of me sitting next to you and we're doing

00:11:56.295 --> 00:12:00.409
a tutoring session, or
me being in your head

00:12:00.563 --> 00:12:02.904
more of an intimate kind
of one-on-one tutoring

00:12:02.904 --> 00:12:05.914
informal type of a framework.

00:12:05.914 --> 00:12:07.258
Martin: We're going to go
ahead and roll that video.

00:12:07.258 --> 00:12:08.707
Let's take a look at Sal's video,

00:12:08.707 --> 00:12:10.585
and then we'll come back
and discuss it further.

00:12:10.585 --> 00:12:15.589
Let's roll that tape.

00:12:15.589 --> 00:12:17.259
Sal: Notice we interpreted the statement

00:12:17.259 --> 00:12:18.424
in two different ways.

00:12:18.424 --> 00:12:20.029
This was just straight left to right doing

00:12:20.029 --> 00:12:22.301
the addition, then the multiplication.

00:12:22.301 --> 00:12:24.341
This way we did the multiplication first

00:12:24.341 --> 00:12:26.442
then the addition. We got
two different answers.

00:12:26.442 --> 00:12:28.672
That's just not cool in mathematics.

00:12:28.672 --> 00:12:32.034
If this was part of some
effort to send something

00:12:32.034 --> 00:12:33.729
to the moon because two people interpreted

00:12:33.729 --> 00:12:35.422
it in a different way, or one computer

00:12:35.422 --> 00:12:36.798
interpreted it one way, another computer

00:12:36.798 --> 00:12:38.475
interpreted it another way, the satellite

00:12:38.475 --> 00:12:42.312
might go to Mars. This is
just completely unacceptable.

00:12:42.312 --> 00:12:44.476
That's why we have to have an agreed upon

00:12:44.476 --> 00:12:46.697
order of operations, an agreed upon way

00:12:46.697 --> 00:12:49.509
to interpret this statement.

00:12:49.509 --> 00:12:54.730
The agreed upon order of operations
is to do parentheses first.

00:12:54.730 --> 00:13:00.764
Let me write it over here,
parentheses. Parentheses first.

00:13:00.764 --> 00:13:03.183
Then do exponents. If you don't know what

00:13:03.183 --> 00:13:06.904
exponents are, don't worry
about it right now. Exponents.

00:13:06.904 --> 00:13:08.226
In this video we're not going to have

00:13:08.226 --> 00:13:10.706
any exponents in our examples so you don't

00:13:10.706 --> 00:13:12.767
really have to worry
about them for this video.

00:13:12.767 --> 00:13:14.769
Then you do multiplication.

00:13:14.769 --> 00:13:18.920
I'll just right mult,
short for multiplication.

00:13:18.920 --> 00:13:20.342
The you do multiplication
and division next.

00:13:20.342 --> 00:13:23.143
They kind of have the
same level of priority.

00:13:23.143 --> 00:13:26.951
Then finally, you do
addition and subtraction.

00:13:26.951 --> 00:13:33.957
Finally, you do addition and subtractions.

00:13:33.957 --> 00:13:37.124
A neuron can be a
reasonably normal sized cell

00:13:37.124 --> 00:13:38.244
although there is a huge range,

00:13:38.244 --> 00:13:40.321
but the axons can be quite long.

00:13:40.321 --> 00:13:42.158
They could be short sometimes in the brain

00:13:42.158 --> 00:13:43.988
you might have very small axons,

00:13:43.988 --> 00:13:46.392
but you might have axons that go down the

00:13:46.392 --> 00:13:48.784
spinal column or that go
along one of your limbs,

00:13:48.784 --> 00:13:50.201
or if you're talking about a dinosaur,

00:13:50.201 --> 00:13:51.936
going along one of a dinosaur's limbs.

00:13:51.936 --> 00:13:54.707
The axon can actually
stretch several feet.

00:13:54.707 --> 00:13:56.591
Not all neuron's axons are several feet,

00:13:56.591 --> 00:13:58.275
but they could be, and this is really

00:13:58.275 --> 00:14:02.659
where a lot of the distance
of the signal gets traveled.

00:14:02.659 --> 00:14:05.834
Let me draw the axon.

00:14:05.834 --> 00:14:09.289
The axon will look something like this,

00:14:09.289 --> 00:14:13.080
and at the end it ends
at the axon terminal

00:14:13.080 --> 00:14:16.154
where it can connect to other dendrites,

00:14:16.154 --> 00:14:18.541
or maybe to other types
of tissue or muscle

00:14:18.541 --> 00:14:20.527
if the poor point of this neuron is

00:14:20.527 --> 00:14:26.375
to tell a muscle to do something.

00:14:26.375 --> 00:14:29.869
Let's say I go to the local grocery store.

00:14:29.869 --> 00:14:31.914
Let me draw that in orange.

00:14:31.914 --> 00:14:35.082
Let's say I go to some
grocery store over here.

00:14:35.082 --> 00:14:38.375
I'll say G for grocery,
and I buy $100 worth

00:14:38.375 --> 00:14:40.476
of groceries and I want to pay with my

00:14:40.476 --> 00:14:42.415
newly issued credit card.

00:14:42.415 --> 00:14:43.346
Let me write this down.

00:14:43.346 --> 00:14:45.716
This is the issuing, issuer.

00:14:45.716 --> 00:14:47.370
This is the issuing bank.

00:14:47.370 --> 00:14:48.414
I go to the grocery store.

00:14:48.414 --> 00:14:50.779
I say, "Hey, I'd like to
pay with a credit card."

00:14:50.779 --> 00:14:53.145
The grocery store, if
they accept credit cards,

00:14:53.145 --> 00:14:55.245
they need to have some relationship with

00:14:55.245 --> 00:14:58.259
another bank someplace
on this Visa network

00:14:58.259 --> 00:15:01.115
in order for them to accept a Visa card.

00:15:01.115 --> 00:15:03.542
Let's say that they have a relationship

00:15:03.542 --> 00:15:05.591
with Bank B over here.

00:15:05.591 --> 00:15:07.802
This would be the merchant bank,

00:15:07.802 --> 00:15:09.451
or we could say the retailers bank,

00:15:09.451 --> 00:15:11.530
or it's often in credit card lingo

00:15:11.530 --> 00:15:14.539
called the acquiring
bank, or the acquirer.

00:15:14.539 --> 00:15:16.789
You might wonder why is
it called the acquirer?

00:15:16.789 --> 00:15:18.292
It's called the acquirer
because this is the

00:15:18.292 --> 00:15:21.286
player that goes out and
goes to each of the merchants

00:15:21.286 --> 00:15:23.709
and says, "Hey, right
now you only accept cash,

00:15:23.709 --> 00:15:25.534
"or you only accept American Express.

00:15:25.534 --> 00:15:26.837
"Wouldn't it be great if you also

00:15:26.837 --> 00:15:28.755
"accepted Visa or Mastercard?

00:15:28.755 --> 00:15:31.364
"That way you'll have more appeal to more

00:15:31.364 --> 00:15:34.203
"customers and it will be more convenient

00:15:34.203 --> 00:15:35.457
"for your customers and every time a

00:15:35.457 --> 00:15:36.782
"transaction happens, we'll just take

00:15:36.782 --> 00:15:39.677
"a little bit of a cut
of that transaction."

00:15:39.677 --> 00:15:43.826
So they go out and acquire
different retailers.

00:15:43.826 --> 00:15:46.113
Martin: That was some sample
videos from Kahn Academy.

00:15:46.113 --> 00:15:47.490
I like your style of delivery

00:15:47.490 --> 00:15:49.125
because I don't think
you're going to lose anyone.

00:15:49.125 --> 00:15:52.547
It's kind of folksy. You're
not rushing through it,

00:15:52.547 --> 00:15:54.856
but it looks like the videos
are very simple to produce.

00:15:54.856 --> 00:15:59.356
It looks like they cost
next to nothing to create.

00:15:59.356 --> 00:16:00.997
Is there anything preventing other people

00:16:00.997 --> 00:16:02.408
from also jumping into this field

00:16:02.408 --> 00:16:05.188
and creating their own similar videos.

00:16:05.188 --> 00:16:06.721
Sal: No, and I hope they do it.

00:16:06.721 --> 00:16:08.226
Literally to produce these videos

00:16:08.226 --> 00:16:09.580
I think some of the people at home

00:16:09.580 --> 00:16:10.614
could start doing it tonight.

00:16:10.614 --> 00:16:12.211
You just need a little
pen tablet you can get

00:16:12.211 --> 00:16:14.620
at the local electronics
store for under $100.

00:16:14.620 --> 00:16:17.322
I use Screen Capture. You
can get a shareware version.

00:16:17.322 --> 00:16:18.523
Then I'm just using an art program.

00:16:18.523 --> 00:16:19.828
I started doing Microsoft Paint.

00:16:19.828 --> 00:16:22.446
I'm now using other slightly more fancy

00:16:22.446 --> 00:16:23.981
shareware pieces of programming,

00:16:23.981 --> 00:16:27.144
but it's very simple, very easy.

00:16:27.144 --> 00:16:29.628
I started doing it just
because I was remotely

00:16:29.628 --> 00:16:31.245
tutoring my cousins in New Orleans,

00:16:31.245 --> 00:16:32.662
and when I was doing that we just had

00:16:32.662 --> 00:16:34.744
a shared whiteboard and
we didn't see each other,

00:16:34.744 --> 00:16:36.383
and it seemed to work so I figured why not

00:16:36.383 --> 00:16:37.739
do the same thing then
I wouldn't have to get

00:16:37.739 --> 00:16:40.678
a camera crew and all that.

00:16:40.678 --> 00:16:41.688
Martin: How are the videos used?

00:16:41.688 --> 00:16:43.209
Is this something that
a person just watches

00:16:43.209 --> 00:16:46.244
at home alone, or can this be brought into

00:16:46.244 --> 00:16:48.295
a classroom situation?

00:16:48.295 --> 00:16:50.188
Sal: When I started, I envisioned it being

00:16:50.188 --> 00:16:52.822
some type of a supplemental
material for students

00:16:52.822 --> 00:16:54.787
when they're home if
they need to remediate,

00:16:54.787 --> 00:16:56.200
fill in gaps in their knowledge,

00:16:56.200 --> 00:16:58.115
they can just dive in and
get a 10 minute nugget

00:16:58.115 --> 00:17:00.409
that fills in a basic building block.

00:17:00.409 --> 00:17:02.491
They can pause and repeat
it as much as they want.

00:17:02.491 --> 00:17:03.448
I've gotten a lot of feedback.

00:17:03.448 --> 00:17:04.916
It's starting to be used in the classroom.

00:17:04.916 --> 00:17:06.616
Really it's an organic process.

00:17:06.616 --> 00:17:09.495
It makes a lot of sense if
you think about it right now.

00:17:09.495 --> 00:17:11.660
I've gotten an email
from a teacher in London

00:17:11.660 --> 00:17:13.359
that said, "We've flipped the model.

00:17:13.359 --> 00:17:15.528
"We are now, instead of doing lecture

00:17:15.528 --> 00:17:17.954
"in the classroom, and homework at home,

00:17:17.954 --> 00:17:20.500
"I now assign Kahn Academy videos at home

00:17:20.500 --> 00:17:21.592
"where the students can
watch it at their own pace,

00:17:21.592 --> 00:17:23.822
"at their own time, pause and repeat,

00:17:23.822 --> 00:17:26.484
"fill in the gaps in their knowledge,

00:17:26.484 --> 00:17:27.762
"and then when you come to the classroom,

00:17:27.762 --> 00:17:28.755
"then you do your homework.

00:17:28.755 --> 00:17:30.628
"Then you can get the benefit of a teacher

00:17:30.628 --> 00:17:32.427
"being around. The
teacher can observe what

00:17:32.427 --> 00:17:33.788
"the students are doing,
and the students can help

00:17:33.788 --> 00:17:35.518
"each other so you're
actually taking advantage

00:17:35.518 --> 00:17:38.819
"of the social aspects of a classroom

00:17:38.819 --> 00:17:40.195
"to actually teach each other."

00:17:40.195 --> 00:17:42.393
It can be used either.

00:17:42.393 --> 00:17:43.814
It could be used for a home school.

00:17:43.814 --> 00:17:46.749
I've gotten letters from parents who,

00:17:46.749 --> 00:17:49.852
one, they use it for their
kids, but they also use it

00:17:49.852 --> 00:17:51.188
to stay ahead of their
kids so that they can

00:17:51.188 --> 00:17:54.127
teach them one step ahead.

00:17:54.127 --> 00:17:56.478
It's really I'm learning
of new applications

00:17:56.478 --> 00:17:57.927
for it every day.

00:17:57.927 --> 00:18:01.428
Martin: How do the teachers know
that the kids master the material?

00:18:01.428 --> 00:18:03.481
Would they still have the
same traditional test?

00:18:03.481 --> 00:18:05.816
Or could you have a thing
where a child finishes

00:18:05.816 --> 00:18:09.684
one video. they somehow
demonstrate that they've

00:18:09.684 --> 00:18:12.194
absorbed what it taught,
and then they go on

00:18:12.194 --> 00:18:16.490
to the next video so people
kind of work at their own pace?

00:18:16.490 --> 00:18:18.567
Sal: Yeah. When I
started the Kahn Academy,

00:18:18.567 --> 00:18:20.321
it's most known for the videos,

00:18:20.321 --> 00:18:21.320
but there's an entire software piece

00:18:21.320 --> 00:18:22.949
that I started really
building for my cousins

00:18:22.949 --> 00:18:24.622
and now several tens
of thousands of people

00:18:24.622 --> 00:18:26.123
are using the software.

00:18:26.123 --> 00:18:27.821
The idea is you start everyone at 1 + 1.

00:18:27.821 --> 00:18:28.791
There's these little modules.

00:18:28.791 --> 00:18:31.316
People can log in right now
and start working on it.

00:18:31.316 --> 00:18:35.127
It starts at 1 + 1 = 2,
and the paradigm isn't

00:18:35.127 --> 00:18:36.853
get 80% right and you're a C student,

00:18:36.853 --> 00:18:38.198
or 90% right and you're a B,

00:18:38.198 --> 00:18:39.895
or 95% and you're an A student.

00:18:39.895 --> 00:18:41.955
The paradigm is get ten in a row

00:18:41.955 --> 00:18:42.906
because even if you're an A student

00:18:42.956 --> 00:18:45.489
and you've gotten 95%
right, what was that 5%?

00:18:45.489 --> 00:18:47.715
In math, I think we can all
appreciate in mathematics,

00:18:47.715 --> 00:18:49.583
if you have even a 5% gap, when you build

00:18:49.583 --> 00:18:52.293
on top of that, you don't
know what something is

00:18:52.293 --> 00:18:54.157
to the zero power, then when you see it

00:18:54.157 --> 00:18:55.543
in calculus, you're
like, "Gee, I don't know.

00:18:55.543 --> 00:18:56.662
"I was an A student,
but I still didn't know

00:18:56.662 --> 00:18:57.762
"that one special case."

00:18:57.762 --> 00:18:59.427
So the paradigm is get ten in a row,

00:18:59.427 --> 00:19:00.589
and as you get ten in a row you get,

00:19:00.589 --> 00:19:02.133
and while you're doing the modules

00:19:02.133 --> 00:19:04.600
it's tracking everything,
every interaction

00:19:04.600 --> 00:19:07.375
with the actual software,
so if you think about it

00:19:07.375 --> 00:19:08.961
you're getting instruction from the video.

00:19:08.961 --> 00:19:10.552
You're getting practice and feedback

00:19:10.552 --> 00:19:12.706
directly from the software in real time,

00:19:12.706 --> 00:19:14.025
and then everything is being tracked

00:19:14.025 --> 00:19:15.762
so it's actual real-time assesment

00:19:15.762 --> 00:19:17.213
that's actionable that the teachers

00:19:17.213 --> 00:19:19.781
can actually get data on what
to do about what students.

00:19:19.781 --> 00:19:21.359
Everyone is working at their own pace.

00:19:21.359 --> 00:19:22.492
Martin: Of course, the
tradition is that everybody

00:19:22.492 --> 00:19:25.796
goes in lock step which
is bad in two respects.

00:19:25.796 --> 00:19:28.714
One respect, the slow
kids get left behind.

00:19:28.714 --> 00:19:32.299
The other respect is that
the fast kids are held back.

00:19:32.299 --> 00:19:34.327
Sal: The real irony is sometimes there's

00:19:34.327 --> 00:19:36.859
a flipping of, we've
had the experience where

00:19:36.859 --> 00:19:38.656
this is easy and you're kind of bored.

00:19:38.656 --> 00:19:40.416
Then all of a sudden,
"Wait, I missed that."

00:19:40.416 --> 00:19:44.265
You've now fallen behind
and I've seen it in the data

00:19:44.265 --> 00:19:46.682
of students using the software is that

00:19:46.682 --> 00:19:48.714
sometimes a student will,
when they're working

00:19:48.714 --> 00:19:50.925
at their own pace, a
student that you might say

00:19:50.925 --> 00:19:52.874
is slow initially because
they're spending more time

00:19:52.874 --> 00:19:55.863
on one concept, once they
get that out of the way,

00:19:55.863 --> 00:19:57.213
they race forward so
it's actually very hard

00:19:57.213 --> 00:20:00.049
to predict who are the
slow or the fast students.

00:20:00.049 --> 00:20:02.541
Just going back to the traditional model

00:20:02.541 --> 00:20:05.625
on some level we've gotten so used to it

00:20:05.625 --> 00:20:07.375
because it's 1,000 years old,

00:20:07.375 --> 00:20:09.615
but we don't question
this idea of passively

00:20:09.615 --> 00:20:12.165
getting lectures, then you
go home and you do things

00:20:12.165 --> 00:20:14.131
in a vacuum, and you
keep doing that process

00:20:14.131 --> 00:20:16.880
for several days and then you
get a snapshot assessment.

00:20:16.880 --> 00:20:18.588
When you get the assessment, it tells you

00:20:18.588 --> 00:20:21.020
you knew 80% of that concept.

00:20:21.020 --> 00:20:22.927
In a normal world when
you're learning something,

00:20:22.927 --> 00:20:25.483
if I only know how to ride
a bike 80% of the way,

00:20:25.483 --> 00:20:27.131
I'm going to keep sitting on that bike

00:20:27.131 --> 00:20:31.160
until I can always before
I try out a unicycle.

00:20:31.160 --> 00:20:31.935
Martin: A lot of people seem to have

00:20:31.935 --> 00:20:33.416
a real math phobia. I've
known people who just

00:20:33.416 --> 00:20:35.926
don't believe they can
understand anything in math.

00:20:35.926 --> 00:20:38.659
It might be because they missed one

00:20:38.659 --> 00:20:40.793
like it's a chain of
knowledge and if one link

00:20:40.793 --> 00:20:42.495
in the chain is broken, then you lose

00:20:42.495 --> 00:20:43.714
the rest of the chain,

00:20:43.714 --> 00:20:46.510
but here you don't
advance to the next link

00:20:46.510 --> 00:20:49.093
until you're sure that
you've mastered this link.

00:20:49.093 --> 00:20:51.355
Sal: Right. There's a couple of reasons.

00:20:51.355 --> 00:20:53.595
I'm convinced that a
lot of the frustration

00:20:53.595 --> 00:20:55.520
that goes on in say an algebra class isn't

00:20:55.520 --> 00:20:57.601
because the student is slow,

00:20:57.601 --> 00:20:59.222
or because the teacher is bad.

00:20:59.222 --> 00:21:00.790
It's just that the student has a weakness

00:21:00.790 --> 00:21:03.592
in borrowing numbers, or negative numbers.

00:21:03.592 --> 00:21:05.387
There's no way in that algebra class

00:21:05.387 --> 00:21:07.292
to address that negative number.

00:21:07.292 --> 00:21:08.139
The student might not even know

00:21:08.139 --> 00:21:09.827
that they have that basic weakness

00:21:09.827 --> 00:21:10.994
in negative numbers and they just keep

00:21:10.994 --> 00:21:12.634
talking past each other.

00:21:12.634 --> 00:21:13.968
I think you're exactly right.

00:21:13.968 --> 00:21:16.088
That's the problem is
that no matter how good

00:21:16.088 --> 00:21:18.417
you do in traditional model,

00:21:18.417 --> 00:21:19.339
how good the actors are in it,

00:21:19.339 --> 00:21:20.627
if you have this basic core weakness,

00:21:20.627 --> 00:21:22.506
there's no way to address
it in the traditional model.

00:21:22.506 --> 00:21:23.693
Martin: Let me throw out a question that

00:21:23.693 --> 00:21:26.086
any of you can feel free to answer.

00:21:26.086 --> 00:21:28.454
Is learning itself an art?

00:21:28.454 --> 00:21:31.955
The usual model is that the child is

00:21:31.955 --> 00:21:35.921
a passive vessel in which
you pour the knowledge.

00:21:35.921 --> 00:21:38.298
Is learning something
that you have to know

00:21:38.298 --> 00:21:40.003
how to do like you have
to learn how to learn

00:21:40.003 --> 00:21:43.887
before you can even start?

00:21:43.887 --> 00:21:48.860
Peter: At the museum, the game program,

00:21:48.860 --> 00:21:53.251
and in your methodology really teaches us

00:21:53.251 --> 00:21:56.635
and we learn it that
there is a different way

00:21:56.635 --> 00:21:59.081
of learning where you are the master

00:21:59.081 --> 00:22:01.435
of the speed how fast you learn.

00:22:01.435 --> 00:22:04.618
You go forwards and
backwards. It's your choice.

00:22:04.618 --> 00:22:08.551
People who come to museums,
they give random a chance.

00:22:08.551 --> 00:22:12.174
The run around. They
discover their talents.

00:22:12.174 --> 00:22:15.797
The learning is not working
in the future I think

00:22:15.797 --> 00:22:19.339
with a teacher outside and
a lot of kids sitting there

00:22:19.339 --> 00:22:21.539
and just watching at this teacher.

00:22:21.539 --> 00:22:23.758
I think we want to be part
of this learning process,

00:22:23.758 --> 00:22:26.671
and we want to really
organize it ourselves.

00:22:26.671 --> 00:22:28.685
I think in all of our three cases

00:22:28.685 --> 00:22:30.462
that's happening nowadays.

00:22:30.462 --> 00:22:32.319
Keith: That's the power of a video game.

00:22:32.319 --> 00:22:34.424
In a video game, the player is the star

00:22:34.424 --> 00:22:36.158
of that universe. It revolves around you.

00:22:36.158 --> 00:22:37.718
They're designed that way.

00:22:37.718 --> 00:22:40.193
Remember human beings as a species,

00:22:40.193 --> 00:22:42.695
we survived because we learned to learn.

00:22:42.695 --> 00:22:44.186
We are the learning species.

00:22:44.186 --> 00:22:46.321
We are programmed from birth to learn

00:22:46.321 --> 00:22:48.649
in an environment where
it's important to learn.

00:22:48.649 --> 00:22:50.160
Peter: And you're getting
immediately feedback.

00:22:50.160 --> 00:22:51.948
Keith: And you get immediate feedback.

00:22:51.948 --> 00:22:53.968
Just as with Sal's, video game learning

00:22:53.968 --> 00:22:55.134
it reverses everything.

00:22:55.134 --> 00:22:56.262
What does the teacher say?

00:22:56.262 --> 00:23:00.446
Go home tonight. Your homework
is to acquire the Sword of Doom.

00:23:00.446 --> 00:23:02.021
We build that game so
acquiring the Sword of Doom

00:23:02.021 --> 00:23:03.972
requires solving some math problems.

00:23:03.972 --> 00:23:05.805
The child probably
won't solve the problems

00:23:05.805 --> 00:23:08.816
that night so they go
back and the teacher says,

00:23:08.816 --> 00:23:10.697
"Go look at Khan Academy and you'll find

00:23:10.697 --> 00:23:13.101
on Video 35 exactly what you'll need

00:23:13.101 --> 00:23:14.965
to go back in tomorrow night

00:23:14.965 --> 00:23:17.077
and capture the Sword of Doom.

00:23:17.077 --> 00:23:20.088
The child now is motivated
in a right environment,

00:23:20.088 --> 00:23:22.206
and they've got all of
these sources available;

00:23:22.206 --> 00:23:26.029
teacher, textbooks, videos.
Brings it all together.

00:23:26.029 --> 00:23:27.392
Martin: I think a lot
of people who have made

00:23:27.392 --> 00:23:29.488
the greatest contributions
in computer science

00:23:29.488 --> 00:23:31.340
didn't make it because
of what they learned

00:23:31.340 --> 00:23:32.584
sitting in classrooms.

00:23:32.584 --> 00:23:33.994
It's what they did at home playing

00:23:33.994 --> 00:23:35.360
and putting things together.

00:23:35.360 --> 00:23:38.624
Kevin: They dropped out. Many
of them dropped out of school.

00:23:38.624 --> 00:23:40.545
Sal: To your point about
this learning to learn,

00:23:40.545 --> 00:23:44.837
and is there, I have a 15 month old son.

00:23:44.837 --> 00:23:46.207
He is a natural learner
just likewhat these

00:23:46.207 --> 00:23:47.829
guys are talking about.

00:23:47.829 --> 00:23:49.412
That's all he wants to do.

00:23:49.412 --> 00:23:51.417
In fact, if you take
him away from exploring

00:23:51.417 --> 00:23:52.489
and playing with something,

00:23:52.489 --> 00:23:54.827
and seeing and understanding,
that's what upsets him.

00:23:54.827 --> 00:23:57.032
I think the problem isn't that we need

00:23:57.032 --> 00:23:58.198
to teach people how to learn.

00:23:58.198 --> 00:24:00.799
I think a lot of our current institutions

00:24:00.799 --> 00:24:03.098
actually go in the opposite direction

00:24:03.098 --> 00:24:04.984
of our natural learning instincts.

00:24:04.984 --> 00:24:07.073
They force, even though
you want to be active

00:24:07.073 --> 00:24:10.323
and engaged, and explore things,

00:24:10.323 --> 00:24:12.069
they're treating you like a vessel

00:24:12.069 --> 00:24:14.203
that needs information to be poured in.

00:24:14.203 --> 00:24:15.320
Martin: Go ahead.

00:24:15.320 --> 00:24:18.839
Peter: In 1980, that's now 30 years ago,

00:24:18.839 --> 00:24:20.974
I learned Latin at a school.

00:24:20.974 --> 00:24:22.813
I was not really good at Latin

00:24:22.813 --> 00:24:25.164
so I bought one of the first laptops.

00:24:25.164 --> 00:24:27.348
I put all the vocabulary of this book

00:24:27.348 --> 00:24:29.344
into this little computer,

00:24:29.344 --> 00:24:32.316
and the computer was asking me the word.

00:24:32.316 --> 00:24:36.733
I typed it in, and when I typed
it correctly, it erased it.

00:24:36.733 --> 00:24:40.142
If I made an error, it recorded it.

00:24:40.142 --> 00:24:43.140
Then he asked me the wrong ones again.

00:24:43.140 --> 00:24:47.393
I basically learned how to
program Basic in those days.

00:24:47.393 --> 00:24:49.987
My Latin didn't really improve.

00:24:49.987 --> 00:24:51.778
Martin: Instant feedback
is really important.

00:24:51.778 --> 00:24:54.165
You don't pour knowledge
into the vessel all year,

00:24:54.165 --> 00:24:55.809
and at the end of the
year you give a one-time

00:24:55.809 --> 00:24:57.794
test to see what they learned.

00:24:57.794 --> 00:25:00.262
Sal: And then move on if they didn't.

00:25:00.262 --> 00:25:01.226
Martin: There are a lot of good methods

00:25:01.226 --> 00:25:03.530
to improve education, but, for example,

00:25:03.530 --> 00:25:05.550
here in the state of
California education is

00:25:05.550 --> 00:25:08.526
a huge bureaucracy, and bureaucracies are

00:25:08.526 --> 00:25:11.140
highly resistant to change.

00:25:11.140 --> 00:25:14.059
Is there any way that some of the ideas

00:25:14.059 --> 00:25:15.807
we're talking about could actually

00:25:15.807 --> 00:25:20.478
find its way into this big
massive inertial system?

00:25:20.478 --> 00:25:23.474
Sal: One thing I've seen just from letters

00:25:23.474 --> 00:25:25.330
from Kahn Academy users, and I'm getting

00:25:25.330 --> 00:25:26.893
a couple hundred every day now,

00:25:26.893 --> 00:25:29.220
is that some students
are using Kahn Academy

00:25:29.220 --> 00:25:30.801
as their primary
instruction, and they're just

00:25:30.801 --> 00:25:33.764
showing up at their university
or their high school

00:25:33.764 --> 00:25:35.834
just to kind of show what they've learned.

00:25:35.834 --> 00:25:39.386
I think it's hard to change the system.

00:25:39.386 --> 00:25:41.646
It's a big beast and you got to kind

00:25:41.646 --> 00:25:42.559
of massage it slowly.

00:25:42.559 --> 00:25:44.333
But I think over time when people find

00:25:44.333 --> 00:25:45.858
these alternate sources for learning

00:25:45.858 --> 00:25:47.473
their information and
professors start to say,

00:25:47.473 --> 00:25:49.173
"Wait. Gee, people are just showing up.

00:25:49.173 --> 00:25:50.892
"I'm just a test administrator.

00:25:50.892 --> 00:25:53.768
"I'm not actually, they're
learning someplace else."

00:25:53.768 --> 00:25:55.067
Hopefully, the system itself will say,

00:25:55.067 --> 00:25:57.361
"Gee, maybe we need to reflect."

00:25:57.361 --> 00:25:58.830
I don't understand why
there are 300 person

00:25:58.830 --> 00:26:00.259
lecture rooms anymore.

00:26:00.259 --> 00:26:02.936
If you think about it,
on-demand video is better

00:26:02.936 --> 00:26:04.120
in every single way.

00:26:04.120 --> 00:26:06.492
A 300 person lecture room
is a complete broadcast,

00:26:06.492 --> 00:26:07.856
completely passive.

00:26:07.856 --> 00:26:10.518
On-demand video you can pause,
repeat, watch at your own time.

00:26:10.518 --> 00:26:13.166
The inertia of the bureaucracy
is continuing to do.

00:26:13.166 --> 00:26:14.736
Even a 20 person classroom,
you have to question,

00:26:14.736 --> 00:26:17.157
but 300 person, I can't,
I've challenged everyone.

00:26:17.157 --> 00:26:18.608
No one can think of why this exists,

00:26:18.608 --> 00:26:20.634
but at every university
you pay $30,000 a year.

00:26:20.634 --> 00:26:21.757
They stick you in these rooms,

00:26:21.757 --> 00:26:22.902
and you get a broadcast lecture.

00:26:22.902 --> 00:26:24.195
Peter: I think we're in the middle of that

00:26:24.195 --> 00:26:27.246
really social change
already. It's happening.

00:26:27.246 --> 00:26:28.893
You prove it.

00:26:28.893 --> 00:26:31.465
Keith: Jumping on the edges,
but it can happen on the edges

00:26:31.465 --> 00:26:34.160
because one guy in a
converted closet can reach

00:26:34.160 --> 00:26:35.817
16 million people.

00:26:35.817 --> 00:26:36.222
Sal: Yeah.

00:26:36.222 --> 00:26:38.174
Keith: I mean the technology
allows small groups

00:26:38.174 --> 00:26:39.743
of people to make big change.

00:26:39.743 --> 00:26:40.985
Martin: The internet
is really the backbone

00:26:40.985 --> 00:26:42.678
of the change because that is what enables

00:26:42.678 --> 00:26:45.709
the instant communication from anywhere

00:26:45.709 --> 00:26:49.124
to anyone at almost no cost.

00:26:49.124 --> 00:26:51.430
We're always looking for
new ways to apply this

00:26:51.430 --> 00:26:53.201
and we're probably at the very beginning

00:26:53.201 --> 00:26:56.651
of figuring out how to really apply it.

00:26:56.651 --> 00:26:58.230
Sal: Yeah.

00:26:58.230 --> 00:27:00.347
Martin: What's your
economic model for this?

00:27:00.347 --> 00:27:02.175
You give the product away for nothing.

00:27:02.175 --> 00:27:06.246
Sal: (laughs) That's a mysterious ...

00:27:06.246 --> 00:27:08.092
I used to work in the hedge fund world.

00:27:08.092 --> 00:27:09.848
I was an analyst and I was doing all

00:27:09.848 --> 00:27:11.588
of this part time starting for my cousins

00:27:11.588 --> 00:27:13.439
really then it started to take off.

00:27:13.439 --> 00:27:15.444
In September, I just
felt, and it's all for a

00:27:15.444 --> 00:27:16.270
not for profit basis.

00:27:16.270 --> 00:27:18.655
Kahn Academy is a 501C3 organization.

00:27:18.655 --> 00:27:21.109
We could talk about why
I decided to do that.

00:27:21.109 --> 00:27:22.769
There was some temptation to go on a ...

00:27:22.769 --> 00:27:24.764
Martin: People can donate without ...

00:27:24.764 --> 00:27:30.548
Sal: Yeah. They can donate, but
then I'm limited doing this.

00:27:30.548 --> 00:27:34.541
It was initially essentially self-funded.

00:27:34.541 --> 00:27:36.797
There was some donations
coming from the viewers

00:27:36.797 --> 00:27:38.259
just spontaneous donations.

00:27:38.259 --> 00:27:39.388
There was a little bit of advertising

00:27:39.388 --> 00:27:41.382
that's going to kahnacademy.org.

00:27:41.382 --> 00:27:44.031
I wasn't taking a salary
until very recently.

00:27:44.031 --> 00:27:45.154
Martin: Unfortunately, I'm
going to have to cut you off

00:27:45.154 --> 00:27:46.294
because I just got the signal that we're

00:27:46.294 --> 00:27:47.435
just about totally out of time.

00:27:47.435 --> 00:27:48.459
Sal: Okay.

00:27:48.459 --> 00:27:49.820
Martin: So we're going
to have to wrap the show.

00:27:49.820 --> 00:27:52.166
I'd like to thank my three
very distinguished guests,

00:27:52.166 --> 00:27:54.863
Peter Friess, Keith Devlin, Salman Kahn.

00:27:54.863 --> 00:27:56.298
Thanks to all of you for being here

00:27:56.298 --> 00:27:58.985
and advancing public knowledge on how

00:27:58.985 --> 00:28:01.652
to improve math training
so we can continue

00:28:01.652 --> 00:28:05.184
to maintain this huge technological
society we've created.

00:28:05.184 --> 00:28:06.500
Thank you for watching.

00:28:06.500 --> 00:28:07.696
Be sure to tune in next time.

00:28:07.696 --> 00:28:10.296
I'm Marty Wasserman. See you next time.

00:28:10.296 --> 00:28:14.296
(lively music)


Introduction to the doppler effect

WEBVTT
Kind: captions
Language: en

00:00:00.530 --> 00:00:02.180
What we're going to do in
this video is think

00:00:02.180 --> 00:00:04.660
about two wave sources.

00:00:04.660 --> 00:00:08.890
But one of them is going to be
stationary and the other one

00:00:08.890 --> 00:00:10.000
is going to be moving.

00:00:10.000 --> 00:00:12.890
And just to have a concrete
number, it's moving at 5

00:00:12.890 --> 00:00:15.570
meters per second
to the right.

00:00:15.570 --> 00:00:18.960
And what we're going to think
about is where are the crests

00:00:18.960 --> 00:00:21.280
of the wave that it's
been releasing for

00:00:21.280 --> 00:00:23.340
the last 3 or 4 seconds?

00:00:23.340 --> 00:00:26.565
So let's say that in both cases,
they are releasing a

00:00:26.565 --> 00:00:30.860
wave. So the velocity of the
wave is going to be 10 meters

00:00:30.860 --> 00:00:31.450
per second.

00:00:31.450 --> 00:00:34.420
You could visualize this, maybe,
as a sound wave, but

00:00:34.420 --> 00:00:37.120
sound and air move much, much,
much, much faster than 10

00:00:37.120 --> 00:00:38.050
meters per second.

00:00:38.050 --> 00:00:39.890
But this'll make the
math work out easy.

00:00:39.890 --> 00:00:42.040
Especially relative to this
guy, who is moving to the

00:00:42.040 --> 00:00:44.220
right at 5 meters per second.

00:00:44.220 --> 00:00:45.760
And that's the whole point, to
give you the intuition and

00:00:45.760 --> 00:00:47.330
make the math really
simple here.

00:00:47.330 --> 00:00:50.400
And both of these guys are going
to be, the wave that

00:00:50.400 --> 00:00:52.040
they're emitting is at
10 meters per second.

00:00:52.040 --> 00:00:54.110
And the period of the wave
is going to be at

00:00:54.110 --> 00:00:57.370
1 second per cycle.

00:00:57.370 --> 00:00:59.940
And if the period is 1 second
per cycle, you take the

00:00:59.940 --> 00:01:04.430
inverse of that-- the frequency
of the source, I

00:01:04.430 --> 00:01:07.570
guess you could call it, of the
wave, as being emitted is

00:01:07.570 --> 00:01:08.710
going to be the inverse
of this.

00:01:08.710 --> 00:01:10.100
The inverse of 1 is just 1.

00:01:10.100 --> 00:01:14.680
But 1 cycle per second.

00:01:14.680 --> 00:01:17.910
If it takes a second for a
cycle, it's also in 1 second,

00:01:17.910 --> 00:01:21.180
you're also going to see 1
cycle, so 1 cycle per second.

00:01:21.180 --> 00:01:23.740
So let's think about what's
happening here.

00:01:23.740 --> 00:01:27.250
So let's think about where--
let's say it emitted a crest

00:01:27.250 --> 00:01:29.810
of it's a wave exactly
1 second ago.

00:01:29.810 --> 00:01:31.570
Where is that crest
going to be now?

00:01:31.570 --> 00:01:33.750
Let's think about the stationary
character.

00:01:33.750 --> 00:01:36.630
Well, this guy emitted
a crest 1 second ago.

00:01:36.630 --> 00:01:37.850
It's moving outward.

00:01:37.850 --> 00:01:38.760
So this is outward.

00:01:38.760 --> 00:01:40.710
It's movie outward radially.

00:01:40.710 --> 00:01:43.660
We need to give a direction if
I'm giving a vector quantity.

00:01:43.660 --> 00:01:45.410
So it's moving outward at
10 meters per second.

00:01:45.410 --> 00:01:48.260
So if it emitted it 1 second
ago, it's going to be 10

00:01:48.260 --> 00:01:50.480
meters radially outward
from the source.

00:01:50.480 --> 00:01:56.380
So maybe that is right
over there.

00:01:56.380 --> 00:01:58.090
Well, let me draw it a little
bit neater like that.

00:02:03.420 --> 00:02:05.880
So that's where that
crest will be.

00:02:05.880 --> 00:02:06.730
Now what about this guy?

00:02:06.730 --> 00:02:10.940
Where's the crest that this
guy emitted 1 second ago?

00:02:10.940 --> 00:02:13.960
You might want to just draw a
radius 10 meters around this

00:02:13.960 --> 00:02:14.460
guy as well.

00:02:14.460 --> 00:02:17.070
But he wasn't here
1 second ago.

00:02:17.070 --> 00:02:18.910
He was 5 meters to the left.

00:02:18.910 --> 00:02:21.390
Remember, he's moving 5 meters
per second to the right.

00:02:21.390 --> 00:02:24.810
1 second ago, he was 5
meters to the left.

00:02:24.810 --> 00:02:28.680
So maybe that places him
right over there.

00:02:28.680 --> 00:02:35.300
So the crest that he emitted 1
second ago isn't going to be

00:02:35.300 --> 00:02:36.150
10 meters from this guy.

00:02:36.150 --> 00:02:37.440
It's going to be 10
meters radially

00:02:37.440 --> 00:02:38.690
outward from that guy.

00:02:48.670 --> 00:02:50.090
So this is where he is now.

00:02:50.090 --> 00:02:54.250
That's where he was 1 second
ago, where he emitted this

00:02:54.250 --> 00:02:56.600
crest that has now traveled
10 meters away.

00:02:56.600 --> 00:02:58.520
This a little inexact,
so I could draw it a

00:02:58.520 --> 00:02:59.510
little bit like that.

00:02:59.510 --> 00:03:00.360
This is 5 meters.

00:03:00.360 --> 00:03:01.700
That's 10 meters away.

00:03:01.700 --> 00:03:03.520
But you get the general idea.

00:03:03.520 --> 00:03:05.350
Now let's keep going.

00:03:05.350 --> 00:03:08.760
Let's think about the crest
that both of these guys

00:03:08.760 --> 00:03:11.130
emitted 2 seconds ago.

00:03:11.130 --> 00:03:13.700
This guy's been stationary
the whole time.

00:03:13.700 --> 00:03:17.430
If he emitted it 2 seconds
ago, it's traveling at 10

00:03:17.430 --> 00:03:18.860
meters per second.

00:03:18.860 --> 00:03:22.580
It's going to be 20 meters
radially outward from the

00:03:22.580 --> 00:03:24.030
center, from the source.

00:03:24.030 --> 00:03:30.750
So it will look something
like that.

00:03:30.750 --> 00:03:32.810
I'm just drawing the
crest of the waves.

00:03:32.810 --> 00:03:35.335
If you think of water, a pebble
being dropped into the

00:03:35.335 --> 00:03:38.010
pond, these are just the high
points on the wave that

00:03:38.010 --> 00:03:41.240
spreads radially outward from
where the pebble was dropped.

00:03:41.240 --> 00:03:43.510
Now this guy, once again, you
can't just draw a circle

00:03:43.510 --> 00:03:46.520
around this because he wasn't
here 2 seconds ago.

00:03:46.520 --> 00:03:48.770
He was right here.

00:03:48.770 --> 00:03:50.650
He was right here
2 seconds ago.

00:03:50.650 --> 00:03:52.870
1 second ago, he was 5
meters to the left.

00:03:52.870 --> 00:03:55.990
A second before that, he was
5 meters more to the left.

00:03:55.990 --> 00:04:00.060
So that wave that he emitted
then is going to be 20 meters

00:04:00.060 --> 00:04:01.965
radially outward from
this point.

00:04:07.980 --> 00:04:10.595
So the center isn't going
to be that or that.

00:04:10.595 --> 00:04:14.055
It's going to be that point
where he was 2 seconds ago.

00:04:19.200 --> 00:04:23.630
So what about the crest that
either of these of sources

00:04:23.630 --> 00:04:26.020
emitted 3 seconds ago?

00:04:26.020 --> 00:04:29.590
Well, it would be 30 meters
radially outward, so another

00:04:29.590 --> 00:04:31.000
10 meters from the last one.

00:04:31.000 --> 00:04:35.110
So it will be out here.

00:04:35.110 --> 00:04:40.920
It will be out there
just like that.

00:04:40.920 --> 00:04:43.840
This guy has been stationary
the whole time.

00:04:43.840 --> 00:04:45.250
But what about this guy?

00:04:45.250 --> 00:04:48.310
He wasn't here 3 seconds ago.

00:04:48.310 --> 00:04:49.980
He was here.

00:04:49.980 --> 00:04:50.160
Right?

00:04:50.160 --> 00:04:51.050
1 second ago, here.

00:04:51.050 --> 00:04:52.060
2 seconds ago, there.

00:04:52.060 --> 00:04:53.350
3 seconds ago, there.

00:04:53.350 --> 00:04:55.000
So we're going to be
30 meters radially

00:04:55.000 --> 00:04:56.320
outward from this point.

00:04:56.320 --> 00:04:59.170
So once again, I can just copy
and paste this right here.

00:05:02.720 --> 00:05:05.355
And it should be centered
around that point.

00:05:08.590 --> 00:05:12.470
Now, let's think a little bit
about what the perceived

00:05:12.470 --> 00:05:15.750
frequency of this wave would be
for a couple of observers.

00:05:15.750 --> 00:05:17.880
So we could put an observer
here, really

00:05:17.880 --> 00:05:19.930
anywhere around this guy.

00:05:19.930 --> 00:05:22.770
We could put an observer
right here.

00:05:22.770 --> 00:05:26.560
And then we could put another
observer right here.

00:05:26.560 --> 00:05:28.550
Now, what's this guy
going to perceive?

00:05:28.550 --> 00:05:32.670
Well, every second he's getting
a pulse-- well,

00:05:32.670 --> 00:05:33.700
there's a couple of things
to think about.

00:05:33.700 --> 00:05:36.240
First of all, what is the
wavelength of, at least this

00:05:36.240 --> 00:05:37.580
wave right here.

00:05:37.580 --> 00:05:40.520
Well, every second, he's
emitting a pulse.

00:05:40.520 --> 00:05:42.460
So, a second ago, the pulses
out there would

00:05:42.460 --> 00:05:43.430
have traveled 10 meters.

00:05:43.430 --> 00:05:45.060
And then he emits
another pulse.

00:05:45.060 --> 00:05:48.400
So the pulses are going to be 1
second apart, but since they

00:05:48.400 --> 00:05:50.720
traveled 10 meters in that 1
second, they are also going to

00:05:50.720 --> 00:05:52.340
be 10 meters apart.

00:05:52.340 --> 00:05:54.740
So the wavelength,
in this case, is

00:05:54.740 --> 00:05:57.000
going to be 10 meters.

00:05:57.000 --> 00:06:01.340
The distance between these
crests are 10 meters.

00:06:01.340 --> 00:06:04.600
Now what about this situation
right here?

00:06:04.600 --> 00:06:07.640
It depends on what side, whether
the source is coming

00:06:07.640 --> 00:06:10.080
towards you or whether it's
going away from you.

00:06:10.080 --> 00:06:11.990
That's the situation
with this guy.

00:06:11.990 --> 00:06:15.450
When it's moving towards you,
it's emitting a pulse-- so

00:06:15.450 --> 00:06:18.550
let's say it emitted a pulse
right here-- and then, it

00:06:18.550 --> 00:06:20.750
moves 5 meters to
the right before

00:06:20.750 --> 00:06:22.290
emitting the next pulse.

00:06:22.290 --> 00:06:25.920
So instead of them being 10
meters apart, in this case,

00:06:25.920 --> 00:06:27.980
this guy has closed
the distance by

00:06:27.980 --> 00:06:29.550
5 meters over here.

00:06:29.550 --> 00:06:33.220
So these pulses are only going
to be 5 meters apart.

00:06:33.220 --> 00:06:36.700
So over here, the wavelength
is only 5 meters.

00:06:36.700 --> 00:06:37.730
You can see it visually.

00:06:37.730 --> 00:06:40.340
This distance right here is
half of this distance.

00:06:40.340 --> 00:06:42.530
These are 5 meters apart.

00:06:42.530 --> 00:06:45.500
And on the left-hand side, if
you're on the side of the

00:06:45.500 --> 00:06:49.480
source that the source is moving
away from, it would be

00:06:49.480 --> 00:06:52.970
10 meters, but every second the
source is also moving 5

00:06:52.970 --> 00:06:54.760
more meters away from you.

00:06:54.760 --> 00:06:58.940
So this perceived wavelength
right here is

00:06:58.940 --> 00:07:01.890
going to be 15 meters.

00:07:01.890 --> 00:07:02.870
And we can see it visually.

00:07:02.870 --> 00:07:05.980
That's the whole reason why
I drew it this way.

00:07:05.980 --> 00:07:07.360
Now what's going to
be the perceived

00:07:07.360 --> 00:07:08.360
frequencies for this?

00:07:08.360 --> 00:07:12.530
Well, this guy has one crest
passing him right now.

00:07:12.530 --> 00:07:15.270
It's going to take exactly 1
second for the next crest to

00:07:15.270 --> 00:07:16.350
get to him because
it's traveling at

00:07:16.350 --> 00:07:17.580
10 meters per second.

00:07:17.580 --> 00:07:24.890
So he is going to perceive 1
crest, or 1 cycle per second,

00:07:24.890 --> 00:07:28.080
or a frequency of 1 hertz,
which makes sense.

00:07:28.080 --> 00:07:28.860
This is stationary.

00:07:28.860 --> 00:07:30.880
They're both stationary relative
to each other.

00:07:30.880 --> 00:07:32.590
And we're also talking about
classical physics.

00:07:32.590 --> 00:07:34.390
We're not getting to relativity
and all that.

00:07:34.390 --> 00:07:37.940
But the observed frequency is
the exact frequency that was

00:07:37.940 --> 00:07:40.840
emitted by this guy
right there.

00:07:40.840 --> 00:07:43.770
Now what about this situation?

00:07:43.770 --> 00:07:47.660
Each of these crests are 5
meters apart for this guy.

00:07:47.660 --> 00:07:50.230
If you imagined that this was
some type of a train coming

00:07:50.230 --> 00:07:53.950
towards this guy, each of these
crests are only 5 meters

00:07:53.950 --> 00:07:57.450
apart, but they're traveling
at 10 meters per second.

00:07:57.450 --> 00:08:01.020
So how many crests are you
going to see in a second?

00:08:01.020 --> 00:08:02.120
Well, you're going to
see two of them.

00:08:02.120 --> 00:08:03.956
This one's going to take 1/2 a
second to return you, and then

00:08:03.956 --> 00:08:06.230
in the next 1/2 a second, this
one's going to get to you.

00:08:06.230 --> 00:08:08.300
Or you could say this one takes
1/2 second to reach you,

00:08:08.300 --> 00:08:10.300
and this is going to take
1 second to reach you.

00:08:10.300 --> 00:08:12.150
So you're going to see two.

00:08:12.150 --> 00:08:13.230
So there's two ways
to think of it.

00:08:13.230 --> 00:08:17.850
You could say your period in
this situation is 1/2 of a

00:08:17.850 --> 00:08:20.500
second per cycle.

00:08:20.500 --> 00:08:22.513
Or you could invert it and you
could say that the frequency--

00:08:22.513 --> 00:08:26.140
I mean we could put the observed
frequency-- is going

00:08:26.140 --> 00:08:30.810
to be 2 cycles per second.

00:08:30.810 --> 00:08:32.840
And already notice, this guy's
experiencing a higher

00:08:32.840 --> 00:08:35.760
frequency then this guy over
here, because these wave

00:08:35.760 --> 00:08:38.520
fronts or these crests are
just passing by him more

00:08:38.520 --> 00:08:41.000
frequently.

00:08:41.000 --> 00:08:43.020
Because this guy is moving in
the same direction as this

00:08:43.020 --> 00:08:44.770
guy, they are closer together.

00:08:44.770 --> 00:08:47.470
Now this guy's going to
experience the opposite thing.

00:08:47.470 --> 00:08:50.450
Let's say that this crest
is just passing him by.

00:08:50.450 --> 00:08:51.890
How long will it take for
the next crest to

00:08:51.890 --> 00:08:53.800
cover that 15 meters?

00:08:53.800 --> 00:08:55.520
Well, they're going at
10 meters per second.

00:08:55.520 --> 00:09:03.730
It's going to be 1.5 seconds per
crest. That's going to be

00:09:03.730 --> 00:09:05.540
the observed period
for this guy.

00:09:05.540 --> 00:09:09.230
You have to take the inverse of
that-- that's 1.5 is 3/2,

00:09:09.230 --> 00:09:14.890
that's 2/3 of a --or you could
say crest or 2/3 of a cycle

00:09:14.890 --> 00:09:17.150
per second.

00:09:17.150 --> 00:09:21.300
So when the source is moving
away from this observer, the

00:09:21.300 --> 00:09:24.270
frequency, or the perceived
frequency, is the lower than

00:09:24.270 --> 00:09:28.520
the frequency of the actual
emitted wave. When the source

00:09:28.520 --> 00:09:30.570
is moving towards the
observer, the

00:09:30.570 --> 00:09:31.840
frequency is higher.

00:09:31.840 --> 00:09:33.810
This might seem some like some
type of bizarre thing but

00:09:33.810 --> 00:09:35.770
you've experienced it before.

00:09:35.770 --> 00:09:38.230
It's called the Doppler
effect, which you've

00:09:38.230 --> 00:09:39.360
probably heard of.

00:09:39.360 --> 00:09:44.420
And that's exactly what you
experience when you sit at,

00:09:44.420 --> 00:09:45.760
maybe, a train crossing.

00:09:45.760 --> 00:09:47.410
Be careful not to
sit too close.

00:09:47.410 --> 00:09:51.990
And as a train is approaching
you, you noticed-- say it has

00:09:51.990 --> 00:09:54.320
its horn going on.

00:09:54.320 --> 00:09:55.990
It'd be very high-pitched.

00:09:55.990 --> 00:09:58.250
And then right when it passes
you, and it starts moving away

00:09:58.250 --> 00:10:00.660
from you, it has a
much lower pitch.

00:10:00.660 --> 00:10:03.680
And that perceived pitch, that's
your brain and your

00:10:03.680 --> 00:10:05.660
ears' way of sensing
frequency.

00:10:05.660 --> 00:10:08.800
So when the train is coming
toward you, it's a high pitch,

00:10:08.800 --> 00:10:09.930
high frequency.

00:10:09.930 --> 00:10:13.080
When it's going away from you,
low pitch, low frequency.

00:10:13.080 --> 00:10:16.310
And hopefully, drawing it out
this way gives you a visual

00:10:16.310 --> 00:10:20.710
understanding of why that is;
why these points on the cycle,

00:10:20.710 --> 00:10:23.290
or these crests, are closer
together when it's moving in

00:10:23.290 --> 00:10:25.660
your direction then when they're
farther apart-- when

00:10:25.660 --> 00:10:27.020
it's moving away from you.

00:10:27.020 --> 00:10:28.750
In the next video, we'll do
these with more abstract

00:10:28.750 --> 00:10:30.670
numbers so we can actually
figure out generalized

00:10:30.670 --> 00:10:34.040
formulas for relating the
observed frequency with the

00:10:34.040 --> 00:10:35.680
emitted frequency.