Euler's line proof

WEBVTT
Kind: captions
Language: en

00:00:00.499 --> 00:00:03.222
What I want to do in this video
is that for some triangle--

00:00:03.222 --> 00:00:04.680
we're going to
focus on this larger

00:00:04.680 --> 00:00:07.700
triangle over
here, triangle ABC.

00:00:07.700 --> 00:00:11.170
What I want to do is prove
that the circumcenter

00:00:11.170 --> 00:00:13.290
of this triangle--
remember, the circumcenter

00:00:13.290 --> 00:00:16.760
is the intersection of its
perpendicular bisectors.

00:00:16.760 --> 00:00:19.620
That the circumcenter
for this triangle,

00:00:19.620 --> 00:00:22.190
the centroid of this
triangle-- the centroid

00:00:22.190 --> 00:00:24.170
is the intersection
of its medians--

00:00:24.170 --> 00:00:26.530
and the orthocenter of
this triangle-- that's

00:00:26.530 --> 00:00:28.840
the intersection
of its altitudes--

00:00:28.840 --> 00:00:31.610
all sit on the same line.

00:00:31.610 --> 00:00:35.060
Or that OI right over here
really is a line segment,

00:00:35.060 --> 00:00:39.670
or that OG and GI are really
just two segments that make up

00:00:39.670 --> 00:00:45.020
this larger line segment, which
is part of the Euler Line.

00:00:45.020 --> 00:00:47.880
And to do that, I've
set up a medial triangle

00:00:47.880 --> 00:00:50.820
right over here, triangle
FED, or actually I

00:00:50.820 --> 00:00:56.680
should say triangle DEF, which
is the medial triangle for ABC.

00:00:56.680 --> 00:00:58.480
And there's already
a bunch of things

00:00:58.480 --> 00:01:00.320
that we know about
medial triangles,

00:01:00.320 --> 00:01:02.480
and we've proven this
in previous videos.

00:01:02.480 --> 00:01:05.260
One thing we know is
that the medial triangle

00:01:05.260 --> 00:01:10.580
DEF is going to be
similar to the larger

00:01:10.580 --> 00:01:14.530
triangle, the triangle it
is a medial triangle of.

00:01:14.530 --> 00:01:17.220
And that ratio from the
larger triangle to the smaller

00:01:17.220 --> 00:01:19.640
triangle is a 2 to
1 ratio, and this

00:01:19.640 --> 00:01:21.810
is going to be really
important to our proof.

00:01:21.810 --> 00:01:24.660
When two triangles are similar
with a given ratio, that

00:01:24.660 --> 00:01:26.950
means that if you take the
distance between any two

00:01:26.950 --> 00:01:29.970
corresponding parts of
the two similar triangles,

00:01:29.970 --> 00:01:33.290
that ratio will be 2 to 1.

00:01:33.290 --> 00:01:35.210
Now, the other relationship
that we've already

00:01:35.210 --> 00:01:38.380
shown-- the other relationship
between a medial triangle,

00:01:38.380 --> 00:01:40.880
and the triangle it is
the medial triangle of--

00:01:40.880 --> 00:01:43.270
is that we've shown
that the orthocenter

00:01:43.270 --> 00:01:50.880
of the medial triangle is the
circumcenter of the larger

00:01:50.880 --> 00:01:52.080
triangle.

00:01:52.080 --> 00:01:54.650
So one way to think
about it-- point O,

00:01:54.650 --> 00:01:57.020
we already mentioned,
is the circumcenter

00:01:57.020 --> 00:01:58.820
of the larger triangle.

00:01:58.820 --> 00:02:05.250
It is also the orthocenter
of the smaller triangle.

00:02:05.250 --> 00:02:06.500
And we actually wrote up here.

00:02:06.500 --> 00:02:10.999
So point O, notice it
is on this perpendicular

00:02:10.999 --> 00:02:11.790
bisector over here.

00:02:11.790 --> 00:02:13.498
And I actually draw
a bunch of other ones

00:02:13.498 --> 00:02:16.310
in this dark gray
color, but I didn't

00:02:16.310 --> 00:02:18.220
want to make this
diagram too messy.

00:02:18.220 --> 00:02:20.910
But this is the circumcenter
of the larger triangle,

00:02:20.910 --> 00:02:24.310
and it is also the
orthocenter of the smaller

00:02:24.310 --> 00:02:26.200
triangle-- of DEF.

00:02:26.200 --> 00:02:27.750
And we actually
used this fact when

00:02:27.750 --> 00:02:31.110
we wanted to prove that
orthocenters are concurrent.

00:02:31.110 --> 00:02:33.410
We started with the
medial triangle.

00:02:33.410 --> 00:02:37.875
We said, OK, let's think about
where the altitudes intersect.

00:02:37.875 --> 00:02:39.780
And we said, well, look,
all of the altitudes

00:02:39.780 --> 00:02:42.664
are actually perpendicular
bisectors for our larger

00:02:42.664 --> 00:02:44.080
triangle if we
assume that this is

00:02:44.080 --> 00:02:46.980
the medial triangle of
that larger triangle.

00:02:46.980 --> 00:02:49.540
So point O, and this is going
to be important to our proof.

00:02:49.540 --> 00:02:52.130
It is a circumcenter
of triangle ABC,

00:02:52.130 --> 00:02:54.940
but it's the orthocenter
of DEF, and we've already

00:02:54.940 --> 00:02:57.460
talked about this
in previous videos.

00:02:57.460 --> 00:03:02.230
Now, in order to prove
that O, G, and I all sit

00:03:02.230 --> 00:03:05.930
on the same line--
or the same segment,

00:03:05.930 --> 00:03:07.910
in this case, what
I'm going to do

00:03:07.910 --> 00:03:21.090
is prove that triangle
FOG is similar is

00:03:21.090 --> 00:03:23.482
similar to triangle CIG.

00:03:28.950 --> 00:03:31.800
Because if I can prove that,
then their corresponding angles

00:03:31.800 --> 00:03:33.060
are going to be equivalent.

00:03:33.060 --> 00:03:34.750
You could say that
this angle is going

00:03:34.750 --> 00:03:37.030
to be equal to this
angle over here.

00:03:37.030 --> 00:03:39.815
And so OI would have to be
a transversal because we're

00:03:39.815 --> 00:03:42.190
going to see that these two
lines over here are parallel.

00:03:42.190 --> 00:03:45.280
Or if they have these two
triangles are similar-- so

00:03:45.280 --> 00:03:47.792
remember, we're looking at
this triangle right over here

00:03:47.792 --> 00:03:49.000
and this triangle over there.

00:03:49.000 --> 00:03:51.030
If they really are
similar, then this angle

00:03:51.030 --> 00:03:53.790
is going to be
equal to that angle,

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so these really would
be vertical angles.

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And so this really
would be a line.

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So let's go to the actual proof.

00:04:01.470 --> 00:04:03.920
So maybe I-- well, I
won't leave those two

00:04:03.920 --> 00:04:05.510
highlighted right there.

00:04:05.510 --> 00:04:08.260
So one thing, and I
hinted at this already.

00:04:08.260 --> 00:04:10.380
We know that this line
right over here-- we

00:04:10.380 --> 00:04:12.240
can call this line XC.

00:04:12.240 --> 00:04:15.280
We know this is
perpendicular to line AB.

00:04:15.280 --> 00:04:16.720
It is an altitude.

00:04:16.720 --> 00:04:20.079
And we also know that
FY right over here

00:04:20.079 --> 00:04:22.115
is perpendicular to AB.

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It is a perpendicular bisector.

00:04:24.850 --> 00:04:28.210
So they both form the same
angle with a transversal.

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You could view AB
as a transversal.

00:04:30.020 --> 00:04:31.550
So they must to be parallel.

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So we know that FY
is parallel to XC.

00:04:39.190 --> 00:04:41.520
Segment FY is
parallel to segment XC

00:04:41.520 --> 00:04:43.990
and we could write it like this.

00:04:43.990 --> 00:04:47.040
This guy is parallel
to that guy there.

00:04:47.040 --> 00:04:49.060
And that's useful
because we know

00:04:49.060 --> 00:04:52.250
that alternate interior
angles of a transversal,

00:04:52.250 --> 00:04:54.330
when a transversal intersects
two parallel lines,

00:04:54.330 --> 00:04:55.065
are congruent.

00:04:58.900 --> 00:05:02.400
So we know that FC is a line.

00:05:02.400 --> 00:05:06.660
It is a median of this larger
triangle, triangle ABC.

00:05:06.660 --> 00:05:09.850
So you have a line intersecting
two parallel lines.

00:05:09.850 --> 00:05:13.010
Alternate interior
angles are congruent.

00:05:13.010 --> 00:05:15.570
So that angle is going to
be congruent to that angle.

00:05:15.570 --> 00:05:26.720
So we could say angle OFG
is congruent to angle ICG.

00:05:30.660 --> 00:05:33.880
Now, the other thing
we know-- and this

00:05:33.880 --> 00:05:41.840
is a property of medians--
is that the centroid

00:05:41.840 --> 00:05:43.850
splits the median
into two segments that

00:05:43.850 --> 00:05:45.096
have a ratio of 2 to 1.

00:05:45.096 --> 00:05:46.970
Or another way to think
about is the centroid

00:05:46.970 --> 00:05:50.970
is 2/3 along the median.

00:05:50.970 --> 00:05:53.870
So we've proven this
in a previous video.

00:05:53.870 --> 00:06:01.590
We know that CG is
equal to 2 times GF.

00:06:01.590 --> 00:06:03.490
And I think you see
where we're going here.

00:06:03.490 --> 00:06:04.410
We have an angle.

00:06:04.410 --> 00:06:07.340
I showed you that the ratio
of this side to this side

00:06:07.340 --> 00:06:08.140
is 2 to 1.

00:06:08.140 --> 00:06:10.890
And that's just the property
of centroids and medians.

00:06:10.890 --> 00:06:14.433
And now, if we can show you
that the ratio of this side, CI

00:06:14.433 --> 00:06:18.300
to FO, is 2 to 1, then we
have two corresponding sides

00:06:18.300 --> 00:06:19.770
where the ratio is 2 to 1.

00:06:19.770 --> 00:06:21.810
And we have the angle
in between is congruent.

00:06:21.810 --> 00:06:24.810
We could use SAS similarity
to show that these two

00:06:24.810 --> 00:06:26.810
triangles are actually similar.

00:06:26.810 --> 00:06:28.620
So let's actually
think about that.

00:06:28.620 --> 00:06:34.840
CI is the distance between
the larger triangle's point C

00:06:34.840 --> 00:06:36.740
and its orthocenter.

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Right?

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I is the orthocenter
of the larger triangle.

00:06:40.510 --> 00:06:42.030
Well, what is FO?

00:06:42.030 --> 00:06:44.250
Well, F is the
corresponding point

00:06:44.250 --> 00:06:47.120
to point C on the
medial triangle,

00:06:47.120 --> 00:06:49.000
and we made sure
that we specified

00:06:49.000 --> 00:06:54.130
the similarity with the right--
F corresponds to point C.

00:06:54.130 --> 00:06:59.350
So FO is the distance between F
on the smaller medial triangle

00:06:59.350 --> 00:07:03.130
and the smaller medial
triangle's orthocenter.

00:07:03.130 --> 00:07:04.670
So this is the
distance between C

00:07:04.670 --> 00:07:07.310
and the orthocenter of
the larger triangle.

00:07:07.310 --> 00:07:09.440
This is the distance between
the corresponding side

00:07:09.440 --> 00:07:13.040
of the medial triangle
and its orthocenter.

00:07:13.040 --> 00:07:15.950
So this is the same
corresponding distance

00:07:15.950 --> 00:07:18.255
on the larger triangle and
on the medial triangle.

00:07:18.255 --> 00:07:21.970
And we already know they're
similar with a ratio of 2 to 1.

00:07:21.970 --> 00:07:24.450
And so, the
corresponding distances

00:07:24.450 --> 00:07:26.720
between any two points
on the two triangles

00:07:26.720 --> 00:07:28.850
are going to have
the same ratio.

00:07:28.850 --> 00:07:32.990
So because of that
similarity, we

00:07:32.990 --> 00:07:39.060
know that CI is going to
be equal to 2 times FO.

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I want to emphasize this.

00:07:40.780 --> 00:07:43.190
C is a corresponding
point to F when

00:07:43.190 --> 00:07:46.340
we look at both of
these similar triangles.

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I is the orthocenter
of the larger triangle.

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O is the orthocenter of
the smaller triangle.

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You're taking a
corresponding point

00:07:52.220 --> 00:07:54.995
to the orthocenter of the larger
triangle, corresponding point

00:07:54.995 --> 00:07:57.370
of the smaller triangle to
the orthocenter of the smaller

00:07:57.370 --> 00:07:58.240
triangle.

00:07:58.240 --> 00:08:00.500
The triangles are similar
in a ratio of 2 to 1.

00:08:00.500 --> 00:08:02.940
So the ratio of this
length to this length

00:08:02.940 --> 00:08:05.080
is going to be 2 to 1.

00:08:05.080 --> 00:08:10.340
So we've shown that the ratio
of this side to this side

00:08:10.340 --> 00:08:11.900
is 2 to 1.

00:08:11.900 --> 00:08:16.010
We've shown that the ratio
of this side to this side

00:08:16.010 --> 00:08:17.670
is also 2 to 1.

00:08:17.670 --> 00:08:24.100
And we've shown that the angle
in between them is congruent.

00:08:24.100 --> 00:08:27.120
So we have proven
by SAS similarity--

00:08:27.120 --> 00:08:30.250
let me scroll down a little bit.

00:08:30.250 --> 00:08:36.030
By SAS similarity-- not
congruency, similarity.

00:08:36.030 --> 00:08:43.500
We've proven that triangle FOG
is similar to triangle CIG.

00:08:43.500 --> 00:08:46.510
And so we know corresponding
angles are congruent.

00:08:46.510 --> 00:08:52.320
We know that angle CIG
corresponds to angle FOG,

00:08:52.320 --> 00:08:54.300
so those are going
to be congruent.

00:08:54.300 --> 00:08:58.830
And we also know
that angle CGI--

00:08:58.830 --> 00:09:00.800
let me do this in a new color.

00:09:00.800 --> 00:09:04.850
Angle CGI corresponds
to angle OGF,

00:09:04.850 --> 00:09:06.541
so they are also
going to be congruent.

00:09:06.541 --> 00:09:08.290
So you can look at
this in different ways.

00:09:08.290 --> 00:09:10.520
If this angle and this
angle are the same,

00:09:10.520 --> 00:09:13.240
you could now view
OI as a true line--

00:09:13.240 --> 00:09:15.541
as a transversal of
these two parallel lines.

00:09:15.541 --> 00:09:17.040
So that lets you
know it's one line.

00:09:17.040 --> 00:09:18.748
Or you could look at
these two over here.

00:09:18.748 --> 00:09:21.200
Say, look, these two
angles are equivalent.

00:09:21.200 --> 00:09:22.790
So these must be
vertical angles.

00:09:22.790 --> 00:09:26.660
And so this must actually
be the same line.

00:09:26.660 --> 00:09:30.085
The angle that is approaching
this median right over

00:09:30.085 --> 00:09:32.000
here is the same angle
that it's leaving.

00:09:32.000 --> 00:09:35.690
So these are definitely
on the same line.

00:09:35.690 --> 00:09:37.930
So it's a very simple
proof, once again,

00:09:37.930 --> 00:09:43.200
for a very profound idea-- that
the orthocenter, the centroid,

00:09:43.200 --> 00:09:46.050
and the median of
any triangle all

00:09:46.050 --> 00:09:50.030
sit on this magical
Euler's Line.


Chronometric revolution

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:03.060
If we want to understand
where we've come from,

00:00:03.060 --> 00:00:06.440
the stories that have led
us to our present condition,

00:00:06.440 --> 00:00:09.600
if we want to
understand our history,

00:00:09.600 --> 00:00:12.150
one of the
prerequisites is to have

00:00:12.150 --> 00:00:14.620
a good sense of chronometry.

00:00:14.620 --> 00:00:16.910
And chronometry,
very fancy word,

00:00:16.910 --> 00:00:20.640
but it really is just the
science of the passage of time.

00:00:20.640 --> 00:00:22.900
Chrono relating to time.

00:00:22.900 --> 00:00:25.710
Metry, time measurement.

00:00:25.710 --> 00:00:28.780
And we take many, many things
for granted these days.

00:00:28.780 --> 00:00:31.500
We assume that we know
what happened the last 50

00:00:31.500 --> 00:00:33.280
years, the last 100 years.

00:00:33.280 --> 00:00:34.860
And now we're
starting to assume we

00:00:34.860 --> 00:00:37.450
know what happened
10,000 years ago,

00:00:37.450 --> 00:00:40.560
or what happened to our planet
100 million years ago or 1

00:00:40.560 --> 00:00:41.640
billion years ago.

00:00:41.640 --> 00:00:45.140
But these are all very,
very, very new phenomena,

00:00:45.140 --> 00:00:49.830
this ability to kind of
shine a light on the past.

00:00:49.830 --> 00:00:52.070
And even the traditional
notions of history,

00:00:52.070 --> 00:00:55.850
the traditional stories
of, what led to what?

00:00:55.850 --> 00:00:59.270
The political nations that
formed, the migrations

00:00:59.270 --> 00:01:01.590
of people, and then
when they happened,

00:01:01.590 --> 00:01:03.270
that traditional
notion of history

00:01:03.270 --> 00:01:05.740
is even fairly
new when you think

00:01:05.740 --> 00:01:08.950
about just the scope of
how long we think humans

00:01:08.950 --> 00:01:11.090
have now been on this planet.

00:01:11.090 --> 00:01:14.540
And that first traditional
notion of history

00:01:14.540 --> 00:01:18.600
you can kind of view as the
first chronometric revolution.

00:01:18.600 --> 00:01:21.110
And that first
chronometric revolution

00:01:21.110 --> 00:01:23.520
that gives us this kind
of traditional notion

00:01:23.520 --> 00:01:28.300
of history really just comes out
of humanity's ability to write.

00:01:28.300 --> 00:01:34.762
So writing gives us our first
chronometric revolution.

00:01:34.762 --> 00:01:36.720
Because this was the
first time, even though we

00:01:36.720 --> 00:01:39.180
think humans or
human like creatures

00:01:39.180 --> 00:01:41.290
have been around for
hundreds of thousands

00:01:41.290 --> 00:01:43.780
of years at this
point, they weren't

00:01:43.780 --> 00:01:48.220
able to keep their stories
in a very exact way.

00:01:48.220 --> 00:01:49.990
They might have had
an oral tradition.

00:01:49.990 --> 00:01:52.400
It might have gone from one
generation to the other.

00:01:52.400 --> 00:01:54.620
But with those oral traditions
things would get lost.

00:01:54.620 --> 00:01:56.870
And the most important
information that would get lost

00:01:56.870 --> 00:01:59.340
is how long ago did
these stories start up?

00:01:59.340 --> 00:02:02.100
And we weren't
able, as a species,

00:02:02.100 --> 00:02:03.980
to really have a
firm understanding

00:02:03.980 --> 00:02:08.570
of when things happened, and
how long ago things happened

00:02:08.570 --> 00:02:13.740
until writing became mainstream,
and until writing was done

00:02:13.740 --> 00:02:15.710
in a way that it
became permanent.

00:02:15.710 --> 00:02:18.530
And our best sense of when
this happened the first time

00:02:18.530 --> 00:02:21.460
was by the Sumerians
with cuneiform.

00:02:21.460 --> 00:02:24.910
And this happened right around
the third millennia BC, so

00:02:24.910 --> 00:02:29.020
around 5,000 years
before the present time.

00:02:29.020 --> 00:02:32.130
And this is what some of that
earliest writing looked like.

00:02:32.130 --> 00:02:35.630
This is actually a letter from,
I believe this is from a king.

00:02:35.630 --> 00:02:39.380
And you can see it's just
highly symbolic carvings.

00:02:39.380 --> 00:02:42.450
This is what we more
traditionally associate

00:02:42.450 --> 00:02:43.950
with cuneiform.

00:02:43.950 --> 00:02:46.520
And it was symbolic-based,
as opposed to now.

00:02:46.520 --> 00:02:49.470
Most of our languages
are based on phonetics.

00:02:49.470 --> 00:02:52.600
So you have fewer symbols that
can represent more meanings.

00:02:52.600 --> 00:02:55.920
But this was a huge
technological revolution.

00:02:55.920 --> 00:02:59.190
I could say, for humanity,
because now with the advent

00:02:59.190 --> 00:03:01.970
of cuneiform you now had
permanent writing that someone

00:03:01.970 --> 00:03:05.640
could look at 1,000 years
later, 2,000 years later.

00:03:05.640 --> 00:03:07.980
And if they can
decipher the cuneiform,

00:03:07.980 --> 00:03:11.000
they can get a written
testimony of what

00:03:11.000 --> 00:03:13.560
was happening at
that time, and they

00:03:13.560 --> 00:03:15.670
didn't have to rely
on an oral tradition,

00:03:15.670 --> 00:03:19.590
or even guess when that oral
story might have started.

00:03:19.590 --> 00:03:22.810
But writing, since it only
happened about 5,000 years

00:03:22.810 --> 00:03:30.815
ago-- so this is 5,000
years before the present,

00:03:30.815 --> 00:03:37.210
or you could say 3,000
years BC, give or take.

00:03:37.210 --> 00:03:38.040
That was a start.

00:03:38.040 --> 00:03:41.220
But this only gave us stories
of about 5,000 years old.

00:03:41.220 --> 00:03:44.700
And even then it was a very
spotty historical record.

00:03:44.700 --> 00:03:46.440
We didn't really get
really deep history,

00:03:46.440 --> 00:03:48.180
depending on where
you are in the world,

00:03:48.180 --> 00:03:50.870
until really the last
few thousand years.

00:03:50.870 --> 00:03:51.740
But it was a start.

00:03:51.740 --> 00:03:54.820
This was the first
chronometric revolution.

00:03:54.820 --> 00:03:57.320
But what you may or may
not realize is that we are,

00:03:57.320 --> 00:03:59.950
frankly, I believe, at
the very early stages

00:03:59.950 --> 00:04:03.120
of another chronometric
revolution that has really

00:04:03.120 --> 00:04:07.700
just begun to accelerate in
the last 50, 60, 70 years.

00:04:07.700 --> 00:04:15.460
And this second
chronometric revolution-- I

00:04:15.460 --> 00:04:17.350
should write
revolution up here too.

00:04:17.350 --> 00:04:18.740
This was a revolution.

00:04:18.740 --> 00:04:21.329
It allowed us to keep
time in a permanent way,

00:04:21.329 --> 00:04:23.940
to understand things, to not
have to talk to the people

00:04:23.940 --> 00:04:25.410
to whom something happened.

00:04:25.410 --> 00:04:28.200
We can see their
written testimony of it.

00:04:28.200 --> 00:04:30.850
But the second revolution
really comes out

00:04:30.850 --> 00:04:32.940
of the advent of a lot
of our understanding

00:04:32.940 --> 00:04:34.610
of modern science.

00:04:34.610 --> 00:04:37.870
So in the late 1800s
you have radioactivity

00:04:37.870 --> 00:04:41.360
gets discovered by
Marie and Pierre Curie.

00:04:41.360 --> 00:04:43.032
So this is 1900 right here.

00:04:43.032 --> 00:04:44.240
So this is relatively recent.

00:04:44.240 --> 00:04:47.430
Remember, we're talking about
a species that has been around

00:04:47.430 --> 00:04:49.650
for several hundreds
of thousands of years,

00:04:49.650 --> 00:04:53.140
and protohumans have been
around for millions of years.

00:04:53.140 --> 00:04:56.980
And now only 5,000 years ago,
at least as far as we know,

00:04:56.980 --> 00:04:58.910
was the first writing.

00:04:58.910 --> 00:05:01.420
And then only a little
over 100 years ago

00:05:01.420 --> 00:05:03.833
was the discovery
of radioactivity.

00:05:07.430 --> 00:05:09.907
And then the ability
to use radioactivity.

00:05:09.907 --> 00:05:11.240
So radioactivity is interesting.

00:05:11.240 --> 00:05:14.710
It's this idea that,
essentially elements, can change

00:05:14.710 --> 00:05:18.770
from one variation to another
of an element over long periods

00:05:18.770 --> 00:05:21.150
of time, so through
radioactivity.

00:05:21.150 --> 00:05:23.950
So they become kind
of this natural clock.

00:05:23.950 --> 00:05:27.610
No one had to go there and
set up a times piece for it.

00:05:27.610 --> 00:05:29.360
That luckily, there
are these things

00:05:29.360 --> 00:05:31.580
that decay at a very
predictable rate.

00:05:31.580 --> 00:05:35.140
So we discover radioactivity
a little over 100 years ago,

00:05:35.140 --> 00:05:37.490
and then over the course
of the 20th century

00:05:37.490 --> 00:05:40.010
we got better and better,
more sophisticated

00:05:40.010 --> 00:05:42.680
at really understanding
radioactivity

00:05:42.680 --> 00:05:45.710
to be able to use it to
measure the times of things.

00:05:45.710 --> 00:05:47.460
And if you fast forward
to the second half

00:05:47.460 --> 00:05:50.680
of the 20th century, so
now say we're at 1950,

00:05:50.680 --> 00:05:53.970
this is where the second
chronometric revolution really

00:05:53.970 --> 00:05:55.230
took hold.

00:05:55.230 --> 00:05:57.020
This is where it
really took hold,

00:05:57.020 --> 00:05:59.420
where we started to
understand carbon-14 dating,

00:05:59.420 --> 00:06:01.690
we started to understand
some of the other techniques

00:06:01.690 --> 00:06:05.160
that we talk about as we start
to date older and older things.

00:06:05.160 --> 00:06:06.560
And I want to be clear.

00:06:06.560 --> 00:06:09.100
The radioactivity, the
understanding of radioactivity,

00:06:09.100 --> 00:06:12.670
was just the beginning of this
second chronometric revolution.

00:06:12.670 --> 00:06:15.270
The second chronometric,
which frankly, we are still

00:06:15.270 --> 00:06:17.530
a part of, isn't
just radioactivity.

00:06:17.530 --> 00:06:19.110
It's also understanding
the expansion

00:06:19.110 --> 00:06:21.870
of the universe, the
constancy, kind of the speed

00:06:21.870 --> 00:06:24.880
limit of light that
now lets us figure out,

00:06:24.880 --> 00:06:27.360
wow, that background
radiation we're getting,

00:06:27.360 --> 00:06:32.310
that must have been traveling
for 13.7 billion years ago.

00:06:32.310 --> 00:06:36.500
So we can now look at
evidence from our environment.

00:06:36.500 --> 00:06:39.520
And our environment is
not just the Earth itself.

00:06:39.520 --> 00:06:42.470
It's radiation
bombarding us from space

00:06:42.470 --> 00:06:45.440
that gives us clues
as to not just

00:06:45.440 --> 00:06:49.990
the age of us, of humanity,
the age of species,

00:06:49.990 --> 00:06:53.360
the age of the plant, but the
age of the universe itself.

00:06:53.360 --> 00:06:55.500
So it isn't just
about radioactivity.

00:06:55.500 --> 00:06:58.670
Radioactivity is a big part of
our chronometric revolution.

00:06:58.670 --> 00:07:01.210
This is what allowed
us for the first time,

00:07:01.210 --> 00:07:04.400
if we have layers on the
Earth, people have known

00:07:04.400 --> 00:07:06.200
for a long time
that if we assume

00:07:06.200 --> 00:07:08.170
that these layers
haven't been jostled,

00:07:08.170 --> 00:07:11.580
that something at a lower
layer, down here, is probably

00:07:11.580 --> 00:07:13.690
going to be older than
at an upper layer.

00:07:13.690 --> 00:07:15.895
Because year after
year you have deposits,

00:07:15.895 --> 00:07:18.280
if it hasn't been
messed up in some way.

00:07:18.280 --> 00:07:19.020
But no one knew.

00:07:19.020 --> 00:07:21.290
They said, OK, well,
this is relative dating.

00:07:21.290 --> 00:07:23.210
This is older.

00:07:23.210 --> 00:07:24.630
This is a younger.

00:07:24.630 --> 00:07:26.850
But we had no way of
knowing that, hey,

00:07:26.850 --> 00:07:27.880
is this 1,000 years old?

00:07:27.880 --> 00:07:29.171
Or is this 1 million years old?

00:07:29.171 --> 00:07:30.590
Or is this 1 billion years old?

00:07:30.590 --> 00:07:33.740
But now with radioactivity
we could start to say,

00:07:33.740 --> 00:07:35.790
hey, we can date some
of the rocks here

00:07:35.790 --> 00:07:38.070
that are 150 million years old.

00:07:38.070 --> 00:07:40.990
And some of the rocks here are
about 100 million years old.

00:07:40.990 --> 00:07:43.620
So maybe this fossil of a
fish that we're finding,

00:07:43.620 --> 00:07:46.560
or this primitive fish-like
creature right over here, this

00:07:46.560 --> 00:07:50.537
would be between 100 and
150 million years old.

00:07:50.537 --> 00:07:52.120
And the only way
we're able to do this

00:07:52.120 --> 00:07:57.070
was with being able to date
things using radioactivity.

00:07:57.070 --> 00:07:58.570
But radioactivity
is just the start.

00:07:58.570 --> 00:08:00.540
As I mentioned, we're getting
better and better understanding

00:08:00.540 --> 00:08:01.600
of cosmology.

00:08:01.600 --> 00:08:03.000
We're getting
better measurements

00:08:03.000 --> 00:08:04.220
of the universe itself.

00:08:04.220 --> 00:08:07.460
We're understanding
physics at a deeper level.

00:08:07.460 --> 00:08:09.500
Now we can start to
look at the genome,

00:08:09.500 --> 00:08:12.730
and think about how the genome
diverges from one species

00:08:12.730 --> 00:08:15.054
to another, and how
quickly it changes.

00:08:15.054 --> 00:08:16.720
So all of these things
are just allowing

00:08:16.720 --> 00:08:20.340
us to get better and better
refinements on the chronology.

00:08:20.340 --> 00:08:22.280
Obviously this is a
start, but you still

00:08:22.280 --> 00:08:25.020
don't know plus or minus 50
million years how old this is

00:08:25.020 --> 00:08:27.870
and how this relates to other
things that we might find.

00:08:27.870 --> 00:08:29.670
So I just wanted
to point this out,

00:08:29.670 --> 00:08:31.660
that what we take
for granted now,

00:08:31.660 --> 00:08:34.489
the age of the universe,
the age of Earth at 4

00:08:34.489 --> 00:08:36.110
and 1/2 billion
years old, humans

00:08:36.110 --> 00:08:38.600
being around for several
hundreds of thousands of years,

00:08:38.600 --> 00:08:42.159
this understanding is a very,
very, very new phenomenon.

00:08:42.159 --> 00:08:45.250
It's due to the second
chronometric revolution

00:08:45.250 --> 00:08:47.510
that I think we are
still a part of.

00:08:47.510 --> 00:08:49.650
And even the first
chronometric revolution,

00:08:49.650 --> 00:08:52.640
this version of history--
and I want to be clear.

00:08:52.640 --> 00:08:55.870
History was limited by this
first chronometric revolution.

00:08:55.870 --> 00:08:58.280
It was limited by
whatever was documented.

00:08:58.280 --> 00:09:01.507
But now maybe we can expand
our notion of history.

00:09:01.507 --> 00:09:03.340
And a lot of the videos
I've been working on

00:09:03.340 --> 00:09:08.470
have been for this big history
project, which says, hey,

00:09:08.470 --> 00:09:10.960
before history was limited
by the first chronometric

00:09:10.960 --> 00:09:14.100
revolution, to what was written,
by what was testified by people

00:09:14.100 --> 00:09:16.150
and was made
permanent in some way,

00:09:16.150 --> 00:09:20.120
now chronometry has taken us,
so that we can understand things

00:09:20.120 --> 00:09:24.210
into our deep past, before
even the Earth has existed.

00:09:24.210 --> 00:09:26.820
So why not redefine
history in a big way

00:09:26.820 --> 00:09:31.430
for it to encompass everything,
for it to be big history.

00:09:31.430 --> 00:09:32.800
Anyway, I'll leave you there.

00:09:32.800 --> 00:09:35.170
And actually I want
to also emphasize

00:09:35.170 --> 00:09:37.970
that the second chronometric
revolutions is a big deal.

00:09:37.970 --> 00:09:41.370
It allows us to transform even
our understandings of history.

00:09:41.370 --> 00:09:44.100
But even this first
chronometric revolution right

00:09:44.100 --> 00:09:47.100
over here, 5,000
years is still not

00:09:47.100 --> 00:09:52.434
very long in the entire scope
of even human civilization.


K-Ar dating calculation

WEBVTT
Kind: captions
Language: en

00:00:00.540 --> 00:00:02.590
In the last video, we
give a bit of an overview

00:00:02.590 --> 00:00:04.769
of potassium-argon dating.

00:00:04.769 --> 00:00:07.060
In this video, I want to go
through a concrete example.

00:00:07.060 --> 00:00:08.434
And it'll get a
little bit mathy,

00:00:08.434 --> 00:00:10.220
usually involving a
little bit of algebra

00:00:10.220 --> 00:00:12.210
or a little bit of
exponential decay,

00:00:12.210 --> 00:00:14.710
but to really show you how
you can actually figure out

00:00:14.710 --> 00:00:17.950
the age of some volcanic
rock using this technique,

00:00:17.950 --> 00:00:20.440
using a little bit
of mathematics.

00:00:20.440 --> 00:00:24.330
So we know that anything that is
experiencing radioactive decay,

00:00:24.330 --> 00:00:26.600
it's experiencing
exponential decay.

00:00:26.600 --> 00:00:28.452
And we know that there's
a generalized way

00:00:28.452 --> 00:00:29.160
to describe that.

00:00:29.160 --> 00:00:30.590
And we go into
more depth and kind

00:00:30.590 --> 00:00:33.470
of prove it in other
Khan Academy videos.

00:00:33.470 --> 00:00:36.940
But we know that the amount
as a function of time--

00:00:36.940 --> 00:00:40.390
so if we say N is the amount
of a radioactive sample we have

00:00:40.390 --> 00:00:44.191
at some time-- we know that's
equal to the initial amount we

00:00:44.191 --> 00:00:44.690
have.

00:00:44.690 --> 00:00:49.830
We'll call that N sub 0, times
e to the negative kt-- where

00:00:49.830 --> 00:00:54.570
this constant is particular
to that thing's half-life.

00:00:54.570 --> 00:00:58.170
In order to do this for the
example of potassium-40,

00:00:58.170 --> 00:01:02.670
we know that when time
is 1.25 billion years,

00:01:02.670 --> 00:01:05.680
that the amount we have left
is half of our initial amount.

00:01:05.680 --> 00:01:06.940
So let's write it that way.

00:01:06.940 --> 00:01:11.756
So let's say we start with
N0, whatever that might be.

00:01:11.756 --> 00:01:13.930
It might be 1 gram,
kilogram, 5 grams-- whatever

00:01:13.930 --> 00:01:16.220
it might be-- whatever
we start with,

00:01:16.220 --> 00:01:20.890
we take e to the negative
k times 1.25 billion years.

00:01:20.890 --> 00:01:23.730
That's the half-life
of potassium-40.

00:01:23.730 --> 00:01:25.300
So 1.25 billion years.

00:01:25.300 --> 00:01:27.900
We know, after that long,
that half of the sample

00:01:27.900 --> 00:01:29.010
will be left.

00:01:29.010 --> 00:01:32.399
So we will have 1/2 N0 left.

00:01:32.399 --> 00:01:33.940
Whatever we started
with, we're going

00:01:33.940 --> 00:01:37.210
to have half left after
1.25 billion years.

00:01:37.210 --> 00:01:38.710
Divide both sides by N0.

00:01:41.450 --> 00:01:43.650
And then to solve
for k, we can take

00:01:43.650 --> 00:01:45.720
the natural log of both sides.

00:01:45.720 --> 00:01:48.349
So you get the
natural log of 1/2--

00:01:48.349 --> 00:01:49.890
we don't have that
N0 there anymore--

00:01:49.890 --> 00:01:52.200
is equal to the natural
log of this thing.

00:01:52.200 --> 00:01:54.340
The natural log is
just saying-- to what

00:01:54.340 --> 00:01:57.250
power do I have to
raise e to get e

00:01:57.250 --> 00:01:59.900
to the negative k
times 1.25 billion?

00:01:59.900 --> 00:02:02.600
So the natural log of this--
the power they'd have to raise e

00:02:02.600 --> 00:02:06.870
to to get to e to the negative
k times 1.25 billion--

00:02:06.870 --> 00:02:09.229
is just negative k
times 1.25 billion.

00:02:09.229 --> 00:02:14.520
Or I could write it as negative
1.25-- let me write times-- 10

00:02:14.520 --> 00:02:18.380
to the ninth k.

00:02:18.380 --> 00:02:20.620
That's the same thing
as 1.25 billion.

00:02:20.620 --> 00:02:23.220
We have our negative
sign, and we have our k.

00:02:23.220 --> 00:02:26.660
And then, to solve for k,
we can divide both sides

00:02:26.660 --> 00:02:29.480
by negative 1.25 billion.

00:02:29.480 --> 00:02:30.780
And so we get k.

00:02:30.780 --> 00:02:32.330
And I'll just flip
the sides here.

00:02:32.330 --> 00:02:39.250
k is equal to the natural log
of 1/2 times negative 1.25 times

00:02:39.250 --> 00:02:40.294
10 to the ninth power.

00:02:40.294 --> 00:02:41.835
And what we can do
is we can multiply

00:02:41.835 --> 00:02:43.150
the negative times the top.

00:02:43.150 --> 00:02:44.640
Or you could view
it as multiplying

00:02:44.640 --> 00:02:46.840
the numerator and the
denominator by a negative

00:02:46.840 --> 00:02:48.710
so that a negative
shows up at the top.

00:02:48.710 --> 00:02:52.760
And so we could make this
as over 1.25 times 10

00:02:52.760 --> 00:02:53.420
to the ninth.

00:02:53.420 --> 00:02:55.940
It's just 1.25 billion.

00:02:55.940 --> 00:02:59.544
Let me write it over here
in a different color.

00:02:59.544 --> 00:03:02.210
The negative natural log-- well,
I could just write it this way.

00:03:02.210 --> 00:03:06.274
If I have a natural log of
b-- we know from our logarithm

00:03:06.274 --> 00:03:07.690
properties, this
is the same thing

00:03:07.690 --> 00:03:10.860
as the natural log
of b to the a power.

00:03:10.860 --> 00:03:13.310
So the negative
natural log of 1/2

00:03:13.310 --> 00:03:16.230
is the same thing as
the natural log of 1/2

00:03:16.230 --> 00:03:17.990
to the negative 1 power.

00:03:17.990 --> 00:03:19.507
And so this is the same thing.

00:03:19.507 --> 00:03:21.090
Anything to the
negative power is just

00:03:21.090 --> 00:03:23.170
its multiplicative inverse.

00:03:23.170 --> 00:03:25.670
So this is just the
natural log of 2.

00:03:25.670 --> 00:03:27.580
So negative natural
log of 1 half

00:03:27.580 --> 00:03:30.080
is just the natural
log of 2 over here.

00:03:30.080 --> 00:03:33.180
So we were able to
figure out our k.

00:03:33.180 --> 00:03:34.870
It's essentially
the natural log of 2

00:03:34.870 --> 00:03:36.670
over the half-life
of the substance.

00:03:36.670 --> 00:03:38.170
So we could actually
generalize this

00:03:38.170 --> 00:03:41.020
if we were talking about some
other radioactive substance.

00:03:41.020 --> 00:03:43.380
And now let's think
about a situation--

00:03:43.380 --> 00:03:46.590
now that we've figured out a k--
let's think about a situation

00:03:46.590 --> 00:03:50.290
where we find in some
sample-- so let's say

00:03:50.290 --> 00:03:54.350
the potassium that we
find is 1 milligram.

00:03:54.350 --> 00:03:56.690
I'm just going to
make up these numbers.

00:03:56.690 --> 00:03:57.753
And usually, these
aren't measured directly,

00:03:57.753 --> 00:03:59.700
and you really care about
the relative amounts.

00:03:59.700 --> 00:04:00.730
But let's say you were
able to figure out

00:04:00.730 --> 00:04:02.117
the potassium is 1 milligram.

00:04:02.117 --> 00:04:03.950
And let's say that the
argon-- actually, I'm

00:04:03.950 --> 00:04:05.510
going to say the
potassium-40 found,

00:04:05.510 --> 00:04:08.490
and let's say the
argon-40 found--

00:04:08.490 --> 00:04:15.660
let's say it is 0.01 milligram.

00:04:15.660 --> 00:04:18.700
So how can we use this
information-- in what we just

00:04:18.700 --> 00:04:21.040
figured out here, which is
derived from the half-life--

00:04:21.040 --> 00:04:25.400
to figure out how old this
sample right over here?

00:04:25.400 --> 00:04:28.600
How do we figure out
how old this sample

00:04:28.600 --> 00:04:30.230
is right over there?

00:04:30.230 --> 00:04:32.200
Well, what we need
to figure out--

00:04:32.200 --> 00:04:36.000
we know that n, the
amount we were left with,

00:04:36.000 --> 00:04:38.010
is this thing right over here.

00:04:38.010 --> 00:04:40.155
So we know that we're
left with 1 milligram.

00:04:43.820 --> 00:04:48.020
And that's going to be equal
to some initial amount--

00:04:48.020 --> 00:04:49.590
when we use both
of this information

00:04:49.590 --> 00:04:52.760
to figure that initial
amount out-- times e

00:04:52.760 --> 00:04:56.630
to the negative kt.

00:04:56.630 --> 00:04:57.770
And we know what k is.

00:04:57.770 --> 00:04:59.020
And we'll figure it out later.

00:04:59.020 --> 00:05:01.324
So k is this thing
right over here.

00:05:01.324 --> 00:05:03.490
So we need to figure out
what our initial amount is.

00:05:03.490 --> 00:05:05.520
We know what k is, and
then we can solve for t.

00:05:05.520 --> 00:05:08.339
How old is this sample?

00:05:08.339 --> 00:05:09.880
And to figure out
our initial amount,

00:05:09.880 --> 00:05:16.490
we just have to remember that
for every argon-40 we see,

00:05:16.490 --> 00:05:23.320
that must have decayed from--
when you have potassium-40,

00:05:23.320 --> 00:05:28.730
when it decays, 11% decays into
argon-40 and the rest-- 89%--

00:05:28.730 --> 00:05:30.050
decays into calcium-40.

00:05:30.050 --> 00:05:31.600
We saw that in the last video.

00:05:31.600 --> 00:05:35.774
So however much argon-40, that
is 11% of the decay product.

00:05:35.774 --> 00:05:37.690
So if you want to think
about the total number

00:05:37.690 --> 00:05:41.500
of potassium-40s
that have decayed

00:05:41.500 --> 00:05:44.265
since this was kind
of stuck in the lava.

00:05:44.265 --> 00:05:46.390
And we learned that anything
that was there before,

00:05:46.390 --> 00:05:48.340
any argon-40 that
was there before

00:05:48.340 --> 00:05:50.620
would have been able to
get out of the liquid lava

00:05:50.620 --> 00:05:53.240
before it froze or
before it hardened.

00:05:53.240 --> 00:05:56.520
So to figure out how
much potassium-40 this

00:05:56.520 --> 00:06:00.930
is derived from, we
just divide it by 11%.

00:06:00.930 --> 00:06:07.910
So maybe I could say k initial--
the potassium-40 initial-- is

00:06:07.910 --> 00:06:10.990
going to be equal to the amount
of potassium 40 we have today--

00:06:10.990 --> 00:06:14.650
1 milligram-- plus the
amount of potassium-40

00:06:14.650 --> 00:06:18.280
we needed to get this
amount of argon-40.

00:06:18.280 --> 00:06:22.520
We have this amount of
argon-40-- 0.01 milligrams.

00:06:22.520 --> 00:06:26.890
And that number of milligrams
there, it's really just 11%

00:06:26.890 --> 00:06:30.440
of the original potassium-40
that it had to come from.

00:06:30.440 --> 00:06:33.090
The rest of it turned
into calcium-40.

00:06:33.090 --> 00:06:36.460
So we divide it by 11% or 0.11.

00:06:36.460 --> 00:06:40.531
And this isn't the exact number,
but it'll get the general idea.

00:06:40.531 --> 00:06:42.030
And so our initial--
which is really

00:06:42.030 --> 00:06:43.154
this thing right over here.

00:06:43.154 --> 00:06:46.220
I could call this N0.

00:06:46.220 --> 00:06:48.269
This is going to
be equal to-- and I

00:06:48.269 --> 00:06:49.810
won't do any of the
math-- so we have

00:06:49.810 --> 00:06:55.180
1 milligram we have left is
equal to 1 milligram-- which

00:06:55.180 --> 00:07:04.160
is what we found-- plus
0.01 milligram over 0.11.

00:07:04.160 --> 00:07:10.170
And then, all of that
times e to the negative kt.

00:07:10.170 --> 00:07:11.950
And what you see
here is, when we

00:07:11.950 --> 00:07:13.875
want to solve for t--
assuming we know k,

00:07:13.875 --> 00:07:17.770
and we do know k now-- that
really, the absolute amount

00:07:17.770 --> 00:07:18.490
doesn't matter.

00:07:18.490 --> 00:07:20.390
What actually
matters is the ratio.

00:07:20.390 --> 00:07:22.200
Because if we're
solving for t, you

00:07:22.200 --> 00:07:24.050
want to divide both
sides of this equation

00:07:24.050 --> 00:07:25.950
by this quantity
right over here.

00:07:25.950 --> 00:07:28.280
So you get this side--
the left-hand side--

00:07:28.280 --> 00:07:29.030
divide both sides.

00:07:29.030 --> 00:07:32.150
You get 1 milligram over
this quantity-- I'll write it

00:07:32.150 --> 00:07:33.940
in blue-- over this
quantity is going

00:07:33.940 --> 00:07:36.550
to be 1 plus-- I'm just
going to assume, actually,

00:07:36.550 --> 00:07:38.760
that the units here
are milligrams.

00:07:38.760 --> 00:07:41.760
So you get 1 over
this quantity, which

00:07:41.760 --> 00:07:48.530
is 1 plus 0.01 over the 11%.

00:07:48.530 --> 00:07:52.460
That is equal to e
to the negative kt.

00:07:52.460 --> 00:07:54.360
And then, if you
want to solve for t,

00:07:54.360 --> 00:07:58.550
you want to take the
natural log of both sides.

00:07:58.550 --> 00:08:00.762
This is equal right over here.

00:08:00.762 --> 00:08:02.720
You want to take the
natural log of both sides.

00:08:02.720 --> 00:08:05.260
So you get the natural
log of 1 over 1

00:08:05.260 --> 00:08:14.232
plus 0.01 over 0.11 or 11%
is equal to negative kt.

00:08:14.232 --> 00:08:16.190
And then, to solve for
t, you divide both sides

00:08:16.190 --> 00:08:17.210
by negative k.

00:08:17.210 --> 00:08:18.370
So I'll write it over here.

00:08:18.370 --> 00:08:20.911
And you can see, this a little
bit cumbersome mathematically,

00:08:20.911 --> 00:08:22.260
but we're getting to the answer.

00:08:22.260 --> 00:08:31.330
So we got the natural log of
1 over 1 plus 0.01 over 0.11

00:08:31.330 --> 00:08:33.450
over negative k.

00:08:33.450 --> 00:08:34.897
Well, what is negative k?

00:08:34.897 --> 00:08:37.480
We're just dividing both sides
of this equation by negative k.

00:08:37.480 --> 00:08:39.039
Negative k is the
negative of this

00:08:39.039 --> 00:08:45.540
over the negative natural
log of 2 over 1.25 times

00:08:45.540 --> 00:08:46.302
10 to the ninth.

00:08:46.302 --> 00:08:48.260
And now, we can get our
calculator out and just

00:08:48.260 --> 00:08:49.927
solve for what this time is.

00:08:49.927 --> 00:08:51.760
And it's going to be
in years because that's

00:08:51.760 --> 00:08:53.640
how we figured
out this constant.

00:08:53.640 --> 00:08:55.860
So let's get my handy TI-85.

00:08:59.409 --> 00:09:00.450
First, I'll do this part.

00:09:00.450 --> 00:09:09.820
So this is 1 divided by 1
plus 0.01 divided by 0.11.

00:09:09.820 --> 00:09:12.160
So that's this part
right over here.

00:09:12.160 --> 00:09:15.040
That gives us that number.

00:09:15.040 --> 00:09:17.990
And then, we want to take
the natural log of that.

00:09:17.990 --> 00:09:21.400
So let's take the natural
log of our previous answer.

00:09:21.400 --> 00:09:24.245
So it's the natural
log of 0.9166667.

00:09:24.245 --> 00:09:27.960
It gives us negative 0.087.

00:09:27.960 --> 00:09:30.160
So that's this
numerator over here.

00:09:30.160 --> 00:09:31.510
And we're going to divide that.

00:09:31.510 --> 00:09:33.880
So this number is our
numerator right over here.

00:09:33.880 --> 00:09:38.040
We're going to divide
that by the negative--

00:09:38.040 --> 00:09:45.240
I'll use parentheses carefully--
the negative natural log of 2--

00:09:45.240 --> 00:09:55.360
that's that there-- divided
by 1.25 times 10 to the ninth.

00:09:55.360 --> 00:09:58.440
So it's negative natural
log of 2 divided by 1.25.

00:09:58.440 --> 00:10:00.650
E9 means times 10 to the ninth.

00:10:00.650 --> 00:10:02.930
And I closed both parentheses.

00:10:02.930 --> 00:10:04.590
And now, we need our drum roll.

00:10:04.590 --> 00:10:08.750
So this should give
us our t in years.

00:10:08.750 --> 00:10:11.310
Let's see how many--
this is thousands,

00:10:11.310 --> 00:10:16.830
so it's 3,000-- so we
get 156 million or 156.9

00:10:16.830 --> 00:10:19.130
million years if we round.

00:10:19.130 --> 00:10:26.839
So this is approximately a
157-million-year-old sample.

00:10:26.839 --> 00:10:29.380
So the whole point of this-- I
know the math was a little bit

00:10:29.380 --> 00:10:30.930
involved, but it's something
that you would actually

00:10:30.930 --> 00:10:33.510
see in a pre-calculus
class or an algebra 2 class

00:10:33.510 --> 00:10:36.146
when you're studying
exponential growth and decay.

00:10:36.146 --> 00:10:37.770
But the whole point
I wanted to do this

00:10:37.770 --> 00:10:40.130
is to show you that it's
not some crazy voodoo here.

00:10:40.130 --> 00:10:42.760
And, you know, Sal, gave this
very high-level explanation,

00:10:42.760 --> 00:10:44.176
and then, you say,
oh, well, there

00:10:44.176 --> 00:10:46.430
must be some super difficult
mathematics after that.

00:10:46.430 --> 00:10:47.888
The mathematics
really is something

00:10:47.888 --> 00:10:50.280
that you would see
in high school.

00:10:50.280 --> 00:10:53.740
If you saw a sample that
had this ratio of argon-40

00:10:53.740 --> 00:10:55.500
to potassium-40,
you would actually

00:10:55.500 --> 00:10:58.512
be able to do that high
school mathematics.

00:10:58.512 --> 00:11:00.595
You would be able to do
that to figure out this is

00:11:00.595 --> 00:11:06.610
a 157-million-year-old
sample of volcanic rock.


Potassium-argon (K-Ar) dating

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:02.440
We know that an
element is defined

00:00:02.440 --> 00:00:04.350
by the number of protons it has.

00:00:04.350 --> 00:00:05.401
For example, potassium.

00:00:05.401 --> 00:00:07.150
We look at the periodic
table of elements.

00:00:07.150 --> 00:00:09.700
And I have a snapshot of
it, of not the entire table

00:00:09.700 --> 00:00:10.720
but part of it here.

00:00:10.720 --> 00:00:12.920
Potassium has 19 protons.

00:00:12.920 --> 00:00:14.360
And we could write it like this.

00:00:14.360 --> 00:00:15.818
And this is a little
bit redundant.

00:00:15.818 --> 00:00:18.280
We know that if it's potassium
that atom has 19 protons.

00:00:18.280 --> 00:00:20.720
And we know if an
atom has 19 protons

00:00:20.720 --> 00:00:23.260
it is going to be potassium.

00:00:23.260 --> 00:00:28.920
Now, we also know that not all
of the atoms of a given element

00:00:28.920 --> 00:00:31.260
have the same
number of neutrons.

00:00:31.260 --> 00:00:33.340
And when we talk
about a given element,

00:00:33.340 --> 00:00:35.070
but we have different
numbers of neutrons

00:00:35.070 --> 00:00:37.640
we call them isotopes
of that element.

00:00:37.640 --> 00:00:40.930
So for example,
potassium can come

00:00:40.930 --> 00:00:43.980
in a form that has
exactly 20 neutrons.

00:00:43.980 --> 00:00:45.230
And we call that potassium-39.

00:00:48.190 --> 00:00:50.760
And 39, this mass
number, it's a count

00:00:50.760 --> 00:00:56.710
of the 19 protons
plus 20 neutrons.

00:00:56.710 --> 00:00:59.780
And this is actually the most
common isotope of potassium.

00:00:59.780 --> 00:01:03.360
It accounts for, I'm
just rounding off,

00:01:03.360 --> 00:01:08.760
93.3% of the potassium that
you would find on Earth.

00:01:08.760 --> 00:01:12.040
Now, some of the other
isotopes of potassium.

00:01:12.040 --> 00:01:14.240
You also have potassium--
and once again writing

00:01:14.240 --> 00:01:16.490
the K and the 19 are a
little bit redundant--

00:01:16.490 --> 00:01:18.530
you also have potassium-41.

00:01:18.530 --> 00:01:20.460
So this would have 22 neutrons.

00:01:20.460 --> 00:01:22.580
22 plus 19 is 41.

00:01:22.580 --> 00:01:28.180
This accounts for about 6.7%
of the potassium on the planet.

00:01:28.180 --> 00:01:30.550
And then you have a
very scarce isotope

00:01:30.550 --> 00:01:33.890
of potassium called
potassium-40.

00:01:33.890 --> 00:01:38.030
Potassium-40 clearly
has 21 neutrons.

00:01:38.030 --> 00:01:40.380
And it's very, very,
very, very scarce.

00:01:40.380 --> 00:01:46.010
It accounts for only 0.0117%
of all the potassium.

00:01:46.010 --> 00:01:48.590
But this is also the
isotope of potassium

00:01:48.590 --> 00:01:51.350
that's interesting to us
from the point of view

00:01:51.350 --> 00:01:56.490
of dating old, old rock, and
especially old volcanic rock.

00:01:56.490 --> 00:01:59.680
And as we'll see, when you
can date old volcanic rock

00:01:59.680 --> 00:02:01.530
it allows you to date
other types of rock

00:02:01.530 --> 00:02:03.810
or other types of fossils
that might be sandwiched

00:02:03.810 --> 00:02:06.900
in between old volcanic rock.

00:02:06.900 --> 00:02:10.570
And so what's really interesting
about potassium-40 here

00:02:10.570 --> 00:02:15.192
is that it has a half-life
of 1.25 billion years.

00:02:15.192 --> 00:02:17.400
So the good thing about
that, as opposed to something

00:02:17.400 --> 00:02:19.950
like carbon-14, it can
be used to date really,

00:02:19.950 --> 00:02:21.520
really, really old things.

00:02:21.520 --> 00:02:27.160
And every 1.25
billion years-- let

00:02:27.160 --> 00:02:32.660
me write it like this,
that's its half-life--

00:02:32.660 --> 00:02:36.460
so 50% of any given
sample will have decayed.

00:02:36.460 --> 00:02:40.785
And 11% will have
decayed into argon-40.

00:02:45.880 --> 00:02:47.530
So argon is right over here.

00:02:47.530 --> 00:02:49.690
It has 18 protons.

00:02:49.690 --> 00:02:51.960
So when you think about
it decaying into argon-40,

00:02:51.960 --> 00:02:54.050
what you see is that
it lost a proton,

00:02:54.050 --> 00:02:56.060
but it has the same mass number.

00:02:56.060 --> 00:02:59.640
So one of the protons must of
somehow turned into a neutron.

00:02:59.640 --> 00:03:02.240
And it actually captures
one of the inner electrons,

00:03:02.240 --> 00:03:03.827
and then it emits
other things, and I

00:03:03.827 --> 00:03:05.660
won't go into all the
quantum physics of it,

00:03:05.660 --> 00:03:07.380
but it turns into argon-40.

00:03:07.380 --> 00:03:12.686
And 89% turn into calcium-40.

00:03:12.686 --> 00:03:15.060
And you see calcium on the
periodic table right over here

00:03:15.060 --> 00:03:16.480
has 20 protons.

00:03:16.480 --> 00:03:18.760
So this is a situation
where one of the neutrons

00:03:18.760 --> 00:03:20.287
turns into a proton.

00:03:20.287 --> 00:03:22.120
This is a situation
where one of the protons

00:03:22.120 --> 00:03:23.710
turns into a neutron.

00:03:23.710 --> 00:03:25.640
And what's really
interesting to us

00:03:25.640 --> 00:03:29.520
is this part right over here.

00:03:29.520 --> 00:03:32.170
Because what's cool about argon,
and we study this a little bit

00:03:32.170 --> 00:03:36.150
in the chemistry playlist, it is
a noble gas, it is unreactive.

00:03:36.150 --> 00:03:39.230
And so when it is embedded
in something that's

00:03:39.230 --> 00:03:42.310
in a liquid state it'll
kind of just bubble out.

00:03:42.310 --> 00:03:46.160
It's not bonded to
anything, and so it'll just

00:03:46.160 --> 00:03:48.950
bubble out and just go
out into the atmosphere.

00:03:48.950 --> 00:03:50.990
So what's interesting
about this whole situation

00:03:50.990 --> 00:03:54.950
is you can imagine what happens
during a volcanic eruption.

00:03:54.950 --> 00:03:57.410
Let me draw a volcano here.

00:03:57.410 --> 00:04:00.670
So let's say that
this is our volcano.

00:04:00.670 --> 00:04:04.160
And it erupts at some
time in the past.

00:04:04.160 --> 00:04:08.795
So it erupts, and you have
all of this lava flowing.

00:04:12.730 --> 00:04:16.070
That lava will contain some
amount of potassium-40.

00:04:16.070 --> 00:04:17.779
And actually, it'll
already contain

00:04:17.779 --> 00:04:18.805
some amount of argon-40.

00:04:22.570 --> 00:04:24.410
But what's neat
about argon-40 is

00:04:24.410 --> 00:04:27.600
that while it's lava, while it's
in this liquid state-- so let's

00:04:27.600 --> 00:04:30.400
imagine this lava
right over here.

00:04:30.400 --> 00:04:33.890
It's a bunch of stuff
right over here.

00:04:37.080 --> 00:04:39.020
I'll do the potassium-40.

00:04:39.020 --> 00:04:41.600
And let me do it in a color
that I haven't used yet.

00:04:41.600 --> 00:04:44.010
I'll do the
potassium-40 in magenta.

00:04:44.010 --> 00:04:48.090
It'll have some
potassium-40 in it.

00:04:48.090 --> 00:04:49.090
I'm maybe over doing it.

00:04:49.090 --> 00:04:50.940
It's a very scarce isotope.

00:04:50.940 --> 00:04:53.040
But it'll have some
potassium-40 in it.

00:04:53.040 --> 00:05:01.280
And it might already have some
argon-40 in it just like that.

00:05:01.280 --> 00:05:03.187
But argon-40 is a noble gas.

00:05:03.187 --> 00:05:04.520
It's not going to bond anything.

00:05:04.520 --> 00:05:06.980
And while this lava
is in a liquid state

00:05:06.980 --> 00:05:10.090
it's going to be
able to bubble out.

00:05:10.090 --> 00:05:11.420
It'll just float to the top.

00:05:11.420 --> 00:05:12.640
It has no bonds.

00:05:12.640 --> 00:05:14.687
And it'll just evaporate.

00:05:14.687 --> 00:05:15.770
I shouldn't say evaporate.

00:05:15.770 --> 00:05:17.720
It'll just bubble
out essentially,

00:05:17.720 --> 00:05:19.460
because it's not
bonded to anything,

00:05:19.460 --> 00:05:24.990
and it'll sort of just seep out
while we are in a liquid state.

00:05:24.990 --> 00:05:26.820
And what's really
interesting about that

00:05:26.820 --> 00:05:28.778
is that when you have
these volcanic eruptions,

00:05:28.778 --> 00:05:32.900
and because this argon-40
is seeping out, by the time

00:05:32.900 --> 00:05:38.490
this lava has hardened
into volcanic rock--

00:05:38.490 --> 00:05:42.230
and I'll do that volcanic
rock in a different color.

00:05:42.230 --> 00:05:45.910
By the time it has
hardened into volcanic rock

00:05:45.910 --> 00:05:49.360
all of the argon-40
will be gone.

00:05:49.360 --> 00:05:50.960
It won't be there anymore.

00:05:50.960 --> 00:05:53.680
And so what's neat is, this
volcanic event, the fact

00:05:53.680 --> 00:05:55.800
that this rock
has become liquid,

00:05:55.800 --> 00:05:58.600
it kind of resets the
amount of argon-40 there.

00:05:58.600 --> 00:06:01.310
So then you're only going to
be left with potassium-40 here.

00:06:04.281 --> 00:06:06.280
And that's why the argon-40
is more interesting,

00:06:06.280 --> 00:06:09.317
because the calcium-40 won't
necessarily have seeped out.

00:06:09.317 --> 00:06:11.400
And there might have already
been calcium-40 here.

00:06:11.400 --> 00:06:12.775
So it won't
necessarily seep out.

00:06:12.775 --> 00:06:15.010
But the argon-40 will seep out.

00:06:15.010 --> 00:06:16.560
So it kind of resets it.

00:06:16.560 --> 00:06:19.275
The volcanic event resets
the amount of argon-40.

00:06:21.865 --> 00:06:23.240
So right when the
event happened,

00:06:23.240 --> 00:06:27.580
you shouldn't have any argon-40
right when that lava actually

00:06:27.580 --> 00:06:28.980
becomes solid.

00:06:28.980 --> 00:06:32.850
And so if you fast forward
to some future date,

00:06:32.850 --> 00:06:35.840
and if you look at the sample--
let me copy and paste it.

00:06:40.380 --> 00:06:44.980
So if you fast forward to
some future date, and you

00:06:44.980 --> 00:06:51.542
see that there is some
argon-40 there, in that sample,

00:06:51.542 --> 00:06:54.350
you know this is
a volcanic rock.

00:06:54.350 --> 00:06:57.450
You know that it was due to
some previous volcanic event.

00:06:57.450 --> 00:07:02.675
You know that this argon-40 is
from the decayed potassium-40.

00:07:08.230 --> 00:07:12.190
And you know that it has decayed
since that volcanic event,

00:07:12.190 --> 00:07:14.709
because if it was there before
it would have seeped out.

00:07:14.709 --> 00:07:17.250
So the only way that this would
have been able to get trapped

00:07:17.250 --> 00:07:19.760
is, while it was liquid
it would seep out,

00:07:19.760 --> 00:07:22.670
but once it's solid it can
get trapped inside the rock.

00:07:22.670 --> 00:07:25.560
And so you know the only
way this argon-40 can

00:07:25.560 --> 00:07:28.920
exist there is by decay
from that potassium-40.

00:07:28.920 --> 00:07:30.720
So you can look at the ratio.

00:07:30.720 --> 00:07:36.170
So you know for every
one of these argon-40's,

00:07:36.170 --> 00:07:40.580
because only 11% of the decay
products are argon-40's,

00:07:40.580 --> 00:07:43.650
for every one of
those you must have

00:07:43.650 --> 00:07:49.150
on the order of about nine
calcium-40's that also decayed.

00:07:49.150 --> 00:07:52.940
And so for every one of these
argon-40's you know that there

00:07:52.940 --> 00:07:56.425
must have been 10
original potassium-40's.

00:07:56.425 --> 00:07:57.800
And so what you
can do is you can

00:07:57.800 --> 00:08:00.840
look at the ratio of the
number of potassium-40's there

00:08:00.840 --> 00:08:03.330
are today to the number
that there must have been,

00:08:03.330 --> 00:08:05.902
based on this evidence right
over here, to actually date it.

00:08:05.902 --> 00:08:07.360
And in the next
video I'll actually

00:08:07.360 --> 00:08:09.140
go through the
mathematical calculation

00:08:09.140 --> 00:08:11.111
to show you that you
can actually date it.

00:08:11.111 --> 00:08:12.610
And the reason this
is really useful

00:08:12.610 --> 00:08:15.110
is, you can look
at those ratios.

00:08:15.110 --> 00:08:18.179
And volcanic eruptions
aren't happening every day,

00:08:18.179 --> 00:08:20.720
but if you start looking over
millions and millions of years,

00:08:20.720 --> 00:08:22.220
on that time scale,
they're actually

00:08:22.220 --> 00:08:25.520
happening reasonably frequent.

00:08:25.520 --> 00:08:27.040
And so let's dig in the ground.

00:08:27.040 --> 00:08:29.450
So let's say this is the
ground right over here.

00:08:29.450 --> 00:08:33.600
And you dig enough and you
see a volcanic eruption,

00:08:33.600 --> 00:08:37.115
you see some volcanic
rock right over there,

00:08:37.115 --> 00:08:38.240
and then you dig even more.

00:08:38.240 --> 00:08:42.440
There's another layer of
volcanic rock right over there.

00:08:42.440 --> 00:08:44.850
So this is another
layer of volcanic rock.

00:08:47.820 --> 00:08:50.460
So they're all going to have a
certain amount of potassium-40

00:08:50.460 --> 00:08:51.900
in it.

00:08:51.900 --> 00:08:55.420
This is going to have some
amount of potassium-40 in it.

00:08:55.420 --> 00:08:59.060
And then let's say this one
over here has more argon-40.

00:08:59.060 --> 00:09:00.411
This one has a little bit less.

00:09:00.411 --> 00:09:02.910
And using the math that we're
going to do in the next video,

00:09:02.910 --> 00:09:04.790
let's say you're
able to say that this

00:09:04.790 --> 00:09:07.820
is, using the half-life, and
using the ratio of argon-40

00:09:07.820 --> 00:09:12.190
that's left, or using the
ratio of the potassium-40 left

00:09:12.190 --> 00:09:16.200
to what you know was there
before, you say that this must

00:09:16.200 --> 00:09:20.600
have solidified 100
million years ago, 100

00:09:20.600 --> 00:09:23.090
million years
before the present.

00:09:23.090 --> 00:09:25.909
And you know that this layer
right over here solidified.

00:09:25.909 --> 00:09:27.700
Let's say, you know it
solidified about 150

00:09:27.700 --> 00:09:30.220
million years
before the present.

00:09:30.220 --> 00:09:32.870
And let's say you feel pretty
good that this soil hasn't been

00:09:32.870 --> 00:09:34.810
dug up and mixed or
anything like that.

00:09:34.810 --> 00:09:36.810
It looks like it's been
pretty untouched when

00:09:36.810 --> 00:09:39.570
you look at these soil
samples right over here.

00:09:39.570 --> 00:09:45.040
And let's say you see
some fossils in here.

00:09:45.040 --> 00:09:49.070
Then, even though carbon-14
dating is kind of useless,

00:09:49.070 --> 00:09:51.410
really, when you get
beyond 50,000 years,

00:09:51.410 --> 00:09:55.170
you see these fossils in
between these two periods.

00:09:55.170 --> 00:09:56.670
It's a pretty good
indicator, if you

00:09:56.670 --> 00:09:59.910
can assume that this soil hasn't
been dug around and mixed,

00:09:59.910 --> 00:10:03.710
that this fossil is
between 100 million and 150

00:10:03.710 --> 00:10:04.680
million years old.

00:10:04.680 --> 00:10:06.120
This event happened.

00:10:06.120 --> 00:10:08.730
Then you have these
fossils got deposited.

00:10:08.730 --> 00:10:12.049
These animals died, or
they lived and they died.

00:10:12.049 --> 00:10:13.840
And then you had this
other volcanic event.

00:10:13.840 --> 00:10:17.690
So it allows you, even though
you're only directly dating

00:10:17.690 --> 00:10:19.650
the volcanic rock,
it allows you,

00:10:19.650 --> 00:10:22.430
when you look at the layers,
to relatively date things

00:10:22.430 --> 00:10:24.000
in between those layer.

00:10:24.000 --> 00:10:26.140
So it isn't just about
dating volcanic rock.

00:10:26.140 --> 00:10:29.590
It allows us to date things
that are very, very, very old

00:10:29.590 --> 00:10:34.530
and go way further back in time
than just carbon-14 dating.


Financial Times October 2011

WEBVTT
Kind: captions
Language: en

00:00:00.939 --> 00:00:02.495
Voiceover: These are some
questions that I'm going to

00:00:02.495 --> 00:00:05.003
answer for the Financial
Times that they may use in an

00:00:05.003 --> 00:00:07.584
article that they're going
to do about the Khan Academy.

00:00:07.584 --> 00:00:11.336
The first question; to what
do you attribute your ability

00:00:11.336 --> 00:00:14.607
to effectively digest,
synthesize and teach such a

00:00:14.607 --> 00:00:17.418
wide variety of topics?

00:00:18.033 --> 00:00:21.526
I guess the simple answer is
that I really enjoy doing that

00:00:21.526 --> 00:00:26.662
and I think by a set of
circumstances, either by

00:00:26.662 --> 00:00:29.978
maybe the way my brain works or maybe just

00:00:29.978 --> 00:00:31.835
circumstances or maybe
ways that I've been taught

00:00:31.835 --> 00:00:35.333
and I don't remember where
that might have come from.

00:00:35.333 --> 00:00:39.893
I learned a long time ago that
there's two ways to get by

00:00:39.893 --> 00:00:42.604
in our system and actually
I'll say in our system or

00:00:42.604 --> 00:00:45.868
maybe more broadly in society,
you can go and look at

00:00:45.868 --> 00:00:47.938
knowledge as something
where you're memorizing

00:00:47.938 --> 00:00:49.657
things or you're pattern
matching things or you can look

00:00:49.657 --> 00:00:51.622
at it as something to conceptually

00:00:51.622 --> 00:00:54.035
understand and digest and synthesize

00:00:54.035 --> 00:00:57.571
and I think I was fortunate
enough at an early age to

00:00:57.571 --> 00:01:00.475
be much better at the
digestion and the synthesis

00:01:00.475 --> 00:01:02.453
than the memorization
or the pattern matching.

00:01:02.453 --> 00:01:07.148
I actually think I have
quite a bad memory.

00:01:07.148 --> 00:01:11.689
That's how I think I was
able to do reasonably well

00:01:11.689 --> 00:01:16.251
academically and then later
on it transferred over into

00:01:16.251 --> 00:01:21.006
actually contributing in my work life.

00:01:21.006 --> 00:01:22.201
I think there's a natural
high; I don't think

00:01:22.201 --> 00:01:23.882
I'm unique there. I don't
think there's a unique

00:01:23.882 --> 00:01:25.286
quirk to my personality.

00:01:25.286 --> 00:01:29.075
I think when people really
do learn things it's one of

00:01:29.075 --> 00:01:29.938
those natural highs.

00:01:29.938 --> 00:01:32.003
It's one of those things that
differentiates human beings

00:01:32.003 --> 00:01:34.744
from most other animals is
that we really like learning.

00:01:34.744 --> 00:01:38.110
We really like understanding
and we really are

00:01:38.110 --> 00:01:40.849
naturally curious.

00:01:40.849 --> 00:01:43.940
It's actually maybe a little
bit sad that more people aren't

00:01:43.940 --> 00:01:46.273
as excited about trying
to digest and synthesize

00:01:46.273 --> 00:01:48.336
a wide variety of topics.

00:01:48.336 --> 00:01:50.673
Actually just to focus on the second part,

00:01:50.673 --> 00:01:53.156
a wide variety of topics,
what's interesting about that

00:01:53.156 --> 00:01:57.827
for me and I learned a lot
of this to some degree from

00:01:57.827 --> 00:02:01.155
my former jo working for
an investment fund and

00:02:01.155 --> 00:02:02.721
analyzing a bunch of
different companies and a

00:02:02.721 --> 00:02:06.414
bunch of different
industries is the more topics

00:02:06.414 --> 00:02:09.412
you look at, the more that
you see that there are

00:02:09.412 --> 00:02:12.241
common underlying themes
and there more connections

00:02:12.241 --> 00:02:13.258
you're able to make.

00:02:13.258 --> 00:02:15.610
The more you're able to
have a philisophy of how the

00:02:15.610 --> 00:02:16.627
world works.

00:02:16.627 --> 00:02:20.828
I actually think it builds
your understanding of

00:02:20.828 --> 00:02:22.583
every field, the more
fields that you look at and

00:02:22.583 --> 00:02:23.910
you're able to see connections.

00:02:23.910 --> 00:02:27.405
If you just focus on one
field, it'll actually narrow

00:02:27.405 --> 00:02:31.100
your view even of that one field.

00:02:31.100 --> 00:02:34.606
The next question; where
does this polymathic mastery

00:02:34.606 --> 00:02:36.319
of such varied subjects come from?

00:02:36.319 --> 00:02:37.485
There are plenty of intelligent
people who could study

00:02:37.485 --> 00:02:39.410
up on these subjects and
not be able to communicate

00:02:39.410 --> 00:02:41.837
them so effectively.

00:02:42.407 --> 00:02:44.225
A similar answer as the
last; to some degree

00:02:44.225 --> 00:02:46.198
the same answer as the last.

00:02:48.367 --> 00:02:50.403
I enjoy looking at things,
I enjoy learning things,

00:02:50.403 --> 00:02:53.275
and I enjoy thinking.

00:02:53.275 --> 00:02:55.276
I like sitting on a park bench
just thinking about things

00:02:55.276 --> 00:02:56.669
and you need something to
think about and so that's why

00:02:56.669 --> 00:02:59.404
I like studying different
topics and I like seeing where

00:02:59.404 --> 00:03:01.494
there might be parallels or
where there might be ah-ha

00:03:01.494 --> 00:03:03.673
moments or there might be
magical things about that

00:03:03.673 --> 00:03:05.269
subject that maybe
people didn't realize or

00:03:05.269 --> 00:03:07.654
maybe emphasize properly.

00:03:07.654 --> 00:03:11.403
The second part about not
being able to communicate,

00:03:11.403 --> 00:03:13.207
I agree there are plenty
of intelligent people who

00:03:13.207 --> 00:03:15.535
could study up on these subjects.

00:03:15.535 --> 00:03:17.536
The not being able to
communicate them effectively

00:03:17.536 --> 00:03:22.869
I think there are people
out there and I'm hoping

00:03:22.869 --> 00:03:25.003
more and more of them do
decide to communicate them

00:03:25.003 --> 00:03:26.952
effectively and I'm hoping
we can find them and maybe

00:03:26.952 --> 00:03:29.950
they can even join the
Khan Academy faculty.

00:03:29.950 --> 00:03:32.606
I think the important that
a lot of people who do

00:03:32.606 --> 00:03:35.155
have subject matter expertise,
they sometimes have the

00:03:35.155 --> 00:03:41.019
difficulty of getting into
the mind of a learner.

00:03:41.019 --> 00:03:43.985
I'll be frank, a lot of the
way I view the world is fairly;

00:03:43.985 --> 00:03:47.820
I think I have fairly simple
models in mind and I've

00:03:47.820 --> 00:03:49.336
gotten good at taking
complex things and creating

00:03:49.336 --> 00:03:51.068
simple models in my own mind so that

00:03:51.068 --> 00:03:53.209
I can work with those models.

00:03:53.209 --> 00:03:55.406
I think some people are
actually good at keeping

00:03:55.406 --> 00:03:56.827
complicated models in their mind.

00:03:56.827 --> 00:03:58.898
When you have a complicated
model in your mind,

00:03:58.898 --> 00:04:00.669
it's obviously much
harder to communicate them

00:04:00.669 --> 00:04:02.480
because it's complicated,
but I think most of those

00:04:02.480 --> 00:04:05.716
models can be distilled down
to a more simple and more

00:04:05.716 --> 00:04:08.072
elegant ways of thinking about things.

00:04:08.072 --> 00:04:10.335
Next question; were you
always drawn to such a

00:04:10.335 --> 00:04:12.218
variety of subjects, how do
you maintain your curiosity,

00:04:12.218 --> 00:04:14.298
is there anything that
strikes you as too dry to

00:04:14.298 --> 00:04:16.269
learn and teach?

00:04:16.269 --> 00:04:19.002
Once again, yes, I was always drawn -

00:04:19.002 --> 00:04:21.228
Well you know, actually
I'll take that back.

00:04:21.228 --> 00:04:24.364
Early in my life there were
two things that I really liked.

00:04:24.364 --> 00:04:28.940
I really liked art and
drawing and painting when I

00:04:28.940 --> 00:04:31.140
was very early on.

00:04:31.140 --> 00:04:32.537
When I was actually in
school, people viewed me as

00:04:32.537 --> 00:04:34.406
the art guy, the guy who
would draw pictures and

00:04:34.406 --> 00:04:37.069
cartoons and stuff like that

00:04:37.069 --> 00:04:38.947
and I really mathematics.

00:04:38.947 --> 00:04:41.276
What I didn't enjoy in my
earliest schooling is I

00:04:41.276 --> 00:04:43.473
wasn't a big fan of reading
and I wasn't a big fan of

00:04:43.473 --> 00:04:46.733
writing in my early school
and I viewed those things

00:04:46.733 --> 00:04:48.853
that I just wasn't good at.

00:04:48.853 --> 00:04:51.269
Sometimes when I used to
read, I would just sit and

00:04:51.269 --> 00:04:53.407
fixate on one sentence and
have to read it over and

00:04:53.407 --> 00:04:54.654
over and over again and it would take me

00:04:54.654 --> 00:04:56.578
forever to read a page.

00:04:56.578 --> 00:04:59.779
It was something that
actually frustrated me a lot.

00:04:59.779 --> 00:05:03.533
It wasn't until later that
I kind of, I don't know,

00:05:03.533 --> 00:05:05.464
to some degree destressed
how I viewed those some of

00:05:05.464 --> 00:05:07.760
those things and I let
myself explore things

00:05:07.760 --> 00:05:09.748
without the stress of
judging myself or having

00:05:09.748 --> 00:05:12.691
other people judge me that
I started realizing wow,

00:05:12.691 --> 00:05:13.953
I actually do like reading and

00:05:13.953 --> 00:05:16.548
I actually do like writing,
this is a form of communication

00:05:16.548 --> 00:05:18.738
and I love just thinking
analytically about how do

00:05:18.738 --> 00:05:20.275
you make an argument.

00:05:20.275 --> 00:05:24.910
I think the underlying lesson
there is when you thought

00:05:24.910 --> 00:05:26.669
you didn't like something
and then you learned that

00:05:26.669 --> 00:05:28.941
not only do you not not
like it but you actually

00:05:28.941 --> 00:05:33.704
like it, you're like well maybe
I'm prejudging everything.

00:05:34.150 --> 00:05:35.604
The second part of this
question, is there anything

00:05:35.604 --> 00:05:39.936
that strikes you as too
dry to learn and teach, no.

00:05:39.936 --> 00:05:41.141
There's nothing.

00:05:41.141 --> 00:05:43.821
There's things that right
now I perceive as dry,

00:05:43.821 --> 00:05:47.072
but my gut feeling tells me
that it's just the way it has

00:05:47.072 --> 00:05:49.228
been taught or marketed to the world

00:05:49.228 --> 00:05:51.230
that people make it dry.

00:05:51.230 --> 00:05:53.004
One of my big discoveries is even

00:05:53.004 --> 00:05:53.995
something like accounting.

00:05:53.995 --> 00:05:55.494
You tell someone accounting
and they think it's this

00:05:55.494 --> 00:05:57.667
dry subject, but I remember
when I went to business

00:05:57.667 --> 00:06:00.075
school, kind of this big
ah-ha moment was this is a

00:06:00.075 --> 00:06:01.269
really fascinating subject.

00:06:01.269 --> 00:06:02.669
It isn't just about bean counting.

00:06:02.669 --> 00:06:06.007
It isn't just about bookkeeping.

00:06:06.007 --> 00:06:10.342
It's about using symbols
and numbers to reflect a

00:06:10.342 --> 00:06:13.407
certain reality of what this
business or this process

00:06:13.407 --> 00:06:15.574
is actually doing.

00:06:15.574 --> 00:06:16.608
When a lot of people hear that,
they still might say well,

00:06:16.608 --> 00:06:19.718
that's not that, but trust me,

00:06:19.718 --> 00:06:21.366
it can be very interesting.

00:06:21.366 --> 00:06:23.403
In fact, this whole financial
crisis is driven people's

00:06:23.403 --> 00:06:27.575
different philosophies or
understanding of accounting.

00:06:27.575 --> 00:06:32.863
I think my philosophy and I
haven't had a topic yet that

00:06:32.863 --> 00:06:35.876
has disproven this philosophy
is that what's dry is

00:06:35.876 --> 00:06:38.789
how the topic is presented,
not the topic itself.

00:06:38.789 --> 00:06:42.804
Really almost any topic
can be very intellectually

00:06:42.804 --> 00:06:46.403
interesting if it's
looked at the right way.

00:06:46.403 --> 00:06:49.070
What do you do for fun? What do you read?

00:06:49.070 --> 00:06:50.956
What movies, films and arts do you enjoy

00:06:50.956 --> 00:06:53.542
during your free time?

00:06:53.542 --> 00:06:54.939
One could get the
impression that Khan Academy

00:06:54.939 --> 00:06:56.669
is all you do.

00:06:56.669 --> 00:06:59.406
In terms of fun and this
answer has changed a lot

00:06:59.406 --> 00:07:04.214
over the last three years
since having children,

00:07:04.214 --> 00:07:07.720
so my time is limited now
and I can't do all of the

00:07:07.720 --> 00:07:09.603
stuff that I used to like to do.

00:07:09.603 --> 00:07:11.343
One of the things that I used
to like to do when it was

00:07:11.343 --> 00:07:13.007
just me and my wife or
even before I was married,

00:07:13.007 --> 00:07:16.269
I liked the outdoors a lot.

00:07:16.269 --> 00:07:17.069
I liked to go hiking.

00:07:17.069 --> 00:07:19.150
It's something I hope to
do with my children soon,

00:07:19.150 --> 00:07:21.074
but they're a little too
young to go hiking or

00:07:21.074 --> 00:07:24.939
camping just yet, but that
is one of the things I really

00:07:24.939 --> 00:07:29.603
liked doing, just outdoors things.

00:07:29.603 --> 00:07:38.157
I'm a hobbyist guitarist and
painter and I don't claim

00:07:38.157 --> 00:07:40.866
at all to be good at those
thing, but they are things

00:07:40.866 --> 00:07:42.340
that I like to do for fun.

00:07:42.340 --> 00:07:46.669
They're a form of creative expression.

00:07:46.669 --> 00:07:51.007
In terms of what do I
read, I read a lot of

00:07:51.007 --> 00:07:54.120
science fiction which may
not surprise a lot of people,

00:07:54.120 --> 00:07:57.489
so a lot of science fiction
and frankly I also like to

00:07:57.489 --> 00:08:01.298
revisit a lot of the books
that I was forced to read,

00:08:01.298 --> 00:08:03.669
so to speak, in high school and college.

00:08:03.669 --> 00:08:05.273
When I revisit them and
I'm reading them for fun,

00:08:05.273 --> 00:08:07.336
I'm starting to really enjoy them.

00:08:07.336 --> 00:08:09.330
Frankly, I read a lot
of science fiction and

00:08:09.330 --> 00:08:12.235
I read a lot of the classics
for fun and I've found

00:08:12.235 --> 00:08:14.736
that they take on a new light.

00:08:14.736 --> 00:08:16.401
One, when you read them for
fun, you're a little older

00:08:16.401 --> 00:08:20.593
now and you have a little
bit more perspective on life.

00:08:20.593 --> 00:08:21.800
Although hopefully, I have a lot more

00:08:21.800 --> 00:08:23.672
perspective to get.

00:08:23.672 --> 00:08:26.819
Science fiction, they're fun.

00:08:26.819 --> 00:08:28.662
They're fun by themselves,
they tend to be good stories,

00:08:28.662 --> 00:08:32.153
but they kind of expand
your mind and really

00:08:32.153 --> 00:08:33.991
make you think.

00:08:33.991 --> 00:08:36.075
A lot of things that we take
for granted in our society,

00:08:36.075 --> 00:08:38.484
science fiction books are
really good at exposing them

00:08:38.484 --> 00:08:41.038
as somewhat arbitrary and
that there are other ways to

00:08:41.038 --> 00:08:43.003
do things and I think there really are.

00:08:43.003 --> 00:08:44.962
They are some of the
best things you can read

00:08:44.962 --> 00:08:48.341
to expand your view of what is possible.

00:08:48.341 --> 00:08:49.340
What movies, films and arts do you enjoy

00:08:49.340 --> 00:08:51.610
during your free time?

00:08:51.610 --> 00:08:57.574
Once again, I love science
fiction and I love epic

00:08:57.574 --> 00:09:02.409
things generally, whether
it's Braveheart or

00:09:02.409 --> 00:09:05.330
Lord of the Rings or the Godfather movies.

00:09:05.330 --> 00:09:07.200
I don't think I'm alone in
liking those types of things,

00:09:07.200 --> 00:09:12.206
but my wife every now and
then gets me to watch an

00:09:12.206 --> 00:09:15.857
episode of Felicity on
Netflix and I enjoy that too

00:09:15.857 --> 00:09:19.003
which is a little bit embarrassing.

00:09:19.003 --> 00:09:20.339
One could the impression that Khan Academy

00:09:20.339 --> 00:09:21.080
is all you do.

00:09:21.080 --> 00:09:22.783
Well, it's a lot of what I do now,

00:09:22.783 --> 00:09:24.624
especially with children I think.

00:09:24.624 --> 00:09:26.739
I try to during the day,

00:09:26.739 --> 00:09:28.536
focus on Khan Academy,
in the evening focus on

00:09:28.536 --> 00:09:32.562
wife and children, but
within that context I try to

00:09:32.562 --> 00:09:34.737
at least to have one good
book to read while I'm

00:09:34.737 --> 00:09:38.336
travelling or maybe
right before I go to bed.

00:09:38.336 --> 00:09:39.866
Now that my kids are getting
a little older I'm getting

00:09:39.866 --> 00:09:41.808
a little bit more time to
go back to a little bit of

00:09:41.808 --> 00:09:44.200
the outdoor stuff and a little bit of the

00:09:44.200 --> 00:09:46.531
creative projects.

00:09:46.531 --> 00:09:48.054
What do you want Khan Academy

00:09:48.054 --> 00:09:49.606
curriculum to encompass?

00:09:49.606 --> 00:09:51.146
Is it K-12 basics on
math and science or is it

00:09:51.146 --> 00:09:52.485
broader than that?

00:09:52.485 --> 00:09:54.724
Will it ever be complete?

00:09:54.724 --> 00:09:57.376
The second answer is easy to answer; no.

00:09:57.376 --> 00:09:59.071
It will never be complete.

00:09:59.071 --> 00:10:01.609
I think there's an infinite
number of topics to cover and

00:10:01.609 --> 00:10:03.685
I think we can always
improve on what's covered

00:10:03.685 --> 00:10:05.870
and we can always attack
it from a different angle.

00:10:05.870 --> 00:10:08.072
I don't think it will ever be complete.

00:10:08.072 --> 00:10:10.225
It isn't just K-12 basics.

00:10:10.225 --> 00:10:13.476
In fact, even now it
isn't just K-12 basics.

00:10:13.476 --> 00:10:16.987
There's a lot of content
about college level material,

00:10:16.987 --> 00:10:18.737
even graduate level material.

00:10:18.737 --> 00:10:21.561
There's stuff about economics
and finance and we've

00:10:21.561 --> 00:10:24.873
just brought on two
art history professors.

00:10:24.873 --> 00:10:27.228
They're the new first
editions to the Khan Academy

00:10:27.228 --> 00:10:29.974
faculty and they're doing
art history really at an

00:10:29.974 --> 00:10:33.942
advanced level and we're
starting to do some videos

00:10:33.942 --> 00:10:37.030
with professors at
Stanford medical school and

00:10:37.030 --> 00:10:39.852
other places where we're
attacking even medical stuff.

00:10:39.852 --> 00:10:42.948
There's no end and we
really want it to encompass

00:10:42.948 --> 00:10:48.075
everything that helps people
form a view of the world

00:10:48.075 --> 00:10:50.782
and understand the world
around them and become

00:10:50.782 --> 00:10:54.928
productive and happy and people
with rich lives, I guess.

00:10:54.928 --> 00:10:56.667
So it's pretty much everything. (laughs)

00:10:56.667 --> 00:10:58.692
Next question; as Khan
Academy continues to find a

00:10:58.692 --> 00:11:00.736
larger audience, do you
have any concerns about a

00:11:00.736 --> 00:11:03.400
growing number of students
learning from one source?

00:11:03.400 --> 00:11:05.136
Is there a risk of having
a uniformity of primary

00:11:05.136 --> 00:11:07.472
materials for students?

00:11:07.472 --> 00:11:10.026
We think about this issue
and this is why we are

00:11:10.026 --> 00:11:12.472
expanding the faculty and
there's actually going to be

00:11:12.472 --> 00:11:14.538
someone who joins also
on the math side and she

00:11:14.538 --> 00:11:17.336
teaches things with slightly
different view, although,

00:11:17.336 --> 00:11:20.869
I think we have similar sensibilities.

00:11:20.869 --> 00:11:23.400
Our goal is to iterate and
we're actually starting to

00:11:23.400 --> 00:11:26.961
get more analytical about
what makes a video good.

00:11:26.961 --> 00:11:28.538
If someone makes another
good video on something or

00:11:28.538 --> 00:11:30.780
there's another way to view
things, we hope to include

00:11:30.780 --> 00:11:32.030
those in the library.

00:11:32.030 --> 00:11:33.866
We don't think we'll have a
million different teachers, but

00:11:33.866 --> 00:11:35.870
we think on a topic you
might have two or three

00:11:35.870 --> 00:11:37.701
different view points on something.

00:11:37.701 --> 00:11:39.283
We think that's good.

00:11:39.283 --> 00:11:41.523
We're also starting to
introduce across the board

00:11:41.523 --> 00:11:43.000
and we've done this with
the medicine videos and some

00:11:43.000 --> 00:11:44.873
of the economics videos
is we're starting to have

00:11:44.873 --> 00:11:46.272
conversations in our videos.

00:11:46.272 --> 00:11:48.610
This is what the two art
historians do, Beth Harris

00:11:48.610 --> 00:11:49.469
and Steven Zucker.

00:11:49.469 --> 00:11:51.736
They have art conversations,
so it's them two talking

00:11:51.736 --> 00:11:54.208
about a piece of art or
me and a professor talking

00:11:54.208 --> 00:11:56.272
about some scientific phenomenon.

00:11:56.272 --> 00:11:58.026
You're really getting a
conversation and seeing that

00:11:58.026 --> 00:11:59.550
there's two sides to it.

00:11:59.550 --> 00:12:02.736
Frankly, I think it's better.

00:12:02.736 --> 00:12:04.878
You can go to a university that has many

00:12:04.878 --> 00:12:07.376
professors, but when you take
intro to American History,

00:12:07.376 --> 00:12:08.804
you get only one source.

00:12:08.804 --> 00:12:11.326
You're getting that one
professor or there is only one

00:12:11.326 --> 00:12:14.207
textbook right now that
dominates each field.

00:12:14.207 --> 00:12:18.137
We actually think we can
provide more voices than what

00:12:18.137 --> 00:12:19.804
is traditionally provided.

00:12:19.804 --> 00:12:21.706
The powerful thing about
the internet now is I don't

00:12:21.706 --> 00:12:24.647
think anyone can capitalize
as one voice and if anyone

00:12:24.647 --> 00:12:27.078
did, especially if that was
bad quality, they would lose

00:12:27.078 --> 00:12:31.206
because the internet gets
rid of all intermediaries.

00:12:31.206 --> 00:12:32.547
There's no gate keepers anymore.

00:12:32.547 --> 00:12:35.141
It's not like we're a publishing
firm 50 years ago where

00:12:35.141 --> 00:12:37.474
only what's published
is what people get at.

00:12:37.474 --> 00:12:39.672
Now people can get anything
anywhere and frankly,

00:12:39.672 --> 00:12:42.604
anyone can do what I did
over You Tube and people are

00:12:42.604 --> 00:12:45.291
and I think that's a really
healthy thing that you can

00:12:45.291 --> 00:12:48.406
always get the other points of view.

00:12:48.406 --> 00:12:54.009
Next question; why are
you focusing on education?

00:12:54.009 --> 00:12:56.672
I guess the simple answer
is, well I guess this may be

00:12:56.672 --> 00:12:59.468
all together are you concerned
about public education.

00:12:59.468 --> 00:13:06.405
Regardless of whether we're
all professional educators,

00:13:06.405 --> 00:13:09.160
we've all spent significant time in the

00:13:09.160 --> 00:13:10.537
education system.

00:13:10.537 --> 00:13:12.066
I'm no exception.

00:13:12.066 --> 00:13:14.269
I did just have a nagging
feeling while I went through

00:13:14.269 --> 00:13:16.669
it that there's got to be
a better way to do this.

00:13:16.669 --> 00:13:18.169
I saw how many students
were just pattern matching,

00:13:18.169 --> 00:13:20.006
how many were memorizing,
how little retention people

00:13:20.006 --> 00:13:24.059
have, how many resources
people have, and still not

00:13:24.059 --> 00:13:25.943
coming out on the other
side having done creative

00:13:25.943 --> 00:13:30.231
things and really
stretched their thinking.

00:13:30.231 --> 00:13:32.653
It seems like we're at an
inflection point in history

00:13:32.653 --> 00:13:36.803
and this is the information
revolution and it's crazy

00:13:36.803 --> 00:13:42.385
that almost every other field
is getting revolutionized

00:13:42.431 --> 00:13:43.542
except for education.

00:13:43.542 --> 00:13:46.135
I think it's just right
for it and just answering

00:13:46.135 --> 00:13:47.984
some of those early
questions about my interests,

00:13:47.984 --> 00:13:48.982
it's what I love doing.

00:13:48.982 --> 00:13:52.339
I entered the investment
world because I loved learning

00:13:52.339 --> 00:13:53.603
about different issues.

00:13:53.603 --> 00:13:56.005
I loved talking to an
ag producer one hour and

00:13:56.005 --> 00:13:57.273
talking to a railroad
company the next hour and

00:13:57.273 --> 00:13:58.543
talking to a software
company the next hour and

00:13:58.543 --> 00:14:01.669
talking to a natural gas
pipeline owner the next hour

00:14:01.669 --> 00:14:03.553
because you'd learn how the world works.

00:14:03.553 --> 00:14:07.287
That's what education is,
learning how the world works,

00:14:07.287 --> 00:14:10.979
learning ways of thinking.

00:14:10.979 --> 00:14:12.809
Sometimes with the goal
of becoming a productive,

00:14:12.809 --> 00:14:17.482
happy member of society with a rich life.

00:14:17.482 --> 00:14:18.980
I can't imagine anything
better to focus on I guess

00:14:18.980 --> 00:14:20.672
is a simple answer.

00:14:20.672 --> 00:14:25.342
It's something that's
interesting to me personally,

00:14:25.342 --> 00:14:29.144
but obviously it can scale
now and it has ripple effects

00:14:29.144 --> 00:14:32.152
that can go on not just
for a few years, it can go

00:14:32.152 --> 00:14:33.480
on for generations.

00:14:33.480 --> 00:14:36.945
It's one of these epic
ideas and I already told you

00:14:36.945 --> 00:14:39.268
I like epic things.

00:14:39.268 --> 00:14:40.910
Are you concerned about the
state of public education

00:14:40.910 --> 00:14:42.008
in the US?

00:14:42.008 --> 00:14:43.348
I'm concerned about the state of

00:14:43.348 --> 00:14:44.689
public education everywhere.

00:14:44.689 --> 00:14:47.539
In fact, I'll say I'm
concerned about the state of

00:14:47.539 --> 00:14:51.806
education everywhere.

00:14:51.806 --> 00:14:55.414
Franky, people dump on
the public schools a lot,

00:14:55.414 --> 00:14:57.870
but I don't think the private
schools are much better.

00:14:57.870 --> 00:15:00.140
They're selecting for
students who would probably

00:15:00.140 --> 00:15:03.613
do well if you gave them a
textbook and who come from

00:15:03.613 --> 00:15:06.002
college educated families
who are wealthy, who can

00:15:06.002 --> 00:15:07.469
afford private tutors.

00:15:07.469 --> 00:15:09.617
They charge them out here in the Bay area

00:15:09.617 --> 00:15:12.021
$30,000 a year.

00:15:12.021 --> 00:15:14.028
I don't know what they're
doing with those resources

00:15:14.028 --> 00:15:16.694
and I don't see substantially
different results from

00:15:16.694 --> 00:15:20.403
private schools charging
$30,000 a year to the public

00:15:20.403 --> 00:15:22.806
schools that are serving
the same demographic.

00:15:22.806 --> 00:15:24.025
They seem to be about
the same or some of those

00:15:24.025 --> 00:15:26.141
public schools are even better.

00:15:26.141 --> 00:15:27.945
I actually think the whole
model and it's even true

00:15:27.945 --> 00:15:31.402
of...People talk about our
university system as the

00:15:31.402 --> 00:15:32.872
best thing out.

00:15:32.872 --> 00:15:34.275
They do good research.

00:15:34.275 --> 00:15:35.400
That's why they're famous.

00:15:35.400 --> 00:15:38.652
That's why they are but in
terms of how they're teaching,

00:15:38.652 --> 00:15:42.832
there's nothing that I
find particularly ground

00:15:42.832 --> 00:15:47.540
breaking or something that
you can't improve upon.

00:15:47.540 --> 00:15:49.692
I think there's a lot that can be done.

00:15:49.692 --> 00:15:53.129
I'm actually concerned
about the general state of,

00:15:53.129 --> 00:15:54.440
actually when you say
education, I'm concerned about

00:15:54.440 --> 00:15:59.689
the general state of
people's learning in life,

00:15:59.689 --> 00:16:03.203
irrespective of what the
education system if doing.

00:16:03.203 --> 00:16:05.273
What are your thoughts on
the importance of primary

00:16:05.273 --> 00:16:06.791
education as a means to a productive

00:16:06.791 --> 00:16:10.438
and prosperous society?

00:16:10.438 --> 00:16:11.606
That's what it's all about.

00:16:11.606 --> 00:16:15.771
If you don't have that
primary education, there's no

00:16:15.771 --> 00:16:17.695
way to have a productive
and prosperous society.

00:16:17.695 --> 00:16:21.970
You need basic security, you
need basic infrastructure

00:16:21.970 --> 00:16:24.545
and you need an educated population.

00:16:24.545 --> 00:16:27.731
It's now true more than ever.

00:16:27.731 --> 00:16:31.941
Back in the old days,
there were jobs where just

00:16:31.941 --> 00:16:35.336
raw labor was relevant,
but with technology that

00:16:35.336 --> 00:16:37.943
becomes less and less relevant every day.

00:16:37.943 --> 00:16:41.133
In order for people to be
productive and to contribute

00:16:41.133 --> 00:16:44.273
and to feel needed, they really have to

00:16:44.273 --> 00:16:47.136
step up the chain.

00:16:47.136 --> 00:16:48.779
Raw labor is needed
less and less because of

00:16:48.779 --> 00:16:51.332
mechanical technology and because of

00:16:51.332 --> 00:16:53.885
informational technology.

00:16:53.885 --> 00:16:56.006
Processed oriented white collar work

00:16:56.006 --> 00:16:57.358
is also going to go away.

00:16:57.358 --> 00:16:59.112
It's just going to push
everyone, the really

00:16:59.112 --> 00:17:02.619
needed jobs are the highly creative ones.

00:17:02.619 --> 00:17:04.934
It's not good enough
just to teach people some

00:17:04.934 --> 00:17:08.269
process or some formula
or some pattern matching.

00:17:08.269 --> 00:17:09.663
We have to teach them to be creative,

00:17:09.678 --> 00:17:11.473
we have to teach them to innovate,

00:17:11.473 --> 00:17:15.269
to problem solve things that
they've never seen before.

00:17:15.269 --> 00:17:18.796
Yes, I think it's not just an ingredient.

00:17:18.796 --> 00:17:20.776
It's actually the foundation
of having a productive and

00:17:20.776 --> 00:17:22.499
prosperous society.

00:17:22.499 --> 00:17:25.075
Last question; is it your
hope that Khan Academy can

00:17:25.075 --> 00:17:26.870
help reverse some of the
losses we have suffered

00:17:26.870 --> 00:17:29.359
in the quality of public schooling?

00:17:29.359 --> 00:17:31.867
Just going to the previous
education, I don't think

00:17:31.867 --> 00:17:33.405
it's about public schooling
or private schooling or

00:17:33.405 --> 00:17:35.947
primary or secondary education.

00:17:35.947 --> 00:17:42.195
I hope it can help elevate
the state of knowledge

00:17:42.195 --> 00:17:45.613
or learning generally
and I won't make any bold

00:17:45.613 --> 00:17:47.783
claim that we've solved
the problem yet or we're

00:17:47.783 --> 00:17:49.862
anywhere close to it, but I
think what's exciting about

00:17:49.862 --> 00:17:53.073
Khan Academy is that we
have a lot of traction and

00:17:53.073 --> 00:17:55.472
we're trying to be as
thoughtful about improving

00:17:55.472 --> 00:17:57.610
on what we have.

00:17:57.610 --> 00:18:00.136
You combine the traction
with our ability to iterate,

00:18:00.136 --> 00:18:02.803
move quickly and improve and
hopefully in a thoughtful

00:18:02.803 --> 00:18:05.406
way and we can only get better.

00:18:05.406 --> 00:18:06.831
I think we're really just
in the top of the first

00:18:06.831 --> 00:18:09.266
inning and there's a long
way to go here, but I'm

00:18:09.266 --> 00:18:12.514
hoping that it can
improve the state of how

00:18:12.514 --> 00:18:15.000
people learn generally.