Continuity over an interval

WEBVTT
Kind: captions
Language: en

00:00:01.077 --> 00:00:02.878
- [Instructor] What we're
going to do in this video

00:00:02.878 --> 00:00:06.209
is explore continuity over an interval.

00:00:06.209 --> 00:00:08.485
But to do that, let's refresh our memory

00:00:08.485 --> 00:00:10.951
about continuity at a point.

00:00:10.951 --> 00:00:12.779
So we say that f

00:00:12.779 --> 00:00:13.862
is continuous

00:00:15.339 --> 00:00:16.172
when

00:00:17.070 --> 00:00:18.403
x is equal to c,

00:00:19.665 --> 00:00:21.251
if and only if,

00:00:21.251 --> 00:00:24.002
so I'm gonna make these
two-way arrows right over here,

00:00:24.002 --> 00:00:25.442
the limit

00:00:25.442 --> 00:00:26.275
of f of x

00:00:27.196 --> 00:00:29.659
as x approaches c

00:00:29.659 --> 00:00:31.242
is equal to f of c.

00:00:32.667 --> 00:00:33.929
And when we first introduced this,

00:00:33.929 --> 00:00:36.062
we said, hey, this looks
a little bit technical,

00:00:36.062 --> 00:00:37.911
but it's actually pretty intuitive.

00:00:37.911 --> 00:00:39.404
Think about what's happening.

00:00:39.404 --> 00:00:41.830
The limit as x approaches c of f of x,

00:00:41.830 --> 00:00:45.631
so let's say that f of x as x approaches c

00:00:45.631 --> 00:00:47.106
is approaching some value.

00:00:47.106 --> 00:00:48.501
So if we approach,

00:00:48.501 --> 00:00:50.742
if we approach from the left,

00:00:50.742 --> 00:00:52.398
we're getting to this value.

00:00:52.398 --> 00:00:55.048
If we approach from the right,
we're getting this value.

00:00:55.048 --> 00:00:57.921
Well, in order for the
function to be continuous,

00:00:57.921 --> 00:01:00.984
if I had to draw this function
without picking up my pen,

00:01:00.984 --> 00:01:03.815
well, the value of the
function at that point

00:01:03.815 --> 00:01:06.735
should be the same as the limit.

00:01:06.735 --> 00:01:10.367
This is really just a more
rigorous way of describing

00:01:10.367 --> 00:01:12.469
this notion of not having
to pick up your pencil,

00:01:12.469 --> 00:01:14.243
this notion of connectedness,

00:01:14.243 --> 00:01:15.712
that you don't have any jumps

00:01:15.712 --> 00:01:18.876
or any discontinuities of any kind.

00:01:18.876 --> 00:01:19.891
So with that out the way,

00:01:19.891 --> 00:01:24.007
let's discuss continuity over intervals.

00:01:24.007 --> 00:01:25.621
Let me delete this really fast,

00:01:25.621 --> 00:01:28.438
so I have space to work with.

00:01:28.438 --> 00:01:31.752
So we say, so I'm gonna first
talk about an open interval,

00:01:31.752 --> 00:01:33.276
and then we're gonna talk
about a closed interval

00:01:33.276 --> 00:01:35.888
because a closed interval gets
a little bit more involved.

00:01:35.888 --> 00:01:36.805
So we say f

00:01:37.642 --> 00:01:38.725
is continuous

00:01:40.238 --> 00:01:43.071
over an open interval from a to b.

00:01:44.342 --> 00:01:46.694
So the parentheses instead of brackets,

00:01:46.694 --> 00:01:48.999
this shows that we're not
including the endpoint.

00:01:48.999 --> 00:01:52.164
So this would be all of the
points between x equals a

00:01:52.164 --> 00:01:53.664
and x equals b,

00:01:54.504 --> 00:01:57.590
but not equaling x
equals a and x equals b.

00:01:57.590 --> 00:02:00.934
So f is continuous over
this open interval,

00:02:00.934 --> 00:02:02.740
if and only if,

00:02:02.740 --> 00:02:03.990
if and only if,

00:02:05.115 --> 00:02:06.973
f is continuous,

00:02:06.973 --> 00:02:08.223
f is continuous

00:02:10.230 --> 00:02:11.465
over

00:02:11.465 --> 00:02:13.216
every point in,

00:02:13.216 --> 00:02:14.549
over every point

00:02:16.732 --> 00:02:17.914
in

00:02:17.914 --> 00:02:18.997
the interval.

00:02:20.397 --> 00:02:23.112
So let's do a couple of examples of that.

00:02:23.112 --> 00:02:26.025
So let's say we're talking
about the open interval

00:02:26.025 --> 00:02:27.855
from negative seven

00:02:27.855 --> 00:02:29.272
to negative five.

00:02:30.433 --> 00:02:33.635
Is f continuous over that interval?

00:02:33.635 --> 00:02:36.358
Let's see, we're going from negative seven

00:02:36.358 --> 00:02:37.775
to negative five,

00:02:38.895 --> 00:02:40.301
and there's a couple of
ways you could do it.

00:02:40.301 --> 00:02:42.852
There's the
not-so-mathematically-rigorous way,

00:02:42.852 --> 00:02:45.041
where you could say, hey,
look, if I start here,

00:02:45.041 --> 00:02:47.374
I can get all the way to negative five

00:02:47.374 --> 00:02:49.649
without having to pick up my pencil.

00:02:49.649 --> 00:02:51.348
If you wanted to do more rigorously

00:02:51.348 --> 00:02:53.567
and you actually had the
definition of the function,

00:02:53.567 --> 00:02:55.112
you might be able to do a proof,

00:02:55.112 --> 00:02:57.239
that for any of these
points over the interval,

00:02:57.239 --> 00:03:00.612
that the limit as x approaches
any one of these points

00:03:00.612 --> 00:03:03.315
of f of x is equal to
the value of the function

00:03:03.315 --> 00:03:04.496
at that point.

00:03:04.496 --> 00:03:06.609
It's harder to do when
you only have a graph.

00:03:06.609 --> 00:03:07.518
When you only have a graph,

00:03:07.518 --> 00:03:08.881
you can only just do it by inspection,

00:03:08.881 --> 00:03:11.327
and say, okay, I can go from
that point to that point

00:03:11.327 --> 00:03:12.798
without picking up my pencil,

00:03:12.798 --> 00:03:15.866
so I feel pretty good about it.

00:03:15.866 --> 00:03:17.884
Now let's do another interval.

00:03:17.884 --> 00:03:20.344
Let's say the, so let me
put a check mark here,

00:03:20.344 --> 00:03:21.986
that is continuous.

00:03:21.986 --> 00:03:26.341
Let's think about the
interval from negative two

00:03:26.341 --> 00:03:29.258
to positive one, the open interval.

00:03:30.315 --> 00:03:32.542
So this is interesting
because the function

00:03:32.542 --> 00:03:34.611
at negative two is up here.

00:03:34.611 --> 00:03:36.501
And so if you really wanted
to start at negative two,

00:03:36.501 --> 00:03:39.360
you would have to start here
and then jump immediately down

00:03:39.360 --> 00:03:41.262
as soon as you get slightly
larger than negative two

00:03:41.262 --> 00:03:42.775
and then keep going.

00:03:42.775 --> 00:03:44.068
But this is an open interval,

00:03:44.068 --> 00:03:45.671
so we're not actually concerned

00:03:45.671 --> 00:03:48.103
with what exactly happens at negative two,

00:03:48.103 --> 00:03:51.195
we're concerned what happens when we are

00:03:51.195 --> 00:03:53.386
all the numbers larger than negative two.

00:03:53.386 --> 00:03:57.093
So we would actually
start right over here,

00:03:57.093 --> 00:04:00.157
and then we would go to one.

00:04:00.157 --> 00:04:02.317
And once again, based on the intuitive

00:04:02.317 --> 00:04:04.702
I didn't have to pick up my pen idea,

00:04:04.702 --> 00:04:07.995
this function would be continuous

00:04:07.995 --> 00:04:08.828
over this,

00:04:09.750 --> 00:04:11.819
over this interval.

00:04:11.819 --> 00:04:13.804
So what's an example of an interval

00:04:13.804 --> 00:04:16.221
where the function
would not be continuous?

00:04:16.221 --> 00:04:19.287
Well, think about the interval from,

00:04:19.287 --> 00:04:20.694
well, this is a pretty
straightforward one,

00:04:20.694 --> 00:04:24.221
the open interval from three to five.

00:04:24.221 --> 00:04:27.236
The function is here
when x is equal to three.

00:04:27.236 --> 00:04:28.991
But if we wanted to get to five,

00:04:28.991 --> 00:04:31.033
it looks like we're asymptoting,

00:04:31.033 --> 00:04:34.581
it looks like we're
asymptoting up towards infinity

00:04:34.581 --> 00:04:37.476
and we just keep on going
for a very long time.

00:04:37.476 --> 00:04:40.498
And then we would have to pick
up our pencil and jump over,

00:04:40.498 --> 00:04:44.779
and then we would come
back down right over here.

00:04:44.779 --> 00:04:48.852
And so here we are not
continuous over that interval.

00:04:48.852 --> 00:04:51.051
So now let's think about the more,

00:04:51.051 --> 00:04:52.578
the slightly more involved interval.

00:04:52.578 --> 00:04:54.328
The slightly more involved case

00:04:54.328 --> 00:04:56.505
is when you have a closed interval.

00:04:56.505 --> 00:04:57.755
F is continuous

00:04:59.261 --> 00:05:02.431
over the closed interval from a to b.

00:05:02.431 --> 00:05:05.002
So this includes not just
the points between a and b,

00:05:05.002 --> 00:05:06.837
but the endpoints as well,

00:05:06.837 --> 00:05:08.087
if and only if,

00:05:09.264 --> 00:05:10.097
f is

00:05:10.980 --> 00:05:12.530
continuous

00:05:12.530 --> 00:05:14.363
over the open interval

00:05:15.830 --> 00:05:18.101
and the one-sided limits.

00:05:18.101 --> 00:05:19.009
Let me right this.

00:05:19.009 --> 00:05:19.842
And

00:05:20.982 --> 00:05:21.815
the limit

00:05:23.394 --> 00:05:25.061
as x approaches a

00:05:26.072 --> 00:05:27.239
from the right

00:05:28.230 --> 00:05:29.753
of f of x

00:05:29.753 --> 00:05:31.336
is equal to f of a,

00:05:32.244 --> 00:05:33.327
and the limit

00:05:34.675 --> 00:05:37.147
as x approaches b

00:05:37.147 --> 00:05:38.314
from the left,

00:05:39.594 --> 00:05:41.511
from the left of f of x

00:05:42.436 --> 00:05:44.019
is equal to f of b.

00:05:46.112 --> 00:05:47.117
Now what's going on here?

00:05:47.117 --> 00:05:49.662
Well, it's just saying
that the one-sided limit,

00:05:49.662 --> 00:05:51.986
when you're operating within the Interval,

00:05:51.986 --> 00:05:54.925
has to approach the same
value as the function.

00:05:54.925 --> 00:05:58.308
So for example, if we
said the closed interval

00:05:58.308 --> 00:06:01.644
from negative seven to negative five,

00:06:01.644 --> 00:06:03.009
well, this one is still reasonable,

00:06:03.009 --> 00:06:05.156
you know, just based on the
picking up your pencil thing.

00:06:05.156 --> 00:06:07.653
You don't have to pick up your pencil.

00:06:07.653 --> 00:06:10.372
And what you would do is at the endpoint,

00:06:10.372 --> 00:06:11.584
and at negative seven,

00:06:11.584 --> 00:06:14.101
this function is just
plain old continuous,

00:06:14.101 --> 00:06:16.761
but if it wasn't defined over here,

00:06:16.761 --> 00:06:19.369
it could still be continuous
because you would do

00:06:19.369 --> 00:06:21.377
the right-handed limit towards it.

00:06:21.377 --> 00:06:22.837
And you'd say, okay,
the right-handed limit

00:06:22.837 --> 00:06:24.748
is equal to the value of the function.

00:06:24.748 --> 00:06:27.075
And then at this endpoint,
at the second endpoint,

00:06:27.075 --> 00:06:29.385
you'd say, okay, the left-handed limit

00:06:29.385 --> 00:06:32.371
is equal to the function, even
if it wasn't defined here,

00:06:32.371 --> 00:06:35.698
even if the two-sided
limit were not defined.

00:06:35.698 --> 00:06:37.890
And so we could actually
look at an example of that.

00:06:37.890 --> 00:06:39.637
If we were looking at

00:06:39.637 --> 00:06:42.118
the interval from the closed,

00:06:42.118 --> 00:06:44.516
and you could have one
side open, one side closed,

00:06:44.516 --> 00:06:47.764
but let's just do the closed
interval from negative three

00:06:47.764 --> 00:06:49.514
to negative two.

00:06:49.514 --> 00:06:53.219
So notice I did not have
to pick up my pencil.

00:06:53.219 --> 00:06:54.584
I'm including negative three,

00:06:54.584 --> 00:06:57.435
and I'm getting all the
way to negative two.

00:06:57.435 --> 00:07:00.320
If you knew the analytic
definition of this function,

00:07:00.320 --> 00:07:03.300
you could prove that, hey, the
limit at any of these points

00:07:03.300 --> 00:07:05.535
inside, between negative
three and negative two,

00:07:05.535 --> 00:07:08.351
is equal to the value of the function.

00:07:08.351 --> 00:07:11.145
Negative three, the function
is clearly, at negative three,

00:07:11.145 --> 00:07:13.052
the function is just plain old continuous.

00:07:13.052 --> 00:07:16.187
The two-sided limit approaches
the value of the function.

00:07:16.187 --> 00:07:19.324
But at negative two, the
two-sided limit does not exist.

00:07:19.324 --> 00:07:21.179
When you approach from the left,

00:07:21.179 --> 00:07:23.051
it looks like you're approaching zero.

00:07:23.051 --> 00:07:24.785
F of x is equal to zero.

00:07:24.785 --> 00:07:26.833
When you approach from the right,

00:07:26.833 --> 00:07:29.954
it looks like f of x is
approaching negative three.

00:07:29.954 --> 00:07:33.532
So even though the two-sided
limit does not exist,

00:07:33.532 --> 00:07:35.188
we can still be good

00:07:35.188 --> 00:07:39.150
because the left-handed limit does exist.

00:07:39.150 --> 00:07:41.979
And the left-handed limit is approaching

00:07:41.979 --> 00:07:44.099
the value of the function.

00:07:44.099 --> 00:07:47.356
So we actually are continuous
over that interval.

00:07:47.356 --> 00:07:49.367
But then if we did the interval,

00:07:49.367 --> 00:07:53.828
if we did the closed
interval from negative two to

00:07:53.828 --> 00:07:56.166
negative two to one,

00:07:56.166 --> 00:07:57.543
pause the video and think about,

00:07:57.543 --> 00:07:59.270
based on what we just talked about,

00:07:59.270 --> 00:08:03.043
are we continuous over this interval?

00:08:03.043 --> 00:08:06.219
Well, we're going from negative two

00:08:06.219 --> 00:08:07.052
to one,

00:08:08.053 --> 00:08:10.563
and negative two is the lower bound.

00:08:10.563 --> 00:08:13.072
So is this right over here,

00:08:13.072 --> 00:08:15.112
is this right over here true?

00:08:15.112 --> 00:08:19.143
Is the limit as we approach
negative two from the right,

00:08:19.143 --> 00:08:22.353
is that the same thing
as f of negative two?

00:08:22.353 --> 00:08:24.302
Well, the limit as we
approach from the right

00:08:24.302 --> 00:08:26.520
seems to be approaching negative three,

00:08:26.520 --> 00:08:29.237
and f of negative two is zero.

00:08:29.237 --> 00:08:31.779
So this limit does not, this, this,

00:08:31.779 --> 00:08:35.130
these two things, the limit
as we approach from the right

00:08:35.130 --> 00:08:37.606
and the value of the
function are not the same.

00:08:37.606 --> 00:08:39.881
And so we do not have
that, I guess you could say

00:08:39.881 --> 00:08:42.470
that one-sided (laughs)
continuity at negative two.

00:08:42.470 --> 00:08:43.770
And that also makes sense.

00:08:43.770 --> 00:08:45.243
If I start at negative two,

00:08:45.243 --> 00:08:46.856
let me do this in a color you can see,

00:08:46.856 --> 00:08:48.293
if I start at negative two

00:08:48.293 --> 00:08:50.924
and I want to go the rest
of the interval to one,

00:08:50.924 --> 00:08:52.545
I have to pick up my pencil.

00:08:52.545 --> 00:08:55.339
Pick up my pencil, go here,
and then keep on going.

00:08:55.339 --> 00:08:59.506
So this is, we are not
continuous over that interval.


Better Takes Practice: The Full Story - Official SAT Practice on Khan Academy

WEBVTT
Kind: captions
Language: en

00:00:07.186 --> 00:00:09.310
- I couldn't stand up in front of a crowd.

00:00:09.310 --> 00:00:11.780
Everything was just intimidating to me.

00:00:11.780 --> 00:00:13.635
- I was a fish out of water.

00:00:13.635 --> 00:00:15.620
They're gonna think I'm a
crazy girl with a camera

00:00:15.620 --> 00:00:17.059
asking them do a pose for me.

00:00:17.059 --> 00:00:18.223
This is for the yearbook.

00:00:18.223 --> 00:00:19.727
- Oh, you should join the band.

00:00:19.727 --> 00:00:22.058
I'm, like, I don't know.

00:00:22.058 --> 00:00:24.836
- I've always been short,
so I'm just thinking

00:00:24.836 --> 00:00:27.356
about the others watching me.

00:00:27.356 --> 00:00:29.547
- I can't even count how nervous I was.

00:00:29.547 --> 00:00:31.165
- [Girl] Like the year before I was.

00:00:31.165 --> 00:00:31.998
- [Girl] I feel free.

00:00:31.998 --> 00:00:32.958
- [Boy] Then make it creative.

00:00:32.958 --> 00:00:35.733
- [Girl] I didn't like anybody.

00:00:35.733 --> 00:00:36.656
- [Girl] There is no reason to go

00:00:36.656 --> 00:00:39.989
if you're not going to give it your all.

00:00:48.338 --> 00:00:50.029
- It's really hard studying for the SAT

00:00:50.029 --> 00:00:51.769
especially as a senior because you have

00:00:51.769 --> 00:00:53.519
so many things to do.

00:00:56.560 --> 00:01:01.135
- Whether you want to do it or
you don't, it all starts now.

00:01:01.135 --> 00:01:03.743
- I will feel confident
if I practice more.

00:01:03.743 --> 00:01:07.910
- Some people come in talented,
but that's not enough.

00:01:10.078 --> 00:01:12.363
You have to set goals
that you have to hit.

00:01:12.363 --> 00:01:15.402
- I will put a 110% 'cause
this is what I want to do.

00:01:15.402 --> 00:01:19.152
This is my goal, and I
want to accomplish it.

00:01:20.260 --> 00:01:21.093
- Look at me now.

00:01:21.093 --> 00:01:23.282
I'm number one, I'm in charge.

00:01:23.282 --> 00:01:24.782
To the rear heart.

00:01:28.568 --> 00:01:32.573
- If it's state championship
or test like the SAT,

00:01:32.573 --> 00:01:36.740
it all comes from practice
which you've been doing before.

00:01:38.499 --> 00:01:40.319
- You shouldn't be as scared
to do it the second time

00:01:40.319 --> 00:01:42.473
because you already know what to expect.

00:01:42.473 --> 00:01:43.854
- The point of doing it is so your brain

00:01:43.854 --> 00:01:48.021
has that muscle memory like a
second nature kind of thing.

00:01:51.645 --> 00:01:52.603
- You've got it.

00:01:52.603 --> 00:01:53.436
You remember this.

00:01:53.436 --> 00:01:56.429
- [Boy] The game goes silent.

00:01:56.429 --> 00:01:59.012
(upbeat music)

00:02:27.614 --> 00:02:29.114
- In the moment, you don't really realize

00:02:29.114 --> 00:02:31.460
that shift of confidence.

00:02:31.460 --> 00:02:34.445
- You've trained so hard
to know what to expect,

00:02:34.445 --> 00:02:37.862
and then once you see it, it's like, wow!


Graphical limit example

WEBVTT
Kind: captions
Language: en

00:00:00.404 --> 00:00:02.873
- [Instructor] We are
asked, what is a reasonable

00:00:02.873 --> 00:00:07.785
estimate for the limit of g
of x as x approaches three?

00:00:07.785 --> 00:00:10.510
So what we have here in
blue, this is the graph

00:00:10.510 --> 00:00:14.929
of y is equal to g of x,
and we wanna think about

00:00:14.929 --> 00:00:17.798
what is the limit as x approaches three,

00:00:17.798 --> 00:00:20.367
so this is x equals three here.

00:00:20.367 --> 00:00:21.630
So what you need to do is,

00:00:21.630 --> 00:00:24.108
think about what is the
limit of this function

00:00:24.108 --> 00:00:26.547
as we approach three from the left,

00:00:26.547 --> 00:00:27.542
and we're also gonna think about

00:00:27.542 --> 00:00:28.956
what is the limit of this function,

00:00:28.956 --> 00:00:30.729
what does it appear to be from the graph,

00:00:30.729 --> 00:00:33.109
as we approach this value from the right.

00:00:33.109 --> 00:00:35.750
And if it looks like we're
approaching the same value,

00:00:35.750 --> 00:00:38.387
then that would be a reasonable
estimate for the limit,

00:00:38.387 --> 00:00:40.005
and the reason why they
say reasonable estimate

00:00:40.005 --> 00:00:42.403
is 'cause we're gonna do it by inspection.

00:00:42.403 --> 00:00:44.649
We don't have a lot more
information about the graph

00:00:44.649 --> 00:00:46.762
to know for sure, but from the graph,

00:00:46.762 --> 00:00:48.864
we can come up with a reasonable estimate.

00:00:48.864 --> 00:00:51.106
So pause this video and see
if you can figure it out

00:00:51.106 --> 00:00:52.106
on your own.

00:00:53.139 --> 00:00:57.275
Alright, so let's think
about it in two parts.

00:00:57.275 --> 00:01:00.665
Let's think about
approaching x equals three,

00:01:00.665 --> 00:01:03.095
or let's think about the
limit as x approaches three

00:01:03.095 --> 00:01:07.262
from the left, as we approach
x equals three from the left.

00:01:08.365 --> 00:01:11.505
So as we approach x equals
three from the left,

00:01:11.505 --> 00:01:15.005
our graph seems to be, our graph seems to,

00:01:16.599 --> 00:01:20.054
if I just eyeball it,
seems to be approaching

00:01:20.054 --> 00:01:21.832
the value four.

00:01:21.832 --> 00:01:25.999
So from the left, it looks
like we are approaching four.

00:01:27.364 --> 00:01:28.717
Approaching, or let me write it this way,

00:01:28.717 --> 00:01:31.541
g of x approaching four.

00:01:31.541 --> 00:01:33.791
G of x approaching four,

00:01:37.636 --> 00:01:40.886
as x approaches three from the left.

00:01:42.215 --> 00:01:44.044
Now let's think about it from the right.

00:01:44.044 --> 00:01:46.746
As x approaches three from the right,

00:01:46.746 --> 00:01:49.536
what does it look like
g of x is approaching?

00:01:49.536 --> 00:01:53.065
Well, it looks like g of x is
approaching negative three,

00:01:53.065 --> 00:01:56.998
as x approaches three from the right.

00:01:56.998 --> 00:02:00.165
So I could say, g of x approaching,

00:02:02.325 --> 00:02:06.492
approaching negative three
as x approaches three

00:02:08.474 --> 00:02:09.724
from the right.

00:02:12.239 --> 00:02:14.463
And so we have two different values here.

00:02:14.463 --> 00:02:16.015
When we approach from the left,

00:02:16.015 --> 00:02:18.418
it looks like g of x is approaching four,

00:02:18.418 --> 00:02:20.116
and when we approach from the right,

00:02:20.116 --> 00:02:22.933
it looks like g of x is
approaching negative three.

00:02:22.933 --> 00:02:24.600
And so because of that, we would say

00:02:24.600 --> 00:02:26.054
that this limit right over here,

00:02:26.054 --> 00:02:29.990
it's reasonable to say that
this limit doesn't exist.

00:02:29.990 --> 00:02:32.490
So I'll write, does not exist,

00:02:34.675 --> 00:02:39.277
based on looking at this
graph right over here.

00:02:39.277 --> 00:02:41.802
And a good clue that it won't exist

00:02:41.802 --> 00:02:45.457
is the x value where we're
trying to find the limit at,

00:02:45.457 --> 00:02:48.766
you see this jump in the
graph right over here,

00:02:48.766 --> 00:02:52.969
it is discontinuous, it jumps
from one value to another,

00:02:52.969 --> 00:02:57.136
which is a good clue that the
limit might not exist here.


Connecting limits and graphical behavior

WEBVTT
Kind: captions
Language: en

00:00:00.938 --> 00:00:02.656
- [Instructor] So we have the graph

00:00:02.656 --> 00:00:05.466
of y is equal to g of x right over here.

00:00:05.466 --> 00:00:07.904
And I wanna think about what is the limit

00:00:07.904 --> 00:00:09.821
as x approaches five

00:00:10.969 --> 00:00:11.802
of g of x?

00:00:13.128 --> 00:00:15.056
Well we've done this multiple times.

00:00:15.056 --> 00:00:17.052
Let's think about what g of x approaches

00:00:17.052 --> 00:00:19.769
as x approaches five from the left.

00:00:19.769 --> 00:00:23.763
g of x is approaching negative six.

00:00:23.763 --> 00:00:26.364
As x approaches five from the right,

00:00:26.364 --> 00:00:29.266
g of x looks like it's
approaching negative six.

00:00:29.266 --> 00:00:32.099
So a reasonable estimate
based on looking at this graph

00:00:32.099 --> 00:00:34.630
is that as x approaches five,

00:00:34.630 --> 00:00:37.649
g of x is approaching negative six.

00:00:37.649 --> 00:00:38.833
And it's worth noting

00:00:38.833 --> 00:00:41.271
that that's not what g of five is.

00:00:41.271 --> 00:00:43.639
g of five is a different value.

00:00:43.639 --> 00:00:45.613
But the whole point of this video

00:00:45.613 --> 00:00:48.399
is to appreciate all that a limit does.

00:00:48.399 --> 00:00:50.791
A limit only describes
the behavior of a function

00:00:50.791 --> 00:00:53.020
as it approaches a point.

00:00:53.020 --> 00:00:55.899
It doesn't tell us exactly
what's happening at that point,

00:00:55.899 --> 00:00:57.200
what g of five is,

00:00:57.200 --> 00:00:59.057
and it doesn't tell us much

00:00:59.057 --> 00:01:00.683
about the rest of the function,

00:01:00.683 --> 00:01:02.494
about the rest of the graph.

00:01:02.494 --> 00:01:05.745
For example, I could construct
many different functions

00:01:05.745 --> 00:01:08.252
for which the limit as x approaches five

00:01:08.252 --> 00:01:09.669
is equal to negative six,

00:01:09.669 --> 00:01:12.200
and they would look very
different from g of x.

00:01:12.200 --> 00:01:15.033
For example, I could say the limit of

00:01:15.033 --> 00:01:16.542
f of x

00:01:16.542 --> 00:01:19.096
as x approaches five

00:01:19.096 --> 00:01:20.652
is equal to negative six,

00:01:20.652 --> 00:01:23.136
and I can construct an
f of x that does this

00:01:23.136 --> 00:01:25.040
that looks very different than g of x.

00:01:25.040 --> 00:01:26.341
In fact if you're up for it,

00:01:26.341 --> 00:01:28.013
pause this video and see
if you can so the same,

00:01:28.013 --> 00:01:30.219
if you have some graph paper,
or even just sketch it.

00:01:30.219 --> 00:01:33.191
Well the key thing is that
the behavior of the function

00:01:33.191 --> 00:01:36.558
as x approaches five from both sides,

00:01:36.558 --> 00:01:37.672
from the left and the right,

00:01:37.672 --> 00:01:39.646
it has to be approaching negative six.

00:01:39.646 --> 00:01:40.896
So for example,

00:01:42.688 --> 00:01:45.915
a function that looks like this,

00:01:45.915 --> 00:01:48.028
so let me draw f of x,

00:01:48.028 --> 00:01:51.674
an f of x that looks like this,

00:01:51.674 --> 00:01:53.694
and is even defined right over there,

00:01:53.694 --> 00:01:57.339
and then does something like this.

00:01:57.339 --> 00:01:58.756
That would work.

00:01:58.756 --> 00:02:00.335
As we approach from the left,

00:02:00.335 --> 00:02:01.380
we're approaching negative six.

00:02:01.380 --> 00:02:02.750
As we approach from the right,

00:02:02.750 --> 00:02:04.747
we approaching negative six.

00:02:04.747 --> 00:02:07.510
You could have a function

00:02:07.510 --> 00:02:10.093
like this, let's say the limit,

00:02:11.480 --> 00:02:13.408
let's call it h of x,

00:02:13.408 --> 00:02:15.706
as x approaches five

00:02:15.706 --> 00:02:18.307
is equal to negative six.

00:02:18.307 --> 00:02:19.770
You could have a function like this,

00:02:19.770 --> 00:02:21.767
maybe it's defined up to there,

00:02:21.767 --> 00:02:24.042
then it's you have a circle there,

00:02:24.042 --> 00:02:26.527
and then it keeps going.

00:02:26.527 --> 00:02:31.148
Maybe it's not defined at
all for any of these values,

00:02:31.148 --> 00:02:33.052
and then maybe down here

00:02:33.052 --> 00:02:36.813
it is defined for all x values
greater than or equal to four

00:02:36.813 --> 00:02:39.600
and it just goes right
through negative six.

00:02:39.600 --> 00:02:40.854
So notice,

00:02:40.854 --> 00:02:42.293
all of these,

00:02:42.293 --> 00:02:44.801
all of these functions
as x approaches five,

00:02:44.801 --> 00:02:46.566
they all have the limit defined

00:02:46.566 --> 00:02:48.145
and it's equal to negative six,

00:02:48.145 --> 00:02:52.440
but these functions all look
very very very different.

00:02:52.440 --> 00:02:54.484
Now another thing to appreciate is

00:02:54.484 --> 00:02:56.132
for a given function,

00:02:56.132 --> 00:02:58.083
and let me delete these.

00:02:58.083 --> 00:02:59.801
Oftentimes we're asked to find the limits

00:02:59.801 --> 00:03:02.704
as x approaches some type
of an interesting value.

00:03:02.704 --> 00:03:03.795
So for example,

00:03:03.795 --> 00:03:05.467
x approaches five,

00:03:05.467 --> 00:03:06.883
five is interesting right over here

00:03:06.883 --> 00:03:09.948
because we have this point discontinuity.

00:03:09.948 --> 00:03:10.993
But you could take the limit

00:03:10.993 --> 00:03:12.827
on an infinite number of points

00:03:12.827 --> 00:03:15.057
for this function right over here.

00:03:15.057 --> 00:03:17.007
You could say the limit

00:03:17.007 --> 00:03:17.840
of g of x

00:03:19.492 --> 00:03:21.024
as x approaches,

00:03:21.024 --> 00:03:24.024
not x equals, as x approaches,

00:03:25.041 --> 00:03:26.481
one, what would that be?

00:03:26.481 --> 00:03:28.315
Pause the video and try to figure it out.

00:03:28.315 --> 00:03:29.569
Well let's see,

00:03:29.569 --> 00:03:32.959
as x approaches one
from the left-hand side,

00:03:32.959 --> 00:03:37.116
it looks like we are
approaching this value here.

00:03:37.116 --> 00:03:40.715
And as x approaches one
from the right-hand side,

00:03:40.715 --> 00:03:43.037
it looks like we are
approaching that value there.

00:03:43.037 --> 00:03:46.195
So that would be equal to g of one.

00:03:46.195 --> 00:03:48.377
That is equal to g of one

00:03:48.377 --> 00:03:49.979
based on that would be a reasonable,

00:03:49.979 --> 00:03:52.626
that's a reasonable conclusion to make

00:03:52.626 --> 00:03:54.089
looking at this graph.

00:03:54.089 --> 00:03:56.620
And if we were to
estimate that g of one is,

00:03:56.620 --> 00:04:00.382
looks like it's approximately negative 5.1

00:04:00.382 --> 00:04:02.132
or 5.2, negative 5.1.

00:04:05.096 --> 00:04:07.510
We could find the limit

00:04:07.510 --> 00:04:08.997
of g of x

00:04:08.997 --> 00:04:10.830
as x approaches pi.

00:04:12.828 --> 00:04:15.336
So pi is right around there.

00:04:15.336 --> 00:04:17.774
As x approaches pi from the left,

00:04:17.774 --> 00:04:19.980
we're approaching that value

00:04:19.980 --> 00:04:22.046
which just looks actually pretty close

00:04:22.046 --> 00:04:23.463
to the one we just thought about.

00:04:23.463 --> 00:04:25.134
As we approach from the right,

00:04:25.134 --> 00:04:26.203
we're approaching that value.

00:04:26.203 --> 00:04:27.503
And once again in this case,

00:04:27.503 --> 00:04:31.032
this is gonna be equal to g of pi.

00:04:31.032 --> 00:04:32.843
We don't have any interesting
discontinuities there

00:04:32.843 --> 00:04:34.655
or anything like that.

00:04:34.655 --> 00:04:36.837
So there's two big takeaways here.

00:04:36.837 --> 00:04:39.090
You can construct many different functions

00:04:39.090 --> 00:04:42.224
that would have the same limit at a point,

00:04:42.224 --> 00:04:44.221
and for a given function,

00:04:44.221 --> 00:04:46.659
you can take the limit
at many different points,

00:04:46.659 --> 00:04:49.608
in fact an infinite number
of different points.

00:04:49.608 --> 00:04:52.209
And it's important to point that out,

00:04:52.209 --> 00:04:53.672
no pun intended,

00:04:53.672 --> 00:04:56.760
because oftentimes we
get used to seeing limits

00:04:56.760 --> 00:04:59.036
only at points where something

00:04:59.036 --> 00:05:01.536
strange seems to be happening.


Better Takes Practice: Ian - Official SAT Practice on Khan Academy

WEBVTT
Kind: captions
Language: en

00:00:02.018 --> 00:00:03.984
- The first thing I
learned to play was a flam.

00:00:03.984 --> 00:00:06.098
You start putting them
together, getting the flam

00:00:06.098 --> 00:00:08.756
with a triplet, the flam accent.

00:00:08.756 --> 00:00:10.195
Then it turns into a different rudiment.

00:00:10.195 --> 00:00:12.487
You put a diddle, which is
the double note on one hand

00:00:12.487 --> 00:00:16.258
on the flam, and that's called the cheese.

00:00:16.258 --> 00:00:18.089
There's a lot of funny
names for percussion stuff.

00:00:18.089 --> 00:00:19.290
(percussive music)

00:00:19.290 --> 00:00:21.422
There's always more room for improvement,

00:00:21.422 --> 00:00:23.348
especially with my SAT scores.

00:00:23.348 --> 00:00:25.979
Some people come in talented,
but that's not enough.

00:00:25.979 --> 00:00:28.054
The more you do it, the
better you'll get at it.

00:00:28.054 --> 00:00:30.682
You would say talent, and you
need hard work and practice.

00:00:30.682 --> 00:00:32.407
- [Man] Hey, trumpets!

00:00:32.407 --> 00:00:34.381
- Push it with the toe.

00:00:34.381 --> 00:00:35.486
- [Man] Come back to the bandstand.

00:00:35.486 --> 00:00:36.755
- The point of doing that is so your brain

00:00:36.755 --> 00:00:39.258
has that muscle memory, that,

00:00:39.258 --> 00:00:41.381
like a second nature kind of thing.

00:00:41.381 --> 00:00:42.934
There's no better feeling than practicing

00:00:42.934 --> 00:00:45.528
that same, let's say, two measures

00:00:45.528 --> 00:00:47.024
(percussive band music)

00:00:47.024 --> 00:00:48.996
and finally getting perfect

00:00:48.996 --> 00:00:49.974
like finally, I got it.

00:00:49.974 --> 00:00:51.809
I can move on, this is
gonna sound amazing.

00:00:51.809 --> 00:00:52.990
I know it's gonna sound amazing.

00:00:52.990 --> 00:00:56.573
(exiting percussive music)


Better Takes Practice: Gillian - Official SAT Practice on Khan Academy

WEBVTT
Kind: captions
Language: en

00:00:00.842 --> 00:00:02.861
- When I look through
the lens, I feel like I'm

00:00:02.861 --> 00:00:04.192
in a whole new universe.

00:00:04.192 --> 00:00:06.982
Having a camera, I don't
know, it makes me different

00:00:06.982 --> 00:00:09.046
than other people, you know? (giggling)

00:00:09.046 --> 00:00:11.116
Getting that picture,
it's like you can't fake

00:00:11.116 --> 00:00:14.279
that expression, you
can't fake that emotion.

00:00:14.279 --> 00:00:15.112
You know what I mean?

00:00:15.112 --> 00:00:16.427
That's why I'm there.

00:00:16.427 --> 00:00:18.906
I say you know what I mean way too much.

00:00:18.906 --> 00:00:21.979
(uptempo music)

00:00:21.979 --> 00:00:22.967
It's for the yearbook.

00:00:22.967 --> 00:00:24.586
It's really hard studying for the SAT

00:00:24.586 --> 00:00:26.860
because you have so many things to do.

00:00:26.860 --> 00:00:28.719
You're not gonna get
better in one sitting.

00:00:28.719 --> 00:00:31.128
You kinda have to be immersed in it.

00:00:31.128 --> 00:00:33.589
You have to use that
experienced that you've gained

00:00:33.589 --> 00:00:35.158
over and over and over.

00:00:35.158 --> 00:00:37.673
Like you're able to spot the quality

00:00:37.673 --> 00:00:42.279
in something that you do
when you care about it.

00:00:42.279 --> 00:00:43.903
I'm usually like hey,
this is not good enough.

00:00:43.903 --> 00:00:48.374
I need to get better just
purely out of my own desire

00:00:48.374 --> 00:00:50.291
to do good, to do well.

00:00:51.674 --> 00:00:52.925
I'll say it how I want to say it.

00:00:52.925 --> 00:00:53.758
No, I'm just kidding.

00:00:53.758 --> 00:00:54.591
I'm joking.

00:00:54.591 --> 00:00:57.841
(upbeat hip hop music)


Better Takes Practice: Diana - Official SAT Practice on Khan Academy

WEBVTT
Kind: captions
Language: en

00:00:01.735 --> 00:00:03.168
- Used to stutter a lot.

00:00:03.168 --> 00:00:04.254
I couldn't speak to someone.

00:00:04.254 --> 00:00:05.400
I couldn't look at them in the eyes.

00:00:05.400 --> 00:00:07.140
Everything was just intimidating to me.

00:00:07.140 --> 00:00:08.705
I used to be a totally different person

00:00:08.705 --> 00:00:11.205
before I got into the program.

00:00:12.165 --> 00:00:12.998
Look at me now.

00:00:12.998 --> 00:00:14.347
I'm the group commander.

00:00:14.347 --> 00:00:15.180
I'm number one.

00:00:15.180 --> 00:00:16.013
I'm in charge.

00:00:16.013 --> 00:00:16.846
To the rear.

00:00:16.846 --> 00:00:17.679
March!

00:00:18.933 --> 00:00:21.541
I really wanna be a lawyer
inside the military.

00:00:21.541 --> 00:00:25.553
And I have to do a lot
of things to get there.

00:00:25.553 --> 00:00:27.735
That's what I love about it
because it pushed me to study

00:00:27.735 --> 00:00:29.818
just like ROTC pushed me.

00:00:30.995 --> 00:00:32.375
I'm a very determined person.

00:00:32.375 --> 00:00:34.233
I won't stop until I get what I want,

00:00:34.233 --> 00:00:38.341
so practice, practice, practice
and practice for my SAT.

00:00:38.341 --> 00:00:40.799
If I have to study more,
if I have to stay up,

00:00:40.799 --> 00:00:42.907
I will do it to get there.

00:00:42.907 --> 00:00:44.077
I know there's a reward at the end,

00:00:44.077 --> 00:00:45.997
but I'm not working for the reward.

00:00:45.997 --> 00:00:48.233
I'm working for something bigger.

00:00:48.233 --> 00:00:50.359
I'm gonna keep going because
this is what I wanna do.

00:00:50.359 --> 00:00:52.403
This is my goal, and
I wanna accomplish it.

00:00:52.403 --> 00:00:55.736
(upbeat, driving music)


Better Takes Practice: Azulaye - Official SAT Practice on Khan Academy

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:01.557
(cheerleaders talking over each other)

00:00:01.557 --> 00:00:04.871
- Jumps are the prettiest
thing that a cheerleader can do

00:00:04.871 --> 00:00:08.110
and just one part can mess it up.

00:00:08.110 --> 00:00:10.812
Once I throw her, I'm
just like, okay that's it.

00:00:10.812 --> 00:00:14.537
I'm not scared anymore, she's
already up there, I got it.

00:00:14.537 --> 00:00:17.966
Performing and taking a
test, it's all the same.

00:00:17.966 --> 00:00:20.474
I practice and practice and practice it,

00:00:20.474 --> 00:00:25.443
and I still don't feel as if
I got it, I practice more.

00:00:25.443 --> 00:00:28.186
I feel like there is no reason to go

00:00:28.186 --> 00:00:29.921
if you're not going to give it your all.

00:00:29.921 --> 00:00:31.648
I love it when the girls get so frustrated

00:00:31.648 --> 00:00:33.272
to the point where they're
mad at theirselves.

00:00:33.272 --> 00:00:36.008
Like I just want to walk
away, like it's all too much.

00:00:36.008 --> 00:00:37.195
But then it's like no, no, no, no,

00:00:37.195 --> 00:00:39.063
you can't quit, like I'm
not gonna let you give up

00:00:39.063 --> 00:00:40.809
because you didn't let me give up.

00:00:40.809 --> 00:00:43.769
There's always more that you
can do, there's always better.

00:00:43.769 --> 00:00:45.313
It's a rush at the same time,

00:00:45.313 --> 00:00:47.787
it's just like you got
it, you remember this,

00:00:47.787 --> 00:00:49.810
you've done this before.

00:00:49.810 --> 00:00:51.624
Once we get it set,

00:00:51.624 --> 00:00:54.203
then I'm like okay, it's go time.

00:00:54.203 --> 00:00:57.953
(energetic electronic music)


Better Takes Practice: Cameron - Official SAT Practice on Khan Academy

WEBVTT
Kind: captions
Language: en

00:00:01.625 --> 00:00:03.765
- After I've done my homework,
after I've learned all day,

00:00:03.765 --> 00:00:06.243
the one thing I want to
do is just make music.

00:00:06.243 --> 00:00:09.487
My car is the number one place
where I can just sit there

00:00:09.487 --> 00:00:12.304
and make the music
right there in my hands.

00:00:12.304 --> 00:00:16.202
At least until I run outta gas or battery.

00:00:16.202 --> 00:00:18.251
The SAT is extremely
important when it comes

00:00:18.251 --> 00:00:20.495
to getting into college.

00:00:20.495 --> 00:00:23.003
You can never be too
prepared for something.

00:00:23.003 --> 00:00:24.140
Like if you're trying to learn a song

00:00:24.140 --> 00:00:25.513
and you wanna perform it to people,

00:00:25.513 --> 00:00:27.173
ultimately you don't
want to go over it once

00:00:27.173 --> 00:00:28.429
and be like alright, I'm ready.

00:00:28.429 --> 00:00:30.474
You should always put time and practice

00:00:30.474 --> 00:00:31.940
into anything you do.

00:00:31.940 --> 00:00:33.037
Not only are you prepared,

00:00:33.037 --> 00:00:35.205
you also feel confident
in what you're doing.

00:00:35.205 --> 00:00:36.256
If you want to become anything

00:00:36.256 --> 00:00:38.192
there's a correct step you need to take.

00:00:38.192 --> 00:00:40.973
It's always baby steps and
it's always practicing.

00:00:40.973 --> 00:00:44.089
I want to make something that
people can really connect with

00:00:44.089 --> 00:00:46.228
and to be able to do that for a living.

00:00:46.228 --> 00:00:48.432
I feel a lot more confident

00:00:48.432 --> 00:00:50.709
doing things that I've practiced for.

00:00:50.709 --> 00:00:51.578
You don't want to do something

00:00:51.578 --> 00:00:55.745
that you haven't taken the
time to really get down.


Title: Better Takes Practice: D'Andre - Official SAT Practice on Khan Academy

WEBVTT
Kind: captions
Language: en

00:00:00.240 --> 00:00:01.987
(players chanting)

00:00:01.987 --> 00:00:03.131
- There's always pressure,

00:00:03.131 --> 00:00:06.048
it's just, when do you tune it out?

00:00:07.666 --> 00:00:08.765
Come on, I want you guys to go over it.

00:00:08.765 --> 00:00:09.598
Counter, no counter?

00:00:09.598 --> 00:00:11.574
It's not about what you're doing,

00:00:11.574 --> 00:00:14.901
it's about how you're doing it.

00:00:14.901 --> 00:00:16.897
So, whether that be me studying film,

00:00:16.897 --> 00:00:19.065
applying to colleges, or
just studying for a test

00:00:19.065 --> 00:00:21.560
like the SAT, it all
comes from your practice,

00:00:21.560 --> 00:00:23.906
which you've been doing before.

00:00:23.906 --> 00:00:26.159
We've done this hundreds of times,

00:00:26.159 --> 00:00:28.492
ran this thousands of times.

00:00:30.450 --> 00:00:32.862
The phrase that we use,
"Practice how we play,"

00:00:32.862 --> 00:00:34.612
that's pretty much our slogan,

00:00:34.612 --> 00:00:37.588
whether we're on the
field or off the field.

00:00:37.588 --> 00:00:40.339
It all starts now, so
working little by little

00:00:40.339 --> 00:00:43.099
to get to that goal, and we
practice, practice, practice

00:00:43.099 --> 00:00:45.170
so that when the game comes along,

00:00:45.170 --> 00:00:47.080
you already know what to expect.

00:00:47.080 --> 00:00:49.452
You just know what you're going to do.

00:00:49.452 --> 00:00:50.979
You can go out any day
and do the same thing

00:00:50.979 --> 00:00:53.646
over and over, and it'll happen.

00:00:55.059 --> 00:00:58.226
(inspirational music)


Better Takes Practice - Official SAT Practice on Khan Academy

WEBVTT
Kind: captions
Language: en

00:00:01.128 --> 00:00:05.231
- [Man] If the state championship
were tests like the SAT,

00:00:05.231 --> 00:00:07.285
it's all comes from your practice.

00:00:07.285 --> 00:00:10.330
- [Man] You can never be
too prepared for something.

00:00:10.330 --> 00:00:12.625
- [Woman] You have to use that
experience that you've gained

00:00:12.625 --> 00:00:14.825
over and over and over.

00:00:14.825 --> 00:00:16.890
- [Woman] I still don't
feel as if I got it,

00:00:16.890 --> 00:00:18.223
I practice more.

00:00:19.785 --> 00:00:20.996
- [Woman] You know there's
a reward at the end,

00:00:20.996 --> 00:00:22.875
but I'm working for the reward.

00:00:22.875 --> 00:00:24.419
I'm working for something bigger.

00:00:24.419 --> 00:00:27.086
(driving music)


Comparing Roman and Byzantine Empires

WEBVTT
Kind: captions
Language: en

00:00:00.625 --> 00:00:01.820
- [Instructor] We already
have several videos

00:00:01.820 --> 00:00:04.232
talking about the Byzantine
Empire which is really just

00:00:04.232 --> 00:00:07.840
the continuation of the
Roman Empire after its fall

00:00:07.840 --> 00:00:10.589
and they even call
themselves the Roman Empire.

00:00:10.589 --> 00:00:13.506
But I wanna do in this video
is a bit of a deep dive

00:00:13.506 --> 00:00:15.980
to make sure we understand
the different elements

00:00:15.980 --> 00:00:19.333
of continuity and change
between what we consider

00:00:19.333 --> 00:00:22.527
the Roman Empire when it
was one unified western

00:00:22.527 --> 00:00:26.318
and eastern Roman Empire
and then what we later call

00:00:26.318 --> 00:00:29.795
the Byzantine Empire, so what
was the same between them

00:00:29.795 --> 00:00:33.193
and then what changed over time?

00:00:33.193 --> 00:00:36.399
So let's just do a review,
this is what things look like

00:00:36.399 --> 00:00:38.398
at around the year 400.

00:00:38.398 --> 00:00:41.447
As you can see from an
administrative point of view,

00:00:41.447 --> 00:00:43.445
even though it was considered one empire,

00:00:43.445 --> 00:00:46.268
it was already being governed separately,

00:00:46.268 --> 00:00:48.094
the west being governed from Rome,

00:00:48.094 --> 00:00:51.042
the east being governed
from Constantinople.

00:00:51.042 --> 00:00:53.861
And most historians mark the
beginning of the Byzantine

00:00:53.861 --> 00:00:57.347
Empire with the rule of
Constantine, who moves the capital

00:00:57.347 --> 00:01:01.710
to Byzantium, it gets
renamed Constantinople.

00:01:01.710 --> 00:01:04.013
But as we've talked
about in multiple videos,

00:01:04.013 --> 00:01:08.180
in 476, you have the fall
of the western Roman Empire

00:01:09.298 --> 00:01:12.084
and the west becomes
fragmented, a bunch of various

00:01:12.084 --> 00:01:14.958
Germanic kingdoms, but
the eastern Roman Empire

00:01:14.958 --> 00:01:18.282
with its capital at
Constantinople, continues.

00:01:18.282 --> 00:01:20.975
And once again, they did not
call themselves the Byzantines,

00:01:20.975 --> 00:01:22.603
they called themselves the Romans,

00:01:22.603 --> 00:01:24.908
they called themselves the Roman Empire.

00:01:24.908 --> 00:01:26.827
It was only much much
later that historians

00:01:26.827 --> 00:01:29.847
tried to separate this
period of the Roman Empire

00:01:29.847 --> 00:01:32.645
by calling it the Byzantine Empire.

00:01:32.645 --> 00:01:35.794
There is a bit of a
resurgence under Justinian,

00:01:35.794 --> 00:01:39.075
he's able to capture
significant portions of the west

00:01:39.075 --> 00:01:42.553
including the Italian
peninsula but then over time

00:01:42.553 --> 00:01:46.258
the Byzantine Empire contracts,
especially in the east,

00:01:46.258 --> 00:01:49.590
it has to contend with
the spread of Islam.

00:01:49.590 --> 00:01:52.460
As we go even further in time,
as we enter into the second

00:01:52.460 --> 00:01:55.504
millennium, we can see
that the Muslim Turks

00:01:55.504 --> 00:01:59.632
make further inroads into
the Byzantine Empire.

00:01:59.632 --> 00:02:01.349
Also during the Fourth Crusades,

00:02:01.349 --> 00:02:05.234
western crusaders sack Constantinople.

00:02:05.234 --> 00:02:08.321
And we can go all the way to 1453

00:02:08.321 --> 00:02:12.240
where all that was left at the
time of the Byzantine Empire

00:02:12.240 --> 00:02:15.362
or you could say the eastern
Roman Empire is Constantinople

00:02:15.362 --> 00:02:19.529
and in 1453, that also
gets sacked by the Ottomans

00:02:20.407 --> 00:02:22.911
and that's the official end
of the Byzantine Empire,

00:02:22.911 --> 00:02:25.330
the eastern Roman Empire,
which you can see continues on

00:02:25.330 --> 00:02:28.431
for another 1000 years after the fall

00:02:28.431 --> 00:02:30.515
of the western Roman Empire.

00:02:30.515 --> 00:02:32.548
Now with that review out of the way,

00:02:32.548 --> 00:02:35.090
let's think about how the Byzantine Empire

00:02:35.090 --> 00:02:39.173
was the same and different
from the Roman Empire.

00:02:40.707 --> 00:02:43.645
So first let's think
about the center of power.

00:02:43.645 --> 00:02:46.755
Well the Roman Empire is
named after its seat of power

00:02:46.755 --> 00:02:49.799
during the great majority of its history.

00:02:49.799 --> 00:02:53.308
The seat of power of the
Roman Empire is Rome.

00:02:53.308 --> 00:02:57.041
Near the end of the western
Roman Empire it becomes Ravenna

00:02:57.041 --> 00:02:59.803
and of course we talk
about Constantine changing

00:02:59.803 --> 00:03:02.064
the capital to Byzantium
which eventually became

00:03:02.064 --> 00:03:04.724
Constantinople and
that's the official start

00:03:04.724 --> 00:03:06.877
of at least the roots
of the Byzantine Empire

00:03:06.877 --> 00:03:09.009
although Constantine was emperor of both.

00:03:09.009 --> 00:03:11.238
It's fair to say that Rome
was the capital of the Roman

00:03:11.238 --> 00:03:14.760
Empire from its early days as
a kingdom all the way until

00:03:14.760 --> 00:03:18.056
the first several centuries
of the common era.

00:03:18.056 --> 00:03:21.649
The roots of the Byzantine
Empire are with Constantine

00:03:21.649 --> 00:03:24.686
changing the capital, the
seat of power of the combined

00:03:24.686 --> 00:03:28.539
empire and moving it
from Rome to Byzantium,

00:03:28.539 --> 00:03:32.777
which will eventually be
called Constantinople.

00:03:32.777 --> 00:03:34.914
Now let's think about language.

00:03:34.914 --> 00:03:37.944
So the language of the
Roman Empire is Latin.

00:03:37.944 --> 00:03:40.649
In the early days of the Byzantine Empire,

00:03:40.649 --> 00:03:44.659
Latin is used in conjunction with Greek

00:03:44.659 --> 00:03:48.556
but over time, it becomes more Greek.

00:03:48.556 --> 00:03:50.758
In fact, Heraclius in the seventh century

00:03:50.758 --> 00:03:55.577
makes Greek the official
language of the Byzantine Empire.

00:03:55.577 --> 00:03:58.577
Now religion, for most of Roman history,

00:03:58.577 --> 00:04:01.879
their religion is the Roman Pantheon.

00:04:01.879 --> 00:04:05.343
Now near the end of what
is called the Roman Empire,

00:04:05.343 --> 00:04:08.838
when Constantine comes around
in the early fourth century,

00:04:08.838 --> 00:04:11.565
Christianity gets
legalized and Theodosius,

00:04:11.565 --> 00:04:16.347
who is the last emperor to
rule over both east and west,

00:04:16.347 --> 00:04:20.670
he makes Christianity
the official religion.

00:04:20.670 --> 00:04:23.199
Since the eastern Roman
Empire's roots, the Byzantine

00:04:23.199 --> 00:04:26.651
empire's roots are considered
to be with Constantine.

00:04:26.651 --> 00:04:30.359
It has a Christian
nature from the beginning

00:04:30.359 --> 00:04:33.974
and it only becomes more and
more Christian over time.

00:04:33.974 --> 00:04:37.094
In other videos, we will talk
about the eventual spiritual

00:04:37.094 --> 00:04:40.388
split between east and west,
the Latin Christian church

00:04:40.388 --> 00:04:43.335
and the Greek Christian church
and they're going to diverge

00:04:43.335 --> 00:04:46.572
more and more as we go into the year 1054

00:04:46.572 --> 00:04:49.162
when there is the official Great Schism.

00:04:49.162 --> 00:04:52.508
In terms of law, the Roman
Empire has a long tradition

00:04:52.508 --> 00:04:56.446
of law and I guess we could
just call it the Roman law.

00:04:56.446 --> 00:04:58.568
In fact, so profound
has its influence been

00:04:58.568 --> 00:05:00.939
on western civilization that many of our

00:05:00.939 --> 00:05:04.389
legal terms today come from Latin.

00:05:04.389 --> 00:05:06.663
What historians would
consider the Byzantine Empire

00:05:06.663 --> 00:05:10.863
would continue Roman law,
much of it written in Latin.

00:05:10.863 --> 00:05:13.795
Justinian would famously
try to reform Roman law,

00:05:13.795 --> 00:05:16.259
make it more consistent,
make it more clear.

00:05:16.259 --> 00:05:17.676
Justinian's code.

00:05:18.675 --> 00:05:23.208
And you have the emperor Leo
III has the famous Ecloga

00:05:23.208 --> 00:05:26.135
but as you have these revisions
and these reformations

00:05:26.135 --> 00:05:29.161
of Roman law, they are more
and more written in Greek

00:05:29.161 --> 00:05:31.283
than Latin and they do have more

00:05:31.283 --> 00:05:33.700
and more of a Christian influence.

00:05:33.700 --> 00:05:37.936
In terms of governance,
especially under the Roman Empire,

00:05:37.936 --> 00:05:42.255
the notion of a province
was the main subdivision

00:05:42.255 --> 00:05:45.940
under which the empire was governed.

00:05:45.940 --> 00:05:49.091
Once you have Emperor
Dioclesian come onto the scene

00:05:49.091 --> 00:05:51.456
and this is shortly before
the time of Constantine,

00:05:51.456 --> 00:05:56.108
he reformed it and he set up
what is known as a tetrarchy

00:05:56.108 --> 00:06:00.329
where you had these two emperors
of east and west and then

00:06:00.329 --> 00:06:03.527
you would have essentially
their subordinate emperors

00:06:03.527 --> 00:06:07.025
but along with that, he
redefined what a province is,

00:06:07.025 --> 00:06:09.358
so you had smaller provinces

00:06:10.545 --> 00:06:12.935
which then would go into
diocese, which would then go into

00:06:12.935 --> 00:06:16.071
prefects, which would
then go into a tetrarch.

00:06:16.071 --> 00:06:18.805
Once you have the start
of the Byzantine Empire,

00:06:18.805 --> 00:06:21.517
they would have elements of this.

00:06:21.517 --> 00:06:24.546
Constantine, remember Constantine
wasn't only the Byzantine,

00:06:24.546 --> 00:06:26.823
wasn't only the emperor of the east,

00:06:26.823 --> 00:06:28.930
he was emperor of both east and west,

00:06:28.930 --> 00:06:32.137
but he got rid of the tetrarchy
but he kept Dioclesian's

00:06:32.137 --> 00:06:35.437
notions of these smaller
provinces going into diocese,

00:06:35.437 --> 00:06:39.000
going into prefects, so
you have that continuity

00:06:39.000 --> 00:06:42.274
but then later on in
the mid seventh century,

00:06:42.274 --> 00:06:45.323
it was turned into more
of a feudal-themed system

00:06:45.323 --> 00:06:47.255
in the Byzantine Empire, and
once again, this was under

00:06:47.255 --> 00:06:51.382
Heraclius who also made
Greek the official language.

00:06:51.382 --> 00:06:53.396
And the reason why I say it's
feudal, it was comparable

00:06:53.396 --> 00:06:56.310
to the feudal system in
western Europe at the time,

00:06:56.310 --> 00:06:59.757
was that it provided land
grants to local rulers

00:06:59.757 --> 00:07:03.354
in exchange for their military
service and the ability

00:07:03.354 --> 00:07:07.104
for them to send resources
up to the emperor.

00:07:08.347 --> 00:07:11.166
In terms of culture, you
have many of the things

00:07:11.166 --> 00:07:13.030
that we associate with the Roman Empire,

00:07:13.030 --> 00:07:17.197
you have chariot racing,
you have gladiator fights,

00:07:18.513 --> 00:07:22.680
you have imperial birthdays,
you have the Olympics,

00:07:23.639 --> 00:07:25.943
which carries over from the
Ancient Greeks that actually

00:07:25.943 --> 00:07:30.110
lasts over 1000 years as we
go into the Roman Empire.

00:07:31.044 --> 00:07:33.863
Some of these continue
and some of them don't.

00:07:33.863 --> 00:07:36.613
So for example, the notion
of chariot racing does

00:07:36.613 --> 00:07:39.177
and famously Justinian
is almost overthrown

00:07:39.177 --> 00:07:44.010
after a rowdy chariot race,
you don't have the Olympics,

00:07:44.010 --> 00:07:46.646
Theodosius felt that it wasn't in line

00:07:46.646 --> 00:07:49.886
with Christian tradition,
but you did have things

00:07:49.886 --> 00:07:53.803
like imperial celebrations,
imperial birthdays,

00:07:54.677 --> 00:07:56.220
so the Byzantine Empire
definitely continued

00:07:56.220 --> 00:08:00.598
some of the traditions but
also eliminated others.

00:08:00.598 --> 00:08:02.573
So this is a just a rough overview.

00:08:02.573 --> 00:08:04.482
I encourage you to
think about it yourself.

00:08:04.482 --> 00:08:06.103
Are we missing any dimensions?

00:08:06.103 --> 00:08:09.523
And what other aspects do
you think were the same

00:08:09.523 --> 00:08:12.360
as we go from the traditional Roman Empire

00:08:12.360 --> 00:08:15.169
into the continuation of the Roman Empire,

00:08:15.169 --> 00:08:18.505
which historians will later
call the Byzantine Empire?


Comparison: Rise of empires

WEBVTT
Kind: captions
Language: en

00:00:00.656 --> 00:00:02.219
- [Instructor] What we're
going to do in this video

00:00:02.219 --> 00:00:06.011
is think about the rise of
empires and make the comparison

00:00:06.011 --> 00:00:10.232
with four very early empires
that we have studied,

00:00:10.232 --> 00:00:14.399
Achaemenid Persia, the Maurya
Empire in India, Han China,

00:00:17.125 --> 00:00:19.486
and the Roman Empire.

00:00:19.486 --> 00:00:22.647
So let's just start with
a general framework.

00:00:22.647 --> 00:00:26.230
So the first question
is what is an empire?

00:00:27.389 --> 00:00:30.145
A broad definition of an
empire is when one group

00:00:30.145 --> 00:00:33.895
has control over a fairly
diverse population.

00:00:35.370 --> 00:00:37.380
One group has control over another group

00:00:37.380 --> 00:00:40.032
that might have different
linguistic practices,

00:00:40.032 --> 00:00:44.136
different culture, that's when
it is considered an empire.

00:00:44.136 --> 00:00:45.249
Well what's the general framework

00:00:45.249 --> 00:00:48.014
for how empires tend to form?

00:00:48.014 --> 00:00:50.490
Well let's say that I
am a ruler and I control

00:00:50.490 --> 00:00:54.991
this territory right over
here and either through

00:00:54.991 --> 00:00:59.158
my charisma, my military tactics,
maybe I have a new weapon,

00:01:01.047 --> 00:01:04.106
some political intrigue,
some weak neighbors,

00:01:04.106 --> 00:01:07.666
I'm able to conquer some more
territory right over here.

00:01:07.666 --> 00:01:09.056
What does that do for me?

00:01:09.056 --> 00:01:12.056
As I expand, this gives me more land

00:01:14.782 --> 00:01:17.928
and more people to rule over

00:01:17.928 --> 00:01:22.095
and I can tax that land and
people to have more wealth

00:01:24.585 --> 00:01:28.472
and larger armies and so these two things

00:01:28.472 --> 00:01:31.935
are pretty good ingredients
to be able to take on

00:01:31.935 --> 00:01:36.102
even more of my neighbors
and expand even further.

00:01:37.699 --> 00:01:39.537
And so you might say well,
why doesn't that process

00:01:39.537 --> 00:01:42.454
just keep on going on indefinitely?

00:01:43.440 --> 00:01:47.056
Well it does go pretty far,
you see these various empires

00:01:47.056 --> 00:01:50.500
are quite large especially when
you consider the technology

00:01:50.500 --> 00:01:53.757
of the time, the communications
ability of the time

00:01:53.757 --> 00:01:57.146
but at some point, you
might have weak leadership,

00:01:57.146 --> 00:01:59.859
you might have trouble
controlling these large

00:01:59.859 --> 00:02:02.447
and spread out empires especially
if you can't communicate,

00:02:02.447 --> 00:02:04.424
if you can't get good information.

00:02:04.424 --> 00:02:05.710
But now let's dive a little bit deeper

00:02:05.710 --> 00:02:09.210
into the four empires we just referred to.

00:02:10.381 --> 00:02:14.126
So let's start Achaemenid
Persia, founded in 550 BCE

00:02:14.126 --> 00:02:16.228
by Cyrus the Great.

00:02:16.228 --> 00:02:19.238
This is so far in the past
that most of our accounts

00:02:19.238 --> 00:02:22.081
of how Cyrus comes to
power come from the Greeks

00:02:22.081 --> 00:02:24.529
who were not friends with the Persians,

00:02:24.529 --> 00:02:27.725
they were famous rivals,
but one thing comes clear

00:02:27.725 --> 00:02:30.264
in the narrative, which
is that Cyrus the Great

00:02:30.264 --> 00:02:33.918
was considered a very
strong and effective leader

00:02:33.918 --> 00:02:36.278
so I'll definitely put leadership there.

00:02:36.278 --> 00:02:39.017
He starts off as a relatively minor king

00:02:39.017 --> 00:02:42.564
subject to you could say
the emperor of Medes,

00:02:42.564 --> 00:02:46.065
who is his grandfather, and
he's able to overthrow him

00:02:46.065 --> 00:02:48.696
but because of his military leadership,

00:02:48.696 --> 00:02:51.400
his ability to bring people into the fold,

00:02:51.400 --> 00:02:53.978
he was known as being
tolerant of the people

00:02:53.978 --> 00:02:57.220
he would rule over, that
that all helped him control

00:02:57.220 --> 00:02:59.706
and expand a large empire.

00:02:59.706 --> 00:03:02.741
So I would say leadership is
definitely first for Cyrus

00:03:02.741 --> 00:03:06.749
the Great and then I would say
culture would be part of it.

00:03:06.749 --> 00:03:08.948
Now let's think about Maurya, India.

00:03:08.948 --> 00:03:12.543
Maurya, India was founded
by Chandragupta Maurya

00:03:12.543 --> 00:03:15.257
and here once again,
I would say leadership

00:03:15.257 --> 00:03:19.560
was a major factor, he was
aided by his political advisor

00:03:19.560 --> 00:03:22.350
Chanakya who is famous in Indian history

00:03:22.350 --> 00:03:24.945
for his strategic thinking.

00:03:24.945 --> 00:03:27.898
Chandragupta Maurya, legend
has it, met Alexander the Great

00:03:27.898 --> 00:03:30.622
when he came into the
Indus but once Alexander

00:03:30.622 --> 00:03:33.580
the Great left, there was a power vacuum.

00:03:33.580 --> 00:03:36.600
You could say that that
power vacuum helped

00:03:36.600 --> 00:03:39.110
the Maurya Empire be founded.

00:03:39.110 --> 00:03:41.236
It's similar to the notion
of having weaker neighbors

00:03:41.236 --> 00:03:44.216
once Alexander the Great left.

00:03:44.216 --> 00:03:47.497
And so Han China, Han
China is interesting.

00:03:47.497 --> 00:03:51.397
The first emperors of Han
China aren't the ones to first

00:03:51.397 --> 00:03:55.430
unify China, that happens
under the Qin Dynasty,

00:03:55.430 --> 00:04:00.047
Q-I-N, Qin Dynasty that
preceded the Han Dynasty

00:04:00.047 --> 00:04:03.560
and they were able to do
that by being very strong,

00:04:03.560 --> 00:04:07.580
very authoritarian, very
centralized but once the Qin

00:04:07.580 --> 00:04:11.915
emperor dies, it leaves
a clear power vacuum

00:04:11.915 --> 00:04:13.774
and then you have a succession battle

00:04:13.774 --> 00:04:16.721
but eventually the Han Dynasty is formed.

00:04:16.721 --> 00:04:19.632
One of the ways that the Han
Dynasty is able to keep power

00:04:19.632 --> 00:04:23.624
despite not being as
authoritarian as the Qin

00:04:23.624 --> 00:04:27.254
is that they revitalized
Confucianism and used

00:04:27.254 --> 00:04:30.313
that ideology and used that culture

00:04:30.313 --> 00:04:34.486
in order to more unify the Chinese people.

00:04:34.486 --> 00:04:37.745
The Roman empire we study in some detail.

00:04:37.745 --> 00:04:39.482
It's hard to pin a date on exactly

00:04:39.482 --> 00:04:41.237
when it becomes an empire.

00:04:41.237 --> 00:04:44.050
On this timeline, this
first period right over here

00:04:44.050 --> 00:04:47.144
is when we have the Roman
kingdom, then you have the Roman

00:04:47.144 --> 00:04:50.669
Republic, and then you
have the Roman Empire.

00:04:50.669 --> 00:04:53.983
And so you could debate when
it actually becomes an empire,

00:04:53.983 --> 00:04:57.514
even when it was an early
kingdom, it was conquering

00:04:57.514 --> 00:05:01.011
neighboring people on
the Italian peninsula

00:05:01.011 --> 00:05:04.249
and at that time period, it
might have felt like an empire

00:05:04.249 --> 00:05:06.433
because those people
might have felt different.

00:05:06.433 --> 00:05:10.005
As time passed and they
were under a unified state,

00:05:10.005 --> 00:05:13.206
under a unified kingdom, they
probably felt more similar

00:05:13.206 --> 00:05:15.740
but then when they conquered
even more territory,

00:05:15.740 --> 00:05:18.794
that might have felt more
and more like an empire.

00:05:18.794 --> 00:05:20.960
But what is clear is even as we get

00:05:20.960 --> 00:05:24.632
into the late republic
period, it was an empire.

00:05:24.632 --> 00:05:28.234
Julius Caesar famously
conquered Gaul, these Germanic

00:05:28.234 --> 00:05:31.872
peoples, before coming back
and essentially taking control

00:05:31.872 --> 00:05:34.407
to be succeeded by the
first official Roman Empire

00:05:34.407 --> 00:05:38.516
after a long and bloody
civil war, Augustus Caesar.

00:05:38.516 --> 00:05:41.665
These other three empires
happened relatively quickly,

00:05:41.665 --> 00:05:45.510
we're talking within a
period of less than 50 years

00:05:45.510 --> 00:05:49.069
while the Roman Empire took
hundreds of years to form.

00:05:49.069 --> 00:05:53.933
And so it's hard to ascribe
the empire to any one leader.

00:05:53.933 --> 00:05:58.125
You could say that there
was a culture of expansion,

00:05:58.125 --> 00:05:59.887
one could make the argument
that they were more

00:05:59.887 --> 00:06:03.003
technologically sophisticated
than some of their neighbors,

00:06:03.003 --> 00:06:05.988
especially when it came to military might

00:06:05.988 --> 00:06:10.021
and as it expanded, it definitely
was able to take advantage

00:06:10.021 --> 00:06:14.726
of weak neighbors so now
let's just take a step back.

00:06:14.726 --> 00:06:18.403
What we've done in this exercise
is a rough approximation

00:06:18.403 --> 00:06:20.150
of the various dimensions that might

00:06:20.150 --> 00:06:22.706
lead to an empire rising.

00:06:22.706 --> 00:06:25.490
It's by no means comprehensive
and I suggest for you

00:06:25.490 --> 00:06:28.533
to think about what dimensions
would you add to this?

00:06:28.533 --> 00:06:30.652
Maybe you could add a political dimension

00:06:30.652 --> 00:06:32.348
or maybe that's captured by leadership.

00:06:32.348 --> 00:06:34.424
Maybe you would add an economic dimension,

00:06:34.424 --> 00:06:36.482
how much wealth a nation has.

00:06:36.482 --> 00:06:39.082
And as we go forward in history,
we're gonna see different

00:06:39.082 --> 00:06:41.455
weights on these different dimensions

00:06:41.455 --> 00:06:44.604
for how important they
are for empire formation.

00:06:44.604 --> 00:06:47.834
Especially as we get closer
and closer to modern times,

00:06:47.834 --> 00:06:50.854
technology increases as a factor

00:06:50.854 --> 00:06:53.295
in terms of creating an empire.

00:06:53.295 --> 00:06:56.319
Ideology plays a
significant role in empires

00:06:56.319 --> 00:06:59.718
based on religion but we
also have empires based on

00:06:59.718 --> 00:07:04.344
economic ideology,
communism versus capitalism.

00:07:04.344 --> 00:07:06.758
And on political ideology.

00:07:06.758 --> 00:07:10.281
And does an empire have
to be strict control?

00:07:10.281 --> 00:07:11.855
Can you have a cultural empire

00:07:11.855 --> 00:07:16.754
without necessarily having
direct control over people?

00:07:16.754 --> 00:07:18.914
So I will leave you with these questions,

00:07:18.914 --> 00:07:20.474
they're fascinating
questions to think about

00:07:20.474 --> 00:07:22.930
within the context of these empires

00:07:22.930 --> 00:07:26.005
but also as we study all of world history.


Continuity-Sikhism connections to Hinduism and Islam

WEBVTT
Kind: captions
Language: en

00:00:00.740 --> 00:00:02.806
- [Instructor] In previous
videos, we've gone into

00:00:02.806 --> 00:00:05.768
reasonable depth on the
narrative of how the Sikh

00:00:05.768 --> 00:00:08.692
religion was started,
initially by Guru Nanak

00:00:08.692 --> 00:00:11.479
and then it how it developed
under the next gurus

00:00:11.479 --> 00:00:13.655
all the way until the
tenth guru and finally

00:00:13.655 --> 00:00:16.963
as it was compiled in
the Guru Granth Sahib,

00:00:16.963 --> 00:00:21.220
which is considered by Sikhs
to be the last and final guru.

00:00:21.220 --> 00:00:25.498
Sikhism is oftentimes compared
to both Hinduism and Islam,

00:00:25.498 --> 00:00:28.862
sometimes with reference to
the idea that it has elements

00:00:28.862 --> 00:00:31.207
of both, while others would argue that no,

00:00:31.207 --> 00:00:34.183
it is a completely independent
religion and any similarity

00:00:34.183 --> 00:00:38.756
is just coincidental, so let's
tackle that central question.

00:00:38.756 --> 00:00:42.870
What elements of continuity
does Sikhism represent?

00:00:42.870 --> 00:00:45.776
And in this video, we're
gonna think about continuity

00:00:45.776 --> 00:00:49.477
in terms of religious
continuity and in particular,

00:00:49.477 --> 00:00:53.791
does it have elements from
Islam or Hinduism in it?

00:00:53.791 --> 00:00:56.764
So we could first focus on
some of the cultural trappings

00:00:56.764 --> 00:00:59.449
or some of the historical
trappings of Sikhism

00:00:59.449 --> 00:01:03.376
and think about the connections
to both Hinduism and Islam.

00:01:03.376 --> 00:01:06.906
The first obvious connections
is that Guru Nanak,

00:01:06.906 --> 00:01:09.401
the first guru, and
many of the early gurus

00:01:09.401 --> 00:01:11.568
grew up in Hindu families.

00:01:14.564 --> 00:01:17.357
But there are also cultural
connections to Islam.

00:01:17.357 --> 00:01:22.180
The Sikh religion emerges in
Punjab, which is where or near

00:01:22.180 --> 00:01:26.027
the various Muslim rulers of
the time held their capitals,

00:01:26.027 --> 00:01:27.798
whether we're talking
about the Delhi sultanate,

00:01:27.798 --> 00:01:31.329
which was in power for over
250 years when Sikhism started

00:01:31.329 --> 00:01:34.935
to emerge with Guru Nanak,
but also the Moghul empire,

00:01:34.935 --> 00:01:38.215
which really developed in its
early stages at the same time

00:01:38.215 --> 00:01:40.605
that Sikhism develops, so
that many of the followers

00:01:40.605 --> 00:01:43.772
of Sikhism were both Hindu and Muslim.

00:01:45.579 --> 00:01:49.305
A lot of the terminology
of Sikhism borrows words

00:01:49.305 --> 00:01:53.133
and borrows ideas from
both Islam and Hinduism.

00:01:53.133 --> 00:01:57.168
The word Allah is used
to refer to god in parts

00:01:57.168 --> 00:02:01.478
of the Guru Granth Sahib
but so is the word Ram.

00:02:01.478 --> 00:02:04.916
One of the first and closest
followers of Guru Nanak,

00:02:04.916 --> 00:02:08.641
who was with him most of
his life was Bhai Mardana

00:02:08.641 --> 00:02:12.271
and even today, many
pictures of Guru Nanak

00:02:12.271 --> 00:02:15.143
would have Bhai Mardana in them.

00:02:15.143 --> 00:02:17.833
Guru Nanak famously as
someone who was spiritually

00:02:17.833 --> 00:02:20.306
precocious and spiritually curious,

00:02:20.306 --> 00:02:23.478
traveled through India and
Persia and the Middle East

00:02:23.478 --> 00:02:28.045
so he visited many temples
but there's also many historic

00:02:28.045 --> 00:02:32.428
accounts of him going to
Mecca and performing hajj.

00:02:32.428 --> 00:02:35.155
The Guru Granth Sahib, which
is considered the spiritual

00:02:35.155 --> 00:02:38.499
book the 11th and final
guru for the Sikhs,

00:02:38.499 --> 00:02:41.183
of the contributors to
them, you have Kabir,

00:02:41.183 --> 00:02:44.883
who grew up in a Muslim
family, he lived either around

00:02:44.883 --> 00:02:48.391
the time of Guru Nanak or in
the century before Guru Nanak

00:02:48.391 --> 00:02:50.847
and would write about both Allah and Ram,

00:02:50.847 --> 00:02:53.745
although he was often critical
of both Hinduism and Islam,

00:02:53.745 --> 00:02:58.480
and you also have Shaikh Farid,
who was a Muslim Sufi writer

00:02:58.480 --> 00:03:01.545
and spiritual figure and
he has also contributed

00:03:01.545 --> 00:03:03.405
to the Guru Granth Sahib.

00:03:03.405 --> 00:03:06.389
There's also important rituals
that come from Hinduism,

00:03:06.389 --> 00:03:10.512
so for example, when Sikhs
pass away, like Hindus,

00:03:10.512 --> 00:03:13.742
they are cremated, so
just looking at this list,

00:03:13.742 --> 00:03:16.448
you immediately see that
there's definitely cultural

00:03:16.448 --> 00:03:18.267
elements whether we're
talking about words,

00:03:18.267 --> 00:03:19.841
whether we're talking about rituals,

00:03:19.841 --> 00:03:21.515
whether we're talking about
even just the historical

00:03:21.515 --> 00:03:23.690
narrative of how and where Sikhism started

00:03:23.690 --> 00:03:26.550
that are closely tied to ideas of Hinduism

00:03:26.550 --> 00:03:29.671
and closely tied to ideas of Islam.

00:03:29.671 --> 00:03:32.059
But now let's look at the
scripture itself and see if

00:03:32.059 --> 00:03:36.238
we can glean any more
similarities or differences.

00:03:36.238 --> 00:03:40.893
This is the Mool Mantar
which means main mantra

00:03:40.893 --> 00:03:43.976
or the basic teaching of
Sikhism and it comes from

00:03:43.976 --> 00:03:46.522
Guru Nanak and this is
an English translation,

00:03:46.522 --> 00:03:49.376
you'll see variations of
this but it essentially says

00:03:49.376 --> 00:03:53.126
one universal creator
god, the name is truth,

00:03:54.930 --> 00:03:59.094
creative being personified,
no fear, no hatred,

00:03:59.094 --> 00:04:03.623
image of the undying,
beyond birth, self-existent,

00:04:03.623 --> 00:04:05.708
by guru's grace.

00:04:05.708 --> 00:04:07.950
Throughout the Guru Granth
Sahib and much of the writings

00:04:07.950 --> 00:04:12.237
of especially Guru Nanak
focus on devotion to god,

00:04:12.237 --> 00:04:15.019
the one universal god, and
so many of you might think,

00:04:15.019 --> 00:04:17.209
well that seems to have
connections to Islam

00:04:17.209 --> 00:04:19.164
but then you could say,
well even in Hinduism,

00:04:19.164 --> 00:04:22.267
although there are many aspects
of god, the various deities,

00:04:22.267 --> 00:04:25.909
but there's this notion of a
fundamental reality of Brahman

00:04:25.909 --> 00:04:28.201
so maybe it has elements of
that or maybe this is just

00:04:28.201 --> 00:04:30.706
independently developed but
there definitely are parts

00:04:30.706 --> 00:04:34.303
of the Guru Granth Sahib
which seem to have elements

00:04:34.303 --> 00:04:36.667
that are close to Islam.

00:04:36.667 --> 00:04:38.658
This is a quote from Guru Nanak.

00:04:38.658 --> 00:04:41.600
He is Allah, the unknowable,
the inaccessible,

00:04:41.600 --> 00:04:43.874
all-powerful and merciful creator.

00:04:43.874 --> 00:04:47.991
So one argument is he's using
the Arabic word for god,

00:04:47.991 --> 00:04:49.254
he's using Allah.

00:04:49.254 --> 00:04:51.445
Now another argument,
counterargument, would be well,

00:04:51.445 --> 00:04:53.961
he's just using the language
that his followers knew

00:04:53.961 --> 00:04:56.555
and many of his followers
were Muslim and so would have

00:04:56.555 --> 00:04:59.651
used the word Allah for
god, but he is not saying

00:04:59.651 --> 00:05:02.018
that it necessarily has to be the exact

00:05:02.018 --> 00:05:05.065
concept of god as in Islam.

00:05:05.065 --> 00:05:07.113
Now this is from Kabir.

00:05:07.113 --> 00:05:10.395
Someone sets up a stone idol
and all the world worships it

00:05:10.395 --> 00:05:13.483
as the lord, those who hold to this belief

00:05:13.483 --> 00:05:15.909
will be drowned in the river of darkness,

00:05:15.909 --> 00:05:17.784
and this is in the Guru Granth Sahib.

00:05:17.784 --> 00:05:20.281
This notion of being against idol worship

00:05:20.281 --> 00:05:22.881
comes out very clear in this
quotation and that is another

00:05:22.881 --> 00:05:26.843
idea that is often associated with Islam.

00:05:26.843 --> 00:05:27.767
But as I mentioned,

00:05:27.767 --> 00:05:30.444
there's also many parallels with Hinduism.

00:05:30.444 --> 00:05:32.637
In the first video on
Sikhism, I gave you this quote

00:05:32.637 --> 00:05:36.225
from Guru Nanak, the world is
a drama, staged in a dream.

00:05:36.225 --> 00:05:39.250
Which alludes to the Hindu notion of maya,

00:05:39.250 --> 00:05:41.641
the physical reality is all an illusion,

00:05:41.641 --> 00:05:44.403
we wanna pierce through that veil.

00:05:44.403 --> 00:05:46.770
What should the yogi have to fear?

00:05:46.770 --> 00:05:50.584
Trees, plants, and all
that is inside and outside

00:05:50.584 --> 00:05:51.751
is he himself.

00:05:53.398 --> 00:05:55.544
So this is an idea that
we get very clearly

00:05:55.544 --> 00:05:58.738
from the Upanishads,
any notion of duality,

00:05:58.738 --> 00:06:02.508
of me being different from
you or even one versus god,

00:06:02.508 --> 00:06:05.805
it's all an illusion, all is one.

00:06:05.805 --> 00:06:10.202
By the karma of past actions,
the robe of this physical body

00:06:10.202 --> 00:06:14.369
is obtained, by his grace the
gate of liberation is found.

00:06:15.965 --> 00:06:19.560
So clear references to the
Hindu notions of karma,

00:06:19.560 --> 00:06:23.230
that action drives
consequences, that you enter one

00:06:23.230 --> 00:06:26.735
physical body after another,
but that's not your true self,

00:06:26.735 --> 00:06:29.865
the robe of this physical,
there's a true self

00:06:29.865 --> 00:06:34.194
and eventually, through the
grace of the ultimate reality,

00:06:34.194 --> 00:06:38.078
you might be able to have
liberation, have moksha,

00:06:38.078 --> 00:06:40.758
so clear Hindu parallels as well.

00:06:40.758 --> 00:06:44.073
One angle is that Guru Nanak
and Sikhism was attempting

00:06:44.073 --> 00:06:47.862
a reformation of both, taking
elements that were compelling

00:06:47.862 --> 00:06:50.882
in either and then purifying
them, making them more

00:06:50.882 --> 00:06:54.160
internal focused, less focused on ritual,

00:06:54.160 --> 00:06:57.691
less focused on the external,
and more focused on meditation

00:06:57.691 --> 00:06:59.022
and the true self.

00:06:59.022 --> 00:07:01.766
There's a lot of quotations
in reference to both religions

00:07:01.766 --> 00:07:04.738
that make it clear that
it was something different

00:07:04.738 --> 00:07:08.439
and is critical of at least
how both religions seemed

00:07:08.439 --> 00:07:11.606
to be practiced in India at that time.

00:07:12.642 --> 00:07:15.604
Guru Nanak famously
said there is no Hindu,

00:07:15.604 --> 00:07:17.984
there is no Musalman.

00:07:17.984 --> 00:07:20.170
Most people feel that he's
saying this distinction

00:07:20.170 --> 00:07:22.427
that we make between human
beings based on these

00:07:22.427 --> 00:07:24.751
belief systems, that
these are superficial,

00:07:24.751 --> 00:07:27.448
that these are to some degree transient,

00:07:27.448 --> 00:07:29.568
that we are all part of the universal,

00:07:29.568 --> 00:07:32.649
part of the ultimate reality, part of god.

00:07:32.649 --> 00:07:35.574
This is from Guru Arjan,
the Muslim god Allah

00:07:35.574 --> 00:07:40.113
and the Hindu god Paarbrahm
are one and the same.

00:07:40.113 --> 00:07:43.016
So here, trying to unify
these ideas, and listen,

00:07:43.016 --> 00:07:45.696
this is in a context where many
of the followers are Muslim

00:07:45.696 --> 00:07:47.979
and many are Hindu and putting it in words

00:07:47.979 --> 00:07:49.862
that they understand.

00:07:49.862 --> 00:07:52.700
My body and breath of
life belong to Allah,

00:07:52.700 --> 00:07:55.529
to Ram, the god of both.

00:07:55.529 --> 00:07:58.691
So once again it's this
bhakti, this devotional aspect,

00:07:58.691 --> 00:08:02.192
surrendering to god and using
the terminology that would be

00:08:02.192 --> 00:08:06.359
familiar to people in that
time and in that space.

00:08:07.252 --> 00:08:09.335
So I encourage you, go
out there, research,

00:08:09.335 --> 00:08:12.161
think about it for yourself,
Sikhism for sure has its own

00:08:12.161 --> 00:08:15.597
unique identity and
pretty much every religion

00:08:15.597 --> 00:08:18.504
is a product of the
context in which it emerged

00:08:18.504 --> 00:08:20.559
and has elements from other religions,

00:08:20.559 --> 00:08:22.449
whether or not that
was done intentionally,

00:08:22.449 --> 00:08:25.791
whether or not it's chance,
there does seem to be parallels.

00:08:25.791 --> 00:08:28.785
We can make a whole tree
of religions if we like,

00:08:28.785 --> 00:08:33.108
if we put Sikhism right here,
the question mark of this

00:08:33.108 --> 00:08:37.059
video is you have this narrative of Islam,

00:08:37.059 --> 00:08:40.196
to what degree does it influence Sikhism?

00:08:40.196 --> 00:08:43.632
And many would say that especially
the Sufi orders of Islam

00:08:43.632 --> 00:08:45.756
have much to do with Sikhism.

00:08:45.756 --> 00:08:49.702
Sufism is a school of Islam
that is more inward looking,

00:08:49.702 --> 00:08:52.201
that is about devotional love to god

00:08:52.201 --> 00:08:54.987
and that's what a lot of
Sikhism is focused on,

00:08:54.987 --> 00:08:58.002
but as mentioned, one could
also think about Hinduism,

00:08:58.002 --> 00:09:00.698
which is much older than
pretty much any other living

00:09:00.698 --> 00:09:03.825
religion today and in other videos,

00:09:03.825 --> 00:09:06.983
we talk about the bhakti movement,
which is about devotional

00:09:06.983 --> 00:09:10.697
love to god, there's also a
school of thought in Hinduism

00:09:10.697 --> 00:09:13.674
known as Vedanta, which is
more focused on the core

00:09:13.674 --> 00:09:16.037
spiritual ideas of the Upanishads,

00:09:16.037 --> 00:09:19.406
the notion of the ultimate
self, the ultimate reality,

00:09:19.406 --> 00:09:21.979
escaping from the cycle
of births and deaths,

00:09:21.979 --> 00:09:24.853
from samsara, achieving
liberation, moksha.

00:09:24.853 --> 00:09:27.702
All of these ideas are in Sikhism

00:09:27.702 --> 00:09:29.651
and to make the point clear
that all of our major religions

00:09:29.651 --> 00:09:34.232
are connected to each other,
we can keep drawing this tree.

00:09:34.232 --> 00:09:38.130
We talk about how Buddhism
springs out of Hinduism,

00:09:38.130 --> 00:09:40.843
that Buddha was a Hindu and
it might have been in reaction

00:09:40.843 --> 00:09:44.123
to some of the ritual and
the caste that Buddha saw

00:09:44.123 --> 00:09:46.396
in Hinduism or at least in Hindu culture.

00:09:46.396 --> 00:09:47.683
In fact, some of those same motivations

00:09:47.683 --> 00:09:49.974
might have motivated Guru Nanak.

00:09:49.974 --> 00:09:51.953
Islam, we talk about in other videos,

00:09:51.953 --> 00:09:56.120
famously emerges from a
Judeo-Christian tradition.

00:09:57.162 --> 00:10:00.360
The most important prophets
in Islam after Mohammed

00:10:00.360 --> 00:10:04.465
are Jesus, Moses, and Abraham
and Christianity of course

00:10:04.465 --> 00:10:08.632
comes out of a Jewish
tradition, Jesus was Jewish.

00:10:10.320 --> 00:10:12.438
And one could say that there's
even some direct connections

00:10:12.438 --> 00:10:16.843
between Judaism and Islam,
notions of not eating pork,

00:10:16.843 --> 00:10:21.318
notions of halal and kosher,
ideas of circumcision.

00:10:21.318 --> 00:10:24.102
And one could even argue
that Judaism and Islam

00:10:24.102 --> 00:10:27.352
also have close ties to Zoroastrianism,

00:10:28.276 --> 00:10:31.855
a very ancient monotheistic
religion and Cyrus the Great

00:10:31.855 --> 00:10:35.382
of Persia was the one who
really spread Zoroastrianism

00:10:35.382 --> 00:10:39.107
and he is considered a messiah
amongst the Jewish people

00:10:39.107 --> 00:10:41.990
because he liberated them
from the Babylonian captivity,

00:10:41.990 --> 00:10:44.112
helped them re-settle in Jerusalem,

00:10:44.112 --> 00:10:47.434
and helped rebuild the
temple at Jerusalem.

00:10:47.434 --> 00:10:50.340
Zoroastrianism also has ties to Islam.

00:10:50.340 --> 00:10:54.323
Zoroastrians pray five times
a day just like Muslims,

00:10:54.323 --> 00:10:56.667
they have the ritual
bathing before the prayer,

00:10:56.667 --> 00:10:59.439
just like Muslims, at
the same time of day.

00:10:59.439 --> 00:11:01.809
So once again, amongst
all of these religions,

00:11:01.809 --> 00:11:04.161
they definitely came in
contact with each other

00:11:04.161 --> 00:11:06.836
and you definitely have
ideas that are shared

00:11:06.836 --> 00:11:09.338
amongst the religions, so with that,

00:11:09.338 --> 00:11:12.877
I'll leave you with one
last quote from Guru Nanak.

00:11:12.877 --> 00:11:16.064
And this one would arguable
be addressed to his Muslim

00:11:16.064 --> 00:11:19.127
followers but it gives
you a sense of his trying

00:11:19.127 --> 00:11:21.140
to bring people back to the internal,

00:11:21.140 --> 00:11:24.232
trying to make people less
focused on external ritual,

00:11:24.232 --> 00:11:28.704
external physical reality,
and more on internal goodness

00:11:28.704 --> 00:11:31.101
and your actions being more important

00:11:31.101 --> 00:11:33.935
than your words or your rituals.

00:11:33.935 --> 00:11:37.825
"Make kindness your mosque,
sincerity your prayer carpet,

00:11:37.825 --> 00:11:40.620
"what is just and lawful your Quran,

00:11:40.620 --> 00:11:44.761
"modesty your circumcision,
civility your fasting,

00:11:44.761 --> 00:11:48.760
"so shalt thou be a
Musalman," or a Muslim.

00:11:48.760 --> 00:11:51.846
"Make right conduct your
Kaaba," making reference

00:11:51.846 --> 00:11:55.875
to the pilgrimage site Muslims
go to and pray towards,

00:11:55.875 --> 00:11:58.888
"truth your spiritual
guide, good works your creed

00:11:58.888 --> 00:12:01.870
"and your prayer, the
will of god your rosary,

00:12:01.870 --> 00:12:05.787
"and god will preserve
your honor," Guru Nanak.


Contextualization--Islam

WEBVTT
Kind: captions
Language: en

00:00:00.261 --> 00:00:01.291
- [Instructor] Here is a passage

00:00:01.291 --> 00:00:03.543
from the Scottish philosopher, writer,

00:00:03.543 --> 00:00:08.168
even a little bit of mathematics,
historian Thomas Carlyle.

00:00:08.168 --> 00:00:11.280
And, he wrote this On
Heroes, Hero-Worship,

00:00:11.280 --> 00:00:13.188
& the Heroic in History.

00:00:13.188 --> 00:00:15.839
And this is in reference to his view

00:00:15.839 --> 00:00:18.640
on Mohammed and the spread of Islam.

00:00:18.640 --> 00:00:20.839
A poor shepherd people,

00:00:20.839 --> 00:00:24.023
he's referring to the
Arabs before Mohammed,

00:00:24.023 --> 00:00:26.125
roaming unnoticed in its deserts

00:00:26.125 --> 00:00:28.214
since the creation of the world:

00:00:28.214 --> 00:00:30.877
a Hero-Prophet was sent down to them

00:00:30.877 --> 00:00:33.075
with a word they could believe;

00:00:33.075 --> 00:00:37.213
see the unnoticed becomes
the world-notable,

00:00:37.213 --> 00:00:39.697
the small has grown world-great;

00:00:39.697 --> 00:00:41.404
within one century afterwards,

00:00:41.404 --> 00:00:45.923
Arabia is at Grenada on
this hand, at Delhi on that.

00:00:45.923 --> 00:00:49.182
He's speaking of within 100
years of Mohammed's death,

00:00:49.182 --> 00:00:52.797
the Muslim empire has spread
from what would eventually

00:00:52.797 --> 00:00:56.508
be Southern Spain, all
the was to Northern India.

00:00:56.508 --> 00:01:01.286
These Arabs, the man Mahomet,
and that one century,

00:01:01.286 --> 00:01:05.054
is it not as if a spark
had fallen, one spark,

00:01:05.054 --> 00:01:08.419
on a world of what seemed
black unnoticeable sand;

00:01:08.419 --> 00:01:12.143
but lo, the sand proves explosive powder,

00:01:12.143 --> 00:01:15.567
blazes heaven high from Delhi to Grenada.

00:01:15.567 --> 00:01:19.734
I said, the Great Man was always
as lightning out of Heaven;

00:01:21.308 --> 00:01:24.311
the rest of men waited for him like fuel,

00:01:24.311 --> 00:01:27.529
and then they too would flame.

00:01:27.529 --> 00:01:30.862
And Thomas Carlyle is known
as one of the proponents

00:01:30.862 --> 00:01:33.885
of the of Great Man view of history,

00:01:33.885 --> 00:01:35.934
that history is nothing but the story

00:01:35.934 --> 00:01:38.485
of a series of great men,

00:01:38.485 --> 00:01:43.026
who changed the direction
in which humanity travels.

00:01:43.026 --> 00:01:44.878
So, what we're gonna do in this video

00:01:44.878 --> 00:01:49.435
is think about whether it
really is all about a great man,

00:01:49.435 --> 00:01:52.259
or were there other things
that were in the context

00:01:52.259 --> 00:01:56.426
of the time and space in
which these things occur.

00:01:57.462 --> 00:02:01.079
This is what the world
looked like in the year 600.

00:02:01.079 --> 00:02:05.380
Mohammed starts spreading
his revelations in 610,

00:02:05.380 --> 00:02:09.570
and so you can see on this
map, there's two major powers:

00:02:09.570 --> 00:02:12.700
the Byzantine, which is
the Eastern Roman Empire,

00:02:12.700 --> 00:02:15.288
the vestiges of the Roman Empire,

00:02:15.288 --> 00:02:18.966
and you also have the
Sassanid Persian Empire.

00:02:18.966 --> 00:02:21.630
The Byzantines are a Christian empire,

00:02:21.630 --> 00:02:24.354
and the Sassanids are Zoroastrian,

00:02:24.354 --> 00:02:27.028
and Mohammed is from the Quraysh tribe,

00:02:27.028 --> 00:02:28.773
which is in charge of Mecca,

00:02:28.773 --> 00:02:30.483
which is considered a pilgrimage site

00:02:30.483 --> 00:02:33.168
for the various tribes of Arabia.

00:02:33.168 --> 00:02:36.118
But, you can see that
Arabia is fragmented,

00:02:36.118 --> 00:02:39.716
and this doesn't even do justice
to how fragmented it was.

00:02:39.716 --> 00:02:43.883
But, if you fast forward 200
years, you see a major change,

00:02:45.529 --> 00:02:48.229
and in fact, you wouldn't
have to go all the way to 800,

00:02:48.229 --> 00:02:50.746
even by the early eighth century,

00:02:50.746 --> 00:02:52.421
you see that Islam has spread

00:02:52.421 --> 00:02:56.524
from the Iberian peninsula
all the way to the Indus,

00:02:56.524 --> 00:02:58.629
and most of this, as mentioned,

00:02:58.629 --> 00:03:01.779
happens within 100 years
after Mohammed's death.

00:03:01.779 --> 00:03:04.779
But, let's ask our central question:

00:03:05.644 --> 00:03:09.811
why did Islam emerge so
rapidly where and when it did?

00:03:11.693 --> 00:03:14.791
And there's no clear right
or wrong answer here,

00:03:14.791 --> 00:03:16.647
it's all going to be conjecture,

00:03:16.647 --> 00:03:18.209
but that's what's fun about history,

00:03:18.209 --> 00:03:21.156
we can think about what we think we know,

00:03:21.156 --> 00:03:23.607
and then we can debate,
and think about are there

00:03:23.607 --> 00:03:26.753
some patterns here that we
see over and over in history?

00:03:26.753 --> 00:03:28.810
Well, what's the context?

00:03:28.810 --> 00:03:32.977
So, we know for a fact
that Arabia was fragmented,

00:03:34.636 --> 00:03:37.348
that the law of the land
in Arabia was tribal,

00:03:37.348 --> 00:03:39.548
and tribal justice, and this is the world

00:03:39.548 --> 00:03:41.276
that Mohammed grew up in.

00:03:41.276 --> 00:03:44.805
The various tribes often
worshiping different gods.

00:03:44.805 --> 00:03:47.291
We also know at this time that Mohammed

00:03:47.291 --> 00:03:49.450
had exposure to other religions,

00:03:49.450 --> 00:03:53.119
some of which had penetrated
the various tribes of Arabia.

00:03:53.119 --> 00:03:55.831
Most notably, you have Christianity,

00:03:55.831 --> 00:03:59.454
and Mohammed's wife's cousin
was, in fact, a Christian.

00:03:59.454 --> 00:04:01.621
And you also have Judaism.

00:04:02.725 --> 00:04:05.557
These two clearly being related religions,

00:04:05.557 --> 00:04:08.480
Christianity coming out
of a Jewish tradition.

00:04:08.480 --> 00:04:11.011
We also know that the
two great empires here,

00:04:11.011 --> 00:04:13.514
the Byzantines and Persian empires

00:04:13.514 --> 00:04:15.641
are in constant conflict, and in fact,

00:04:15.641 --> 00:04:17.852
the Arabs and many in the Middle East

00:04:17.852 --> 00:04:20.856
are the pawns in that conflict.

00:04:20.856 --> 00:04:25.023
And so, you have the
Byzantines versus the Persians,

00:04:26.871 --> 00:04:30.312
with the possibility of
those living in their lands

00:04:30.312 --> 00:04:32.989
might not have been happy with either.

00:04:32.989 --> 00:04:35.932
There's also the sense that
we're at the very beginning

00:04:35.932 --> 00:04:39.515
of a long decline for
the Byzantine Empire.

00:04:42.043 --> 00:04:46.210
So, one thesis could be that
Mohammed was able to bring

00:04:47.890 --> 00:04:51.512
many of the ideas of
Christianity and Judaism,

00:04:51.512 --> 00:04:55.679
but these ideas helped to
unify a fragmented Arab people.

00:04:58.469 --> 00:05:00.568
And not only did it unify them,

00:05:00.568 --> 00:05:02.519
but it gave them the energy

00:05:02.519 --> 00:05:05.162
that you could have
through religious zeal,

00:05:05.162 --> 00:05:07.233
and that energy is what allowed them

00:05:07.233 --> 00:05:10.349
not only to unify in Arabia,

00:05:10.349 --> 00:05:12.273
and they're able to unify most of Arabia

00:05:12.273 --> 00:05:14.505
by the time of Mohammed's death.

00:05:14.505 --> 00:05:16.590
But, within 100 years of his death,

00:05:16.590 --> 00:05:20.102
they're able to take over
the entire Sassanid Empire

00:05:20.102 --> 00:05:24.311
and make major inroads
into the Byzantine Empire.

00:05:24.311 --> 00:05:26.275
And so, one argument might be,

00:05:26.275 --> 00:05:28.726
and I encourage you to argue with me,

00:05:28.726 --> 00:05:32.333
that they were unified, they
had this missionary zeal,

00:05:32.333 --> 00:05:35.849
which perhaps was only seen
in Christianity before Islam,

00:05:35.849 --> 00:05:38.749
and they were able to
take advantage of conflict

00:05:38.749 --> 00:05:41.647
and discontent between the Byzantines

00:05:41.647 --> 00:05:44.314
and Persians in order to spread.

00:05:45.186 --> 00:05:48.592
Now, another question is do
we see any patterns here?

00:05:48.592 --> 00:05:51.792
Are there any other examples
in history of this happening?

00:05:51.792 --> 00:05:54.888
Well, the most comparable
religion is Christianity,

00:05:54.888 --> 00:05:57.536
which is, today, larger than Islam,

00:05:57.536 --> 00:06:02.160
but Christianity, you have
a long period between Jesus,

00:06:02.160 --> 00:06:05.790
who is the central figure of Christianity,

00:06:05.790 --> 00:06:08.224
who is the underlying spiritual figure,

00:06:08.224 --> 00:06:11.139
and when Christianity really spreads,

00:06:11.139 --> 00:06:12.992
and really becomes and empire,

00:06:12.992 --> 00:06:16.325
and that really starts with Constantine,

00:06:17.592 --> 00:06:21.590
roughly 300 years after the time of Jesus.

00:06:21.590 --> 00:06:24.292
What's interesting about
the example in this video,

00:06:24.292 --> 00:06:27.606
the example of Islam, in
terms of the religion,

00:06:27.606 --> 00:06:31.164
Mohammed plays a little
bit of both of these roles.

00:06:31.164 --> 00:06:35.580
He is a spiritual figure,
he has revelations,

00:06:35.580 --> 00:06:38.966
but he is also the founder of an empire,

00:06:38.966 --> 00:06:43.133
he also governs, he is also a
military and political figure.

00:06:44.379 --> 00:06:48.875
And so, perhaps for the first
time in history on this scale,

00:06:48.875 --> 00:06:52.149
you have the combination
of religious zeal,

00:06:52.149 --> 00:06:57.102
of spiritual belief, of faith,
combined with governance,

00:06:57.102 --> 00:07:00.750
combined with the desire
to create an empire.

00:07:00.750 --> 00:07:04.172
In terms of empire, the only
thing that might be comparable

00:07:04.172 --> 00:07:07.465
in terms of the vastness and
the speed in which it happens,

00:07:07.465 --> 00:07:12.125
is the Mongol empire, the
Mongols are an example

00:07:12.125 --> 00:07:16.105
of people who were
fragmented initially, tribal,

00:07:16.105 --> 00:07:19.885
unified by Genghis Khan,
and through that unification

00:07:19.885 --> 00:07:22.977
were able to spread incredibly rapidly,

00:07:22.977 --> 00:07:26.289
and take on some long historic

00:07:26.289 --> 00:07:28.872
and possibly declining empires.

00:07:29.761 --> 00:07:32.264
So, I'll leave you there,
it's a fascinating question

00:07:32.264 --> 00:07:34.819
that historians debate to this day.

00:07:34.819 --> 00:07:38.905
Islam started awfully fast,
and spread awfully fast.

00:07:38.905 --> 00:07:40.528
Why did this happen?

00:07:40.528 --> 00:07:43.187
Was it some unique
characteristics of Mohammed?

00:07:43.187 --> 00:07:45.741
Was it some unique
characteristics of the religion?

00:07:45.741 --> 00:07:48.491
Or, as Thomas Carlyle alludes to,

00:07:49.521 --> 00:07:51.784
maybe this whole region was just waiting

00:07:51.784 --> 00:07:53.283
for something like this,

00:07:53.283 --> 00:07:55.409
something to unify the tribes of Arabia

00:07:55.409 --> 00:07:59.576
and take on the decaying
Byzantine and Sassanid empires.