Neo-Confucianism and Zhu Xi

WEBVTT
Kind: captions
Language: en

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- [Instructor] In previous videos,

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we've talked about some of
the major schools of thought

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that emerged at the end
of the Zhou Dynasty,

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especially as we start to enter
the warring states period,

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the famous hundred schools of thought.

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And most prominent amongst
them is Confucianism,

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started or based on the
teachings of Confucius,

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who lived around 2,500 years ago,

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and it was all about how does
a society live in harmony.

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Confucianism is based
in a lot of teachings

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that were already part of Chinese culture.

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And Confucius, one could
say, put them together,

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but put them together in a contextual way

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and made them more relevant.

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And you can see on this diagram,

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Confucianism was really
focused on the ethical,

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but Confucius himself tried
to apply some of his teachings

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into the more practical realm.

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Now, out of that hundred
schools of thought,

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you also have Taoism that we
talk about in other videos.

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Now, Taoism is really based on this idea

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of the Tao or the way

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and we could do many videos on Taoism,

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but it's this idea of letting go

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and you could even think of
it as going with the flow

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in a simplicity, a return to nature,

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freeing yourself from desires,

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and it was definitely more philosophical

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and more focused on the
spiritual than Confucianism.

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Now, in other videos,
we talk about Legalism,

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which was a key part of the Chin Dynasty,

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which was the first real imperial dynasty.

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China is named after the Chin Dynasty,

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but it was fairly harsh.

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It was really this idea that hey,

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human beings really
need strong leadership,

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sometimes harsh leadership,

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in order for society to actually work.

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Now, the school of thought
that we have here up the top,

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Buddhism is interesting
because it did not emerge

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from that hundred
schools of thought period

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that we get at the end
of the Zhou Dynastic.

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Buddhism emerges in India
at around the same time,

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roughly 2,500 years ago with
the teachings of Buddha,

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a Hindu prince who lived in
Northeast India, Southern Nepal,

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and his teachings are, in some ways,

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you can almost view

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as a reformation of Hinduism at the time,

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a return to the idea that
someone through meditation,

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through realization, can become one with,

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at least in Buddhism,
the emptiness, nirvana,

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can escape from clinging to
desires of this non-reality

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that we think we live in.

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Now, we've talked about in previous videos

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how the Chin Dynasty was really based

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on this Legalist philosophy,

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but the Han Dynasty is considered
the Golden Age of China.

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Now, under the Han Dynasty,

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Confucianism really took hold

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and became the dominant
philosophical structure of China

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and to some degree would stay that way.

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Now, at the end of the Han Dynasty,

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China goes into a chaotic
period for several hundred years

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until we get to the Sixth
Century when the Sui Dynasty

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is able to finally reunify
China for the most part.

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And in that interim,

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Confucianism starts to
give way, to some degree,

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to both Taoism and Buddhism,

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these things that are more
focused on the spiritual,

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areas where Confucianism
was not as interested.

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And what's interesting about Buddhism,

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even though it started in India,

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famously Ashoka in the Third Century BCE

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really becomes a patron of Buddhism

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and even sends missionaries
out to spread it

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and it comes to China via
Central Asia and Southeast Asia,

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it really takes on a
uniquely Chinese nature

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as it enters China.

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Really, it eventually evolves
into Mahayana Buddhism.

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And under the Tang Dynasty,

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which is considered one of the high points

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of Chinese civilization,

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Buddhism is really able to take hold,

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especially in the early Tang Dynasty.

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However, as we get into
the late Tang Dynasty,

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Buddhism starts to get some push back

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and even gets persecuted to some degree.

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People arguing that hey,

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Buddhism is a foreign belief system.

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In some ways,

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it's not concerned enough
with social cohesion.

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It's all about the
individual through meditation

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trying to separate
themselves from reality,

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becoming one with the emptiness.

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And so at around the same time,

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someone argue in reaction
to the strength of Buddhism.

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You have a movement known
as Neo-Confucianism,

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taking the central ideas of Confucius,

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but using some frameworks and terminology

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from Taoism and Buddhism,

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and there were many
Neo-Confucian philosophers

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that began to emerge in
the late Tang Dynasty,

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but it's really considered
the Song Dynasty

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where Neo-Confucianism really takes hold.

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And the most famous of the
Neo-Confucian philosophers

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sometimes ranked second
to Confucius himself

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in terms of influence on
Chinese philosophy is Zhu Xi.

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He lived from 1130 to 1200

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and he's most known
for his, one could say,

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curation of Confucian texts.

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He famously curated the Four Books,

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Analects of Confucius,

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Mencius or The Mencius, by Mencius,

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Great Learning, Doctrine of the Mean,

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written by Confucian followers.

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This curation of Confucian thought

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shortly after Zhu Xi's life,

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it becomes the bedrock of
the Chinese education system

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and the civil service examinations

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as we go through the Yuan,
Ming, and Ching Dynasties,

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all the way to the early 20th Century.

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Now, he also wrote books
on tradition and rituals

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which are, in some ways, very Confucian

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because they're focused on the practical,

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they're focused on the family,

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they're focused on social cohesion.

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But he also dabbled in the more spiritual,

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wrote extensively about notions of Taiji

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which is really a Taoist
or even a pre-Taoist idea,

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thinking about what is
the fundamental nature

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of the universe and the Taiji
itself is the great ultimate,

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sometimes represented
by the Yin Yang symbol.

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Really, this is showing Taiji

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divided into this dualistic
nature between Yin and Yang,

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how at the center of each
or the extreme of each,

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they become the other.

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He writes about Qi, this
life force or energy.

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And once again, these are
ideas he takes from Taoism.

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But in Neo-Confucian thought,

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there's this idea of you
shouldn't just detach yourself

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from physical reality,
you should study it.

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There's an order, there's
a logic to the universe

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that could be understood.

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And because of the influence
of the Neo-Confucians,

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especially their focus on belief

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in an order and logic of the universe,

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it's no coincidence that the Song Dynasty

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saw some of the major
technological advancements

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not just of China, but of the world,

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advancements that really put China

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at the technological forefront.

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Remember, Europe at this
time is in the Middle Ages.

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The Middle East is under
the Golden Age of Islam,

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but it's really the Chinese

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who are pushing the envelope here.

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Let's get a flavor of
some of Zhu Xi's writing.

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Original mind is principle,
as derived from Tai Ji,

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in itself, unmoved, and perfectly good,

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while physical nature, on the other hand,

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is principle mixed with
material force, qi.

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It is the aroused state,
involving both good and evil.

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The two natures, however,
are always inter-fused,

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one the substance and the other, function.

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So once again, even
though he was Confucian,

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he was a Confucian philosopher,

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this is very Taoist in nature

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and even this notion of
talking about original mind

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is principle in itself,
unmoved, and perfectly good,

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this feels very Buddhist or
even Hindu in its thinking.

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Now, one could debate
whether it was to what degree

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it was influenced by Buddhism,

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it is a very central
idea that all of reality,

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all of sentience, is
emergent from this Atman,

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from this Brahman, from
this original mind,

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emerges from the emptiness.

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But what makes it Neo-Confucian
is beyond the metaphysical,

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beyond the philosophical,
they bring it down to reality.

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They bring it down to practical concerns.

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How does this affect how one governs?

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How does this affect how one should learn?

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How does this affect how one
should be in social harmony

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with those around them?


Early Medieval Trade

WEBVTT
Kind: captions
Language: en

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- [Narrator] In this video
I want to start to answer

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the question of how did
the environment and how did

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political factor impact trade?

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And that is a really big
question that we're not

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gonna answer in one video,
but I want to use a specific

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example to illustrate
the role of environment

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and the role of politics in shaping trade.

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So I want to start in
Birka, which is roughly here

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in present day Sweden.

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And the reason I start
here is that in the late

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1800s a team of archeologists
working in this site

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uncovered a woman's
grave, among other things,

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and found in that grave
the ring that we see

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in the photo here.

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And they've dated this
grave and the ring they

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found in it to somewhere
in the 9th century.

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So somewhere in between
the years 800 and 900 or so

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and we can see in our bigger
timeline that that falls

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right into what's called the viking age

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and the vikings were people
living in Scandinavia

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and this region shaded in red.

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They weren't a single political entity,

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there were a lot of smaller
more independent communities,

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but they shared a lot of
cultural characteristics.

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So back to our ring,
firstly it's made of silver.

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Secondly, the bead that's
set into it is made of

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a really high quality glass.

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And that's of a higher
quality that archeologists

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have found in Scandinavia
from this time period.

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So those two facts would
indicate that the ring is

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probably from somewhere else.

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There's an inscription on the ring,

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it's kind of hard to see,
but if you look closely

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you can sort of make it
out and linguists and

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archeologists who have
looked at this are fairly

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certain that this is a
form of old Arabic script.

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And they think it says
something along the lines

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of to or for Allah.

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And I mentioned that the
vikings shared a lot of

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cultural characteristics and
one of those characteristics

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was that they all spoke Norse languages.

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So an Arabic inscription
on the ring implies really

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strongly that the ring did
not come from Scandinavia.

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So that should raise the
question for you of where

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did this ring come from and
how did it end up in Birka?

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So the first factor we can
look at to try and figure

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out where this ring came
from and how it got here

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is to look at the political context.

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The political context at any given time

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is gonna determine where
and what goods are traded.

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So think about it like this,
if there are two groups

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of people and they have a
relatively good political

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relationship it's more
likely that they're gonna

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trade with each other, too.

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So if we look at the political
situation, broadly speaking,

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during the viking age we
have three major empires.

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The first in purple we
have the Byzantine Empire,

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which was what was left of
the Roman empire at this time.

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We have, in yellow, the Abbasid Caliphate,

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and this is the Islamic
empire that was founded

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in about 750.

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And then we have, in blue,
the Carolingian empire

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in Europe, and that's
named after Charlemagne who

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in Latin is Carolis Magnus,
so Carolingian comes

00:03:01.487 --> 00:03:02.828
from that.

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And I should point out on
the timeline the Carolingian

00:03:05.078 --> 00:03:08.988
empire does continue
after Charlemagne's death,

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it just becomes a little bit
more fractured politically.

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Empires tend to have large cities,

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they can support larger
concentrations of people,

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which means larger
concentrations of wealth,

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which in turn means that
there is more demand.

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So cities become attractive
to traders because you

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have a lot of customers in
one spot and those imperial

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cities, especially, tend to
concentrate a lot of wealth

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if they are the seat of government too.

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So I'm gonna pull our cities onto the map,

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and as we look around here
we can see Aachen is the

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capital of the Carolingian
empire, which is actually

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geographically quite close to the vikings.

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We have Constantinople
as the Byzantine capital,

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and then we have Baghdad
which is the Abbasid capital

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down here.

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And when we look at those
three empires and those three

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cities specifically,
only one of them speaks

00:03:59.408 --> 00:04:01.389
Arabic and writes Arabic.

00:04:01.389 --> 00:04:03.768
And that would be the Abbasid Caliphate.

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So that would mean that
the most likely place of

00:04:05.805 --> 00:04:08.981
origin for this ring was
somewhere in the Abbasid

00:04:08.981 --> 00:04:11.281
Caliphate in yellow down here.

00:04:11.281 --> 00:04:13.087
So we want to think about
why would the vikings be

00:04:13.087 --> 00:04:16.632
trading with the empire that's
farthest away from them?

00:04:16.632 --> 00:04:18.021
Well, part of the answer is political.

00:04:18.021 --> 00:04:20.871
So if we look at the
relationship between the vikings

00:04:20.871 --> 00:04:24.214
and the Carolingians, for
example, one of Charlemagne's

00:04:24.214 --> 00:04:28.094
big projects as the ruler
of the Carolingian empire

00:04:28.094 --> 00:04:32.261
was to wage war against and
try to convert the Pagans

00:04:33.432 --> 00:04:36.444
who were living on the
northeastern edge of his empire.

00:04:36.444 --> 00:04:40.138
So there's this ongoing
conflict between Charlemagne

00:04:40.138 --> 00:04:43.192
and non-Christians, including the vikings,

00:04:43.192 --> 00:04:46.489
and that tends to hurt the
potential economic relationships

00:04:46.489 --> 00:04:47.460
that they could have.

00:04:47.460 --> 00:04:50.714
And you actually see the
vikings raid the coast of the

00:04:50.714 --> 00:04:54.747
Carolingian empire in the
ninth century, as well.

00:04:54.747 --> 00:04:57.455
So the vikings are trading
with the Byzantines

00:04:57.455 --> 00:04:59.285
and with the Abbasids,
what they're engaging in is

00:04:59.285 --> 00:05:01.300
what we call long distance trade.

00:05:01.300 --> 00:05:04.241
So when we talk about long distance trade,

00:05:04.241 --> 00:05:07.245
what we usually see are luxury goods.

00:05:07.245 --> 00:05:10.971
And luxury goods are goods
that are rare and expensive.

00:05:10.971 --> 00:05:12.795
And so in all of these
empires what we see is

00:05:12.795 --> 00:05:15.294
the political context, the
fact that they have large

00:05:15.294 --> 00:05:18.425
powerful empires, makes it
likely that they have more

00:05:18.425 --> 00:05:20.585
advanced technology which
means that they're able to

00:05:20.585 --> 00:05:23.599
produce higher quality, more
technologically advanced,

00:05:23.599 --> 00:05:25.025
goods.

00:05:25.025 --> 00:05:27.263
But then we have to ask what
do the vikings have that

00:05:27.263 --> 00:05:30.264
they would be trading with
these more advanced empires?

00:05:30.264 --> 00:05:33.516
Well one thing we can point
out here is that the vikings

00:05:33.516 --> 00:05:37.121
in Scandinavia are in a
very different climate

00:05:37.121 --> 00:05:39.312
than we have down in the Byzantine empire,

00:05:39.312 --> 00:05:42.049
in the Abbasid Caliphate,
and to a certain extent,

00:05:42.049 --> 00:05:44.154
different than even what
the Carolingians have,

00:05:44.154 --> 00:05:46.017
although we pointed out
some of the political issues

00:05:46.017 --> 00:05:49.149
prevented more trade from
occurring between them.

00:05:49.149 --> 00:05:51.952
And the point we could make
about the different climates

00:05:51.952 --> 00:05:56.119
is that climates determine
what resources are available.

00:05:57.493 --> 00:05:59.612
So if we look at what
the vikings are trading,

00:05:59.612 --> 00:06:02.658
we see things that are somewhat
unique to their climate.

00:06:02.658 --> 00:06:05.793
And when we talk about the viking traders,

00:06:05.793 --> 00:06:08.283
a lot of what they're doing
is actually coming across

00:06:08.283 --> 00:06:12.506
the Baltic Sea into this
region here, the Baltic region,

00:06:12.506 --> 00:06:16.673
we call that and they are
obtaining goods such as timber.

00:06:17.898 --> 00:06:20.600
And specifically the timber
they want are from pine trees.

00:06:20.600 --> 00:06:23.793
And pines in the Baltic tend
to grow very tall and straight

00:06:23.793 --> 00:06:26.648
and that makes them really
attractive for building material.

00:06:26.648 --> 00:06:30.330
Also, it's much colder in
this climate and animals,

00:06:30.330 --> 00:06:33.032
fur-bearing mammals,
especially will tend to grow

00:06:33.032 --> 00:06:37.207
nicer thicker coats if
they live in cold climates

00:06:37.207 --> 00:06:40.180
and that makes them more
attractive then as potential

00:06:40.180 --> 00:06:42.133
clothing items.

00:06:42.133 --> 00:06:44.402
Another resource we see
frequently in the Baltic region

00:06:44.402 --> 00:06:47.445
is amber, and that is dried tree resin.

00:06:47.445 --> 00:06:50.420
And that can be polished
and shaped into stones for

00:06:50.420 --> 00:06:53.911
jewelry, for decoration, as well.

00:06:53.911 --> 00:06:56.538
And the vikings also do
engage in the slave trade.

00:06:56.538 --> 00:06:59.415
They'll kidnap and take people
from this region and then

00:06:59.415 --> 00:07:01.982
trade them as slaves with
these imperial capitals,

00:07:01.982 --> 00:07:04.440
that is not something that's
necessarily influenced by

00:07:04.440 --> 00:07:09.166
the environment, but it is
also a part of this trade.

00:07:09.166 --> 00:07:11.726
Some of the most popular
items that the vikings are

00:07:11.726 --> 00:07:15.586
trading for are things like
fabrics, especially silk,

00:07:15.586 --> 00:07:17.734
which is produced in these empires.

00:07:17.734 --> 00:07:19.712
I also mentioned glass earlier.

00:07:19.712 --> 00:07:22.248
We saw the glass inset in the ring,

00:07:22.248 --> 00:07:25.710
they also are making glass
vessels like drinking glasses.

00:07:25.710 --> 00:07:27.477
You can see a picture of one here.

00:07:27.477 --> 00:07:30.275
And that is gonna be of a
much better quality than

00:07:30.275 --> 00:07:32.806
anything that the vikings
are able to produce.

00:07:32.806 --> 00:07:36.121
So that glass becomes an
attractive technology.

00:07:36.121 --> 00:07:38.978
There's a lot of silver
coming out of, especially,

00:07:38.978 --> 00:07:40.636
the Abbasid Caliphate.

00:07:40.636 --> 00:07:42.745
One of the reasons that
they know this trade was

00:07:42.745 --> 00:07:45.755
occurring more broadly is
that in the Baltic region

00:07:45.755 --> 00:07:49.018
and along some of the travel
routes between the Baltic

00:07:49.018 --> 00:07:51.573
and the Abbasid Caliphate
archeologists have found

00:07:51.573 --> 00:07:56.571
hordes, or large collections,
of silver Abbasid coins.

00:07:56.571 --> 00:07:59.299
And so we see here both silver and glass,

00:07:59.299 --> 00:08:01.666
the elements of that
ring that we discovered,

00:08:01.666 --> 00:08:04.698
are things that are being
traded for by the vikings

00:08:04.698 --> 00:08:07.354
coming from this region.

00:08:07.354 --> 00:08:10.859
So we see the climate
impacting to a certain extent

00:08:10.859 --> 00:08:13.274
what goods exist in different regions.

00:08:13.274 --> 00:08:15.432
So there's an environmental impact there.

00:08:15.432 --> 00:08:19.271
We also see geography or
environment affecting the

00:08:19.271 --> 00:08:21.271
transportation of goods.

00:08:22.162 --> 00:08:24.375
So what I want to do next
is pull in the commonly

00:08:24.375 --> 00:08:27.363
used trade routes at this time.

00:08:27.363 --> 00:08:29.724
And this helps us to
understand how these goods

00:08:29.724 --> 00:08:32.447
actually move between these places.

00:08:32.447 --> 00:08:35.000
So we see that the major
trade routes between the

00:08:35.000 --> 00:08:38.239
Baltic region and the
Byzantines and the Abbasids

00:08:38.239 --> 00:08:40.839
follow major river systems.

00:08:40.839 --> 00:08:43.660
And the vikings are able
to take advantage of these

00:08:43.660 --> 00:08:46.167
river systems in part
because of the technology

00:08:46.167 --> 00:08:47.804
that they possess.

00:08:47.804 --> 00:08:49.772
So again we see the environment
playing a role in trade

00:08:49.772 --> 00:08:53.276
and determining what
routes are convenient to

00:08:53.276 --> 00:08:55.022
transport goods.

00:08:55.022 --> 00:08:58.833
And one other point I would
make about these routes

00:08:58.833 --> 00:09:02.480
that develop is we see
these cities of Novgorod,

00:09:02.480 --> 00:09:06.647
of Kiev, and of Bulgar that
pop along these trade routes

00:09:07.588 --> 00:09:10.368
and these cities sort of
grow because the trade

00:09:10.368 --> 00:09:11.668
routes exist.

00:09:11.668 --> 00:09:15.848
These cities themselves become
center of trade over time.

00:09:15.848 --> 00:09:18.072
So to come back to our
ring that we started the

00:09:18.072 --> 00:09:20.366
video with, hopefully
this is looking less like

00:09:20.366 --> 00:09:24.533
an anomaly, a strange find,
and more like the natural

00:09:25.433 --> 00:09:28.887
result of the existing
trade networks that were

00:09:28.887 --> 00:09:31.707
in in place because of the
environmental and because

00:09:31.707 --> 00:09:35.207
of the political conditions at this time.


Great Schism part 1

WEBVTT
Kind: captions
Language: en

00:00:00.399 --> 00:00:02.140
- [Narrator] In previous
videos we talked about

00:00:02.140 --> 00:00:04.558
the dramatic turn around
in the fourth century

00:00:04.558 --> 00:00:06.218
in terms of how Christianity

00:00:06.218 --> 00:00:08.266
was treated in the Roman Empire.

00:00:08.266 --> 00:00:10.435
As you enter into the fourth century

00:00:10.435 --> 00:00:13.090
it's persecuted by Diocletian

00:00:13.090 --> 00:00:15.309
but then Constantine takes power.

00:00:15.309 --> 00:00:17.107
He's sympathetic to the Christians.

00:00:17.107 --> 00:00:20.185
He even convinced them in
order to unify the Christians

00:00:20.185 --> 00:00:21.645
to have a more unified sense

00:00:21.645 --> 00:00:23.011
of what it means to be Christian,

00:00:23.011 --> 00:00:27.021
in order to settle things
like the Arian controversy

00:00:27.021 --> 00:00:29.274
and he converts himself to Christianity.

00:00:29.274 --> 00:00:31.372
And as we exit the fourth century

00:00:31.372 --> 00:00:33.741
you have Theodosius who makes Christianity

00:00:33.741 --> 00:00:37.023
the official religion of the Roman Empire

00:00:37.023 --> 00:00:40.701
and then begins to
persecute other religions.

00:00:40.701 --> 00:00:42.897
Now what we're going to do in this video

00:00:42.897 --> 00:00:45.759
is continue the narrative
and in particular,

00:00:45.759 --> 00:00:48.368
we're going to see how
there's an evolution

00:00:48.368 --> 00:00:52.399
between the church in the west
and the church in the east.

00:00:52.399 --> 00:00:54.752
In previous videos we already talk about

00:00:54.752 --> 00:00:56.826
how the Roman Empire itself has

00:00:56.826 --> 00:01:00.977
initially administered
between west and east,

00:01:00.977 --> 00:01:03.688
and then that administration
becomes more and more formal.

00:01:03.688 --> 00:01:08.108
Theodosius is the last emperor
to truly rule both halves.

00:01:08.108 --> 00:01:10.219
They start getting ruled separately

00:01:10.219 --> 00:01:13.225
and as you get into the latter
half of the fifth century

00:01:13.225 --> 00:01:17.392
the western empire itself
falls to Germanic conquerors.

00:01:18.803 --> 00:01:21.517
Now in previous videos we talk about

00:01:21.517 --> 00:01:26.029
how the emperors who
rule from Constantinople

00:01:26.029 --> 00:01:29.327
consider themselves to
continue the Roman Empire.

00:01:29.327 --> 00:01:31.897
They didn't call themselves
the Byzantine Empire

00:01:31.897 --> 00:01:33.258
as we now call them.

00:01:33.258 --> 00:01:35.167
They call themselves the Roman Empire.

00:01:35.167 --> 00:01:37.851
They consider themselves Roman emperors.

00:01:37.851 --> 00:01:40.414
The west falls as I just mentioned

00:01:40.414 --> 00:01:43.247
into a bunch of Germanic kingdoms.

00:01:44.852 --> 00:01:48.646
Justinian is able to
reclaim a lot of the land

00:01:48.646 --> 00:01:52.146
formerly lost in the Western Roman Empire.

00:01:52.992 --> 00:01:55.098
Now there's some interesting actors

00:01:55.098 --> 00:01:57.783
we see emerging on this map

00:01:57.783 --> 00:02:01.092
and once again, we're
now in the sixth century.

00:02:01.092 --> 00:02:02.906
You have these Germanic tribes,

00:02:02.906 --> 00:02:06.398
the Visigothic Kingdoms
here in modern day Spain

00:02:06.398 --> 00:02:09.672
and here in modern day
France you have the Franks,

00:02:09.672 --> 00:02:12.002
and the word France really is referring to

00:02:12.002 --> 00:02:16.075
land of the Franks,
another Germanic tribe.

00:02:16.075 --> 00:02:20.511
Now, they are about to factor
much, much more relevantly

00:02:20.511 --> 00:02:21.497
and when I say about I'm saying

00:02:21.497 --> 00:02:23.450
over the next several hundred years

00:02:23.450 --> 00:02:27.963
in this eventual division
culturally and religiously

00:02:27.963 --> 00:02:30.429
between east and west.

00:02:30.429 --> 00:02:33.298
As I mentioned in previous videos,

00:02:33.298 --> 00:02:37.067
the division, yes, it will
center on notions of language.

00:02:37.067 --> 00:02:40.321
In the west especially in
the church Latin is used.

00:02:40.321 --> 00:02:43.398
In the east in the church Greek is used.

00:02:43.398 --> 00:02:44.623
There's spiritual debates

00:02:44.623 --> 00:02:46.562
that we will touch on in a few minutes

00:02:46.562 --> 00:02:48.582
but there's also a power struggle.

00:02:48.582 --> 00:02:53.069
You have the Byzantine emperor
seated in Constantinople.

00:02:53.069 --> 00:02:56.148
You have the bishop of Rome

00:02:56.148 --> 00:02:59.550
now known as the pope,
really the pope of Rome

00:02:59.550 --> 00:03:01.890
who considers themselves more and more

00:03:01.890 --> 00:03:03.319
the leader of all of Christianity.

00:03:03.319 --> 00:03:04.784
And their argument there is

00:03:04.784 --> 00:03:07.861
look, this is the church
that according to tradition

00:03:07.861 --> 00:03:11.852
was founded by Peter,
first amongst the apostles.

00:03:11.852 --> 00:03:14.477
You have the patriarch of Constantinople

00:03:14.477 --> 00:03:18.239
and patriarchs of other
significant centers of Christianity

00:03:18.239 --> 00:03:20.528
to say, wait, hold on a second.

00:03:20.528 --> 00:03:24.756
Yes, bishop of Rome you are very important

00:03:24.756 --> 00:03:27.983
but we consider you to
be first amongst equals.

00:03:27.983 --> 00:03:31.287
You don't have jurisdiction
over all of Christendom.

00:03:31.287 --> 00:03:34.283
Together we have jurisdiction.

00:03:34.283 --> 00:03:38.174
And this was to some degree
the case under Justinian

00:03:38.174 --> 00:03:39.753
and it was very clear at this time

00:03:39.753 --> 00:03:42.100
that the Byzantine
emperor was very powerful

00:03:42.100 --> 00:03:43.673
not just over the temporal realm

00:03:43.673 --> 00:03:46.415
really referring to the
day to day material realm,

00:03:46.415 --> 00:03:48.993
but also a lot of influence
on the spiritual realm

00:03:48.993 --> 00:03:50.769
which was really supposed to be the domain

00:03:50.769 --> 00:03:53.899
of the bishops or the
popes or the patriarchs.

00:03:53.899 --> 00:03:56.490
This notion of the Pentarchy was codified

00:03:56.490 --> 00:03:57.720
in the Justinian law,

00:03:57.720 --> 00:04:00.840
this idea that these five
centers of Christianity

00:04:00.840 --> 00:04:03.282
really have extra weight and collectively

00:04:03.282 --> 00:04:06.310
are really leading Christendom.

00:04:06.310 --> 00:04:08.708
Now as I mentioned, things get interesting

00:04:08.708 --> 00:04:11.625
as we fast forward about 250 years.

00:04:13.153 --> 00:04:15.236
Let's go to the year 800.

00:04:17.096 --> 00:04:20.167
One thing you might notice
is that group in yellow,

00:04:20.167 --> 00:04:22.549
the Franks have now conquered a lot more

00:04:22.549 --> 00:04:24.594
and they're conquering
it under the leadership

00:04:24.594 --> 00:04:26.200
of Charlemagne.

00:04:26.200 --> 00:04:30.595
At the same time, you
see this green over here,

00:04:30.595 --> 00:04:34.821
Islam has dramatically
spread from its founding

00:04:34.821 --> 00:04:38.804
in the early seventh
century all the way now

00:04:38.804 --> 00:04:41.953
as we're exiting the eighth century

00:04:41.953 --> 00:04:45.098
to cover most of the Middle East, Persia,

00:04:45.098 --> 00:04:48.871
bordering on modern day
Pakistan, India, North Africa

00:04:48.871 --> 00:04:51.849
and even going into modern day Spain.

00:04:51.849 --> 00:04:54.781
At the same time especially because

00:04:54.781 --> 00:04:56.523
of this Islamic conquest,

00:04:56.523 --> 00:04:59.634
the Byzantine Empire and
the Byzantine emperor

00:04:59.634 --> 00:05:01.634
is significantly weaker.

00:05:02.500 --> 00:05:05.075
You could imagine the pope
in Rome here is saying,

00:05:05.075 --> 00:05:06.867
"Well, who's going to protect me

00:05:06.867 --> 00:05:09.529
"especially from my political enemies?"

00:05:09.529 --> 00:05:11.309
Now Charlemagne considers himself

00:05:11.309 --> 00:05:14.289
something of a protector of Christianity.

00:05:14.289 --> 00:05:17.132
And Pope Leo III goes
to him for protection

00:05:17.132 --> 00:05:20.927
and Charlemagne is able
to actually provide it.

00:05:20.927 --> 00:05:24.507
And in exchange or perhaps
in thanks for that,

00:05:24.507 --> 00:05:28.674
the pope crowns Charlemagne
as Holy Roman Emperor.

00:05:29.776 --> 00:05:31.688
Now what's significant about this

00:05:31.688 --> 00:05:36.007
is it really introduces
a fourth actor here

00:05:36.007 --> 00:05:38.611
because the title Holy Roman Emperor

00:05:38.611 --> 00:05:40.785
was intentionally given to say, look,

00:05:40.785 --> 00:05:43.505
now you Charlemagne, you are the heir

00:05:43.505 --> 00:05:45.109
to the grandeur of Rome.

00:05:45.109 --> 00:05:47.421
You are the heir to the Roman emperors.

00:05:47.421 --> 00:05:49.081
Now, you might be saying wait,

00:05:49.081 --> 00:05:51.377
isn't that what the Byzantine
emperors thought they were?

00:05:51.377 --> 00:05:53.774
Didn't they think this
was the Roman Empire?

00:05:53.774 --> 00:05:56.917
And at that time their
emperor was an empress.

00:05:56.917 --> 00:06:00.103
It was Empress Irene of Athens.

00:06:00.103 --> 00:06:03.197
And so once again, this is
creating further tension.

00:06:03.197 --> 00:06:07.284
They're using different
languages, Latin versus Greek.

00:06:07.284 --> 00:06:08.978
You now have the western pope

00:06:08.978 --> 00:06:12.133
recognizing a different as you could say

00:06:12.133 --> 00:06:14.522
Roman emperor in Charlemagne.

00:06:14.522 --> 00:06:17.555
The nature of the west
is becoming more Germanic

00:06:17.555 --> 00:06:19.715
and using the language Latin,

00:06:19.715 --> 00:06:21.611
while the nature of the east

00:06:21.611 --> 00:06:25.012
is continuing in Greek traditions.

00:06:25.012 --> 00:06:28.762
On top of that what you
have in the year 800,

00:06:29.645 --> 00:06:31.536
you're actually in this period

00:06:31.536 --> 00:06:33.182
where you've had several conflicts

00:06:33.182 --> 00:06:36.305
over this notion of Iconoclasm.

00:06:36.305 --> 00:06:38.958
This Iconoclasm movement you could say

00:06:38.958 --> 00:06:42.814
started in 726 when the
Byzantine emperor said

00:06:42.814 --> 00:06:46.626
enough of these images of
Jesus and the Virgin Mary

00:06:46.626 --> 00:06:49.154
and other figures of
Christianity in our churches.

00:06:49.154 --> 00:06:51.152
Citing references in the
Old Testament saying that

00:06:51.152 --> 00:06:53.755
hey, we shouldn't have these images.

00:06:53.755 --> 00:06:57.605
And so, this Iconoclasm or
this destroying of icons

00:06:57.605 --> 00:06:59.166
starts to begin.

00:06:59.166 --> 00:07:01.664
Well, the pope in the west they say,

00:07:01.664 --> 00:07:04.782
"Hey, we don't think we
have to listen to you.

00:07:04.782 --> 00:07:06.287
"I am the bishop of Rome.

00:07:06.287 --> 00:07:08.467
"I have universal jurisdiction."

00:07:08.467 --> 00:07:11.897
And then to add insult
to injury now in 800,

00:07:11.897 --> 00:07:15.833
you have Charlemagne being
crowned Holy Roman Emperor.

00:07:15.833 --> 00:07:17.889
Now a thread further running through this

00:07:17.889 --> 00:07:20.227
is something that we've talked
about in a previous video,

00:07:20.227 --> 00:07:22.925
this notion of filioque.

00:07:22.925 --> 00:07:26.331
Where in 381 the Council
of Constantinople,

00:07:26.331 --> 00:07:28.739
they augment the Nicene
Creed where they say,

00:07:28.739 --> 00:07:30.139
"And we believe in the Holy Spirit,

00:07:30.139 --> 00:07:31.891
"the Lord and Giver of Life,

00:07:31.891 --> 00:07:34.339
"who proceeds from the Father."

00:07:34.339 --> 00:07:37.524
While in the west they add
the Latin term filioque

00:07:37.524 --> 00:07:39.008
which means and the Son.

00:07:39.008 --> 00:07:40.681
And this is touching
on some of these notion

00:07:40.681 --> 00:07:42.255
in the Arian Heresy where

00:07:42.255 --> 00:07:44.455
where does the Holy Spirit proceed from

00:07:44.455 --> 00:07:47.211
if the Father and Son
are really co-divine,

00:07:47.211 --> 00:07:49.645
co-equal, of the same substance?

00:07:49.645 --> 00:07:51.654
Shouldn't the Holy
Spirit proceed from both

00:07:51.654 --> 00:07:53.276
rather than just one?

00:07:53.276 --> 00:07:54.411
While those in the east said hey,

00:07:54.411 --> 00:07:55.846
this isn't what we agreed to.

00:07:55.846 --> 00:07:56.697
While those in the west say

00:07:56.697 --> 00:07:59.027
we don't think it's so important
that you agree to things

00:07:59.027 --> 00:08:01.686
because we have the seat at Rome,

00:08:01.686 --> 00:08:04.829
the seat that was established by Peter.


Arian Controversy and the Council of Nicaea

WEBVTT
Kind: captions
Language: en

00:00:00.704 --> 00:00:01.596
- [Instructor] In previous videos,

00:00:01.596 --> 00:00:04.955
we have talked about
how Christianity evolved

00:00:04.955 --> 00:00:08.723
and developed under the Roman Empire.

00:00:08.723 --> 00:00:11.122
In particular we saw
that as we entered into

00:00:11.122 --> 00:00:14.337
the 4th century, that
Christianity continued

00:00:14.337 --> 00:00:16.797
to be persecuted, in particular by

00:00:16.797 --> 00:00:18.979
the Emperor Diocletian, who had some of

00:00:18.979 --> 00:00:22.851
the worst persecutions of the Christians.

00:00:22.851 --> 00:00:24.967
But over the course of the next century,

00:00:24.967 --> 00:00:28.555
from roughly 300 to 400,
the relationship between

00:00:28.555 --> 00:00:30.477
the Roman Empire and Christianity

00:00:30.477 --> 00:00:34.268
goes completely in the opposite direction.

00:00:34.268 --> 00:00:36.611
As Constantine takes over, he becomes

00:00:36.611 --> 00:00:38.331
sympathetic to the Christians and he

00:00:38.331 --> 00:00:41.683
eventually becomes Christian himself.

00:00:41.683 --> 00:00:43.730
Even then, there was a lot of diversity

00:00:43.730 --> 00:00:45.877
within the Christian Church.

00:00:45.877 --> 00:00:47.660
There were debates about the nature of

00:00:47.660 --> 00:00:50.660
Jesus Christ relative to the Father,

00:00:51.517 --> 00:00:53.458
relative to the Holy Spirit.

00:00:53.458 --> 00:00:57.094
There were multiple sects of Christianity.

00:00:57.094 --> 00:01:01.042
And one in particular
started to create a debate.

00:01:01.042 --> 00:01:03.315
There was a priest in Alexandria,

00:01:03.315 --> 00:01:06.693
which was one of the major
cities of the Roman Empire.

00:01:06.693 --> 00:01:08.886
Now remember, by this
point, Rome of course is

00:01:08.886 --> 00:01:11.011
one of the most significant,

00:01:11.011 --> 00:01:13.013
if not the most significant city.

00:01:13.013 --> 00:01:16.747
Now Constantine sets up
a capital at Byzantium,

00:01:16.747 --> 00:01:19.795
which will eventually be
known as Constantinople.

00:01:19.795 --> 00:01:21.891
And Alexandria, which
was originally founded

00:01:21.891 --> 00:01:23.390
by Alexander the Great, is also

00:01:23.390 --> 00:01:27.057
one of the significant
cities of the Empire.

00:01:28.066 --> 00:01:30.411
And in Alexandria there
is a Christian priest

00:01:30.411 --> 00:01:34.244
by the name of Arius,
who has a view on Christ

00:01:35.235 --> 00:01:38.235
that becomes a bit of a controversy.

00:01:39.227 --> 00:01:41.858
And to understand that, here is an account

00:01:41.858 --> 00:01:44.525
of his writings, or his beliefs.

00:01:45.714 --> 00:01:48.523
So this is Arius of Alexandria.

00:01:48.523 --> 00:01:52.546
If the Father begat the
Son, he that was begotten

00:01:52.546 --> 00:01:56.198
had a beginning of existence:
and from this it is evident,

00:01:56.198 --> 00:01:59.941
that there was a time
when the Son was not.

00:01:59.941 --> 00:02:02.972
It therefore necessarily follows that He,

00:02:02.972 --> 00:02:06.305
the Son, had his substance from nothing.

00:02:07.259 --> 00:02:10.662
So, he's drawing a distinction
between the essence

00:02:10.662 --> 00:02:14.829
of the Father and the Son, who's
manifested as Jesus Christ.

00:02:16.571 --> 00:02:19.259
Now this is very
controversial, because even

00:02:19.259 --> 00:02:22.386
his own bishop in
Alexandria viewed the Father

00:02:22.386 --> 00:02:25.931
and the Son to be of the same substance.

00:02:25.931 --> 00:02:29.042
Now, today, you might say,
hey, isn't this just word play?

00:02:29.042 --> 00:02:31.911
It feels like it's
semantic, which is really

00:02:31.911 --> 00:02:34.680
debating around the meaning of words.

00:02:34.680 --> 00:02:37.268
But, at the end of the Roman Empire

00:02:37.268 --> 00:02:39.037
and as we get into the Middle Ages,

00:02:39.037 --> 00:02:42.144
this was a major issue of philosophical

00:02:42.144 --> 00:02:46.311
and it would sometimes bleed
over into political debate.

00:02:47.471 --> 00:02:50.418
And so Constantine, who we
mentioned has a sympathy

00:02:50.418 --> 00:02:53.626
towards the Christians,
he allows Christianity

00:02:53.626 --> 00:02:57.793
to be tolerated, he does not
like this idea of this debate

00:02:58.803 --> 00:03:02.109
and he wants to help unify the Christians.

00:03:02.109 --> 00:03:05.609
So, in 325 he calls the Council of Nicaea,

00:03:07.101 --> 00:03:10.490
to help resolve this controversy,

00:03:10.490 --> 00:03:13.882
which gets known as the Arian Controversy,

00:03:13.882 --> 00:03:16.162
named after Arius of Alexandria.

00:03:16.162 --> 00:03:17.675
Now it's worth mentioning, Arius wasn't

00:03:17.675 --> 00:03:20.019
the first person to make this argument,

00:03:20.019 --> 00:03:22.415
that the Father in some
way was more divine

00:03:22.415 --> 00:03:25.322
than the Son, because He begat the Son,

00:03:25.322 --> 00:03:27.162
He existed before the Son.

00:03:27.162 --> 00:03:30.379
But this controversy really
revolves around Arius,

00:03:30.379 --> 00:03:31.821
because he was especially persuasive about

00:03:31.821 --> 00:03:34.891
spreading this view of
the relationship between

00:03:34.891 --> 00:03:38.558
the Father and the Son,
manifested by Jesus.

00:03:42.418 --> 00:03:45.515
And at the Council of
Nicaea, many of the bishops

00:03:45.515 --> 00:03:48.351
throughout Christendom are in attendance,

00:03:48.351 --> 00:03:51.520
it's known as the First
Ecumenical Conference,

00:03:51.520 --> 00:03:53.368
the word ecumenical comes from

00:03:53.368 --> 00:03:55.928
the Greek word for the inhabited Earth.

00:03:55.928 --> 00:03:57.481
So you can view it as the Church leaders

00:03:57.481 --> 00:04:00.384
from the inhabited
Earth, in order to create

00:04:00.384 --> 00:04:05.193
a consensus about what it
means to be a Christian.

00:04:05.193 --> 00:04:07.127
And Arius of Alexandria was there

00:04:07.127 --> 00:04:09.585
to defend his position, but the majority

00:04:09.585 --> 00:04:13.976
of those there did not
like his point of view.

00:04:13.976 --> 00:04:15.897
So they declared Arius' beliefs

00:04:15.897 --> 00:04:18.314
as heresy and they exile him.

00:04:19.224 --> 00:04:22.127
And to be very clear
that they do not believe

00:04:22.127 --> 00:04:24.817
that the Son is of a different substance

00:04:24.817 --> 00:04:28.400
of the Father, they
issue the Nicene Creed.

00:04:32.779 --> 00:04:34.155
So what I have here, this is known as

00:04:34.155 --> 00:04:37.155
the Nicene-Constantinopolitan Creed.

00:04:38.370 --> 00:04:41.193
And this is based on the Nicene Creed,

00:04:41.193 --> 00:04:44.015
which was established in
325, which was shorter,

00:04:44.015 --> 00:04:46.631
but then in 381, under
Theodosius, you have

00:04:46.631 --> 00:04:49.408
your Second Ecumenical
Council, which is held

00:04:49.408 --> 00:04:51.983
in Constantinople, to reaffirm

00:04:51.983 --> 00:04:55.316
some of the ideas of the Nicene Council.

00:04:56.327 --> 00:04:58.192
And so as I read this, keep a look out for

00:04:58.192 --> 00:05:00.575
some of these words, which
were really put there

00:05:00.575 --> 00:05:03.825
to try to settle the Arian Controversy,

00:05:04.753 --> 00:05:06.927
to try to ensure that that type

00:05:06.927 --> 00:05:10.168
of belief does not surface again.

00:05:10.168 --> 00:05:13.696
We believe in one God,
the Father Almighty,

00:05:13.696 --> 00:05:15.393
Maker of heaven and earth, and of

00:05:15.393 --> 00:05:18.951
all things visible and invisible.

00:05:18.951 --> 00:05:22.273
And in one Lord Jesus
Christ, the Son of God,

00:05:22.273 --> 00:05:26.440
the Only-begotten, Begotten
of the Father before all ages.

00:05:28.311 --> 00:05:30.383
So, not like Arius was
arguing, that there was a time

00:05:30.383 --> 00:05:34.569
where the Father existed
before the Son existed.

00:05:34.569 --> 00:05:36.064
Here it says begotten of the Father,

00:05:36.064 --> 00:05:38.988
but before all ages, so there was

00:05:38.988 --> 00:05:41.416
always a time when there was a Son.

00:05:41.416 --> 00:05:45.583
Light of Light, Very God of
Very God, Begotten, not made;

00:05:46.704 --> 00:05:49.663
of one essence with the Father,

00:05:49.663 --> 00:05:52.335
by whom all things were made.

00:05:52.335 --> 00:05:55.240
So, once again, really addressing
this Arian Controversy,

00:05:55.240 --> 00:05:57.424
the Arian Heresy as it becomes known,

00:05:57.424 --> 00:06:01.400
that the Father and the Son
are of the same essence,

00:06:01.400 --> 00:06:04.230
one is not more divine than the other.

00:06:04.230 --> 00:06:07.009
Who for us men and for our salvation

00:06:07.009 --> 00:06:09.808
came down from heaven, and was incarnate

00:06:09.808 --> 00:06:13.975
of the Holy Spirit and the
Virgin Mary, and was made man.

00:06:14.936 --> 00:06:18.312
And was crucified also for
us under Pontius Pilate,

00:06:18.312 --> 00:06:21.163
and suffered, and was buried.

00:06:21.163 --> 00:06:23.063
And the third day He rose again,

00:06:23.063 --> 00:06:25.185
according to the Scriptures.

00:06:25.185 --> 00:06:26.936
And ascended into heaven, and sits

00:06:26.936 --> 00:06:29.855
at the right hand of the Father.

00:06:29.855 --> 00:06:31.728
And He shall come again with glory

00:06:31.728 --> 00:06:33.537
to judge the living and the dead,

00:06:33.537 --> 00:06:36.768
Whose kingdom shall have no end.

00:06:36.768 --> 00:06:39.768
And we believe in the
Holy Spirit, the Lord,

00:06:39.768 --> 00:06:43.768
and Giver of Life, Who
proceeds from the Father.

00:06:45.104 --> 00:06:49.568
Now here in brackets I've
written filoque and the son?

00:06:49.568 --> 00:06:51.864
Because even though the official Nicene-

00:06:51.864 --> 00:06:55.137
Constantinopolitan Creed just says

00:06:55.137 --> 00:06:57.806
Who proceeds from the
Father, as we will see

00:06:57.806 --> 00:07:01.009
later on, as the Church starts to become

00:07:01.009 --> 00:07:04.137
more and more divided,
in the West, in Latin,

00:07:04.137 --> 00:07:08.362
the term filoque gets added,
which means and the son.

00:07:08.362 --> 00:07:11.040
And, once again, this
is starting to address

00:07:11.040 --> 00:07:15.578
this notion of how does the
Son relate to the Father?

00:07:15.578 --> 00:07:18.416
So, when you add filoque,
you're saying, hey,

00:07:18.416 --> 00:07:20.235
the Holy Spirit is emanating from both

00:07:20.235 --> 00:07:21.847
the Father and the Son, versus just

00:07:21.847 --> 00:07:24.072
the Father, but we'll get into that.

00:07:24.072 --> 00:07:25.768
This was not a matter of debate

00:07:25.768 --> 00:07:29.935
in the 4th century, but it
will become a matter of debate

00:07:29.935 --> 00:07:34.000
as we go into the 6th century and beyond.

00:07:34.000 --> 00:07:35.696
And we believe in the
Holy Spirit, the Lord,

00:07:35.696 --> 00:07:38.298
and Giver of Life, Who
proceeds from the Father.

00:07:38.298 --> 00:07:40.809
Who with the Father and the Son together

00:07:40.809 --> 00:07:45.584
is worshiped and glorified,
Who spoke by the Prophets.

00:07:45.584 --> 00:07:47.615
And we believe in one, holy, catholic,

00:07:47.615 --> 00:07:51.191
meaning universal, and apostolic Church.

00:07:51.191 --> 00:07:54.881
We acknowledge one Baptism
for the remission of sins.

00:07:54.881 --> 00:07:57.039
We look for the Resurrection of the dead,

00:07:57.039 --> 00:08:00.206
and the life of the age to come, Amen.

00:08:02.338 --> 00:08:04.351
So this is interesting, because it's,

00:08:04.351 --> 00:08:08.335
you can view it as a
unification of Christendom.

00:08:08.335 --> 00:08:12.057
Now, as we will see,
that unification does not

00:08:12.057 --> 00:08:15.279
hold well over the next
several hundred years.

00:08:15.279 --> 00:08:19.446
Even though Arius is exiled
and he dies shortly thereafter,

00:08:20.474 --> 00:08:23.455
you continue to have sympathetic bishops

00:08:23.455 --> 00:08:27.841
and even Roman Emperors,
to the Arian Doctrine.

00:08:27.841 --> 00:08:30.017
You also, this debate between the relation

00:08:30.017 --> 00:08:32.215
of the Father and the Son continues,

00:08:32.215 --> 00:08:34.800
we'll talk about this filoque debate.

00:08:34.800 --> 00:08:37.551
But maybe most important
and the biggest cause

00:08:37.551 --> 00:08:40.447
of the eventual divisions
between the Church,

00:08:40.447 --> 00:08:43.183
ones that carry on even to today,

00:08:43.183 --> 00:08:46.100
it's really about a power struggle.

00:08:47.975 --> 00:08:50.312
So, as we've been talking about the late

00:08:50.312 --> 00:08:54.201
Roman Empire and even the
fall of the Western Empire

00:08:54.201 --> 00:08:56.232
and the beginning of the Byzantine Empire,

00:08:56.232 --> 00:08:57.885
you might already notice that there are

00:08:57.885 --> 00:09:00.487
several very powerful actors here.

00:09:00.487 --> 00:09:02.359
With the fall of the Western Roman Empire,

00:09:02.359 --> 00:09:04.591
you have the Byzantine Emperor,

00:09:04.591 --> 00:09:07.063
who considers him, and as we'll see,

00:09:07.063 --> 00:09:09.975
also herself, the Roman Emperor.

00:09:09.975 --> 00:09:12.423
We have the Bishop, the Patriarch, or,

00:09:12.423 --> 00:09:15.671
often known, the Pope of Rome.

00:09:15.671 --> 00:09:18.032
Now Rome is significant,
because according to tradition

00:09:18.032 --> 00:09:21.985
the Church at Rome was
founded by the Apostle Peter,

00:09:21.985 --> 00:09:23.488
who is considered by many to be

00:09:23.488 --> 00:09:26.007
the first amongst the Apostles.

00:09:26.007 --> 00:09:29.173
But of course Rome was the
seat of the Roman Empire

00:09:29.173 --> 00:09:31.951
for a very, very, very long time.

00:09:31.951 --> 00:09:33.344
And so you could imagine the Bishop of

00:09:33.344 --> 00:09:36.376
the Church of Rome, the Pope of Rome

00:09:36.376 --> 00:09:39.250
would be a very powerful figure.

00:09:39.250 --> 00:09:41.447
Now you also have the
Bishop or the Patriarch

00:09:41.447 --> 00:09:44.253
of Constantinople,
which is another capital

00:09:44.253 --> 00:09:48.351
and really the capital
of the Byzantine Empire.

00:09:48.351 --> 00:09:49.551
And so what we're going
to see, over the next

00:09:49.551 --> 00:09:52.768
several hundred years, is
the jockeying for position

00:09:52.768 --> 00:09:54.887
amongst these three, in particular

00:09:54.887 --> 00:09:58.920
the Byzantine Emperor
and the Pope of Rome.

00:09:58.920 --> 00:10:01.192
The Pope of Rome starts
to consider themselves

00:10:01.192 --> 00:10:05.213
as really the leader
of all of Christendom.

00:10:05.213 --> 00:10:08.192
The Patriarch of
Constantinople and the bishops

00:10:08.192 --> 00:10:11.585
of the other major
centers of Christianity,

00:10:11.585 --> 00:10:14.874
like Antioch and Jerusalem and Alexandria,

00:10:14.874 --> 00:10:18.275
they view themselves as
all kind of a college of,

00:10:18.275 --> 00:10:22.116
as peers and they will
give extra space for

00:10:22.116 --> 00:10:25.257
the Pope of Rome or the Bishop of Rome,

00:10:25.257 --> 00:10:28.379
because of the importance of
that city and the significance

00:10:28.379 --> 00:10:32.002
of how the Church of Rome was founded.

00:10:32.002 --> 00:10:34.650
And this gets, this jockeying for power

00:10:34.650 --> 00:10:36.420
over the next several hundred years

00:10:36.420 --> 00:10:39.904
gets even more complex as the West,

00:10:39.904 --> 00:10:42.306
what was the Western Roman Empire,

00:10:42.306 --> 00:10:44.939
or some of the areas of
the Western Roman Empire,

00:10:44.939 --> 00:10:46.478
start to get consolidated under

00:10:46.478 --> 00:10:49.395
Germanic rule really, Frankish rule

00:10:50.459 --> 00:10:51.971
and you start having this notion of a

00:10:51.971 --> 00:10:54.185
Holy Roman Emperor that we'll talk about

00:10:54.185 --> 00:10:58.265
in a few hundred years down our timeline.

00:10:58.265 --> 00:11:00.413
So, keep a look out for
this power struggle.

00:11:00.413 --> 00:11:02.338
We're going to talk
about particular issues

00:11:02.338 --> 00:11:04.995
of theological doctrine, things like

00:11:04.995 --> 00:11:07.695
the filoque issue, things
like the relationship

00:11:07.695 --> 00:11:09.316
between the Father and the Son,

00:11:09.316 --> 00:11:11.550
whether you should have icons.

00:11:11.550 --> 00:11:13.289
But, at the end of the day,

00:11:13.289 --> 00:11:14.727
what's eventually going to lead to

00:11:14.727 --> 00:11:17.265
the Great Schism, in the beginning

00:11:17.265 --> 00:11:21.348
of the Second Millennium,
is this power struggle.


Spread of Islamic Culture

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:01.137
- [David] Hi Eman.

00:00:01.137 --> 00:00:01.970
- [Eman] Hi David.

00:00:01.970 --> 00:00:03.197
- [David] So what we're
gonna do in this video

00:00:03.197 --> 00:00:06.185
is talk about the
cultural spread of Islam.

00:00:06.185 --> 00:00:08.221
Where are we and when are we right now?

00:00:08.221 --> 00:00:12.194
- [Eman] So we are around
the early seventh century,

00:00:12.194 --> 00:00:13.027
- [David] Okay

00:00:13.027 --> 00:00:15.272
- [Eman] And here we see
the Byzantine empire,

00:00:15.272 --> 00:00:18.002
which, at the time was still
a continuation of Rome,

00:00:18.002 --> 00:00:19.908
so this is like the eastern roman empire,

00:00:19.908 --> 00:00:20.741
- [David] Right.

00:00:20.741 --> 00:00:22.863
- [Eman] and it's an aging
empire and we also have

00:00:22.863 --> 00:00:26.778
Sassanid Persia which
started in the third century

00:00:26.778 --> 00:00:28.984
and is still continuing into this period.

00:00:28.984 --> 00:00:30.354
- [David] Right, so
we've got on the timeline

00:00:30.354 --> 00:00:32.114
it's going beyond our start point here.

00:00:32.114 --> 00:00:35.544
- [Eman] Yep. So these are two very
powerful empires who often

00:00:35.544 --> 00:00:36.860
are in tension with one another.

00:00:36.860 --> 00:00:38.885
As you can see they neighbor each other.

00:00:38.885 --> 00:00:40.026
And around this time

00:00:40.026 --> 00:00:44.731
they're involved in some
pretty powerful struggles here.

00:00:44.731 --> 00:00:49.146
- [David] Right. So in 628 it
leads to a lot of instability

00:00:49.146 --> 00:00:51.063
within Sassanid Persia.

00:00:52.119 --> 00:00:54.358
- [Eman] Certainly, and in some
ways as well the Byzantines

00:00:54.358 --> 00:00:56.712
are weakened by how many resources

00:00:56.712 --> 00:00:59.215
they've exhausted in these tensions.

00:00:59.215 --> 00:01:02.359
So around this time, a
new religion emerges.

00:01:02.359 --> 00:01:06.114
Muhammad is born in
Arabia, and pretty soon

00:01:06.114 --> 00:01:09.419
during his lifetime and
immediately after his lifetime,

00:01:09.419 --> 00:01:12.264
the religion of Islam spreads rapidly

00:01:12.264 --> 00:01:15.013
through Islamic conquests,
which Saul talked about

00:01:15.013 --> 00:01:16.293
in an earlier video.

00:01:16.293 --> 00:01:18.161
- [David] I mean, just to
give you an impression,

00:01:18.161 --> 00:01:20.743
Muhammad died in the year 633?

00:01:20.743 --> 00:01:21.576
- [Eman] Yes.

00:01:21.576 --> 00:01:24.212
- [David] So by 750, this is what

00:01:24.212 --> 00:01:26.723
the state of the Islamic
world looked like.

00:01:26.723 --> 00:01:29.530
- [Eman] They took over most
of Persia and a large part

00:01:29.530 --> 00:01:31.879
of the Byzantine empire, as we can see

00:01:31.879 --> 00:01:34.196
and then even beyond,
it goes further east,

00:01:34.196 --> 00:01:36.961
further west, all the way over to Spain.

00:01:36.961 --> 00:01:39.342
And this happens really really quickly,

00:01:39.342 --> 00:01:42.348
but it's not the case that Islamic culture

00:01:42.348 --> 00:01:46.351
necessarily takes in all of
these areas that quickly.

00:01:46.351 --> 00:01:48.848
So it takes a little bit
longer for that to really

00:01:48.848 --> 00:01:51.691
take hold, and it also takes hold in areas

00:01:51.691 --> 00:01:53.984
far beyond this empire as well.

00:01:53.984 --> 00:01:57.928
So certainly the presence
of Islamic or Muslim rulers

00:01:57.928 --> 00:01:59.567
in these areas certainly did affect

00:01:59.567 --> 00:02:01.346
the culture of these places.

00:02:01.346 --> 00:02:04.007
But what's more important
is sort of the ways

00:02:04.007 --> 00:02:06.448
in which Islam slowly integrated

00:02:06.448 --> 00:02:07.573
with some of these cultures.

00:02:07.573 --> 00:02:11.047
And that happened through
trade, through missionaries,

00:02:11.047 --> 00:02:14.166
and also through pilgramage
routes that happened,

00:02:14.166 --> 00:02:16.070
emanating out from Mecca.

00:02:16.070 --> 00:02:19.562
And these religious ideas weren't static.

00:02:19.562 --> 00:02:21.202
As they moved through different areas

00:02:21.202 --> 00:02:23.723
and as they moved
through different routes,

00:02:23.723 --> 00:02:25.776
they changed and they
started to take the shape

00:02:25.776 --> 00:02:29.120
of the local culture and
the local flavor as well.

00:02:29.120 --> 00:02:31.649
- [David] So let me pull
up some trade routes.

00:02:31.649 --> 00:02:34.846
These were the active
trade routes of the period.

00:02:34.846 --> 00:02:37.571
And you can see this is a
continuation of the silk road.

00:02:37.571 --> 00:02:40.219
It goes all the way from Rome to China.

00:02:40.219 --> 00:02:43.806
This is Xian, which was
then known as Chang'an.

00:02:43.806 --> 00:02:47.188
This is the imperial capital of at least

00:02:47.188 --> 00:02:49.344
ten different Chinese dynasties.

00:02:49.344 --> 00:02:51.975
There's also a very large mosque here.

00:02:51.975 --> 00:02:55.125
- [Eman] So here we have
the great mosque at Xian,

00:02:55.125 --> 00:02:57.544
and what's really
interesting about this mosque

00:02:57.544 --> 00:02:59.894
is that it really fuses a lot of

00:02:59.894 --> 00:03:02.369
Islamic and Chinese ideas.

00:03:02.369 --> 00:03:05.873
So for example, it still
sort of has the structure

00:03:05.873 --> 00:03:07.941
of an imperial building, and the way

00:03:07.941 --> 00:03:09.549
that the courtyards are set up.

00:03:09.549 --> 00:03:10.382
- [David] Sure.

00:03:10.382 --> 00:03:11.884
- [Eman] But instead of
following sort of the rules of

00:03:11.884 --> 00:03:15.163
Feng Shui, it is oriented towards Mecca,

00:03:15.163 --> 00:03:19.125
which is the direction in which
Muslims look when they pray.

00:03:19.125 --> 00:03:21.902
But it still has a very Chinese character.

00:03:21.902 --> 00:03:22.965
- [David] Right.

00:03:22.965 --> 00:03:25.327
- [Eman] And this makes sense
because these trade routes

00:03:25.327 --> 00:03:27.637
basically had to go
through the Islamic empire.

00:03:27.637 --> 00:03:30.722
And so as people traveled, so did ideas.

00:03:30.722 --> 00:03:33.457
And those ideas transformed along the way.

00:03:33.457 --> 00:03:36.071
- [David] What's next on
our whistle stop tour, Eman?

00:03:36.071 --> 00:03:39.508
- [Eman] Let's look at
the mosque in Djenne.

00:03:39.508 --> 00:03:43.553
- [David] Okay. So Djenne
is in what is today, Mali,

00:03:43.553 --> 00:03:46.795
just south of Timbuktu or
Tombuktu as it's called today.

00:03:46.795 --> 00:03:50.389
So it was a great center
of Islamic learning.

00:03:50.389 --> 00:03:53.496
And in Djenne is the site
of the world's largest

00:03:53.496 --> 00:03:55.960
mud brick building, the
grand mosque of Djenne.

00:03:55.960 --> 00:03:57.648
Let me pull it up.

00:03:57.648 --> 00:04:00.220
It's a really incredible building

00:04:00.220 --> 00:04:04.053
that gets a lot of
elements of Malian culture.

00:04:05.615 --> 00:04:08.227
So this is the grand mosque of Djenne,

00:04:08.227 --> 00:04:09.429
this is a mud brick building.

00:04:09.429 --> 00:04:11.036
We have an article about
this on Khan Academy

00:04:11.036 --> 00:04:12.669
in the art history section.

00:04:12.669 --> 00:04:15.280
What's really cool to me about
the grand mosque of Djenne

00:04:15.280 --> 00:04:18.536
is the way that is
incorporates Malian traditions

00:04:18.536 --> 00:04:20.605
into Islamic tradition.

00:04:20.605 --> 00:04:22.385
So you can see on top of these spires,

00:04:22.385 --> 00:04:24.764
some of these spires are
minarets, from which issue

00:04:24.764 --> 00:04:26.327
the call to prayer.

00:04:26.327 --> 00:04:27.786
You can't see them as detailed,

00:04:27.786 --> 00:04:29.821
but there are little
ostrich eggs on top of

00:04:29.821 --> 00:04:30.979
- [Eman] Ostrich eggs?

00:04:30.979 --> 00:04:33.814
- [David] Yeah, in Mali,
ostrich eggs represent

00:04:33.814 --> 00:04:35.389
purity and fertility.

00:04:35.389 --> 00:04:39.119
And so even within the
constraints of building

00:04:39.119 --> 00:04:42.518
a religious building,
there's still expressions

00:04:42.518 --> 00:04:43.935
of local culture.

00:04:45.341 --> 00:04:47.306
- [Eman] Yeah, and it's
really interesting how that

00:04:47.306 --> 00:04:49.399
spread through trade, but
it also spread another way,

00:04:49.399 --> 00:04:52.298
which is through pilgramage,
through missionaries,

00:04:52.298 --> 00:04:55.243
through preachers, and that also took on

00:04:55.243 --> 00:04:57.676
the local traditions in interesting ways.

00:04:57.676 --> 00:04:59.702
So let's go to southern,

00:04:59.702 --> 00:05:00.759
to South India.

00:05:00.759 --> 00:05:01.692
- [David] Okay.

00:05:01.692 --> 00:05:03.296
- [Eman] Near Kerala.

00:05:03.296 --> 00:05:07.684
- [David] So this is the
Cheraman Juma mosque.

00:05:07.684 --> 00:05:08.964
This is supposed to be one

00:05:08.964 --> 00:05:11.720
of the earliest mosques in history.

00:05:11.720 --> 00:05:13.870
It's construction dates to about 630.

00:05:13.870 --> 00:05:15.671
- [Eman] Yep, 629 to be precise.

00:05:15.671 --> 00:05:16.552
- [David] Thank you.

00:05:16.552 --> 00:05:18.587
- [Eman] This was actually
during the life of the prophet,

00:05:18.587 --> 00:05:20.288
and it's quite far from Mecca,

00:05:20.288 --> 00:05:24.048
so it's really fascinating
how quickly it traveled there.

00:05:24.048 --> 00:05:26.223
But it traveled with a preacher

00:05:26.223 --> 00:05:30.802
and as you can see, this is a
very distinctly Indian mosque.

00:05:30.802 --> 00:05:34.619
Another way that Islam
traveled through preachers

00:05:34.619 --> 00:05:36.514
was through Sufis.

00:05:36.514 --> 00:05:38.956
So let's talk about
Sufis for just a minute.

00:05:38.956 --> 00:05:39.789
- [David] Sure.

00:05:39.789 --> 00:05:42.155
- [Eman] Sufis were like a
mystical devotional practice,

00:05:42.155 --> 00:05:43.920
and we see many iterations of Sufism

00:05:43.920 --> 00:05:45.936
in all different sects of Islam.

00:05:45.936 --> 00:05:47.720
But they were particularly successful

00:05:47.720 --> 00:05:49.624
at spreading Islam for a few reasons.

00:05:49.624 --> 00:05:51.606
One of them was that they
adapted the teachings

00:05:51.606 --> 00:05:53.000
to local traditions.

00:05:53.000 --> 00:05:56.344
And another reason was
that they built lodges

00:05:56.344 --> 00:05:58.304
and places of worship along the way.

00:05:58.304 --> 00:06:00.127
And these sometimes function
like community centers

00:06:00.127 --> 00:06:01.086
and monasteries.

00:06:01.086 --> 00:06:02.687
So let's have a look at a couple of them.

00:06:02.687 --> 00:06:03.520
- [David] Sure.

00:06:03.520 --> 00:06:05.330
- [Eman] Let's look at
some North African ones.

00:06:05.330 --> 00:06:09.324
- [David] So this is a Ribat in Tunisia.

00:06:09.324 --> 00:06:12.941
- [Eman] Yes, so a Ribat
is kind of like a hostel,

00:06:12.941 --> 00:06:14.900
you have travelers staying there.

00:06:14.900 --> 00:06:16.827
Early on in their history,

00:06:16.827 --> 00:06:18.440
there were soldiers that stayed there.

00:06:18.440 --> 00:06:20.225
Over time, they sort of took on

00:06:20.225 --> 00:06:22.725
a monastery culture for Sufis.

00:06:24.535 --> 00:06:27.521
We also have something called a Zawiya.

00:06:27.521 --> 00:06:30.143
So here is an example of one.

00:06:30.143 --> 00:06:33.140
And similarly this was
a place of learning,

00:06:33.140 --> 00:06:35.177
it was a place of worship.

00:06:35.177 --> 00:06:37.820
People often lived there for a long time,

00:06:37.820 --> 00:06:40.891
so they sort of have
this monastic tradition

00:06:40.891 --> 00:06:43.584
that created a permanent
presence for Islam

00:06:43.584 --> 00:06:45.113
along these routes.

00:06:45.113 --> 00:06:48.904
And this was really really
integral in the spread of Islam.

00:06:48.904 --> 00:06:52.025
And it's not just in North
Africa, but even farther east,

00:06:52.025 --> 00:06:54.027
you see different iterations of that.

00:06:54.027 --> 00:06:57.273
So once you get into former
Persian territory and

00:06:57.273 --> 00:07:01.546
in Indian territory you have
something called a Hanka.

00:07:01.546 --> 00:07:04.578
So here's an example from Kashmir.

00:07:04.578 --> 00:07:07.332
This is called the Shah Hamdan mosque.

00:07:07.332 --> 00:07:09.060
And it's a fourteenth century mosque.

00:07:09.060 --> 00:07:11.162
And this is a commemorative building,

00:07:11.162 --> 00:07:13.298
it commemorates an important Sufi leader.

00:07:13.298 --> 00:07:15.667
But again, you see some
of the local flavor here.

00:07:15.667 --> 00:07:18.520
You see that there's some
intricate wood carvings,

00:07:18.520 --> 00:07:20.509
which is really,

00:07:20.509 --> 00:07:21.585
- [David] Very Kashmir-y

00:07:21.585 --> 00:07:23.089
- [Eman] Very Kashmir-y, certainly.

00:07:23.089 --> 00:07:25.505
And similarly this was a place of worship

00:07:25.505 --> 00:07:28.132
but also a place where
people passed through

00:07:28.132 --> 00:07:30.339
and interacted and learned.

00:07:30.339 --> 00:07:34.273
So it was a site of spreading
Islamic tradition as well.

00:07:34.273 --> 00:07:35.360
- [David] So that was about,

00:07:35.360 --> 00:07:37.989
sorry I should have said, that
was about here in Srinagar.

00:07:37.989 --> 00:07:39.961
- [Eman] Yes, about there.

00:07:39.961 --> 00:07:43.547
- [David] Yeah and so, in this
way Islam was also spread.

00:07:43.547 --> 00:07:45.149
- [Eman] Certainly.

00:07:45.149 --> 00:07:47.490
Let's have a look at sort of the bounds

00:07:47.490 --> 00:07:48.962
of the Islamic empire.

00:07:48.962 --> 00:07:49.807
- [David] Sure.

00:07:49.807 --> 00:07:53.736
- [Eman] And where we see
some of these instances

00:07:53.736 --> 00:07:56.964
of new Islamic traditions were no longer

00:07:56.964 --> 00:07:59.114
in the heart of the Islamic empire.

00:07:59.114 --> 00:08:00.010
We're beyond that.

00:08:00.010 --> 00:08:02.978
And that's because Islam was
carried in many different ways.

00:08:02.978 --> 00:08:05.619
And as we can see it ended up with some

00:08:05.619 --> 00:08:09.119
really really diverse iterations of Islam.


Differentiating functions: Find the error

WEBVTT
Kind: captions
Language: en

00:00:00.258 --> 00:00:02.217
- [Instructor] What we're gonna do

00:00:02.217 --> 00:00:04.262
in this video is look at
the work of other people

00:00:04.262 --> 00:00:06.034
as they try to take derivatives

00:00:06.034 --> 00:00:07.862
and see if their reasoning is correct

00:00:07.862 --> 00:00:09.165
and if it's not correct,

00:00:09.165 --> 00:00:11.376
try to identify what they should have done

00:00:11.376 --> 00:00:13.764
or where their reasoning went wrong.

00:00:13.764 --> 00:00:15.716
So over here it says Nate tried to find

00:00:15.716 --> 00:00:18.824
the derivative of X squared plus five X

00:00:18.824 --> 00:00:20.706
times sine of X.

00:00:20.706 --> 00:00:22.152
Here is his work.

00:00:22.152 --> 00:00:23.858
Is Nate's work correct?

00:00:23.858 --> 00:00:26.365
If not, what's his mistake?

00:00:26.365 --> 00:00:28.723
So pause the video and see
if you can answer this.

00:00:28.723 --> 00:00:30.438
Is Nate's work correct,

00:00:30.438 --> 00:00:33.021
and if not, what's his mistake?

00:00:33.991 --> 00:00:36.965
All right so I'm assuming
you've had a go at it.

00:00:36.965 --> 00:00:39.387
So let's work though this step by step.

00:00:39.387 --> 00:00:41.542
So over here he's just trying to apply

00:00:41.542 --> 00:00:43.826
the derivative operator to the expression.

00:00:43.826 --> 00:00:45.509
Which is exactly what he needed to do.

00:00:45.509 --> 00:00:47.443
He's trying to find the
derivative of this thing,

00:00:47.443 --> 00:00:51.405
and he says okay this is a
product of two expressions,

00:00:51.405 --> 00:00:54.566
and then he says okay,
well this is gonna be

00:00:54.566 --> 00:00:56.300
the same thing as the derivative

00:00:56.300 --> 00:00:59.922
or this is the same thing as
the product of the derivatives.

00:00:59.922 --> 00:01:02.485
Now this is a problem.

00:01:02.485 --> 00:01:04.568
You are probably familiar,

00:01:04.568 --> 00:01:07.191
if I take the derivative
of the sum of two things.

00:01:07.191 --> 00:01:10.454
So the derivative with
respect to X of F of X

00:01:10.454 --> 00:01:11.454
plus G of X,

00:01:12.832 --> 00:01:16.370
that indeed is equal to
the derivative of the first

00:01:16.370 --> 00:01:20.153
F prime of X plus the
derivative of the second,

00:01:20.153 --> 00:01:23.798
but that is not true if we
are dealing with the product

00:01:23.798 --> 00:01:25.196
of functions.

00:01:25.196 --> 00:01:29.363
The derivative with respect
to X of F of X, G of X

00:01:31.970 --> 00:01:33.776
is not necessarily,

00:01:33.776 --> 00:01:36.098
maybe there's some very
special circumstance,

00:01:36.098 --> 00:01:38.256
but in general it's not going to be

00:01:38.256 --> 00:01:40.785
just the product of the derivative.

00:01:40.785 --> 00:01:45.209
It's not going to be just
F prime of X, G prime of X.

00:01:45.209 --> 00:01:48.229
Here we would want to
apply the product rule.

00:01:48.229 --> 00:01:51.026
This is going to be equal to,

00:01:51.026 --> 00:01:52.597
this is going to be
equal to the derivative

00:01:52.597 --> 00:01:55.791
of the first function
times the second function,

00:01:55.791 --> 00:01:58.091
plus the derivative, or
let me write it this way.

00:01:58.091 --> 00:02:00.400
Plus the first function,
not taking its derivative,

00:02:00.400 --> 00:02:03.135
times the derivative
of the second function.

00:02:03.135 --> 00:02:06.374
So he should have applied
the product rule here,

00:02:06.374 --> 00:02:07.743
and so let's do that

00:02:07.743 --> 00:02:10.344
just to see what his
answer should have been.

00:02:10.344 --> 00:02:11.873
So what he should have done here,

00:02:11.873 --> 00:02:14.674
I'll get my correcting red pen out here.

00:02:14.674 --> 00:02:16.661
Say no that's not what
he should have done.

00:02:16.661 --> 00:02:19.412
He says let's take the
derivative of this first thing.

00:02:19.412 --> 00:02:21.749
So actually let me color code it.

00:02:21.749 --> 00:02:24.511
So the derivative of
this is two X plus five.

00:02:24.511 --> 00:02:27.678
So it should have been two X plus five

00:02:29.461 --> 00:02:32.085
times the second thing.

00:02:32.085 --> 00:02:33.668
So times sine of X.

00:02:35.052 --> 00:02:37.802
Times, we do it in another color.

00:02:40.549 --> 00:02:42.132
Time the sine of X,

00:02:43.879 --> 00:02:47.406
and then to that he would
add the first thing,

00:02:47.406 --> 00:02:49.906
which is X squared plus five X

00:02:51.912 --> 00:02:54.729
times the derivative of the second thing.

00:02:54.729 --> 00:02:58.218
So the derivative of
sine of X is cosine of X.

00:02:58.218 --> 00:03:00.787
So this is what we should have been seeing

00:03:00.787 --> 00:03:02.522
at this step right over here.

00:03:02.522 --> 00:03:05.103
He shouldn't have just taken the product

00:03:05.103 --> 00:03:06.352
of the derivatives.

00:03:06.352 --> 00:03:07.963
He should have applied the product rule.

00:03:07.963 --> 00:03:09.232
So his work is not correct,

00:03:09.232 --> 00:03:11.281
and his mistake is that he
didn't apply the product rule.

00:03:11.281 --> 00:03:13.886
He just assumed that the
derivative of the products

00:03:13.886 --> 00:03:16.749
is the same thing as the
product of the derivatives.

00:03:16.749 --> 00:03:18.666
Let's do more examples.

00:03:20.579 --> 00:03:22.079
Okay so let's see.

00:03:23.409 --> 00:03:26.435
It says Katy tried to find the derivative

00:03:26.435 --> 00:03:28.522
of two X squared minus four.

00:03:28.522 --> 00:03:30.052
All of that to the third power.

00:03:30.052 --> 00:03:31.133
Here's her work.

00:03:31.133 --> 00:03:32.578
Is Katy's work correct?

00:03:32.578 --> 00:03:34.512
If not, what is her mistake?

00:03:34.512 --> 00:03:36.237
So once again, pause the video.

00:03:36.237 --> 00:03:37.999
See if you can figure it out.

00:03:37.999 --> 00:03:40.818
All right now let's inspect Katy's work.

00:03:40.818 --> 00:03:44.159
So she's taking the derivative
of this and let's see,

00:03:44.159 --> 00:03:45.815
over here it looks like she's taking

00:03:45.815 --> 00:03:48.284
the derivative of the entire expression

00:03:48.284 --> 00:03:51.284
with respect to the inner expression

00:03:53.241 --> 00:03:56.933
and that is close to applying
the chain rule properly

00:03:56.933 --> 00:03:59.578
but it's not applying
the chain rule properly.

00:03:59.578 --> 00:04:01.036
So her work is not correct,

00:04:01.036 --> 00:04:03.080
and her mistake is she's not correctly

00:04:03.080 --> 00:04:04.438
applying the chain rule.

00:04:04.438 --> 00:04:06.362
Just as a review, the
chain rule says look,

00:04:06.362 --> 00:04:08.736
if we're trying tot ake the
derivative with respect to X

00:04:08.736 --> 00:04:09.986
of F of G of X,

00:04:14.258 --> 00:04:15.258
F of G of X,

00:04:16.139 --> 00:04:18.691
that this is going to be equal to,

00:04:18.691 --> 00:04:20.918
this is going to be
equal to the derivative

00:04:20.918 --> 00:04:23.064
of the whole thing with respect to G of X.

00:04:23.064 --> 00:04:26.647
So I could write that
as F prime of G of X.

00:04:29.068 --> 00:04:33.022
F prime of G of X times the
derivative of the inner function

00:04:33.022 --> 00:04:34.241
with respect to X.

00:04:34.241 --> 00:04:35.959
Times G prime of X.

00:04:35.959 --> 00:04:37.042
So over here,

00:04:38.129 --> 00:04:40.993
we could view our F function as a thing

00:04:40.993 --> 00:04:45.064
that takes its input and
takes it to the third power,

00:04:45.064 --> 00:04:49.038
and so this right over
here is F prime of G of X.

00:04:49.038 --> 00:04:52.388
So this thing is the F prime of G of X

00:04:52.388 --> 00:04:54.688
but she forgot to multiply
it by the derivative

00:04:54.688 --> 00:04:57.223
of the inner function with respect to X.

00:04:57.223 --> 00:05:00.887
So she forgot to multiply
this times the derivative

00:05:00.887 --> 00:05:05.483
of two X squared minus
four with respect to X.

00:05:05.483 --> 00:05:07.088
Which is gonna be, let's see,

00:05:07.088 --> 00:05:08.840
the derivative of two X squared,

00:05:08.840 --> 00:05:10.767
power rule two times two is four,

00:05:10.767 --> 00:05:13.244
so it's gonna be four X to the first,

00:05:13.244 --> 00:05:15.960
and then the derivative of
negative four is just a zero.

00:05:15.960 --> 00:05:18.463
So it's just gonna be times four X.

00:05:18.463 --> 00:05:21.071
So that's what she needed
to do in order for it

00:05:21.071 --> 00:05:22.279
to be correct.

00:05:22.279 --> 00:05:24.992
So she had to have this times four X here.

00:05:24.992 --> 00:05:26.614
Times four X.

00:05:26.614 --> 00:05:27.662
So not correct.

00:05:27.662 --> 00:05:31.162
She didn't correctly apply the chain rule.

00:05:32.649 --> 00:05:35.399
So let's do another one of these.

00:05:36.560 --> 00:05:38.118
So here,

00:05:38.118 --> 00:05:41.639
it says Njoman tried to
find the derivative of sine

00:05:41.639 --> 00:05:43.804
of seven X squared plus four X.

00:05:43.804 --> 00:05:45.040
Here's his work.

00:05:45.040 --> 00:05:46.335
Is Njoman's work correct?

00:05:46.335 --> 00:05:47.606
If not, what is his mistake?

00:05:47.606 --> 00:05:50.027
Pause the video, see if
you can figure it out.

00:05:50.027 --> 00:05:54.616
All right, so it's a derivative
of sine of this expression.

00:05:54.616 --> 00:05:56.497
So you'd wanna use the chain rule.

00:05:56.497 --> 00:05:58.149
In fact, using the chain
rule you wanna find

00:05:58.149 --> 00:05:59.785
the derivative of the outside function

00:05:59.785 --> 00:06:01.223
with respect to the inside.

00:06:01.223 --> 00:06:03.356
So the derivative of sine of something

00:06:03.356 --> 00:06:05.031
with respect to that something

00:06:05.031 --> 00:06:07.657
is gonna be cosine of that something.

00:06:07.657 --> 00:06:09.195
So that's right,

00:06:09.195 --> 00:06:11.724
and then you wanna multiply that

00:06:11.724 --> 00:06:15.137
times the derivative of the
inside with respect to X.

00:06:15.137 --> 00:06:17.937
So the derivative of
seven X squared is 14 X.

00:06:17.937 --> 00:06:19.969
The derivative of four X is four.

00:06:19.969 --> 00:06:22.380
So this is actually, that step looks good.

00:06:22.380 --> 00:06:25.632
But then Njoman does
something strange over here.

00:06:25.632 --> 00:06:28.627
This is the cosine of seven
X squared plus four X.

00:06:28.627 --> 00:06:31.320
Then that whole thing
times 14 X plus four,

00:06:31.320 --> 00:06:34.540
but they get confused where just looking

00:06:34.540 --> 00:06:36.945
at these parentheses and this
tends to happen sometimes.

00:06:36.945 --> 00:06:38.888
This is actually one of the key errors

00:06:38.888 --> 00:06:40.713
that the folks at the college board,

00:06:40.713 --> 00:06:42.592
AP folks told us about.

00:06:42.592 --> 00:06:44.629
Is that when dealing with
these transcendental functions

00:06:44.629 --> 00:06:46.244
cosine, sine, tangent,

00:06:46.244 --> 00:06:48.014
natural log that are written like this

00:06:48.014 --> 00:06:49.474
and people see the parentheses

00:06:49.474 --> 00:06:51.007
and see another parentheses,

00:06:51.007 --> 00:06:52.947
their brain just says oh let me multiply

00:06:52.947 --> 00:06:54.686
these two expressions in parentheses,

00:06:54.686 --> 00:06:55.981
but that's not right,

00:06:55.981 --> 00:06:57.736
because if we were to add parentheses

00:06:57.736 --> 00:06:59.146
this is what this is implying.

00:06:59.146 --> 00:07:01.049
So you can't just take the 14 X plus four

00:07:01.049 --> 00:07:02.476
and multiply it by this,

00:07:02.476 --> 00:07:05.102
and assuming you're taking
the cosine of the whole thing.

00:07:05.102 --> 00:07:07.656
So this is where Njoman makes the mistake.

00:07:07.656 --> 00:07:08.999
The work is not correct,

00:07:08.999 --> 00:07:11.335
and the mistake is trying to multiply

00:07:11.335 --> 00:07:13.897
these two expressions
and taking the cosine

00:07:13.897 --> 00:07:15.174
of the whole thing.

00:07:15.174 --> 00:07:16.724
Let's do one more of these.

00:07:16.724 --> 00:07:18.773
I find these strangely fun.

00:07:18.773 --> 00:07:20.694
All right this one is involved.

00:07:20.694 --> 00:07:22.535
Tom tried to find the derivative of

00:07:22.535 --> 00:07:24.404
the square root of X over X to the fourth.

00:07:24.404 --> 00:07:25.576
Here is his work.

00:07:25.576 --> 00:07:27.016
Is Tom's work correct?

00:07:27.016 --> 00:07:28.493
If not, what's his mistake?

00:07:28.493 --> 00:07:31.144
Pause the video and see if
you can figure that out.

00:07:31.144 --> 00:07:34.098
So it looks like he's trying
to apply the quotient rule.

00:07:34.098 --> 00:07:36.771
So applying the quotient rule, you would,

00:07:36.771 --> 00:07:40.525
in the numerator you
would take the derivative

00:07:40.525 --> 00:07:44.527
of the first expression
times the second expression

00:07:44.527 --> 00:07:47.156
and then minus the first expression

00:07:47.156 --> 00:07:49.321
times the derivative of
the second expression

00:07:49.321 --> 00:07:50.422
all of that over,

00:07:50.422 --> 00:07:53.614
or I should say the derivative
of the numerator expression

00:07:53.614 --> 00:07:56.334
times the denominator expression,

00:07:56.334 --> 00:08:00.804
minus the numerator expression
times the derivative

00:08:00.804 --> 00:08:02.303
of the denominator expression,

00:08:02.303 --> 00:08:04.332
all of that over the
denominator expression squared.

00:08:04.332 --> 00:08:05.845
So this looks correct actually.

00:08:05.845 --> 00:08:08.232
It's a correct application
of the the quotient rule.

00:08:08.232 --> 00:08:10.989
It looks like Tom is
correctly simplifying.

00:08:10.989 --> 00:08:13.085
So the derivative of X to the one half

00:08:13.085 --> 00:08:15.258
is one half X to the negative one half.

00:08:15.258 --> 00:08:16.614
So that looks right.

00:08:16.614 --> 00:08:19.610
Derivative of X to the fourth
is four X to the third.

00:08:19.610 --> 00:08:20.798
So that looks right.

00:08:20.798 --> 00:08:22.703
All of this looks algebraically right,

00:08:22.703 --> 00:08:24.766
and let's see, when you simplify this.

00:08:24.766 --> 00:08:27.813
So let's see, X to the negative one half

00:08:27.813 --> 00:08:30.896
times X to the fourth is indeed X to,

00:08:32.873 --> 00:08:35.598
well that's going to be X to the.

00:08:35.598 --> 00:08:37.152
Oh this correlates.

00:08:37.152 --> 00:08:39.842
So this simplifies to that.

00:08:39.842 --> 00:08:44.147
Which looks correct, and
that simplifies to that.

00:08:44.147 --> 00:08:46.184
Which looks correct.

00:08:46.184 --> 00:08:48.249
We're just using exponent
properties there,

00:08:48.249 --> 00:08:50.749
and then divide everything by,

00:08:51.660 --> 00:08:54.705
let's see, oh there, everything
is terms of X to 3.5.

00:08:54.705 --> 00:08:58.455
So we're going to have
negative 3.5 X to 3.5,

00:09:01.378 --> 00:09:02.938
and then you use exploder problems.

00:09:02.938 --> 00:09:05.250
So actually it looks like
he did everything correctly.

00:09:05.250 --> 00:09:06.815
This is the right answer.

00:09:06.815 --> 00:09:08.572
So his work is correct.

00:09:08.572 --> 00:09:10.375
He did not make any mistakes.

00:09:10.375 --> 00:09:12.379
But I do have a bone to pick.

00:09:12.379 --> 00:09:13.695
So speak with Tom,

00:09:13.695 --> 00:09:16.153
because he didn't have to
apply the quotient rule here.

00:09:16.153 --> 00:09:18.172
He did all of this hairy calculus

00:09:18.172 --> 00:09:20.429
and algebra but it could have been

00:09:20.429 --> 00:09:21.904
a very simple simplification

00:09:21.904 --> 00:09:23.359
he could have made up here,

00:09:23.359 --> 00:09:24.947
and this is a key thing to realize.

00:09:24.947 --> 00:09:26.116
He could have said hey,

00:09:26.116 --> 00:09:27.868
you know what, this is the same thing.

00:09:27.868 --> 00:09:31.496
It's the derivative with respect to X of

00:09:31.496 --> 00:09:33.367
X to the one half.

00:09:33.367 --> 00:09:35.189
That's what the square root of X is.

00:09:35.189 --> 00:09:38.203
Times X to the negative four power.

00:09:38.203 --> 00:09:41.383
That's what one over X to the fourth is.

00:09:41.383 --> 00:09:43.698
And so let me color code it.

00:09:43.698 --> 00:09:46.369
So that is the same thing as that,

00:09:46.369 --> 00:09:49.983
and that is the same thing as that,

00:09:49.983 --> 00:09:51.940
and you wouldn't even have
to use the product rule here.

00:09:51.940 --> 00:09:53.801
You could simplify this even further.

00:09:53.801 --> 00:09:55.345
This is the same thing

00:09:55.345 --> 00:09:58.262
as the derivative with respect to X

00:09:59.249 --> 00:10:02.583
of just, we have the same base.

00:10:02.583 --> 00:10:04.367
We can add the (mumbles) products.

00:10:04.367 --> 00:10:08.534
It's gonna be X to the negative
3., X to the negative 3.5,

00:10:11.190 --> 00:10:12.791
and so you can just use the power rule.

00:10:12.791 --> 00:10:14.281
So this is going to be equal to,

00:10:14.281 --> 00:10:16.089
bring the negative 3.5 out front.

00:10:16.089 --> 00:10:18.510
Negative 3.5 X to the,

00:10:18.510 --> 00:10:20.402
and then we just
decrement this one by one.

00:10:20.402 --> 00:10:21.692
We subtract one from that.

00:10:21.692 --> 00:10:23.915
Negative 4.5 power.

00:10:23.915 --> 00:10:25.084
So as you can see.

00:10:25.084 --> 00:10:26.527
He could have gotten this answer

00:10:26.527 --> 00:10:29.142
much much much much much much quicker,

00:10:29.142 --> 00:10:30.633
but he didn't make any mistakes.

00:10:30.633 --> 00:10:32.404
There's a little bit of a judgment error

00:10:32.404 --> 00:10:35.560
just immediately going
forth with the quotient rule

00:10:35.560 --> 00:10:37.871
which gets quite hairy quite fast.