WEBVTT

00:00:15.526 --> 00:00:17.050
This image of the Vitruvian Man,

00:00:17.074 --> 00:00:18.302
taken from Leonardo's sketches,

00:00:18.326 --> 00:00:20.184
has become one of the most recognizable

00:00:20.208 --> 00:00:21.625
symbols of the Renaissance.

00:00:21.649 --> 00:00:22.719
But why?

00:00:22.743 --> 00:00:24.696
It's a simple pen and ink drawing, right?

00:00:24.720 --> 00:00:25.979
Wrong!

00:00:26.003 --> 00:00:27.373
Let's start to answer this question

00:00:27.397 --> 00:00:28.610
with a math problem.

00:00:28.634 --> 00:00:30.777
I know how to calculate
the area of a circle.

00:00:30.801 --> 00:00:32.075
I take the value for pi

00:00:32.099 --> 00:00:34.323
and multiply it by the radius squared.

00:00:34.347 --> 00:00:36.541
I also know how to take
the area of a square.

00:00:36.565 --> 00:00:39.340
I multiply the base by itself.

00:00:39.364 --> 00:00:41.384
But how can I take the area of a circle

00:00:41.408 --> 00:00:43.775
and create a square with an equal area?

00:00:43.799 --> 00:00:45.715
This is a problem often
called "squaring a circle"

00:00:45.739 --> 00:00:48.023
that was first proposed
in the ancient world.

00:00:48.047 --> 00:00:49.634
And like many of ideas
of the ancient world,

00:00:49.658 --> 00:00:51.870
it was given new life
during the Renaissance.

00:00:51.894 --> 00:00:53.054
As it turns out,

00:00:53.078 --> 00:00:54.442
this problem is impossible to solve

00:00:54.466 --> 00:00:56.066
because of the nature of pi,

00:00:56.090 --> 00:00:57.888
but that's another story.

00:00:57.912 --> 00:00:58.602
Leonardo's sketch,

00:00:58.626 --> 00:00:59.856
which is influenced by the writings

00:00:59.880 --> 00:01:01.881
of the Roman architect, Vitruvius,

00:01:01.905 --> 00:01:03.486
places a man firmly at the center

00:01:03.510 --> 00:01:05.483
of a circle and a square.

00:01:05.507 --> 00:01:06.818
Vitruvius claimed the navel

00:01:06.842 --> 00:01:08.079
is the center of the human body

00:01:08.103 --> 00:01:09.605
and that if one takes a compass

00:01:09.629 --> 00:01:11.534
and places the fixed point on the navel,

00:01:11.558 --> 00:01:13.991
a circle can be drawn
perfectly around the body.

00:01:14.015 --> 00:01:15.980
Additionally, Vitruvius recognized

00:01:16.004 --> 00:01:17.082
that arm span and height

00:01:17.106 --> 00:01:19.726
have a nearly perfect
correspondence in the human body,

00:01:19.750 --> 00:01:22.833
thus placing the body perfectly
inside a square as well.

00:01:22.857 --> 00:01:24.207
Leonardo used the ideas of Vitruvius

00:01:24.231 --> 00:01:27.003
to solve the problem of squaring
a circle metaphorically

00:01:27.027 --> 00:01:29.711
using mankind as the area for both shapes.

00:01:29.735 --> 00:01:32.587
Leonardo wasn't just thinking
about Vitruvius, though.

00:01:32.611 --> 00:01:33.791
There was an intellectual movement

00:01:33.815 --> 00:01:34.889
in Italy at the time

00:01:34.913 --> 00:01:36.297
called Neoplatonism.

00:01:36.321 --> 00:01:37.717
This movement took an old concept

00:01:37.741 --> 00:01:40.421
from the 4th century developed
by Plato and Aristotle,

00:01:40.445 --> 00:01:42.254
called "The Great Chain of Being".

00:01:42.278 --> 00:01:44.659
This belief holds
that the universe is a hierarchy

00:01:44.683 --> 00:01:45.590
resembling a chain,

00:01:45.614 --> 00:01:47.755
and that chain starts at the top with God,

00:01:47.779 --> 00:01:49.712
then travels down through the angels,

00:01:49.736 --> 00:01:50.289
planets,

00:01:50.313 --> 00:01:50.878
stars,

00:01:50.902 --> 00:01:51.958
and all lifeforms

00:01:51.982 --> 00:01:54.042
before ending with demons and devils.

00:01:54.066 --> 00:01:55.789
Early in this philosophic movement,

00:01:55.813 --> 00:01:58.147
it was thought
that mankind's place in this chain

00:01:58.171 --> 00:01:59.503
was exactly in the center.

00:01:59.527 --> 00:02:01.202
Because humans have a mortal body

00:02:01.226 --> 00:02:03.134
accompanied by an immortal soul,

00:02:03.158 --> 00:02:05.284
we divide the universe nicely in half.

00:02:05.308 --> 00:02:07.043
Around the time Leonardo sketched

00:02:07.067 --> 00:02:08.662
the Vitruvian Man, however,

00:02:08.686 --> 00:02:10.847
a Neoplatonist named Pico della Mirandola

00:02:10.871 --> 00:02:12.212
had a different idea.

00:02:12.236 --> 00:02:13.790
He pried mankind off the chain

00:02:13.814 --> 00:02:15.957
and claimed that humans
have a unique ability

00:02:15.981 --> 00:02:17.621
to take any position they want.

00:02:17.645 --> 00:02:19.204
Pico claimed that God desired

00:02:19.228 --> 00:02:20.752
a being capable of comprehending

00:02:20.776 --> 00:02:23.545
the beautiful and complicated
universe he had created.

00:02:23.569 --> 00:02:25.464
This led to the creation of mankind,

00:02:25.488 --> 00:02:27.584
which he placed at the center
of the universe

00:02:27.608 --> 00:02:30.018
with the ability to take
whatever form he pleases.

00:02:30.042 --> 00:02:32.117
Mankind, according to Pico,

00:02:32.141 --> 00:02:34.678
could crawl down the chain
and behave like an animal

00:02:34.702 --> 00:02:36.899
or crawl up the chain
and behave like a god,

00:02:36.923 --> 00:02:38.204
it's our choice.

00:02:38.228 --> 00:02:39.457
Looking back at the sketch,

00:02:39.481 --> 00:02:41.567
we can see that by changing
the position of the man,

00:02:41.591 --> 00:02:43.306
he can fill the irreconcilable areas

00:02:43.330 --> 00:02:44.986
of a circle and a square.

00:02:45.010 --> 00:02:47.289
If geometry is the language
the universe is written in,

00:02:47.313 --> 00:02:48.694
then this sketch seems to say

00:02:48.718 --> 00:02:50.493
we can exist within all its elements.

00:02:50.517 --> 00:02:52.034
Mankind can fill whatever shape

00:02:52.058 --> 00:02:53.329
he pleases geometrically

00:02:53.353 --> 00:02:55.248
and philosophically as well.

00:02:55.272 --> 00:02:56.328
In this one sketch,

00:02:56.352 --> 00:02:57.618
Leondardo was able to combine

00:02:57.642 --> 00:02:58.424
the mathematics,

00:02:58.448 --> 00:02:59.106
religion,

00:02:59.130 --> 00:02:59.920
philosophy,

00:02:59.944 --> 00:03:00.780
architecture,

00:03:00.804 --> 00:03:02.503
and artistic skill of his age.

00:03:02.527 --> 00:03:04.242
No wonder it has become such an icon

00:03:04.266 --> 00:03:06.278
for the entire time period.