WEBVTT

00:00:15.584 --> 00:00:17.074
This image of the Vitruvian Man,

00:00:17.074 --> 00:00:18.326
taken from Leonardo's sketches,

00:00:18.326 --> 00:00:20.037
has become one of the most recognizable

00:00:20.037 --> 00:00:21.649
symbols of the Renaissance.

00:00:21.649 --> 00:00:22.743
But why?

00:00:22.743 --> 00:00:24.680
It's a simple pen and ink drawing, right?

00:00:24.680 --> 00:00:26.003
Wrong!

00:00:26.003 --> 00:00:27.397
Let's start to answer this question

00:00:27.397 --> 00:00:28.634
with a math problem.

00:00:28.634 --> 00:00:30.720
I know how to calculate the area of a circle.

00:00:30.720 --> 00:00:32.099
I take the value for pi

00:00:32.099 --> 00:00:34.347
and multiply it by the radius squared.

00:00:34.347 --> 00:00:36.565
I also know how to take the area of a square.

00:00:36.565 --> 00:00:39.364
I multiply the base by itself.

00:00:39.364 --> 00:00:41.408
But how can I take the area of a circle

00:00:41.408 --> 00:00:43.799
and create a square with an equal area?

00:00:43.799 --> 00:00:45.739
This is a problem often called "squaring a circle"

00:00:45.739 --> 00:00:48.047
that was first proposed in the ancient world.

00:00:48.047 --> 00:00:49.658
And like many of ideas of the ancient world,

00:00:49.658 --> 00:00:51.894
it was given new life during the Renaissance.

00:00:51.894 --> 00:00:53.078
As it turns out,

00:00:53.078 --> 00:00:54.466
this problem is impossible to solve

00:00:54.466 --> 00:00:56.090
because of the nature of pi,

00:00:56.090 --> 00:00:57.912
but that's another story.

00:00:57.912 --> 00:00:58.626
Leonardo's sketch,

00:00:58.626 --> 00:00:59.880
which is influenced by the writings

00:00:59.880 --> 00:01:01.905
of the Roman architect, Vitruvius,

00:01:01.905 --> 00:01:03.510
places a man firmly at the center

00:01:03.510 --> 00:01:05.507
of a circle and a square.

00:01:05.507 --> 00:01:06.842
Vitruvius claimed the navel

00:01:06.842 --> 00:01:08.103
is the center of the human body

00:01:08.103 --> 00:01:09.629
and that if one takes a compass

00:01:09.629 --> 00:01:11.375
and places the fixed point on the navel,

00:01:11.375 --> 00:01:14.015
a circle can be drawn perfectly around the body.

00:01:14.015 --> 00:01:16.004
Additionally, Vitruvius recognized

00:01:16.004 --> 00:01:17.106
that arm span and height

00:01:17.106 --> 00:01:19.692
have a nearly perfect correspondence in the human body,

00:01:19.692 --> 00:01:22.857
thus placing the body perfectly inside a square as well.

00:01:22.857 --> 00:01:24.231
Leonardo used the ideas of Vitruvius

00:01:24.231 --> 00:01:27.027
to solve the problem of squaring a circle metaphorically

00:01:27.027 --> 00:01:29.735
using mankind as the area for both shapes.

00:01:29.735 --> 00:01:32.611
Leonardo wasn't just thinking about Vitruvius, though.

00:01:32.611 --> 00:01:33.815
There was an intellectual movement

00:01:33.815 --> 00:01:34.913
in Italy at the time

00:01:34.913 --> 00:01:36.321
called Neoplatonism.

00:01:36.321 --> 00:01:37.741
This movement took an old concept

00:01:37.741 --> 00:01:40.445
from the 4th century developed by Plato and Aristotle,

00:01:40.445 --> 00:01:42.278
called "The Great Chain of Being".

00:01:42.278 --> 00:01:44.447
This belief holds that the universe is a hierarchy

00:01:44.447 --> 00:01:45.614
resembling a chain,

00:01:45.614 --> 00:01:47.779
and that chain starts at the top with God,

00:01:47.779 --> 00:01:49.736
then travels down through the angels,

00:01:49.736 --> 00:01:50.313
planets,

00:01:50.313 --> 00:01:50.902
stars,

00:01:50.902 --> 00:01:51.982
and all lifeforms

00:01:51.982 --> 00:01:54.066
before ending with demons and devils.

00:01:54.066 --> 00:01:55.813
Early in this philosophic movement,

00:01:55.813 --> 00:01:58.015
it was thought that mankind's place in this chain

00:01:58.015 --> 00:01:59.527
was exactly in the center.

00:01:59.527 --> 00:02:01.226
Because humans have a mortal body

00:02:01.226 --> 00:02:03.158
accompanied by an immortal soul,

00:02:03.158 --> 00:02:05.308
we divide the universe nicely in half.

00:02:05.308 --> 00:02:07.067
Around the time Leonardo sketched

00:02:07.067 --> 00:02:08.686
the Vitruvian Man, however,

00:02:08.686 --> 00:02:10.871
a Neoplatonist named Pico della Mirandola

00:02:10.871 --> 00:02:12.236
had a different idea.

00:02:12.236 --> 00:02:13.814
He pried mankind off the chain

00:02:13.814 --> 00:02:15.779
and claimed that humans have a unique ability

00:02:15.779 --> 00:02:17.645
to take any position they want.

00:02:17.645 --> 00:02:19.228
Pico claimed that God desired

00:02:19.228 --> 00:02:20.700
a being capable of comprehending

00:02:20.700 --> 00:02:23.569
the beautiful and complicated universe he had created.

00:02:23.569 --> 00:02:25.488
This led to the creation of mankind,

00:02:25.488 --> 00:02:27.236
which he placed at the center of the universe

00:02:27.236 --> 00:02:30.042
with the ability to take whatever form he pleases.

00:02:30.042 --> 00:02:32.141
Mankind, according to Pico,

00:02:32.141 --> 00:02:34.702
could crawl down the chain and behave like an animal

00:02:34.702 --> 00:02:36.923
or crawl up the chain and behave like a god,

00:02:36.923 --> 00:02:38.228
it's our choice.

00:02:38.228 --> 00:02:39.481
Looking back at the sketch,

00:02:39.481 --> 00:02:41.591
we can see that by changing the position of the man,

00:02:41.591 --> 00:02:43.147
he can fill the irreconcilable areas

00:02:43.147 --> 00:02:45.010
of a circle and a square.

00:02:45.010 --> 00:02:47.313
If geometry is the language the universe is written in,

00:02:47.313 --> 00:02:48.680
then this sketch seems to say

00:02:48.680 --> 00:02:50.517
we can exist within all its elements.

00:02:50.517 --> 00:02:52.058
Mankind can fill whatever shape

00:02:52.058 --> 00:02:53.353
he pleases geometrically

00:02:53.353 --> 00:02:55.272
and philosophically as well.

00:02:55.272 --> 00:02:56.352
In this one sketch,

00:02:56.352 --> 00:02:57.642
Leondardo was able to combine

00:02:57.642 --> 00:02:58.448
the mathematics,

00:02:58.448 --> 00:02:59.130
religion,

00:02:59.130 --> 00:02:59.944
philosophy,

00:02:59.944 --> 00:03:00.804
architecture,

00:03:00.804 --> 00:03:02.527
and artistic skill of his age.

00:03:02.527 --> 00:03:03.729
No wonder it has become such an icon

00:03:03.729 --> 00:03:05.741
for the entire time period.