1
00:00:15,000 --> 00:00:17,000
This image of the Vitruvian Man,

2
00:00:17,000 --> 00:00:18,000
taken from Leonardo's sketches,

3
00:00:18,000 --> 00:00:20,000
has become one of the most recognizable

4
00:00:20,000 --> 00:00:21,000
symbols of the Renaissance.

5
00:00:21,000 --> 00:00:22,000
But why?

6
00:00:22,000 --> 00:00:24,000
It's a simple pen and ink drawing, right?

7
00:00:24,000 --> 00:00:26,000
Wrong!

8
00:00:26,000 --> 00:00:27,000
Let's start to answer this question

9
00:00:27,000 --> 00:00:28,000
with a math problem.

10
00:00:28,000 --> 00:00:30,000
I know how to calculate the area of a circle.

11
00:00:30,000 --> 00:00:32,000
I take the value for pi

12
00:00:32,000 --> 00:00:34,000
and multiply it by the radius squared.

13
00:00:34,000 --> 00:00:36,000
I also know how to take the area of a square.

14
00:00:36,000 --> 00:00:39,000
I multiply the base by itself.

15
00:00:39,000 --> 00:00:41,000
But, how can I take the area of a circle

16
00:00:41,000 --> 00:00:43,000
and create a square with an equal area?

17
00:00:43,000 --> 00:00:45,000
This is a problem often called "squaring a circle"

18
00:00:45,000 --> 00:00:48,000
that was first proposed in the ancient world.

19
00:00:48,000 --> 00:00:49,000
And like many of ideas of the ancient world,

20
00:00:49,000 --> 00:00:51,000
it was given new life during the Renaissance.

21
00:00:51,000 --> 00:00:53,000
As it turns out,

22
00:00:53,000 --> 00:00:54,000
this problem is impossible to solve

23
00:00:54,000 --> 00:00:56,000
because of the nature of pi,

24
00:00:56,000 --> 00:00:57,000
but that's another story.

25
00:00:57,000 --> 00:00:58,000
Leonardo's sketch,

26
00:00:58,000 --> 00:00:59,000
which is influenced by the writings

27
00:00:59,000 --> 00:01:01,000
of a Roman architect, Vitruvius,

28
00:01:01,000 --> 00:01:03,000
places a man firmly at the center

29
00:01:03,000 --> 00:01:05,000
of a circle and a square.

30
00:01:05,000 --> 00:01:06,000
Vitruvius claimed the navel

31
00:01:06,000 --> 00:01:08,000
is the center of the human body

32
00:01:08,000 --> 00:01:09,000
and that if one takes a compass

33
00:01:09,000 --> 00:01:11,000
and places the fixed point on the navel,

34
00:01:11,000 --> 00:01:14,000
a circle can be drawn perfectly around the body.

35
00:01:14,000 --> 00:01:16,000
Additionally, Vitruvius recognized

36
00:01:16,000 --> 00:01:17,000
that arm span and height

37
00:01:17,000 --> 00:01:19,000
have a nearly perfect correspondence in the human body,

38
00:01:19,000 --> 00:01:22,000
thus placing the body perfectly inside a square as well.

39
00:01:22,000 --> 00:01:24,000
Leonardo used the ideas of Vitruvius

40
00:01:24,000 --> 00:01:27,000
to solve the problem of squaring a circle metaphorically

41
00:01:27,000 --> 00:01:29,000
using mankind as the area for both shapes.

42
00:01:29,000 --> 00:01:32,000
Leonardo wasn't just thinking about Vitruvius, though.

43
00:01:32,000 --> 00:01:33,000
There was an intellectual movement

44
00:01:33,000 --> 00:01:34,000
in Italy at the time

45
00:01:34,000 --> 00:01:36,000
called Neoplatonism.

46
00:01:36,000 --> 00:01:37,000
This movement took an old concept

47
00:01:37,000 --> 00:01:40,000
from the 4th century developed by Plato and Aristotle,

48
00:01:40,000 --> 00:01:42,000
called "The Great Chain of Being".

49
00:01:42,000 --> 00:01:44,000
This belief holds that the universe is a hierarchy

50
00:01:44,000 --> 00:01:45,000
resembling a chain,

51
00:01:45,000 --> 00:01:47,000
and that chain starts at the top with God,

52
00:01:47,000 --> 00:01:49,000
then travels down through the angels,

53
00:01:49,000 --> 00:01:50,000
planets,

54
00:01:50,000 --> 00:01:50,000
stars,

55
00:01:50,000 --> 00:01:51,000
and all lifeforms

56
00:01:51,000 --> 00:01:54,000
before ending with demons and devils.

57
00:01:54,000 --> 00:01:55,000
Early in this philosophic movement,

58
00:01:55,000 --> 00:01:58,000
it was thought that mankind's place in this chain

59
00:01:58,000 --> 00:01:59,000
was exactly in the center.

60
00:01:59,000 --> 00:02:01,000
Because humans have a mortal body

61
00:02:01,000 --> 00:02:03,000
accompanied by an immortal soul,

62
00:02:03,000 --> 00:02:05,000
we divide the universe nicely in half.

63
00:02:05,000 --> 00:02:07,000
Around the time Leonardo sketched

64
00:02:07,000 --> 00:02:08,000
the Vitruvian Man, however,

65
00:02:08,000 --> 00:02:10,000
a Neoplatonist named Pico della Mirandola

66
00:02:10,000 --> 00:02:12,000
had a different idea.

67
00:02:12,000 --> 00:02:13,000
He pried mankind off the chain

68
00:02:13,000 --> 00:02:15,000
and claimed that humans have a unique ability

69
00:02:15,000 --> 00:02:17,000
to take any position they want.

70
00:02:17,000 --> 00:02:19,000
Pico claimed that God desired

71
00:02:19,000 --> 00:02:20,000
a being capable of comprehending

72
00:02:20,000 --> 00:02:23,000
the beautiful and complicated universe he had created.

73
00:02:23,000 --> 00:02:25,000
This led to the creation of mankind,

74
00:02:25,000 --> 00:02:27,000
which he placed at the center of the universe

75
00:02:27,000 --> 00:02:30,000
with the ability to take whatever form he pleases.

76
00:02:30,000 --> 00:02:32,000
Mankind, according to Pico,

77
00:02:32,000 --> 00:02:34,000
can crawl down the chain and behave like an animal

78
00:02:34,000 --> 00:02:36,000
or crawl up the chain and behave like a god,

79
00:02:36,000 --> 00:02:38,000
it's our choice.

80
00:02:38,000 --> 00:02:39,000
Looking back at the sketch,

81
00:02:39,000 --> 00:02:41,000
we can see that by changing the position of the man,

82
00:02:41,000 --> 00:02:43,000
he can fill the irreconcillible areas

83
00:02:43,000 --> 00:02:45,000
of a circle and a square.

84
00:02:45,000 --> 00:02:47,000
If geometry is the language the universe is written in,

85
00:02:47,000 --> 00:02:48,000
then this sketch seems to say

86
00:02:48,000 --> 00:02:50,000
we can exist within all its elements.

87
00:02:50,000 --> 00:02:52,000
Mankind can fill whatever shape

88
00:02:52,000 --> 00:02:53,000
he pleases geometrically

89
00:02:53,000 --> 00:02:55,000
and philosophically as well.

90
00:02:55,000 --> 00:02:56,000
In this one sketch,

91
00:02:56,000 --> 00:02:57,000
Leondardo was able to combine

92
00:02:57,000 --> 00:02:58,000
the mathematics,

93
00:02:58,000 --> 00:02:59,000
religion,

94
00:02:59,000 --> 00:02:59,000
philosophy,

95
00:02:59,000 --> 00:03:00,000
architecture,

96
00:03:00,000 --> 00:03:02,000
and artistic skill of his age.

97
00:03:02,000 --> 00:03:03,000
No wonder it has become such an icon

98
00:03:03,000 --> 00:03:05,000
for the entire time period.