1 00:00:15,584 --> 00:00:17,074 This image of the Vitruvian Man, 2 00:00:17,074 --> 00:00:18,326 taken from Leonardo's sketches, 3 00:00:18,326 --> 00:00:20,037 has become one of the most recognizable 4 00:00:20,037 --> 00:00:21,649 symbols of the Renaissance. 5 00:00:21,649 --> 00:00:22,743 But why? 6 00:00:22,743 --> 00:00:24,680 It's a simple pen and ink drawing, right? 7 00:00:24,680 --> 00:00:26,003 Wrong! 8 00:00:26,003 --> 00:00:27,397 Let's start to answer this question 9 00:00:27,397 --> 00:00:28,634 with a math problem. 10 00:00:28,634 --> 00:00:30,720 I know how to calculate the area of a circle. 11 00:00:30,720 --> 00:00:32,099 I take the value for pi 12 00:00:32,099 --> 00:00:34,347 and multiply it by the radius squared. 13 00:00:34,347 --> 00:00:36,565 I also know how to take the area of a square. 14 00:00:36,565 --> 00:00:39,364 I multiply the base by itself. 15 00:00:39,364 --> 00:00:41,408 But how can I take the area of a circle 16 00:00:41,408 --> 00:00:43,799 and create a square with an equal area? 17 00:00:43,799 --> 00:00:45,739 This is a problem often called "squaring a circle" 18 00:00:45,739 --> 00:00:48,047 that was first proposed in the ancient world. 19 00:00:48,047 --> 00:00:49,658 And like many of ideas of the ancient world, 20 00:00:49,658 --> 00:00:51,894 it was given new life during the Renaissance. 21 00:00:51,894 --> 00:00:53,078 As it turns out, 22 00:00:53,078 --> 00:00:54,466 this problem is impossible to solve 23 00:00:54,466 --> 00:00:56,090 because of the nature of pi, 24 00:00:56,090 --> 00:00:57,912 but that's another story. 25 00:00:57,912 --> 00:00:58,626 Leonardo's sketch, 26 00:00:58,626 --> 00:00:59,880 which is influenced by the writings 27 00:00:59,880 --> 00:01:01,905 of the Roman architect, Vitruvius, 28 00:01:01,905 --> 00:01:03,510 places a man firmly at the center 29 00:01:03,510 --> 00:01:05,507 of a circle and a square. 30 00:01:05,507 --> 00:01:06,842 Vitruvius claimed the navel 31 00:01:06,842 --> 00:01:08,103 is the center of the human body 32 00:01:08,103 --> 00:01:09,629 and that if one takes a compass 33 00:01:09,629 --> 00:01:11,375 and places the fixed point on the navel, 34 00:01:11,375 --> 00:01:14,015 a circle can be drawn perfectly around the body. 35 00:01:14,015 --> 00:01:16,004 Additionally, Vitruvius recognized 36 00:01:16,004 --> 00:01:17,106 that arm span and height 37 00:01:17,106 --> 00:01:19,692 have a nearly perfect correspondence in the human body, 38 00:01:19,692 --> 00:01:22,857 thus placing the body perfectly inside a square as well. 39 00:01:22,857 --> 00:01:24,231 Leonardo used the ideas of Vitruvius 40 00:01:24,231 --> 00:01:27,027 to solve the problem of squaring a circle metaphorically 41 00:01:27,027 --> 00:01:29,735 using mankind as the area for both shapes. 42 00:01:29,735 --> 00:01:32,611 Leonardo wasn't just thinking about Vitruvius, though. 43 00:01:32,611 --> 00:01:33,815 There was an intellectual movement 44 00:01:33,815 --> 00:01:34,913 in Italy at the time 45 00:01:34,913 --> 00:01:36,321 called Neoplatonism. 46 00:01:36,321 --> 00:01:37,741 This movement took an old concept 47 00:01:37,741 --> 00:01:40,445 from the 4th century developed by Plato and Aristotle, 48 00:01:40,445 --> 00:01:42,278 called "The Great Chain of Being". 49 00:01:42,278 --> 00:01:44,447 This belief holds that the universe is a hierarchy 50 00:01:44,447 --> 00:01:45,614 resembling a chain, 51 00:01:45,614 --> 00:01:47,779 and that chain starts at the top with God, 52 00:01:47,779 --> 00:01:49,736 then travels down through the angels, 53 00:01:49,736 --> 00:01:50,313 planets, 54 00:01:50,313 --> 00:01:50,902 stars, 55 00:01:50,902 --> 00:01:51,982 and all lifeforms 56 00:01:51,982 --> 00:01:54,066 before ending with demons and devils. 57 00:01:54,066 --> 00:01:55,813 Early in this philosophic movement, 58 00:01:55,813 --> 00:01:58,015 it was thought that mankind's place in this chain 59 00:01:58,015 --> 00:01:59,527 was exactly in the center. 60 00:01:59,527 --> 00:02:01,226 Because humans have a mortal body 61 00:02:01,226 --> 00:02:03,158 accompanied by an immortal soul, 62 00:02:03,158 --> 00:02:05,308 we divide the universe nicely in half. 63 00:02:05,308 --> 00:02:07,067 Around the time Leonardo sketched 64 00:02:07,067 --> 00:02:08,686 the Vitruvian Man, however, 65 00:02:08,686 --> 00:02:10,871 a Neoplatonist named Pico della Mirandola 66 00:02:10,871 --> 00:02:12,236 had a different idea. 67 00:02:12,236 --> 00:02:13,814 He pried mankind off the chain 68 00:02:13,814 --> 00:02:15,779 and claimed that humans have a unique ability 69 00:02:15,779 --> 00:02:17,645 to take any position they want. 70 00:02:17,645 --> 00:02:19,228 Pico claimed that God desired 71 00:02:19,228 --> 00:02:20,700 a being capable of comprehending 72 00:02:20,700 --> 00:02:23,569 the beautiful and complicated universe he had created. 73 00:02:23,569 --> 00:02:25,488 This led to the creation of mankind, 74 00:02:25,488 --> 00:02:27,236 which he placed at the center of the universe 75 00:02:27,236 --> 00:02:30,042 with the ability to take whatever form he pleases. 76 00:02:30,042 --> 00:02:32,141 Mankind, according to Pico, 77 00:02:32,141 --> 00:02:34,702 could crawl down the chain and behave like an animal 78 00:02:34,702 --> 00:02:36,923 or crawl up the chain and behave like a god, 79 00:02:36,923 --> 00:02:38,228 it's our choice. 80 00:02:38,228 --> 00:02:39,481 Looking back at the sketch, 81 00:02:39,481 --> 00:02:41,591 we can see that by changing the position of the man, 82 00:02:41,591 --> 00:02:43,147 he can fill the irreconcilable areas 83 00:02:43,147 --> 00:02:45,010 of a circle and a square. 84 00:02:45,010 --> 00:02:47,313 If geometry is the language the universe is written in, 85 00:02:47,313 --> 00:02:48,680 then this sketch seems to say 86 00:02:48,680 --> 00:02:50,517 we can exist within all its elements. 87 00:02:50,517 --> 00:02:52,058 Mankind can fill whatever shape 88 00:02:52,058 --> 00:02:53,353 he pleases geometrically 89 00:02:53,353 --> 00:02:55,272 and philosophically as well. 90 00:02:55,272 --> 00:02:56,352 In this one sketch, 91 00:02:56,352 --> 00:02:57,642 Leondardo was able to combine 92 00:02:57,642 --> 00:02:58,448 the mathematics, 93 00:02:58,448 --> 00:02:59,130 religion, 94 00:02:59,130 --> 00:02:59,944 philosophy, 95 00:02:59,944 --> 00:03:00,804 architecture, 96 00:03:00,804 --> 00:03:02,527 and artistic skill of his age. 97 00:03:02,527 --> 00:03:03,729 No wonder it has become such an icon 98 00:03:03,729 --> 00:03:05,741 for the entire time period.