[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:10.67,0:00:13.78,Default,,0000,0000,0000,,So what makes a piece of music beautiful?
Dialogue: 0,0:00:13.78,0:00:15.81,Default,,0000,0000,0000,,Well, most musicologists would argue
Dialogue: 0,0:00:15.81,0:00:18.73,Default,,0000,0000,0000,,that repetition is a key aspect of beauty.
Dialogue: 0,0:00:18.73,0:00:21.60,Default,,0000,0000,0000,,The idea that we take a melody, a motif, a musical idea,
Dialogue: 0,0:00:21.60,0:00:24.80,Default,,0000,0000,0000,,we repeat it, we set up the expectation for repetition,
Dialogue: 0,0:00:24.80,0:00:27.66,Default,,0000,0000,0000,,and then we either realize it or we break the repetition.
Dialogue: 0,0:00:27.66,0:00:29.77,Default,,0000,0000,0000,,And that's a key component of beauty.
Dialogue: 0,0:00:29.77,0:00:33.04,Default,,0000,0000,0000,,So if repetition and patterns are key to beauty,
Dialogue: 0,0:00:33.04,0:00:36.10,Default,,0000,0000,0000,,then what would the absence of patterns sound like
Dialogue: 0,0:00:36.10,0:00:37.46,Default,,0000,0000,0000,,if we wrote a piece of music
Dialogue: 0,0:00:37.46,0:00:41.31,Default,,0000,0000,0000,,that had no repetition whatsoever in it?
Dialogue: 0,0:00:41.31,0:00:43.38,Default,,0000,0000,0000,,That's actually an interesting mathematical question.
Dialogue: 0,0:00:43.38,0:00:46.91,Default,,0000,0000,0000,,Is it possible to write a piece of music that has no repetition whatsoever?
Dialogue: 0,0:00:46.91,0:00:49.14,Default,,0000,0000,0000,,It's not random. Random is easy.
Dialogue: 0,0:00:49.14,0:00:51.94,Default,,0000,0000,0000,,Repetition-free, it turns out, is extremely difficult
Dialogue: 0,0:00:51.94,0:00:53.91,Default,,0000,0000,0000,,and the only reason that we can actually do it
Dialogue: 0,0:00:53.91,0:00:57.24,Default,,0000,0000,0000,,is because of a man who was hunting for submarines.
Dialogue: 0,0:00:57.24,0:00:59.40,Default,,0000,0000,0000,,It turns out a guy who was trying to develop
Dialogue: 0,0:00:59.40,0:01:01.72,Default,,0000,0000,0000,,the world's perfect sonar ping
Dialogue: 0,0:01:01.72,0:01:04.86,Default,,0000,0000,0000,,solved the problem of writing pattern-free music.
Dialogue: 0,0:01:04.86,0:01:08.06,Default,,0000,0000,0000,,And that's what the topic of the talk is today.
Dialogue: 0,0:01:08.06,0:01:13.02,Default,,0000,0000,0000,,So, recall that in sonar,
Dialogue: 0,0:01:13.02,0:01:15.90,Default,,0000,0000,0000,,you have a ship that sends out some sound in the water,
Dialogue: 0,0:01:15.92,0:01:18.05,Default,,0000,0000,0000,,and it listens for it -- an echo.
Dialogue: 0,0:01:18.05,0:01:20.80,Default,,0000,0000,0000,,The sound goes down, it echoes back, it goes down, echoes back.
Dialogue: 0,0:01:20.80,0:01:23.89,Default,,0000,0000,0000,,The time it takes the sound to come back tells you how far away it is.
Dialogue: 0,0:01:23.89,0:01:26.87,Default,,0000,0000,0000,,If it comes at a higher pitch, it's because the thing is moving toward you.
Dialogue: 0,0:01:26.87,0:01:29.96,Default,,0000,0000,0000,,If it comes back at a lower pitch, it's because it's moving away from you.
Dialogue: 0,0:01:29.96,0:01:32.47,Default,,0000,0000,0000,,So how would you design a perfect sonar ping?
Dialogue: 0,0:01:32.47,0:01:36.58,Default,,0000,0000,0000,,Well, in the 1960s, a guy by the name of John Costas
Dialogue: 0,0:01:36.58,0:01:40.35,Default,,0000,0000,0000,,was working on the Navy's extremely expensive sonar system.
Dialogue: 0,0:01:40.35,0:01:41.55,Default,,0000,0000,0000,,It wasn't working,
Dialogue: 0,0:01:41.55,0:01:44.10,Default,,0000,0000,0000,,and it was because the ping they were using was inappropriate.
Dialogue: 0,0:01:44.10,0:01:46.48,Default,,0000,0000,0000,,It was a ping much like the following here,
Dialogue: 0,0:01:46.48,0:01:49.06,Default,,0000,0000,0000,,which you can think of this as the notes
Dialogue: 0,0:01:49.06,0:01:51.02,Default,,0000,0000,0000,,and this is time.
Dialogue: 0,0:01:51.02,0:01:52.82,Default,,0000,0000,0000,,(Music)
Dialogue: 0,0:01:52.82,0:01:55.57,Default,,0000,0000,0000,,So that was the sonar ping they were using: a down chirp.
Dialogue: 0,0:01:55.57,0:01:57.82,Default,,0000,0000,0000,,It turns out that's a really bad ping.
Dialogue: 0,0:01:57.82,0:02:00.54,Default,,0000,0000,0000,,Why? Because it looks like shifts of itself.
Dialogue: 0,0:02:00.54,0:02:03.20,Default,,0000,0000,0000,,The relationship between the first two notes is the same
Dialogue: 0,0:02:03.20,0:02:05.68,Default,,0000,0000,0000,,as the second two and so forth.
Dialogue: 0,0:02:05.68,0:02:08.18,Default,,0000,0000,0000,,So he designed a different kind of sonar ping:
Dialogue: 0,0:02:08.18,0:02:09.67,Default,,0000,0000,0000,,one that looks random.
Dialogue: 0,0:02:09.67,0:02:12.64,Default,,0000,0000,0000,,These look like a random pattern of dots, but they're not.
Dialogue: 0,0:02:12.64,0:02:15.09,Default,,0000,0000,0000,,If you look very carefully, you may notice
Dialogue: 0,0:02:15.09,0:02:18.81,Default,,0000,0000,0000,,that in fact the relationship between each pair of dots is distinct.
Dialogue: 0,0:02:18.81,0:02:20.84,Default,,0000,0000,0000,,Nothing is ever repeated.
Dialogue: 0,0:02:20.84,0:02:23.68,Default,,0000,0000,0000,,The first two notes and every other pair of notes
Dialogue: 0,0:02:23.68,0:02:26.42,Default,,0000,0000,0000,,have a different relationship.
Dialogue: 0,0:02:26.42,0:02:29.45,Default,,0000,0000,0000,,So the fact that we know about these patterns is unusual.
Dialogue: 0,0:02:29.45,0:02:31.43,Default,,0000,0000,0000,,John Costas is the inventor of these patterns.
Dialogue: 0,0:02:31.43,0:02:33.93,Default,,0000,0000,0000,,This is a picture from 2006, shortly before his death.
Dialogue: 0,0:02:33.93,0:02:37.28,Default,,0000,0000,0000,,He was the sonar engineer working for the Navy.
Dialogue: 0,0:02:37.28,0:02:39.85,Default,,0000,0000,0000,,He was thinking about these patterns
Dialogue: 0,0:02:39.85,0:02:42.35,Default,,0000,0000,0000,,and he was, by hand, able to come up with them to size 12 --
Dialogue: 0,0:02:42.35,0:02:43.73,Default,,0000,0000,0000,,12 by 12.
Dialogue: 0,0:02:43.73,0:02:45.96,Default,,0000,0000,0000,,He couldn't go any further and he thought
Dialogue: 0,0:02:45.96,0:02:47.92,Default,,0000,0000,0000,,maybe they don't exist in any size bigger than 12.
Dialogue: 0,0:02:47.92,0:02:50.33,Default,,0000,0000,0000,,So he wrote a letter to the mathematician in the middle,
Dialogue: 0,0:02:50.33,0:02:52.53,Default,,0000,0000,0000,,who was a young mathematician in California at the time,
Dialogue: 0,0:02:52.53,0:02:53.83,Default,,0000,0000,0000,,Solomon Golomb.
Dialogue: 0,0:02:53.83,0:02:56.02,Default,,0000,0000,0000,,It turns out that Solomon Golomb was one of the
Dialogue: 0,0:02:56.02,0:02:58.96,Default,,0000,0000,0000,,most gifted discrete mathematicians of our time.
Dialogue: 0,0:02:58.96,0:03:02.50,Default,,0000,0000,0000,,John asked Solomon if he could tell him the right reference
Dialogue: 0,0:03:02.50,0:03:04.05,Default,,0000,0000,0000,,to where these patterns were.
Dialogue: 0,0:03:04.05,0:03:05.44,Default,,0000,0000,0000,,There was no reference.
Dialogue: 0,0:03:05.44,0:03:06.99,Default,,0000,0000,0000,,Nobody had ever thought about
Dialogue: 0,0:03:06.99,0:03:10.21,Default,,0000,0000,0000,,a repetition, a pattern-free structure before.
Dialogue: 0,0:03:10.21,0:03:13.30,Default,,0000,0000,0000,,Solomon Golomb spent the summer thinking about the problem.
Dialogue: 0,0:03:13.30,0:03:16.36,Default,,0000,0000,0000,,And he relied on the mathematics of this gentleman here,
Dialogue: 0,0:03:16.36,0:03:17.80,Default,,0000,0000,0000,,Evariste Galois.
Dialogue: 0,0:03:17.80,0:03:19.64,Default,,0000,0000,0000,,Now, Galois is a very famous mathematician.
Dialogue: 0,0:03:19.64,0:03:22.62,Default,,0000,0000,0000,,He's famous because he invented a whole branch of mathematics,
Dialogue: 0,0:03:22.62,0:03:25.22,Default,,0000,0000,0000,,which bears his name, called Galois Field Theory.
Dialogue: 0,0:03:25.22,0:03:28.62,Default,,0000,0000,0000,,It's the mathematics of prime numbers.
Dialogue: 0,0:03:28.62,0:03:31.99,Default,,0000,0000,0000,,He's also famous because of the way that he died.
Dialogue: 0,0:03:31.99,0:03:35.44,Default,,0000,0000,0000,,So the story is that he stood up for the honor of a young woman.
Dialogue: 0,0:03:35.44,0:03:38.90,Default,,0000,0000,0000,,He was challenged to a duel and he accepted.
Dialogue: 0,0:03:38.90,0:03:41.40,Default,,0000,0000,0000,,And shortly before the duel occurred,
Dialogue: 0,0:03:41.40,0:03:43.25,Default,,0000,0000,0000,,he wrote down all of his mathematical ideas,
Dialogue: 0,0:03:43.25,0:03:44.45,Default,,0000,0000,0000,,sent letters to all of his friends,
Dialogue: 0,0:03:44.45,0:03:45.78,Default,,0000,0000,0000,,saying please, please, please --
Dialogue: 0,0:03:45.78,0:03:46.77,Default,,0000,0000,0000,,this is 200 years ago --
Dialogue: 0,0:03:46.77,0:03:47.75,Default,,0000,0000,0000,,please, please, please
Dialogue: 0,0:03:47.75,0:03:50.86,Default,,0000,0000,0000,,see that these things get published eventually.
Dialogue: 0,0:03:50.86,0:03:54.17,Default,,0000,0000,0000,,He then fought the duel, was shot, and died at age 20.
Dialogue: 0,0:03:54.17,0:03:57.12,Default,,0000,0000,0000,,The mathematics that runs your cell phones, the Internet,
Dialogue: 0,0:03:57.12,0:04:00.89,Default,,0000,0000,0000,,that allows us to communicate, DVDs,
Dialogue: 0,0:04:00.89,0:04:03.70,Default,,0000,0000,0000,,all comes from the mind of Evariste Galois,
Dialogue: 0,0:04:03.70,0:04:06.62,Default,,0000,0000,0000,,a mathematician who died 20 years young.
Dialogue: 0,0:04:06.62,0:04:08.80,Default,,0000,0000,0000,,When you talk about the legacy that you leave,
Dialogue: 0,0:04:08.80,0:04:10.62,Default,,0000,0000,0000,,of course he couldn't have even anticipated the way
Dialogue: 0,0:04:10.62,0:04:12.30,Default,,0000,0000,0000,,that his mathematics would be used.
Dialogue: 0,0:04:12.30,0:04:14.45,Default,,0000,0000,0000,,Thankfully, his mathematics was eventually published.
Dialogue: 0,0:04:14.45,0:04:17.26,Default,,0000,0000,0000,,Solomon Golomb realized that that mathematics was
Dialogue: 0,0:04:17.26,0:04:20.30,Default,,0000,0000,0000,,exactly the mathematics needed to solve the problem
Dialogue: 0,0:04:20.30,0:04:22.53,Default,,0000,0000,0000,,of creating a pattern-free structure.
Dialogue: 0,0:04:22.53,0:04:25.98,Default,,0000,0000,0000,,So he sent a letter back to John saying it turns out you can
Dialogue: 0,0:04:25.98,0:04:28.27,Default,,0000,0000,0000,,generate these patterns using prime number theory.
Dialogue: 0,0:04:28.27,0:04:34.49,Default,,0000,0000,0000,,And John went about and solved the sonar problem for the Navy.
Dialogue: 0,0:04:34.49,0:04:36.90,Default,,0000,0000,0000,,So what do these patterns look like again?
Dialogue: 0,0:04:36.90,0:04:38.86,Default,,0000,0000,0000,,Here's a pattern here.
Dialogue: 0,0:04:38.86,0:04:42.83,Default,,0000,0000,0000,,This is an 88 by 88 sized Costas array.
Dialogue: 0,0:04:42.85,0:04:45.14,Default,,0000,0000,0000,,It's generated in a very simple way.
Dialogue: 0,0:04:45.14,0:04:49.25,Default,,0000,0000,0000,,Elementary school mathematics is sufficient to solve this problem.
Dialogue: 0,0:04:49.25,0:04:52.82,Default,,0000,0000,0000,,It's generated by repeatedly multiplying by the number 3.
Dialogue: 0,0:04:52.82,0:04:58.21,Default,,0000,0000,0000,,1, 3, 9, 27, 81, 243 ...
Dialogue: 0,0:04:58.21,0:05:00.59,Default,,0000,0000,0000,,When I get to a bigger [number] that's larger than 89
Dialogue: 0,0:05:00.59,0:05:01.77,Default,,0000,0000,0000,,which happens to be prime,
Dialogue: 0,0:05:01.77,0:05:04.65,Default,,0000,0000,0000,,I keep taking 89s away until I get back below.
Dialogue: 0,0:05:04.65,0:05:08.35,Default,,0000,0000,0000,,And this will eventually fill the entire grid, 88 by 88.
Dialogue: 0,0:05:08.35,0:05:11.70,Default,,0000,0000,0000,,And there happen to be 88 notes on the piano.
Dialogue: 0,0:05:11.70,0:05:14.60,Default,,0000,0000,0000,,So today, we are going to have the world premiere
Dialogue: 0,0:05:14.60,0:05:19.66,Default,,0000,0000,0000,,of the world's first pattern-free piano sonata.
Dialogue: 0,0:05:19.66,0:05:22.50,Default,,0000,0000,0000,,So, back to the question of music.
Dialogue: 0,0:05:22.50,0:05:23.90,Default,,0000,0000,0000,,What makes music beautiful?
Dialogue: 0,0:05:23.90,0:05:26.42,Default,,0000,0000,0000,,Let's think about one of the most beautiful pieces ever written,
Dialogue: 0,0:05:26.42,0:05:27.98,Default,,0000,0000,0000,,Beethoven's Fifth Symphony.
Dialogue: 0,0:05:27.98,0:05:31.52,Default,,0000,0000,0000,,And the famous "da na na na" motif.
Dialogue: 0,0:05:31.52,0:05:34.35,Default,,0000,0000,0000,,That motif occurs hundreds of times in the symphony --
Dialogue: 0,0:05:34.35,0:05:36.70,Default,,0000,0000,0000,,hundreds of times in the first movement alone,
Dialogue: 0,0:05:36.70,0:05:38.80,Default,,0000,0000,0000,,and also in all the other movements as well.
Dialogue: 0,0:05:38.80,0:05:40.67,Default,,0000,0000,0000,,So this repetition, the setting up of this repetition
Dialogue: 0,0:05:40.67,0:05:43.43,Default,,0000,0000,0000,,is so important for beauty.
Dialogue: 0,0:05:43.43,0:05:47.57,Default,,0000,0000,0000,,If we think about random music as being just random notes here,
Dialogue: 0,0:05:47.57,0:05:50.51,Default,,0000,0000,0000,,and over here is somehow Beethoven's Fifth in some kind of pattern,
Dialogue: 0,0:05:50.51,0:05:52.65,Default,,0000,0000,0000,,if we wrote completely pattern-free music,
Dialogue: 0,0:05:52.65,0:05:54.30,Default,,0000,0000,0000,,it would be way out on the tail.
Dialogue: 0,0:05:54.30,0:05:56.43,Default,,0000,0000,0000,,In fact, the end of the tail of music
Dialogue: 0,0:05:56.43,0:05:58.09,Default,,0000,0000,0000,,would be these pattern-free structures.
Dialogue: 0,0:05:58.09,0:06:01.71,Default,,0000,0000,0000,,This music that we saw before, those stars on the grid,
Dialogue: 0,0:06:01.71,0:06:05.34,Default,,0000,0000,0000,,is far, far, far from random.
Dialogue: 0,0:06:05.34,0:06:07.44,Default,,0000,0000,0000,,It's perfectly pattern-free.
Dialogue: 0,0:06:07.44,0:06:10.65,Default,,0000,0000,0000,,It turns out that musicologists --
Dialogue: 0,0:06:10.65,0:06:13.40,Default,,0000,0000,0000,,a famous composer by the name of Arnold Schoenberg --
Dialogue: 0,0:06:13.40,0:06:16.70,Default,,0000,0000,0000,,thought of this in the 1930s, '40s and '50s.
Dialogue: 0,0:06:16.70,0:06:20.28,Default,,0000,0000,0000,,His goal as a composer was to write music that would
Dialogue: 0,0:06:20.28,0:06:22.43,Default,,0000,0000,0000,,free music from total structure.
Dialogue: 0,0:06:22.43,0:06:24.82,Default,,0000,0000,0000,,He called it the emancipation of the dissonance.
Dialogue: 0,0:06:24.82,0:06:26.90,Default,,0000,0000,0000,,He created these structures called tone rows.
Dialogue: 0,0:06:26.90,0:06:28.38,Default,,0000,0000,0000,,This is a tone row there.
Dialogue: 0,0:06:28.38,0:06:30.22,Default,,0000,0000,0000,,It sounds a lot like a Costas array.
Dialogue: 0,0:06:30.22,0:06:34.02,Default,,0000,0000,0000,,Unfortunately, he died 10 years before Costas solved the problem of
Dialogue: 0,0:06:34.02,0:06:37.37,Default,,0000,0000,0000,,how you can mathematically create these structures.
Dialogue: 0,0:06:37.37,0:06:42.38,Default,,0000,0000,0000,,Today, we're going to hear the world premiere of the perfect ping.
Dialogue: 0,0:06:42.38,0:06:46.38,Default,,0000,0000,0000,,This is an 88 by 88 sized Costas array,
Dialogue: 0,0:06:46.38,0:06:48.00,Default,,0000,0000,0000,,mapped to notes on the piano,
Dialogue: 0,0:06:48.00,0:06:51.59,Default,,0000,0000,0000,,played using a structure called a Golomb ruler for the rhythm,
Dialogue: 0,0:06:51.59,0:06:54.05,Default,,0000,0000,0000,,which means the starting time of each pair of notes
Dialogue: 0,0:06:54.05,0:06:55.82,Default,,0000,0000,0000,,is distinct as well.
Dialogue: 0,0:06:55.82,0:06:58.66,Default,,0000,0000,0000,,This is mathematically almost impossible.
Dialogue: 0,0:06:58.66,0:07:01.40,Default,,0000,0000,0000,,Actually, computationally, it would be impossible to create.
Dialogue: 0,0:07:01.40,0:07:04.44,Default,,0000,0000,0000,,Because of the mathematics that was developed 200 years ago --
Dialogue: 0,0:07:04.44,0:07:07.30,Default,,0000,0000,0000,,through another mathematician recently and an engineer --
Dialogue: 0,0:07:07.30,0:07:10.23,Default,,0000,0000,0000,,we are able to actually compose this, or construct this,
Dialogue: 0,0:07:10.23,0:07:12.78,Default,,0000,0000,0000,,using multiplication by the number 3.
Dialogue: 0,0:07:12.78,0:07:15.21,Default,,0000,0000,0000,,The point when you hear this music
Dialogue: 0,0:07:15.21,0:07:17.96,Default,,0000,0000,0000,,is not that it's supposed to be beautiful.
Dialogue: 0,0:07:17.96,0:07:22.38,Default,,0000,0000,0000,,This is supposed to be the world's ugliest piece of music.
Dialogue: 0,0:07:22.38,0:07:25.92,Default,,0000,0000,0000,,In fact, it's music that only a mathematician could write.
Dialogue: 0,0:07:25.92,0:07:29.30,Default,,0000,0000,0000,,When you're listening to this piece of music, I implore you:
Dialogue: 0,0:07:29.30,0:07:31.43,Default,,0000,0000,0000,,Try and find some repetition.
Dialogue: 0,0:07:31.43,0:07:33.92,Default,,0000,0000,0000,,Try and find something that you enjoy,
Dialogue: 0,0:07:33.92,0:07:36.72,Default,,0000,0000,0000,,and then revel in the fact that you won't find it.
Dialogue: 0,0:07:36.72,0:07:38.15,Default,,0000,0000,0000,,Okay?
Dialogue: 0,0:07:38.15,0:07:40.69,Default,,0000,0000,0000,,So without further ado, Michael Linville,
Dialogue: 0,0:07:40.69,0:07:43.52,Default,,0000,0000,0000,,the director of chamber music at the New World Symphony,
Dialogue: 0,0:07:43.52,0:07:48.15,Default,,0000,0000,0000,,will perform the world premiere of the perfect ping.
Dialogue: 0,0:07:49.29,0:07:57.20,Default,,0000,0000,0000,,(Music)
Dialogue: 0,0:09:34.82,0:09:36.68,Default,,0000,0000,0000,,Thank you.
Dialogue: 0,0:09:36.68,0:09:42.26,Default,,0000,0000,0000,,(Applause)