Name: 【TEDx】如何創造出一段難聽的音樂？解析音樂的秘密 The world's ugliest music: Scott Rickard at TEDxMIA
Uploaded: 2014-06-03T17:19:18.000Z
Duration: 9 min 46 s

So what makes a piece of music beautiful?

that repetition is a key aspect of beauty.

The idea that we take a melody, a motif, a musical idea,

我們寫一段旋律、一個主題、一個音樂想法

we repeat it, we set up the expectation for repetition,

and then we either realize it or we break the repetition.

接著要麼我們或者滿足這種期待  或者打破這種重復

So if repetition and patterns are key to beauty,

所以如果重復和模式是美的關鍵

then what would the absence of patterns sound like

那麼要是我們把模式 都拿去會怎麼樣呢？

That's actually an interesting mathematical question.

這實際上是個很有意思的數學問題

Is it possible to write a piece of music that has no repetition whatsoever?

寫一段完全沒有重復的樂曲  有這種可能嗎?

這並不是隨意來寫 隨意寫很簡單

Repetition-free, it turns out, is extremely difficult

事實證明 做到無重復是極其困難的

and the only reason that we can actually do it

而我們能做到無重復的唯一原因

is because of a man who was hunting for submarines.

It turns out a guy who was trying to develop

solved the problem of writing pattern-free music.

And that's what the topic of the talk is today.

you have a ship that sends out some sound in the water,

並且聆聽這個聲音──一個回聲

The sound goes down, it echoes back, it goes down, echoes back.

發出聲音 回聲傳回來  再發出聲音 回聲再傳回來

The time it takes the sound to come back tells you how far away it is.

你通過聲音回傳的時間來判斷距離

If it comes at a higher pitch, it's because the thing is moving toward you.

如果傳回來的音調變高  那說明前方的物體正向你靠近

If it comes back at a lower pitch, it's because it's moving away from you.

如果音調變低  是因為那物體離你越來越遠

So how would you design a perfect sonar ping?

所以你會怎樣設計出完美的聲納音呢？

Well, in the 1960s, a guy by the name of John Costas

在20世紀60年代  一個名叫約翰·科斯塔斯的人

was working on the Navy's extremely expensive sonar system.

當時正在研發海軍極其昂貴的聲納系統

and it was because the ping they were using was inappropriate.

原因是他們使用的聲納音不合適

It was a ping much like the following here,

So that was the sonar ping they were using: a down chirp.

這就是他們當時使用的聲納音：一串降調

Why? Because it looks like shifts of itself.

為什麼？因為它聽起來就像自身的變換

The relationship between the first two notes is the same

後兩個音符的關系一樣  其它的也是

So he designed a different kind of sonar ping:

所以他設計了另外一種不同的聲納音

These look like a random pattern of dots, but they're not.

這些看起來像隨意編寫的音符  但其實它們並非如此

If you look very carefully, you may notice

that in fact the relationship between each pair of dots is distinct.

事實上 每對音符之間的關系都是不同的

The first two notes and every other pair of notes

頭兩個音符及其它每對的音符之間

So the fact that we know about these patterns is unusual.

所以我們了解這些格式的事實是很不平常的

John Costas is the inventor of these patterns.

約翰·科斯塔斯發名了這些格式

This is a picture from 2006, shortly before his death.

這是2006年的照片  在他去世不久之前

He was the sonar engineer working for the Navy.

and he was, by hand, able to come up with them to size 12 --

而且他能親手將這些格式制作成12號的 ──

He couldn't go any further and he thought

他再也做不了比那更大的了 所以他想

maybe they don't exist in any size bigger than 12.

它們可能不會以 大於12乘12的大小出現

So he wrote a letter to the mathematician in the middle,

所以他給中間的那位數學家寫了一封信

who was a young mathematician in California at the time,

那是個年輕的數學家  當時住在加裡福尼亞

It turns out that Solomon Golomb was one of the

most gifted discrete mathematicians of our time.

John asked Solomon if he could tell him the right reference

a repetition, a pattern-free structure before.

Solomon Golomb spent the summer thinking about the problem.

索羅門·哥隆花了一夏天來思考這個問題

And he relied on the mathematics of this gentleman here,

Now, Galois is a very famous mathematician.

現在 伽羅瓦是位家喻戶曉的數學家

He's famous because he invented a whole branch of mathematics,

他的出名源於他發明了數學中一整個分支

which bears his name, called Galois Field Theory.

並以他的名字命名為伽羅瓦理論

He's also famous because of the way that he died.

So the story is that he stood up for the honor of a young woman.

事情是這樣的  為了一個年輕姑娘的名譽

He was challenged to a duel and he accepted.

he wrote down all of his mathematical ideas,

他把他所有數學的理念寫了下來

信上說 請一定，一定，一定──

see that these things get published eventually.

He then fought the duel, was shot, and died at age 20.

之後他進行了決斗  中槍身亡 終年20歲

The mathematics that runs your cell phones, the Internet,

你手機的運轉、實現我們交流的網絡

DVD，運用於這些的那些數學理念

all comes from the mind of Evariste Galois,

都來源於埃瓦裡斯特· 伽羅瓦的思想

When you talk about the legacy that you leave,

當你們談論你們 死後留下的遺產的時候

of course he couldn't have even anticipated the way

Thankfully, his mathematics was eventually published.

謝天謝地 他的理論最終被出版了

Solomon Golomb realized that that mathematics was

索羅門·哥隆意識到那些數學理念

exactly the mathematics needed to solve the problem

正是解決這個問題所需要的理念

So he sent a letter back to John saying it turns out you can

所以他回信給約翰說 其實你可以自己

generate these patterns using prime number theory.