Can you find the next number in this sequence? - Alex Gendler

譯者: iSAAC NgZiLe 審譯者: 瑞文Eleven 林Lim

These are the first five elements of a number sequence.

這是一個有五個數字的數列

Can you figure out what comes next?

你知道下個數是多少嗎？

Pause here if you want to figure it out for yourself.

如果你打算靠自己尋找答案 請按一下暫停

Answer in: 3

答案將在 3 秒後揭曉

Answer in: 2

Answer in: 1

2 秒

1 秒

There is a pattern here,

這是有規律的

but it may not be the kind of pattern you think it is.

但可能跟你想的不太一樣

Look at the sequence again and try reading it aloud.

再看一次這個數列並試著唸出來

Now, look at the next number in the sequence.

現在請看下一個數字

3, 1, 2, 2, 1, 1.

3、1、2、2、1、1

Pause again if you'd like to think about it some more.

如果你打算再想一下的話 請再按一次暫停

Answer in: 3

答案將在 3 秒後揭曉

Answer in: 2

2 秒

Answer in: 1

1 秒

This is what's known as a look and say sequence.

這叫做外觀數列

Unlike many number sequences,

不像其他數列

this relies not on some mathematical property of the numbers themselves,

這種數列和數字本身的數學性質無關

but on their notation.

而是和數字符號有關

Start with the left-most digit of the initial number.

現在從第一個數字的最左邊開始

Now, read out how many times it repeats in succession

唸出它重複了幾次

followed by the name of the digit itself.

再唸出數字本身的名稱

Then move on to the next distinct digit and repeat until you reach the end.

再來看下一個數字

請重複唸，直到唸完所有相異的數字

So the number 1 is read as "one one"

所以第一個數字要唸做「一個 1」

written down the same way we write eleven.

寫起來就像數字 11 一樣

Of course, as part of this sequence, it's not actually the number eleven,

在這個數列中，「11」當然 不是真正的數字「十一」

but 2 ones,

而是兩個 1

which we then write as 2 1.

所以接下來我們寫成 2 1

That number is then read out as 1 2 1 1,

這個數字我們唸成 1 2 1 1

which written out we'd read as one one, one two, two ones, and so on.

代表著一個 1、一個 2 兩個 1，以此類推

These kinds of sequences were first analyzed by mathematician John Conway,

這種數列最早是由數學家 約翰．康威（John Conway）分析的

who noted they have some interesting properties.

他將這些有趣的特性記錄下來

For instance, starting with the number 22, yields an infinite loop of two twos.

例如從數字 22 開始 會產生兩個 2 的無限循環

But when seeded with any other number,

但若插入其他數字

the sequence grows in some very specific ways.

數列就會以某種特殊的方式增加

Notice that although the number of digits keeps increasing,

雖然數字會不斷變長

the increase doesn't seem to be either linear or random.

但變長的方式似乎非線性也非隨機

In fact, if you extend the sequence infinitely, a pattern emerges.

事實上，如果你無限延伸這個數列

規律就會出現

The ratio between the amount of digits in two consecutive terms

相鄰兩數的數字長度的比值

gradually converges to a single number known as Conway's Constant.

將逐漸收斂到被稱為 「康威常數」的數字

This is equal to a little over 1.3,

這個數字比 1.3 大一點點

meaning that the amount of digits increases by about 30%

這代表下一個數字的長度 會增加約 30％

with every step in the sequence.

What about the numbers themselves?

那數字本身有何規律呢？

That gets even more interesting.

這又更有趣了

Except for the repeating sequence of 22,

除了重複 22 的數列外

every possible sequence eventually breaks down into distinct strings of digits.

每個數列最終都將 被分解成不同的數字字串

No matter what order these strings show up in,

不論數字字串以何種順序出現

each appears unbroken in its entirety every time it occurs.

每次發生時，它們都會完整地出現

Conway identified 92 of these elements,

康威找到了 92 種數字字串

all composed only of digits 1, 2, and 3,

全部只由 1、2 和 3 及另外兩個元素組成

as well as two additional elements

whose variations can end with any digit of 4 or greater.

另外兩個元素能以 大於或等於 4 的數字結尾

No matter what number the sequence is seeded with,

不論從哪個數列開始

eventually, it'll just consist of these combinations,

最後都會回到這些組合

with digits 4 or higher only appearing at the end of the two extra elements,

如果有大於或等於 4 的數字

它們只會出現在兩個額外元素的末尾

if at all.

Beyond being a neat puzzle,

外觀數列不僅是一個簡潔的謎題

the look and say sequence has some practical applications.

還有一些實際應用

For example, run-length encoding,

例如運行長度編碼法

a data compression that was once used for television signals and digital graphics,

它曾被用於電視信號 與數位圖像的資料壓縮

is based on a similar concept.

使用的就是類似的概念

The amount of times a data value repeats within the code

在編碼中，資料值重複的次數

is recorded as a data value itself.

會被記錄成資料值

Sequences like this are a good example of how numbers and other symbols

這個數列是很好的例子 讓我們看到如何用數字和符號

can convey meaning on multiple levels.

傳達多層次的意義