Can you find the next number in this sequence

你能找到这个数列下一个数字嘛

来源视频

These are the first five elements of a number sequence.

Can you figure out what comes next?

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

Answer in: 3 

Answer in: 2

Answer in: 1

这些是一个数列最开始的五个数字。

你能想出下一个数字是什么吗？

如果你想要自己先想清楚的话 就在这里暂停一下。

答案倒数 3

答案倒数 2 

答案倒数 1

There is a pattern here,

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

Look at the sequence again and try reading it aloud.

Now, look at the next number in the sequence.

3 ,1 ,2 ,2 ,1 ,1 .

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

Answer in: 3

Answer in: 2

Answer in: 1

这个数列有一个规律，

然而这个规律可能不是你所想的那样。

重新再看一下这个数列。

并尝试读出声来。

现在，让我们来看这一数列的下一个数字。

3，1，2，2，1，1

如果你需要多思考一下的话 可以再暂停一下。

答案倒数 3

答案倒数 2

答案倒数 1

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

Unlike many number sequences,

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

but on their notation.

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

Now, read out how many times  it repeats in succession

followed by the name of the digit itself.

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

这就是所谓的外观数列，

和其它的数字数列不同，

这个数列的规律并不依靠于 数字自身的的数学属性，

而是数字的表示法。

从初始数字的最左数位开始读起。

现在读出它连续重复的次数，

然后再读出这一数字。

下一个数位的读法也是依此类推。

直到读完最后一位。

So the number  is read as "one one"

written down the same way  we write eleven.

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

but 2 ones,

which we then write as 2 1 .

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

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

所以数字读作“一个一”，

和我们写数字十一的方法一样。

自然，作为这个数列的一部分，

11并不是真正的数字十一，

而是“两个一”，

因此我们又写作21。

而这个数字读出来是 1 2 1 1 ，

而1211写出来又可读作 一个一、一个二、二个一，

以此类推。

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

who noted they have  some interesting properties.

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

But when seeded with any other number,

the sequence grows in some very specific ways.

Notice that although the number of digits keeps increasing,

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

这个数列最初是由数学家 John Conway 所发现，

他注意到了这一数列一些很有趣的属性。

比如从数字22开始， 这一数列会生成的“二个二”的无穷循环。

但如果我们从其他数字开始的话，

这个数列就会以一些特殊的方式展开。

请注意，虽然这些数字的位数数量在不断增长，

这些增长似乎并不是线性的或随机的。

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

The ratio between the amount of digits in two consecutive terms

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

This is equal to a little over 1.3,

meaning that the amount of digits increases by about 30%

with every step in the sequence.

事实上，如果你把这个数列无限扩大，

规律就会浮现出来。

相邻两个数字的数位数量之间的比例，

会逐渐趋近 一个被称为“Conway常数”的数字。

这一数字会比1.3稍大一点，

也就是说，数列中每生成下一项数字，

数位的数量大约增长30%。

with every step in the sequence.

What about the numbers themselves?

That gets even more interesting.

Except for the repeating sequence of 22,

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

No matter what order these strings show up in,

each appears unbroken in its entirety every time it occurs.

那么，那些数字本身如何呢？

这就更加有趣了。

除了22这一无限循环的数列，

每一个可能的数列最终会 被分解成不同的数位字符串。

不论这些字符串以怎样的顺序出现，

它们都会不断延续下去。

Conway identified 92 of these elements,

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

as well as two additional elements

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

No matter what number the sequence is seeded with,

eventually, it'll just consist of these combinations,

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

if at all.

Conway 分析了92个字符串，

所有的字符串只包含数字1、2和 3

以及其他两个变化的字符串，

它们以大于或等于4的数字结尾。

无论从哪一个数字开始这一数列，

数列最终都会包含以上这些字符串的组合。

大于或等于4的数字 只出现在两个变化字符串的末尾，

如果出现的话。

Beyond being a neat puzzle,

the look and say sequence has some practical applications.

For example, run-length encoding,

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

is based on a similar concept.

The amount of times a data value repeats within the code

is recorded as a data value itself.

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

can convey meaning on multiple levels.

除了作为一个工整有序的数字谜题之外，

外观数列也被应用到实际中。

以游程编码为例，

它从前被运用到电视信号和 数码图像的数据压缩上。

游程编码也是建立在一个相似的概念上，

在编码中， 数据出现的次数被记作数据值。

这样的数列就是一个很好的例子，

表现数字和其他符号是 怎样在多层次方面传达含义的。