Name: 【TED-Ed】你可以在這個序列中找到下一個數字嗎？ - 亞歷克斯·甘德勒 (Can you find the next number in this sequence? - Alex Gendler) ()
Uploaded: 2017-07-29T08:03:41.000Z
Duration: 4 min 1 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

These are the first five elements of a number sequence.

Reflexive pronouns

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

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.

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

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

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

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.

written down the same way  we write eleven.

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

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

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.

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.

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.

meaning that the amount of digits increases by about 30%

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.

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,

the look and say sequence has some practical applications.

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

The amount of times a data value repeats within the code

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