估算 YouTube 影片總量的方式

Hacker News Daily 上看到「How big is YouTube? (ethanzuckerman.com)」這篇,原文在「How Big is YouTube?」。

算是個老問題了,而且應該是統計學上比較簡單的方法。先列出作者最後的成果:「TubeStats」。

作者用的方法是觀察 YouTube 的 vid:

Here’s how this works: YouTube URLs look like this: https://www.youtube.com/ watch?v=vXPJVwwEmiM

可以分析出來 vid 包括了 64-bit 的資訊,這個資料型態對工程師來說,看起來就很像是 uniformly distributed:

That bit after “watch?v=” is an 11 digit string. The first ten digits can be a-z,A-Z,0-9 and _-. The last digit is special, and can only be one of 16 values. Turns out there are 2^64 possible YouTube addresses, an enormous number: 18.4 quintillion. There are lots of YouTube videos, but not that many. Let’s guess for a moment that there are 1 billion YouTube videos – if you picked URLs at random, you’d only get a valid address roughly once every 18.4 billion tries.

然後就是隨機去產生 vid 去掃,這個方法跟 drunk dialing 的行為很像,算是 random sampling 的方式:

We refer to this method as “drunk dialing”, as it’s basically as sophisticated as taking swigs from a bottle of bourbon and mashing digits on a telephone, hoping to find a human being to speak to. Jason found a couple of cheats that makes the method roughly 32,000 times as efficient, meaning our “phone call” connects lots more often. Kevin Zheng wrote a whole bunch of scripts to do the dialing, and over the course of several months, we collected more than 10,000 truly random YouTube videos.

另外在 2011 年就有提出來利用 autocomplete 機制去算:

By comparing our results to other ways of generating lists of YouTube videos, we can declare them “plausibly random” if they generate similar results. Fortunately, one method does – it was discovered by Jia Zhou et. al. in 2011, and it’s far more efficient than our naïve method. (You generate a five character string where one character is a dash – YouTube will autocomplete those URLs and spit out a matching video if one exists.) Kevin now polls YouTube using the “dash method” and uses the results to maintain our dashboard at Tubestats.

目前他們的預估大約是 13B 左右的影片,換算大約是用掉 33.63 bits 了 (233.6):

In our case, our drunk dials tried roughly 32k numbers at the same time, and we got a “hit” every 50,000 times or so. Our current estimate for the size of YouTube is 13.325 billion videos – we are now updating this number every few weeks at tubestats.org.

而這邊提到的 32768 * 50k 會中一次的部分,這邊的大約是 30.61 bits,這樣加起來是差不多 64 bits 沒錯。

不過要注意的是,他們沒有給出 interval,所以 13B 的上下可能是一倍左右的差距 (6.5B~26B 之類的),這邊的數字當作概念比較好...

44.1kHz 的由來...

在「Explanation of 44.1 kHz CD sampling rate」這邊看到 44.1kHz 的解釋...

這個數字反而是跟 video 有關而設計出來的:

In 60 Hz video, there are 35 blanked lines, leaving 490 lines per frame or 245 lines per field, so the sampling rate is given by :

60 X 245 X 3 = 44.1 KHz

In 50 Hz video, there are 37 lines of blanking, leaving 588 active lines per frame, or 294 per field, so the same sampling rate is given by

50 X 294 X3 = 44.1 Khz.

而後來 44.1kHz 被拿去 CD 規格裡使用而被廣泛應用...