1
$\begingroup$

Somone has suggested that

Within, say, a collection of every possible 30 second long MP3 file encoded at 128kbps, I'd probably be infringing on a few thousand copyrighted works.

128kilobits per second = 128,000 bits per second * 30 seconds = 3,840,000 bits.

There are 2 to the 2,840,000 possible files of that length.

Ignoring the fact that most of those won't be valid mp3s, how can I quantify the amount of space needed to store all those files? For instance, is that more bits than there are atoms in the universe?

  • 1
    According to Wikipedia (http://en.wikipedia.org/wiki/Observable_universe#Matter_content) there are about $10^{80}$ atoms in the universe. So yes, that is far, far more bits than there are atoms!2012-10-30
  • 0
    @Brad - I'll admit it: my math skills are terrible. How do I put 2 to the X in terms of 10 to the Y so I can compare?2012-10-30
  • 1
    Very crudely: 2^2,840,000 = (2^4)^(2,840,000/4) = 16^710,000 > 10^710,000 > 10^80.2012-10-30
  • 1
    For comparison, we generate about 3 quintillion bytes (18 zeros) of data per day on the Earth compared to ~10^80 atoms in the universe.2012-10-30
  • 0
    The first equation has the units incorrect. It is not 128,000 bits, it is 128,000 bits/second. The error is corrected across the second equal sign. Then a typo in the next line.2012-10-30

1 Answers 1