Question 21.43

13. An urban legend is that “the amount of information in the world doubles every three days.” Presumably the claim refers to the amount in bits, the smallest unit of storage in a computer. Show that the claim is absolutely preposterous by doing a little arithmetic and comparing your result with (the number of particles in the universe).

  1. Start with one bit of data and double the number of bits every third day. How long does it take to get past (Hint: Don’t just keep multiplying by 2 over and over. Convince yourself that since the amount of data increases by a factor of 2 every 3 days, then it increases by a factor of every 6 days, a factor of every 12 days, a factor of every 24 days, and so forth.)
  2. Part (a) involves a lot of multiplying by 2, even if you do it efficiently. Another approach is to use the fact that . Thus, the amount of data increases by a factor of more than 1000 every days, or every month (except February, but the 31-day months make up for it). By when will the total surely be past ?

13.

(a) 698 days

(b) After 24 months