All the Books In all the World

We think that we are pretty smart by having 2 TB hard-drives and we are. This is an amazing amount of data to store in a small space.  How much storage is required to store the entire collection of books in the world? We can make a start by considering how data is stored.

A binary digit can store two values, either a 1 or 0. Put two of them together and you can represent four values, 00,01, 10 and 11. For three bits eight values can be stored. In fact for n bits, you can represent 2^n values. If we use binary to code information the commonly used characters in a language could comfortably be represented by a code of 7 bits for each character. This would create 128 different values, which we could assign to the different characters in an alphabet. (A minimal language of 26 upper case letter, 26 lower case letters, 10 numbers and the various punctuation characters would easily fit into a 7-bit code with space to spare for letters from other European based character sets. )

How much space would be needed to store a single book? An average university library book may contain 300 hundred pages and each page, around 40 lines, each line 15 words and each word on average, 10 characters. Using this conservative estimate:

300 pages  x 40 lines  x 15 words  x 10 characters  x 7 bits = 12,600,000 bits.

To find the entire storage requirement, we need to know how many books have ever been written? It is a difficult question as there are many books written but never published or made it into a library,  some research has been carried out. In the US, 4,123,094 book titles, including the “out of print” books according to the Books in Print records provided by Andrew Grabois of R.R. Bowker.

The major libraries of the world have extensive collections of books, the American Library Association (ALA)  keeps a record of the largest libraries by their collection size. The largest libraries in the world is the Library of Congress with more than 32,000,000 volumes.

Estimates of the total number of books in the world are extrapolated from the US proportion of  the world market in books, original books might be between 74 million books and 175 million.

Taking the upper limit as our estimate for the number of books written. Next, we have to consider other languages such as Chinese,  Cyrillic and Greek, mathematics, pictures or anything else we haven’t accounted for.  To  adequately store these things we should probably abandon a simple text code and  convert the books by document scanning. An estimate for memory requirement per 300 page book would be 39 MB, assuming a 600 dpi resolution. The total space required would be 175,000,000 x 39 = 6,825,000,000 MB or 6,508 TB of data. This is a remarkable result. Every single book  in the world could potentially be housed in a small building.

What if we could store bits on a molecular level?  For example, a molecular which exists in two different states, to represent 1 and 0. 6,508 TB of data is equivalent to 6508 x 1024 x 1024 x 1024 x 1024 x 8 bits = 5.73 x 10^16 bits of information.

A large number certainly,  but it pales in comparison to the number of molecules that could be contained within a 1 cm cube of material. A large atom has a diameter of around 5 Angstroms = 5 x 10^-8 cm. A molecule that could exist in two states would be larger, let’s say 10 times as large. This would still mean that 1 cm cube of material would contain, (2 x 10^6)  x (2 x 10^6) x (2 x 10^6)  = 8×10^18 molecules. Our information on all the books in the world would fit on a small fraction of it. or 6 10^16/8 10^18 = 0.0075 of a cm^3 or a cube of side around 2 mm.

How much space is required to store the entire Internet, including video?