In the movie Superman, the infant Kal-El\'s father Jor-El gives him a crystal ab

Question

In the movie Superman, the infant Kal-El's father Jor-El gives him a crystal about the size of a tube of toothpaste and leaves a recorded message telling him that it contains the combined knowledge of the "28 known galaxies." Suppose that this extraterrestrial crystal is a covalently bonded array of atoms spaced about 0.4 nm apart (like diamond on Earth) and that it contains information encoded in defects in the crystal lattice. (For example, a defect could be a missing carbon atom.) Obtain a rough upper bound on the total number of bits of information that such a crystal could contain. (Don't worry about factors of 2 and such.) If a human encyclopedia of the twenty-first century fits comfortably on a digital video disk (4.7 gigabytes, or 38 middot 10^9 bits), about how many encyclopedias-worth of information per "known galaxy" could Jor-El have recorded on his crystal?

Explanation / Answer

a) total number of bits of information = 228

                                                           = 2.68435 * 108

b) number of encyclopeadias = (38 * 109)/228

                                                                        = 141.56

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