This reminds me of Frederik Pohl's [1] book The Gold at Starbow's End, in which Gödelization [2] is used to compress a huge message into a very short one. There's a brief description of that part of the book at MathFiction [3]

[1] http://en.wikipedia.org/wiki/Frederik_Pohl

[2] http://www.encyclopediaofmath.org/index.php/Gödelization

[3] http://kasmana.people.cofc.edu/MATHFICT/mfview.php?callnumbe...