this is really interesting I'll have to think about the possibilities more in the future. One thought:
2 dimensions of infinity to write special characters using both the additive and multiplicative identities. but they are not very bit-efficient, like writing numbers by tally mark.
in this case instead of using tally marks you can intermingle the modes of encoding complicated zeros in order to represent binary codes, making the number of awkward sequences logarithmic rather than tally (linear). I.e. -1*-1*0+-1*0+-1*-1*0 is the encoding of special character 5.
Edited by Acdtrux ()
as for shannon, information theory is one of the great hopes for bridging quantum mechanics and general relativity, since both have ways of measuring information (in particular the information associated with black holes) that have to match up. this means that its not impossible that information theory ends up having a more important long term impact on the field than string theory!
Edited by c_man ()