Of Chargaff's four rules on DNA base composition, only his first parity rule was incorporated into mainstream biology as the DNA double helix. Now, the cluster rule, the second parity rule, and the GC rule, reveal the multiple levels of information in our genomes and potential conflicts between them. In these terms we can understand how double-stranded RNA became an intracellular alarm signal, how potentially recombining nucleic acids can distinguish between 'self' and 'not-self' so leading to the origin of species, how isochores evolved to facilitate gene duplication, and how unlikely it is that any mutation can ever remain truly neutral.