mutations exhibit no information gain

Information, passl? Do you know what the word means, or are you just regurgitating what somebody told you? Anyway, as a statement, it's provably wrong without even experiment.

Very simply, DNA consists of sequences of 'bases', and there are only four of these in nearly all naturally occurring organisms*. They have not-very-long names, but they are almost always referred to as C, G, A and T. One form of mutation is when one base is substituted by another, for example a T instead of a G. This may do nothing (especially if it's in non- coding DNA), or it may subtly change the product of the gene (a protein, say), and that change may be more-or-less neutral, or deleterious (the vast majority of mutations come into these classes), or beneficial - the organism does better because of it. The rare case of an improvement is clearly an increase of information by both technical and non- technical usages of the word.

Lets assume it results in a slight disadvantage, and we therefore class it as a loss of information. But then the reverse mutation is also possible- this time the T is replaced by a G. If the first mutation is a loss of information, the second one is clearly a gain. So increase of information by random mutation is possible, however you choose to look at it.

*RNA also has four bases, C,G,A and U. In many organisms, some of the bases are somewhat modified. And last year some genetic scientists successfully modified a gene to incorporate a fifth base not normally found in either DNA or RNA.