Micaiah: I would advise you not to play with fire. If that sounds condescending, well it probably is, but I would freely admit that I am not fully qualified to answer both your questions and KerrMetric's. But let's give a shot at yours.
1. When a page is photocopied?
Well, for starters it depends on what definition of information you use. From an information-theoretic point of view, there is twice the amount of information since whatever coding system is used twice the amount of bits are required to transmit it. From a human-philosophical point of view, there is the same amount of information, obviously.
Since you have not identified how you wish to measure information, you cannot tell me that I am wrong.
But to take a biological analogy (since it is obvious that you wish to draw inferences to polyploidy speciation) whether or not a polyploidy mutation increases information, it demonstrably changes the biological makeup of the plant which undergoes it, by virtue of the fact that a speciation event occurs. Thus whether or not there has been information change, there has been biological change, and precisely the type evolution needs.
question 2: does evolution require an increase in genetic information? Probably by any definition of genetic information yes. But you will have to show, in turn, that it is impossible for spontaneous events such as mutations to add information to the genome, as well as what exactly you mean by information, if you want to infer that it is impossible for mutations to drive evolution.
Question 3? Nylon bug. Looking at your five criteria for information content in enzymes:
Substrate specificity: the nylon hydrolyzing enzyme shows no activity on homologous substrates. It is specific and represents an increase in information (no enzyme specific to nylon -> an enzyme specific to nylon)
Catalytic activity: AFAIK there are no natural enzymes that act on nylon. So from no catalytic activity -> any amount of catalytic activity represents an information increase.
3, 4, 5: honestly I'm not too sure, both in what you mean (for 3 and 5) and how the nylon bug would fare (for all) For 3 and 5 can you describe examples - what would a protein with low info content under 3 look like, and high info content? Ditto 5? I'm guessing the nylon bug will still count as an increase.
