Well that's a novel definition as you seem to be saying that Macro Evolution == unconstrained. That's not what I mean by the term and I doubt many others mean it either. My definition is the advent and preservation of novel function. By your definition ME isn't necessary for the biological life we see since that is constrained by natural physical law.
Actually, since we were on the subject of GAs, I was refering to the structure and the information in the organism to get modified.
You'll need to explain what you mean by input and output. Are you saying there's no conceivable sequence of small genetic changes that could lead from the genome of a unicellular organism to yours? It seems evident to me that there is. The input is the original genome and the small changes and the output is your genome. In what way is the output greater than the input?
Perhaps a GA explination could provide more light. In a GA program (such as AL), certain structures are pre-defined, and the evolution they can follow are also define (with these definitions, they're useless). However, even in good AL programs, the information and structures in evolved organisms remain either equal to, or less then, the structures and information that one started out with (there's just more of them). However, if you take bacteria, there's structures in humans (such as the brain) that have no equal in bacteria. Completely new structures, completely new information (and if you figure out how to simply that down to basic information iterations, I'm sure there's a math award somewhere out there waiting for your name on it. Information theory would be far simplier if you could do this). This is what I mean about output and input. In AL, the evolved creatures follow the concept
output <= input. I haven't seen one yet that breaks out of that concept (and I've looked). Though I have come across some pretty darn good programs (such as
Framsticks. This AL program will start with simple, basic structures and give you some complex organisms, some walk on land, some swim, others crawl or 'slither'. But one point I'll make to you: The structures and information never increase themselves. At least, not in type, but only in quantity, which produces apparent complexities. Macro Evolution requires Evolution to go beyond this, Micro Evolution, doesn't.)
-The Hajman-
I think we're talking past each other. Here's what I'm saying. Suppose you're given the functions + and X (input variable) and 1 (constant). By composition you can approximate as closely as you like any C-inf function. IMO that's a pretty wide range of outputs and it's possible to build any one simple-step-by-simple-step from a trival case, e.g starting with 1. Koza's technique works like this. Each step adds information so the output never has more than is input and yet the space available is vast and there's an incredible variety of possible behaviors.
Now, take your example of the human brain. It along with the rest of our anatomy is determined by our genes. I don't see any reason there couldn't be a sequence of small changes that take a gemone incapable of developing a brain to one that does. Each step adds information so again there's no greater information in the output than is input. And yet I take it you consider the development of the brain a case of macroevolution.