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I don't see how duplication mutations differ in principle from any other type of mutation. I don't have a problem with mutations. I have a problem with the concept of making random changes to a body of information and gaining information as a result. It is possible for the information to change, but can information be gained or is it lost?

For example, suppose a random change occurs to the recipe for a chocolate cake so that instead of calling for chocolate it now calls for rasberries (let's ignore for the moment the problem of someone having to know how to read the recipe and bake). Have we gained any information? Some would say yes, now we know how to make a rasberry cake! In reality, we have lost our recipe for the original chocolate cake. Or, perhaps we had a duplication recipe and changed only one so that we now have two recipes instead of one!

But do we? The new recipe is certainly different but has new information been created? I think not. If it contains new information that wasn't originally there, then what is it's meaning? What does it convey? Have we now learned how to make a rasberry cake? No. We haven't learned anything because there is no new information in the altered recipe. There's no question that we get something different if we apply the same set of baking rules to different ingredients, but this was known before the change ever took place.

The new recipe is certainly different but has new information been created? I think not. If it contains new information that wasn't originally there, then what is it's meaning? What does it convey? Have we now learned how to make a rasberry cake? No. We haven't learned anything because there is no new information in the altered recipe. There's no question that we get something different if we apply the same set of baking rules to different ingredients, but this was known before the change ever took place.

Hemoglobin, which carries oxygen in blood, arose from a duplication mutation in the gene for myoglobin, which carries oxygen in muscles. Was this not new or useful?

You misunderstand. Your analogy isn't the best, but I'll continue to use it in order to explain.

When the recipe mutates, the line indicating the amount of chocolate get repeated. You now have a double-chocolate cake. Mmmmm....

But since you have two entries for chocolate now, what if the next time you bake it, the second entry changes to raspberries? Now you have three cake species living in your recipe box. A chocolate cake, a double-chocolate cake, and a chocolate-raspberry cake.

Now, when are you inviting us over, because I'm suddenly getting hungry?