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information does not so far as I am aware spontaneously grow without intelligence being involved somewhere

You’re right. Information growth would indicate an intention, a problem solving of some kind. But DNA is just a copy. It doesn’t grow, it doesn’t even replicate perfectly, it has very slight changes. Most of those changes aren’t for the better, and the copy does not fare as well as the thing it was copied from. The changes that are better for survival, survive, by definition. The information doesn’t grow, it does accumulate, that could be the confusion.