I keep debating whether I should be spending my time on this argument. I think that my hypothesis, which I advanced in a casual, agnostic way as just one possibility, was perfectly reasonable and there is no profit for you or me in discussing this at the fine level at which you are trying to parse it. But okay, this is how I've been using these two words:
Complexity - The amount of information in a certain volume.
Information - Any set of values that can be read from some arrangement of material.
How are you defining information? The amount of information most certainly can and does change, otherwise, no one would ever learn anything.
You're simply using a more specific definition of information than I am. It only takes a glance at a few different reference works to see that "information" does not have one authoritative definition. You're defining information as "something meaningful to humans". I'm simply defining it as any set of values. Your definition of information is basically "knowledge encoded as data", and mine does not include "knowledge" as a requirement for something containing information.
If you want some citation of a work that agrees with my definition, then we can simply look at the lede of the "Information" article from Wikipedia, which supports both of our definitions (mine is underlined): "Information (shortened as info or info.) is that which informs, i.e. that from which data and knowledge can be derived (as data represents values attributed to parameters, and knowledge signifies understanding of real things or abstract concepts). As it regards data, the information's existence is not necessarily coupled to an observer (it exists beyond an event horizon, for example), while in the case of knowledge, information requires a cognitive observer. At its most fundamental, information is any propagation of cause and effect within a system."
Now, we've zigzagged all over the place in trying to discuss various analogies, but let's try to keep this limited to the actual topic. No analogy is perfect, so if you delve deeply enough into the subject of computer engineering you can probably find a flaw in my analogy, but that will only detract from the validity of my analogy, not the validity of my original proposition.
I also feel that I failed to complete my original thought because I was trying to get there in steps and the conversation was derailed into nitpicking -- so let me recap and then finish my thought:
1. My initial statement was that "creator+universe" is not necessarily more complex than just "universe". In order to lead you all towards understanding why I would say this, I then suggested that the creator could be "thinking us up". After all, if there is a creator, then it has some sort of mind. It might have decided to think about a universe that develops life. We could be those very thoughts, in its mind.
2. If so, then the total complexity of the scenario is not much greater than the complexity of a universe that developed on its own. Once again, the reason I say this is that a brain has constant complexity on the physical level regardless of what it is being used for. If this creator's intelligence is anything like ours, then before us, he had to have been thinking about something else. Regardless of what subject occupied his mind, the scenario was already as complex as when he thought up the universe, just as a brain filled with random thoughts is as complex as a brain focused on one large task like imagining the flow of logic in a computer program one is designing.
3. The next step in my argument was going to be that, if the creator is using any part of himself to produce the universe, then the complexity is the same -- whether he uses his brain or a portion of his body to construct the universe. The amount of information that he would be dedicating to the universe would be the same whether it came from what we would consider to be its mind or its body (its "active force", to borrow a JWism). It seems that most people assume that a creator would build the universe with new material that it summoned into existence, but this ought to be impossible. It's more logical to imagine that it must use a part of itself.
So if I previously made statements which were more vague than this, I apologize, but this was my intended statement from the beginning.
Mind you, I am not claiming some mystical knowledge of the universe. There is no reason that I think the above proposal has to be true. I consider it equally likely that we are here by accident. I'm sort of taken aback by the determination with which you are attacking this simple idea, and didn't think I would have to spend so much time stating the obvious in order to defend what was only a whimsical suggestion intended to point to other possibilities besides our being here by accident.
As I stated earlier, I consider our existence absurd no matter what, as it's absurd that an intelligent creator could arise from nothing and then make a universe, and it's absurd that intelligent humans could arise from nothing and develop The Sims™.