If you can truly imagine infinite, you are exceptional. What I mean by understand is to actually realise what it is in a positive manner. People can concieve of infinity, but this is by saying what it is not, i.e. without limits. But to actually imagine a number that is infinitely large is something I cannot do, without refering to things it is not.
I don't think there is anything outside of our understanding. The universe is a very real place. ... ...It just happens to fill in your blank spots with benevolent gods, invisible unicorns and happy trees because you don't seem to be able to cope in a world that's honest and truthful.
The problem here is that you are thinking merely inside your own capacities... How can you deny the possibility that there may be things you cannot imagine? Are there things you cannot think? There is no way to answer this as you cannot imagine an unimaginable thing...
I don't think I'm a genius/exceptional or anything of the likes (thought I was placed in a "gifted studies" class as a kid, I think it was more along the lines to get me to think more than be bored to death in school), but I take the world as it's given. Inifinity is easy to imagine. Write a 1 on a sheet of paper and continue writing zeros on it until you die and you still won't be done coming up with a number to define it. The concept, the idea, and the reality of it is easy for me to understand. It just doesn't end. Take off in a spaceship and head in any direction you desire. Correcting for planets, suns, etc. you will travel forever without hitting anything. That's infinite. Even if the theories are true and the Big Bang happened, there's infinite something just outside that horizon of space goo at the estimated edge. IMHO.
Technically, we could have an infinite number being used every day. PI. There's no known limit to the value. It's infinite in nature as far as we are concerned. Dealing with the finite points of it are mostly pointless in our day to day lives, just as trying to find the reason we are here. Yes, there are people looking for that answer. I personally think it's fruitless, but whatever. Also, I don't discount the idea that E=MC
2 is not universal. Heck, it doesn't even cleanly apply to the atomic scale, only galactic. It's the best guess we have for how things work in our part of the universe, but there's no telling if that theory alone will be deprecated or "refined" later. We can only theorize that light is constant, we can only theorize that Gravity is a pushing effect rather than a pulling effect (I happen to think it might be a little of both... but that's only a thought) but that's reality. You just deal with it. There's really no point trying to nail down that last digit of PI because at that point the calculation will be so accurate that you would just stop caring how many decimal places the circumference is because there will be something coming along to change it (temperature, someone stepping on it...) and you'll have to figure it all out again.
First, your perception of the world is not necessarily true...
Who says? You think truth is that we are all batteries?
As far as the "Matrix" world idea. The movie pretty much defined the problem in that. Any system bent on creating an alternative reality will be met by the inquisitive folks who second guess it. In the Matrix, you have Deja-vu. In that Truman Show movie, you had people walking on water in the horizon, but there's always proof that it's not real. Consider that a story "tactic" (can't think of the word right now) to give the reader/watcher the truth or not... if there was a non-potent god controlling things, there would be glitches and someone would find it. (I've already given my thoughts on omnipotence being impossible.) [that was kind of a ramble, sorry]
Reality is what we live in. If a god chooses to be outside that reality, it's not real and has no effect on our experiments so the only logical path is to assume it doesn't exist. ... on that note:
On the topic of having a 25% chance of being wrong, you don't cover the thought that this god might not want you to think about it. You may have a 75% chance of pissing it off and ending that experiment. Why would it create you and want you to think about it? The experiment would be wasted if people changed their lives based on what they thought you wanted. Observational bias. Monkeys behave different when a human is sitting in their tree.