1. Why does bisecting a square (I assume you mean diagonally) create an irrational number? If matter, and space-time itself are not infinitely divisible, then wouldn't that mean any diagonal line is kind of a zigzag when you look at it closely enough? It's not that the sides aren't integers, it's that the diagonal isn't strictly possible.

2. This is not my logic nor what I wrote about someone else's argument. I didn't say that all infinite decimals store infinite information. Obviously you can talk about how much information is stored in a given infinite string but I didn't go there and it's not relevant. It doesn't matter whether you think all real numbers store the same amount of information or not.

I described the claim that if you could physically realize an arbitrary real number you could store unlimited information in the tiniest piece of matter. Which goes against the intuitive idea based on experience that more matter is required to store more information.