This is putting the cart before the horse. No matter how you slice and dice your equations, everyone intuitively understands you can't really store infinite data in your brain. Trying to claim otherwise is simply academic sophistry. No matter how hard you write your proof, it won't make information theory, basic physics, etc go away.
This is a math exercise, it assumes an infinitely long lived person, as well as a lot of simplifications. That's the same kind of arguments that can make sailboats go infinitely fast as long as there is any kind of wind.
It is not useless. It tells you essentially two things. First, it shows the limits of your model. If you have proven that sailboats can go infinitely fast, which is obviously not the case in reality, then it is an indication that your model is incomplete and you have to refine it until it stops giving out nonsense, or establish its limits.
Second, it shows that what you have taken into account in your model is not what limits the speed of sailboats or memory recall.
It's not a math exercise. The author poses a question that is in the realm of psychology or neuropsychology or something like that, and then jumps straight into solving it with pure math, picking premises out from thin air.
The premises are obviously wrong, like assuming an infinitely long lived person, which means the answers arrived at will have no correlation with anything factual. You can't fix that with any sort of refinement. To be refinable would require it to be coarsely correct to begin with.
There have been estimates of how much stuff storytellers from oral traditions could remember, and it’s measured in gigabytes. There are caveats beside the obvious (compressibility) that probably cost you an order of magnitude—stories in oral traditions have evolved for easier recall over the generations—but it’s fair to say that the intrinsic limits of human memory are nowhere near what any of us have deliberately memorized.
