I guess the (crazy, I know) assumption that I made is that I have some analytical, symbolic expression for a function that describes the state of the universe at every point. This "state" describes some fundamental quantity (not necessarily a quantity we have a name for yet).
Then we express the value of any particle field at every point as a (potentially very complex) symbolic expression that only uses the state function from my previous paragraph.
All of these expressions need only finite memory to store. They describe functions with domain R^n to some co-domain of operators or whatever.
Then I can calculate the value of this complex function at any point with any precision I like, with finite memory, although unbounded - I need to allocate more memory when I want more precision.
Point is, I delay the process of "latticization" (calculating the numerical values at each point of a chosen lattice) to the very end - only then I have to choose how fine-grained my lattice is.
> I guess the (crazy, I know) assumption that I made is that I have some analytical, symbolic expression for a function that describes the state of the universe at every point.
This is the error. All you have is some partial differential equation. It has no known symbolic solution.
Then we express the value of any particle field at every point as a (potentially very complex) symbolic expression that only uses the state function from my previous paragraph.
All of these expressions need only finite memory to store. They describe functions with domain R^n to some co-domain of operators or whatever.
Then I can calculate the value of this complex function at any point with any precision I like, with finite memory, although unbounded - I need to allocate more memory when I want more precision.
Point is, I delay the process of "latticization" (calculating the numerical values at each point of a chosen lattice) to the very end - only then I have to choose how fine-grained my lattice is.