Epistemic Status
Conceptual toy model. I am not proposing a physical theory or claiming this models the actual architecture of spacetime. I am simply demonstrating that the common intuition - - that a "Block Universe" cannot logically accommodate the "feeling of a moving Now"—is a result of confusing ontological structure with information access.
There is a persistent debate in the philosophy of time between the **Block Universe** (B-theory/Eternalism) and **Presentism** (A-theory). Critics of the Block Universe often argue that if the future is already "there," then our perception of flow, choice, and sequence must be a contradiction.
I want to show that you can get both interpretations out of a single mathematical construction without changing a single variable. The difference isn't in the "flow" of the math; it’s in the information density available to the observer.
The Construction
Let's define a path within the finite interval [0, 1]. We start at a value x_0 and move toward 1. The path is defined by a rule where the rate of change depends on the remaining distance to the limit, scaled by an external input function f.
1. The Static "Block" View
Consider the continuous case. We define a path x(t) using a standard differential equation:
dxdt=(1−x)f(t)
With a starting point:
x(0)=x0
The solution is:
x(t)=1−(1−x0)e−∫t0f(s)ds
In this view, if you are given the starting value x_0 and the entire function f(t) for all t, the path is a **single, static mathematical object**. It is a curve in a 2D plane. Nothing is "moving" along the curve. The ordering is a coordinate, not a process. This is the Block Universe interpretation.
2. The Sequential "Perceived" View
Now, let’s look at the discrete version of the exact same logic. This is how the structure appears if you are "inside" the sequence:
xn+1=xn+(1−xn)fn
Which implies:
1−xn=(1−x0)n−1∏k=0(1−fk)
If you are an agent at index n, and you only have access to the values of f up to n-1, the future is **unde