I've edited my question to clear any possible confusing parts:
This an exercise from the book "The Theoretical minimum", I'm paraphrasing.
In classical mechanics, dynamical laws must be reversible and deterministic.
Consider the function N(n) where:
N is a point on a infinite line, and n symbolizes time.
Here are some possible dynamical laws of this system:
N(n+1) = N(n) + 1
N(n+1) = N(n) - 1
N(n+1) = N(n) + 2
N(n+1) = N(n)²
Determine which equations are allowable. (deterministic and reversible)
The solutions are on:
What I don't understand is why equation 4, N(n+1) = N(n)² is not allowable.
If N is 2 we get 4 and then 16. If we "reverse the arrows" we get 16, 4 and 2. If N is 1, it will never change.
How is this not deterministic and reversible?
Thanks in advance!