Looking at it macroscopically, highly complex decisionmaking such as the one that the brain produces, has continuity. In chaos theory, a double pendulum may, after a minute, be either on the left or the right depending on tiny changes in initial state; but changing the initial condition continuously, will change the state at the minute mark continuously, and so, the decision.

Looking at it microscopically, even CPUs are continuous, as there is a slim chance of a transistor only producing half the current, because of the quantum behavior of electrons.

It is conceptually weird that there must be a chance for permanently indecisive animals. To me, the true resolve of the paradox is superdeterminism: the choice taken had to happen.

I am glad that paper got rejected.

The algorithm itself is possible. If implemented in a continuous machine, though, it is not guaranteed to reach either point 0 or point 1 in any given timeframe.

In practice, it usually does not matter. One application I can think of, though, is the surprisingly powerful fault injection vulnerabilities which can break the physical implementation of a cryptosystem: http://euler.ecs.umass.edu/ece597/pdf/Fault-Injection-Attack...