Yes, always go left (except if you start at 1) is a solution. It is dismissed by Lamport though because the function is not continuous in 1. Somehow he believes not beiing continuous violates some principles of physics.
That continuous assumption is well-justified in the paper, even for quantum physics, where indeed probability densities are continuous.
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.
So you are saying an algorithm which says always go left unless you start at 1, is physically impossible (apart from using superdeterminism), because the A function would be non-continuous?
> So you are saying an algorithm which says always go left unless you start at 1, is physically impossible
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...
