> As long as there is a decision to take the issue persists, it's only if you always go left (or always go right) that the issue doesn't exist.
That's not true. There are two problems.
1. The math is set up to rule out a lot of obvious solutions. Write out A_t(x) for the decision rule "always walk right at a constant rate." For any rate, A_t(x) becomes a spike at 1 for t > some threshold that depends on the rate.
2. The math rules out randomness. A_t(x) can't be defined for the decision rule, "flip a coin and walk right half the time, left the other half," because you wind up at 0 with probability 1/2 and 1 with probability 1/2 for t > some threshold and the problem is defined so A_t(x) must resolve to a single point.
Once you do that, the only solutions left are kind of mind fucks. But you can't draw any general conclusions from it.
That's not true. There are two problems.
1. The math is set up to rule out a lot of obvious solutions. Write out A_t(x) for the decision rule "always walk right at a constant rate." For any rate, A_t(x) becomes a spike at 1 for t > some threshold that depends on the rate.
2. The math rules out randomness. A_t(x) can't be defined for the decision rule, "flip a coin and walk right half the time, left the other half," because you wind up at 0 with probability 1/2 and 1 with probability 1/2 for t > some threshold and the problem is defined so A_t(x) must resolve to a single point.
Once you do that, the only solutions left are kind of mind fucks. But you can't draw any general conclusions from it.