You are correct. With an answer string where each answer is independent of the others, and access to the oracle as I described, you can find the answer via an exhaustive search that checks no more than 80 interactions.

The test I originally played with, however, was a self referential test, where each question is about the answers to the test itself. On this test, this method does not work.

Aside from this, the point of using this was it is a simple example that serves to demonstrate the fact that the genetic algorithm works, and does so much more efficiently than random chance.

Realistically, this problem is too trivial to bother implementing a genetic algorithm on.

Maybe I'm misunderstanding what's going on here, but it seems to me that due to the known lack of variable interactions, you could find the ideal string in 4 * 20 = 80 iterations.

Start with AAAA...AA, and do each variable one-at-a-time until, at each step, the fitness increases. Then, move onto the next variable.

I had considered bringing that up, but that would've increased the length of the post considerably.

Even ff we assume multiple universes, we still end up with ontological paradoxes, and also predestination paradoxes.

Of course, those paradoxes assume a single timeline the time-traveler navigates like a river, rather than a multiverse with many traversable timelines.

I've no more in-depth knowledge on that issue than the average science fiction fan, though, so perhaps that theory has problems of its own that I'm not considering.

There are in fact 55 unique opening moves, taking transposition into account. This was still an excellent exposition of the game.

The brown eyed people never get to leave. They are also going with the inductive proof laid out, but because they can see 100 blue eyed people, they are trying to determine if they are 101st blue eyed person. All the blue eyed people leave on the 100th night, so on the 101st day, the brown eyed people can infer that they have non-blue eyes, but that is all.

What about the brown-eyed people. How do they know they have brown eyes. How do they know they shouldn't leave?

If we have some pile of sand with X grains in it, and wouldn't consider it to be a heap, the tiny change of 1 grain of sand doesn't turn it into a heap, unless you want to take the position that 99 grains of sand are not a heap, but 100 are. But then you are left to explain the essential difference between a pile of 99 grains of sand and 100 grains of sand that bestows on one heapdom and denies it to the other.

From there we get to the conclusion that, if it is not already a heap of sand, no matter how many more grains of sand you add to it, it still isn't a heap.

Its a paradox because, obviously, at some point it does become a heap. But we cannot pin that point down, because when we try to, we are forced to conclude that it never becomes a heap.

Or, as I said, it can be turned around to conclude that "once a heap, always a heap."

how is the first thing a paradox? it's simply an incorrect statement:

> X grains of sand are not a heap.
> Adding 1 grain of sand to X grains of sand does not make a heap.

obviously the second part is wrong, since it sometimes -does- make a heap. there's no paradox.