You’re left with a friend on a planet in the shape of a big solid sphere
where communication is impossible. What is the fastest way to meet?
You can justify in the comments
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Of course, if the "friend" hacked your random number generator prior to arrival, they may still choose to do the opposite. On a sphere, how long should I expect random movement to take encounter a friend employing honest strategies?
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He said random, not pseudo random.
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Sounds like it make sense, but curious — what would a proof of this look like?
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Also, pure random is very bad. Imagine a 1-D version of problem (equator only). Flip coin to decide to take a step east or west. Would never get enough heads or tails in a row to get to the other side of the planet.
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Well that would not so much depend on the 'type' of randomness as much as where you would apply it in the decision making. You could, for instance, just make a random bearing update between -25 & 25 degrees every so many steps.
End of conversation
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That assumes you know nothing about your friend. You should use your knowledge and devise strategy that works best with strategy you expect from your friend.
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Hard is the human brain to manage this random strategy. It would inevitably fall in a deterministic kind behavior and you'd end up moving around a circle pattern without noticing.
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I don't think there's something that can be described as random.. Nothing is random.. The golden ration is a proof of that..
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