LOST IMMORTALS

走失的人

A. WE'LL START WITH THE simple,physicist-style1 answer: 3000 years.

A．先来一个简化的物理学家式的1答案：3000年。

That's about how long it would take twopeople to find each other, assuming that they were walking around at randomover a sphere for 12 hours per day and had to get within a kilometer to seeeach other.

如果这两个人每天有12小时随机走来走去，并且假设两人相距1千米以内就能看到彼此的话，这差不多是他们能够发现对方所需要的时间。

We can immediately see some problems withthis model. The simplest problem is the assumption that you can always seesomeone if they come within a kilometer of you. That's possible under only themost ideal circumstances; a person walking along a ridge might be visible froma kilometer away, whereas in a thick forest during a rainstorm, two peoplecould pass within a few meters without seeing each other.

但我们立刻就能看出这个模型中的一些问题。最简单的问题是你没法保证在任何时候相距1千米以内的两人能够看到对方，这只有在最理想的情况下才有可能实现。沿着山脊走的两个人可能可以看到1千米外的另一个人，但如果是在茂密的森林中，天空又下着暴雨，那么就算两人只相隔数米，都有可能擦肩而过。

We could try to calculate the averagevisibility across all parts of the Earth, but then we run into anotherquestion: Why would two people who are trying to find each other spend time ina thick jungle? It would seem to make more sense for both of them to stay inflat, open areas where they could easily see and be seen.

我们可以计算出在地球上任意地点的平均可视距离，但我们又会遇到另一个问题：为什么两个急于找到对方的人会跑到茂密的丛林里去？他们应该会到平坦开阔的地方，这样他们就能更容易看到彼此。

Once we start considering the psychology ofour two people, our spherical-immortal-in-a-vacuum model is in trouble. Whyshould we assume our people will walk around randomly at all? The optimalstrategy might be something totally different.

一旦我们开始考虑两人的心理活动，那么之前的那个真空中的球形人的模型就会遇到问题。为什么我们要假设那两个人会到处乱跑？最佳策略可跟它完全不同。

What strategy would make the most sense forour lost immortals?

那么对于那两个永生者来说，什么策略才最靠谱呢？

If they have time to plan beforehand, it'seasy. They can arrange to meet at the North or South Pole, or-if those turn outto be unreachable-at the highest point on land, or the mouth of the longestriver. If there's any ambiguity, they can just travel between all the optionsat random. They have plenty of time.

如果他们事先有时间做好计划，那么事情就很简单。他们可以约定在北极或者南极见面，如果这两个地方因故去不了的话，还可以把见面地点定在陆地上的最高点，或者最长河流的河口。如果这些规定有点模糊不清的话，他们只需要在几个可能的地点之间随机走动就行，反正他们有的是时间。

If they don't have a chance to communicatebeforehand, things get a little harder. Without knowing the other person'sstrategy, how do you know what your strategy should be?

但如果事先他们没有机会交流的话，他们就没法知道另一个人会采取什么策略。那么这时你该怎么做呢？