《那些古怪又讓人憂心的問題》第82期:走失的人(1)
LOST IMMORTALS
走失的人
A. WE'LL START WITH THE simple,physicist-style1 answer: 3000 years.
A．先來一個簡化的物理學家式的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.
如果這兩個人每天有12小時隨機走來走去，並且假設兩人相距1千米以內就能看到彼此的話，這差不多是他們能夠發現對方所需要的時間。
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.
但我們立刻就能看出這個模型中的一些問題。最簡單的問題是你沒法保證在任何時候相距1千米以內的兩人能夠看到對方，這隻有在最理想的情況下才有可能實現。沿着山脊走的兩個人可能可以看到1千米外的另一個人，但如果是在茂密的森林中，天空又下着暴雨，那麼就算兩人只相隔數米，都有可能擦肩而過。
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.
我們可以計算出在地球上任意地點的平均可視距離，但我們又會遇到另一個問題：爲什麼兩個急於找到對方的人會跑到茂密的叢林裏去？他們應該會到平坦開闊的地方，這樣他們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.
一旦我們開始考慮兩人的心理活動，那麼之前的那個真空中的球形人的模型就會遇到問題。爲什麼我們要假設那兩個人會到處亂跑？最佳策略可跟它完全不同。
What strategy would make the most sense forour lost immortals?
那麼對於那兩個永生者來說，什麼策略才最靠譜呢？
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.
如果他們事先有時間做好計劃，那麼事情就很簡單。他們可以約定在北極或者南極見面，如果這兩個地方因故去不了的話，還可以把見面地點定在陸地上的最高點，或者最長河流的河口。如果這些規定有點模糊不清的話，他們只需要在幾個可能的地點之間隨機走動就行，反正他們有的是時間。
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?
但如果事先他們沒有機會交流的話，他們就沒法知道另一個人會採取什麼策略。那麼這時你該怎麼做呢？
