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  • 60-Second Adventures in Thought

    一分鐘腦筋急轉彎

  • Achilles and the Tortoise

    阿基里斯與烏龜

  • How could a humble tortoise

    一隻不起眼的烏龜

  • beat the legendary Greek hero Achilles in a race?

    怎樣才能在賽跑中戰勝希臘英雄阿基里斯呢?

  • The Greek philosopher Zeno liked a challenge

    希臘哲學家齊諾喜歡接受挑戰

  • and came up with this paradox

    提出了以下悖論

  • First, the tortoise is given a slight head start

    首先允許烏龜先跑一段距離

  • Anyone fancying a flutter

    喜歡打賭的人

  • would still rush to put their money on Achilles

    還是會把他們的寶壓在阿基里斯身上

  • But Zeno pointed out that

    但齊諾指出

  • to overtake him

    要趕上烏龜

  • Achilles would first have to cover the distance

    阿基里斯首先必須跑到

  • to the point where the tortoise began

    烏龜和他共同起跑時的起跑點上

  • In that time the tortoise would have moved

    而在這個時間段烏龜又往前跑了一段距離

  • so Achilles would have to cover that distance

    所以阿基里斯還得跑完烏龜跑完的第二段距離

  • giving the tortoise time to amble forwards a bit more

    在這段時間烏龜又向前爬了一截

  • Logically this would carry on forever

    從邏輯上看這樣的過程會一直持續下去

  • However small the gap between them

    無論他們之間的差距多麼微小

  • the tortoise would still be able to move forwards

    在阿基里斯追趕的時間

  • while Achilles was catching up

    烏龜總是能夠向前爬一段距離

  • Meaning that Achilles could never overtake

    這就是說阿基里斯永遠無法趕上烏龜

  • Taken to an extreme

    更極端的情況是

  • this bizarre paradox suggests

    這個奇怪的悖論顯示

  • that all movement is impossible

    所有的運動都是不可能的

  • But it did lead to the realization

    但卻說明了一個理論

  • that something finite can be divided

    即有限的事物

  • an infinite number of times

    總是能被無限次的分割

  • This concept of 'an Infinite Series' is used in finance

    “無限序列”的概念被應用到了金融業

  • to work out mortgage payments...

    用來計算人們的按揭款

  • Which is why they take

    這就是為什麼無論償還多少次

  • an infinite amount of time to pay off!

    他們都無法還清債務的原因

60-Second Adventures in Thought

一分鐘腦筋急轉彎

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阿基里斯與烏龜--60秒思想大冒險 (1/6) (Achilles and the Tortoise - 60-Second Adventures in Thought (1/6))

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