Sixty-second Adventures in Thought
六十秒的思維探險
Number one: Achilles and the Tortoise
How could a humble tortoise beat the legendary Greek hero Achilles in a race? The Greek philosopher Xeno liked the challenge and came up with this paradox.
第一：阿基里斯和烏龜
卑微的烏龜是如何在賽跑時打敗傳奇的希臘英雄阿基里斯？希臘哲學家Xeno喜歡這挑戰並想出了這似是而非的悖論。
First, the tortoise is given a slight head start. Anyone fancying a flutter would still rush to put their money on Achilles. But Xeno pointed out that to overtake him, Achilles would first have to cover the distance to the point where the tortoise began.
首先，給烏龜些許起跑優勢。任何投機客仍會趕著去把錢押注在阿基里斯身上。但Xeno指出，要追上烏龜，阿基里斯首先得要跑完他到烏龜起始點的距離。
In that time, the tortoise would have moved, so Achilles would have to cover that distance giving the tortoise time to amble forward a bit more. Logically, this would carry on forever. However small the gap between them, the tortoise would still be able to move forward while Achilles was catching up, meaning that Achilles could never overtake.
在那段時間內，烏龜會移動，所以阿基里斯非得要跑完那段距離，那給了烏龜時間再往前移動一些。邏輯上來說，這會永無止境的繼續下去。不管他們中間的間隔有多小，當阿基里斯追上來的時候，烏龜還是能夠向前移動，意思是阿基里斯永遠也追不上。
Taken to an extreme, this bizarre paradox suggests that all movement is impossible. But it did lead to a realization that something finite can be divided an infinite number of times.
說得極端一點，這超乎尋常的悖論是在暗示著所有的追趕動作都是辦不到的。但它的確讓我們了解到「某個有限的東西是能夠被分割無限多次的」。
This concept of an infinite series is used in finance to work out mortgage payments, which is why they take an infinite amount of time to pay off.
這無窮級數的觀念在財經上用來計算房貸款項，那也就是為何他們要花上無窮盡的時間去付清。
Number two: The Grandfather Paradox
Will time travel ever be possible? Rene Barjavel was a French journalist and a science fiction writer. He spent a lot of his time thinking about time travel. In 1943, Barjavel asked what would happen if a man went back in time to a date before his parents were born, and kills his own grandfather.
第二：祖父的悖論
時空旅行有可能實現嗎？Rene Barjavel是個法國記者也是個科幻小說作家。他花了很多時間思索時空旅行。1943年時，Barjavel問到如果一個人回到過去一個他父母尚未出世的年代，然後殺死他自己的祖父，會發生什麼事？
With no grandfather, one of the man's parents would never have been born, and therefore the man himself would never have existed. So there will be nobody to go back in time and kill the grandfather in the first place, or the last place, depending on how you look at it.
沒有了祖父，這人的雙親之一將從來也不會出生，因此這人他自己將從沒存在過。所以一開始不會有人回到過去，殺死祖父，或是最後回到過去，就看你如何看待這時間順序了。
The grandfather paradox has been a mainstay of philosophy, physics and the entire "Back to the Future" trilogy. Some people have tried to defend time travel with arguments like the parallel universe resolution, in which the changes made by the time traveler create a new separate history, branching off from the existing one. But the grandfather paradox prevails.
祖父的悖論是哲學、物理學和整個「回到未來」三部曲的中心思想。有些人試著用像是平行宇宙解析的論證來捍衛時空旅行，在其中時空旅行者製造出改變，會創造出一個新的、不同的歷史，從現存的歷史中分支出來。但祖父的悖論仍舊盛行。
Although the paradox only suggests that traveling backward in time is impossible, it doesn't say anything about going the other way.
即便這悖論只有提到回到過去是不可能的，它並沒有說明任何去到未來的事情。
Number three: The Chinese Room
Can a machine ever be truly called intelligent? American philosopher and Rhodes Scholar, John Searle, said they can't. In 1980, he proposed the "Chinese Room Thought Experiment," in order to challenge the concept of strong artificial intelligence, and not because of some 80's design fad.
第三：中文房間
一台機器能夠真的被稱作有智能嗎？美國哲學家同時也是羅德獎學金(牛津大學國際獎學金)學者，John Searle，認為它們不能。在1980年，他提出了「中文房間思維實驗」，為了要挑戰強力人工智慧的概念，而不是因為一些八十年代的設計風潮。
He imagines himself in a room with boxes of Chinese characters he can't understand and a book of instructions which he can. If a Chinese speaker outside the room passes him messages under the door, Searle can follow instructions from the book to select an appropriate response. The person on the other side would think they're chatting with a Chinese speaker, just one that doesn't get out much, but really it's a confused philosopher.
他想像自己在一個房間裡，有幾箱他不了解的中文字母還有一本他能夠理解的說明書。如果一位房間外面說中文的人從門底下傳遞訊息給他，Searle可以按照書本指示選擇一個適當的回應。門另一邊的人會認為他們在和一位說中文的人交談，只不過他是個不太出門的傢伙，但實際上那是個搞不清楚狀況的哲學家。
Now according to Alan Turing, the father of computer science, if a computer program can convince a human they're communicating with another human, then it could be said to think.
然後根據資訊科學之父Alan Turing，如果一個電腦程式可以說服人類他們正在和另一個人類交談，那麼我們可以說它會思考。
The "Chinese Room" suggests that however well you programmed a computer, it doesn't understand Chinese. It only simulates that knowledge, which isn't really intelligence. But then, sometimes humans aren't that intelligent either.
「中文房間」暗示，不論你把一台電腦程式編寫得多完善，它並不了解中文。它只會模擬那知識，那不是真正的智能。然而，有時候人們也不是那麼地有智慧。
Number four: Hilbert's Infinite Hotel
A grand hotel with an infinite number of rooms and an infinite number of guests in those rooms: that was the idea of German mathematician David Hilbert, friend of Albert Einstein and enemy of chambermaids the world over.
第四：Hilbert的無限大飯店
一個大飯店有無限多的房間和無限多的房客：那是德國數學家David Hilbert的點子，他是愛因斯坦的朋友和全世界旅館清潔女工的敵人。
To challenge our ideas about infinity, he asked what happens if someone new comes along looking for a place to stay? Hilbert's answer is to make each guest shift along one room. The guest in room one moves to room two and so on, so the new guest will have a space in room one. And the guestbook would have an infinite number of complaints.
為挑戰我們關於無限的概念，他問，如果一位新客人不期而至，想要一間房，會發生什麼事？Hilbert的答案是要讓每一位房客移動一間房。一號房客人移動到二號房，以此類推，因此新房客可住在一號房。而訪客留言簿會有無限多的怨言。
But what about when a coach containing an infinite number of new guests pulls up?
但當一輛載滿無限多新客人的巴士停下來的話又將如何？
Surely, he can't accommodate all of them. Hilbert frees up an infinite number of rooms by asking the guests to move to the room number, which is double their current one, leaving the infinitely many odd numbers free, easy for the guest in room one, not so easy for the man in room 8,600,597.
當然，他不能容納所有的人。Hilbert透過要求房客移動到兩倍數字的房間號碼，釋出無限多的房間，讓無限多的奇數號房空下來，對一號房客人來說很簡單，對於在8,600,597號房的男人來說並不簡單。
Hilbert's paradox has fascinated mathematicians, physicists and philosophers, even theologians. And they all agree you should get down early for breakfast.
Hilbert的悖論讓數學家、物理學家和哲學家甚至神學家為之著迷。而他們都同意你得要早點下樓吃早餐。
Number five: The Twin Paradox
Albert Einstein didn't have a twin brother, but he had some funny ideas of what you could do with one. He imagined two identical twins. Let's call them Al and Bert.
第五：雙胞胎悖論
愛因斯坦並沒有雙胞胎兄弟，但關於有雙胞胎你可以做些什麼，他有些有趣的點子。他假想兩位同卵雙生的雙胞胎。就稱他們為Al和Bert吧。
Now Al is a couch potato, but Bert likes to travel. So, he hops into a spaceship and zooms off at close to the speed of light. That's when Einstein's special theory of relativity kicks in.
現在Al是個沙發電視宅男，但Bert喜歡旅遊。所以，他跳上太空船並用接近光的速度飛快離開。那就是愛因斯坦特殊相對論發揮功效的時候了。
It says that the faster you travel through space, the slower you move through time. So from Al's point of view, Bert's time would be moving slower than his own. To put it another way, time might fly when you're having fun, but when clocks fly, they run more slowly in relativity.
它指出你在太空中行進得越快，你的時間就過的越慢。所以從Al的觀點來看，Bert的時間會比他自己的要來得緩慢。換句話說，當你在享樂(指看電視)的時候，時光會飛逝，但當時鐘在飛速移動時，它們相對來說跑得比較慢。
After a while, Bert decides to head back, still at close to the speed of light and return to his brother with his holiday snaps. But when Bert arrives home, Al will now be older than his twin, which makes their double dates a lot more awkward.
一陣子之後，Bert決定返航，仍舊以接近光的速度，帶著他的旅遊照回到他兄弟身邊。但當Bert抵達家門，Al現在會比他的雙胞胎來得老，這讓他們兩對男女的一起約會顯得更加尷尬。
Although it seems implausible, Einstein just followed his theory to its logical conclusion, and it turns out he was right. This concept of time dilation provides the basis for our Global Positioning System, which is how your SAT NAV knows you need to turn left in two hundred yards.
儘管它似乎是難以置信的，愛因斯坦就是順著他的理論達成合理的結果，而最後證明他是對的。這時間膨脹的觀念提供了我們全球定位系統的基礎，那就是你的SAT NAV(英國GPS大廠牌)如何得知你需要在兩百碼(約一百八十公尺)後左轉的。
Number six: Schrodinger's Cat
Erwin Schrodinger was a physicist, a theoretical biologist and probably more of a dog person. In the 1920s, scientists discovered quantum mechanics, which said that some particles are so tiny you can't even measure them without changing them. But the theory only worked if before you measure them, the particle is in a superposition of every possible state all at the same time.
第六：Schrodinger的貓
Erwin Schrodinger是個物理學家、理論生物學家還有也許更是個比較愛狗的人。在1920年，科學家發現了量子力學，指出有些粒子太微小你甚至無法在不改變它們的情況下去加以量測(測不準原理)。但這理論僅在若你測量這粒子之前，它是處於所有可能狀態的同時疊加狀態，才會實現。
To tackle that, Schrodinger imagined a cat in a box with a radioactive particle and a Geiger counter attach to a vial of poison. If the particle decays, it triggers the Geiger counter, releases the poison and bye-bye Tiddles.
要處理那個問題，Schrodinger想像一隻貓在箱子裡，箱內有個放射性粒子和一具連著一瓶毒藥的蓋氏輻射計數器。如果這粒子衰退(產生放射線)，它便觸動蓋氏輻射計數器，釋出毒藥然後掰掰Tiddles小貓咪(英國卡通小貓咪)。
But if the particle is in two states, both decayed and not decayed, the cat is also in two states, both dead and not dead until someone looks in the box. In practice, it's impossible to put a cat into a superposition. You have the animal rights lobby up in arms.
但如果粒子處於兩種狀態，同時是衰退以及未衰退，貓咪也處於兩種狀態，同時是死的以及沒死，直到某人往盒子裡一探究竟。實際上，不可能讓一隻貓咪處於疊加狀態。你會讓動物權利遊說團體會非常不開心。
But you can isolate atoms, and they do seem to be in two states at once. Quantum mechanics challenges our whole perception of reality. So maybe it's understandable that Schrodinger himself decided that he didn't like it, and was sorry he ever started on about cats.
但你可以隔離出原子，而它們的確似乎是同時處在兩種狀態。量子力學挑戰我們整個對現實的觀點。所以Schrodinger他自己不喜歡它(量子力學)，而且很抱歉他懲罰了貓咪，也許是可以理解的。
- 「不期而至、到來」- Come Along
He asked what happens if someone new comes along looking for a place to stay?
他問，如果一位新客人不期而至，想要一間房，會發生什麼事？ - 「停車、拉單槓」- Pull Up
But what about when a coach containing an infinite number of new guests pulls up?
但當一輛載滿無限多新客人的巴士停下來的話又將如何？ - 「匆忙地離開、飛快離開」- Zoom Off
So, he hops into a spaceship and zooms off at close to the speed of light.
所以，他跳上太空船並用接近光的速度飛快離開。 - 「發揮功效、起作用」- Kick In
That's when Einstein's special theory of relativity kicks in.
那就是愛因斯坦特殊相對論發揮功效的時候了。 - 「非常憤怒、不開心」- Up In Arms
In practice, it's impossible to put a cat into a superposition. You have the animal-rights lobby up in arms.
實際上，不可能讓一隻貓咪處於疊加狀態。你會讓動物權利遊說團體會非常不開心。
