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Thought Experiments: 史上著名的10個思想實驗
送交者: 湯安 2011年11月30日10:22:19 於 [天下論壇] 發送悄悄話

史上著名的10個思想實驗

Top 10 Most Famous Thought Experiments



FEED YOUR BRAIN...

Thought experiments are mental concepts or hypotheses, often resembling riddles, which are used by philosophers and scientists as simple ways of illuminating what are usually very dense ideas.

Most often, they’re used in more abstract fields like philosophy and theoretical physics, where physical experiments aren’t possible. They serve as some hearty food for thought, but given their complex subject matter, it’s not unusual for even the thought experiment itself to be nearly incomprehensible.

With this in mind, here are ten of the most famous thought experiments, along with explanations of the philosophical, scientific, and ethical ideas they work to explain:

The Trolley Problem
The Cow in the Field
The Ticking Time Bomb
Einstein's Light Beam
The Ship of Theseus
Galileo's Gravity Experiment
Monkeys and Typewriters
The Chinese Room
Schroedinger's Cat and last but not least...
Brain in a Vat

 

 

Y2網上的那個哈佛大學教授講課大堂實況錄像大家估計都看過了。裡面舉出的阻止車禍難題是來自於下文中英國Virtue Eethics倫理哲學家Philippa Foot的著名"電車難題"


不過,她的難題僅僅位列10大 Thought Experiments 中的第10。位列第一的是電影《黑客帝國》裡面引用的用來阻截笛卡爾“我思故我在”哲學論斷的"大腦與模擬環境"。


 

 

 

 


  思想實驗是一種精神上的觀念或假想,通常和謎語相似,是哲學家和科學家用以了解什麼是大眾思想的一種簡單方法。他們的運用在如哲學和理論物理(理論物理無需做實驗)等抽象領域是最為廣泛的。他們像是為思想準備的一份大餐,最終給出複雜的答案。即使思想實驗本身也會有無法理解的時候,這並不奇怪。下面是10個著名的思想實驗,還有他們所要表達的哲學、科學和倫理意義。

  10.電車難題

  它是倫理學領域最為知名的思想實驗之一,內容大致是:一個瘋子把五個無辜的人綁在電車軌道上,一輛失控的電車朝他們駛來,且馬上就要輾過他們。幸運的是,你可以拉一個拉杆,讓電車開到另一條軌道上。但是還有一個問題,那個瘋子在那另一條軌道上也綁了一個人。想想這個情況,你應該拉拉杆嗎?

  意義:

  電車難題最早由哲學家Philippa Foot提出,是用來批判倫理哲學主要理論的,特別是對功利主義的批判。功利主義認為,大部分道德決策都是根據“為最多的人提供最大的利益”的原則做出的。從一個功利主義者的觀點來看,明顯應去拉拉杆,只殺死一個人來拯救五個人。但是功利主義的批判者反駁說,一旦拉了拉杆,你就變得不道德——你要為另一條軌道上那一個人的死負擔部分的責任。然而,其他人認為,這種狀況下要求你要有所作為,什麼都不做也是不道德。總之,不存在完全的道德行為,這也就是重點所在。許多哲學家都用電車難題作為例子來表現現實生活中經常強迫一個人違背自己道德準則的狀況,並且有的時候根本沒有完全道德的做法。

  9.空地上的奶牛

  認知領域中一個重要的思想實驗就是“空地上的奶牛”。實驗是這樣的,一個農民擔心自己獲獎的奶牛走丟了。一個送奶工來到農場後,他讓農民不要擔心,因為他看到那頭奶牛就在附近。雖然農民很願意相信送奶工,但他還是自己去看了下,他看到了熟悉的黑白相間條紋,為自己的奶牛在那裡感到很滿意。過了一會,送奶工到那裡再次進行了確認。那頭奶牛確實在那裡,但它躲在了樹林裡,而且有一大張黑白相間的紙纏繞在了一棵樹上,顯然,農民把這張紙錯當成自己的奶牛了。問題於是來了,就算奶牛一直在那裡,但農民說自己知道那頭奶牛在那裡時是否正確?

  意義:

  空地上的奶牛最初被EdmundGettier用來批判主流對知識定義的 JTB(justifiedtruebelief)理論,即當人們相信一件事時,它就成為了知識;這件事事實上是真的,且可以被充分驗證。實驗中,農民之所以相信奶牛在那裡,是送奶工證詞和他自己所見黑白相間物所共同構成的結果。而之後送奶工的確認,這件事也碰巧是真實的。儘管如此,農民並非真正知道奶牛在那裡,因為他認為奶牛在那裡的結論是建立在錯誤的前提上的。Gettier利用這個實驗和其他一些例子,說明了將知識定義為JTB的理論需要修正。

  8.定時炸彈

  如果你關注近幾年的政治時事,或看過動作電影,那麼你對“定時炸彈”實驗肯定很熟悉。它要求你想象有一個炸彈或其他大規模殺傷性武器藏在你的城市中,並且倒計時馬上將歸零。城市裡有一個知情者,他知道炸彈的埋藏點。你會使用酷刑來讓他吐出情報嗎?

  意義:

  與電車難題類似,定時炸彈實驗也是強迫一個人從兩個不道德行為中選擇其一的倫理問題。它一般用來反駁那些說在任何情況下都不能使用酷刑的言論。它也被用作在極端形勢下法律可以被放在第二位的情況,如美國嚴禁虐囚的法律。歸功於《24小時》之類的電視節目,還有一些政治辯論,定時炸彈已成為最常被提起的思想實驗之一。今年早些時候,一份英國報紙提出了更為極端的看法。這份報紙說,如果這個恐怖分子對酷刑毫無反應,那麼當局者是否願意拷打他的妻子和兒女來逼他吐出情報。

  7.愛因斯坦的光線

  很少有人知道愛因斯坦著名的狹義相對論是受到他16 歲時一個思想實驗的啟發。在他的著作《自述註記》中,愛因斯坦回憶道他當時幻想在宇宙中追逐一道光線。他說如果他能夠以光速在光線旁邊運動,那麼他應該能夠看到光線在空間內呈現為“不斷振盪但停滯着的電磁場”。對於愛因斯坦,這個思想實驗證明了對於他作為一個富有想象力的觀察者,”在有相同定律和一個相對於地球靜止觀察者的情況下,任何事都有可能發生。”

  意義:

  事實上,沒人真正知道這意味着什麼。科學家一直都在爭論一個如此簡單的思想實驗是如何幫助愛因斯坦完成到狹義相對論這個巨大飛躍的。在當時,這個實驗中的想法與現在已被拋棄的“以太”理論相違背。“以太”理論即存在一個隱性的空間供光線穿越。他經過了好多年才證明了自己是正確,但從某種程度上這個實驗對於狹義相對論是“有害的”,他自己這麼說,後者第一次讓他站上了理論物理學的頂點。

  6.忒修斯之船

  史上最為古老的思想實驗之一便是被稱為忒修斯之船的悖論。這個實驗最早出自普魯塔克的記載。它描述了一艘可以在海上航行幾百年的船,這歸功於不斷的維修和部件的替換。只要一塊木板腐爛了,它就會被替換掉,以此類推,直到所有的部件都不再是最初的那些。問題是,最終產生的這艘船還是原來的忒修斯之船,還是一艘完全不同的新船?如果不是原來的船了,那麼從什麼時候開始它不再是原來的船了?哲學家ThomasHobbes後來對此進行了更深刻的探討:如果有人用忒修斯之船上取下來的老部件來重新建造一艘新的船,那麼兩艘船中哪艘才是真正的忒修斯之船?

  意義:

  對於哲學家來說,忒修斯之船被用來研究身份的本質,特別是討論一個物體是否僅僅就是其部件之和。一個更現代的例子是假設有一個樂隊,到某一階段樂隊成員中不再有任何一個原始成員。這個問題還可以應用於其他如商業等領域。商業領域中,在不斷併購和更換股東後仍然保留企業原來的名字;對於人體,人體不斷地進行着新陳代謝和自我修復。這個實驗的核心思想在於強迫人們去反問身份是否僅僅局限在實際物體和現象中這一普遍知識。

  5.伽利略的重力實驗

  史上最早的思想實驗之一,由物理和天文學家伽利略進行實驗。為了反駁亞里士多德的自由落體速度取決於物體質量的理論,伽利略設計了一個簡單的思想實驗:根據亞里士多德的邏輯,如果一個較輕的物體和一個較重的物體綁在一起後從塔上扔下去,那麼教重的物體會下落的比較快,且兩個物體間的繩子會被拉緊。這時較輕的物體會對較重的物體產生一個拽力,使得重物的下落速度變慢。但是,伽利略認為兩個物體綁在一起後的重量應比其中任意一個物體都大,那麼一起下落的速度應該是最快的。於是他用這個矛盾證明了亞里士多德理論是錯誤的。

  意義:

  關於伽利略有一個著名的故事:有一次他從比薩斜塔扔下兩個鐵球,想要證明較重的物體並不較輕的物體下落速度快。現實中這個故事可能只是作為一種傳奇,但這個思想實驗證明了一個關於重力很重要的理論:無論物體的質量,所有物體自由落體的速率都是一樣的。

  4.猴子和打字機

  另一個在流行文化中獲得廣泛關注的思想實驗是“無限猴子定理”,也叫做“猴子和打字機”實驗。該定理認為,如果有無數多的猴子在無限久的時間裡,在無數多的打字機上隨機打字,那麼在某個時間點,它們“幾乎必然”會打出莎士比亞的全部著作。猴子和打字機的設想在20世紀早期由法國數學家EmileBorel推廣,但其基本思想,即無數多的人員和無數多的時間能產生任何/所有東西的理論,可以追溯至亞里士多德。

  意義:

  簡單來說,“猴子和打字機”定理是用來描述無限本質最好的方法之一。人的大腦很難想象無限的空間和無限的時間,無限猴子定理可以幫助理解這些概念。猴子碰巧能寫出《哈姆雷特》,聽上去是天方夜譚,但當一個人考慮到所有的可能性後,這個說法在數學上是可以被證明的。這個定理本身在現實生活中不可重現,但這並沒有阻止一些人的嘗試:2003年,英國修讀科學的學生在一家英國動物園“試驗”了無限猴子定理,他們把一台電腦和一個鍵盤放進了靈長類園區。可惜的是,猴子們沒有打出任何十四行詩。根據研究,它們只打出了5頁幾乎完全是字母“s”的紙。

  3.中文房間

  “中文房間”最早由美國傑出哲學家 JohnSearle於20世紀80年代初提出。這個實驗要求你想象一位只會說英語的人身處一個幾乎完全密閉的房間中,房間門上有一個小窗口。他有一台具有英漢翻譯功能的電腦,房間裡還有足夠的紙、鉛筆和文件櫃。隨後寫着中文的紙片通過小窗口將被送入房間中。根據Searle的理論,房間中的人可以翻譯這些文字並用中文寫上他的回覆。雖然他完全不會中文,但Searle認為通過這個過程,房間裡的人可以讓任何房間外的人以為他會說流利的中文。

  意義:

  Searle 創造了“中文房間”思想實驗來反駁電腦和其他人工智能都能夠真正思考的觀點。房間裡的人不會說中文;他無法用中文思考。但就因為他擁有某些工具,他甚至可以讓以中文為母語的人以為他能說流利的中文。Searle還說,電腦就是這樣工作的。它們無法真正理解他們所給出的信息,但它們可以運行一個程序、處理信息、然後給出一個具有人工智能的印象。

  2.薛定諤的貓

  薛定鍔的貓最早由物理學家薛定鍔提出,是量子力學領域中的一個悖論。內容是:一隻貓被封閉在一個盒子裡一個小時,和它一起的還有一些放射性元素和一瓶毒氣。在一小時內,放射性元素的衰變幾率為50%。如果發生了衰變,那麼會觸發一個連接在蓋革計數器上的錘子,打碎瓶子,釋放毒氣,殺死貓。因為這件事是否發生的概率相等,薛定鍔認為在盒子被打開前,盒子中的貓可以同時被認為是既死又活的。

  意義:

  簡而言之,這個實驗的核心思想是因為事件發生時不存在觀察者,盒子裡的貓可能同時存在所有的狀態(實驗中既死又活)。這個觀念同一個古老的謎題相似,謎題內容為,如果一棵樹倒在了樹木中,且沒有人聽到聲音,那麼它有沒有發出聲響?薛定鍔最早是在回復一篇討論量子態疊加本質的文章時提出這個實驗的。薛定鍔的貓同時也說明了量子力學的理論是多麼奇怪。這個思想實驗因其複雜性而臭名昭著,同時也產生了各種各樣的解釋。其中最古怪的是“多重世界”假說,這個假說表示有一隻既死又活的貓,那麼兩隻貓是存在於不同的宇宙間,且永遠不會有交集。

  1.缸中的大腦

  沒有比所謂“缸中的大腦”更有影響力的思想實驗了,這個思想實驗涵蓋了從認知學到哲學到流行文化等各個領域。這個實驗要求你想象有一個瘋狂科學家把你的大腦從你體內取出,放在一個裝有維持生命液體的缸中。大腦是連着電極,電極還連到一台能產生圖像和感官信號的電腦上。因為你獲取的所有關於世界的信息都是經由大腦過濾,這台電腦就有能力模擬你日常的體驗。如果這確實可能的話,你要如何來證明你周圍的世界是真實的,而不是由一台電腦所產生的模擬環境?

  意義:

  如果你覺得這一切聽起來很像《黑客帝國》,你說對了。這部電影以及其他一些科幻小說和電影,都受到了這個實驗很大的影響。這個實驗的核心思想是讓人們質疑經歷的本質,並思考作為一個人的真正意義是什麼。這個實驗的原型可以追溯至笛卡爾,由希拉里·普特南推廣。在笛卡爾的《第一哲學沉思錄》一書中,笛卡爾提出了是否證明能他所有的感官體驗都是他自己的,而不是由某個“邪惡魔鬼”所產生的幻想。笛卡爾用他的經典名言“我思故我在”回答了這個問題。不幸的是,“缸中的大腦”將問題複雜化了,因為連着電極的大腦仍然可以思考。這個實驗被哲學家廣泛討論,也有許多針對實驗前提的反駁,但仍沒有人能有力的回應其核心問題:你到底怎麼才能知道什麼是真實?

 

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史上最著名的10個思想實驗| jiaren.org

Top 10 Most Famous Thought Experiments


with videos

Thought experiments are mental concepts or hypotheses, often resembling riddles, which are used by philosophers and scientists as simple ways of illuminating what are usually very dense ideas. Most often, they’re used in more abstract fields like philosophy and theoretical physics, where physical experiments aren’t possible. They serve as some hearty food for thought, but given their complex subject matter, it’s not unusual for even the thought experiment itself to be nearly incomprehensible. With this in mind, here are ten of the most famous thought experiments, along with explanations of the philosophical, scientific, and ethical ideas they work to explain:

10. The Trolley Problem


One of the most well known thought experiments in the field of ethics is the “Trolley Problem,” which goes something like this: a madman has tied five innocent people to a trolley track. An out of control trolley car is careening toward them, and is moments away from running them over. Luckily, you can pull a lever and divert the trolley to another track. The only problem is that the madman has also tied a single person to that track. Considering the circumstances, should you pull the lever?

What it Means:

The trolley problem was first proposed by the philosopher Philippa Foot as a means of critiquing the major theories in ethical philosophy, in particular utilitarianism, the system which proposes that the most moral decision is always the one that provides “the greatest good for the greatest number.” From a utilitarian point of view, the obvious choice is to pull the lever, saving five and only killing one. But critics of this theory would state that in pulling the lever you become complicit in what is clearly an immoral act—you are now partially responsible for the death of the lone person on the other track. Others, meanwhile, argue that your mere presence in the situation demands that you act, and that to do nothing would be equally immoral. In short, there is no wholly moral action, and this is the point. Many philosophers have used the trolley problem as an example of the ways that real world situations often force individuals to compromise their own moral codes, and that there are times when there is no totally moral course of action.

9. The Cow in the Field

One of the major thought experiments in epistemology (the field of philosophy that deals with knowledge) is what is known as “The Cow in the Field.” It concerns a farmer who is worried his prize cow has wandered off. When the milkman comes to the farm, he tells the farmer not to worry, because he’s seen that the cow is in a nearby field. Though he’s nearly sure the man is right, the farmer takes a look for himself, sees the familiar black and white shape of his cow, and is satisfied that he knows the cow is there. Later on, the milkman drops by the field to double-check. The cow is indeed there, but it’s hidden in a grove of trees. There is also a large sheet of black and white paper caught in a tree, and it is obvious that the farmer mistook it for his cow. The question, then: even though the cow was in the field, was the farmer correct when he said he knew it was there?

What it Means:

The Cow in the Field was first used by Edmund Gettier as a criticism of the popular definition of knowledge as “justified true belief”—that is, that something becomes knowledge when a person believes it; it is factually true; and they have a verifiable justification for their belief. In the experiment, the farmer’s belief that the cow was there was justified by the testimony of the milkman and his own verification of a black and white object sitting in the field. It also happened to be true, as the milkman later confirmed. But despite all this, the farmer did not truly know the cow was there, because his reasoning for believing it turned out to be based on false premises. Gettier used this experiment, along with a few other examples, as proof of his argument that the definition of knowledge as justified true belief needed to be amended.

8. The Ticking Time Bomb


If you’ve paid any attention to political discourse over the past few years—or ever seen an action movie, for that matter—then you are no doubt familiar with the “ticking time bomb” thought experiment. It asks you to imagine that a bomb or other weapon of mass destruction is hidden in your city, and the timer on it will soon strike zero. You have in your custody a man with knowledge of where the device is planted. Do you resort to torture in order to get him to give up the information?

What it Means:

Like the trolley problem, the ticking time bomb scenario is an ethical problem that forces one to choose between two morally questionable acts. It is most often employed as a counter argument to those who say the use of torture is inexcusable under any circumstances. It’s also used as an example of the way laws—like those the U.S. has against torturing prisoners—will always be set aside given extreme circumstances. Thanks to its fictionalized use in television shows like 24, along with its constant position in political debates, the ticking time bomb scenario has become one of the most frequently repeated thought experiments. An even more extreme take on the problem was presented in a British news article earlier this year. That version proposes that the terrorist in question won’t respond to torture, and asks if one would be willing to resort to torturing the man’s wife and children as a means of extracting the information from him.

7. Einstein’s Light Beam


It’s a little known fact that Albert Einstein’s famous work on special relativity was spurred by a thought experiment he conducted when he was only 16 years old. In his book Autobiographical Notes, Einstein recalls how he once daydreamed about chasing a beam of light as it traveled through space. He reasoned that if he were able to move next to it at the speed of light, he should be able to observe the light frozen in space as “an electromagnetic field at rest though spatially oscillating.” For Einstein, this thought experiment proved that for his imaginary observer “everything would have to happen according to the same laws as for an observer who, relative to the Earth, was at rest.”

What it Means:

In truth, no one really knows for sure. Scientists have long debated how this deceivingly simple thought experiment helped Einstein make the massive theoretical leap required to arrive at special relativity theory. At the time, the ideas in the experiment contradicted the now-debunked belief in the “aether,” an invisible field through which light was believed to travel. It would be years before he could prove he was right, but this thought experiment was somehow the “germ,” as he called it, for Einstein’s theory of special relativity, one of the ideas that first established him as a towering figure in theoretical physics.

6. The Ship of Theseus


One of the oldest of all thought experiments is the paradox known as the Ship of Theseus, which originated in the writings of Plutarch. It describes a ship that remained seaworthy for hundreds of years thanks to constant repairs and replacement parts. As soon as one plank became old and rotted, it would be replaced, and so on until every working part of the ship was no longer original to it. The question is whether this end product is still the same Ship of Theseus, or something completely new and different. If it’s not, at what point did it stop being the same ship? The Philosopher Thomas Hobbes would later take the problem even further: if one were to take all the old parts removed from the Ship of Theseus and build a new ship from them, then which of the two vessels is the real Ship of Theseus?

What it Means:

For philosophers, the story of the Ship of Theseus is used as a means of exploring the nature of identity, specifically the question of whether objects are more than just the sum of their parts. A more modern example would be a band that had evolved over the years to the point that few or no original members remained in the lineup. This notion is also applicable to everything from businesses, which might retain the same name despite mergers and changes in leadership, to the human body, which is constantly regenerating and rebuilding itself. At its heart, the experiment forces one to question the commonly held idea that identity is solely contained in physical objects and phenomena.

5. Galileo’s Gravity Experiment


One of the earliest thought experiments originated with the physicist and astronomer Galileo. In order to refute Aristotle’s claim that the speed of a falling object is dictated by its mass, Galileo devised a simple mental example: According to Aristotelian logic, if a light object and a heavy object were tied together and dropped off a tower, then the heavier object would fall faster, and the rope between the two would become taut. This would allow the lighter object to create drag and slow the heavy one down. But Galileo reasoned that once this occurs, the weight of the two objects together should be heavier than the weight of either one by itself, therefore making the system as a whole fall faster. That this is a contradiction proved that Aristotle’s hypothesis was wrong.

What it Means:

One of the most famous stories about Galileo is that he once dropped two metal balls off the Leaning Tower of Pisa to prove that heavier objects do not fall faster than lighter ones. In actuality, this story is probably just a legend; instead, it was this elegant thought experiment that helped prove a very important theory about gravity: no matter their mass, all objects fall at the same rate of speed.

4. Monkeys and Typewriters


Another thought experiment that gets a lot of play in popular culture is what is known as the “infinite monkey theorem.” Also known as the “monkeys and typewriters” experiment, the theorem states that if an infinite number of monkeys were allowed to randomly hit keys on an infinite number of typewriters for an infinite amount of time, then at some point they would “almost surely” produce the complete works of Shakespeare. The monkeys and typewriters idea was popularized in the early 20th century by the French mathematician Emile Borel, but its basic idea—that infinite agents and infinite time will randomly produce anything and everything—dates back to Aristotle.

What it Means:

Simply put, the “monkeys and typewriters” theorem is one of the best ways to illustrate the nature of infinity. The human mind has a difficult time imagining a universe with no end or time that will never cease, and the infinite monkeys help to illustrate the sheer breadth of possibilities these concepts create. The idea that a monkey could write Hamlet by accident seems counterintuitive, but in fact it is mathematically provable when one considers the probabilities. The theorem itself is impossible to recreate in the real world, but that hasn’t stopped some from trying: In 2003, science students at a zoo in the U.K. “tested” the infinite monkey theorem when they put a computer and a keyboard in a primate enclosure. Unfortunately, the monkeys never got around to composing any sonnets. According to researchers, all they managed to produce was five pages consisting almost entirely of the letter “s.”

3. The Chinese Room


The Chinese Room is a famous thought experiment first proposed in the early 1980s by John Searle, a prominent American philosopher. The experiment asks you to imagine that an English speaking man has been placed in a room that is entirely sealed, save for a small mail slot in the chamber door. He has with him a hard copy in English of a computer program that translates the Chinese language. He also has plenty of spare scratch paper, pencils, and file cabinets. Pieces of paper containing Chinese characters are then slipped through the slot in the door. According to Searle, the man should be able to use his book to translate them and then send back his own response in Chinese. Although he doesn’t speak a word of the language, Searle argues that through this process the man in the room could convince anyone on the outside that he was a fluent speaker of Chinese.

What it Means:

Searle conceived the Chinese Room thought experiment in order to refute the argument that computers and other artificial intelligences could actually think and understand. The man in the room does not speak Chinese; he can’t think in the language. But because he has certain tools at his disposal, he would be able convince even a native speaker that he was fluent in it. According to Searle, computers do the same thing. They don’t ever truly understand the information they’re given, but they can run a program, access information, and give a clear impression of human intelligence.

2. Schrodinger’s Cat


Schrödinger’s Cat is a paradox relating to quantum mechanics that was first proposed by the physicist Erwin Schrödinger. It concerns a cat that is sealed inside a box for one hour along with a radioactive element and a vial of deadly poison. There is a 50/50 chance that the radioactive element will decay over the course of the hour. If it does, then a hammer connected to a Geiger counter will trigger, break the vial, release the poison, and kill the cat. Since there is an equal chance that this will or will not happen, Schrödinger argued that before the box is opened the cat is simultaneously both alive and dead.

What it Means:

In short, the point of the experiment is that because there is no one around to witness what had occurred, the cat existed in all of its possible states (in this case either alive or dead) simultaneously. This notion is similar to the old “if a tree falls in the woods and there’s no one there to hear it, does it make a sound?” riddle. Schrödinger originally conceived of his theoretical cat in response to an article that discussed the nature of quantum superpositions, a theory that defines all the possible states in which an object can exist. Schrödinger’s Cat also helped to illustrate just how weird the rules of quantum mechanics really were. The thought experiment is notorious for its complexity, which has encouraged a wide variety of interpretations. One of the most bizarre is the “many worlds” hypothesis, which states that the cat is both alive and dead, and that both cats exist in different universes that will never overlap with one another.

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