悖论

超真实声音及声音错觉

/ 14 条评论

火星文一则，若看过莫见怪，今天偶然看到后感觉真的很神奇。
播放时请务必戴上耳机，耳机音质越高越好。

虚拟理发店：超级真实的听觉体验。理发师会告诉你这背后的科学知识。
火柴盒：你会听到一个人在你周围各个地方摇动火柴盒，让你感到浑身不自在

Shepard悖论：你会感觉音调不断在上升，但事实上这段声音的开头和结尾音调是一样的。如果不断重复播放这段声音，音调似乎在永无止境地上升。非常神奇。
坠落的铃铛：你会感觉音调在不断下降，但事实上音调在不断上升（从开头重新播放来证实这一点）
加速击打：你会觉得打击声速度在加快，但事实上开头和结尾的速度是一样的（我咋没啥感觉呢）

后面三个声音错觉来自http://www.noah.org/science/audio_paradox，你也可以在那里找到下载的地方

又一个比较诡异的悖论

/ 50 条评论

    不知道大家见过没有，我今天偶然看到，在这里写一下。
    箱子里有两个信封：“一个信封里有1元钱，另一个有10元”有1/2的概率；“一个信封里有10元钱，另一个有100元”有1/4的概率；“一个信封里有100元钱，另一个有1000元”有1/8的概率……也就是说，有1/2^n的概率发生这样的事情，一个信封里有10^(n-1)元钱，另一个信封里有10^n元钱。现在你拿到一个信封，看到了里面有x元钱。给你一次机会换成另外那个信封，问你换不换。
    举个例子，假如我们拿到了100元钱的信封，那么换一个信封得到1000元的概率是得到10元的概率的一半。也就是说，如果我们拿到了x元钱，换一个信封的话有1/3的概率多得9x元，有2/3的概率失去0.9x元。它的期望值是增加2.4x元，这告诉了我们换一个信封显然更好。
    现在的问题是，既然总是换个信封好些，那么为什么我们不一开始就选择另外那个信封呢？

大家可以在下面讨论
我就不参与讨论了，虽然我也不知道是怎么回事

    这个问题让我想到了Newcomb悖论，说有个妖精可以预言你将拿一个箱子还是两个箱子，大家一定见过。

    A highly superior being from another part of the galaxy presents you with two boxes, one open and one closed. In the open box there is a thousand-dollar bill. In the closed box there is either one million dollars or there is nothing. You are to choose between taking both boxes or taking the closed box only. But there's a catch.
    The being claims that he is able to predict what any human being will decide to do. If he predicted you would take only the closed box, then he placed a million dollars in it. But if he predicted you would take both boxes, he left the closed box empty. Furthermore, he has run this experiment with 999 people before, and has been right every time.
    What do you do?
    On the one hand, the evidence is fairly obvious that if you choose to take only the closed box you will get one million dollars, whereas if you take both boxes you get only a measly thousand. You'd be stupid to take both boxes.
    On the other hand, at the time you make your decision, the closed box already is empty or else contains a million dollars. Either way, if you take both boxes you get a thousand dollars more than if you take the closed box only.

    Newcomb悖论是很荒唐的，很不具有数学的科学性。但这篇日志介绍的悖论在科学性上是可以承认的。