N-維空間

　　有一位數學家和一位工程師去聽一場物理學的演講，演講的內容主要在講 Kulza-Klein 定理，這個定理是討論在 9、12維甚至更高維度的空間上的一些物理方法。而正當這位工程師聽得一頭霧水，茫茫然不知演講者所云為何物時，他看到數學家聽得十分起勁，而且陶醉在其中的樣子；甚至到最後，工程師聽到頭都痛起來，而數學家卻還能不斷稱揚這場精采的演講！

　　工程師於是問數學家：「你怎麼會聽得懂那麼複雜的東西？

　　數學家：「哦，我只不過是用點想像力罷了！」

　　工程師：「可是，你要怎麼想像一個發生在 9 維空間的事情呢？」

　　數學家：「這還不簡單，首先你把它們想像成 N-維空間發生的事情，然後再把 N 換成 9 不就行了！」

A mathematician and an engineer attend a lecture by a physicist. The topic concerns Kulza-Klein theories involving physical processes that occur in spaces with dimensions of 9, 12 and even higher. The mathematician is sitting, clearly enjoying the lecture, while the engineer is frowning and looking generally confused and puzzled. By the end the engineer has a terrible headache. At the end, the mathematician comments about the wonderful lecture.

The engineer says "How do you understand this stuff?"
Mathematician: "I just visualize the process."
Engineer: "How can you visualize something that occurs in 9-dimensional space?"
Mathematician: "Easy, first visualize it in N-dimensional space, then let N go to 9."

蘇格蘭的黑羊

一位天文學家、物理學家以及一位數學家去蘇格蘭渡假，坐在火車上，他們發現窗外田野中間有一頭黑色的羊。

　　「多麼有趣呀！」天文學家發現並說道，「所有蘇格蘭的羊都是黑色的！」

　　這時，物理學家回答道：「不！是一些蘇格蘭的羊是黑色的。」

　　數學家懇切地凝視著天空，吟誦地唱道：「在蘇格蘭，至少存在一個田野，這個田野裡至少存在一隻羊，這隻羊至少有一面是黑的！」


An astronomer, a physicist and a mathematician (it is said) were holidaying in Scotland. Glancing from a train window, they observed a black sheep in the middle of a field.

"How interesting," observed the astronomer, "all Scottish sheep are black!"

To which the physicist responded, "No, no! Some Scottish sheep are black!"

The mathematician gazed heavenward in supplication, and then intoned, "In Scotland there exists at least one field, containing at least one sheep, at least one side of which is black."