雙語暢銷書《艾倫圖靈傳》第3章:思考什麼是思考(96)
But by the 1930s it was accepted that 'groups' could be explored in the abstract, without any concrete representation or application in mind.
* There is nothing 'reAl' about 'real numbers'. The term is a historical accident, arising from the equally misleading terms 'complex numbers' and 'imaginary numbers'.
實數並不比其它數更真實，這個名稱只是個歷史意外，是為了區分同樣帶有誤導性的術語"複數"和"虛數"。The reader not familiar with these expressions could think of 'real numbers' as 'lengths defined with a hypothetical infinite precision.'
不熟悉這些的讀者，可以把"實數"看作"假想的無限精度的一段長度"。
* Alan acquired a copy, soon heavily annotated, of Hilbert and Courant's Methoden der Mathematischen Physik in July 1933.
不久前，1933年7月，艾倫得到了一份復件，是希爾伯特和柯朗的《數學物理方法》。* The author of one of the books which described the Central Limit Theorem.
一本描述中心極限定理的書的作者。* A simple example of a topological problem is that of the 'four colour theorem'.
拓撲學一個的簡單例子是『四色定理』。This states that a map such as one of the English counties can always be coloured with just four colours, in such a way that no two adjoining counties share the same colour.
要想為一幅地圖染色，保證每兩個相鄰的國家都是不同的顏色，那麼一共只需要四種顏色。Alan himself took some interest in this problem, but it was to remain an unproved assertion until 1976.
艾倫對這個問題有些興趣，但直到1976年，它一直未能得到證明。* A recent development in pure mathematics, extending and generalising the idea of 'periodicity'.
純數學領域的一個新進展，拓展並推廣了週期的概念。* The arguments also implied two rather different interpretations of the machine 'configuration'.
這兩種論證，表明了對機器狀態的兩種截然不同的解釋。From the first point of view, it was natural to think of the configuration as the machine's internal state—something to be inferred from its different responses to different stimuli, rather as in behaviourist psychology.
對於前者，我們會把狀態理解為機器內在的狀態，就像行為心理學認為的，對不同的刺激作出不同的反應。From the second point of view, however, it was natural to think of the configuration as a written instruction, and the table as a list of instructions, telling the machine what to do.
然而對於後者，我們會把狀態看作一種明確的指令，行為表就像一個指令的列表，告訴機器應該做什麼。The machine could be thought of as obeying one instruction, and then moving to another instruction.
機器執行一條指令，然後再執行下一條，The universal machine could then be pictured as reading and decoding the instructions placed upon the tape.
機器的一切本質就是讀取和解碼紙帶上的指令。Alan Turing himself did not stick to his original abstract term 'configuration', but later described machines quite freely in terms of 'states' and 'instructions', according to the interpretation he had in mind.
圖靈本人並沒有糾纏於這個問題，後來他就直接地使用了狀態和指令這類術語。This free usage will accordingly be employed in what follows.
而這些術語的使用，影響了未來的很多事情。
