评论
打印
But by the 1930s it was accepted that 'groups' could be explored in the abstract, without any concrete representation or application in mind.
到了20世纪30年代，人们就可以抽象地研究"群"，不需要依靠任何实体表示。
* There is nothing 'real' about 'real numbers'. The term is a historical accident, arising from the equally misleading terms 'complex numbers' and 'imaginary numbers'.
实数并不比其它数更真实，这个名称只是个历史意外，是为了区分同样带有误导性的术语"复数"和"虚数"。
The reader not familiar with these expressions could think of 'real numbers' as 'lengths defined with a hypothetical infinite precision.'
不熟悉这些的读者，可以把"实数"看作"假想的无限精度的一段长度"。
* 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，艾伦得到了一份复件，是希尔伯特和柯朗的《数学物理方法》。
* The author of one of the books which described the Central Limit Theorem.
一本描述中心极限定理的书的作者。
* A simple example of a topological problem is that of the 'four colour theorem'.
拓扑学一个的简单例子是『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.
要想为一幅地图染色，保证每两个相邻的国家都是不同的颜色，那么一共只需要四种颜色。
Alan himself took some interest in this problem, but it was to remain an unproved assertion until 1976.
艾伦对这个问题有些兴趣，但直到1976年，它一直未能得到证明。
* A recent development in pure mathematics, extending and generalising the idea of 'periodicity'.
纯数学领域的一个新进展，拓展并推广了周期的概念。
* The arguments also implied two rather different interpretations of the machine 'configuration'.
这两种论证，表明了对机器状态的两种截然不同的解释。
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.
对于前者，我们会把状态理解为机器内在的状态，就像行为心理学认为的，对不同的刺激作出不同的反应。
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.
然而对于后者，我们会把状态看作一种明确的指令，行为表就像一个指令的列表，告诉机器应该做什么。
The machine could be thought of as obeying one instruction, and then moving to another instruction.
机器执行一条指令，然后再执行下一条，
The universal machine could then be pictured as reading and decoding the instructions placed upon the tape.
机器的一切本质就是读取和解码纸带上的指令。
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.
图灵本人并没有纠缠于这个问题，后来他就直接地使用了状态和指令这类术语。
This free usage will accordingly be employed in what follows.
而这些术语的使用，影响了未来的很多事情。
