双语畅销书《艾伦图灵传》第3章:思考什么是思考(83)

Suppose one tried to design a 'Cantor machine' to produce this diagonAl uncomputable number.

假设有人要设计一个康托机，来计算这个对角线上的不可计算数，

Roughly speaking, it would start with a blank tape, and write the number 1.

那大致的过程是这样的：它从空白的纸带开始，先写下数字"1"，

It would then have to produce the first table, and then execute it, stopping at the first digit that it wrote, and adding on one.

产生第1个行为表，然后运行这个表，写下它产生的第1个数字，加1；

Then it would start again, with the number 2, produce the second table, executing it as far as the second digit, and writing this down, adding on one.

接下来，写入数字2，产生第2个行为表，运行，写下它产生的第2个数字，加1；

It would have to continue doing this for ever, so that when its counter read '1000', it would produce the thousandth table, execute it as far as the thousandth digit, add on one to this and write it down.

以此类推，当它的计数器读出"1000"，就产生第1000个行为表，并运行它直到产生第1000个数，然后把它写下来，加1。

One part of this process could certainly be done by one of his machines.

这个过程的一部分，确实可以用机器来做，

For the process of 'looking up the entries' in a given table, and working out what the corresponding machine would do, was itself a 'mechanical process.' A machine could do it.

在一个给定的表中查询某一项，然后运行与之对应的机器，这是一个机械过程，机器可以做到。

There was a difficulty in that the tables were naturally thought of in two-dimensional form, but then it was only a technical matter to encode them in a form in which they could be put on a 'tape'.

有一个问题是，这个表现在是二维的，但这也很好办，要把它编成可以放入纸带的形式，只是个技术问题。

In fact, they could be encoded as integers, rather as Gdel had represented formulae and proofs as integers.

实际上，还可以全部用数字来表示它，哥德尔已经展示了，用数字来表示公式和证明。

Alan called them 'description numbers', so that there was a description number corresponding to each table.

艾伦称之为"描述数"，每个每个表都有对应的描述数。

In one way this was just a technicality, a means of putting tables on to the tape, and arranging them in an 'alphabetical order'.

总之，把这个表放入纸带，按一定顺序排列起来，只是一个技术问题。

But underneath there lay the same powerful idea that Gdel had used, that there was no essential distinction between 'numbers' and operations on numbers.

这其中也体现了哥德尔用过的强力想法，数字本身和对数字的操作，没有实质的区别，

From a modern mathematical point of view, they were all alike symbols.

从现代数学的角度看来，它们都是符号。