An 'infinity of symbols', he wished to argue, did not correspond to anything in reality.
他要论证"无限个符号"是不现实的,
It might be argued that there was an infinity of symbols, in that an Arabic numeral such as 17 or 999999999999999 is normally treated as a single symbol.
假设有无限个符号,就像:一个阿拉伯数,比如17或者999999999999999,通常被看成一个单独的符号。
Similarly in any European language words are treated as single symbols (Chinese, however, attempts to have an enumerable infinity of symbols).
同样,在各种欧洲语言中,一个单词被看成一个单独的符号(中文似乎拥有无限可列个符号)。
But he disposed of this objection with the observation that the differences from our point of view between the single and compound symbols is that the compound symbols, if they are too lengthy, cannot be observed at one glance.
接着,他否定了这样的假设:对我们来说,一个符号和一组符号的区别是,组合符号如果太长,就不能一下子识别。
This is in accordance with experience. We cannot tell at a glance whether 9999999999999999 and 999999999999999 are the same.
这是符合日常经验的,我们不能只看一眼,就说出9999999999999999和999999999999999是否一样。
Accordingly, he felt justified in restricting a machine to a finite repertoire of symbols. Next came a most important idea:
因此,他认为应该限定机器只使用有限的符号。接下来,最重要的想法出场了:
The behaviour of the computer at any moment is determined by the symbols which he is observing, and his 'state of mind' at that moment.
计算者(computer)在任意时刻的行为,都取决于他正在看着的方格,和他此时的思维状态。
We may suppose that there is a bound B to the number of symbols or squares which the computer can observe at one moment.
假设有一个界限B,来限定计算者可以同时有多少条视线,也就是他同时可以看到多少个方格。
If he wishes to observe more, he must use successive observations.
如果他想看到更多,那他必须分成多次来看。
We will also suppose that the number of states of mind which need to be taken into account is finite.
我们假设思维状态的数量也是有限的。
The reasons for this are the same character as those which restrict the number of symbols.
这样做的原因,与限制符号的数量一样。
If we admitted an infinity of states of mind, some of them will be 'arbitrarily close' and will be confused.
如果我们认为思维状态有无限多个,那么其中一些就会无限地相近,并混淆起来。
Again, the restriction is not one which seriously affects computation, since the use of more complicated states of mind can be avoided by writing more symbols on the tape.
而且,这样的限制对计算并不会造成严重的影响,因为可以通过在纸带上记录更多的符号,来避免出现更复杂的思维状态。