双语畅销书《艾伦图灵传》第9章:退隐山林(130)

If the operations are represented by letters, then such a sequence is represented by a 'word'—hence the name of the problem.

对于有限群，这种机械过程显然是存在的。

For a finite group, there would of course exist such a definite method, namely the crude one of working through all the possibilities.

比如可以通过原始的穷举方法，对每一种可能性进行检查。

The problem arises for infinite groups.A 'semi-group' is the abstract version of a set of operations which meets half of the conditions required for a 'group': the operations cannot necessarily be reversed.

但问题在于无限群。"半群"也是一组操作的抽象，但它不一定满足构成"群"的条件，即其操作不一定是可逆的。

A 'cancellation semi-group' is a semi-group with a property which makes it closer to being a group: if AC = BC then it must be that A = B.

"消去半群"是一种半群，但具备一个接近于群的特性：如果有AC=BC，就一定有A=B。

Polanyi rejected this argument, saying that a machine was a machine, a human mind was a human mind, and no amount of evidence could change this a priori fact.

波兰尼反对这个观点，他说机器就是机器，人类就是人类，没有任何理由能改变这个先验事实。

This oscillation between the two concepts of computability found its way into his Programmers' Handbook: on the first page the programmer was greeted by the assertion that

实体计算机的能力，与这两个可计算性的定义略有不同，图灵在《编程人员手册》的第一页做了这样的说明：

There is also a part of the machine called the control which corresponds to the (human) computer himself. If his possible behaviour were very accurately represented this would have to be a formidably complicated circuit.

机器的控制部分，功能相当于人类计算者，如果要让它处理所有可能的行为，就需要一个过度复杂的电路，However we really only require him to be able to obey the written instructions and these can be made so explicit that the control can be quite simple.

因此我们只让他处理手册中设计好的指令，这样可以使机器的控制部分变得简洁。

Thus a contemporary review article44 stated 'The importance of the principle of patterned 'field' activities in the determination of embryonic systems has been generally recognised.

当时有一篇文章评论说："胚胎系统的模式化的形成原则的重要性已经得到了广泛的认识。

Yet their nature and mode of operation are still among the greatest puzzles of modern biology.

但其运作机制和具体模式，仍是现代生物学最大的谜题之一。