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。
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