雙語暢銷書《艾倫圖靈傳》第9章:退隱山林(130)
If the operations are represented by letters, then such a sequence is represented by a 'word'—hence the name of the problem.
對於有限羣，這種機械過程顯然是存在的。
For a finite group, there would of course exist such a definite method, namely the crude one of working through all the possibilities.
比如可以通過原始的窮舉方法，對每一種可能性進行檢查。
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.
但問題在於無限羣。"半羣"也是一組操作的抽象，但它不一定滿足構成"羣"的條件，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.
"消去半羣"是一種半羣，但具備一個接近於羣的特性：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.
波蘭尼反對這個觀點，他說機器就是機器，人類就是人類，沒有任何理由能改變這個先驗事實。
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
實體計算機的能力，與這兩個可計算性的定義略有不同，圖靈在《編程人員手冊》的第一頁做了這樣的說明：
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.
機器的控制部分，功能相當於人類計算者，如果要讓它處理所有可能的行爲，就需要一個過度複雜的電路，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.
因此我們只讓他處理手冊中設計好的指令，這樣可以使機器的控制部分變得簡潔。
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.
當時有一篇文章評論說："胚胎系統的模式化的形成原則的重要性已經得到了廣泛的認識。
Yet their nature and mode of operation are still among the greatest puzzles of modern biology.
但其運作機制和具體模式，仍是現代生物學最大的謎題之一。
