雙語暢銷書《艾倫圖靈傳》第8章:面朝大海(292)
It was entitled Solvable and Unsolvable Problems, and first gave an example of a 'solvable' problem. This was a solitaire game (actually the 'fifteen puzzle') in which, as he described, there were only a finite number of possibilities to consider (namely 16! = 20,922,789,888,000). Hence, in principle, the game could be 'solved' simply by listing all the possible positions.
這篇文章題爲《可解問題與不可解問題》。圖靈首先給出了一個可解問題的例子，這是一個紙牌解謎遊戲，具有有限種可能的情況（即16！= 20, 922, 789, 888, 000），理論上可以窮舉所有的情況，所以這個遊戲是可解的。
This helped to illustrate the nature of an absolutely 'unsolvable' problem, such as he went on to describe, but the large number also demonstrated the gap between theoretical and practical 'solvability'.
通過理解這個問題，有助於理解他接下來給出的"不可解問題"。然而，這個巨大的數字，卻體現了"可解"在理論和實踐上的不同意義。
As it happened, of course, the Bombe had indeed exploited the finiteness of the Enigma by just such a brute force method, but in general the knowledge that a number is 'only' finite is not of practical significance.
圖靈當年的炸彈機，確實利用了謎機的這種有限性，但是一般而言，這種有限性並不總是有用的。
One cannot play chess, nor deduce all the wirings of an Enigma machine, by knowing that the possibilities are finite.
一個人不可能通過窮舉來下棋，同樣也不可能通過窮舉解出謎機的配線。
The 'fifteen puzzle', indeed, poses a tough problem to the computer programmer. Turing machines, when embodied in the physical world, are severely limited by considerations other than those of logic.
事實上，即使對於計算機程序來說，這個紙牌遊戲也是一項非常艱鉅的任務。在邏輯的世界裏，圖靈機享有很大的自由，但他一旦進入物理世界，就會受到各種因素的嚴重限制。
While some physical quantities (such as temperature) may be described by one number, in general they will require a set of numbers; anything like a direction in space, for instance, will do so.
雖然有些物理量（比如溫度）可以表示成一個數，但更一般的情況下，會表示成一個集合，比如一個物體的空間位置。
It is usual to 'index' this set by a letter of the alphabet. From a modern point of view the structure of the set is a reflection of the group of symmetries associated with the physical entity, and it is common to use a different type of letter (e.g. lower-case, upper-case, Greek) when different symmetry groups are implied.
人們通常會用字母來索引這樣的集合。這些集合的結構，反映出一種關於實體的對稱羣，當指稱不同的對稱羣時，人們會使用不同類型的字母（大寫、小寫或希臘字母）。
The word 'fount' made this principle explicit.
"活字"這個詞，直觀地體現了這個理論。
