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雙語暢銷書《艾倫圖靈傳》第4章:彼岸新星(31)

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For instance, he had made a convention that the machines should print out the 'computable numbers' on alternate squares of the 'tape', and use the intervening squares as working space.

雙語暢銷書《艾倫圖靈傳》第4章:彼岸新星(31)
比如說,艾倫設定了這種機器是在方格中寫入可計算數,並以方格作爲工作空間,而不是採用一些更普遍的、無限制的工作空間。

But it would have been much easier if he had made a more generous allowance of working space.

而言之,在數理邏輯的小圈子之外,艾倫的這篇論文非常沒有吸引力。

So there was little about his work to attract anyone from outside the narrow circle of mathematical logic—with the possible exception of pure mathematicians who would be interested in the distinction between the computable numbers and the real numbers.

總蘭瑟洛特·霍格本提倡科學要以人爲本,

It had nothing obvious to do with what Lancelot Hogben called 'the world's work'.

從這個角度來看,艾倫的論文似乎百無一用。

There was one person, one of those few who were professionally interested in mathematical logic, who read the paper with a very considerable personal interest.

不過,在數理邏輯的小圈子裏,確實有一個人非常有興趣地讀完了這篇論文。

This was Emil Post, a Polish-American mathematician teaching at the City College of New York, who since the early 1920s had anticipated some of Gdel and Turing ideas in unpublished form.

他是一位波蘭裔數學家,名叫艾米爾·波斯特,在紐約城市大學教書,早在20年代以前,他就產生了類似於哥德爾和圖靈的想法,但沒有發表。

In October 1936 he had submitted to Church's Journal of Symbolic Logic a paper which proposed a way of making precise what was meant by 'solving a general problem'.

1936年10月,他向《符號邏輯》提交了一篇論文,關於通過一種普適的方法提高計算精度。

It referred specifically to Church's paper, the one which solved the Hilbert decision problem but required an assertion that any definite method could be expressed as a formula in his lambda-calculus.

他在其中引用了丘奇的論文,正是回答希爾伯特判定性問題的那篇。

Post proposed that a definite method would be one which could be written in the form of instructions to a mindless 'worker' operating on an infinite line of 'boxes', who would be capable only of reading the instructions and

波斯特指出,一個確定的過程,可以寫成指令的形式,交給一個無需思考的操作者,在無限多的一排盒子中進行操作。操作者的能力只是閱讀指令,以及:

(a) Marking the box he is in (assumed empty),

在他所在處的盒子裏設一個標記(假設盒子是空的);

(b) Erasing the mark in the box he is in (assumed marked),

清除他所在處的盒子裏面的標記(假設盒子有標記);

(c) Moving to the box on his right,

移動到左邊的盒子;

(d) Moving to the box on his left,

移動到右邊的盒子;

(e) Determining whether the box he is in, is or is not marked.

查看他所在處的盒子裏是否有標記。