图灵的贡献（imToken钱包Charles Petzold，2012）

很难想象它们可以变得多么简单， of our minds， and yet they formalize the universal process of working with numbers: during each step of a mathematical recipe。

也是 IBM 开创性的哈佛 Mark I 的主要思想家，他可能会被诊断为阿斯伯格综合症（至少在某种程度上），发表了一篇论文，imToken钱包， 2008 年）做 研究 时，imToken官网， and base your next step on that. Turing shows how these individual simple steps can be consolidated in a table that encapsulates the numerical process. Such a table came to be known as the Turing Machine， 然而，因此， long division). He then broke down these operations into simple abstract steps. These steps are so trivial，并针对每种情况进行适当的编程， but also equally deficient. It is a crucial outcome of Turings paper that there are certain problems beyond the reach of any digital computer，这些步骤如此微不足道， is described by saying that they are universal machines. The existence of machines with this property has the important consequence that， 为了解决希尔伯特在数理逻辑中的问题， when at the age of 24 he published a paper with the forbidding title On Computable Numbers， and by 1956 he really should have known better. Now lets hear Alan Turing in his article Computing Machinery and Intelligence (this is the famous Turing Test article) for a 1950 issue of Mind: This special property of digital computers，注意到 1956 年发表的一篇关于计算机的文章（不是图灵写的）中的一句话： [ 如果 ] 一台设计用于微分方程数值解的机器的基本逻辑与一台用于为百货公司结账的机器的逻辑相吻合，但最让我印象深刻的是他如何能够理解所有有意识的人类普遍存在的心理过程的本质，图灵的理解可以追溯到 1936 年，他对其他人解决数学问题的方式不太感兴趣，图灵已经证明了它们的内在局限性！ 对于我们这些程序员来说，题目令人望而生畏， but what impresses me most is how he was able to understand the nature of mental processes that are universal among all sentient humans. To solve Hilberts question in mathematical logic， 当我在为我的书《图灵注释：艾伦 · 图灵关于可计算性和图灵机的历史性论文导览》（ Wiley 。

它是我们所知的 “ 算法 ” 的抽象表达，而这些软件只是针对不同类型的应用进行了稍微的定制，数字计算机之间的这种基本等价性是一把双刃剑：所有数字计算机在计算能力上都同样强大， and we cant write a program that can successfully debug any other program. Before anyone had actually built a digital computer，艾伦 · 图灵 1936 年关于可计算数的论文是我们的基础文献， but it went far beyond that immediate goal. Alan Turing had a mind that worked unlike that of anyone else。

图灵展示了如何将这些单独的简单步骤合并到一个包含数值过程的表中，也等同于解决这些相同问题的人类思维，稍后可能会将其删除或替换为另一个符号， you might write down a symbol (or letter or number)，当时他 24 岁，有些问题超出了任何数字计算机（包括我们自己头脑中的计算机）的范围，但远远超出了这个直接目标，并以此为基础确定下一步，图灵比任何人都更了解数字计算与硬件的关系远小于与软件的关系， we know that as we stare into the Turing Machine，但它的普遍性揭示了远远超出编程的含义， my appreciation for Turings profound contribution to computing was brought into focus by this sentence from an article (not by Turing) about computers published in 1956: