双语畅销书《艾伦图灵传》第8章:水银延时线(5)

It was not that they were good at doing large sums, although indeed they were doing sums on desk calculators.

尽管他们用台式计算器做了大量计算工作，但它们却并不擅长计算，

Their problems were roughly analogous to those that faced Alan in calculating the Riemann zeta-function in 1938.

他们遇到的问题，大体上类似于图灵在1938年计算ζ函数时遇到的问题。

When the resources of pure mathematics had been fully exploited, there might still remain a formula, or system of equations, into which actual numbers had to be substituted.

即使充分利用了纯数学，但数论问题最终仍然有可能需要代入某些方程系统。

Actually doing such substitutions on desk calculators was not very interesting;

用台式计算器来处理这种代入，是十分尴尬的。

but the problem of how best to organise the work was a more abstract question, one constituting the branch of mathematics called 'numerical analysis'.

这是一个更为抽象的问题，并形成了一个称为"解析数论"的数学分支注。

One particular problem was that although equations and formulae would generally relate 'real numbers' of infinite precision,

有一个特别存在的问题是，方程系统是基于无穷精度的实数，

practical computation would work with quantities defined only to so many decimal places, thus introducing an error into every step.

但实际的计算精度不得不是有限的，因此每一个计算步骤都会引起误差，

Deducing the effect of such errors and minimising them was an important aspect of numerical analysis.

如何评估并减小这种误差，是解析数论的一个重要问题。

The existence of such problems was partly what made Alan say that automatic computers would not make mathematicians redundant.

正是由于这个问题的存在，使得图灵认为，即使有了自动化的计算机器，数学家也不可能下岗。