11.Thus，for instance，it may come as a shock to mathematicians to learn that the Schrodinger equation for the hydrogen atom is not a literally correct description of this atom，but only an approximation to a somewhat more correct equation taking account of spin，magnetic dipole，and relativistic effects；and that this corrected　equation is itself only an imperfect approximation to an infinite set of　quantum field-theoretical equations.

　　因此，举例来说，对数学家而言，了解到下述情形可能会令其惊愕不已，即薛定谔（Schrodinger）的氢原子方程式并非是对该原子作出的一种绝然正确的描述，而仅仅是个近似值，趋近于一个在某种程度上更为正确的将自旋、磁性偶极子、以及相对论效应考虑在内的方程式；而这个得以纠正的方程式就其本身而言也只是一个不完美的近似值，趋近于无穷无尽的一整套量子场论方程式。

　　12.The physicist rightly dreads precise argument，since an argument that is　convincing only if it is precise loses all its force if the assumptions on　which it is based are slightly changed，whereas an argument that is convincing though imprecise may well be stable under small perturbations of its underlying assumptions.

　　物理学家恐惧于那些精确无误的论据不无道理，因为某种只有在它是精确无误的条件下才令人置信的论据，一旦它赖于建立其上的假设稍有变化，便会失去它一部的作用；而与此相反，一个尽管并不精确无误但却令人置信的论据，在其基本假设（underlying assumption）稍微受干扰的情况下，仍然有可能是站得住脚的。

　　13.However，as they gained cohesion，the Bluestockings came to regard themselves as a women’s group and to possess a sense of female solidarity lacking in the salonnieres，who remained isolated from one another by the primacy each held in her own salon.

　　起初，蓝袜女们确实模仿了法国沙龙女主人，将男性襄括到其小圈子中来。然则，随着她们获得的凝聚力，她们渐趋将自己视作一女性团体，并拥有了一种妇女团结意识，而这种意识在法国沙龙女主人身上则荡然无存，因为她们每个人在其自己的沙龙中自视甚高而彼此孤立隔绝开来。

　　14.As my own studies have advanced，I have been increasingly impressed with the functional　　similarities between insect and vertebrate societies and less so with the structural differences that seem，at first glance，to constitute such an immense gulf between them.

　　随着我的研究不断深入，我对昆虫和脊椎动物群落之间的功能类似性印象愈来愈深刻，而对结构上的差异印象愈发淡漠，虽然这些结构上的差异初看上去似乎构成了二者间一条无法愈越的鸿沟。

　　15. Although fiction assuredly springs from political circumstances，its authors react to those circumstances in ways other than ideological，and talking about novels and stories primarily as instruments of ideology circumvents much of the fictional enterprise.

　　虽然小说无疑起源于政治情状，但其作者则是以非意识形态的方式对这些政治情状作出反应的，而将小说和故事主要地当作意识形态的工具来探讨，会在相当程度上阻碍小说事业。