In the evenings most of the officers would play billiards or drink in the bar, and sometimes Alan did too.
傍晚时，绝大多数官员会玩桌球，或是到吧台喝酒，图灵有时也是这样。
But Donald Bayley, Robin Gandy and Alan Wesley had the idea of doing something more mind-improving, and asked Alan to give a course of lectures on mathematical methods.
但是唐纳德·贝利、罗宾·甘迪和艾伦·卫斯理则更喜欢做一些动脑子的事，于是他们邀请图灵给他们讲数学。
They found a place upstairs in the mansion, which in the winter of 1944 was a singularly cold classroom, and retired thither, somewhat to the amazement of the less zealous.
他们在楼上找了个地方，这地方在1944年的冬天是个极冷的教室，后来就一直闲在那。
Alan wrote out notes, which the others would copy, mainly on Fourier analysis and related material using the calculus of complex numbers.
图灵把要点写出来，方便他们做笔记，主要是关于傅里叶分析以及复数计算一些东西。
He illustrated his discussion of the idea of 'convolution'—the blurring or spreading out of one function in a way defined by some other function—with the example of a mushroom fairy ring.
他用蘑菇圈的例子来演示卷积的概念。
It was not only the mushroom which currently reflected his interest in biological form; on his return from runs he would often show examples of the Fibonacci numbers to Don Bayley, producing fir cones as he had in 1941.
他对生物形态的兴趣，不仅反映在蘑菇上。他在跑步回来的路上，常常给唐·贝利展示斐波那契数列的例子，正如他在1941年展示冷杉。
He was still sure there had to be a reason for it.
他依然对这个很感兴趣，这里面是有原因的。
And he found time for mathematical study of his own, taking up von Neumann's Mathematical Foundations of Quantum Mechanics again.
他自己抽时间学习数学，学习诺伊曼的《量子力学的数学基础》。
In the evening there might also be chess, or card games, which he enjoyed, although these also brought out his most childish side in which—just as when a little boy—if he thought that someone else had cheated or changed the rules, he would storm out and slam the door.
傍晚时，有时他会下棋或打牌，这时他仍然像个小孩子，如果他觉得有人作弊或是擅自改变规则，就会大发脾气，摔门而出。
Such behaviour also typified his dealings with authority, which he still naively expected to maintain literal truth-telling and constancy of policy.
这样的事情，在他与行政官员的交往中也会发生，他一直都天真地保持着政治方面的独立和直接。