A mathematical model of the growing embryo will be described.

描述胚胎生长的数学模型，

This model will be a simplification and an idealization, and consequently a falsification.

该模型是经过简化、理想化和假设化的，

It is to be hoped that the features retained for discussion are those of greatest importance in the present state of knowledge.

我希望首先讨论我们现有认识中，那些最为重要的特征。

The result was applied mathematics par excellence.

这项研究，再一次漂亮地运用了数学。

Just as the simple idea of the Turing machine had sent him into fields beyond the boundaries of Cambridge mathematics, so now this simple idea in physical chemistry took him into a region of new mathematical problems.

曾经的图灵机，使图灵迈出了剑桥的数学边界，而这个简单的物理化学想法，又把他引入了一个新的数学问题。

But this time at least it was all his own work. No one else could make a mess of it for him.

但是这一次，这些完全是由图灵自己研究出来的，再也没有任何人，会给他找麻烦了。

Even with immense simplifications, the mathematical equations corresponding to a soup of only four interacting chemical solutions, were still too intractable.

然而，尽管经过了极大的简化，但是四种化学物质的相互反应，相应的数学方程仍然十分难解。

The problem was that chemical reactions were 'non-linear'.

问题在于化学反应是非线性的。

The equations for electricity and magnetism were 'linear', meaning that if two electromagnetic systems were superimposed (as for example when two radio transmitters radiated simultaneously), then the effects would simply be additive.

电磁方程是线性的，也就是说，如果两个电磁系统相互叠加（比如两个无线电台同时发射无线电），那么结果仅仅是相加，

The two transmitters would not interfere with each other.

两个发射台不会相互影响。

But chemistry was quite different. Double the concentration of reactants, and the reaction might go four times as fast.

但是化学则很不一样，反应物浓度增加一倍，反应速度可能会变成四倍，

Superimpose two solutions, and anything might happen!

如果叠加两个溶剂，那就什么事情都有可能发生。