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Why does a good mathematical equation sometimes prevent the deep understanding of a phenomenon?

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Some years ago, I became fascinated by the electric properties of liquid water. One year ago, I realized that in order to understand these properties I first needed to investigate them in ice (see last post) . But I was lucky. The hard work had already been done. In the sixties, Jaccard developed a complete theory describing how charges are moving through ice. I was surprised. I intensively studied sold states during my studies, but nobody had ever mentioned the peculiarity of electrical conduction in ice.  Fig. 1 How electric conduction is  visualized in most solids. Jaccard understood that there must be a strong coupling between the orientation of the water molecules and the movement of the charges in ice and this really is a rear phenomenon. In most solids charges (like electrons, holes, ions, …) move without changing the structure (see Fig. 1). Not so in ice, however. The mechanism behind this will be addressed in our next post. The theme of this post is not the ex