model’s accuracy. Although she was dubious of the model, she undertook the two experiments. One result fit my predictions and one contradicted them, and today only a dim echo of my model is accepted by either of us. Yet my exhilaration at discovering the model was not balanced by a corresponding disappointment at seeing the model proved wrong, perhaps because my emotional involvement with the problem was an intrigued outsider’s interest rather than an anxiety of frustrated scientific progress.
About a month after my model failed, my wife was continuing the experiments at another lab and called me to say: “We’ve always been thinking of the energy barriers as peaks. What if they are troughs instead?” Immediately I felt that she was right, that she had solved the problem. Her answer was so much simpler than mine had been. With this new perspective, we were amazed that we all had been obtuse for so long. Of course, not everyone is as certain as we are that she is right.
“When you have at last arrived at certainty, your joy is one of the greatest that can be felt by a human soul.” [Pasteur, 1822-1895,b].
The Royal Way
Success or failure in reaching insight often depends on the path followed. Once the goal is achieved, however, the path becomes irrelevant to the evaluation of that insight.
“But any pride I might have felt in my conclusions was perceptibly lessened by the fact that I knew that the solution of these problems had almost always come to me as the gradual generalization of favourable examples, by a series of fortunate conjectures, after many errors. I am fain to compare myself with a wanderer on the mountains, who, not knowing the path, climbs slowly and painfully upwards, and often has to retrace his steps because he can go no farther -- then, whether by taking thought or from luck, discovers a new track that leads him on a little, till at length when he reaches the summit he finds to his shame that there is a royal way, by which he might have ascended, had he only had the wits to find the right approach to it. In my works, I naturally said nothing about my mistakes to the reader, but only described the made track by which he may now reach the same heights without difficulty.” [Helmholtz, 1891]
Between 1899 and 1904 French mathematician Henri Poincaré considered many of the same factors, including in 1904 the same term ‘principle of relativity’, that Albert Einstein brought together in his 1905 paper on special relativity. Yet Poincaré was unable to reach the same insight first. Poincaré says in his 1911 letter of reference for Albert Einstein:
“I do not mean to say that all these predictions [by Einstein] will meet the test of experiment when such tests become possible. Since he seeks in all directions, one must, on the contrary, expect the majority of the paths on which he embarks to be blind alleys. But one must hope at the same time that one of these directions he has indicated may be the right one, and that is enough. This is exactly how one should proceed. The role of mathematical physics is to ask questions and only experiment can answer them.” [cited by Hoffmann, 1972]
Concerning his 1915 discovery of general relativity, Albert Einstein [1879-1955] said:
