6 3 8 D O C U M E N T 3 9 9 K Y O T O L E C T U R E to the law of universal gravitation. I felt a strong desire to somehow find out the reason behind this. But this goal was not easy to reach. What seemed to me most unsatisfactory about the special theory of relativity was that, although the theory beautifully gave the relationship between inertia and energy, the relationship between inertia and weight, i.e., the energy of the gravitational field, was left com- pletely unclear. I felt that the explanation could probably not be found at all in the special theory of relativity. I was sitting in a chair in the Patent Office in Bern when all of a sudden I was struck by a thought: “If a person falls freely, he will certainly not feel his own weight.” I was startled. This simple thought made a really deep impression on me. My ex- citement motivated me to develop a new theory of gravitation. My next thought was: “When a person falls, he is accelerating. His observations are nothing but ob- servations in an accelerated system.” Thus, I decided to generalize the theory of re- lativity from systems moving with constant velocity to accelerated systems. I expected that this generalization would also allow me to solve the problem of gra- vitation. This is because the fact that a falling person does not feel his own weight can be interpreted as due to a new additional gravitational field compensating the gravitational field of the Earth, in other words, because an accelerated system gives a new gravitational field. I could not immediately solve the problem completely on the basis of this in- sight. It would take me eight more years to find the correct relationship. In the meantime, however, I did come to recognize part of the general basis of the solution. Mach also insisted on the fact that all accelerated systems are equivalent. This, however, is clearly incompatible with our geometry, for if accelerated systems are allowed, Euclidean geometry can no longer hold in all systems. Expressing a law without using geometry is like expressing a thought without using language. We first have to find a language for expressing our thoughts. So what are we looking for in this case? This remained an unsolved problem for me until 1912. In that year, I suddenly realized that there was good reason to believe that the Gaussian theory of surfaces might be the key to unlock the mystery. I realized at that point the great importance of Gaussian surface coordinates. However, I was still unaware of the fact that Rie- mann had given an even more profound discussion of the foundations of geometry.[9] I happened to remember that Gauss’s theory had been covered in a course I had taken during my student days with a professor of mathematics named Geiser.[10] From this I developed my ideas,[11] and I arrived at the notion that geo- metry must have physical significance.