I pointed out to him that there were two objections to this, the first being that he was unwell, and the second that I was intruding on his work.
"How illogical!" he answered. "If I interrupt my work to chat with you, I am putting aside exactly what the doctor would deny me if I were to allow him. So, let us make a start. You have probably some conundrum weighing on your mind."
"That may not be far wrong. I have been troubled by something in connexion with Kepler's second law. It almost robbed me of my night's sleep. My thoughts kept returning to a certain question, and I should like to know whether there is any sense in the question itself at all."
"Let us hear it!"
"The law in question states that every planet in describing its elliptic path, sweeps out with its radius vector equal sectorial areas in equal intervals of time. But this seems only half a law, for the radius vectors are only considered drawn from the one focus of the ellipse, namely, the gravitational centre. Now, another focus exists, that may be situated in space somewhere, perhaps far away in totally empty regions, if we assume the orbit to be very eccentric. My question is: What form does this law take if the radius vectors are drawn from this second focus and if the corresponding sectorial areas are considered, instead of these quantities being referred to the first focus exclusively?"
"This question is not devoid of sense, but it serves no useful purpose. It may be solved analytically, but would probably lead to very complicated expressions, that would be of no interest for celestial mechanics. For the second focus is only a constructive addition, that has nothing real in space corresponding to it. What else is troubling you?"
"My next difficulty is a little problem that sounds quite simple and yet is sufficiently awkward to make one rack one's brains. It was suggested to me by an engineer who certainly has a keen mind for such things, and yet, as far as I could judge, he did not get a solution for it. It concerns the position of the hands of a clock."
"You surely are not referring to the children's puzzle of how often and when both hands coincide in position?"
"By no means. As I said just now, it is really quite perplexing. Let us assume the position of the hands at twelve o'clock, when both hands coincide. If they are now interchanged, we still have a possible position of the hands, giving an actual time. But, in another case, say, exactly six o'clock, we get a false position of the hands, if we interchange them, for on a normal clock it is impossible for the large hand to be on the six whilst the small hand is on the twelve. The question is now: When and how often are the two hands situated so that when they are interchanged, the new position gives a possible time on the clock?"
"There, you see," said Einstein, "that is just the right kind of distraction for an invalid. It is quite interesting, and not too easy. But I am afraid the pleasure will not be of great duration, for I already see a way to solve it."