"Put that thing away," Holmes said, pointing his nose at my revolver. He brushed past me and walked toward the exit. I removed it, packed it away, and followed.
"She must have lodging nearby for the night," Holmes said.
"But where? There are dozens of hotels within walking distance."
"Dozens," Holmes said, "but only three of sufficient grandeur for somepony Great and Powerful, and expecting to soon be flush with cash: The Salisbury, the Four Seasons, and the Palomino."
The 4 Seasons and the Palomar are fancy hotels in Philadelphia.
We headed first to the Salisbury, our hooves clopping on the cobblestones, which glistened in the moonlight. "Holmes," I protested as we went, "I admit that you were right about the painting's vulnerability. But the curator inspected the painting she gave him himself, and pronounced it to be genuine. Nothing I have seen tonight justifies hitting anypony on the head. The only crimes I have proof of are that you created a stampede by shouting "fire!" in a museum, and I pointed a gun at a pony. And I am sure Mr. F. would consider burning oil near his paintings to be a third."
Holmes shook his mane and neighed dismissively. "Set aside for the moment the difficulty of conducting a thorough inspection in a cafe, in front of an audience, in a state of shock, as well as the question of Mr. F.'s eyesight. Did you notice Trixie's exact words? She did not ask him whether it was the painting. She told him it was the painting."
I recollected my own strong if temporary conviction that I was suspended upside-down from the ceiling of the cafe. "Mesmerism," I said.
"And with the head curator's insistence that the painting is genuine, the forgery would not be detected until its return to Canterlot at the earliest, at which point the switch would be assumed to have taken place in transit, long after Trixie's departure."
"But," I pointed out, "Trixie did not expect the curator to be present at the show. That was your doing, Holmes. Your theory now implies that you are an accomplice."
"I expect she planned to see him after the show. It could not be overly difficult for a beautiful mare with the powers of mesmerism to persuade our Mr. F. to accompany her to view the painting. No, Watson, the real problem is that she could not possibly have teleported the Starry Night directly out of that drag field."
"What are you saying, Holmes? I saw her do it!"
"You saw, Watson, an impressive light display, followed by the appearance of a painting resembling Luna's Starry Night."
"But, the balloon!"
"Her trick with the balloon was admirable. But it is one thing to teleport a balloon several inches, and quite another to teleport a painting weighing ten stones sixty feet through a drag field. The energies involved would have turned her horn to ash. I have part of a hypothesis, but we are still missing a piece to our puzzle."
"I seem to have no pieces at all," I said. "Tell me your hypothesis."
"An interesting question in teleportation theory," he said, "is how much energy it takes to interchange, by simultaneous teleportation, two completely identical objects." He stopped under a street-lamp, and tapped two cobblestones with his hoof. "Say, for example, that these two cobblestones were perfectly identical. How much magical energy would it take to teleport the first one into the space originally occupied by the second, and simultaneously teleport the second into the space originally occupied by the first?"
"Well," I replied, "obviously, twice as much as it takes to teleport one cobblestone to the location of the other."
Holmes resumed his trot, and smiled in that superior fashion peculiar to him. "You should avoid the word 'obvious', Watson. It is only ever used to attempt to substitute hyperbole for knowledge. It is logically necessary that it would take no energy at all. If they were perfectly identical, and I were to claim that I had just instantaneously interchanged them, I could not be wrong, do you see? A claim can be wrong only if it is contradicted by the evidence – and there is no possible evidence that could contradict that claim."
See en.wikipedia.org/wiki/Identical_particles.
"Aha! I have caught you in your own cleverness, Holmes! You expended no energy; therefore, you could not have exchanged them!"
Holmes shut his eyes, as if hoping thus to shield himself from my stupidity. "Watson. You are trying to proceed from the evidence, to the claim that exchanging them would take energy. You may not assume what you are trying to prove!"
I sighed. "Suppose that I take your word on this for the moment."
"A wise choice, Watson. I recall a case involving two identical unicorn twins, who were not powerful magicians, and couldn't teleport an inch – but they could interchange their bodies, or so they claimed. One started a bar fight, seriously injured another pony, and was apprehended. He then appeared bewildered, and claimed that his brother had just swapped bodies with him, and he was innocent. The brother was brought in, and denied it."
"And was the guilty party ever determined?"
Holmes smiled wryly. "Technically, yes. I was able to establish, by painting different marks on their bodies, that they were not actually swapping bodies, but only swapping minds. The judge ruled that the letter of the law called for punishment of the guilty body, not the guilty mind. As they had hold of the guilty body, it could be legally prosecuted."
I spluttered some expression of shock at his complicity in this injustice. He merely chuckled at my reaction. "Surely, Watson, when one pony suffers an undeserved injury, it is more just, in the sense of equitableness, to choose an innocent pony at random and make him pay the medical bills, than for the equally-innocent victim to suffer both the injury and its expenses. Here we had an even chance of the choosing the aggressor. That necessarily makes it more than twice as just."
My instinct was to protest his taking justice into his own hooves, and moreover trying to quantify something that should be sacred. But I reflected on numerous cases when just such an arrogant intervention by Holmes had averted great, legally-prescribed injustice, and held my tongue.
He shrugged. "In any case, some punishment was necessary, or they both would have had carte blanche to commit any crimes they liked. What I neglected to mention to the jury was that, with the helpful if unwise cooperation of my subjects, I had conducted a series of experiments. When I began with very small marks of similar colors, they did exchange bodies. It was only when I painted one with large, obvious swaths of bright color that they were no longer able to do so, and merely swapped minds. We thus see that the energy needed to interchange two bodies is related to the degree of difference between them. So the energy needed to swap, for example, a painting, with a very good forgery of it, is small. You may think of the forgery as a counterweight, such as that found in an elevator, which makes moving large objects up possible with only a small input of energy by moving an equally large object down."
I was silent for a time, pondering the justice of Holmes' actions more than the lesson in magical physics. "Well, then," I finally said, "there's an end to the mystery. She brought a forgery with her, and swapped it with the painting."
"There are three immediate problems with that theory. First, why alert anyone to her action by displaying the painting? Second, the painting she gave Mr. F. would then have been the real painting, and he would have found a forgery in its place in the museum. Third, recall the magical line passing from start to end of a teleportation. While a synchronized swap of similar items requires low energy, it requires a magical connection of roughly three times the cross-section, and thus nine times as unstable and disruptive, as that for a simple point-to-point teleportation. This would play directly into the other strength of the drag field, that of detecting and squelching such connections. No, the mystery is not solved. We must find out what else Trixie has in her bag of tricks."
"Surely that does not matter," I said, "as long as we recover the painting." Holmes did not reply.
We arrived at the Salisbury. The vestibule opened onto a single vast room. At the center of the hotel, the open space went up twenty floors or more, and one could see ponies relaxing on the balconies of their hotel suites on each floor, all the way up to the skylights overhead. A small park with several tall pine trees stood in its center. It might indeed appeal to someone Great and Powerful. Holmes affected a slumped posture and a shuffling gait, and slowly walked across the vast lobby, to ask the night clerk if he could leave a message for the Great and Powerful Trixie.
"We have no one staying here by that name," the clerk said. "But are you Mr. Holmes?"
Holmes' eyebrows rose sharply, but he managed to suppress any other overt display of surprise. "Yes," he said after a few moments.
The clerk retrieved an envelope from his desk. "I was asked to give this to a Mr. Holmes if he came here inquiring after a Miss Trixie, Great and/or Powerful." He placed it on the check-in counter between them, then levitated a letter-opener and looked at Holmes inquiringly.
"I am quite capable of opening my own letters, thank you!" Holmes said sharply.
"Sorry, sir," the clerk said.
It is not such an easy business for an earth pony to open a sealed envelope, so it was nearly a minute later when Holmes managed to scrape the flap open and dump the contents of the letter onto a coffee table in the lobby. Out fell a room key to a humbler hotel that we had passed on the way here, as well as a slip of paper with something written on it. Holmes bent down to read it, then barked out a laugh. He pushed the paper across to me.
The writing was showy, written in bold strokes with an abundance of curlicues. It read, "Must Trixie do everything for you?"