“I think I understand what this table is for,” he said, breathless.
“Yes?”
“It is — how can I express it? — it is only a demonstration, little more than a toy but it is a Multiplicity Generator. Do you see?”
I held up my hands. “I fear I don’t see a thing.”
“You are familiar enough with the idea of the Multiplicity of Histories, by now…”
“I should be; it’s the basis of your explanation of the divergent Histories we have visited.”
At every moment, in every event (I summarized), History bifurcates. A butterfly’s shadow may fall here or there; the assassin’s bullet may graze and pass on without harm, or lodge itself fatally in the heart of a King… To each possible outcome of each event, there corresponds a fresh version of History. “And all of these Histories are real,” I said, “and — if I understand it right they lie side by side with each other, in some Fourth Dimension, like the pages of a book.”
“Very well. And you see, also, that the action of a Time Machine — including your first prototype — is to cause wider bifurcations, to generate new Histories… some of them impossible without the Machine’s intervention — like this one!” He waved his hands about. “Without your machine, which started off the whole series of events, humans could never have been transported back to the Palaeocene. We should not now be sitting on top of fifty million years of intelligent modification of the cosmos.”
“I see all that,” I said, my patience wearing thin. “But what has it to do with this table?”
“Look.” He set the single ball rolling across the table. “Here is our ball. We must imagine many Histories — a sheaf of them — fanning out around the ball at every moment. The most likely History, of course, is the one containing the classical trajectory — meaning a straightforward roll of the ball across the table. But other Histories — neighboring, but some widely divergent — exist in parallel. It is even possible, though very unlikely, that in one of those Histories the thermal agitation of the ball’s molecules will combine, and cause it to leap up in the air and hit you in the eye.”
“Very well.”
“Now—” He ran his finger around the rim of the nearest pocket. “This green inlay is a clue.”
“It is Plattnerite.”
“Yes. The pockets act as miniature Time Machines — limited in scope and size, but quite effective. And, as we have seen from our own experience, when Time Machines operate — when objects travel into future or past to meet themselves — the chain of cause and effect can be disrupted, and Histories grow like weeds…”
He reminded me of the odd incident we had witnessed with the stationary ball. “That was, perhaps, the clearest example of what I am describing. The ball sat at rest on the table — our ball, we will call it. Then a copy of our ball emerged from a pocket, and knocked our ball aside. Our ball traveled to the cushion, rebounded, and fell into the pocket, leaving the copy at rest on the table, in the precise position of the original.
“Then,” Nebogipfel said slowly, “our ball traveled back through time — do you see? — and emerged from the pocket in the past…”
“And proceeded to knock itself out of the way, and took its own place.” I stared at the innocent-looking table. “Confound it, I see it now! It was the same ball after all. It was resting quite happily on the table — but, because of the bizarre possibilities of time travel, it was able to loop through time and knock itself aside!”
“You have it,” the Morlock said.
“But what made the ball start moving in the first place? Neither of us gave it a shove towards the pocket.”
“A ’shove’ was not necessary,” Nebogipfel said. “In the presence of Time Machines — and this is the point of the demonstration, really — you must abandon your old ideas of causality. Things are not so simple! The collision with the copy was just one possibility for the ball, which the table demonstrated for us. Do you see? In the presence of a Time Machine, causality is so damaged that even a stationary ball is surrounded by an infinite number of such bizarre possibilities. Your questions about ’how it started’ are without meaning, you see: it is a closed causal loop — there was no First Cause.”
“Maybe so,” I said, “but look here: I still have an uneasy feeling about all this. Let’s go back to the two balls on the table again — or rather, the one real ball and its copy. Suddenly, there is twice as much material present as there was before! Where has it all come from?”
He eyed me. “You are worried about the violation of Conservation Laws — the appearance, or disappearance, of Mass.”
“Exactly.”
“I did not notice any such concern when you dived into time in search of your younger self. For that was just as much — more! — of a violation of any Conservation Principle.”
“Nevertheless,” I said, refusing to be goaded, “the objection is valid — isn’t it?”
“In a sense,” he said. “But only in a narrow, single-History sort of way.
“The Universal Constructors have been studying these paradoxes of time travel for centuries now,” he said. “Or rather, apparent paradoxes. And they have formulated a type of Conservation Law which works in the higher Dimension of the Multiplicity of Histories.
“Start with an object like yourself. If, at any given moment, you add in a copy of yourself which may be absent because you have traveled away into past or future — and then subtract any copies doubly present because one of you has traveled to the past then you will find that the sum, overall, stays constant there is ’really’ only one of you — no matter how many times you travel up and down through time. So there is Conservation, of a sort — even though, at any moment in any given History, it may seem that Conservation Laws are broken, because there are suddenly two of you, or none of you.”
I saw it, on thinking it through. “There is only a paradox if you restrict your thinking to a single History,” I observed. “The paradox disappears, if you think in terms of Multiplicity.”
“Exactly. Just as problems of causality are resolved, within the greater frame of the Multiplicity.
“It is the power of this table, you see,” he told me, “that it is able to demonstrate these extraordinary possibilities to us… It is able to use Time Machine technology to show us the possibility — no, the existence — of Multiple, divergent Histories at the macroscopic level. Indeed, it can pick out particular Histories of interest: it has a very subtle design.”
He told me more of the Constructors’ Laws of the Multiplicity.
“One can imagine situations,” he said, “in which the Multiplicity of Histories is zero, one, or many. It is zero if that History is impossible — if it is not self consistent. A Multiplicity of one is the situation imagined by your earlier philosophers — of Newton’s generation, perhaps — in which a single course of events unfolds out of each point in time, consistent and immovable.”
I understood him to be describing my own original — and naive! — view of History, as a sort of immense Room, more or less fixed, through which my Time Machine would let me wander at will.
“A ’dangerous’ path for an object — like you, or our billiard ball — is one which can reach a Time Machine,” he said.