“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.

“Well, that’s clear enough,” I said. “It’s been obvious that I’ve been splitting off new Histories right, left and center since the moment the Time Machine was first switched on. Dangerous indeed!”

“Yes. And as the machine, and its successors, delve ever deeper into the past, so the Multiplicity generated tends towards infinity, and the divergence of the new copies of History grows wider.”

“But,” I said, a little frustrated, “coming back to the matter at hand — what is the purpose of this table? Is it just a trick? — Why have the Constructors given it to us? What are they trying to tell us?”

“I do not know,” he said. “Not yet. It is difficult… The Information Sea is wide, and there are many factions among the Constructors. Information is not offered freely to me — do you understand? — I have to pick up what I can, make the best understanding of it, and so build up an interpretation that way…

I think there is a faction of them who have some scheme — an immense Project whose outlines I can barely make out.”

“What is the nature of this Project?”

Nebogipfel said for answer, “Look: we know that there are many — perhaps an infinite number — of Histories emerging from each event. Imagine yourself, in two such neighboring Histories, separated by — let us say — the details of the rebound of your billiard ball. Now: could those two copies of you communicate with each other?”

I thought about that. “We have discussed this before. I don’t see how. A Time Machine would take me up and down a single History branch. If I’d gone back to change the rebound of the ball, then I would expect to travel forward and observe a difference, because, it seems, if the machine causes a bifurcation, it then tends to follow the newly generated History. No,” I said confidently. “The two versions of me could not communicate.”

“Not even if I allow you any conceivable machine, or measuring device?”

“No. There would be two copies of any such device — each as disconnected from its twin as I was.”