Consequences

by DoctorH

This is a follow-up to "Failure Analysis," but it's not a sequel (and it is much shorter). A Physics professor arrives on DS9 and proposes to conduct experiments on the wormhole. The equation that forms the basis for the experiments is so complicated that almost no one can understand the equation... or its consequences. Sisko must decide whether to allow the experiments to proceed.

6. The mysteries of the equation

Chapter 6: The mysteries of the equation.

"Chief?" Sisko called, as Dax exited Sisko's office and headed toward her post in Ops. "If you have a moment, could you and I discuss something in my office?"

O'Brien was sitting at his post in Ops. He summoned his relief and walked to Sisko's office. On the way, Dax passed him with a wry smile.

O'Brien knew that smile. He wondered what he was in for.

Sisko gestured to the chair in front of his desk. "Chief, have a seat. We need to talk."

"Sir," O'Brien hedged as he and Sisko sat, "does our discussion have anything to do with the visit of Commissioner Nguyen to this station? I saw the Commissioner on the Promenade earlier today."

"As a matter of fact, it does."

O'Brien dreaded asking: "His presence here: it's not related to the USS Observer, is it?"

"No. It's not."

O'Brien breathed a sigh of relief. "Thank goodness. I was worried. I really wanted to put those events behind me."

"Chief, Commissioner Nguyen is Professor Nguyen now. And he's here to study the wormhole."

"Oh?"

"He wants to perform some experiments to see whether the wormhole's observed behavior is what would be predicted by something called Vuldt's Equation. Have you ever heard of Vuldt's Equation?"

"I've heard of it. I've never had much reason to use it. It's too damn complicated, for one thing; and for the work I do, most of the numbers in the equation would be negligible, so doing all of the computations of that equation would not be worthwhile. And besides, it's not really an equation, you know."

Sisko lifted his eyebrows. "What do you mean, 'it's not really an equation?'"

"It's more of a theorized equation. It can't be proven mathematically, and it hasn't been formally proven by experimentation. Maybe that's what Professor Nguyen is here to do: conduct experiments to see whether Vuldt's Equation holds up in the wormhole."

"So he wants to confirm Vuldt's Equation?"

"Or falsify it. Either result would be highly significant."

Sisko turned to the display. "Computer: show the most common form of Vuldt's Equation." The mathematical soup appeared on the wall display. "Chief, can you explain any of this to me? Can you just give me a layperson's understanding?"

O'Brien took a moment to respond. "I'm sorry; I doubt that I can. I mean, the various numbers over here are presented in Pontus form. That's some pretty heavy-duty mathematics right there."

"What is Pontus form? In ordinary language: what is it?"

O'Brien thought for a moment. "Sir: you're familiar with vectors, aren't you?"

"Yes."

"And tensors?"

"Yes, somewhat."

"And complex spaces?"

"I think we've reached the limit of my familiarity, Chief."

"At the risk of over-simplifying the concepts, I'll start with the notion of a vector. You can think of a vector as a number that has two properties: a magnitude and a direction, right?"

"Right."

"Well, a number in Pontus form— in some versions of the Pontus form, that is— has a magnitude, and a direction, and a permanence, and a resilience, and—"

"Just hold it there, Chief. A permanence? A resilience?"

"Yes, sir. I'm going to over-simplify this terribly, but permanence and resilience relate to the propensity of the number to change in response to operations."

Sisko was lost, but he said, "O-o-okay."

O'Brien counted on his fingers as he ticked off the properties of a number in Pontus form. "So a number has a magnitude, a direction, a permanence, a resilience, a recurrence, an exclusion set, a standard spread, and—" He had listed seven properties, but he knew there were eight. "And— one more thing, but I can't remember what it is. Oh! And a dimensional reflectivity. Anyway, the Pontus form incorporates all of those properties, and Pontus operations describe ways in which two numbers in Pontus form, uh, combine or interact."

"I have to tell you, Chief, that I understood almost none of that."

"Well, I got introduced to Pontus operations when I studied warp fields and various force fields and structural integrity fields. But we almost never had to do anything with Pontus operations, since simplified non-Pontus operations give results that are almost as accurate and precise."

Sisko pointed to Vuldt's Equation on the wall display In a somber tone, Sisko asked: "Am I wrong, Chief, in thinking that Pontus operations are just a part of this equation, and that there is more here than that?"

"You are right about that, sir. These operations over there on the right-hand side, set off by that rectangle, I have no idea what they are or what they do. And this notation here on the left-side is totally unfamiliar to me."

"Do you know of anyone aboard this station who might have a little more insight into this subject?"

"Other than Professor Nguyen? I doubt it."

Sisko huffed. "So if Professor Nguyen tells me about an experiment that he wants to conduct, and shows me this equation as explanation, I have no way of knowing whether what he's telling me is true or not, have I?"

"You can ask the computer to check his maths, but that won't tell you the significance of what he's trying to find."

"And so I have no way of knowing whether his proposed experiments are risky or not, do I?"

"Not that I can see."

Sisko pouted. "I wonder whether Admiral Seth and Admiral Ross were in any position to assess the risks, when they authorized Professor Nguyen to go ahead."