Part of USS Polaris: S2E1. Entropic Foliations of the Galactic Fabric and Bravo Fleet: Labyrinth

When The Math Materializes Answers

ASTRA Lab, USS Polaris
Mission Day 5 - 1330 Hours
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The lab was packed. Nearly every physicist, astronomer and mathematician from the Advanced Science, Technology and Research Activity had gathered around the central display, talking in hushed, excited tones as they reviewed the results. Somehow, it all fit together. Every piece. None of them could quite believe it, but math didn’t lie.

As the door hissed open and Admiral Reyes stepped through, Dr. Luke Lockwood turned to greet her. “We’ve got it, Allison!” He was beaming eye-to-eye like a miner who’d just discovered gold. “We’ve fucking got it!”

Looking at the display, the admiral had to admit that she most certainly did not get it. It was just a wall-to-wall, disorganized mess of expressions and equations, and not a single visualization to speak of; further, to make it even more obtuse, the formalism it presented jumped between metric tensors, differential hypersurfaces, topological spaces, and probabilistic waveforms as though they were one smooth continuum.

“You know Luke, I often tell myself that I’m at least reasonably proficient in mathematics,” Admiral Reyes laughed. “But you and your boys do a great job reminding me I’m a complete plebeian. Couldn’t you have included at least one picture?”

A few of the researchers chuckled, but Dr. Lockwood just shot a disapproving glare her way. “Math is the picture, my dear admiral.” He never understood why laymen clung to imagery. Math itself was the truest form of art. You didn’t need anything more than that. “And besides, higher order manifolds lose so much of their beauty when reduced to a 2-dimensional surface.”

“Well you’re going to have to talk me through this then.”

Of course he would, Dr. Lockwood knew. Even his own team, supposedly the best Starfleet had to offer, needed his hand holding to get to where they were now, so of course a mere mortal like Allison Reyes would need it dumbed down.

“The greatest struggle of the past week has been the discontinuity between matter accretion and graviton exhaust,” Dr. Lockwood began, completely neglecting the mortal struggle Polaris Squadron was facing beyond the walls of his lab. “Gravitation should scale with accretion, but as you’ll recall from our initial observations, graviton radiation was outpacing accretion by a factor of 21.97 million.” It sounded like a large number, but when you spoke in cosmic scales, it wasn’t really even all that large.

Admiral Reyes nodded. She was aware of the unexplained oddity.

“As we’ve continued to observe the anomaly over the last few days,” Dr. Lockwood reported, gesturing towards a multivariate curve. “We’ve seen a not-insignificant acceleration of its amplification factor, as it relates to the influence it is exerting on Vespara Prime.”

“Wouldn’t that be explained by the singularity’s growth?” Admiral Reyes asked, acknowledging that, as the mass of the singularity grew, so too would the gravity it created. “Or by the planet’s decaying orbit?” The strength of gravity had an inverse square relationship to the distance between the bodies, meaning that, as the planet drew closer to the singularity, the strength of gravity would accelerate on a steep curve.

“No, that’s not it,” Dr. Lockwood shook his head. Did she really think they’d have gotten hung up on something so simple that she could have picked it out? “Or, more accurately, that’s not all of it.” He gestured at a series of equations that normed out the factors she’d raised. “After correcting for mass accretion and diminishing distance, plus accounting for density variations caused by the plasmatic tidal currents within the convective zone, we’re still measuring significant additional acceleration in graviton radiation.”

That was interesting, Admiral Reyes had to admit, but was it relevant? “Color me intrigued at a theoretical level,” she offered, her intrigue conditional on it tieing to reality. “But how does this connect to our actual problem?” She had no time for purely theoretical exercises when the fate of a world hung in the balance.

“Patience, dearie. Patience,” Dr. Lockwood scolded, wagging his index finger in her direction. “We’ll get there soon enough.” He wanted to enjoy the storytelling first.

Admiral Reyes shot him a look that told him to hurry the hell up. 

“Ok, fine, fine…” Dr. Lockwood ceded. “You see, that probe we fired off Serenity, the one Lieutenant Commander Sharpe helped harden against the gravitational shear, it gave us the next piece of the puzzle. As it fell towards the singularity, instead of an inverse square gradient, its gravimetric sensors recorded a highly exponentiated variation of force amplitude.”

“You mean the force of gravity increased faster than it should have?” Admiral Reyes asked to confirm that she was following along with his technobabble correctly.

Dr. Lockwood nodded.

There was an obvious next question, and Admiral didn’t delay in asking it: “How much faster is it accelerating?” The answer, she knew, could have absolutely massive implications on their mission – or knowing these guys, they could have hauled her down here for nothing more than an academic exercise. It was all the same to the theoreticians.

“Based on the gravimetric readings the probe collected before it imploded, we project the mass-energy equivalent scaling factor at the point of origin to be around 1.19e+28,” Dr. Lockwood reported, making it clear that it was the former. This did matter to their mission.

“1.19 to the 28th power? That’s…” Admiral Reyes’ voice trailed off as she considered the implications. The scaling factor they’d originally observed was ‘only’ 21.97 million. What they were talking about was 54.1 quintillion times that or, put in other terms, it was twenty one orders of magnitude more significant. That scale was so massive she didn’t even need to ask if it fit the standard model of quantum gravity. “So what you’re saying is that gravity gets stronger way faster than it should?”

“Yes, on a gradient that maps smoothly to an exponential of the inverse square,” Dr. Lockwood nodded as he pointed at a transformation on the display that evidenced that. “In the literature, similar observations have been made of singularity-rooted subspace fissures, but even those have never been amplified to anywhere near this order of magnitude. This could be a whole new chapter in the field of subspace mechanics.” His eyes twinkled at the notion.

“Yes, yes, a new chapter and all that…” Admiral Reyes parroted back in a way that said she cared little for the academic implications. This was about the lives of six million people, and certainly not who was going to get a piece above the fold in the next edition of Subspace Today. “If gravitation around this singularity behaves as you’re describing, does that mean the planet’s rate of decay is going to be faster than we originally predicted?”

“Unfortunately yes,” Dr. Brooks jumped in. “I just finished updating Dr. Sh’vot’s model.” As opposed to the theoreticians, he knew what mattered most, and immediately upon the math coming together, he’d gone back to the geophysicist’s work to account for their new discovery.

“And how much time do Agarwal and Lee lose as a result of this development?” Admiral Reyes asked as a pit developed in her stomach. The Archanis Corps of Engineers detachment commander and the Polaris Squadron Engineering Officer were already trying to move mountains, literally, and now, because of some math cooked up in the lab, they might have even less time to do it.

“Thankfully, that timing remains relatively consistent, at least within a few hours, because we’re talking about the de minimis side of the curve,” Dr. Brooks assured her. That was good, at least. “But as the planet’s orbit continues to decay, yes, gravitation will indeed increase faster than anticipated, shortening the planet’s overall viability.” While he conveyed it in very academic terms, those implications were very not good.

“So we’re still on roughly the same clock for the shelters,” Admiral Reyes summarized, just to make sure she hadn’t missed anything. “But the amount of time that there’s still a planet to shelter on, that’s shorter than we originally anticipated?”

“Yes, that’s correct.”

“How much shorter?”

“Sixty three percent.”

The air left the Admiral’s lungs. 

“After Vespara Prime falls out of its habitable zone,” Dr. Brooks concluded. “You will have twenty two days to evacuate the colonists sheltering in place before the planet will begin to break apart as it falls toward the sun.”

“Tom, are we just digging a burial pit for them then?” Admiral Reyes lamented as she looked into the eyes of the aged scientist, seeing nothing but darkness. “Even if we just run max burn round trips to Vega Pyronis, we won’t even manage to relocate a tenth of the colony in time.” 

Fuck Starfleet Command for not having more ships for them. Fuck the universe for taking what time she thought she had away from her. And fuck Dr. Lockwood for calling like he had good news. This was an absolutely fucking disaster.

“I can’t predict the future,” Dr. Brooks reminded her.

Admiral Reyes knew that, in the case of Thomas Duncan Brooks, that wasn’t exactly true – at least not as it related to the broad strokes on how things would unfold – but on this one, it was probably true. It wasn’t like Vespara Prime would ever have been significant enough to have come up during his travels.

“But Admiral,” Dr. Brooks added. “There is some good news.”

As she stood there, still trying to process, she looked first at Dr. Brooks, and then at the others. What the hell would Tom Brooks, or Luke Lockwood, or Akil al-Qadir, or any of them possibly have to tell her that would make up for the fact they’d just stolen thirty seven days from her? Thirty seven days she desperately needed to save the people of Vespara Prime.

“Luke, wanna do the honors?” Dr. Brooks deferred back to the team lead. On one hand, it had been him that pushed Dr. Lockwood to even consider a different foundational basis for the problem, but on the other, it was Dr. Lockwood that had finally wrestled the math to the ground.

Dr. Lockwood stepped back up to the display proudly. “There’s something special about the number 1.19e+28,” he explained as he gestured at a series of equations. “The classical Natario metric, as I’m sure you’ll recognize.”

“Yeah, I got that,” Admiral Reyes nodded as she looked at the first equation in the sequence. It was the solution at the center of warp field theory, and it was taught to every first year scientist and engineer at the Academy. “But what are you doing to those field equations below?” The rest of the math below those first tensors quickly descended into a complex set of transformations that she didn’t understand in the slightest.

“This series projects it out as a generalized subspace-like hypersurface within a higher order manifold,” Dr. Lockwood replied in a matter of fact tone. “And then compresses the foliations within that manifold to the tune of 3.65e+5.”

It sounded so simple when said it that way, but how he got there – the math, the reason for the compression, even the number itself – she wasn’t following any of it, and her face said as much.

“Think of it this way,” Dr. Brooks jumped back in. He was sympathetic to the fact that the Admiral had not spent the last four days crammed in this lab with them, iterating on the solution space until they got to this answer, one that, if it had not fit together so perfectly, would have been considered batshit crazy. “Suppose subspace is a highly elastic blanket. What we’ve done here is bunch it up incredibly tightly, so that, instead of walking from one end to the other, you’re able to near-instantly jump across it.”

“Like a wormhole in subspace, yes,” Admiral Reyes nodded. “I got that. But why 3.65e+5?” That was both a very large and a very specific number.

“It’s within the range of superluminal compression observed by the USS Voyager during its encounter with the Vaadwaur, assuming an acceleration in c to around 1,000 light years per day,” Dr. Lockwood got back to the details. “And because of this…” 

With a flick of the wrist, he materialized an equation on the display that was so ridiculously rudimentary that it seemed crazy to even see it on the same display as the others:

E = m * c ^ 2

“Recognize it?”

“I’m pretty sure even Akil’s nine year old knows that one,” Admiral Reyes grumbled as she glared at him. What was it with Dr. Lockwood and his storytelling? Einstein’s mass-energy equivalence equation was taught to school children alongside Newtonian mechanics right before both were promptly disproven within the quantum, relativistic and subspace domains. She didn’t see, however, how it explained anything.

“Well, try this,” Dr. Lockwood said, and with another flick of the wrist, a couple substitution were made on the display, using numbers already at the root of their discussion:

E = 1.19e+28 * m = m * ( 3.65e+5 * c ) ^ 2

“Woah,” the Admiral remarked, her mouth agape. “That’s not a coincidence, is it?” It was crazy to think that such a simple equation bore an answer to such a great mystery. 

“Most certainly not,” Dr. Lockwood shook his head.

“Okay, well suppose you’re right…”

“I am,” Dr. Lockwood insisted assuredly. “A fissure straight into the compressed foliations of subspace, such as an Underspace aperture or something sufficiently similar, just fits too well, and it definitely explains the degree of gravitational potentiation that we’re seeing here.” That was where Dr. Brooks’ rather crude reference to the elasticity of the blanket came into play in terms of the potential energy loaded up into the system by the compressions.

“It’s also the only thing that the brain trust has come up with that maths out to explain this,” Dr. Brooks added for good measure, aware that there could be other answers, even if they hadn’t come up with them yet. “And, as much as we could iterate on this until the ends of time, given the reports of Underspace apertures suddenly materializing across the quadrant, it’s hard to ignore.”

Since the pragmatic Dr. Brooks was buying it too, it gave Admiral Reyes some assurance that this wasn’t just mathematics unrooted in reality. “If this is an Underspace aperture, why isn’t it behaving like the ones we’ve encountered in the Delta Quadrant, or the others our ships have stumbled across in recent days?”

“I’m not sure I’d generalize the recent reports with anything we know of them from Delta,” Dr. Lockwood cautioned. “The new apertures in the Alpha and Beta Quadrants have been doing all sorts of things inconsistent with any prior observations from Delta.” The team had poured over those reports, and they varied massively in terms of aperture presentation. Some were stable, and others were intermittent. Some were pushing, and others were pulling. Some were traversable, and others were not. “In fact, the only thing consistent about them is their inconsistency. It’s almost as though Underspace has gone mad.” Dr. Brooks had posited some theories about that too, but they were pure supposition not rooted in the math, so Dr. Lockwood was not going to get into them for now.

“Okay, fine,” Admiral Reyes replied, clearly growing impatient with the semantic discussion. “Then how does this differ with the ones we’ve previously observed in the Delta Quadrant?”

“It lacks the negative energy density core that typically mediates the gravitation amplification refracted by the compressed subspace foliations,” Dr. Lockwood answered. “Leading to what we’re seeing now, which is basically a highly energetic subspace singularity.” 

There was an obvious next question, but Dr. Brooks got there before the Admiral could ask it: “And no, we don’t know how to solve for that yet. But we’re working on it.”

That would be the only way to save the six million souls on Vespara Prime.

Comments

  • This was an incredible post with such an accurate depiction of the math that would show the solution as you did. As someone who is in a STEM degree and the field relies heavily on math like you did I really appreciated this post. It was an awesome way to introduce the Underspace into the bigger arch of your story. I loved how you did this post and I am interested to see how the crew might be able to save Vespara Prime. Or if regardless of their attempts the end of Vespara Prime is in the near future. Loved this!

    June 25, 2024
  • The science, math and the poor sanity of Reyes when being explained to the root of what it all means. It is a rhythm of numbers that harmonious come together in this story. You did a wonderful job on portraying both the wizzkid and the noobs in the room to explain the findings. Great rundown and it still gives more questions but the link to underspace is wonderful

    June 25, 2024
  • I fear Admiral Reyes has a much greater grasp of all this than I do! But I fully trust all the maths adds up. At least now they've got some answers, whether it leads to a fuller understanding of the situation and ways to deal with it, only time will tell. Time Vespara Prime, might not have. So you get the 'gold star' for effort and story telling from me.

    June 30, 2024
  • Math should not contain easter eggs. No sir, no easter eggs. I had to sit and read the numbers multiple times and I'm still confused, despite being able to follow some of it. There is layer upon layer here and oh boy! I'm certainly glad all the characters here are far, far smarter than I am and get this. I love Lockwood for his total commitment to The Math and for finding it all exciting while people are suffering. Commitment to the art my friend.

    July 6, 2024