“A set is a Many that allows itself to be thought of as a One.”

Georg Cantor (1845 - 1918)

-x-x-x-

There’s a common saying that guys wanted only one thing, and it was gosh-darn disgusting.

Alas, it turns out that whoever spread that myth must have misheard the word ‘sets’, and from then on there was no turning back.

I had to agree with one thing, though. Sets were disgusting.

The good news: my dantian was now quantised. Yay!

The bad news: it was poorly quantised, because I’d realised too late that since the power set of a set – that is, the set of all subsets of a set – had a number of elements equal to 2 raised to the nth power, things could get out of control far too quickly. There was no way in hell I could work with anything more than 64 subsets (and even keeping aware of all 64 and their relations was a challenge), and so the power dwelling within my dantian was now separated into 6 roughly equivalent chunks.

And, I thought glumly, digging my spoon into the bowl of rice before me. I’ll probably need to rework everything at the next stage…

And thus, my dantian — Elixir Field — was only a set of six questionably-distinct elements, whose power set composed a group.

I know, confusing stuff.

I could have gone the additional layer and considered symmetries of those six elements – the symmetric group S6 for instance, describing all the permutations of a set of 6 elements, or the dihedral group D12 or cyclic group C6 – but that was one step too much for me at the moment. Besides, even without any extra fanciful considerations, there was still the trivial group, and the identity element of ‘do nothing’ was a valid symmetry. Perhaps the most important symmetry of all, in fact.

Why did the power set matter, you may ask? Why not split my dantian into 64 pieces, and just work with those individually rather than considering all possible combinations of subsets?

An excellent question. Beyond the fact that I’d been petrified to split what seemed analogous to my soul Voldemort-style (in a manner of speaking, anyway) into even more pieces, it had taken ages to painstakingly carve out a portion of my dantian and sequester it as its own little packet of soulstuff. It was probably much easier once one got used to breaking their dantian apart, but I was still only a beginner at the art of introspection.

That is, if splitting the dantian was even considered a normal thing to do. There were probably tips and tricks described in manuals to ‘soften’ the dantian and smoothen out the flow, or perhaps stronger spiritual roots possessed by others naturally allowed for ease of use. Whatever the case, things worked out just fine.

Besides that reason, 6 was also objectively and provably better than 64. It was a perfect number, a pronic number, a congruent number, a semiprime, and the size of the smallest non-abelian group S3. What did 64 have going for it other than the fact it was a cube and a square? It wasn’t even associated with a Mersenne prime adjacent to it, that fucking loser. Eww.

Furthermore, working with the power set allowed the formation of a group using the symmetric difference as an operator, the empty set as the identity element, and each element of the power set the inverse of itself within the group. The more relations I could identify within my dantian and hence order I could impose, the better. I was beginning to suspect that was the sole reason why I wasn’t undergoing qi deviation and splintering out a horcrux.

The results spoke for themselves. Even now, sitting on a chair and eating, it was laughably easy to coax each little energy packet dwelling within my soul to move through the networks of meridians feeding outward from the principal vessels. Likewise, combinations of them that made up each of the 64 elements of the power set were just as smooth.

It wasn’t perfect, however. Either by virtue of Yao’s poor cultivation method leaving lasting damage or his lacklustre spiritual roots, my dantian didn’t behave quite the same way other cultivators did. Probably the latter, since Haonan never faced the same issue utilising his rudimentary qi.

My attempt at a fix didn’t eliminate Yao’s primary issue, only alleviate it. Each time I tapped on a sphere to draw upon its power, it would abruptly tense and become rigid, all qi flow within it slowing to a halt as though a non-Newtonian fluid increasing its viscosity in relation to its stress. The time it took to relax was faster than it had been with Yao’s, but still it did mean I had to be tactical in the usage of my qi – a full burst from all six spheres would leave me powerless to act until at least one of them cooled down sufficiently to be drawn upon once more.

Still, it was leagues better than what Yao managed. And to think that it had only taken me four weeks!

… four long, arduous, awfully boring, frustrating, harrowing weeks, in which I’d wanted more than once to quit but fretted too much that stopping the soul-butchery midway might just be worse than completing said butchery…

I shivered. The less I thought of the last month, the better.

Did that make me in the final phase of the Qi Gathering stage now? Heck if I knew. The cut-offs were usually described in complete manuals, alongside useful tips and tricks of how to clear those bottlenecks.

Regardless, with the state of my soul reorganised, my dantian was once again happy to accept the influx of new qi with its increased capacity, meaning I could progress further along the stage of Qi Gathering. Unfortunately, I didn’t have access to spirit stones or qi pills, and was limited to simply cycling ambient qi sequentially into my six containers while catching up with my mathematics studies. I could have hastened it by engaging in breathing exercises and the like, but Yao had no knowledge of how to perform them. Then there was also that whole business with arrays, seals, and formations that I hadn’t even gotten a start on unravelling.

So much to do, so little time…

At the very least, I now had a joke to tell. Still a work in progress, but it goes something like this:

Cultivator Ling Yao has a dantian bag filled with liquefied gooey qi-marbles. He shapes them into 6 distinct qi-marbles. How many marbles does he have?

None, because he’s lost his marbles.

Hehe.

Right. I’d reflected long enough. Time to get back to breakfast!

“Senior Yao?”

“Haonan,” I greeted between mouthfuls of food. He’d clearly spent time in the training field, what with the rips and tears on his already-frayed robes. Some of our fellows in the different phases of Qi Gathering were streaming into the outer disciple mess hall, dishevelled and sweaty from the morning’s exercises that I’d been skipping. “You look like you’ve been training hard.”

He bobbed his head enthusiastically, placing his own rice bowl on the table with a hearty thump as he moved to sit beside me. “Yes, senior brother! I’ve been volunteering in the morning spars every chance I had, just like you advised me!”

I winced. Yes, that had been Yao’s attitude toward training. He’d been a staunch believer that experience was the best teacher, except that he’d taken one such experience to the head too many. At least he practised what he preached.

“Take the time to properly inspect your dantian as well, Haonan,” I advised. “Martial training will only go so far in teaching you to wield qi.”

I didn’t want to go into the details of the method I’d latched on to — certainly not while I still wasn’t certain if there were any risks. Besides, considering Haonan was developing just fine with the Closed Skies Scripture, there wasn’t a need to intervene just yet.

The narrative has been stolen; if detected on Amazon, report the infringement.

“Mmhmm!” the sound came muffled over the food he wolfed down.

Come to think of it, I really owed him a favour or a gift for the tip that he’d bestowed unto me, albeit unknowingly. It wasn’t necessary, but you know what they say: be the change you want to see in the world, right?

Wouldn’t be any time soon, unfortunately. Though I hadn’t purchased cultivation resources since my arrival in Yao’s body, I hadn’t done much in the way of sect duties and additional assignments either, and remained just as poor as ever.

“By the way, Yao,” Haonan asked, hesitant yet eager. His eyes flickered toward his fellow outer disciples, and his voice dropped to a whisper. “If you’re out of your room, does that mean you’ve achieved a breakthrough?”

“I’m not certain yet,” I admitted. “I think that I cleared the bottleneck, but since I didn’t follow an established method, I –”

I halted as Haonan raised his thick arm. I flinched, though my rational mind knew that he wasn’t about to strike.

He thumped me merrily on the back with that thick arm of his, and…

…it didn’t hurt?

“But that’s amazing, senior brother! Congratulations!”

I blinked. Huh. I stared at Haonan’s arm, and he definitely hadn’t controlled his strength. Yao’s physique might as well be a bundle of sticks compared to his junior’s.

I’d tapped on the qi lurking within my organised dantian, and it had felt… natural. Instinctive. Certainly far more responsive than Yao remembered it being.

If any of my thoughts showed, Haonan didn’t react to them. He leaned in conspiratorially.

“And with the other matter…” His boyish face practically shone with excitement. “Have you made progress with your arrays? Will you be challenging that bastard Gao Han soon?”

“Not in the slightest.” I ran my fingers idly on the clay bowl, drafting up my next steps now that the cultivation roadblock was cleared. “There’s other theorems I want to study further – err, cultivation techniques,” I corrected, seeing Haonan’s confusion, though I still had no idea how to relate the two. “I’ll need to find some references for arrays and formations if I intend to go down that route as well, which means I need to take up assignments…”

I trailed off, sighing. There just weren’t enough hours in the day, were there?

“You shall let me know if there’s anything I can do to help, yes?” Haonan eyed my now-empty rice bowl. “Will you be cultivating in private again, senior? I don’t think I remembered seeing your name rostered on any duties today.”

I shrugged. “Maybe? Haven’t thought that far ahead, really. I guess I could go check out what assignments are available.”

I rose from my seat, offering him a quick goodbye before taking my rice bowl with me. He waved enthusiastically, then went over to join a handful of outer disciples that he’d been training with earlier.

The outer disciples’ mess hall was sited on the absolute lowest tier of the Empyreal Sword Sect that carved its throne atop the Quanlong Peaks. There were little in the way of decoration or cultivation facilities for outer disciples to use. Mess halls, training fields, the common dormitories, the duty hall, and the outer disciple quartermaster had been the mainstays of Yao’s time in the sect.

I walked along the tiled paths, watching as other outer disciples went about their scheduled duties of cleaning and fetching items about the different parts of the sect. From the yearning gazes they directed toward the ornate pavilions and lush terraces visible in the distance higher up the mountain’s steps, it was clear that just about everyone wished to earn the favour of any of the sect’s main clans that they might be considered for promotion to the rank of inner or core disciple.

Spars and competitions among the outer sect members were held every month with cultivation resources awarded to the top winners, but that was not the greatest prize. Most hoped that the families would deign to send their younger members to compete so that they might have a chance of impressing a potential patron. It had been one such unfortunate set of spars that saw Yao crushed by Gao Han, though he’d also ultimately failed to earn a superior’s favour.

Otherwise, the only chance for promotion to inner disciple was through the Promotion Trials, a selection exam held every year that tested one’s quality of cultivation, martial skill, and command over qi in the form of qi techniques. I wasn’t certain whether I would make the cut in time for the upcoming one, but progressing to inner disciple was definitely something I was keen on doing.

Sure, inner disciples were still responsible for the day-to-day maintenance of the clans’ estates, but at least they were able to receive higher quality instruction from members of the clans or their core disciples when they visited the inner disciples’ terraces. Their accommodations surely had to be leagues better than those of the outer disciples.

Hopefully, I’d make it there some time soon. My back was killing me from sleeping on the cold stone floor of my room.

Such luxuries were for future me to think about, though. As the locals would say — a toad should not lust after swan meat, eh?

The outer disciples’ logistics wing was abuzz with activity, though it was only now just after breakfast. Most of the tasks distributed here were for unskilled and manual labour, ranging from cleaning of common sect areas and reaping the fields to retrieving supplies from the towns below the mountain. A cultivator of the higher stages from the main families could have done the latter in a fraction of the time by riding a sword down the mountainside, but such menial tasks were apparently beneath their station.

Harried clerks organised the distribution of tasks, many of them outer disciples themselves, though they would have been appointed to their station by either an inner disciple or one of the members of the clans. Wu Guanyao was the duty clerk for the day, an experienced former inner disciple now in his sixties who’d never progressed beyond the late Foundation Establishment stage. The white-haired man stood before the grand noticeboard, organising the duty tablets as his subordinates shouted out the names of disciples who’d taken up each task.

The indistinct clamour resolved into discernible shouts as I drew closer, throngs of outer disciples yelling over each other to be heard.

“Oi, Song! We agreed that Longhua and I were assisting Master Rui!”

“Spirit Beasts! Anyone else wants to take up the Spirit Beasts assignment! Foundation Establishment and above only! Equal distribution of contribution points!”

“Looking for three more for caravan escort to Daxiang Town! Expected two weeks’ journey! All experiences welcome!”

“Xun, you little shit! You stole the assignment I wanted!”

“Sparring partner wanted! Sparring partner wanted!”

“I’m just saying, Zhu Yanling is obviously prettier than Fang Xueer —“

“Does anyone have twelve contribution points they could spare? Please! Just twelve! Ah, Kang! How’s your training been? Oh, that’s great to hear! By the way, would you happen to…”

Man. Though I’d been here quite a few times at the busiest hours already, I always forgot just how animated and annoying this place could be. Uncanny resemblance to social interactions in just about every MMORPG I’ve ever played aside, I couldn’t help but feel vexed by just how inefficient it all was.

Don’t get me wrong, I never did anything even remotely close to logistics management. Still, I’d been an occasional user on the university’s High Performance Computing cluster for some bioinformatics analyses, and had always been amazed by the cluster architecture and how the scheduler processed incoming requests by priority and resource allocation. Automating the allocation of these jobs in a reasonably fair manner would have been a trivial task for the cluster operators back on Earth.

Perhaps I could give it a go setting up a similar scheduler with arrays eventually, once I had even the slightest of how they worked? The practical experience it afforded would doubtlessly be invaluable.

I winced again as someone shouted right by my ear, squeezing past him to have a closer look at the board.

Request from Tianshui Village to hunt down some beasts eating their flock… Tilling the Zhu clan’s spirit fields… Assisting Rui Xudong with his — oh, never mind, someone’s taken that… additional valets for the Dalu family’s banquet in the Wei clan’s estate…

Man, there was nothing that really interested me. Alchemy sounded like it could have been fun, but it got snatched up just as I’d read it. Ehh, probably wasn’t a big loss anyway; the typical cultivation pill in most novels took longer to create than synthesis in a chemistry lab.

What to do, what to do… I could get back to my room and return to mathematical pursuits, though I would admit that getting some contribution points to replace Yao’s worn-out pillow would be very welcome indeed…

I made my decision. Delaying my studies temporarily wouldn’t leave Fourier and Legendre any deader. This was… yes, this was simply applied mathematics!

Whatever task it was needed to be something relatively safe, however. Though Yao’s experiences helped, I’d never so much as held a sword or practised martial arts, never mind footwork techniques or weapon arts. Culling Spirit Beasts was out of the question, as was tracking down a band of bandits estimated to be in the Qi Gathering stage. The average scut work sounded too boring, and —

My brows furrowed. Huh.

Cartography?

Assistant required for Five Elements land survey of Duoshui River and surrounding landmarks following recent upheaval. By appointment only. Selection required. See details overleaf.

- Xu Lin, on behalf of Tang Duhai

That sounded… interesting. I had no idea where the ‘Five Elements’ bit came in compared to a usual topographical one, but surely trigonometry remained the crux of it. I thought it over, taking the sheet off the board. Interested candidates were to report to the Tang clan estate a few days from now for a selection test. I had no experience at all in making maps, but it wouldn’t hurt to try. It was only an ‘assistant’ job, right? They hadn’t even designated a minimum cultivation rank?

I made sure to take in the details, then returned the notice to the board. There weren’t any details about just what the selection would involve, but it wouldn’t hurt for me to get some quick experience for when they interviewed me.

Higher up the mountain, and across the great bridges that spanned the distances between the peaks claimed by the sect, landmarks rose in the form of pavilions, training grounds, gardens, ornate staircases and the like. Behind me were the facilities I’d grown familiar with over the past month in this new life.

Charting those seemed a good enough place to start.

Now, then. Let’s see… I’ll need a protractor or some other method of measuring angles, initial references for lengths, a large sheet of paper, some writing equipment, my trigonometry tables, a whole lot of patience, and…