Each new category page Goblin Cave unlocked raised further questions. A spawn template existed for each mob, for each category, for each tier. It was tempting to sit in place and attempt to feel out every pattern it could, to see the full breadth of the categories as it could find, but...

Well, it would take a lot of time and effort. Its goblin specialization had unlocked a spread of goblin-type mobs across the first five tiers, but it had fully unlocked every goblin spawn up to tier 8 (the tier 9, time spawn still eluded it). It had done this through an exhaustive and extremely tedious exploration of spawn state space, and it wasn't exactly in a rush to do that again, just for another set of what would undoubtedly be weak, difficult-to-spawn mobs.

It was ultimately a matter of combinatorics. Imagine having a set of one hundred ninety six options — say, the height of a goblin spawn: pick one from that set. Simple enough. Now imagine a separate set of options of the same degree — the precise density of their bones. These were both among the tiny fluctuations it could work into a spawn pattern: little ripples in the twisting of the mana thread that spawned the mob. But having picked two 1-in-196 options, the total combinations are multiplied: pairing each height with each bone density lead to a total of 196 times 196 options: 38,416. Add in further simple, cosmetic options: weight, muscle tone, fat distribution, skin color, skin coloration. Eye color. Organ color. Organ arrangement. Hair placement. Each one had thousands of variations, expressed in slight shifts in the tension of the mana thread, and they all stacked on top of each other in multiplicative effusion. Limited to 196 options for each item, and only those variations, and the total number of combinations became 16 octillion, 398 septillion, 978 sextillion, 63 quintillion, 355 quadrillion, 821 trillion, 105 million, 872 thousand and 896.

Now imagine that all but one of those options was unstable, imbalanced, and didn't form a successful spawn pattern, and it had to search through that stack for the single template with the correct resonance. The nature of spawn template 'balance' was much more abstract, defying the kind of physical description Goblin Cave applied to goblins.

It wasn't limited to brute force. Because the overall structure was ordered — 196 items per dimension — it was easy to move along any axis. Taking a smaller space, say, 'red', 'green', 'blue', and 'goblin', 'orc', 'troll', it would be easy to enumerate the indices by decomposing the two axes: let one change every index, 1 2 3, red green blue. Let the other change every third index, 1 4 7, goblin orc troll — and third, here, because the product of all lower-dimensional axes, in this case 1*3, was 3 — and then you could assign each index to a unique combination of the two options. The same logic applied to any space with independent axes.

It could feel through the indices of the hypercube thus defined, following the eddies of feedback, and it had long ago learned that there were certain periodic rhythms to the field. But that was only one part of the structure. Orthographic axes, in this formulation of possibility space, were the equivalent to multiplication. There was a separate kind of paired, branching structure, that was the equivalent to addition: one or the other, this or that. That, too, was trivial to construct — it had already done so, simply by saying "one of a hundred ninety six". But mixing the two, back and forth at different levels, on different axes, gave rise to more complex structures: no longer was the entire possibility space guaranteed to be a perfect, symmetrical hypercube. Instead, it would be a mix of this-and-that, full of eddies and prisms, branches. Instead of being able to extract a position within the space simply by keeping track of the size of each dimensional axis, it would need to construct a more involved symbol.

Those were hardly the only two ways to construct the space; they were the simplest two. There was an equivalent to exponentiation, in addition to addition and multiplication. There were other operators that were translated into this space. But all those were fundamentally still something like arithmetic, not too different really from adding 1+1=2. The big step was the axes: once they stopped being orthogonal and started interacting, letting the value of one axis scythe away or elaborate on the values of another axis, the entire manifold radically changed in shape: one left the static, simple realms of enumerative combinatorics and entered the choppy sea of logical constraint solving.

All of that was pure math: a statement of logical fact. This was the nature of mathematics: partially discovered, since it was a collection of logical facts that had existed and will exist eternally, and partially invented, since the slightest change in assumptions and structure, in angle of approach, in necessity's lens, provided an utterly different framework. One simply plucked the formulation one's eye fell upon, or curated from a selection of infinities.

The question was how to relate it, in even the smallest degree, to the real world. So it could construct a 185-quintillion-dimensional hypercube of spawn variances and it could align all its axes orthogonally so it could enumerate through every one of them, a number best described using scientific notation, without duplication or elision. It could even tackle the problem of non-orthogonal axes, which was needed to ensure it never enumerated through an impossible mana thread — one, say, where the collection of forces it was applying made the thread intersect itself and shatter apart. But what would any of that matter? What was the point of ever doing so?

That came to the second part of math: the generation of meaning. Why would it bother enumerating convolutions of mana threads, when it could very well feel things out itself? Well, for one, if it could actually map an enumeration to spawn state space, then it could tell a control node to sit there and do all the work.

That was far easier said than done. For one, the possibility space was utterly vast. Each pattern needed to have mana pumped into it on the scale of seconds. A single mindless control node twisting mana threads could spend centuries convoluting through useless corners of possibility space and never turn up anything useful. For two... well. It would have to do the mapping and charting. If its understanding of the actual interactions of mana threads was incorrect, then it wouldn't matter how elaborate or involved a possibility space it constructed, or how flawless its execution of its index transforms; it would be wrong from the start, simply because it had failed to make the space reflect reality.

It was frustrating. Not the spawning, but— there was a structure there, in the eddies and flows of spawn templates. It could feel at the edges of it, see that there was a shape there, but every attempt to codify it had escaped it. It was so big and involved that it felt like it could spend years simply trying to map out the edges of it, much less put together any kind of explanation for how it was structured in the first place. That was what it wanted to talk about — 'DID YOU KNOW THERE ARE CERTAIN RESONANCES BETWEEN DISTANT FOLDINGS IN A SPAWN TEMPLATE, AND I THINK MAPPING THE ENTIRE STATE SPACE OUT INTO AN ENUMERATED FRAMEWORK WOULD REVEAL ARITHMETIC CONNECTIONS BETWEEN CERTAIN TRAVERSALS THAT MIGHT ALLOW FOR EASIER PINPOINTING OF VALID SPAWN TEMPLATES?' — but all they wanted to talk about was the relative valuation of different kinds of metals. Goblin Cave did not even have the words in their language to say it. Goblin Cave could hardly grasp at the shape itself. Having a control node attempt it would be rank arrogance.

This was what lead it to build the simulacra template. An imitation of the instructions to make an imitation creature. Amusing. This was partly to attempt to explain the process to anything that wasn't itself. It spun out the shape of a mob spawn — a [Goblin], for old time's sake — in a thread of gold. Then it had to thicken it and reinforce it so that the thread didn't collapse in on itself. It added corrugations in some places to denote where the template's phase changed, muddied it with alloys to change its hue and shine to denote how the tension changed, made it thicker and thinner where the amplitude altered... ultimately, it was left with an enlarged figurine of a goblin made out of whorls and loops of golden thread.

All of the system-approved spawn templates fit neatly within the bodies of the mobs they spawned. Goblin Cave had always taken this as humorous artifice; such a thing wasn't necessary or even relevant. Plenty of its own handmade spawn templates had been messy skeins of mana that fit into no physical pattern, but since there were nearly-infinite ways to pack a given template into physical space certainly some of them would be shaped similarly to the thing they created.

That left it with a flat room of quartz with a golden goblin statue inside. This immediately rose questions with the adventurers, which was in part what Goblin Cave had made it for. It still held out hope that their responses would give it... something. Something it could attempt to draw meaning out of. Something engaging.

"Is that... gold?"

Of course.

"Looks like it. Some kinda... big goblin-shaped hairball?"

The particular adventuring party that had stumbled across the new room (on floor three, opposite to the doorway that lead to its experience-ranking hall) even had a caster in it. There was no sign of recognition.

"How much, uh," one of the adventurers started. "How much do you think it's worth?" they continued, in a lower tone of voice.

One of them peered closer. "It's mostly empty space," they said. "Even if you melted the whole thing down I don't think you'd actually get a lot of material. Plus— uh, I think the dungeon might. Get mad? It's not here to be loot."

WHAT METALS DO YOU CONSIDER TO HAVE LITTLE VALUE? it asked, writing on the wall. The adventurers grimaced and pulled back, taking a few steps away from the glowing lettering that appeared on the way, towards the familiar old dank goblin caves.

"Uh— tin? Maybe? Lead?"

Goblin Cave could work with that, maybe. Tin was less lustrous, and lead was heavy and soft, but it would be nice to be able to make anything and not have the first response to be consideration of its value.

"Wait, can you... make gold? Like you've been making the bronze?" one of the adventurers said. The other two with them made the shushing motion that Goblin Cave was beginning to understand meant 'stop talking'. "I thought your goblins had to die to make loot, but you can just make it?!"

This again. YES, it wrote. WHY DO YOU VALUE METALS?