Chapter 83: Chapter 83 – Proofs of Worth

After the first few tiers, levels, rings, whatever people call them, everything starts to blur a little.

Those first few are very much distinct. The first ring is for… hangers-on, really. If I were being demeaning I’d say it’s basically groupies, but that’s unfair to the families and friends and spectators, delighting in proximity of the people they love. The second ring, then, is for novices and children, for people who basically know nothing but are willing to try; you get enough easy lobs if you’re genuinely engaged, and you won’t get relegated.

After that is where it starts to blur.

I mostly play Hagah for a dozen rings. People are a weird mix of condescending and curious, past the first half-dozen; as the rules unlock through my climb, they treat it as a given that they can just throw some sort of tediously complex pattern at me and stymie me.

“The four-rule set is: count, vertex to the edge’s power; sort, number of edges; validate, only a prime total number of vertices; finally,” and there was an unfair rule if there ever was one, “separate out a number of each shape by the index on the color wheel that.”

Once I hit the thirteenth ring, the Hagah tokens are gone, which is kind of a shame, because I’d thought up a really neat five-layer that nobody had been able to solve, though one nephil had gotten really close before the gathered folks had started to shuffle around a bit, and they’d knocked their fists and muttered something distractedly. Instead of Hagah, I start pulling out proofs; I start with geometry and move on to trigonometry and calculus, but it turns out that Cadorans have a perfectly good understanding of all of those, and pretty soon I’m in the realms of pure mathematics and computational theory.

More or less my childhood jam, I guess. Not everyone’s a fan. So more than one interaction goes like so:

“What do you mean, demonstrate this?”

“I mean that this is true, for the conditions I’ve laid out; what’s the proof?”

“This is rank nonsense.”

The complainer’s some schmuck of a wind, bound to an array of bowls laid out in some sort of intentional pattern. It floats its disk over the main one, which I think would probably be a breach of etiquette for anyone else but for it, it’s clearly appropriate from an assistive perspective. “It’s not even that complicated!” I glare at where its voice is coming from, where there’s a rippling in the air that’s vaguely bipedal and hominid, if confused about how big it should be at any given moment. “I learned this when I was a child, so if you can’t solve it, maybe yield the center.”

“It’s not even a puzzle! I call for your relegation. Learn some manners.”

“A relegation vote.” This is a new voice, a gravelly-low gotz voice. “I have a solution for the puzzle; it is a fair puzzle. I vote for the relegation of Wind Five-Settles.”

That time, I don’t say a word until Five-Settles, which I guess was its name, is off the disk and heading down, and then the gotz squats in front of me and sketches out the proof; they’re right on the money, though their proof that a non-deterministic finite automaton isn’t any more powerful in theory than a deterministic one is less efficient, space-wise, than it needs to be. Still, for someone who’s never seen an automaton before? I’m impressed.

She tells me her name, the short version of which is Crushing Stonefall, and knocks her fists together. And so I keep rising.

I don’t repeat the same proof twice, but I do pretty often need to pull out a whole sequence of them, as the people I’m talking to are getting disgustingly clever. When they solve mine, I get to solve one of theirs; riddles, brain teasers, mathematical tricks and twisters, logic puzzles, and a category new to me, something they call clever crossings. It’s a staircase shape of words; the second word goes under the first one, shifted one to the right, and let me tell you it’s a wild moment of double take when I realize I’ve been reading backwards through Omniglot and not even noticed, and the third goes under the second one shifted another, and so on.

The clues are wordplay and instruction both, and it takes me a little while to get used to them. I get relegated once, laughing and calling it fair play, and then I come back with an absolutely vicious puzzle based on probability permutations, which I manage to use Interface and my Visor to manifest into a sort of what-you-ask-is-what-you-receive display in the main disk. The disk itself does most of the heavy lifting on it; it’s impressive, I’m impressed, and I study the runework on the disk while the tazi who called for my relegation gets more and more flustered.

It’s definitely mean-spirited of me to smirk the way I do, but fuck him, anyway.

You are reading story Frameshift at novel35.com

I pull out some of my favorites for the last few rings, mostly logic puzzles with a clever trick inside them or in their structure. There’s a game that they call Bombfinder and we called by a different name, where it’s all about pattern-matching on how many adjacent spaces are safe; I give someone a grid that, if you decode it after solving it, spells And So I Rise, which I think is clever, even if it did get a bit of a teeth-grind. There’s a game that’s a variant of magic squares; I’ve got a wicked variant called the Miracle that I picked up via the Interstellar Puzzle Quest, courtesy of someone I’ve never met but might like to one day who goes by Lee, and that one gets me a rise, too, eventually.

“I’m not saying that you’re lying.” The orc sitting cross-legged looks absolutely furious, but his voice is totally calm, though he grows a lot more formal after he realizes he just sort of accused the Magelord of definitely-not-lying. “In fact, I concede; let that be quite clear. But I would appreciate a hint as to the solution, and I will accept relegation if it is obvious.”

“So, we went over the general rules for the magic square variant, and you folks have that already, right? So nothing new there.” He nods slowly, giving a gesture that I’m guessing means continue. “Add two constraints. Constraint one: the L-move can’t contain the same digit, nor can two adjacent cells, neither orthogonal nor diagonal. Constraint two: orthogonally adjacent cells can’t contain consecutive digits.”

“To go with the columnar, row, and subgrid rules.”

“Yeah. And you only get these two numbers. Row five, column three is a 1; row six, column seven is a 2.”

“And with all respect, Magelord James, I ask for a hint sufficient to demonstrate that there exists a way forwards.”

I lean forwards, smiling wide enough to hurt my face. It’s not actually a complex puzzle, and there’s absolutely no wild twist or leap of logic, but the puzzle is beautiful. “To anyone listening,” I say in a carrying voice, “I advise trying to solve it on your own, yeah? Take a moment.”

While I say that, I’m drawing a series of lines. From the 1, I mark the adjacent and L-move boxes that can’t have another 1, and the columnar constraint from the base form; from the 2, I mark the consecutive constraints.

The orc’s fists come together like a thunderclap, and not a single voice calls for his relegation.

Ironically, the twenty third ring, penultimate of them all, gives me the least trouble. It’s been less than four weeks, as they reckon time here, since I crashed, or landed, really, any landing you can walk away from even if four nines of your boat is in pieces smaller than a kilogram applies quadruple to interdimensional travel into a gravity well and an atmosphere, but my point is, it’s been less than four weeks. And the first thing new thing I did that broke the System’s rules to the point where something got taken away from me and all I was left with was a stupid Feat was to make an Oracle, and that meant knowing exactly what isn’t an oracle. Or, in this case, doesn’t need one.

“So, I get the distinction between a rune ‘er a set a runes what eventually stops an’ one what doesn’t. An’ obviously you can’t have a runeset, in th’ abstract, what tells ya, fer any given set a’ glyphs ye hand it, whether that runeset runs till it’s outta mana or stops aforehand; ye’d just flip it and feed it itself, and then ye’ve a paradox.”

“Right.” The nephil towers over me, three meters tall even when sitting down, but they’ve already feather-gently tapped their fists together before asking for the explanation, and they’re rapidly understanding exactly what I’m talking about, despite the accent and mannerisms that Omniglot is rendering as over-the-top bumpkin. “But then how d’ye get t’ this, where ye can take a… two-tape bounded automaton, and wit’ that, tell ye if any two-tape’ll halt?”

“You’re overthinking it.” I grin at the nephil, or maybe I’m smirking. “I didn’t say that it would run in any sane amount of time, did I? C’mon, think about it, what’s the difference between the abstract runeset and even the most powerful actual runic computational machine?”

“Well.” They draw it out for about five syllables, and then gently, oh so gently, plant their face in their hands. “Th’ state’s finite. Ye jes brute force it. If’n it’s still runnin’ after… what, th’ fullest expression’d be space, state, ‘n alphabet?”

“Vaguely.” I shrug. “I don’t remember what the exact formula is, could re-derive it, I think the alphabet gets a multiplier or a power or something. But the point is, you can compute the longest possible computation that a finite machine can ever do, and just…”

“Wait that long.” The nephil shakes his head, grinning at me. “G’wan, git yerself up. Gavonne is waitin’, I figger.”

I’m already walking to the disk, nerves alight with tension and delight, stomach churning with anticipation. “Hope so.” I grin at them, before I look upwards again, and inwards, to that last platform. “Came all this way to see them, after all.”

You can find story with these keywords: Frameshift, Read Frameshift, Frameshift novel, Frameshift book, Frameshift story, Frameshift full, Frameshift Latest Chapter