109. Rocks to Rules: Climbing a Rickety-But-Interoperable Semantic Ladder
DO NOT TAKE THIS SERIOUSLY YET. I PUBLISHED THIS WITH A LOT OF LLM INFILL TO HAVE IT VAGUELY COMPLETE AND REASONABLY CORRECT RATHER THAN EXTREMELY INCOMPLETE AND UGLY, AND TO BE ABLE TO POST 110. I WILL COME BACK TO THIS BY THE END OF THE MONTH; THIS IS JUST EXTREMELY OVERDUE ALREADY. ANYTHING NOT IN ARIAL SHOULD BE SUSPECT. THIS IS NOT IN FINAL FORM.
(Epistemic status: A promising but weird research direction in agent foundations and philosophy of language. A half-built conceptual tower whose mortar and paint are both still wet: please excuse our mess while we innovate. Some of it, I'm confident in as pretty much right; some of it is merely suggestive; probably much of it is wrong or incomplete. Certainly it lacks the math it'd need to be truly correct. The prior art here is strange and thin: Gärdenfors, Tarski, and the later Mohists make for odd bedfellows, and I can't tell whether that's a warning sign or a moat I can easily clear. I gave the simplest parts of this as a talk extremely recently in Berkeley at a luminously-named venue for a conference with a Grecian name. For JSW, but also AD, GD, PR, JRM, DK, MM, and EA; I hope they enjoyed the oranges.)
Have you ever seen a pop culture corporation argue itself into a laughably self-defeating position, twisting ontology and linguistic philosophy around, undermining the very framework they painstakingly set up in their stories, just to make a few bucks? You're about to. Picture this: it's 2003, in the United States Court of International Trade, and the court has just now been asked to rule on whether the X-Men are human. According to US law, "dolls" are figures representing humans, and "toys" are anything else; under the tariff schedule of the day, it's the latter that gets taxed at a higher rate. If you're Marvel, what do you do? Obviously, you send lawyers to argue the X-Men aren't humans and never were! Never mind that you've cut the legs out from under the entire frame your superhero stories live and breathe: you've made a quick buck, dodged import taxes, and ignored narrative in favor of legislative victory, and that's the real win. When unstoppable real money met an immovable class of noun, the noun class moved.
Now swap the tariff schedule out for a reward function and read that paragraph again. Specification gaming is the exact same maneuver run by a different litigant in a different court to similar ends: hostile category re-drawing, adversarial downward-binding, with categories relitigated from above by whatever's got stakes and leverage. (Hold on to that idea; we'll ground it better by the end.)
One more piece of scene-setting, because we love our historical witnesses to our hot fresh epistemological constructions, here: some 2,300 years ago, the School of Names was one of the foremost philosophical traditions in China. We know this because their works survived at all. The Disputers, as they were sometimes known, spent entire careers on the paradox of whether a white horse is a horse; they were mocked for it by every other respectable school of the Warring States period from the Confucians to the Daoists, and then Qin Shihuang (probably) burned their scrolls. Here's the thing: I think that they were on to something - mockery, fire, white horses, and all. Blog posts are a little harder to burn than scrolls, and in the modern day I can appoint a great many more Disputers. (Gentle reader: your job is to break what follows and hand me the repair. Dispute like - and with - the best of them.) As for what follows? What binds; in what order; how it is shared; what deforms it; and given that this is a research direction and not a victory lap, what theorems are missing. (What shame, what agony, for JSW to point out that it is now me who lacks sufficient math in their work.)
To take a leaf out of my own book (see "32. What Do You Want That Definition For, Anyway?"), time to tell you what I even want this conceptual structure for. Take two idealized reasoners - probably Bayesian ones - with similar predictions about the world but potentially different models of that same shared world; they trade messages, seeking to communicate. (This is the "interoperable" in "interoperable semantics".) The tokens that make up their messages may be categorized as a ladder's worth of types, which I'll call "binding-types" or "semantic types". Each such rung - each such type - is characterized by what types the two reasoners must already jointly understand in order to translate between them. Rung \(n\) is specified by a set of translatability conditions over Rung \(n-1\): the conditions under which your rung-\(n\) thing is guaranteed to be intelligible as a function of my rung-\(n-1\) terms. That right there is the JSW-native framing that proposes to let two Solomonoff inductors sharing no language still figure out how to communicate about drinks at a bar, and which stopped so abruptly after sketching out precisely how and gesturing at how to talk about what kinds of drinks they are. Better yet, it thus comes with a stark acceptance criterion that I apply to every rung: if I can't cash it out in terms of simple everyday objects and situations, it's not worth the glucose spent to think it. A universal model of communication had better be universal, and had better be something you can ground out in whatever seems to you to be everyday. "The red cup is on the table; I pick it up." A model of semantics that waffles and has critical trouble with a sentence like that is nothing but foulest sophistry.
Alright, enough alluding to the semantic ladder without defining it. What's going on with it? What we have is a hierarchically arranged set of conceptual spaces - a semantic ladder. Those spaces have assorted points within them, each of which represents an object or element from that space; they also have axes of variability. Here, we're operating among an existing family of frames: Gärdenfors's conceptual spaces, Wentworth's interoperable semantics, "words pointing to clusters in thing-space". (Nouns, actually, for that last.)
We look around, and the universe we see has lots of assorted stuff in it, and they're doing lots of actions, and the stuff has all sorts of qualities, and the actions are done all kinds of ways. Within all of this fertile chaotic primordial ooze, we declare: "Let there be nouns!". And there are nouns, given to us in some more or less natural way by clusters of qualities in the conceptual space of thing-space. So far, so anodyne, if you know what words are and how ontology works. The thing is, I take this significantly further. I stick to clear next steps implied by the LessWrongian frame: if we have a cluster in thing-space, we can move around inside of the region that some noun-shaped concept marks out - "rock", say - and subdivide any given such cluster hierarchically by properties that points within the subcluster share with each other, but don't share with other elements outside the subcluster. These internal coordinates give us useful subclassifications of the noun; ways in which we can locate a point more precisely within a cluster in thing-space, avoiding leaving that cluster. We can then figure out whether a given internal coordinate shows up decently often across noun-clusters; if it does, then we might tentatively abstract an adjective corresponding to that direction: "hard", say, or "blue", or "tasty". For every type, we can construct a typed hole: so it is here, where we get pronouns, pointers, and question words like "it", "that", and "which": words that ask to be replaced with the right sort of word. And that's where the story ends: adjectives are where we run out of road.
...is what I would have to say if I hadn't thought about this more - this is the part where I add to prior art. We've implicitly seen two operations already: "cluster", where we take in some raw point-cloud sort of distribution and return a set of conceptual buckets that comprise a type, and "specify", where we then look at internal variability shared across a few conceptual buckets and return a modifier corresponding to that shared direction. Now I can start adding a few more. The very first one, I call "predicativize": take an interior coordinate, a modifier, and mint a new 1-ary predicate from it. "Hard", the direction, becomes "is-hard", the predicate, the claim. Tied to this move, equally facile-looking, is "saturate" in Tarski's sense: take something that has a place where one or more arguments are supposed to go and fill them. These may seem like trifling moves, but it buys us deceptively much: it's right here that we can first construct a full sentence, and so it's here that we can first be wrong, can be mistaken, can lie. We should take a moment here to note that in Korean, verbs and adjectives are not so cleanly separable as they are in English: you can tense-inflect adjectives fluently to talk about something that will be blue or used to be tasty just as easily as you can talk in English about the darkening of the sky in the evening. In Lojban, brivla blur the distinction between verbs, adjectives, and even nouns; it may be a constructed language, but it's one that people can speak naturally and have found useful. This may look like a problem for my frame; it is not, and we'll see why in a moment.
Next up, "arity-climb": we already have unary predicates; we may as well do a little cheeky uncurrying to, having first pointed to the abstractable modifier of (e.g.) "inside-the-box" as shared between assorted kinds of nouns for small concrete objects, then unfold that deeply awkward modifier into a preposition of place, or a simple transitive verb of relation: "inside", "from", "with", "above"; "loves", "wants", "has"; all sorts of binary and general n-ary relations. For the moment we're still in a static frame, if we squint a little and treat relational verbs that most naturally play out over a period of time as existing in a single timeless moment.
Of course, the very next thing that we do is resolve this tension and "temporalize". (Though I'll cheerfully defend this admittedly arbitrary choice of how to linearize the poset: binary configurations are strictly poorer semantically than time-indexed trajectories, and I want for this ladder to run from poor to rich, simple to complex.) Once time enters the picture - clock time, subjective time, even logical time - configuration-space enriches into path-space. This is the part where we get all the rest of the verbs: verbs of motion and location-change, possession-transfer, and general transformation, along with path-prepositions like "along", "towards", and "from".
No need for new operators for the moment either: just as nouns gave us adjectives, verbs and prepositions (especially in light of temporalization) give us adverbs as interior coordinates of configuration-space and path-space; this is where we also get tense (when it happened), aspect (when it started and stopped happening), mood (whether it happened), and evidentiality (how you know it happened). "Quickly" is to a trajectory in path-space as "hard" is to an object in thing-space, and that's not a cute coincidence, but glorious parsimony.
The next part is a little strange but justified. Just as we predicativized adjectives into simple stative verbs, thus do we also notice that "never" and "always" are such curious adjectives, and "should" such a strange modal verb. Looking at whole sets of trajectories, especially those marked with "never"s and "should"s, what makes the most sense to call the resultingly filtered sets? I think the answer is rules. A new operator, then: "constrain". Just as the nouns could have been anything arbitrarily strange or stupid, depending on the things, and the verbs could have been anything arbitrarily strange or stupid, depending on the actions, so too the rules: "kept" versus "violated" is nothing more mysterious here than set membership; a given trajectory either is or isn't in the permitted set. There's no need to posit enforcement here: this is just about convergent concepts and the syntactic and semantic substructure that makes them possible. The modifer
[beneath this is a part that I have not written up yet, at least in part; there's redundancies to merge at the least]There's no need to posit enforcement here to define the set: this is just about convergent concepts and the syntactic and semantic substructure that makes them possible. But look closely at this edge all the same, because it is not predicativization wearing a bigger coat, and I briefly mistook it for one. The ascent decomposes in two: first, yes, a predicativization-shaped move — path-coordinates mint trajectory-predicates, "is-swift," "passes-through-the-market," descriptions still, no teeth. Then the genuinely new operator, the deontic lift: from is-F to let-all-be-F, from description to prescription, and no amount of stacking descriptions gets you there for free. This edge has an older name — it's Hume's guillotine, drawn as a rung-transition — and if the bridge-smearing prediction is worth anything it should smear here too. It does: generics. "Dogs bark." "Boys don't cry." Grammatically a description, functionally a rule, and every parent and drill sergeant knows which one they're uttering (***need: verify the normative-generics literature before citing — Leslie?). The grammar even has a name for the smear — the gnomic, the mood of timeless truths — which stands revealed as the mood of bids: a generic is a move in the boundary war dressed as a field observation, doing politics at the noun-border while claiming to do zoology. And one honest admission, squaring with the no-enforcement point above: defining the set costs nothing, but the lift implies a lifter. The deontic force isn't in the syntax; it arrives with whoever has stakes enough to hold the constraint against its violators — which means the dynamics we'll meet properly at the pact rung are already reaching down one floor early, and "pure rules," adopted by nobody, exist in R the way unclaimed land exists on maps. Should-ness enters the ladder exactly where agents do; if you're aiming this apparatus at values, read that as load-bearing rather than embarrassing. The modifier rail keeps pace — "strictly," "usually," "by default" are rule-coordinates — and notice the Zipf tell while we're here: the highest-frequency binding machinery keeps getting compressed into short words, and then, diachronically, into grammar itself. Tense, aspect, mood, case: wherever a language has ground a mechanism down to an affix, suspect a load-bearing rung underneath. This is the rung-detector, and we'll hand it a work order when the room's objections arrive.
Conventions, the shoulder just below the summit: precedent plus expectation, with no adoption anywhere in sight. Which side of the trail you pass a stranger on. Nobody signed anything; everybody knows; it mostly holds. And notice what this is, structurally: not a rung but the smear on the 2→3 bridge — Lewis-force operating directly on rule-space with no pact object anywhere, dynamics without statics. The smearing prediction, run on the top bridge, pays out one more time: the vocabulary here — "custom," "norm," "tradition," "usage" — is the most category-unstable in the whole stack, exactly as a smear should be. Keep this shoulder's poverty in mind; it makes the next rung's wealth visible.
Adopt. Now the strange one. Let R be the space of expressible rules. It is enormous, and it is almost entirely junk — irrelevant, unsatisfiable, or mutually contradictory, a landfill of "every third Tuesday, hop." A pact is a set of agents A, with |A| ≥ 2, jointly binding themselves to some subset S ⊆ R. A commitment is the |A| = 1 case — and it is the special case that turns out deep rather than degenerate, because one agent across time-slices is a coalition across bargaining positions. (Ainslie worked out the intertemporal bargaining, if you want the literature; if you want the phenomenon, consult your diet's ongoing negotiations with your midnight self.) And a conjecture, flagged as exactly that: adoption is the one operator on this ladder that no lone agent can run at n ≥ 2. Everything below it, a sufficiently patient hermit could build alone in the woods. This rung is where the woods stop sufficing.
Pact-space has structure worth the name. Call a subset of R jointly satisfiable if some trajectory keeps all of it. Satisfiability is downward-closed — deleting rules cannot create a contradiction — and a downward-closed family of sets is an abstract simplicial complex, K(R). Viable pacts select faces of it. Maximal faces are maximal consistent rule-sets (Lindenbaum, wearing sunglasses). Two pacts are compatible exactly when their faces share a coface. That is the statics: what a pact is. What makes a pact bind — mutual expectation, common knowledge, the whole Lewisian apparatus — is a separate layer entirely, a dynamics on pact-space. Do not let anyone sell you the statics as the dynamics, or the reverse; a solid half of the confusion in this neighborhood is that sale, made in both directions daily.
Why does this get its own rung, rather than a bunk in the rules dorm? Machinery inventory. To build a pact you need: the power-set move over R; an adoption operator; agent-indexing; and, for n ≥ 2, the mutual-expectation apparatus. None of that machinery exists at the rules rung. New machinery, new rung — I've gone back and forth on this all summer, and as of this writing the inventory argument wins.
And one thin arrow running the wrong way, down the whole right margin of the board: reify, written ⌜·⌝ — Quine's corner-quotes, not the ceiling function, and I will be taking no further questions from the floor-function lobby. Reification takes any rung and mints a noun from it: quotation, nominalization, "the rule that—," "the pact whereby—." This is where meta-levels come from, free of charge. File it away that this is also the operator that manufactures, all day long, exactly the deterministic-function variables that one of our four formal programs is uniquely comfortable hosting.
Surface grammar, throughout all of this, is not binding structure. Korean and Lojban scramble the surface categories and the bindings stay put. But the theory says something sharper than "ignore surface grammar," and I want credit for the sharpness: the bridges should smear. Prediction, falsifiable-ish: wherever the ladder posits a bridge, cross-linguistic typology should exhibit an unstable surface category straddling it. Two bridges, two smears, both found: at the adjective/verb line, Korean's descriptive verbs and Lojban's brivla; at the statics/dynamics line, place-versus-path prepositions and Talmy's entire verb-framed/satellite-framed typology, in which the path component migrates between the verb and its satellite depending on the language. (Jackendoff had the decomposition written down decades ago: PATH functions eat PLACE arguments; TO(IN(house)) = "into the house.") The contrapositive is the useful part: a proposed bridge with no typological smear is evidence against the bridge. I would like more of my claims to be shaped like that, and I commend the shape to you generally.
[above this is a part that I have not written up yet, at least in part; there's redundancies to merge at the least]
| Level | Space | Entities | Modifiers | Pro-forms (typed holes) | Reached by |
|---|---|---|---|---|---|
| 0 | thing-space | nouns (rock, fox, star) | adjectives (hard, tasty, blue) | it, this, who/which; such, so | literally just looking around and thinking |
| 1 | configuration-space | place-prepositions (within, on, around); static relations (genitives, binary relations, ...); some corresponding stative verbs (lives (in many senses), sees, likes) | adverbs | here, there, where; completely, almost; "the X-er"/"the X-ed" | predicativize and saturate, then arity-climb |
| 1′ | path-space (time enters) | verbs of motion, possession, and transformation; path-prepositions | more adverbs, TAME | do so/it/the same; thus, so, how; thither, whence (largely obsolete in English!) | temporalize (remember, persist, predict) |
| 2 | sets-of-trajectories | rules | strictly, usually, by default | ditto, likewise, as above, mutatis mutandis (register-bound); "unwritten rules"? | predicativize path-coordinates, then the deontic lift |
| 3 | pact-space | pacts (commitments at n = 1) | with-carveouts, unilateral, revisable | "the usual," same terms as last time, so moved / seconded, amen (ceremony-bound) | adopt |
What's the pattern here? Why some entities, so strangely precisely carved out, treated as first-class, and not others? What we have is a core ladder and its dependently resonating offshoot. Within each space I identify, there are things; the type is clearly inhabited. Those things can then be clustered into first-class entities: regions of density, things to point at. These form the primary ladder: nouns, something like "most verbs and also some other stative and relational words", "rules", and "pacts/commitments/agreements", as we ascend. Looking more closely at the clusters, we always find it useful to describe elements within a cluster in terms of something like local coordinates within its cluster - where those local coordinates need not be the same as those on the larger space, and might even be given in terms of other clusters (sky-blue, lightning-quick, state-legibly). Some concise operator then lets us abstract similarly used modifiers from across clusters to move to the next space up the ladder - enriching the space, minting predicates at bridges, and the like. It's worth putting some effort in to keep these two ladders separate; surface-grammar in whatever your native language is often comes from eliding the operator.
Admittedly, the canonical object here is a partial order, and a decidedly provisional one, although surely rules must come after rocks. PR made the point that from the right frame, it's verbs, not nouns, that should lie at the very bottom; we will address her commentary in good time. The levels here hold types of entity solidly, and modifiers on those entities live mostly on the level of the entity they like to modify but put a foot on the next rung up; this is no accident nor messiness but exactly how we find the bridges we need.
[beneath this is a part that I have not written up yet, at least in part; there's redundancies to merge at the least]No second towerSaturation's products — assertions, the things that can be wrong — have been haunting this climb without a listed address, along with their pro-forms (yes, no, "what she said," ^this). An earlier draft solved this the expensive way: an entire second tower of claim-spaces beside the object-ladder, with new staircases and a new operator family to staff it. Symmetric, elegant-feeling, and unearned — which, for a young theory, is just a slower word for wrong. So instead, the razor that killed the tower, stated for reuse: new ontology only where decomposition provably fails. The pact rung is the exemplar; it earned its rung by machinery inventory, by showing that no lower-rung construction yields adoption. Everyone else pays the same toll or decomposes. Watch the tenants decompose. Assertions. The content of a claim is already a noun — that was ⌜·⌝'s job description from the start: the arrow makes nouns out of rungs, sentences included. The asserting is an act — a move made by an agent, living where acts live, answerable to norms a few paragraphs south. Use and mention were two different things all along, one an act and one a noun; the surface word "sentence" straddles them — and that is a prediction cashing out, not an embarrassment. The famous, literature-consuming tangle of proposition versus sentence versus statement versus utterance versus claim is exactly the smear the bridge-smearing rule forecasts over a straddled distinction: philosophy's century of disentangling, reread as typological instability observed in the wild. Truth itself never needed rehousing — it entered at the ground-floor bridge, purchased with the ability to be wrong, and has been fine there the whole time. And Tarski's seat at my thin-prior-art table now costs one sentence: ⌜snow is white⌝ is true iff snow is white. Disquotation is the claim that ⌜·⌝ runs faithfully. No further apparatus. The pro-sentences sort accordingly: "what she said" and ^this are anaphora on reified utterances — pro-nouns over ⌜·⌝-images — while yes and amen are assent-acts, ceremony-bound. It should have tipped me off that the pro-form column had already seated them beside "so moved." The connectives were never architecture; they're vocabulary in borrowed clothes. Composition exists at every level — "salt and pepper" conjoins nouns without anyone building noun-logic a tower — and the bare skeleton (and, or, not, if) is as short and frequent as maximally load-bearing machinery should be, per the Zipf detector. The interesting question is what each connective borrows: "and then" wears path-space's clock; "but" and "although" are conjunction wearing a rule-modifier, an exception flag raised against a standing usually; "because" borrows dependency structure, and splits — where grammar bothers — into a causal and an evidential because; "or else" is disjunction wearing the pact rung's enforcement face. Ask any parent. The census question is what each borrows, and from which floor. The evidentials relocate honestly rather than triumphantly: allegedly, reportedly, as-I-saw-it are modifiers on assertion-acts, provenance-coordinates — the table above bets they ride the modifier rail with a foot on the next rung up, and which floor the assertion-acts themselves finally file under, I'm leaving open. I'd rather carry an open question than a spare tower. Truthfulness — which is not truth — is a norm on assertion-conduct: assert only what you take true. A norm of that shape binds at pact grade; Lewis built language itself on exactly this standing convention of truthfulness and trust (***need: verify — Lewis, "Languages and Language"), and lying is defection against that pact, which is why it stings differently than error does. And proofs: a proof is a rule-licensed sequence of reified contents — which is why you can print one; being noun-strings is formalization's entire point — while the reason exhibiting a proof ends an argument lives nowhere in the sequence. It lives in the standing pact mathematics runs: in the taxonomy waiting above the treeline, a proof is a protocol for belief-transfer, a pact compiled to run trustlessly. You needn't trust me; run the checker. Everything higher requires lower stuff, on schedule — reification, then rules, then the settling force from the top of the tower. The one tower there is. The white horse climbsNow the schema — the one thing on the board I'd tattoo on the inside of the field's eyelids, if the field would hold still: ext(m·e) ⊆ ext(e) — and yet — latent(m·e) ≠ latent(e). Gloss: ext(X) is the extension, the set of instances X applies to. latent(X) is the predictive bundle the label carries — everything you're licensed to infer once you know X applies. Modify an expression, and the extension can only narrow or hold still. The latent, meanwhile, moves. Gongsun Long's sophism — 白馬非馬, "a white horse is not a horse" — derives the negation of the schema's first half from the truth of its second, and the trick is not one error but one error per rung: "to eat quickly is not to eat," at verbs. "To follow a rule strictly is not to follow it," at rules. Climb as high as you like; the scope error climbs with you, fit as ever. The sting in the schema's tail: whether the first half even holds depends on the modifier's type. "White" on horses is subsective — a white horse is a horse, and the paradox dies on contact. "Fake" is privative — a fake gun is no gun at all. And "coerced," as in "coerced agreement," is privative by codification: some ledger, somewhere, with someone's hand on it, ruled that a coerced pact is void — and could have ruled otherwise, and in other centuries did. The room asked whether this typology infects adjectives and not just their nouns, and the answer is yes, per-modifier and per-head all the way up both rails — "white" means differently on wine than on horses, comparison-class trouble rather than privation, same five letters, different clerk. Who decides which modifiers are which is not a lexicography question. It is the top of the ladder, reaching down. And because consilience is the house epistemology: the later Mohists, in the Xiaoqu, had both halves of the schema — "riding a white horse is riding a horse," and yet "killing a robber is not killing a person" — mapped, worked, and filed 2,300 years ago by people whose library largely did not survive to tell us. When a structure gets independently rediscovered across that kind of loss, take the hint. There is a real attractor here, and we are not its first visitors, only its best-resourced ones. Downward, and sidewaysIf the ladder were a crystal, reference would flow up only: nouns fixed by the world, everything above built on them, majestic, inert. Case law laughs at the crystal. You've met Toy Biz. Meet the chicken tax: a 1963 tariff spat over frozen poultry has been warping the sheet metal of the world's light trucks for sixty-odd years since — vans imported with rear seats installed so as to enter the ledger as passenger vehicles, the seats then shredded by the palletload on the far side of the border. And I have already told you about arguing pastry with the TSA as with the Fair Folk (see 104): frosting is not a gel in exactly the way a white horse is not a horse, in exactly the way your reward function's "helpful" is not your "helpful." So annotate the board honestly, and this is the pair of claims I'd most like stress-tested. T1: the machinery is acyclic. You cannot build the pact-rung's operators without the rungs below; the tower's scaffolding really does run bottom-up, and no tariff court can change that. T2: the extensions are cyclic, and stakes-dependent. What counts as a doll, a truck, a gel — the boundaries — get rewritten from above whenever enough money, power, or optimization leans on them. Both claims at once, no contradiction: the crystal-worshipper's error is denying T2, the cynic's error is denying T1, and the interesting theory lives in the coupling. It even comes with a prediction you could take to data: where coordination stakes are high, expect boundary-mutation pressure — measurable, if you like, as bunching at the notches of any schedule with notches — and where stakes are low, the crystal approximation holds and the lexicographers may rest. Sideways, too, because not everything that moves a boundary signs a treaty: capability moves boundaries without anyone's consent. Junk DNA became regulatory gold when we learned to read it; slag became aggregate; the internet's data exhaust became the most valuable training substrate on Earth. "Waste" was never a natural category — it is capability-indexed, the discard side of a cut, and the cut migrates when your tools do. I keep candied citrus peel in the pantry as a standing sermon on this point (see 97), and at the talk I ran the whole argument with a bag of oranges and a jar: by the end of the hour, the peels' extraction had visibly begun. Meaning pulled from what the type system discarded, on the timescale of one talk. While we're violating the crystal: why do bounded agents keep building trees over a world that is, if we're honest with ourselves at 2 a.m., rhizomatic? Because a tree is the data structure with affordable invalidation. When the world moves, a tree lets you find and fix the entries it broke; a flat associative soup makes you re-audit everything. Taxonomies and modes are what precipitate out of the flux under coordination pressure plus compute budgets — and sometimes, no irony anywhere, you really do need a tree. (The Deleuzeans in the room will be seated shortly; I haven't forgotten you.) Four programs, one missing objectHere is the section where I am supposed to unveil the grand unification, and here instead is me telling you the truth: what I have is a seating chart and a list of empty chairs. Four live formal programs each hold one face of this object, and mostly do not talk to each other.
One cell of the crossings table between these rows is filled (***need: the Gillen–Chiang '26 cell — link, and its one-line statement). The rest are shaped holes, and I will name the biggest one plainly, because it is the entire reason an alignment blog is hosting a linguistics ladder: the natural-rule conditions. Natural latents tells you when your "dog" is guaranteed to be a function of my "dog." Nobody has the corresponding theorem for when your "murder" — a constraint over trajectory-sets — is a function of mine. That is the translatability theorem for rules; it does not exist; and it is no coincidence that it is the alignment-relevant one. A reward function is a rule you hope binds the way you meant it. Specification gaming is what its downward audit looks like when you lose. The theorem I want is the one that says when you don't have to lose. I'll be honest about the seam, since I've been honest about everything else: as unifications go, this section is currently a promissory one — I've seated the programs at one table and pointed at the empty chairs, and the follow-through is the research program, not the post. If that disappoints you, good; it disappoints me too, and disappointment with a work order attached is the local currency. Reordered universes, or: why time comes in "late"Two of the sharpest shouts from the room were one question wearing two coats: why do nouns get the bottom rung? and why does time enter so late? — the first of them PR's commentary, promised its address above; consider this good time. The answer to both is that the bottom rung is forced by the environment, not chosen by the theory. Nounables are wherever the redundant, translatable information lives — and in our neighborhood of the universe, it lives overwhelmingly in persistent, localized, spatial correlations. Clumps. Rocks, cups, grandmothers. A universe gets a noun-first ladder if and only if its cheap redundancy is clumped, and ours, conveniently for the invention of pointing, is. But you can order a different universe off-menu. Consider the wave-worlds — open ocean surface, acoustics, a plasma — where nothing persists in place and durable identity is a mode of oscillation. There, the recurring temporal motif is the cheap redundancy, there is nothing clumped to point at, and the natural bottom rung comes out verb-shaped. Time enters our ladder "late" because our clumps let us defer it; a wave-world spots you nothing, and time enters on the ground floor. Cellular automata make an honest test-bed for the whole question: a glider in Life is a process through and through — pure pattern, no persistent substrate — and we nounify it anyway, the instant it proves localized and persistent. That's the filter, caught in the act. I have, it turns out, written this filter down before, wearing different clothes. "78. Why Everything is a Spring" runs the same two-step: (i) selection — what sticks around to be observed is the approximately-or-eventually periodic, the too-fast and the never-repeating being observationally forbidden to us; (ii) mechanism — perturb a stable equilibrium and get oscillation. The springs post's observables and this ladder's nounables are one filter applied at different rungs, and in a wave-world the two collapse into each other outright: the normal modes are the springs, and the springs are the nounables. When two posts written months apart click together like that without either being consulted, I take it as weak evidence I'm carving somewhere near a joint — weak, I said; put down the confetti. (So, to the Deleuze-and-Guattari contingent, as promised, your seat: you are not wrong that the flux is real. You are describing the wave-world's ladder — or the pre-cache substrate of ours, over which the trees are built for the invalidation-cost reasons above. The disagreement between us is about where the redundancy lives, and that is an empirical parameter of a universe, not a metaphysical loyalty oath. Bring me a rigorous rhizome-first binding structure and I will personally buy the drinks while we look for its bridges.) The parking lotThe talk ran under a traction rule — objections count iff they hand us a repair, a test, or a sharper definition — and the room obliged. Here is the parking lot, transcribed and lightly triaged. None of these are adjudicated; all of them are appreciated; several are now work orders.
Why care, if what you care about is alignmentBecause four separate payouts land on this one ladder, in descending order of my confidence. Value alignment is a pact-rung problem being attacked with noun-rung tools. "Load the values into the system" treats alignment as level-0 translation — get its "happiness" cluster near ours and hope. But the values with stakes attached are rules and pacts: murder is out of bounds is a constraint over trajectory-sets, jointly adopted and enforced, and the clerk fights over "coerced" and "consent" are level-3 politics all the way down. Aligning at the noun rung and praying it propagates upward is stacking basements and calling it a tower. The missing rule-theorem from the four-programs section is this paragraph wearing formal clothes — and the ladder adds one more usable edge: being a party to a pact is a machinery claim. Does the system host the adopt operator, the agent-indexing, the mutual-expectation apparatus? Type-checkable in principle, which beats vibes. Ontology clashes get coordinates. I have put a type signature on ontological mismatch once before (see 42); the ladder upgrades the mismatch from a scalar to a located event — a clash happens at a rung, and T2 tells you the aftermath is stakes-dependent boundary war, bunching-at-notches signature and all. When a capable optimizer's ontology and yours diverge, "where on the ladder" is the first diagnostic question, and "who holds the clerk's pen at that rung" is the second. The sample-efficiency mystery gets a suspect. Human children learn words from absurdly few exposures (***need: verify before citing — fast mapping, Carey? syntactic bootstrapping, Gleitman?) — a capabilities anomaly hiding in plain sight for decades. The ladder's answer-shape: the child is not searching label-space over raw sense-data. A new word arrives pre-typed; its rung slashes the hypothesis space by orders of magnitude before the second exposure; and the convergence theorems — natural latents, condensation — are exactly the reasons her latents land on ours rather than merely near them. Sample efficiency is what learning looks like when both parties climb the same ladder. Current systems brute-force the result with oceanic data; whether one could instead host the ladder natively is a question I will leave exactly as loaded as it sounds. And embedded agency touches down through the indexicals — offered at half confidence, the most speculative payout on the list. I, here, now are the coordinates of an agent inside the world it models, bound at every rung by a crosscutting piece of the apparatus I've kept offstage tonight for length — which tells you something about how long the full tour runs. Every value referent we might want to hand a system — keep humans safe; our endorsed extrapolation — arrives carrying indexicals whose binding must be performed from inside the very extension being bound. The de se problem, drawn on this ladder, sits at the crossing of that indexical machinery and the pact rung, and I suspect the crossing is where "value referent" stops being a philosopher's phrase and starts being an engineering spec. Suspect, I said. The confetti stays down. Above the treeline, and the asksAbove pacts the air gets thin and the objects get strange: norms, institutions, conventions-at-scale, protocols, constitutions, currencies, gods. My present unifying guess, held loosely: these are technologies for scaling pact-force beyond the mutual-expectation horizon. Common knowledge stops scaling embarrassingly early — Lewis-force is a short-range interaction — and everything on that list is a hack for propagating bindingness past it. A constitution is a pact about pact-formation. A protocol is a pact compiled to run trustlessly. A currency is a pact reified into a bearer-tradable object — and here I decline the armchair, because I run a small silver-backed instance of exactly this and can report from inside the lab (see 22 for the mechanism, 88 for the theology, and 104 for what happens when the note is presented for audit). A god is a pact internalized via a personified enforcer (***need: verify the big-gods / supernatural-punishment cites — Norenzayan? Johnson? — before naming names in public). And language itself is the strange loop in the middle of the whole apparatus: the one instance of the ladder that the ladder is written in, climbing itself, hand over hand. Open problems, in descending order of what I'd pay for them:
The Disputers' scrolls burned, mostly. Ours are cloud-hosted, which is a different kind of flammable. So here is the tower, half-built on purpose in public: scaffolding showing, mortar wet, holes labeled in my own hand. If you can break a rung, break it — and then, house rules, hand me what goes in the hole. A repair, a test, or a sharper definition; demolition without a move is mere vandalism, and the Mohists have been disappointed in that kind of thing for 2,300 years, and they're tired. Bring me rows for the table. Bring me smears for the bridges. Bring me, above all, the rule-theorem, or the reason it can't exist — I will take either, and pay in the house currency for both. The cut is real. It is also provisional. That's the whole theory; now go put your weight on it. | |||
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