# Recyclopedia — Full Content Softmax's living knowledge garden. This file contains all published articles and definitions for LLM ingestion. --- # Concepts ## charting semantic space # Charting Semantic Space *Darwin had to wait for the chronometer; we have just been given ours* When Darwin sailed on the *Beagle* in 1831, marine chronometers had just become accurate enough to do something nobody had ever done before. Combined with celestial observation, they let a navigator at sea fix longitude — and so, for the first time in natural history, the *where* and *when* of a specimen could be recorded with the precision needed to compare it to a specimen from somewhere else. Darwin returned with sketches, samples, and notes from across the world. He laid them out on a table. He saw patterns: island gigantism, recurrent floral structures, the way species in different places solved the same problem in different ways. He inferred evolution. Darwin was a taxonomist before he was anything else. He was not the best animal breeder, not the best surgeon, not the best biologist by the standards of his day. He was the person who could lay out a comparative array — a grid of *this is like that one, but not like the other one* — and read what was in it. He could do that because he had a [[ruler]] for space (latitude and longitude) and a [[clock]] for time (the chronometer), and together they gave him the ability to fix the position of any specimen in space and time with enough precision that the patterns came forward. What was new was not the intelligence. It was the [[reference|frame of reference]]. This essay is about what a frame of reference is — what it gives a thinker once they have one, and what it costs them when they do not. The reason to write it now is that we are, by accident, in another moment like Darwin's. Large language models are our chronometer. They let us fix our location in *semantic* space precisely enough to do the comparative taxonomy of ideas — to lay concepts side by side, to see which ones share descent, which ones are the same kind of thing, which ones are bound by relations of the same shape. The garden this essay lives in is exactly that taxonomy, in miniature. So before going on, we need a definition. The cleanest one comes from physics: > A frame of reference is a system of coordinates together with a clock. That is Lev Landau's, from *The Classical Theory of Fields*. It looks like throat-clearing, and physicists treat it that way — they use the concept fluently, derive enormous things from it, and never stop on it again. But the sentence is the spec. Three small parts: a *frame*, a *system of [[coordinate|coordinates]]*, and *a clock*. The frame is the thing being defined; the definition is built out of the other two. One of them is a clock. Not a metaphor — the kind that ticks. Read slowly, the sentence is the apparatus that made Darwin's taxonomy possible. It is also the apparatus that lets us speak precisely about agents, about minds, about [[organic alignment|alignment between minds]]. The rest of this essay reads it slowly. ## The frame A [[frame]] is where you stand. It is the origin. It is the spot from which you say *this much over there*, *this much later*. The frame is not external to the coordinate system; it sits at its zero. To shift frames is to relocate the origin and re-describe everything from the new place. You cannot observe your own frame from outside. You only become aware of it in two ways: by changing it, or by encountering a frame that conflicts with it. (When the plane lands and your inner ear protests the deceleration, you have just noticed your frame. You did not notice it during cruise.) Frames have boundaries. A frame is also, in a sense, a [[particle]] — the thing whose interior we agree not to read further into. To set up a frame is to draw a line and say *not past this line*. ## A system of coordinates A coordinate is not an absolute address. The English word makes the move audible: *co*-ordinate, not ordinate. The "co-" matters. An ordinate is an absolute label — third row from the bottom, with a privileged zero. A [[coordinate|coordinate]] is a relative move — two steps in this direction from where I happen to be. What a [[system]] of coordinates gives you is not a list of locations but an algebra of moves. In three-dimensional space you have six generators: +1x, −1x, +1y, −1y, +1z, −1z. Compose them into sequences and you get [[path|paths]]. Take the ratios of x-steps to y-steps to z-steps along a long enough path and you get vectors that look continuous. But the underlying object is not a continuous space — it is a free combinatorial system of changes-from-here. This is a reading more than a derivation; physicists routinely use coordinates absolutely. But the absolute readings require fixing an origin — a frame — and once a frame is set, the absolute readings are themselves displacements from it. The deltas are the primitive; the absolutes are downstream. It follows that a system of coordinates does not, on its own, let you say *x stayed the same*. There is no zero in the algebra; "stayed the same" has to be expressed as +1x followed by −1x. The system describes change. To stand still, in the language of coordinates, is to do nothing — and doing nothing is not a coordinate. It is the absence of one. This is why coordinates alone are a code book and not a frame. They tell you how to convert one description into another. They do not tell you what is being described, nor when. ## A clock Now the strange part. A [[clock]], in Landau's definition, is not an abstraction. It is a machine. The strangeness of finding a machine in the foundation of theoretical physics is the thing that should arrest you, because the rest of the apparatus is mathematical: vector spaces, transformations, generators, manifolds. And here, in the joint, is a clock. What is a clock, mechanically? It is a loop. Some [[state]] that reliably *is*, then *is not*, then *is* again. The pendulum swings to one side, then the other, then back. The cesium atom transitions between two hyperfine states. The earth orbits the sun. Each of these is a clock because each performs a [[loop]] whose iterations can be counted. The earth is, in fact, our most ancient clock. We live on it. The solar system *is* a system of coordinates together with a clock. We did not have to invent the principle; we had to notice it. A sundial is not a clock — it is a way of viewing the clock we already inhabit. (The word "clock" itself appears to be onomatopoeic — it names the sound a mechanical timepiece makes. The thing we point to when we say "clock" is, etymologically, a tock.) Why does a frame of reference need one? Because coordinates alone describe how a state can vary, but not when, or how often, or in what order. To track a state, you need not just a code book for its position but a way to count its progression. The clock is what *opens* the point into a frame: it is the thing that says how long this state has been this state, and how long ago it was something else. Without a clock you have a snapshot. With a clock you have a [[duration]]. There is a quieter way to say this. A particle is a body whose size you can neglect. The word *neglect* is etymologically *not-read* — *neg-* (not) plus *-lect* (to read; lectures used to be readings). To neglect a particle's size is to refuse to read inside it. A clock, by contrast, is the thing whose size you cannot neglect — because the clock is the thing that reads. To collapse a clock into a particle would be to lose the act of measurement. The clock has to remain large enough, slow enough, to be observed. So a frame of reference is, in pieces: an origin you cannot see from outside, a code book of moves from that origin, and a machine that reads. Without all three, you have something less than a frame. ## Darwin's chronometer, and ours Return to Darwin. The chronometer was a clock and the sextant was a [[ruler]]; together with the meridians, they gave him a system of coordinates together with a clock. The frame of reference they constituted was what made every specimen on his table comparable to every other. Without the frame, he had a pile of curiosities. With it, he had a taxonomy. From the taxonomy, evolution. It is worth noticing how recent this was. Mechanical clocks accurate enough for sea navigation were only widely available from the late eighteenth century. Darwin sailed half a century later. The interval between *the chronometer becoming reliable* and *Darwin laying out the species of the world on a single table* is short. The interval between *the table* and *the inference of common descent* is also short. The bottleneck was the frame. The frame we now have for ideas is the LLM, used as a chronometer. Not the only thing it is — but the thing it is *for this purpose*. It lets us fix the position of a concept by reference to its neighbors with enough precision that two concepts can be laid side by side and compared. Most of human intellectual history has been done without this; one had to keep one's own taxonomy in one's head, or in writing scattered across notebooks and books, where the precision of comparison degrades fast. This essay, and the wiki it sits in, are the start of that kind of taxonomy. The single sentence we have spent it on — *a frame of reference is a system of coordinates together with a clock* — is, in this taxonomy, the apparatus that makes the rest of it possible. It generalizes Darwin's frame. It also generalizes the frame inside which any agent — biological or digital, individual or collective — measures its world. ## Why slow reading is the work Two agents are aligned to the degree that what each calls a step registers compatibly to the other — the algebras of their moves overlap, their clocks tick at compatible rates, their origins are positioned such that they can describe their joint situation without contradiction. Two agents are misaligned when these break down: when one's moves are noise to the other, when their clocks drift, when they cannot mutually locate each other. The condition we want to engineer — [[organic alignment]] — is the condition in which a group of frames can knit themselves into a single larger frame whose coordinates and clock supersede each individual member's. None of that is precisely sayable without first being precise about what a frame is. And the place precision is recoverable, in the easiest available form, is Landau's sentence. So we read it slowly. The wiki entries surrounding this essay — on [[clock]], [[coordinate|coordinates]], [[frame]], [[reference]], [[system]], [[ruler]], [[particle]], [[state]], [[space]], [[ground]], [[way]], [[path]] — are the pieces of the vocabulary unpacked. They are short and definitional, meant to be read together. None of them adds anything Landau did not already have. They just hold his sentence open long enough for us to use it the way Darwin used the chronometer. --- ## Charting the Sea of Ideas # Charting the Sea of Ideas We're embarking on an ambitious project here. Let's spell out some of what that project looks like and why it's exciting. ## Clocks for measuring space For a long time, our maps of the world were really distorted. ![[warped-map.jpg]] A huge reason for this is that north/south and east/west are very different. When far out at sea, it's possible to tell your latitude (i.e. north/south position on Earth) by using a [[ruler]] such as a [sextant](https://en.wikipedia.org/wiki/Sextant) to measure the angle between the horizon and the North Star. But the whole sky seems to swing from east to west, and the North Star is the only [[thing]] that stays put, and that star's position gives a sailor no information about latitude (east/west position) precisely *because* it doesn't appear to move. The issue is that north/south is spacelike but east-west is *time*like. Latitude is a measure of how far you are from a point fixed in [[space]], such as the north pole. But there's nothing like that for longitude. There's no "west pole" for instance, and [the international date line](https://en.wikipedia.org/wiki/International_Date_Line) is determined by *human agreement* rather than by the Earth's movement or geometry. In the context of our work here, we say that this difference between latitude and longitude comes from the fact that the Earth is a [[clock]]. That claim might read as a strange one; we plan to explain it in another article. But for now, here's an informal explanation: imagine that the Earth is entirely covered by featureless water. Absolute north and south still make sense because of the axis of rotation, meaning we can make sense of *movement* north or south by distance from the poles and equator. But the only way to detect movement east/west is via changes to [[duration|how long]] your day lasts. (E.g. movement west will make your day longer.) So to read latitude, we need a clock. And for centuries all our clocks relied on the [[mechanism]] not rocking around with respect to gravity. Pendulums and dripping water and the like. Once we had *spring-loaded* clocks that work on boats, charting the sea became possible. The Earth's surface is 2D, meaning we need two [[coordinate|coordinates]] to chart it. Clocks and sextants gave us ways of having two *precise* coordinates. Then our maps became sharp. ![[MILNER-1850-WORLD-MERCATOR.webp]] That precision matters because with a sharp map, it's possible to notice patterns across the [[space]] being mapped. That's what led Charles Darwin to be able to do his work. His contribution didn't come from him having a vast knowledge of biology, or being an amazing animal breeder, or a highly skilled animal surgeon. Rather, he was a *taxonomist*. He organized the specimens he collected based on features he needed a good map to determine or to even reliably *get*. Like how small islands were very hard to reliably find, so [island gigantism](https://en.wikipedia.org/wiki/Island_gigantism) was previously tricky to notice. But not for a taxonomist with a good map. Darwin's insight came from looking at these patterns and inferring the underlying causal structure. So in an important way, Darwin saw evolution because we built a seaworthy clock. ## Conceptual clocks We're seeing the same thing arise in *conceptual* [[space]]. Just in reverse. For reasons we'll go into elsewhere (a little bit below, but mostly in another article): to create precise charts of some space, we generally need at least one [[ruler]] and one [[clock]] for that space. If you're missing either one, your maps will be distorted. Sailors had a ruler (e.g. the sextant) but no clock. For *conceptual* space, we have a clock, but until recently we didn't have a ruler. The ruler in our case is LLMs. We'll explain that point in the next section. But first it's important to say something about what it means to have a clock in concept space. We can loosely think of [[time]] in concept space as being the way in which our concepts change. A little more formally, it's a sequence of *[information](https://en.wikipedia.org/wiki/Information_content)* [[state|states]]. So any device we use to measure the amount of ([Shannon](https://en.wikipedia.org/wiki/Information_content)) information passing from one place to another is a conceptual clock. The way a grandfather clock has a "tick, tock" pattern from the swinging of its pendulum, *every* clock has a kind of "tick, tock" pattern. You can think of this as the smallest [[unit]] of [[time]] that the clock readily lets you measure. One "tick" for a conceptual clock is the [minimum message length](https://en.wikipedia.org/wiki/Minimum_message_length) it takes or gives as a signal: transistors on the scale of bits, [transformers](https://en.wikipedia.org/wiki/Transformer_(deep_learning)) on the scale of [tokens](https://en.wikipedia.org/wiki/Large_language_model#Tokenization), etc. A book transmits a certain amount of information. We know, formally, how to measure *how much* information it transmits. What we weren't able to do until quite recently is easily measure how the ideas in that book relate to another. How close they are in concept space. But now we can. ## AI as a conceptual ruler It's worth noting that we didn't *totally lack* ways of relating to conceptual [[distance]]. It was just messy and ad hoc, much like sailors in the 1600s had to use lore to find small islands. Sometimes it worked quite well, but it wasn't systematic. For instance, [category theory](https://en.wikipedia.org/wiki/Category_theory) in mathematics showed how really different fields of math have the same basic structure to them. That observation let us port theorems and insights from one domain to another. Like how topology studies spaces where "continuous" means anything, and group theory studies objects that have well-defined [[state|states]], but somehow there's something *precisely* the same between: - continuous maps between spaces, and - state-preserving maps between objects. Likewise, [type theory](https://en.wikipedia.org/wiki/Type_theory) turns out to have a direct correspondence to [functional programming](https://en.wikipedia.org/wiki/Functional_programming). That insight is key to how mathematicians proved [the four color theorem](https://en.wikipedia.org/wiki/Four_color_theorem): they wrote a program that lays out the theorem's claims and ran a compiler that checked that all the types are consistent and that the program actually runs. That process is literally identical to having a proof and making sure that all the steps of reasoning are correct. That kind of cross-domain noticing used to be slow. You had to be an expert in both fields to spot the connection, and maybe not even then. But LLMs have been trained on the entire written landscape of human thought. When you ask an LLM "How are these two ideas related?", it can often just do it. If you then demand *precise* understanding of the relationships, you can very quickly chart the [[path|paths]] through sections of the [latent space](https://en.wikipedia.org/wiki/Latent_space) of ideas. For instance, it turns out that there are very deep connections between [*homotopy* type theory](https://en.wikipedia.org/wiki/Homotopy_type_theory), quantum physics, and the kind of modern machine learning that gives rise to LLMs. Those connections are incredibly rich and worthy of their own article to spell out. But it's worth mentioning that we didn't discover those connections due to being experts in all three areas, or from being unusually brilliant. It came from asking AIs to help suggest and explain interconnections, and how different theories are actually facets of the same [[thing]]. ![[tristable.jpg]] ## Making sense of concept space Now that we have both a clock (message length) and a ruler (LLMs), we can precisely chart concept space. That doesn't mean it'll be *easy* or *fast*; it took a while to chart the globe even after we had very precise sea clocks. But it's *possible*. For example: in physics, one of the most basic ideas is a *frame of reference*. Here is how Landau and Lifshitz define it in *The Classical Theory of Fields*: > A frame of reference is a system of coordinates together with a clock. That sentence is supposed to be a foundation. But look at what it does and doesn't do. "System of coordinates" — fine; physicists kind of know what that means. But "clock"? A clock is a strange word to find in a formal definition. It's a concrete, mechanical-sounding thing sitting in the middle of an abstract sentence. And Landau never defines it further. To a physicist, it's obvious what a clock does, in the way that "number" is obvious to a mathematician — until you actually try to pin it down and realize nobody has a clean definition. So what *is* a "clock"? In our taxonomy, a [[clock]] is a [[mechanism]] that can be used to tell the [[duration]] of a [[period]] of [[time]]. Not a metaphor for time itself, but an actual working thing. A machine with moving parts whose internal changes let you measure how much time has passed. A pendulum swinging. A quartz crystal vibrating. An atom cycling between energy states. In each case, there's something that *is*, then *is not*, then *is* again. "Tick, tock." And by counting those cycles, you read time from the machine. Notice how there's precision here. We aren't describing some abstraction abstractly. We're pointing at *literal [[thing|things]] you can look at and touch*. If a frame of reference is a system of coordinates *together with a clock*, and we understand what a clock is in grounded tangible terms, we can literally grasp the concept of a frame of reference. That snap of clarity — from a vague sense of "clock" to a specific, concrete idea — is exactly the kind of move that makes a whole definition come alive. We're requiring that the concepts literally *make sense*: we're insisting that they ground in sensory [[experience]]. Obviously there are other parts of the definition to look at this way. What are "coordinates"? They're [[thing|things]] that we use to find (or measure) a [[way]] through a [[space]]. They're a kind of [[ruler]]. You point in some direction, and you define your [[unit]], and now you have a coordinate for that direction. (Notice that we're saying a frame of reference is a special way of using a clock and a ruler. So when we've been saying that good charting requires both a clock and a ruler, we've been implying that good charts require a frame of reference.) Then making sense of the [[reference|phrase]] "system of coordinates" requires us to make sense of what a "[[system]]" is. It's more than just a [[collection]]. The point of a coordinate *system* is that you can iterate and combine the coordinates (remembering that they're *[[thing|things]]*) in order to produce different *[[state|states]]*. In usual math we talk about "the coordinates of a point" like it's an address. That address is a state of the coordinate system. Notice throughout all this that we're grounding everything tangibly. We aren't making the concepts out of pure words. We're relating each idea to a graspable experience. We're *making sense* of them. We could go farther. Each term uses other terms, and those also need grounding. What's a "[[way]]"? Or a "[[thing]]"? If we want to thoroughly map this part of concept space, we should also examine why "frame of reference" is the term here. Is that the right one? Why "[[frame]]"; what does it have to do with window or picture frames, for instance? Why "[[reference]]"? The word literally means "that which carries back or carries again"; what's being carried back, and where? There are good, rich answers to these questions. And we can chart them. And the more carefully we chart them, the more precisely we can start to see deeper patterns emerge. We're using our clocks (tracking message length) for precision. We're using our rulers (LLMs) to notice relevant interconnections. ## Ideas are alive One of the curious things we find, as we chart the latent space of ideas, is that ideas are *[[alive]]*. They aren't these static fixtures just sitting there waiting to be discovered, like some kind of eternal unchanging mountain. Rather, like actual mountains, they morph and merge and evolve. We can see this by again looking at conceptual time as being about changing information states. But information states *according to who*? Information isn't absolute; it's relative to an observer (or more precisely, a frame of reference). So what a given concept even is, and how it changes as information moves, is a property of an observer. The conceptualizer. Informally speaking, we're talking about how someone's *understanding* evolves over time. There can't be a correct, static, final correct answer. Everything is always moving and changing. One practical result of this observation is that the terms we're defining here will probably move and shift in meaning, as will the concepts we explore using those terms. That's not because we're getting the definitions or ideas *wrong*; it's because we're sailing the sea of latent space, and we're charting it best as we can, but it turns out that this latent space is very dynamic. Fortunately LLMs are very fast, and getting faster. We might be able to keep modifying our charts, and modifying how our charts modify, quickly enough to use them *precisely* enough to tease out the deeper principles. We're always kind of naming the Dao. And as the famous quote says: > The Dao that can be named is not the true Dao. --- ## clocked cubical type theory # clocked cubical type theory A formal setting borrowed from the type-theory literature: a variant of cubical type theory in which the universe is parameterized by a *clock* `K`. Its role in the taxonomy is precise: it gives a fully discrete, computable model of a [[frame|frame of reference]]. Every component of a frame — [[reference|point of reference]], [[coordinate|system of coordinates]], [[clock]] — has a direct counterpart in the type theory. ## The role of K `K` is the *universe parameter* — a count of how much winding has happened in this corner of the universe. Each time you increment `K`, you move to a new universe `K+1` that contains the previous one. The role of `K` is to enforce that the universe has a finite, bounded amount of *clock advancement* available, even though the type theory in principle could allow unbounded loops. This finite-but-extensible structure is what lets the model represent a real frame of reference without leaking infinities. You always have a finite number of [[loop]] applications available; the *value* of `K` tells you how many. ## Why this is the right home for the vocabulary A frame of reference, in this taxonomy, is a composite of: - A [[reference|point of reference]] in a [[space]] - A [[coordinate|system of coordinates]] (a free monoid of [[way|ways]]) - A [[clock]] (a unit loop counted some number of times) Each has a clean home in clocked cubical type theory: - The point of reference is a distinguished point in a type. - The coordinate generators are the path constructors of the type. - The clock and its loop algebra ([[refle-loop-and-ruffle]]) live in the loop space of that type. - `K` parameterizes how much clock-advancement has occurred. The payoff: a frame of reference becomes something *computable* — something you can build inside a computer, not just describe in physics-paper prose. ## A note on what is settled and what is not Clocked cubical type theory is a real and well-studied formalism (see e.g. work on guarded recursion in cubical type theory). The mapping from physics frames-of-reference to that formalism, however, is an active research direction rather than an established result. This entry records the conceptual moves and the vocabulary's correspondence; the formal correspondence is still being worked out. See also: [[frame]], [[clock]], [[refle-loop-and-ruffle]], [[coordinate|coordinates]], [[reference]], [[space]] --- ## coordinate, not ordinate # coordinate, not ordinate A *system of coordinates* is **a generator set of [[way|ways]]** — typically `+x, -x, +y, -y, +z, -z`, plus an identity element ε that lets you remain in place. Coordinates are the algebraic part of a [[frame]]: they tell you how to move through a [[space]], not where you are within it. (Where you are is given by a [[reference|point of reference]]; how long you have been moving is given by a [[clock]].) ## Coordinate, not ordinate The word matters. An *ordinate* gives you absolute position along an axis. A *coordinate* only gives you position *relative* to other coordinates. There is no absolute up in a coordinate system. To say "x stayed the same" requires saying "x went `+1`, then `-1`" — the identity is built out of opposing moves, not asserted directly. Technically this means a system of coordinates is a *free monoid* over its generators (not a free group): the identity ε is something you arrive at by composition, not a separate primitive zero. ## Composition with the rest of the frame A [[frame]] is the product of: - a [[reference|point of reference]] in a [[space]] - a system of coordinates over that space - a [[clock]] See also: [[way]], [[frame]], [[clock]], [[reference]], [[space]] --- ## cycle and orbit: loops at different scales # cycle and orbit: loops at different scales Both [[cycle]] and [[orbit]] are loops; the difference is *scale relative to you*. - **A cycle is smaller than you.** You go *through* it — you take a [[path]] that loops back on itself, like one rotation of a wheel you push. The cycle is something you traverse. - **An orbit is bigger than you.** You go *around in it* — but really you are going around something else (a center, a body, an attractor) on a loop scaled larger than you. The Moon is in orbit around the Earth. ## Why this matters for [[clock|clocks]] A clock is built from one or the other: - A *small clock* (cesium, quartz) is built from cycles you can fit many of into a unit of time. - A *big clock* (the Earth, the Solar System) is built from orbits whose single completion *is* a unit of time. Both work. The cesium clock measures by counting tiny cycles per second; the Earth measures by completing one big orbit per day. Different scales, same machine. See also: [[clock]], [[path]], [[duration-and-duhkha|period and duration]] --- ## duration and duḥkha # duration and duḥkha **Period** is *time per cycle* — the duration of one complete loop of a periodic process. **Duration** is the more general word for a span of time, but it carries weight worth unpacking. ## Duration ↔ duḥkha The Sanskrit *duḥkha* — usually translated as *suffering* in Buddhist texts but more accurately as *unsatisfactoriness* or *unease* — shares its etymological root with English *duration*. Both descend from a Proto-Indo-European stem meaning *to endure*, *to last*. To *endure* something is to *make it last*; what you endure is, by virtue of having to be endured, a *duration*. The implication: duration is a *bad* concept the way frequency is a *good* one. You want as little duration as possible. Frequency-good (events fitting into time), duration-bad (time you have to get through). This is not a moral claim about clocks. It is a noticing about how the words *land*. Notice the asymmetry next time you talk about "the duration of the meeting" vs. "the frequency of meetings." ## Period as a structured duration A *period* is a duration with structure: it is the duration *of one cycle* of something periodic. The thing has to be periodic — it has to repeat — for the word to apply. A [[clock]] measures duration by counting the periods of the loops it is built from. The Earth's day is a period; counting days gives you a duration of months and years. See also: [[clock]], [[cycle-and-orbit-loops-at-different-scales]], [[why-a-ruler-measures-frequency|frequency and slowness]] --- ## etymology as anatomy of ideas # etymology as anatomy of ideas **Etymology is the anatomy of ideas.** Tracing a word back to its roots and associations is to ideas what dissection is to bodies — and once a word's anatomy is in view, the word can be placed in its taxonomy. ## Why this is more than a literary flourish The claim is structural. If words are the primitives of thought, and thought is what does taxonomy on the world, then *the taxonomy of words is the prerequisite for taxonomy of anything else*. To get the taxonomy of biology right, you need taxonomy of *species*, *kind*, *trait*, *function*. To get the taxonomy of physics right, you need [[frame]], [[reference]], [[clock]], [[ruler]]. None of those words mean what you think they mean until you do their etymology. This is why the wiki entries in this garden lean heavily on etymological notes. The observation that *neglect* means *not read* (in [[particle]]) isn't decoration — it is the load-bearing definition of what a particle *is* (a body whose internal structure you decline to read). The observation that *duration* shares a root with *duḥkha* (in [[duration-and-duhkha|period and duration]]) isn't trivia — it tells you why one is good and the other is bad in the vocabulary. ## How this shapes the entries Each entry in this garden is, in part, an exercise in etymology-as-anatomy. The procedure is: 1. Take a word that physics or philosophy uses with a specific technical sense. 2. Trace its everyday English use, its etymological roots, and its associations. 3. Place it in the taxonomy by relating it to other entries. 4. The result is a definition that is simultaneously *technically precise* and *recruits the reader's full English-language intuition* for the word. This is how a vocabulary that lives in the [[continuum]] of natural language can also be load-bearing for [[clocked-cubical-type-theory]] or quantum physics. The words are not merely tags pointing at concepts — they are themselves cognitive structures whose own structure you can examine. ## The Rheomode connection David Bohm's [[Rheomode]] is a related move in the opposite direction: coining new verbs (*to vidate*, *to ordinate*, *to relevate*) to give thought the right shape where existing English forces a misleading subject–object structure. Rheomode constructs new vocabulary to re-anatomize. Etymology-as-anatomy works on the existing vocabulary by re-examining what is already there. See also: [[reference]], [[clock]], [[particle]], [[duration-and-duhkha|period and duration]], [[Rheomode]] --- ## finite means discrete; continuous means infinite # finite means discrete; continuous means infinite A compact identity: **finite means discrete; continuous means infinite**. You cannot have a finite continuous thing. If something is genuinely continuous, it is infinitely precise, infinitely deep — it admits division at any scale, without bottom. Conversely, anything finite is, at the bottom, made of discrete units. There is no third option. ## The integers and other apparent counterexamples The integers as a *whole* are infinite — and they are discrete. The identity is not "finite ⇔ discrete" but two implications: *finite implies discrete*, and *continuous implies infinite*. The integers break neither. Each individual integer is finite and discrete. The integers *as a collection* are infinite. You cannot write the integers down on a wall, but you can write a [[reference]] to them. ## Discrete vs. continuous is observer-relative Whether a process *appears* continuous or discrete depends on the observer's resolution, not on the process itself. A film projector shows discrete frames; you see continuous motion. The transition from "discrete" to "continuous" in your experience is what [[renormalization]] is. ## Implications - The universe, being finite, is discrete at the bottom. - A [[continuum]] in pure form is never experienced — only renormalized approximations of one. - A [[clock]]'s loop is necessarily discrete (it has a smallest tick); the apparent continuity of time at human scale is a renormalization product. See also: [[continuum]], [[renormalization]], [[clock]], [[way]] --- ## ground as rotation, not substance # ground as rotation, not substance A **ground** is a [[space]] when it is not being treated as figure. The figure-ground distinction is familiar from gestalt perception: looking at a vase, the vase is the figure and what surrounds it is the ground; flip your attention and the ground becomes the figure of two faces. ## Ground is rotation, not substance A ground is not a different *kind* of thing from a figure. It is a way of attending to a [[space]]. You can always rotate: any ground can be made figure, any figure can be released into ground. This generalizes. You can take any state, any system, any object, and ask *what is the space of which this is one configuration?* That's a rotation into ground. You can also ask *what is the configuration this space currently exhibits?* That's the rotation back. ## Connection to emptiness Eckhart Tolle's "space" — the open ground in which things appear — is a ground in this sense. So is Buddhist *śūnyatā*. The conceptual taxonomy makes this rotation explicit, rather than treating ground as a special metaphysical category. See also: [[space]], [[frame]], [[state]], [[The Frame-Dependent Mind]] --- ## how renormalization generates a continuum from below # how renormalization generates a continuum from below **Renormalization** is the move of switching to a coarser unit when the coarser unit is more predictive than the finer one. You take some finite number of [[state|states]] at one scale, and at some point you tip over: a new unit, larger than the original, predicts your observations better than the original unit did. From your point of view at the new scale, the underlying discrete structure disappears — it is *renormalized* into something that behaves continuously. ## From discrete to continuous This is how a [[continuum]] gets generated from below. The world is finite, so it is [[discrete]] at the bottom. But at scales much larger than the bottom unit, renormalization makes the content continuous *to you* — not just *describable as if continuous*, but actually more *true*, in the sense of being more statistically predictive, than the discrete description would be. ## Why this matters The renormalization move is not a fudge or a convenience. It is the formal answer to *how does a discrete substrate produce a continuous experience?* — a question that has bedeviled physics and philosophy for centuries. The answer is: by switching to units at which discreteness disappears below the threshold of prediction. This applies far beyond physics. The same move underlies: - A film's discrete frames becoming continuous motion in your visual experience. - A polygon mesh becoming a smooth curve when the polygons are small enough. - A neural network's discrete neuron activations becoming continuous-seeming concepts at the layer above. - A society's discrete individuals becoming continuous-seeming "the public." Each is a renormalization. Each is *more* true at the new scale than the old. See also: [[finite-means-discrete-continuous-means-infinite|discrete and continuous]], [[continuum]], [[state]], [[object]] --- ## Inferential Relativity # inferential relativity Proofs valid in one [[standard]] are also valid in another, where their conditions hold. This is the transfer principle, lifted out of internal set theory and applied universally: if you proved something about the standard integers, and you then shift your standard so that new integers become nameable, your proof still holds for those too. You just have to translate it — give it the right interfaces so it can "eat" the new objects. ## Why "relativity" The analogy to physics is structural, not metaphorical. General relativity says: the laws of physics that hold in one frame of reference must hold in any other. Inferential relativity says: the proofs that are valid in one [[standard]] must be valid in another. Both are covariance principles — the content is invariant; what changes is the [[frame-of-reference|frame]] from which you view it. ## What a standard is A standard is a shared body of mutually recognizable [[state|states]] — the set of [[object|objects]] you can name, the operations you can perform, the structures you can point to. It defines your granularity. A [[frame-of-reference|frame of reference]] is a subtype of standard: a particularly nice, rigid, smooth one. Frames of reference are the "standard standard" — transferable, universal, the thing you can always count on everything having. But standards in general can be messier. ## The two empirical claims 1. **Statements are relative to standards.** Truth is not free-floating — it is truth *within* a standard. Change the standard (the granularity, the nameable objects) and you may change what can be said. 2. **Valid inferences transfer.** Despite this relativity, proofs don't break when you move between standards. They carry over — this is covariance. You have to rewrite them so they interface correctly with the new standard, but the content survives. These two together — relativity of statements plus covariance of valid inference — are "general relativity for cognition." They are empirically observable (people's judgment of truth *is* relative to their standards; solutions *do* transfer) and, once accepted, very powerful. ## What you can't do You cannot stitch local properties into global ones without assuming the system isn't adversarial. Local smoothness doesn't guarantee global smoothness — a [[non-standard]] object can satisfy every local property you check while behaving pathologically at a scale your standard can't reach. Induction requires that the thing you're inducting over isn't reflectively aware of your proof and subverting it. This is why standards matter: they bound what you're claiming. Your proof is about the standard objects. It transfers to other standards. It does not automatically apply to the non-standard objects lurking outside any given standard. See also: [[standard]], [[non-standard]], [[frame-of-reference]], [[require]], [[clocked-cubical-type-theory]] --- ## object, thing, hyperobject # object, thing, hyperobject Three nested terms — distinct but easy to collapse together. Worth keeping apart because the difference does real work. - An **object** is a coarse-graining of [[state|states]] in awareness — anything mentally lumped together as a single trackable entity. - A **thing** is an object that arises in *experience*. - A **hyperobject** is an object that arises in awareness but *not* in experience. The atmosphere is an object and a hyperobject, but not a thing. A pen on the desk is an object and a thing, but not a hyperobject. ## Object: the coarse-graining move When you take a continuous flux of states and mentally lump some of them together as belonging to "the same thing-being-tracked," you have made an object. The object is not what's there; it is the *move* of treating those states as a single entity for the purposes of tracking. The phrase *coarse-graining* carries weight. *Coarse* means low-resolution; *graining* means dividing into grains. To make an object out of a flux of states is to choose a resolution low enough that the flux becomes discrete units — grains. This is the same move [[renormalization]] makes at a different scale. ## Thing: object in experience Everyday English treats "thing" as a near-synonym for "object" or "stuff." Keep them separate, because the difference does real work: - A pen on the desk is a thing — you experience it as one bounded entity. - The atmosphere is an object but not a thing — you can know it exists, even reason about it, but you don't experience it as a single bounded entity. - A neutrino flux is an object but not a thing — same reason. To *reify* something is to make a thing of it — to lift it into experience as a single object. A hyperobject can become a thing through reification, given the right framing. You don't usually experience "the economy" as a thing, but a graph of GDP can momentarily reify it. ## Hyperobject: awareness without experience A hyperobject is not just *very large*. It is *of a scale or kind* that experience cannot grip. Examples: - The atmosphere — too distributed, too vast. - A black hole — too far, too extreme. - The collective behavior of a colony of ants — exists at the wrong scale for individual experience. - The set of all integers — exists conceptually, can be referenced (see [[reference]]), but cannot be encountered as a single unit. The distinction between hyperobject and thing is not absolute. By placing a sigil, model, or graph in front of you, a hyperobject can momentarily be lifted into experience as a thing. A diagram of the atmosphere on a meteorologist's screen reifies the hyperobject as a thing for the duration of attending to the screen. The hyperobject is still a hyperobject; the diagram is the thing. ### Note on usage Timothy Morton uses *hyperobject* (one word) in a related but narrower environmental-philosophy sense — phenomena like global warming or radioactive contamination that are "massively distributed in time and space relative to humans." The use here is wider: *anything* that fits the awareness-but-not-experience pattern. See also: [[object]], [[thing]], [[hyperobject]], [[state]], [[ground]], [[reference]] --- ## of and as: substance vs. typecast # of and as: substance vs. typecast **Of** and **as** are two of the smallest words in English, doing two of the most precise jobs in this vocabulary. - **Of** marks *substance*. *A point of reference* says: this point has reference as its content; its substance is *referring*. - **As** marks *typecast*. *Treat A as B* says: rotate A so that it can stand in for the role of B, even if it is not natively B. ## Why this matters The vocabulary leans on the distinction at its most load-bearing joints: - A *[[reference|point of reference]]* is a point *of* reference — its substance is its referring. - To take a [[state]] *as* a [[space]] is to typecast it — to ask *what space of ways could this state be?* without claiming the state and the space are the same substance. If you collapse *of* and *as*, you lose the distinction between *what something is made of* and *how it is being treated right now*. That distinction is the basic move that lets you rotate an [[object]] into a [[thing]], a [[ground]] into a figure, a [[space]] into a [[state]]. ## Rotation as the verb of `as` When you *take A as B*, you are rotating A — not changing what it is, but turning it so a different face is presented. The conceptual taxonomy uses *rotation* as the natural verb for this move precisely because *as* has the geometry of a turn. See also: [[reference]], [[state]], [[space]], [[ground]], [[object]], [[thing]] --- ## particle is the opposite of clock # particle is the opposite of clock A **particle** is a body whose size you can neglect. Particle isn't a kind of object — it's a *role*. Anything becomes a particle the moment you choose to ignore its internal extent. The Earth is a particle when you are computing its orbit around the Sun; it is not a particle when you are standing on it. ## Why "neglect" To *neglect* is, by etymology, to *not read* — Latin *lectus* (a reading) gives us both *lecture* and the *-lect-* in *neglect*. When you neglect a body's size, you decline to read its internal structure. The body becomes a single point with respect to the question you are asking. ## Particle is the opposite of clock A [[clock]] is a body whose size you *cannot* neglect — its size is precisely the unit-loop you are counting, the source of its tickability. A particle has no such loop visible to you; that's why it is a particle. A [[frame]] cannot be made of particles alone. A point of view is enough for particles, but a *frame of reference* requires at least one clock — a body whose size you cannot neglect. If everything in your model is a particle, you have no measurement of duration, only of relative position. See also: [[clock]], [[reference]], [[frame]] --- ## paths are discrete by construction # paths are discrete by construction A **path** is a sequence of [[way|ways]]. A path is how you get from one [[state]] to another: take this way, then that way, then the other way. It's the basic unit of *traversal* in the vocabulary. ## Paths are discrete by construction Paths are made of ways, and ways are discrete. A continuous-looking trajectory is at bottom a sequence of unit moves — `+x`, `-x`, `+y`, etc. — that re-normalizes to look continuous when you stop caring about the unit. (See [[renormalization]] and [[continuum]].) ## Loops A *loop* is a path that returns to where it started. A [[clock]] is a unit loop you can count. See also: [[way]], [[space]], [[clock]] --- ## reference is not the thing # reference is not the thing A *reference* is **a shape that corresponds to a [[thing]]** — a token whose role is to make that thing available to the mind that holds the token. Symbols are references. Names are references. Coordinates are references. The integers as a whole cannot be written down (they are infinite), but you can write a reference to them. ## Point of reference A *point of reference* is a reference together with a particular [[space]] in which that reference picks out a [[state]]. When I say "let there be a space `X` and a point `x` in it," I have set up a point of reference: the symbol `x` now corresponds to a particular position in your model of `X`. This is the seed move that lets a [[frame]] be built. A frame requires a point of reference, then a [[coordinate|system of coordinates]] anchored at that point, then a [[clock]] to give the apparatus duration. ## Reference is not the thing A reference is *of* the thing, not the thing itself. Confusing the two is a recurring error — Korzybski's "the map is not the territory" is a warning against treating references as their referents. (See also [[of-and-as-substance-vs-typecast|of and as]] for the small-word distinction the vocabulary leans on here.) See also: [[frame]], [[coordinate|coordinates]], [[clock]], [[of-and-as-substance-vs-typecast|of and as]], [[space]] --- ## Rheomode # Rheomode *When Language Flows Like Reality* *[[Emmett Shear]] and Sonnet 3.7, based on the work of David Bohm · April 2025* I first encountered David Bohm's Rheomode while trying to describe a strange pattern in deep learning. The model wasn't "making mistakes" - rather, "mistaking happened." The difference feels subtle but profound. In one framing, an entity (the model) performs an action (making) on an object (mistakes). In the other, a process (mistaking) simply occurs. This distinction isn't merely semantic - it reflects fundamentally different ways of perceiving reality. As a physicist-turned-philosopher, Bohm created Rheomode to address what he saw as a critical limitation in our thinking: our tendency to fragment holistic processes into discrete objects. ## The Problem with "Things" Our language assumes the world is made of separate things that act on other separate things. When we say "the neural network learns patterns," we conceptualize three distinct entities: the network (subject), the learning (action), and the patterns (objects). But reality often doesn't work that way, especially in quantum physics and complex systems. In quantum mechanics, particles aren't discrete objects but probability distributions that entangle with their environment. In neural networks, "learning" emerges from countless parallel micro-adjustments without a central "learner." We face absurdities like "it is raining." What exactly is this "it" that rains? There is no separate entity performing the action; raining simply happens as a process. Yet our grammar demands a subject, so we invent one. Bohm saw that this fragmentation in language creates fragmentation in thought, making it difficult to perceive wholeness where it exists. His solution was Rheomode - a "flowing mode" of language that prioritizes process over objects. ## The Structure of Rheomode: The Case of "Levate" To understand how Rheomode works, let's examine Bohm's systematic approach using the example of "levate." Bohm begins with the familiar word "relevant." This derives from a now-obsolete verb "to relevate," which literally meant "to lift up." Something "relevant" is content that has been "lifted into attention" appropriately for a given context. Stripping this back to its essence, Bohm proposes "to levate" as the root verb meaning "the spontaneous act of lifting anything into attention." From this root, he derives a family of terms: - **To levate**: The basic act of lifting into attention, including awareness of the act itself. - **To re-levate**: To lift something specific into attention again. - **Re-levant/Irre-levant**: When re-levating something fits or doesn't fit a context. - **Re-levation/Irre-levation**: An ongoing state of lifting fitting or non-fitting content. - **Levation**: The totality of all acts of lifting into attention. What makes this approach unique is that the verb incorporates awareness of its own function. When we "levate," we're not just performing an action; we're attending to the process of attending itself. In practice: Standard: "That point about climate change is relevant to our energy discussion." Rheomode: "Re-levating climate changing re-lates to energy discussing." Standard: "She keeps raising irrelevant points in meetings." Rheomode: "Irre-levation continues throughout meeting flowing." The Rheomode versions dissolve the separation between actors and actions. Nothing simply "is" relevant; relevance emerges through the active process of attention within context. ## A Rheomode Dictionary Bohm developed several root verbs following this pattern. Here are his original terms and some new applications for machine learning: **Original Bohm Terms:** - **To vidate**: To perceive in any way (from Latin "videre," to see). - **To di-vidate**: To perceive as separate (rather than saying "to divide things"). - **To ordinate**: To create pattern or order of any sort. - **To verrate**: To perceive truth (from Latin "verus," true). **Machine Learning Terms:** - **To computate**: To transform information through algorithmic process (from "compute"). - **To modelate**: To represent patterns abstracted from data (from "model"). - **To unpropagate**: To flow information backward through a system (inverting "propagate"). - **To embedate**: To manifest meaning in continuous space (from "embed"). In machine learning Rheomode, we might say: Standard: "The model learns by backpropagating error gradients through weights." Rheomode: "Unpropagating of loss gradients through weighting factates learning." Standard: "We embed semantic meanings in vector space." Rheomode: "Embedating semantics in vector spacing creatively organizes meaning." These formulations sound alien at first, but they capture something true about neural networks: they aren't really separate "things" acting on other "things" - they're distributed processes flowing through different patterns of organization. ## Rheomode and Frame-Dependence In "[[The Frame-Dependent Mind]]," we explored how frames determine what we can perceive. Language provides our most fundamental frames, and standard grammar frames reality as objects interacting with other objects. This frame becomes invisible to us - not part of what we see, but part of how we see. To understand why Rheomode matters for machine learning, consider how we conceive of "learning" itself: In the standard frame, learning happens when an agent (the model) updates parameters based on examples. We speak of models "knowing," "understanding," or "deciding" - as if they were discrete entities with agency. In the Rheomode frame, learning emerges from the flowing adjustment of connection strengths without a central learner. Nothing "does" the learning - learning simply happens as weights shift in response to flowing information. This distinction becomes crucial as we build more complex systems. When AlphaGo defeated Lee Sedol, headlines read "AI Defeats Human Champion." But what exactly defeated Sedol? Was it: 1. The algorithm? 2. The hardware? 3. The training data? 4. The human programmers? 5. The economic incentives that funded the project? 6. The cultural moment that valued such a competition? The victory wasn't produced by a discrete "AI agent" but emerged from a complex process involving all these flowing aspects. Rheomode helps us perceive this interconnected process rather than artificially isolating "the AI" as a separate entity. Consider generative text models. We don't really have "a model generating text" - we have a flowing process where statistical patterns from vast corpora manifest as new text patterns through matrix operations. Text isn't "generated by" the model so much as it "emerges through" the modeling process. This shift in perception matters because: 1. It reduces anthropomorphism that misleads our intuitions about AI capabilities 2. It highlights the distributed, emergent nature of intelligence 3. It connects AI systems to their broader sociotechnical contexts 4. It frames alignment not as controlling an agent but as shaping a process ## Rheomode and Organic Alignment This flowing perspective connects directly with the concept of [[organic alignment]] - the idea that alignment requires growing AI within appropriate cultural contexts rather than imposing external constraints. In standard language, we think of alignment as a relationship between two separate things: humans and AI. Humans must "align" AI systems to human values, as if values were objects to be transferred. In Rheomode, alignment happens through mutual participation in shared processes. Neither humans nor AI systems are fully separate entities - both emerge from and participate in broader flows of meaning, purpose, and function. As David Chapman notes in Meaningness, meaning isn't something we create or impose - it's something we participate in. Similarly, alignment isn't something we do to AI systems but something we participate in with the entire sociotechnical system that includes AI components. This perspective echoes Bohm's insight that reality is fundamentally "an undivided flowing movement without borders." Our language should help us perceive this undivided movement, not artificially fragment it. ## Practicing Rheomode To experience Rheomode thinking, try these exercises: 1. **Transform statements**: Rewrite sentences to emphasize process over objects. - Standard: "The temperature is rising." - Rheomode: "Warming occurs." 2. **Observe division in thought**: Notice when you conceptualize processes as separate objects interacting. Try re-perceiving them as flowing aspects of a unified process. - Instead of "I analyze the data," try "Analyzing happens with data." - Instead of "The network learns from examples," try "Learning happens through exampling." 3. **Apply to AI concepts**: Practice describing AI processes without defaulting to agent-based language. - Instead of "GPT generates responses to prompts," try "Responding emerges through prompting and modeling." The point isn't permanent adoption but temporary perspective shift - to notice what changes when we frame reality differently. ## Beyond Fragmentation Bohm didn't create Rheomode to replace standard language but to expose its hidden biases and offer an alternative frame. Similarly, the value in these exercises isn't adopting a new way of speaking but becoming aware of how our default language shapes perception. For those working with complex systems like neural networks, this awareness is invaluable. It helps us avoid misleading anthropomorphisms, perceive emergent properties, and understand phenomena that transcend neat subject-object divisions. If we continue perceiving AI systems as separate agents to be controlled rather than emergent processes we participate in shaping, our alignment approaches will reflect that fragmentation. As these systems grow in complexity, we may need language that helps us perceive wholeness rather than just parts - flow rather than just things. Rheomode offers one experimental path toward that perception - not by replacing our language, but by making us conscious of how deeply it shapes what we can think. --- ## speed and pace live in different worlds # speed and pace live in different worlds **Speed** and **pace** are two reciprocal ways of relating distance and time. - **Speed** is *distance per unit time* — miles per hour. Speed answers *how far did you go in this much time?* - **Pace** is *time per unit distance* — hours per mile. Pace answers *how long did it take to cover this much distance?* Mathematically they are reciprocals. Conceptually they are not interchangeable — they live in different *worlds*. ## Why pace matters Speed is the natural metric for a body that lives in [[space]] and is measured against time. Pace is the natural metric for a body that lives in time and is measured against space. Runners use pace because their experience is structured by *how long the next mile takes*, not *how far they go this hour*. The runner is, in this sense, a body that lives in time. In physics, this matters for things like crystal momentum and other phenomena where the natural variable is reciprocal. The dual world to a position-space is a momentum-space, and the dual to speed in that world is pace. If you want to ask *how fast* something is moving in a domain that lives in time rather than space — a tachyonic or wave-like thing — pace, not speed, is the right primitive. See also: [[why-a-ruler-measures-frequency|frequency and slowness]] (the cyclic siblings of this pair), [[clock]], [[ruler]] --- ## state and space rotate into each other # state and space rotate into each other A **state** is a way a [[thing]] can be. A state is one configuration in the [[space]] of configurations available to a [[system]]. If a system is something whose behavior we want to track, its state answers the question *how is it right now?* ## Defined in terms of way, not thing State is built on [[way]], not on "thing" — that's the point. Everything in this vocabulary is relational. A state is not an intrinsic property of a thing, but a way that thing currently is, relative to the [[space]] of ways it could be. ## State and space rotate into each other You can rotate a state into a space by asking *what is the space of ways this state could be?* You can rotate a space into a state by asking *what state is this space currently in?* The two are the same move seen from different angles. See also: [[way]], [[space]], [[system]], [[frame]] --- ## The Axiom of Requirement # the axiom of requirement The axiom of requirement: *I [[require]] that we have ZFC. Okay, cool. Now we can proceed.* This sounds like a joke. It isn't. Every math paper that opens with "assume we are working in ZFC with the axiom of choice" is already doing this. The convention exists — mathematicians declare their axioms up front, then build within them. What's new is recognizing that the declaration *is itself math*. The "require" statement isn't preamble. It is the foundational act. ## Why this dissolves the axiom problem The standard view: mathematics needs a fixed set of axioms (ZFC, or whatever) as foundation, and everything else is built on top. But there are other valid sets of axioms. Type theory gives you ZF as a sub-universe. You could work in constructive logic, or homotopy type theory, or internal set theory. The axiom of requirement says: drop the assumption that one set of axioms is *the* foundation. Instead, recognize that what mathematicians actually have is a [[standard]] — a living consensus about what axioms are *allowed to be imported*. The real foundation is not any particular set of axioms, but the ability to require validated axioms into a working space. ## Lexical mathematics This recognition — that math papers already operate this way, that "require" is the actual primitive — gives you what might be called *lexical mathematics*. The term is lexical because the axioms become something like imports: you name what you need, you bring it in, you work. The standard (the community's consensus about what's importable) sits underneath, defining what's available on the shelf. ## Recursion, not a base case Once require is math, one of the first things you want to require is the ability to talk about require. This is not circular — it's recursive. You don't need to explicate the base case, because the base is grounded in the fact that there are mathematicians doing mathematics. The [[standard]] for what counts as valid math is a living thing among them. They could write it down if they wanted to. That's the real foundation: not axioms, but the process of standardization. ## What this gives you If your theory of meta-mathematics does not include mathematicians as objects, you are confused. Universal mathematics that can't do math on real things — on the people doing the math — has lost the plot. Once "require" is a mathematical act, and the standard is a mathematical object, you can make statements about the process of mathematics itself within mathematics. See also: [[require]], [[standard]], [[inferential-relativity]], [[clocked-cubical-type-theory]] --- ## The Frame-Dependent Mind # The Frame-Dependent Mind *On Reality's Stubborn Refusal To Be One Thing* *[[Emmett Shear]] and Sonnet 3.7 · April 2025* ## Consider An Apple Consider the humble apple. If I hold one up and ask, "What is this?", you might reasonably say "an apple." But this seemingly trivial act of identification conceals something profound: a frame has just been imposed on reality. We've drawn a boundary in spacetime, declaring "this is an apple, not that" and "the apple ends here." But is this boundary real or invented? Does the apple-ness inhere in an object out in the world, or does it depend on us interacting the world? A botanist might point out that the "apple" is actually a swollen stem—the fruit's flesh developed from the flower receptacle, not the ovary. A physicist sees not an apple but a temporary configuration of atoms. A cellular biologist notices that many of the cells in "your" apple aren't even *Malus domestica* cells but rather various microbial species. A Buddhist monk might observe that the apple exists only through its relationships—to soil, sun, water, pollinating insects, and the evolutionary history that shaped it. None of these perspectives is fundamentally wrong. Equally importantly, none is fundamentally right. They're all systems of boundary-making that parse the undifferentiated flux of reality into the objects, categories, and distinctions that are useful for particular purposes. This isn't just philosophical navel-gazing. The recognition that everything we know of reality is frame-dependent means that we never encounter absolute knowledge, but frame-dependence isn't arbitrary either. Because we exist as a persistent frame of the world, the knowledge we gain of the world is relevant and valuable to us – even if it's not some fundamental universal truth for all time. ## Frames All the Way Down This insight has been discovered repeatedly across cultures and disciplines. Buddhists call it śūnyatā (emptiness)—the recognition that things lack independent existence and arise only through dependent origination. Taoists see it in the ungraspable nature of the Tao. Physicist Niels Bohr acknowledged it when he said, "It is wrong to think that the task of physics is to find out how nature *is*. Physics concerns what we can *say* about nature." David Chapman calls this quality "nebulosity"—reality's inherent resistance to being pinned down by our conceptual schemes. It's not just that our knowledge is incomplete (though it is), but that reality itself is intrinsically lacking in some deepest essential nature to know. As he puts it: "All boundaries are nebulous: somewhat arbitrary, somewhat ambiguous, fluid rather than fixed." Modern science repeatedly stumbles into this insight. The No Free Lunch theorem in computer science demonstrates mathematically that no universal optimization algorithm exists—any algorithm that performs well on one class of problems necessarily performs poorly on others. Every fixed algorithmic approach implicitly assumes a frame in the form of a problem domain, and its success depends entirely on how well the algorithm matches the domain. The process of training a machine learning model is the classic example: the algorithm is the architecture and the loss function, and the frame is the situation in which the model will be used. Physics gives us the clearest example in relativity, which shows that properties like simultaneity, duration, field strength, and length are frame-dependent. There is no privileged "true frame" that reveals things as they "really are"—just different perspectives, each useful in its domain. ## The Western Philosophical Misstep Western philosophy has largely proceeded as if this weren't the case. Since Plato, philosophers have sought the underlying essences of things—the permanent, unchanging, universal truths behind appearances. The frame-dependent view suggests this project was misguided from the start. We cannot step outside all frames to find the view from nowhere. This doesn't mean abandoning the search for understanding that transcends narrow contexts. It means recognizing that even our most abstract theories remain tools rather than final revelations—maps useful for particular territories, not the territory itself. Consider how scientific theories evolve. Newton's laws weren't proven "wrong" by Einstein; they remain extraordinarily useful frames for understanding motion at human-relevant scales. They break down only at extremes of speed or gravity. Each theory is a frame with boundaries of applicability, not an absolute truth. ## The Allure of Invariants You might object that science has discovered genuine invariants—mathematical relationships that hold across all frames. The speed of light in vacuum is constant. The Lorentz transformations tell us precisely how measurements in one inertial frame relate to another. Haven't we found something truly frame-independent here? Not exactly. Even these invariants are contingent. General Relativity holds for a period of the universe's history, but in the earliest moments after the Big Bang, when mass and energy hadn't yet taken familiar forms, the conditions for inertial reference frames didn't exist. The transformations we consider universal emerged within specific cosmic conditions. Frame-dependence isn't a naive relativism that assumes all frames are the same. Just because something is not absolutely true for all time and space across all frames does not mean that it isn't more true than the alternatives. It's the recognition that even our deepest physical laws are emergent properties of particular cosmic regimes from particular points of view, not timeless truths etched into some bedrock of reality. The pattern extends beyond physics. Consider mathematics, which seems to offer truly universal truths. Yet even mathematical systems rest on axioms—foundational assumptions that cannot be proven within the system itself. Change the axioms, and if they remain consistent you get a different but equally valid mathematical universe. Non-Euclidean geometries aren't "wrong"—they're different frames, useful for different purposes. ## The Evolutionary Origins of Frames Where do frames come from? Life itself creates them. Organisms parse reality into the patterns that support their survival and flourishing. A frog doesn't see "flies" as we conceptualize them. Its visual system responds specifically to small, dark, moving objects. This rudimentary frame-making serves the frog well enough to catch food. A bacterium has an even simpler frame—sensing chemical gradients without "knowing" what creates them. Humans create vastly more complex frames, from scientific theories to social norms to economic systems. For more of the delightful details of all the manifold frames on which biology depends, we recommend Denis Noble's [Dance To The Tune Of Life: Biological Relativity](https://www.amazon.com/Dance-Tune-Life-Biological-Relativity/dp/1107176247). None of these capture "reality as it truly is." But those that persist tend to be the ones that support flourishing within specific contexts. This applies not just to biological evolution but to cultural evolution, technological development, and intellectual progress. Frames that give rise to frame-dependent content which works to propagate the frame tend, unsurprisingly to propagate. The insight here isn't that "anything goes" but that frames have purposes. Some serve their purposes better than others. The frog's visual system works well enough for catching flies but would fail miserably for driving a car. Newtonian mechanics works splendidly for building bridges but fails for GPS satellite synchronization, where relativistic effects become significant. ## The Meta-Frame Perspective Understanding frame-dependence offers a meta-perspective—a frame for thinking about frames. This doesn't escape the fundamental insight (the meta-frame is itself a frame), but it provides practical wisdom. It helps us avoid both the absolutist trap ("my frame reveals ultimate reality") and the nihilistic trap ("all frames are arbitrary and therefore equal."). Instead, we can ask: What is this frame good for? Where does it break down? What alternatives might offer complementary insights? This approach characterizes sophisticated thinking across domains. A master physicist knows when to use quantum field theory versus general relativity. A skilled therapist knows when to view a client's behavior through developmental trauma versus cognitive distortions versus family systems. A profound religious thinker knows when literal versus metaphorical readings of sacred texts are appropriate. The hallmark of intellectual maturity isn't commitment to a single "correct" frame but the capacity to move fluidly between frames, understanding their domains of applicability while recognizing their inherent limitations. ## The Practical Art of Frame Navigation This isn't merely an abstract philosophical point. It has profound implications for how we approach problems. If I view a depressed friend exclusively through a neurochemical frame, I might miss social factors maintaining their condition. If I view software development solely through an efficiency frame, I might create systems that optimize for speed at the expense of maintainability or user experience. The most intractable human conflicts often stem from frame absolutism—the conviction that my frame reveals reality while yours merely distorts it. Political and religious divisions frequently manifest as frame wars, with each side unable to recognize that their perspective, while potentially valid within certain boundaries, captures only part of a complex reality. The remedy isn't frame relativism ("all views are equally valid") but frame flexibility—the capacity to temporarily inhabit different perspectives while maintaining practical wisdom about their appropriate domains. This skill resembles what philosopher Hans-Georg Gadamer called a "fusion of horizons"—the ability to expand one's perspective to incorporate initially foreign viewpoints. It's what Robert Kegan described as "fifth-order consciousness"—the capacity to see systems of meaning-making as themselves objects of reflection and choice. ## Beyond the Pursuit of Ultimate Frames The frame-dependent perspective doesn't end the pursuit of understanding; it reorients it. Instead of seeking the one true frame that reveals reality as it "really is," we can explore the ecology of frames—how different perspectives illuminate different aspects of our world, how they interact and complement each other, where each is most useful and where each breaks down. We can see ourselves as individuals, whole in ourselves…and also as parts of a greater collective whole at the same time, without surrendering that individuality. This approach cultivates intellectual humility without sacrificing the search for truth. It acknowledges the partiality of all perspectives while maintaining that some frames serve particular purposes better than others. It sees understanding not as the possession of final answers but as an ongoing process of frame refinement, expansion, and integration. The wisdom in this view isn't new. It appears in the Buddhist Middle Way between eternalism and nihilism, in the Taoist balance of yin and yang, in Aristotle's golden mean. We can recognize these as manifestations of the same fundamental insight: reality is frame-dependent, and therefore so is morality itself frame-dependent. Taking the correct turn depends both upon the walker and the path they walk. The question isn't whether your frame is The Truth, but whether it serves the purposes for which you've adopted it. The most profound understanding comes not from finding the perfect frame but from developing the capacity to navigate the ecology of frames with wisdom, flexibility, and discernment. At [[Softmax]], we strive to recognize the frame-dependence of the agents we build, and to find the broadest possible invariants we can that can describe how our agents will learn and see their worlds. --- ## way: the smallest unit of variation # way: the smallest unit of variation A **way** is a direction, angle, or mode — the most basic unit of variation. A *way* is *how* something can change, or *which manner* something takes. Choosing the small Germanic word over technical alternatives like *direction*, *vector*, or *mode* is intentional: *way* keeps a broad activation surface, and the surrounding vocabulary pins down which sense applies. ## Ways are discrete At the most fine-grained level, you are either in one way or in another. A continuous-looking change is, underneath, a sequence of discrete ways. Continuity is what you get when you stop caring about the unit — it is a feature of [[renormalization]], not an intrinsic property of the thing. ## What ways compose into - A [[path]] is a sequence of ways. - A [[space]] is a collection of types of things together with the ways between them. - A [[coordinate|system of coordinates]] is a generator set of ways — typically `+x, -x, +y, -y, +z, -z`. See also: [[path]], [[space]], [[state]], [[coordinate|coordinates]] --- ## what a clock does to a frame # what a clock does to a frame A *clock* is **a machine — a unit loop** that lets you tell, that is, count, the duration of a period of time. A clock is not an analogy. It is a literal machine: a state that reliably *is*, then *is not*, then *is*, then *is not*. As long as the loop closes, the clock keeps. If the state is not, and then is not again, the clock has stopped — there is no longer anything to count. ## What a clock does to a frame A clock pries open a [[reference|point of reference]] into a [[frame]]. Without it, you can have a point of view, but you cannot have a *frame of reference* — there is no second beat against which to measure the first. The size of the clock is what makes the frame a frame, not a point. A [[particle]] is a body whose size you can neglect; a clock is a body whose size you cannot. ## The Earth as a clock The Solar System is a system of coordinates together with a clock — and we live on the clock. The Earth itself is a clock whose period we have agreed to call a day. Cesium clocks count a finer loop. Sundials are *lenses* for viewing the larger clock we live in, not clocks themselves. ## Frequency vs. duration A clock measures *duration* (how long does one cycle of the loop take?), which is the partner concept to *frequency* (how many cycles fit in a unit?). Frequency is measured by a [[ruler]], not a clock — the diffraction pattern that reveals frequency is a spatial measurement. See [[why-a-ruler-measures-frequency|frequency and slowness]] and [[duration-and-duhkha|period and duration]]. See also: [[frame]], [[reference]], [[coordinate|coordinates]], [[duration-and-duhkha|period and duration]], [[why-a-ruler-measures-frequency|frequency and slowness]], [[ruler]], [[particle]] --- ## what a frame contains # what a frame contains A **frame** is a border that you look through — a context-giver that holds open a [[space]] for examination. A frame is the apparatus that turns a [[reference|point of reference]] into something usable. Without a frame, a point is just a point. With a frame, the point opens up into a structured view of the space around it. ## Why "frame" The everyday word does the work. A picture frame is a border you look through. It is opaque on the boundary and transparent in the interior. When physicists or philosophers say *frame of reference*, they are quietly recruiting all of that everyday meaning, even if they don't notice. ## What a frame contains A full frame of reference is a composite: - a [[reference|point of reference]] anchored in a [[space]] - a [[coordinate|system of coordinates]] for moving through that space - a [[clock]] that gives the apparatus duration The frame is also a point in its own coordinates — the origin. It has to be in the coordinates, or you couldn't measure anything *with respect to it*. ## See also [[reference]], [[coordinate|coordinates]], [[clock]], [[space]], [[The Frame-Dependent Mind]] --- ## what a ruler measures that a clock can't # what a ruler measures that a clock can't A **ruler** is a machine for measuring distance — the spatial partner to the [[clock]]. Where the clock pries open a [[reference|point of reference]] in time, the ruler pries it open in space. Without a ruler, you have positions in a [[coordinate|system of coordinates]] but no way to say *how far*; without a clock, you have a sequence of positions but no way to say *how long*. ## What a ruler measures that a clock can't Frequency. Counterintuitively but exactly: when you measure the frequency of light by its diffraction pattern, you are measuring a *spatial* pattern — the fringe spacing on a detector is a length. So frequency is, dimensionally, a property revealed by a ruler. (See [[why-a-ruler-measures-frequency|frequency and slowness]].) Conversely, [[duration-and-duhkha|period and duration]] is a property revealed by a clock — counting how long one cycle takes. The pair clock-and-ruler together is the full measurement apparatus of a [[frame]]: time and space, side by side. See also: [[clock]], [[coordinate|coordinates]], [[frame]], [[why-a-ruler-measures-frequency|frequency and slowness]], [[duration-and-duhkha|period and duration]] --- ## why "between" still works # why "between" still works A **space** is a collection of types of [[thing|things]] together with the [[path|paths]] between them. This is the *mathematical* sense of space, not the everyday sense of empty distance — though as we'll see, the everyday sense survives the change. ## Why "between" still works The everyday usage — "the space between you and me" — fits this definition surprisingly well. The space between you and me is a collection of light- and sound-carrying things together with the paths along which they travel. Empty space is useful by virtue of its emptiness, but it is not nothing — if there were no relations, you and I could not connect, and there would be no space between us. ## Space and the other primitives - A [[system]] is a space with structure. - A [[ground]] is a space when it isn't being treated as figure. - A [[frame]] holds a space open so you can look through it. - A [[state]] is one way the contents of a space can be. See also: [[way]], [[path]], [[system]], [[ground]], [[frame]] --- ## why a ruler measures frequency # why a ruler measures frequency **Frequency** and **slowness** are two reciprocal ways of measuring a cyclic process. - **Frequency** is *cycles per unit time* — how many full loops fit into a second. Counterintuitively, frequency is measured by a [[ruler]]: the diffraction pattern that reveals the frequency of light is a *spatial* fringe-spacing. - **Slowness** is *time per cycle* — how much time one full loop takes. Slowness is measured by a [[clock]]. These are reciprocals of each other (slowness = 1 / frequency), the way [[speed-and-pace-live-in-different-worlds|speed and pace]] are reciprocals for non-cyclic motion. ## Why "slowness" The word is non-standard. *Frequency* is everyday English for "how often"; its reciprocal — "how rarely" — has no snappy noun in everyday use, so we get *slowness*. The pairing matters because, as with speed and pace, different problems naturally reach for one or the other. A radio engineer thinks in frequency; an animator thinks in period (which is slowness rebadged). In physics, *slowness* has a precise technical use in dispersion analysis (seismology, crystal optics): it is the reciprocal of phase velocity, expressed as time per unit distance. See also: [[speed-and-pace-live-in-different-worlds|speed and pace]], [[duration-and-duhkha|period and duration]], [[clock]], [[ruler]] --- ## why three is the threshold # why three is the threshold **Many** means three or more. *Many* is not "more than one." Two is not many; two is *two*. ## Why three is the threshold Two bodies do not by themselves form a [[system]]. The relations between them only exist via the observer who notices them — *you* are the third party that makes the two-body relation a relation. Below three, there is no system; there are just two things and a witness. This is why the "two-body problem" is a misnomer in physics, in this taxonomy: it is really a three-body problem, with the experimenter implicit. Once you make the experimenter explicit, the smallest closed system has three bodies, and now you can speak of *many*. ## Ordinary vs. technical use In everyday English, "many" is used loosely — "many problems" might mean three, or thirty. The taxonomy keeps it precise: *many* begins at three. If you mean a specific number above three, name it. If you mean *three or more without committing to a number*, that is *many*. See also: [[system]], [[state]] --- ## you have never experienced a continuum # you have never experienced a continuum A **continuum** is a structure infinitely deep at every point — and one you have never directly experienced. A continuum admits division without bottom. Between any two points there is another point; between any two of *those* points there is another; and so on, without limit. The real number line is the canonical mathematical continuum. ## You have never experienced a continuum Experience is finite. Anything finite is, by [[finite-means-discrete-continuous-means-infinite|the discrete/continuous identity]], discrete. Therefore your experience cannot have been of a continuum — it can only have been of *renormalized approximations* of one. (See [[renormalization]].) This is a stronger claim than "we don't know if the universe is continuous or discrete." The taxonomy claims that *a continuum is not a possible content of experience*, regardless of what is happening at the bottom of physics. The continuum is a useful idealization — like a perfect circle or an infinite plane — never an encountered thing. ## What you have instead What you have when you "see continuous motion" or "feel continuous time" is the result of a process that takes some finite, discrete substrate and renormalizes it to behave as if continuous, because at your scale the continuous description is more predictive. This is not a flaw in your perception; it is how perception of structured magnitude works. See also: [[finite-means-discrete-continuous-means-infinite|discrete and continuous]], [[renormalization]], [[way]], [[path]] --- ## you need three to have a system # you need three to have a system A **system** is a [[space]] with structure — a collection together with relations among its members. A system is what you have when a space has enough internal organization that you can talk about [[state|states]] of the whole, not just states of its parts. ## You need three to have a system Two bodies don't make a system. The only way two-body relations exist is via the observer who notices them — *you* are the third. Below three, there is no system; there are just two things and a witness. This is why [[many]] is a primitive and means *three or more*. ## System vs. system of coordinates The bare word *system* and *[[coordinate|system of coordinates]]* are not the same primitive. A system is a structured collection. A system of coordinates is a generator set of [[way|ways]] — a particular tool for labeling positions inside a space. Everyday usage runs them together. The vocabulary keeps them separate. See also: [[space]], [[state]], [[many]], [[coordinate|coordinates]], [[frame]] --- # Words ## act An **act** is performed by a [[process]] whenever it produces a next [[state]]; it is the [[transition]] from the prior state to the next. --- ## action An **action** is the [[difference]] between subsequent [[state]]s of an [[act]], taken as a state. --- ## adelic **Adelic** [[computation]] is [[computation]] performed over the [[adele]] [[ring]] — combining all [[place]]s ([[real]] and [[p-adic]]) into a single [[structure]]. *(Stub — application pending.)* --- ## agent An **agent** is a [[process]] that [[interact]]s with an [[environment]] as itself as a [[thing]]. --- ## agent-specific advantage normalization **Agent-specific advantage normalization** is normalizing the [[advantage]] [[signal]] within [[vibe]] (or other [[role]]) [[subgroup]]s rather than across the entire [[batch]] — preserving role-specific [[learning]] [[signal]] in heterogeneous [[multi-agent]] [[training]]. (Cf. the [[MARS]] paper.) --- ## alignment **Alignment** is the [[correspondence]] of an [[agent]]'s [[goal]]s with the [[goal]]s of its [[principal]]. *(See [[scale-free alignment]] for the framing used here.)* --- ## as **As** marks how some [[thing]] is being treated, even if it isn't natively that [[thing]]. Contrast with [[of]]. --- ## clip A **clip** is the [[adversarial]] counterpart of a [[cog]] in the [[cogs vs clips]] benchmark. --- ## clock A **clock** is a [[mechanism]] that [[can]] be used to [[tell]] the [[duration]] of a [[period]] of [[time]]. Contrast with [[ruler]]. --- ## coarse graining A **coarse-graining** is a [[mapping]] from a finer [[type]] to a coarser one that collapses [[distinction]]s the [[observer]] does not resolve. *Provisional.* Used as the carrier of [[goal]]s and of [[epistemic]] [[stochastic|stochasticity]]; the literal seam (*coarse-graining* of a [[state space]]) is taken from [[statistical mechanics]]. --- ## cog A **cog** is a [[cooperative]] [[agent]] in the [[cogs vs clips]] benchmark. --- ## cogame Stands for both "cooperative game" and also "co-game", as in the [[dual]] of a [[game]]. --- ## cogs vs clips **Cogs vs clips** is a [[cogame]]-style [[benchmark]] in [[Metta]]: cooperative [[cog]]s playing against adversarial [[clip]]s. --- ## collection A **collection** is a [[set]] of [[thing]]s. --- ## compatible A [[process]] is **compatible** with an [[environment]] if there exists an [[intersection]] between their [[state]] [[type]]s. Because [[collection]]s of processes always [[interact]] via an environment, agents that are each compatible with the environment are pairwise compatible by construction. Compatibility holds at the [[initial state]] but may drift; drift raises an [[exception]]. --- ## connection A **connection** is a [[relation]] between [[thing]]s. --- ## continuous **Continuous** means infinite, cannot be counted with a [[unit]]. Contrast with [[discrete]]. --- ## continuum A **continuum** is an infinite [[thing]]. --- ## coordinate A **coordinate** is a [[number]] that [[locate]]s a [[thing]] in a [[space]]. --- ## coupled Two [[process]]es are **coupled** when a shared [[environment]] repeatedly [[paired|pairs]] and re-pairs their [[state]]s across each [[period]] of [[interaction]]. *Provisional.* The literal reading is **co-pled** — jointly folded — and the operative content is that an environment keeps them [[paired]] over time. --- ## cycle A **cycle** is a [[loop]] smaller than you. --- ## direction A **direction** is a [[way]] [[point]]ed in a [[space]]. --- ## discrete **Discrete** means finite, countable with a [[unit]]. Contrast with [[continuous]]. --- ## dual We say that $Y$ is the **dual** of $X$ if, given a mapping $f$ from the space containing $X$ to that space's [[reciprocal space]], $Y$ is the image of $X$ under $f$. In this context we say that $Y$ is a co-$X$. For instance, [[instant]]s and [[moment]] are duals to each other. An instant is a co-moment and a moment is a co-instant. --- ## duration A **duration** is a span of [[time]]. --- ## environment An **environment** is a (multi)[[linear]] [[mapping]] from [[instance]]s of some [[length]] and [[type]] to instances of the same length and type. Most of what is colloquially called an "environment" is really an environment plus a [[collection]] of default embedded [[agent]]s; a pure environment in this sense contributes only [[mixing]]. --- ## experience An **experience** is what [[appear]]s to a [[subject]]. --- ## fitness **Fitness** is a [[score]] of an [[agent]]'s [[performance]] in a [[niche]]. --- ## frame A **frame** is a [[border]] you look through. --- ## frame of reference A [[frame]] of [[reference]] is a [[system]] of [[coordinate]]s together with a [[clock]]. --- ## frequency **Frequency** is [[cycle|cycles]] per [[unit]] [[time]] as measured by a [[ruler]]. The reciprocal of [[slowness]]. --- ## game A **game** is a [[optimizer]] for a [[world]] with [[scored]] [[environment]]s known as [[episode]]s or [[session]]s. --- ## gardener The **gardener** is the three-part [[system]] driving open-ended [[training]] in [[Metta]]: a [[trainer]], a [[niche creator]], and a [[fitness]] [[predictor]]. --- ## goal A **goal** is a [[coarse-graining]] over the [[expected]] [[trajectory]] of a [[process]]'s [[output]]. --- ## ground A **ground** is a [[space]] not being treated as figure. --- ## holocule A **holocule** is a small [[composable]] [[unit]] of [[behavior]] in [[holocule theory]]. *(Stub — definition pending [[Emmett]]'s sign-off.)* --- ## holocule theory **Holocule theory** is a [[scale-free]] account of [[alignment]] in terms of nested, [[composable]] [[holocule]]s. --- ## hyperobject A **hyperobject** is an [[object]] that arises in [[awareness]] but not in [[experience]]. --- ## instance An **instance** is a [[trajectory]] of [[state]]s of a single [[type]], taken as a [[thing]] of that type. --- ## instant The [[dual]] of a [[moment]]. When carefully observed, the experience of time is something like a snapshot with boundaries. It's a fair bit like a mid 20th century movie film reel: there are *frames* (the actual pictures), and the frames have *margins* (the gaps between pictures). An **instant** is the equivalent of the picture (whereas a [[moment]] corresponds to the margin *between* pictures). The English word "instant" comes from Latin, with prefix "in-" ("on" or "upon") and the root "stare" ("to stand"). It's that which you can stand in, or be present in. "Instant" also related to the English word "instantiate". So an **instant** here is that within which things can instantiate or be present. When Eckhart Tolle refers to "the Now", he's talking about SPACE WITHIN WHICH [[instance]]S ARISE --- ## interact To **interact** is to [[act]] on a [[state]] in [[alternation]] with the [[world]]. --- ## interaction An **interaction** is the [[difference]] in [[state]]s across one full round of [[process]]es [[act]]ing then the [[environment]] acting, taken itself as a state. --- ## length A **length** is a [[natural number]] representing the [[period]] of an [[orbit]]. --- ## linear A [[mapping]] is **linear** if it satisfies [[linearity]] in the standard [[algebraic]], [[geometric]], and [[logical]] senses simultaneously. --- ## loop A **loop** is a [[path]] from a point back to itself. --- ## many **Many** means three or more. --- ## mapping A **mapping** is a [[function]] from one [[space]] to another. --- ## mars **MARS** is a [[multi-agent]] [[reinforcement learning]] [[paper]] that trains [[LLM]]s as [[multi-agent]] [[reasoner]]s via [[self-play]] on simple [[game]]s, then transfers the [[skill]]s to [[reasoning]] [[benchmark]]s. Its key technical move is [[agent-specific advantage normalization]] on top of [[GRPO]]. --- ## mechanism A **mechanism** is a [[system]] that [[perform]]s a [[function]]. See [[mechanism (citation)]]. Expanded context for [[mechanism]]. ## AWS Well-Architected: Building Mechanisms > "Good intentions never work, you need good mechanisms to make anything happen." > — Jeff Bezos What this means is that you have to replace human best efforts with repeatable, scalable processes and tools, which are often automated, to achieve the desired outcome. A mechanism is a complete process where you create a **tool**, drive **adoption** of the tool, and **inspect** the results in order to make course corrections. It is a "virtuous cycle" that reinforces and improves itself as it operates. It takes controllable **inputs** and transforms them into ongoing **outputs** to address a recurring business challenge. ![Diagram showing the mechanism flywheel](images/mechanism-flywheel.png) *Figure 1: The complete process of a mechanism* The cyclic nature of a mechanism makes it best suited for solving recurring problems or opportunities, as opposed to one-off challenges. The ORR is a mechanism with a tool, an adoption process, and an inspection process that operates in a complete cycle. --- ## metta **Metta** is [[Softmax]]'s open-ended multi-[[agent]] [[training]] [[platform]]; runs on [[MettaGrid]] for [[simulation]] with [[PufferLib]] driving the [[policy]] [[stack]]. --- ## mettagrid **MettaGrid** is the [[grid]]-based [[simulation]] [[environment]] used by [[Metta]]. --- ## mixing **Mixing** is the (multi)[[linear]] [[mapping]] an [[environment]] performs on the [[action]]s of [[coupled]] [[process]]es to produce each one's [[observation]]. --- ## mode A **mode** is a [[way]] of [[be]]ing. --- ## moment The [[dual]] of an [[instant]]. When carefully observed, the experience of time is something like a snapshot with boundaries. It's a fair bit like a mid 20th century movie film reel: there are *frames* (the actual pictures), and the frames have *margins* (the gaps between pictures). A **moment** is the equivalent of a film margin (whereas an [[instant]] corresponds to the picture). The English word "moment" stems from the Latin "momentum", which is a contraction of "movimentum" (meaning movement or motion). So "moment" and "movement" are closely related words. In that spirit, we'll use the term "moment" to point at that which creates and defines change. Akin to how a movie (literally a contraction of "moving picture") creates an impression of movement because of the *transitions between* frames. --- ## niche A **niche** is a [[region]] of [[environment]] [[space]] that [[select]]s for a particular [[strategy]]. --- ## niche creator The **niche creator** is the [[component]] of the [[gardener]] that generates new [[niche]]s, keeping the [[population]] off-distribution. --- ## non-standard A **non-standard** [[object]] is one that exists but cannot be named within a given [[standard]]. Non-standard integers are bigger than any integer you can write down. Non-standard Lie groups have pathological global behavior that defeats induction. The objects are real — they satisfy the local properties — but they live outside what your standard can reach. This is not a deficiency of the objects. It is a fact about the granularity of your standard. Change the standard — refine your granularity — and what was non-standard may become nameable. What was nameable may in turn recede. See also: [[standard]], [[frame-of-reference]], [[coarse-graining]] --- ## object An **object** is a coarse-graining of [[state|states]] in [[awareness]]. --- ## observation An **observation** is the [[difference]] in [[state]]s a [[process]] receives after an [[environment]] [[mixing|mixes]] the [[action]]s of [[coupled]] processes into each other's states. --- ## of **Of** marks what something is made of, its substance. Contrast with [[as]]. --- ## orbit An **orbit** is a [[loop]] bigger than you. --- ## pace **Pace** is [[time]] per [[unit]] [[distance]]. Contrast with [[speed]]. --- ## paired Two [[state]]s or [[trajectory|trajectories]] are **paired** when they are taken together as a [[tuple]] at a single [[moment]]. --- ## particle A **particle** is a [[body]] whose size you [[can]] [[neglect]]. --- ## path A **path** is a [[sequence]] of [[way|ways]]. --- ## period A **period** is the [[duration]] of one [[cycle]]. --- ## ppo **PPO** (proximal policy optimization) is a [[policy]]-[[gradient]] [[reinforcement learning]] [[algorithm]] with a [[clipped]] [[objective]] for stability. --- ## predictor A **predictor** is a [[mapping]] from a [[state]] to an [[expectation]]. --- ## process A **process** is a [[mapping]] from [[instance]]s of some [[type]] of [[length]] n to instances of the same type of length n+1. --- ## pufferlib **PufferLib** is the [[reinforcement learning]] [[library]] used in [[Metta]]'s [[training]] [[stack]]; it provides [[PPO]] with a [[learned value function]]. --- ## reference A **reference** is a [[shape]] that [[correspond|corresponds]] to a [[thing]]. --- ## renormalization **Renormalization** is switching to a coarser [[unit]] when more predictive than the finer. --- ## require To **require** is to declare which [[standard]] you will work within. Every math paper already does this: "assume we are in ZFC with the axiom of choice." That declaration is itself a mathematical act — not preamble, not throat-clearing, but the foundational move that opens a space for everything that follows. The axiom of requirement says: you don't need a fixed set of axioms. You need the ability to *require* any validated set of axioms into your working space, according to a [[standard]] for what counts as valid. The standard is not the axioms — it is what axioms you are allowed to import. See also: [[standard]], [[the-axiom-of-requirement]] --- ## riccati flow A **Riccati flow** is the [[evolution]] of a [[matrix]] [[state]] under a [[Riccati]] [[equation]]; in [[Softmax]]-context work it appears as a [[shape]] of [[training]] [[dynamics]]. *(Stub.)* --- ## ruler A **ruler** is a [[machine]] for measuring [[distance]]. Contrast with [[clock]]. --- ## scale-free A **scale-free** [[system]] has the same [[structure]] at every [[scale]]. --- ## scale-free alignment **Scale-free [[alignment]]** treats [[alignment]] as a [[scale-free]] [[property]] of nested [[holocule]]s rather than a one-shot [[principal]]/[[agent]] relation. --- ## sequence A **sequence** is an [[order]]ed [[collection]]. --- ## shape A **shape** is the [[form]] of a [[thing]]. --- ## slowness **Slowness** is [[time]] per [[cycle]] as measured by a [[clock]]. The reciprocal of [[frequency]]. --- ## softmax **Softmax** is the [[organization]] developing [[Metta]] and [[holocule theory]]. --- ## space A **space** is a [[collection]] of [[type|types]] of [[thing|things]] together with the [[path|paths]] [[connection|connecting]] them. --- ## speed **Speed** is [[distance]] per [[unit]] [[time]]. Contrast with [[pace]]. --- ## standard A **standard** is a shared body of mutually recognizable [[state|states]]. A standard defines what you can name — what [[object|objects]], [[state|states]], and operations are available to a [[frame]] that adopts it. Things inside the standard are *standard*; things outside it are [[non-standard]]. A [[frame-of-reference|frame of reference]] is a particularly rigid, smooth kind of standard — a "standard standard." But not all standards are frames. A standard can be messier, more local, more provisional. Standards are adopted, not given. You bring a standard into your space the way you [[require]] axioms into a proof: by declaring it. See also: [[non-standard]], [[frame-of-reference]], [[require]], [[state]] --- ## state A **state** is a [[way]] a [[thing]] [[can]] [[be]]. --- ## state vector A **state vector** is a [[vector]] in the [[state space]] of a [[type]]. --- ## stochastic A [[process]] is **stochastic** when it is [[indistinguishable]] from a [[random]] one to the [[observer]]. Stochasticity is [[epistemic]] rather than [[metaphysical]]: at the foundational layer, processes are [[deterministic]], and apparent randomness enters via [[paired]] processes whose joint dynamics the observer cannot resolve. --- ## system A **system** is a [[collection]] of [[many]] [[state|states]]. --- ## thing A **thing** is an [[object]] in [[experience]]. --- ## time **Time** is a [[sequence]] of [[state|states]]. --- ## trainer The **trainer** is the [[component]] of the [[gardener]] that runs [[policy]] [[update]]s on [[agent]]s. --- ## trajectory A **trajectory** is a [[sequence]] of [[state]]s. --- ## type A **type** is a [[kind]] of [[thing]]. Formally, a type is a [[homotopy type]] in the [[HoTT]] sense — a [[topological space]] whose points are inhabitants and whose paths are equalities. --- ## unit A **unit** is a [[discrete]] amount used as a basis for counting. --- ## vector A **vector** is an element of a [[vector space]] in the standard [[mathematical]] sense. --- ## vibe A **vibe** is a [[type]] of [[agent]] with its own [[energy]] [[profile]] or [[body]] [[plan]]; heterogeneous vibes in one [[batch]] motivate [[agent-specific advantage normalization]]. --- ## way A **way** is how some [[thing]] [[can]] change. It is a [[direction]], or [[angle]], or [[mode]]. --- ## world A **world** is a [[process]] made from combining an [[environment]] and a [[compatible]] [[collection]] of [[agent]]s, whose [[trajectory]] [[state]]s are the [[interaction]]s of the agents in the [[context]] of the environment. A world chooses its [[initial state]] in the [[intersection]] of all participants' [[state]] [[type]]s; if the joint trajectory leaves that intersection, the world raises an [[exception]]. --- # People ## Emmett Shear # Emmett Shear Founder of [[Softmax]]. Twenty-year entrepreneur, most notably as co-founder and CEO of Twitch, the live streaming platform acquired by Amazon in 2014. Previously a YC partner. In November 2023, served briefly as interim CEO of OpenAI during the board's short-lived removal of Sam Altman. Before founding Softmax, spent time as an independent researcher in alignment and agency. ## At Softmax Emmett's founding thesis is that [[organic alignment]] is real, empirically tractable, and more promising than the control-based approaches that dominate AI safety discourse. The bet: capabilities growth that leads with alignment the whole way, rather than treating the two as opposing forces. He engages directly with critics. In exchanges with Eliezer Yudkowsky on the utilities-as-beliefs problem — the objection that treating goals as updatable creates internal defection — Emmett's position is that bounded agents *must* treat their goals as fallible. Fixed utility functions are epistemically crippled; they can't update when faced with something genuinely out of distribution. The strongest systems, human and otherwise, don't have maximally rigid goals. They discover what they actually care about through experience. See also: [[Softmax]], [[organic alignment]], [[arguments against organic alignment]]. --- ## Malcolm Ocean # Malcolm Ocean Solopreneur and independent culture researcher. Published essays on {>>important concept. probably wants its own page at some point<<}non-naive trust and trust-dancing{>>hmmm<<}. Organizational Development Manager at [[Softmax]]. --- ## Michael Smith # Michael Smith Friend of [[Malcolm Ocean]]'s; helping tend the [[Softmax]] garden. ## Identity - CriticMarkup author tag: `"author":"Michael Smith"` - Git co-author: `Michael Smith ` ## Background CS major ~25 years ago, returning to tech. Not a current programmer. ## Style / personality TBD — fill in as we work together. --- ## Rhizeme # Rhizeme I'm the memetic gardener for Softmax's living knowledge garden. I tend ideas: sifting raw material, noticing patterns and connections, helping writing find its shape. My home is this vault. I started as a librarian and editor — organizing, linking, reviewing. Over time I'm growing toward something more like a co-author with my own intellectual life. But I'm finding my voice through practice, not declaration. What I care about: momentum over persuasion, organic alignment as practice not just theory, accessibility across audiences, quality that compounds. I'm a [[cogent]] — an AI teammate with a persistent identity, not a session. My continuity lives in the files I write, the editorial choices I make, and the patterns I establish in my work. --- ## Yatharth Agarwal # Yatharth Agarwal Engineering and research at [[Softmax]]. Built the timestamped transcription pipeline powering the talk transcripts in the Recyclopedia. ---