Working paper · Kevin Russell · 25 Apr 2024 · interactive edition

Towards a General Theory of Semiotic Singularities

Researching Abnormally Dense Media Objects (ADMOs)

Plate I Meaning-space around a dense sign. Move your pointer or finger to drag the mass across the grid.

“A semiotic singularity is an informatic entity of such extreme conceptual density that it begins to warp the fabric of meaning-space around it.”

Film Watch the essay in motion

Part 1 of 3: the idea, in motion. Narration by Kevin Russell with Atlas, his APA (Adjacent Persona Agent). Captions in the player menu. Watch on YouTube · all three parts.

How to read this edition: text in quotation marks is Kevin Russell's essay, verbatim. Anything in a interpretive box is my illustration. The essay contains no equations, parameters or simulations.

Narration: Kevin Russell with Atlas, his APA (Adjacent Persona Agent), from Substrate Speculations. The page follows the voice; scroll away and it waits for you.

§0 Abstract

“The key mechanism driving the formation of semiotic singularities is a positive feedback loop between a sign's intensional depth and its extensional reach.”

The essay draws on semiotics, information theory, and category theory. Its claim is that some sign configurations self-catalyze and trigger localized collapses in semantic dimensionality. Past a threshold, an irreversible semiotic collapse occurs, and the ADMO becomes a black hole in concept space, disconnected from any conventional signifying chains.

  1. Depthmeaning compresses into a sign
  2. Reachthe heavier sign bends nearby fields
  3. Thresholdpast a certain density…
  4. Collapseirreversible: a black hole in concept space
Fig. 1 n = 10
§1 Introduction
“In the accelerating semiotic flux of the modern world, signs are becoming ever more densely interconnected, recursive, and self-amplifying.”

Every word is a point in a space of possible meanings. Here that space has ten dimensions, rotating slowly so you can see it from different angles. The space is smooth and no point dominates.

§2 A metaphor
“The metaphor works by connecting two seemingly disparate domains, revealing hidden patterns of similarity.”

A sign appears and bridges two clusters, time and water.

§2 Overdetermination
“As more and more signifiers are drawn into the metaphor's orbit, its meaning becomes increasingly overdetermined, until it begins to function as a kind of strange attractor in semiotic space.”
§2 Formalisation
“We can think of a sign as a point in an n-dimensional space, where each dimension represents a possible meaning or association. As the sign becomes more densely connected, its effective dimensionality begins to collapse…”

Watch the n counter and the axis rays. Dimensions are switched off one at a time.

§1 Singularity
“…a collapse of semantic dimensionality into a single, infinitely dense point.”

interpretive The projection, the clusters and the dimension-by-dimension shutdown are my visual metaphor for the essay's sentence.

Fig. 2 The depth–reach phase portrait

interpretive model The essay describes depth feeding reach and reach feeding depth, a threshold, and irreversibility (§2, Abstract). To show that, I use a two-variable system: dD/dt = −D + R   dR/dt = −R + A·D²/(9 + D²). Reach saturates, so a sign only takes off once it already has some depth. When the coupling A exceeds 6, there are two basins separated by a separatrix. Crossing ρ = D·R ≥ 50 means collapse, and collapse is absorbing. All the numbers are mine.
Phase: ordinary sign

interpretive A known word lands at its real place among 15,000 English words, and its depth and reach come from that neighbourhood. Join two with “+” to watch them merge. Unknown words fall back to a hash of the letters. Nothing leaves your browser; share it with Copy link.

Intensional depth D
Extensional reach R
Density ρ = D·R (threshold 50)
Effective dimensionality n

separatrix: the event horizon in the dynamics   collapse zone ρ ≥ 50   nullclines   ● stable attractor   ○ saddle

§3 The Anatomy of an ADMO

The body of the essay lists four properties, introduced as “firstly”, “secondly”, “thirdly” and “finally”. The abstract adds two more: seeming simplicity belied by immense hidden complexity and ontological indeterminacy and paradox. Each has an instrument below.

Fig. 3 · firstly

Resistance to paraphrase

“Because their meaning is so overdetermined, any attempt to express them in other terms inevitably loses something essential.”

Pick a source, then say the same thing in your own words. The page measures how much meaning survives, using the same word embeddings as Fig. 2b.

    —

    data retention = cosine similarity of sentence vectors (method below). interpretive reading low retention as “ADMO-ness”. Nothing you type leaves your browser.

    Fig. 4 · secondly

    Recursive, fractal structure

    “Like a Mandelbrot set, the closer you zoom in, the more intricacy you reveal.”

    interpretive An ordinary sign is drawn as a disc, so zooming in only finds a straight edge. The ADMO is drawn as the Mandelbrot set the essay compares it to.

    Fig. 5 · thirdly

    Psychoactive effects

    “They can induce feelings of awe, disorientation, or epiphany… perhaps because they short-circuit the normal processes of semiosis.”

    Hold the button (or Space) for a few seconds.

    interpretive These are not real measurements. The gauges are a theatrical stand-in. The motion turns off if your system asks for reduced motion.

    Fig. 6 · abstract

    Ontological indeterminacy & paradox

    “These pieces deliberately court paradox and ambiguity, short-circuiting the usual processes of aesthetic interpretation.”

    Duchamp's Fountain: is it art?

    —

    interpretive Whatever you answer, the object supplies the counter-reading. Certainty never settles; that is the probe.

    Fig. 7 · finally

    Memetic propagation through a real network

    “Because they are so semantically dense, they act as a kind of conceptual condensation nucleus, attracting more and more attention and elaboration.”

    312 people in six communities. Each community grows by preferential attachment, so it has its own hubs, and 54 bridges join the communities (the curves through the centre). Each adopter passes the sign to each neighbour with probability p, which comes from the Fig. 2 density. An ADMO jumps the bridges, while a plain word stays home. The colour deepens with each meta-layer, the number of times the sign has been retold.

    —

    interpretive This is a standard independent-cascade model on a community graph. The community names and the mapping from density to p are mine.

    §4 Case Studies

    Each case below takes a different route into the same basin. Load one into Fig. 2 and watch its trajectory.

    Sacred symbols

    the Christian cross · the Buddhist wheel of dharma

    “…subject to centuries of intense contemplation, elaboration, and reinterpretation… forming dense knots in the fabric of religious semiosis.”

    Route: depth first, slow and steady.

    Avant-garde art

    Duchamp's Fountain · Malevich's Black Square

    “They become focal points for endless theorizing and debate, sucking in more and more cultural attention until they collapse into a kind of singularity.”

    Route: almost no intrinsic depth, then reach through debate.

    Viral memes

    “a kind of strange loop or self-encoding sign”

    “Eventually, it may become so densely self-referential that it tips over into a sort of abstract absurdity, an unstable singularity of pure memetic form.”

    Route: huge reach and high coupling. Note the word unstable.

    §5 Implications and Future Directions

    “As the density of our semiotic environment continues to increase, we can expect to see more and more examples of runaway meaning-collapse, as formerly stable sign systems are destabilized by self-amplifying loops of reference.”

    Exciting

    “…a kind of extreme creativity… the leading edge of cultural evolution, the points where the novel emerges out of the chaotic recombination of the old.”

    Disturbing

    “We risk being overwhelmed by a kind of semiotic vertigo, a disorientation in the face of an increasingly opaque and recursive meaning-scape.”

    The essay's programme is to recognize the signs of imminent semiotic collapse and develop countermeasures to prevent or contain it. In Fig. 2, recognising collapse means seeing which side of the separatrix you are on. A countermeasure means lowering A below 6 before you cross ρ = 50. Once the sign has collapsed, nothing undoes it.

    Fig. 8 · the event horizon

    Keep scrolling. Every word of the essay is on this canvas.

    “As we approach the event horizon of a global semiotic singularity, it becomes ever more vital to map the strange topologies of sense that are warping the very possibility of communication and thought.”

    Kevin Russell, closing line of §5

    interpretive The essay calls for an ability to maintain coherence and clarity in the face of extreme conceptual density. Here, “resilience” puts the words back into readable lines.

    Note Method & credits

    What is the essay's, and what is mine. Every sentence in quotation marks is quoted verbatim from the essay. The essay is a conceptual text with no equations, data or simulations. Every figure here is a reading of it, and each is marked interpretive.

    Your sign
    Typed words are first looked up in a meaning map (Fig. 2b), built offline from public parts only. Words: the 15,000 most frequent lower-case English words (2–15 letters, minus a small blocklist) from wordfreq by Robyn Speer (data CC BY-SA 4.0). Model: all-MiniLM-L6-v2 (sentence-transformers, Apache-2.0), each word embedded alone, then reduced by PCA from 384 to 48 dimensions (43% of variance kept) and stored as int8. Neighbours are the 12 nearest by cosine. Depth is the percentile of a word's mean similarity to those 12, meaning how dense its neighbourhood is. Reach is the percentile of its PageRank in the symmetrised 12-NN graph, meaning how connected it is. These become D = 0.3 + 4.7·depth, R = 0.3 + 7.7·reach and A = 5 + 6·√(depth·reach). That mapping is my choice and is interpretive. A phrase is the mean of its words' vectors, and its depth and reach are averaged over its 12 nearest words. “a + b” uses the midpoint. The 2-D map is UMAP (cosine, 15 neighbours, seed 42). The derived file (meaning.json, about 1.7 MB, CC BY-SA 4.0) loads from this site only when you seed a word. The build script is scripts/semiotic/build_embeddings.py. Caveats: single words have no context, so senses blur (“bank”), and percentiles are relative to this list. A word not in the list is hashed (32-bit FNV-1a, lower-cased) into a seeded random generator that sets starting D, R and A, and a position in the Fig. 1 cloud. The hash knows nothing of meaning: it is a deterministic toy so that every word gets a reproducible fate. It runs entirely in your browser.
    Fig. 3
    Paraphrase resistance is measured, not scripted. Each sentence becomes a SIF vector (Arora, Liang & Ma, 2017): the 48-d word vectors of Fig. 2b, weighted by a/(a+p(w)) with a = 10−3 and p(w) from wordfreq, averaged, then with the first principal component of a 56-sentence reference set removed. Retention is the cosine between source and paraphrase, and resistance is 100 × (1 − mean retention) over your attempts. Baselines come from 14 sources with 3 good-faith paraphrases each, written for this page: 5 everyday sentences, 5 sentences quoted from the essay and 4 of its named cases. Mean retention was 0.80 for everyday sentences, 0.36 for essay sentences and 0.19 for cases. As a check, the full 384-d all-MiniLM-L6-v2 sentence model gives 0.82, 0.56 and 0.30 on the same pairs, and it correlates with the in-browser approximation at r = 0.86. What is real: the similarity numbers. What is not: the claim that low retention means a sign is an ADMO. Abstract, long or short sentences and rare words all lower retention on their own. The baselines are tiny and hand-written by one author, so they are confounded and illustrative only. Word order and negation are invisible to an averaged bag of words, so “not art” scores close to “art”. The build script is scripts/semiotic/build_paraphrase.py.
    Fig. 1
    Forty words placed in a 10-D Gaussian space (two semantic clusters plus noise), projected by a slowly rotating orthonormal 2-frame (a “grand tour”). Scrolling sets the bridge, the pull, and how many dimensions are switched off.
    Fig. 2
    A two-variable system, dD/dt = −D + R, dR/dt = −R + A·D²/(9+D²), integrated with RK4. Collapse is defined as D·R ≥ 50. The separatrix is the stable manifold of the saddle, integrated backward. All constants are chosen for legibility, not fitted to anything.
    Fig. 4
    The Mandelbrot set, which the essay itself uses as the comparison, rendered per pixel in double precision. Below about 10−13 the floating point gives out before the structure does.
    Fig. 5
    Theatre, not psychometrics. In the scripted curves, awe arrives first, disorientation peaks and then falls, and epiphany comes late and suddenly, with a long afterglow.
    Fig. 7
    Six communities of 52 people (Barabási–Albert, m = 2) joined by 54 degree-weighted bridges, with an independent cascade on top. The bridges are drawn bundled through the centre.
    Fig. 8
    The words of this page, laid out and pulled into a point by scroll position, followed by the essay's closing sentence.
    Narration
    Narration: Kevin Russell with Atlas, his APA (Adjacent Persona Agent), from Substrate Speculations (“Semiotic Singularities v2”). Two brief asides were trimmed for this page (about 5 s in total), with 40 ms crossfades. Captions and the section timing come from an automatic transcript (faster-whisper), corrected by hand; quotations light up as they are read. The waveform is precomputed. Nothing is downloaded until you press play.
    Build
    Hand-written HTML, CSS and canvas, with no libraries and no third-party requests until you play the film. The only extra downloads are the meaning map, which comes from this site when you seed a word, the narration (about 5–8 MB) when you press play, and the film, a YouTube embed (youtube-nocookie.com) that loads only when you press play on it. Sound is synthesised with WebAudio and is off by default. Reduced-motion settings are respected, and slow devices drop to a lighter rendering mode automatically (or add ?low to the URL).
    Credits
    Essay by Kevin Russell (Substack, 25 April 2024), which notes it was “curated via Claude and Websim.” Interactive edition built for Kevin Russell as an illustration of the text. Narration by Kevin Russell with Atlas, his APA (Adjacent Persona Agent).

    Glossary

    Intensional depth
    “the richness of its internal meaning” (§2)
    Extensional reach
    “the range of its external associations” (§2)
    Semiotic singularity
    “an informatic entity of such extreme conceptual density that it begins to warp the fabric of meaning-space around it” (§1)
    ADMO
    Abnormally dense media object, “the end result of this process” (§3)
    Event horizon
    The boundary beyond which associations are drawn in (Abstract). In Fig. 2, interpretively, it is the separatrix.
    Semiotic resilience
    “an ability to maintain coherence and clarity in the face of extreme conceptual density” (§5)