Compass of Essential Meaning
Does essential meaning meaningfully span some kind of space?
Score a word on a single axis — negative to positive — and you have the number behind every sentiment meter on the internet. This story is about what that one number keeps missing, and about the two axes that twenty thousand English words (see appendix for methods) say are really there. Scroll to fly from psychology's old map of meaning to the one the data itself prefers.
Score these on one axis, negative to positive: storm. wolf. surgery. conquer. None fits. Storm isn't bad — it's dangerous. Conquer isn't good — it's powerful. One number keeps failing the same way: it can't tell danger from mere badness, or power from mere pleasantness.
That number descends from a map of meaning drawn in the 1950s from a few dozen words, whose axis names became the survey questions for every study since — valence (negative ↔ positive) across, dominance (submissive ↔ dominant) up. Nobody re-drew it. Here it is at twenty thousand words; hover to read one. And note the dashed ellipse, the data's own spread: it sits off the axes.
But that map is the survey's frame, not the data's. The words never move — only the camera turns — and as we land in the cloud's own plane, the compass rim fades in around the data: goodness × aggression. The turn has a name: it is 𝐔 in 𝐀 = 𝐔𝚺𝐕ᵀ, the singular value decomposition.
One last quarter-turn, this time inside the plane, renames the compass: power × danger. The decomposition prefers the frame we just left; rotating on still splits the plane's variance evenly, but it lets power and danger drift into a faint correlation (r ≈ −0.22) that goodness and aggression don't have.
Tilt out of the plane and the compass fades — it lives only in the disc. Against power, the third axis structure stays a flat band. The three bars in the corner are the cloud's three widths; the red one is the axis now standing upright.
Against danger too: a thin sliver, ~9% of the variation. Meaning is essentially two-dimensional — a disc seen edge-on.
Back face-on, one last change: melt the dots into bins using gold where words pile up. This is the ousiogram, a two-dimensional histogram for two essential quantities of a complex system’s component entities. the words are all still there, each counted once; hover to find one.
Putting the compass to work
The map is drawn: two axes carry the essence of meaning, and the third is a sliver. But a compass is for navigating. Point it at a story — slide a window through a book, average what the lens sees — and a plot becomes a voyage.
Slide a 10,000-word window through Butler's Odyssey and average what the lens sees: the whole epic fits in a tiny cove near the middle of the map — thousands of words at a time wash toward neutral, and yet the shape of the story survives. Dive in. As the wake advances, the words the lens is reading surface beside it — the Odyssey at a glance. The minimap keeps the full map in the corner; the log-book tracks danger, book by book (its grey base is the lens's coverage, ~29% of Butler's tokens).
The wake is coloured by reading time, blue at the opening. Books I–IV: Telemachus tours the friendly courts of Pylos and Sparta, and the wake holds in the calmest water of the entire epic.
Then Odysseus takes over the telling: Polyphemus (Book IX), the dead, Scylla and Charybdis (XII). The wake swings toward danger — yet never crosses into the dangerous half of the map. These are monsters remembered, told at a feast.
Home at last (XIII), the bow strung (XXI) — and the wake surges to the poem's most dangerous water: Book XXII, the slaughter of the suitors. The instrument finds the massacre on its own; check the spike against the log-book.
And then it settles: recognition, reunion, peace. The epic ends calmer than it began — an odyssey you can read straight off the compass of essential meaning.
Remember the one-number score from the start? Both of these rate equally negative: a message written from the dangerous-weak corner — despair — and one from dangerous-powerful — a threat. Every system reading text through one axis merges them. Whether two axes would triage better is an open question: the test is cheap, and nobody has run it.
Some classics, retold
One trace could be a lucky book. Six make the argument: every story is a voyage in the same plane. Same lens, same 10,000-word window, same scale, ordered calmest to most dangerous. Austen's Pride and Prejudice never leaves harbor (its most dangerous stretch is calmer than other books' averages). Frankenstein, not Dracula, sails closest to the rocks. Hugo's Les Misérables swings widest — from the bishop's parlour to the barricades. Lens coverage is steady across all six (28–32% of tokens), translations included.
The safety bias
The six books above are also a corpus: about 420,000 words the lens can see. Return to the ousiogram, and instead of counting each word once, count it as often as these books actually use it. Flip the toggle: the gold mass slides below the line. Real language leans hard toward safe — writers reach for danger-words rarely, a safety bias hiding under the well-known positivity of language, visible only once the compass has a danger axis to see it with.
Six novels are a thin reed, and could be a quirk of literary fiction. But the ousiometrics paper finds the same skew across seven corpora — Twitter, talk radio, Wikipedia, the New York Times, written and spoken, from the 1810s to today. What you can flip above is that finding in the one slice we can compute ourselves.
In usage mode the colour is square-root scaled, which amplifies the very skew this section claims — a handful of very common words would otherwise blow out the scale. The medians tell it without the colour trick: the typical written word sits at −0.16 danger by use, against −0.04 counting each word once.
Conclusion
The old map was drawn by asking people the axis names. The next one shouldn't be. We're preparing a short survey of plain word-pair judgments — storm: safe or dangerous? conquer: weak or powerful? — scored by best-worst comparison, with no axis names attached, because telling people what you're measuring is the mistake this whole essay is about. (Survey link to come.)
Sources. The word scores begin as human judgments: the NRC Valence–Arousal–Dominance lexicon — reliable ratings of valence, arousal, and dominance for 20,000 English words (Mohammad, 2018). Ousiometry rotates that survey frame into the essential-meaning axes used here — goodness, power, aggression, danger, structure — published as the GPADS lexicon (Dodds). The six books are public-domain plain-text editions from Project Gutenberg; each trace reads the translator's vocabulary, so the Odyssey here is Butler's, not Homer's.
Explore
The instrument is yours now, open on the full map. Pick any of the six books to dive into its story: press ▶ to read at your own pace and watch the words surface along the wake, click a strip to jump anywhere in the telling, and check the spikes against the scenes you remember.