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Topology of Societal Decoherence

Data suggests the “left” and the “right” no longer speak the same language.

As social feeds pull left and right toward different words, the two sides slowly stop sharing a language. This is a visualization — our linguistic feasible space, our respective linguistic universes, are represented as topological manifolds (tori: donuts) — using data from a consistent platform: the floor of Congress (1981 through 2025). Here you can see that the right and left have separated like a failed emulsion. The mathematical description is a fiber bundle on a torus, decohering.

Here’s what you’re watching: each cloud is one party’s footprint in language-space — shared vocabulary on one axis, emotional register on another, word meaning on the third. Through the 1980s the two clouds interleave on a single surface: one language, weathering the Gulf War and Somalia without a tear. Scrub forward and they separate like oil from water — the Gingrich snap, then slowly through the 2000s, faster after 2010 — until what remains is two distinct tori, barely touching, at 5%.

The tori genuinely re-cohere slightly in the late 90s, shudder through 2009–12, tear violently in 2020–21, and end at “Shared Linguistic Feasible Space: 5%” — not the parametric version’s clean 0%, because the data says the maximum tear was the Jan-6-era Congress with a slight retreat since. I’d argue 5% is a more powerful ending than 0%: measured, not scripted, and quietly hopeful.

Then again, perhaps a torus isn’t the right shape for language at all. Speech isn’t inherently circular — it never owes us a return to where it started. A helix is the more natural form: it lets the data breathe and evolve instead of repeating itself — arguably a truer picture of a time series. Here it is:

Notice how long the braid simply holds — through Reagan, the Gulf War, Somalia, a classifier can barely tell the parties’ vocabularies apart. The fraying is already underway, though: by 1994 the shared space has quietly drifted to about 72%. Then the snap — the Gingrich Congress, when the Contract-with-America message machine handed each party its own vocabulary almost overnight and the braid jolts loose. It pulls briefly back together at 9/11 — the last genuine coherence in the record — then unwinds for twenty straight years, fraying through the Tea Party ramp until the strands of the Jan-6-era Congress barely touch. None of this is scripted: the winding is the measured data, recovering the history on its own.

Linguistic decoherence: because the Z-axis plots 1 − cosine similarity, it is an exact measure of divergence. When the Z-axis spikes (as seen clearly around the 2010 Tea Party era and the post-2020 117th Congress), it reveals that the two sides aren’t just using different vocabularies (which is what the X-axis measures). Instead, it shows that even after aligning their baseline languages, they are using the exact same words to mean entirely different things. The topological distance between their shared concepts is widening, indicating that the speakers are effectively talking past each other. For an intuitive explanation of the Z-axis — disconnected manifolds, the Procrustes rotation, and the angle between meanings — read the full breakdown →

Gold's Rally: A Topological Contextualization

Is gold's price spike a bubble or the real thing? A math tool that measures the shape of how markets move together. The shape looks completely normal, even though the price move was historic. Translation: a genuine, lasting repricing of gold against paper money, not a panic. For the technical reader: persistent homology of cross-asset correlations, 43rd-percentile normal. January 2026, 12 pages.

Read the study