Anthropology lets a reader start with a person, find the kinds of news associated with that person, follow those news patterns to other people, and return to the articles. Its research paper, The Dual Geometry of People and News, describes the system and its evidence. This companion explains the mathematics one operation at a time.
The starting point is The Mathematics of Eigen Times. That book explains how articles become vectors, how covariance reveals recurring news directions, and how projections describe a new story. Here we take the next step. A collection of articles associated with a person becomes a profile in news space. A population of profiles produces another set of directions: patterns of how people are covered. One loading matrix connects the two spaces.
You need arithmetic and a willingness to read a small table. The next two chapters introduce the vector and matrix ideas needed to continue. When a prerequisite deserves a longer explanation, a link takes you to the relevant Eigen Times section. We do not repeat its derivations of text weighting, efficient matrix decomposition, or clustering thresholds. We spend that space on the new questions: how to combine a person’s articles, what to compare that coverage with, what a people pattern means, why navigation works in both directions, and how shared ontology concepts could connect different news corpora.
One fictional example runs through the book. It has four people, three news coordinates, two source-and-decade cells, and 45 distinct articles. The running example and plotted numerical matrices are generated by the accompanying script. Short additional arithmetic illustrations are written out in the text. Figures use blue for positive values and rust for negative values; color describes a sign, never a judgment about a person. Displayed values are rounded, while computations use their full precision.
The empirical examples come from the Anthropology paper’s 2 October 2026 edition. Its people models retain the 1 October snapshot. The catalog has subsequently grown to 59,399 people and organizations, but the fitted models still contain 217 Hacker News profiles and 61 general-news profiles. A catalog identity and a supported mathematical profile are different objects. None of the fictional numbers below is a measurement of a real person.
Version 1.1.0. This teaching expansion works through lengths, residuals, covariance, eigenvectors, SVD, profile aggregation, neighbor geometry, attention, and proposed ontology models in smaller steps. The complete Python and native OCaml notebooks compute the new synthetic examples as well as the original fixtures. Original numerical evidence, figure inputs, and the dated Jeff Dean journey are unchanged.
We will also keep implemented operations separate from research proposals. The published system computes the profiles, people basis, reciprocal indexes, and dated news overlay described here. Incremental profile refresh, learned ontology calibration, and a validated alignment between the two corpora are extensions to evaluate. Explaining their mathematics does not make them deployed features.
| If you want more on | Read in the Eigen Times companion |
|---|---|
| Turning words into numbers | Text as vectors |
| Dot products and angles | Cosine similarity |
| Rows, columns, multiplication, transpose | Matrices pictured |
| Means, covariance, and eigenvectors | The axes of a point cloud |
| Singular value decomposition (SVD) and low-rank approximation | The singular value decomposition |
| Naming axes by rotation | Varimax |
| Projection and missing information | Projection, reconstruction, residual |
| Updating sums without rereading everything | Sums over blocks |