How we map cognitive topology

Validated psychometrics, topological data analysis, and the philosophical lineage that informs the work.

Validated instruments

Our input layer is a six-instrument suite of validated psychometrics with peer-reviewed publication history: BFI-2 (Big Five), HEXACO-60 (adds Honesty-Humility, the dimension BFI-2 misses), IPIP-NEO-120 (30 facets at deeper resolution), ECR-R (adult attachment — avoidance + anxiety), PERMA (wellbeing across five domains), and Ryff Psychological Wellbeing (six eudaimonic dimensions). A seventh, PID-5-BF, is a clinical screening instrument and is unlocked only when there’s a licensed interpreter in the loop.

Topological data analysis

Each completed instrument suite produces a vector — a point in a high-dimensional space where each axis is a personality dimension or facet. The traditional move is to average across people and report aggregate scores, which loses everything interesting about how members differ.

Topological data analysis takes the other path. Treat the vectors as a point cloud; ask what its shape looks like. Are there clusters? Where are the gaps? Which points sit between clusters, holding them together? TDA asks those questions directly — persistent homology, clustering over scale, mapper-style projection — and returns the answers as readable structure. Our implementation is deterministic, reproducible, and benchmarked: it has to recover structure we plant in synthetic teams before we trust it on yours.

00.511.5merge distance (ε)merges at ε = 0.331merges at ε = 0.394merges at ε = 0.454merges at ε = 0.671merges at ε = 0.724merges at ε = 1.293merges at ε = 1.622never merges — the team's single connected component∞chosen scale ε = 1.243 bars survive → 3 cognitive clustersborn 0, dies 0.331born 0, dies 0.394born 0, dies 0.454born 0, dies 0.671born 0, dies 0.724born 0, dies 1.293born 0, dies 1.622birthdeathH0 is born at ε = 0 by construction

The dashed line marks the scale our pipeline selects with the largest-persistence-gap heuristic: below it, within-cluster noise has died; what survives is structure.

This team shows no loop structure (H1 is empty); we say so rather than decorate.

Persistence intervals (merge distances): 0.331, 0.394, 0.454, 0.671, 0.724, 1.293, 1.622, plus one component that never merges. At the chosen scale 1.236, 3 clusters remain.

Persistent homology of an illustrative eight-person leadership team, computed by our pipeline — reproducible from the committed generator script.

For a leadership team that translates into five practical outputs: a coverage map showing which regions of the measured personality space are represented and which are gaps; the team topology map — the clusters and the bridges between them, rendered on your real team (the shape above); bridge scores measuring how much the team’s cluster structure depends on each member — the load-bearing connections, not a social graph; a resilience score summarising how well that structure survives any single departure; and a Cognitive Diversity Index, a single summary number for how spread out the team’s profiles are. Persistent homology, illustrated here, is the mathematical backbone underneath.

Lineage

Personality testing on its own gives you traits. It doesn’t tell you what to do with them, or why some combinations of minds produce wisdom and others produce committee. We pair the psychometrics with three other disciplines:

  • Cognitive science of meaning — John Vervaeke’s work on relevance realization and 4E (embodied, embedded, enacted, extended) cognition gives a language for what differently-configured minds bring to a shared problem: they realise different aspects of the same situation as relevant. That’s the working hypothesis our team engagements examine, not a settled law.
  • Depth psychology — Jung and the post-Jungian tradition take the long view of individuation: what it means for a person (or a team) to develop along the seams where their shadow material concentrates. Useful framing for the “why is this gap structural and not just a hiring problem” question.
  • Contemplative traditions — practices for attention and pattern recognition that long predate psychometrics, mapped onto the same dimensions modern science now measures. They give the lived-experience counterpart to the data.

Validated instruments give us measurement. TDA gives us structure. Interdisciplinary lineage gives us the language to translate the structure back into something a leadership team can act on. The lineage is interpretation, not evidence — the first two have to stand on their own, and they do.

What the report produces

For individuals: facet-level personality profile across all instruments you have access to, with narrative interpretation. For teams: Cognitive Diversity Index, coverage map, bridge connector identification, resilience analysis, and recommendations sized to the engagement. See a sample team report or a sample individual report.

Take it with you

A one-page summary suitable for sharing with colleagues or sending alongside a discovery call. Download the methodology brief (PDF) →