Published

26 October 2026

Neogenerative Semiotics / Foundations

[Part 3/3]: Measurement

Measuring meaning: Adherence, Convergence and Stability in the Semantic Cloud.

This chapter closes the Foundations with a practical proposal: measuring communication quality within the Semantic Cloud through three indices on a 0–100 scale. Adherence quantifies the gap between intention and audience response; Convergence describes how interpretations cluster around the core; Stability assesses durability over time and signals semantic drift. Each index includes signals, small practical actions and interpretative thresholds; a technical appendix provides basic and advanced formulas ready for implementation. The approach remains practical: not a theory of metrics, but tools for designing messages that work and hold across time and contexts.

Abstract [Part 1/3]

In the first chapter of this trilogy, we mapped the conceptual coordinates of Neogenerative Semiotics: the sign as a field of possibilities, the Gaussian Semantic Cloud as the distributional space of meaning, and precipitation as a guided interpretative collapse. We explored the shape of meaning, its distribution and its probabilistic trajectories. We saw how every message occupies a space, not a point, and how that space can be designed, compressed, extended or calibrated.

If you have not read the first article yet, you can find it here:
Neogenerative Semiotics / Foundations [Part 1/3]: The shape of meaning

Abstract [Part 2/3]

In the second chapter, we focused on precipitation: what makes interpretations collapse around a stable core. We distinguished controlled blur, which protects flexibility and context, from unwanted distortions, introduced a quick diagnostic for deviations and showed how to anchor a message with coherent verbal and visual frameworks. The aim: to make readings converge towards the centre while maintaining readability and durability over time.

If you have not read the second article yet, you can find it here:
Neogenerative Semiotics / Foundations – [Part 2/3]: Precipitation

01. Semantic Adherence Index
02. Semantic Convergence Index
03. Semantic Stability Index
04. Overall Index / GOVERNANCE

Introduction

In this third and final part, we complete the trilogy laying the foundations for Neogenerative Semiotics.

The idea of this final part is to address the principle that not measuring means improvising. I therefore introduce my three working indices: Adherence, Convergence and Stability, to assess how well meaning holds across time, contexts and perceptions. These “measures” make sense only on an empirical, practical level, with rules adapted each time to the context and design purpose. Yet they often serve as my compass for achieving consistent, valid and stable precipitations.

01 Semantic Adherence Index

Guiding question: is what people understand what I intend to communicate?

Within the Semantic Cloud, my communicative intention takes the form of a spherical blob: mobile and variable over time, yet, if well contextualised and designed, stable enough to fulfil its purpose as conditions change. But the message “travels” through space and time. Its context and audience can change; external events, manipulation and interference can occur, and much more. When the message arrives, the bubble may no longer have its original shape. A simple but revealing example: on a poor telephone line, one person says certain things while the listener cannot hear properly, misses parts or, worse, believes they heard something that was never said. Or imagine two people looking at the same scene or painting. Do they really see the same thing? Or does each see the result of their own ability to notice details, relate different parts and read between the lines – the result of their culture, sensitivity, experience and expectations? Again, meaning is not a fixed point but a bubble that deforms as soon as the gaze passing through it changes. In practice, measurement is not always possible, at least not with the numerical precision we usually associate with it. But we can approach it probabilistically, or better still statistically, limiting variance and minimising the gap between what I intend to communicate and what is actually understood in a given context and time. That is precisely what we are discussing. Adherence measures this gap between intention and perception.

Objective: meaning should land where we want it, not wherever it happens to fall.

Technical appendix – Adherence Index (0–100)

Advanced formula (cosine similarity):

\[ \text{Adherence} = 100 \times \frac{\mathbf{I}\cdot\mathbf{R}}{\lVert \mathbf{I} \rVert\,\lVert \mathbf{R} \rVert} \]

Basic formula (weighted overlap between concepts):

\[ \text{Adherence} = 100 \times \frac{\sum_{i=1}^{K} \min(w_i, v_i)}{\sum_{i=1}^{K} \max(w_i, v_i)} \]

Key

\(\mathbf{I}\): intention vector, the mean embedding of the 3–5 core sentences.
\(\mathbf{R}\): mean vector of the audience’s interpretations.
\(w_i\)/\(v_i\): weight of concept i in intention/interpretations.
\(K\): number of concepts considered.

02 Semantic Convergence Index

Guiding question: do different interpretations converge on a shared core?

Not everyone interprets in the same way, and that is as it should be. The aim, however, is to bring them closer to the centre and make them converge. This index helps reveal how readings are distributed around the intended peak.

Useful signals and metrics:

clustering of readings
residual variance between groups
stability of the peak across different people or contexts

Possible applications include:

presenting the same message to different groups, such as users, partners and investors, and checking whether the resulting keywords are consistent
comparing how the same message is received by people who saw only the text and those who saw text plus image, to see whether convergence improves

Objective: avoid dispersion and maintain coherence of interpretation even when the angle changes.

Technical appendix – Convergence Index (0–100)

Advanced formula (with groups/clusters):

\[ \text{Convergence} = 100 \times \frac{\displaystyle \sum_{g=1}^{G}\left(\frac{n_g}{N}\right)^2 - \frac{1}{G}} {\displaystyle 1 - \frac{1}{G}} \]

Basic formula (without groups):

\[ \text{Convergence} = 100 \times \left( 1 - \frac{\bar{d}}{d_{\max}} \right) \]

Key

\(N\): number of interpretations collected;
\(G\): number of groups/clusters selected.
\(n_g\): elements in group \(g\). The sum \(\sum_{g=1}^{G}(n_g/N)^2\) is the group concentration index.
\(\mathbf r_j\): vector (embedding) of response \(j\);
\(\boldsymbol{\mu}\): centroid \(=\frac{1}{N}\sum_{j=1}^{N}\mathbf r_j\).
\(\bar{d}\): mean distance from the centroid \(=\frac{1}{N}\sum_{j=1}^{N}\operatorname{dist}(\mathbf r_j,\boldsymbol{\mu})\).
\(\operatorname{dist}\): chosen metric, such as cosine or Euclidean distance;
\(d_{\max}\): reference value for normalisation, such as the metric’s theoretical maximum or the observed 95th percentile.

03 Semantic Stability Index

Guiding question: do different interpretations converge on a shared core?

How can we anticipate how a message might change over time, in the future? By monitoring semantic drift. Assessing change highlights trends and allows us to track durability over time. When stability is lost, the message arriving is too distorted, too far from the intention, and we need to react and act. This index measures durability over time.

Useful signals and metrics:

monitoring semantic drift before and after events: comparing how perceived meaning changes around a significant event, such as a pandemic, crisis or cultural shift
consistency of the peak across communication cycles: checking whether the central meaning remains stable through successive campaigns
resilience to narrative crises: observing whether the message withstands misunderstandings, attacks and controversy or deforms until it loses its identity

Objective: make meaning robust and antifragile, able to adapt without losing its identity.

Technical appendix – Stability Index (0–100)

Advanced formula (between periods \(t\) and \(t+\Delta\)):

\[ \text{Stability} = 100 \times \cos\!\big(\boldsymbol{\mu}_t,\, \boldsymbol{\mu}_{t+\Delta}\big) \]

Basic formula (normalised drift):

\[ \text{Stability} = 100 - 100 \times \frac{ \operatorname{dist}\!\big(\boldsymbol{\mu}_t,\, \boldsymbol{\mu}_{t+\Delta}\big) }{ d_{\max} } \]

Key

\(\mathbf r_j^{(t)}\): vector (embedding) of response \(j\) in period \(t\);
\(N_t\): number of responses in period \(t\).
\(\boldsymbol{\mu}_t\): centroid of period \(t\) \(=\frac{1}{N_t}\sum_{j=1}^{N_t}\mathbf r_j^{(t)}\); similarly \(\boldsymbol{\mu}_{t+\Delta}\).
\(\cos(\cdot,\cdot)\): cosine similarity;
\(\operatorname{dist}\): metric, such as cosine or Euclidean distance.
\(d_{\max}\): normalisation value, such as the metric’s theoretical maximum or the observed 95th percentile between periods.

04 Overall Index / GOVERNANCE

An approach complementing the three indices of Adherence, Convergence and Stability.

The three indices measured what happens to the Semantic Cloud when we communicate: how closely the audience reflects our intention (Adherence), how readings concentrate around the core (Convergence) and how well meaning holds over time (Stability).

Now we go a step further, from measurement to governance. The idea is simple: to guide the bubble over time, knowing whether it works is not enough. I need to adjust four levers, all measurable on a 0–100 scale:

Internal coherence
How closely the content I publish stays to the core. The upstream check: am I producing material aligned with what I declare?
External adherence
How closely the audience’s interpretations stay to the core. The downstream mirror: does what gets through match what I intended?
Controlled variance
The bubble’s breadth relative to its designed breadth. Not just “how concentrated are we?”, but “are we staying within the intended breathing room?” Too narrow means rigidity; too broad means cacophony.
Drift dynamics
The core’s movement over time within an optimal window, penalising both stagnation, with no change, and excessive drift.

How this differs from the previous approach:

Convergence vs. controlled variance: Convergence observes concentration as it is; controlled variance compares it with how broad we intended it to be. It introduces a design target for blur.
Monotonic stability vs. optimal window: previously we rewarded similarity over time; here we reward guided change, neither too slow nor uncontrolled.
New lever: internal coherence. Missing from the initial trio, it now closes the loop between what we produce and what is understood.

Practical benefits

A single readable metric, the Overall Index from 0–100, for reports and comparisons, without losing the diagnostic detail of the four components.
Strategic alignment: set the desired breadth of the bubble and pace of evolution in advance rather than simply undergoing them.
Adjustability: the weights of the four levers can be adapted to brands, campaign stages and markets.
Replicability: the formulas can be implemented in a simple spreadsheet and fit seamlessly with the three indices already presented.
Practical interpretation: if the Overall Index falls, you know where to intervene – the editorial product, verbal/visual framework, the bubble’s breathing room or the pace of change.

In short, the three indices tell you how the Cloud is doing. The Overall Index, built on four levers, lets you guide it where needed, balancing coherence, breathing room and time.

Overall Index (0–100)

\[ \text{Overall Index}(t)= w_1\,\underbrace{S_{\mathrm{int}}(t)}_{\text{internal coherence}} + w_2\,\underbrace{S_{\mathrm{ext}}(t)}_{\text{external adherence}} + w_3\,\underbrace{\operatorname{VarianceScore}(t)}_{\text{controlled breadth}} + w_4\,\underbrace{\operatorname{DriftScore}(t)}_{\text{dynamics over time}}, \qquad \sum_i w_i = 1 \]

Key (optional)

\(S_{\mathrm{int}}(t)=100\times \operatorname{mean}_c\,\cos(\mathbf v_c,\mathbf v_0)\)
\(S_{\mathrm{ext}}(t)=100\times \operatorname{mean}_i\,\cos(\mathbf v_i,\mathbf v_0)\)
\(\operatorname{VarianceScore}(t)=100\times \max\!\left(0,\,1-\frac{\lvert V(t)-V_{\text{target}}\rvert}{R}\right)\)
\(\operatorname{DriftScore}(t)=100\times \max\!\left(0,\,1-\left(\frac{d(t)-d^{\star}}{r}\right)^{2}\right)\)

Conservative defaults: \(w_1{=}0{.}35,\;w_2{=}0{.}35,\;w_3{=}0{.}15,\;w_4{=}0{.}15\) (adjustable).

Conclusion

Designing meaning means shaping its form. The Semantic Gaussian “forces” us to see that word, image and time are not separate ingredients: they jointly determine the interpretative field. Reducing risk does mean sterilising messages, certainly, but above all it aims to find consistent ways to govern their distribution, ensuring precipitation occurs in the right area and any tails do not reverse the intention. In the near future, I would like to explore each index properly and develop real practical examples demonstrating applications, particularly in branding and business communication.

This is the first step.

Copywriting and generative AI

Neogenerative Semiotics / Foundations – [Part 2/3]: Precipitation