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Based on Stibbe (2019) and Vallego (2026); full references in REFERENCES below.
"""
import textwrap
from functools import lru_cache
from pathlib import Path
import gradio as gr
import numpy as np
import pandas as pd
import plotly.graph_objects as go
from sentence_transformers import SentenceTransformer
from geometry import AXES, analyse, build_space, voronoi_zones
MODEL_NAME = "sentence-transformers/all-mpnet-base-v2"
# Relevance filter: a sentence is "on topic" if its cosine similarity to the centre of all
# pole exemplars is at least this value. Starting guess; calibrate with real texts
# (each sentence's relevance is shown when hovering over it in the first plot).
RELEVANCE_THRESHOLD = 0.30
# Links for the citations. Paste the URLs here; an empty string shows the citation without a link.
VALLEGO_URL = "https://papers.ssrn.com/sol3/papers.cfm?abstract_id=6387958" # SSRN page of the framework paper
STIBBE_URL = "https://eprints.glos.ac.uk/8163/" # open-access copy, University of Gloucestershire repository
APP_URL = "https://huggingface.co/spaces/neovalle/DiscourseGeometry" # this app's public address
APP_DOI = "" # e.g. a Zenodo DOI for the app's code, once archived ("10.5281/zenodo.β¦")
def cite(label, url):
return f"[{label}]({url})" if url else label
def _url_or_doi(url, doi=""):
return f"https://doi.org/{doi}" if doi else url
PAPER_TITLE = ("A Spatial-Geometric Framework for Discourse Comparison: Centroid Projection, "
"Frobenius Norm, and Eigenanalysis in a Constructed Semantic Measurement Space")
CITE_MD = f"""
**If you use DiscourseGeometry in your work, please cite the paper and the app.**
1. Vallego, J. (2026). *{PAPER_TITLE}*. SSRN.{" " + VALLEGO_URL if VALLEGO_URL else ""}
2. Vallego, J. (2026). *DiscourseGeometry* [Computer software]. Hugging Face. {_url_or_doi(APP_URL, APP_DOI)}
The three axes draw on: Stibbe, A. (2019). Education for sustainability and the search for new stories
to live by. In J. Armon, S. Scoffham & C. Armon (Eds.), *Prioritizing Sustainability Education:
A Comprehensive Approach* (pp. 233β243). Routledge.
"""
CITE_BIBTEX = f"""@misc{{vallego2026framework,
author = {{Vallego, Jorge}},
title = {{{PAPER_TITLE}}},
year = {{2026}},
howpublished = {{SSRN}}{f",{chr(10)} url = {{{VALLEGO_URL}}}" if VALLEGO_URL else ""}
}}
@software{{vallego2026discoursegeometry,
author = {{Vallego, Jorge}},
title = {{DiscourseGeometry}},
year = {{2026}},
publisher = {{Hugging Face}},
url = {{{APP_URL}}}{f",{chr(10)} doi = {{{APP_DOI}}}" if APP_DOI else ""}
}}
@incollection{{stibbe2019education,
author = {{Stibbe, Arran}},
title = {{Education for sustainability and the search for new stories to live by}},
booktitle = {{Prioritizing Sustainability Education: A Comprehensive Approach}},
editor = {{Armon, J. and Scoffham, S. and Armon, C.}},
publisher = {{Routledge}},
address = {{London; New York}},
year = {{2019}},
pages = {{233--243}}
}}"""
REFERENCES = f"""
**References**
Stibbe, A. (2019). {cite("Education for sustainability and the search for new stories to live by", STIBBE_URL)}.
In: J. Armon, S. Scoffham, and C. Armon, eds. *Prioritizing Sustainability Education: A Comprehensive Approach*.
London; New York: Routledge, pp. 233β243.
Vallego, J. (2026). {cite("A Spatial-Geometric Framework for Discourse Comparison: Centroid Projection, Frobenius Norm, and Eigenanalysis in a Constructed Semantic Measurement Space", VALLEGO_URL)}.
"""
POLES_FILE = Path(__file__).parent / "poles.tsv"
# Worldview positions (in % on each axis), read from the worldview map. Edit the file to change them.
LANDMARKS_FILE = Path(__file__).parent / "landmarks.tsv"
# One colour per axis; the low pole is drawn hollow, the high pole solid.
AXIS_COLOURS = {"eco": "#2e8b57", "change": "#3b6fd1", "outlook": "#d9822b"}
EXAMPLES = [
"At Northfield Energy we are proud to power economic growth across the region. "
"Our new gas field will create 2,000 jobs and secure affordable energy for decades. "
"We are committed to sustainability: by improving efficiency and investing in carbon offsets, "
"we will reach net zero by 2050 without compromising the comfort our customers expect. "
"Nature is one of our region's greatest assets, attracting visitors and investment.",
"The river is coming back to life. Since the weir was removed, salmon have returned to spawn "
"and otters hunt again along the banks. The valley was never ours to drain; it is a community "
"of beings, and we are only one of them. If we let go of the idea that every field must produce, "
"the land shows us how quickly it can heal. A different way of living here is possible, "
"and it has already begun.",
"Another summer of fires, another report ignored. The glaciers are going, the insects are going, "
"and the politicians keep promising targets they will never meet. Recycling and electric cars "
"won't save us. I struggle to see how this ends well.",
]
@lru_cache(maxsize=1)
def model():
return SentenceTransformer(MODEL_NAME, device="cpu")
def encode(texts):
return model().encode(texts, batch_size=32, show_progress_bar=False)
@lru_cache(maxsize=1)
def space():
poles = pd.read_csv(POLES_FILE, sep="\t")
return build_space(poles, encode)
def wrap(s, width=60):
return "<br>".join(textwrap.wrap(s, width))
def axis_title(ax):
# Short name only: this label moves with the 3D scene.
return ax["name"]
def scale_note(sp):
# Fixed text outside the 3D scene explaining what 0% and 100% mean on each axis.
lines = [f"<b>{ax['name']}</b>: 0% = {ax['low']} Β· 100% = {ax['high']}" for ax in sp.axes]
return dict(text="<br>".join(lines), xref="paper", yref="paper", x=0, y=1,
xanchor="left", yanchor="bottom", showarrow=False, align="left",
font=dict(size=12, color="#333333"))
def make_figure(res, sp, show_exemplars=False):
fig = go.Figure()
names = [ax["id"] for ax in sp.axes]
# Pole exemplar sentences (hidden by default; toggle in the legend)
for ax in sp.axes:
for pole in ("low", "high"):
texts, xyz = sp.pole_points[(ax["id"], pole)]
label = ax[pole]
fig.add_trace(go.Scatter3d(
x=xyz[:, 0], y=xyz[:, 1], z=xyz[:, 2], mode="markers",
marker=dict(size=3, color=AXIS_COLOURS[ax["id"]],
symbol="circle-open" if pole == "low" else "circle", opacity=0.5),
name=f"{label} exemplars",
legendgroup=f"ex-{ax['id']}",
hovertext=[wrap(t) for t in texts], hoverinfo="text",
visible=True if show_exemplars else "legendonly",
))
# Pole centres: where 0% and 100% are defined
for ax in sp.axes:
for pole in ("low", "high"):
c = sp.pole_centroids[(ax["id"], pole)]
fig.add_trace(go.Scatter3d(
x=[c[0]], y=[c[1]], z=[c[2]], mode="markers+text",
marker=dict(size=9, color=AXIS_COLOURS[ax["id"]],
symbol="diamond-open" if pole == "low" else "diamond",
line=dict(width=2, color=AXIS_COLOURS[ax["id"]])),
text=[ax[pole]], textposition="top center",
textfont=dict(color=AXIS_COLOURS[ax["id"]], size=12),
name=f"{ax[pole]} pole centre",
legendgroup="poles", showlegend=False,
hovertemplate=f"<b>{ax[pole]} pole centre</b><extra></extra>",
))
# Sentences of the text: analysed ones in grey, off-topic ones (filtered out) faded
def sentence_hover(sents, xyz, rel):
return [
wrap(s) + "<br>" + "<br>".join(
f"{a['low']}β{a['high']}: {v:.0f}%" for a, v in zip(sp.axes, row))
+ f"<br>Relevance to topic: {r:.2f}"
for s, row, r in zip(sents, xyz, rel)
]
sx = res["sent_xyz"]
fig.add_trace(go.Scatter3d(
x=sx[:, 0], y=sx[:, 1], z=sx[:, 2], mode="markers",
marker=dict(size=4, color="#7f7f7f", opacity=0.8),
name="Sentences analysed",
hovertext=sentence_hover(res["sentences"], sx, res["sent_rel"]), hoverinfo="text",
))
ox = res["off_xyz"]
if len(ox):
fig.add_trace(go.Scatter3d(
x=ox[:, 0], y=ox[:, 1], z=ox[:, 2], mode="markers",
marker=dict(size=3, color="#bbbbbb", opacity=0.35),
name="Off-topic sentences (not analysed)",
hovertext=sentence_hover(res["off_sentences"], ox, res["off_rel"]), hoverinfo="text",
))
# The text as a whole (centroid of its sentences)
t = res["text_xyz"]
fig.add_trace(go.Scatter3d(
x=[t[0]], y=[t[1]], z=[t[2]], mode="markers+text",
marker=dict(size=11, color="#111111", symbol="diamond",
line=dict(width=2, color="#ffffff")),
text=["Your text"], textposition="bottom center",
textfont=dict(size=13, color="#111111"),
name="Your text (overall)",
hovertemplate="<b>Your text</b><br>" + "<br>".join(
f"{a['low']}β{a['high']}: {v:.0f}%" for a, v in zip(sp.axes, t)) + "<extra></extra>",
))
# Axis ranges: always show 0β100 with some margin, widen if points fall outside
allpts = np.vstack([sx, t[None, :]] + [v for v in sp.pole_centroids.values()])
lo = np.minimum(allpts.min(axis=0), 0) - 10
hi = np.maximum(allpts.max(axis=0), 100) + 10
def axis(k):
return dict(title=dict(text=axis_title(sp.axes[k])), range=[lo[k], hi[k]],
tickvals=[0, 25, 50, 75, 100], ticksuffix="%",
backgroundcolor="#f7f7f7", gridcolor="#dddddd", zeroline=False)
fig.update_layout(
scene=dict(xaxis=axis(0), yaxis=axis(1), zaxis=axis(2), aspectmode="cube",
camera=dict(eye=dict(x=1.6, y=1.6, z=1.1))),
height=720, margin=dict(l=0, r=0, t=80, b=0),
annotations=[scale_note(sp)],
legend=dict(orientation="h", yanchor="top", y=-0.02, x=0),
paper_bgcolor="white",
)
return fig
def load_landmarks():
# Re-read on every run so edits to the file show up without restarting the app.
df = pd.read_csv(LANDMARKS_FILE, sep="\t")
if "description" not in df.columns:
df["description"] = ""
return df.fillna({"description": ""})
def make_landmark_figure(res, sp, lm):
fig = go.Figure()
ids = [ax["id"] for ax in sp.axes]
xyz = lm[ids].to_numpy(dtype=float)
fig.add_trace(go.Scatter3d(
x=xyz[:, 0], y=xyz[:, 1], z=xyz[:, 2], mode="markers+text",
marker=dict(size=7, color="#5b5ea6", opacity=0.85),
text=lm["name"].tolist(), textposition="top center",
textfont=dict(size=11, color="#3a3c75"),
name="Worldviews",
hovertext=[
f"<b>{n}</b><br>{wrap(d)}<br>" + "<br>".join(
f"{a['low']}β{a['high']}: {v:.0f}%" for a, v in zip(sp.axes, row))
for n, d, row in zip(lm["name"], lm["description"], xyz)
],
hoverinfo="text",
))
t = res["text_xyz"]
fig.add_trace(go.Scatter3d(
x=[t[0]], y=[t[1]], z=[t[2]], mode="markers+text",
marker=dict(size=11, color="#111111", symbol="diamond",
line=dict(width=2, color="#ffffff")),
text=["Your text"], textposition="bottom center",
textfont=dict(size=13, color="#111111"),
name="Your text (overall)",
hovertemplate="<b>Your text</b><br>" + "<br>".join(
f"{a['low']}β{a['high']}: {v:.0f}%" for a, v in zip(sp.axes, t)) + "<extra></extra>",
))
allpts = np.vstack([xyz, t[None, :]])
lo = np.minimum(allpts.min(axis=0), 0) - 10
hi = np.maximum(allpts.max(axis=0), 100) + 10
def axis(k):
return dict(title=dict(text=axis_title(sp.axes[k])), range=[lo[k], hi[k]],
tickvals=[0, 25, 50, 75, 100], ticksuffix="%",
backgroundcolor="#f7f7f7", gridcolor="#dddddd", zeroline=False)
fig.update_layout(
scene=dict(xaxis=axis(0), yaxis=axis(1), zaxis=axis(2), aspectmode="cube",
camera=dict(eye=dict(x=1.6, y=1.6, z=1.1))),
height=720, margin=dict(l=0, r=0, t=80, b=0),
annotations=[scale_note(sp)],
legend=dict(orientation="h", yanchor="top", y=-0.02, x=0),
paper_bgcolor="white",
)
return fig
def make_spread_figure(res, sp):
"""Explains the Frobenius norm and eigenanalysis: the sentence cloud, its
1-standard-deviation ellipsoid, and its principal directions."""
fig = go.Figure()
sx, t, c = res["sent_xyz"], res["text_xyz"], res["cloud"]
centre = sx.mean(axis=0)
fig.add_trace(go.Scatter3d(
x=sx[:, 0], y=sx[:, 1], z=sx[:, 2], mode="markers",
marker=dict(size=4, color="#7f7f7f", opacity=0.9),
name="Sentences of the text",
hovertext=[wrap(s) for s in res["sentences"]], hoverinfo="text",
))
fig.add_trace(go.Scatter3d(
x=[centre[0]], y=[centre[1]], z=[centre[2]], mode="markers",
marker=dict(size=9, color="#111111", symbol="diamond"),
name="Text centre", hoverinfo="skip",
))
if "eigvals" in c:
vals, vecs = c["eigvals"], c["eigvecs"]
sd = np.sqrt(vals)
# Ellipsoid: the spread of the sentences (its overall size is what the Frobenius norm summarises)
u, v = np.mgrid[0:2 * np.pi:40j, 0:np.pi:20j]
sphere = np.stack([np.cos(u) * np.sin(v), np.sin(u) * np.sin(v), np.cos(v)], axis=-1)
ell = sphere @ (vecs * sd).T + centre
fig.add_trace(go.Surface(
x=ell[..., 0], y=ell[..., 1], z=ell[..., 2], opacity=0.15,
colorscale=[[0, "#5b5ea6"], [1, "#5b5ea6"]], showscale=False,
name="Spread (1 standard deviation)", showlegend=True, hoverinfo="skip",
))
# Principal directions, drawn 1 standard deviation either side of the centre
styles = [("#c0392b", 7), ("#e67e22", 4), ("#95a5a6", 3)]
total = vals.sum() if vals.sum() > 0 else 1.0
for k in range(3):
if sd[k] <= 0:
continue
a, b = centre - vecs[:, k] * sd[k], centre + vecs[:, k] * sd[k]
label = ("Main direction" if k == 0 else f"Direction {k + 1}") + f" ({100 * vals[k] / total:.0f}%)"
fig.add_trace(go.Scatter3d(
x=[a[0], b[0]], y=[a[1], b[1]], z=[a[2], b[2]], mode="lines+text",
line=dict(color=styles[k][0], width=styles[k][1]),
text=["", label if k == 0 else ""], textposition="top center",
textfont=dict(color=styles[k][0], size=12),
name=label, hoverinfo="skip",
))
allpts = np.vstack([sx, t[None, :]])
lo = np.minimum(allpts.min(axis=0), 0) - 10
hi = np.maximum(allpts.max(axis=0), 100) + 10
def axis(k):
return dict(title=dict(text=axis_title(sp.axes[k])), range=[lo[k], hi[k]],
tickvals=[0, 25, 50, 75, 100], ticksuffix="%",
backgroundcolor="#f7f7f7", gridcolor="#dddddd", zeroline=False)
fig.update_layout(
scene=dict(xaxis=axis(0), yaxis=axis(1), zaxis=axis(2), aspectmode="cube",
camera=dict(eye=dict(x=1.6, y=1.6, z=1.1))),
height=720, margin=dict(l=0, r=0, t=80, b=0),
annotations=[scale_note(sp)],
legend=dict(orientation="h", yanchor="top", y=-0.02, x=0),
paper_bgcolor="white",
)
return fig
SPREAD_NOTE = (
"Each grey dot is a sentence. The shaded shape shows how far the sentences spread around "
"the text's centre: its overall size is what the **Frobenius norm** summarises. The red line is the "
"**main direction** found by eigenanalysis, the direction along which the sentences differ most; "
"the percentage is its share of the spread. Needs at least three sentences."
)
def signed(v):
return f"{v:+.1f}".replace("-", "β")
def distance_table(res, sp, lm):
"""Distance from the text to each worldview: Euclidean overall, plus the
per-axis difference (text minus worldview), ranked from closest."""
ids = [ax["id"] for ax in sp.axes]
diffs = res["text_xyz"] - lm[ids].to_numpy(dtype=float)
dist = np.linalg.norm(diffs, axis=1)
rows = []
for rank, i in enumerate(np.argsort(dist), start=1):
row = {"Rank": rank, "Worldview": lm["name"].iloc[i], "Distance": round(float(dist[i]), 1)}
for k, ax in enumerate(sp.axes):
row[f"Ξ {ax['name']}"] = signed(diffs[i, k])
rows.append(row)
return pd.DataFrame(rows)
DISTANCE_NOTE = (
"**Overall distance** is the straight-line (Euclidean) distance between your text and each "
"worldview in the 3D plot: the square root of the sum of the three squared differences. It is in "
"percentage points, the same units as the axes, and smaller means closer.\n\n"
"The **differences** (Ξ) show where that distance comes from, axis by axis: your text's position minus "
"the worldview's. A positive value means your text sits further towards the 100% end of that axis "
"(more ecocentric, more transformative, more pessimistic) than the worldview; a negative value means "
"further towards the 0% end."
)
def summary_md(res, sp):
n, total = len(res["sentences"]), res["n_total"]
if res["threshold"] is None:
first = f"**All {total} sentence(s) analysed** (topic filter off)."
elif res["fallback"]:
first = (f"**No sentence reached the topic threshold ({res['threshold']:.2f}), "
f"so all {total} were analysed.** Read the results with caution.")
else:
first = (f"**{n} of {total} sentence(s) are on topic and were analysed.** "
"Off-topic sentences are shown faded in the first plot.")
if n < total:
u = res["unfiltered_xyz"]
first += (" Using all sentences instead, the positions would be "
+ ", ".join(f"{a['name']} {v:.0f}%" for a, v in zip(sp.axes, u)) + ".")
lines = [first,
"0% = centre of the first pole's exemplars, 100% = centre of the second pole's. "
"Values below 0% or above 100% lie further out than the typical exemplar."]
return "\n\n".join(lines)
# Outlook colour scale for the worldview map: light = optimistic (0%), black = pessimistic (100%)
OUTLOOK_SCALE = [[0.0, "#f3eeb8"], [0.5, "#7a7a7a"], [1.0, "#000000"]]
def make_map_figure(res, sp, lm):
"""2D worldview map: Societal change (x) by Ecocentrism (y). Each worldview owns the zone
of the plane closer to it than to any other worldview. Outlook is shown by marker colour."""
ax_eco, ax_change, ax_out = sp.axes[0], sp.axes[1], sp.axes[2]
pts = lm[["change", "eco"]].to_numpy(dtype=float)
t = res["text_xyz"]
tx, ty, tout = float(t[1]), float(t[0]), float(t[2])
xmin, xmax = min(0.0, tx) - 5, max(100.0, tx) + 5
ymin, ymax = min(0.0, ty) - 5, max(100.0, ty) + 5
zones = voronoi_zones(pts, (xmin, xmax, ymin, ymax))
home = int(np.argmin(((pts - [tx, ty]) ** 2).sum(axis=1)))
fig = go.Figure()
for i, (poly, name, desc) in enumerate(zip(zones, lm["name"], lm["description"])):
if len(poly) < 3:
continue
closed = np.vstack([poly, poly[:1]])
fig.add_trace(go.Scatter(
x=closed[:, 0], y=closed[:, 1], mode="lines", fill="toself",
fillcolor="#cfe3d6" if i == home else "#eef1ec",
line=dict(color="#a9b4ad", width=1.5),
hoveron="fills", hoverinfo="text", text=f"<b>{name}</b><br>{wrap(desc)}",
showlegend=False,
))
out = lm["outlook"].to_numpy(dtype=float)
fig.add_trace(go.Scatter(
x=pts[:, 0], y=pts[:, 1], mode="markers+text",
marker=dict(size=13, color=out, coloraxis="coloraxis", line=dict(width=1.5, color="#333333")),
text=lm["name"].tolist(), textposition="top center",
textfont=dict(size=12, color="#1f2a24"),
name="Worldviews",
hovertext=[f"<b>{n}</b><br>{ax_change['name']}: {x:.0f}%<br>{ax_eco['name']}: {y:.0f}%<br>"
f"{ax_out['name']}: {o:.0f}%" for n, x, y, o in zip(lm["name"], pts[:, 0], pts[:, 1], out)],
hoverinfo="text",
))
fig.add_trace(go.Scatter(
x=[tx], y=[ty], mode="markers+text",
marker=dict(size=24, symbol="diamond", color=[tout], coloraxis="coloraxis",
line=dict(width=3, color="#c0392b")),
text=["Your text"], textposition="bottom center",
textfont=dict(size=14, color="#c0392b"),
name="Your text",
hovertemplate=(f"<b>Your text</b><br>{ax_change['name']}: {tx:.0f}%<br>{ax_eco['name']}: {ty:.0f}%"
f"<br>{ax_out['name']}: {tout:.0f}%<extra></extra>"),
))
fig.update_layout(
xaxis=dict(title=dict(text=f"{ax_change['name']}: {ax_change['low']} (0%) β {ax_change['high']} (100%)"),
range=[xmin, xmax], tickvals=[0, 25, 50, 75, 100], ticksuffix="%",
showgrid=False, zeroline=False),
yaxis=dict(title=dict(text=f"{ax_eco['name']}: {ax_eco['low']} (0%) β {ax_eco['high']} (100%)"),
range=[ymin, ymax], tickvals=[0, 25, 50, 75, 100], ticksuffix="%",
showgrid=False, zeroline=False, scaleanchor="x", scaleratio=1),
coloraxis=dict(colorscale=OUTLOOK_SCALE, cmin=0, cmax=100,
colorbar=dict(title=dict(text=f"{ax_out['name']}<br>(marker colour)"),
tickvals=[0, 50, 100],
ticktext=[f"0% {ax_out['low']}", "50%", f"100% {ax_out['high']}"])),
height=720, margin=dict(l=10, r=10, t=30, b=10),
plot_bgcolor="white", paper_bgcolor="white", showlegend=False,
)
return fig, lm["name"].iloc[home]
def map_md(res, sp, home):
out = res["text_xyz"][2]
ax = sp.axes[2]
return (f"Your text falls in the **{home}** zone (highlighted). Its outlook is **{out:.0f}%**, shown by the "
f"colour of its diamond: light yellow is {ax['low'].lower()}, black is {ax['high'].lower()}.")
MAP_NOTE = (
"**Zones.** The map divides the plane between the worldviews: each zone is the area closer to that "
"worldview than to any other, using only Societal change and Ecocentrism. A text falls in the zone of "
"the nearest worldview on these two axes.\n\n"
"**Colour.** Marker colour shows Outlook, from light yellow (optimistic, 0%) to black (pessimistic, 100%), for the "
"worldviews and for your text, so you can compare them.\n\n"
"The zone may differ from the top row of the distance table, because the table also counts Outlook."
)
def run(text, show_exemplars, use_filter=True):
sp = space()
res = analyse(text or "", sp, encode, RELEVANCE_THRESHOLD if use_filter else None)
lm = load_landmarks()
map_fig, home = make_map_figure(res, sp, lm)
return (summary_md(res, sp), res["table"], make_figure(res, sp, show_exemplars),
distance_table(res, sp, lm), make_landmark_figure(res, sp, lm),
res["cloud_table"], make_spread_figure(res, sp),
map_fig, map_md(res, sp, home))
ABOUT = """
### How it works
1. Each axis is defined by two **poles**, each a set of exemplar sentences (`poles.tsv`).
The axis direction runs from the centre of one pole's exemplars to the centre of the other's.
2. The three axes overlap in meaning (see the table below), so they are **orthogonalised**:
symmetric orthogonalisation finds the three perpendicular directions closest to the originals,
treating all three axes equally. This lets them be drawn as the x, y and z of one 3D space.
3. The text is split into sentences. Each sentence, and the text as a whole (the centroid of its
sentences), is placed on the three axes. Positions are expressed as percentages between the poles.
4. **Spread** is the standard deviation of sentence positions on each axis: low spread means the text
is consistent on that dimension; high spread means it moves between positions.
5. **Frobenius norm**: the Frobenius norm of the sentences' positions around the text centre, divided by
β(number of sentences), i.e. the average distance of a sentence from the centre across all three axes.
*Variation captured by the axes* splits the sentences' total variation in the full embedding space
into the part lying along the three axes and the rest (a Pythagorean decomposition of the squared
Frobenius norm).
6. **Eigenanalysis**: the eigenvectors of the 3Γ3 covariance of sentence positions give the directions
along which the sentences vary; the eigenvalues give how much variation lies along each.
7. **Topic filter**: in a long text with only a few passages about the environment, off-topic sentences
would dilute the result and pull it towards wherever unrelated text happens to fall. With the filter on,
only sentences whose similarity to the centre of all pole exemplars reaches a threshold are analysed;
the others are shown faded in the first plot. If no sentence reaches the threshold, all are used.
The *Before orthogonalisation* column shows each position measured on the raw, overlapping axis,
so you can see how much orthogonalisation changes the reading.
Sentence encoder: `all-mpnet-base-v2`.
"""
TABLE_CSS = """
<style>
/* Distance table: let headers wrap onto two lines instead of being cut off with "..." */
#dist-table th, #dist-table th * {
white-space: normal !important;
overflow: visible !important;
text-overflow: clip !important;
}
/* Keep each worldview name on one line */
#dist-table td:nth-child(2), #dist-table td:nth-child(2) * {
white-space: nowrap !important;
}
</style>
"""
with gr.Blocks(title="DiscourseGeometry") as demo:
gr.HTML(TABLE_CSS)
gr.Markdown(
"# DiscourseGeometry\n"
"Where does a text sit on three axes of ecological discourse: "
"**anthropocentric β ecocentric**, **conservative β transformative** and "
"**optimistic β pessimistic**? "
f"Based on {cite('Stibbe (2019)', STIBBE_URL)} and {cite('Vallego (2026)', VALLEGO_URL)}."
)
cite_btn = gr.Button("π Cite this work", size="sm", variant="secondary")
cite_open = gr.State(False)
with gr.Column(visible=False) as cite_box:
gr.Markdown(CITE_MD)
gr.Code(CITE_BIBTEX, label="BibTeX (use the copy button)", interactive=False)
def toggle_cite(is_open):
return not is_open, gr.Column(visible=not is_open)
cite_btn.click(toggle_cite, cite_open, [cite_open, cite_box])
with gr.Row():
with gr.Column(scale=2):
text = gr.Textbox(label="Text to analyse", value=EXAMPLES[0], lines=9)
use_filter = gr.Checkbox(label="Analyse only sentences about the topic", value=True)
show_ex = gr.Checkbox(label="Show pole exemplar sentences in the plot", value=False)
btn = gr.Button("Analyse", variant="primary")
gr.Examples(EXAMPLES, inputs=text, label="Example texts")
with gr.Column(scale=3):
summary = gr.Markdown()
table = gr.Dataframe(label="Position on each axis (%)", interactive=False, wrap=True)
cloud_tbl = gr.Dataframe(label="Whole-text measures", interactive=False, wrap=True)
plot = gr.Plot(label="Three-axis semantic space")
gr.Markdown("### How the sentences spread: Frobenius norm and eigenanalysis")
gr.Markdown(SPREAD_NOTE)
plot3 = gr.Plot(label="Spread and main direction of variation")
gr.Markdown("### Your text among worldviews")
with gr.Row():
with gr.Column(scale=3):
plot2 = gr.Plot(label="Worldviews on the same three axes")
with gr.Column(scale=2):
nearest = gr.Dataframe(label="Distance from your text to each worldview",
interactive=False, wrap=True, elem_id="dist-table",
column_widths=["7%", "36%", "12%", "15%", "15%", "15%"])
gr.Markdown(DISTANCE_NOTE)
gr.Markdown("### Worldview map")
with gr.Row():
with gr.Column(scale=3):
plot4 = gr.Plot(label="Worldview map: Societal change Γ Ecocentrism, Outlook as colour")
with gr.Column(scale=2):
map_info = gr.Markdown()
gr.Markdown(MAP_NOTE)
with gr.Accordion("About the method and the axes", open=False):
gr.Markdown(ABOUT)
overlap = gr.Dataframe(label="Overlap between the raw axes (cosine; 0 = independent)",
interactive=False)
gr.Markdown(REFERENCES)
btn.click(run, [text, show_ex, use_filter], [summary, table, plot, nearest, plot2, cloud_tbl, plot3, plot4, map_info])
show_ex.change(run, [text, show_ex, use_filter], [summary, table, plot, nearest, plot2, cloud_tbl, plot3, plot4, map_info])
use_filter.change(run, [text, show_ex, use_filter], [summary, table, plot, nearest, plot2, cloud_tbl, plot3, plot4, map_info])
demo.load(run, [text, show_ex, use_filter], [summary, table, plot, nearest, plot2, cloud_tbl, plot3, plot4, map_info])
demo.load(lambda: space().overlap.reset_index(names=""), None, overlap)
if __name__ == "__main__":
demo.launch()
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